Within the limits necessarily prescribed to this article, it is impossible to do more than touch upon a few points belonging to the subject. A complete treatise upon the theory and practice of music, according to the received doctrines, would contain about six thousand articles, and would fill several volumes. In writing this article, we have frequently availed ourselves of materials offered by the best and latest musical authorities. When so many works have been published by skilful professional musicians upon their art, we have not the presumption to suppose that we can add much that is new; more especially as we have no new theory to propose, and to maintain with Quixotic zeal and recklessness. Whenever we differ from authorities generally followed, we express our dissent, and give our reasons for it. Our main purpose is to direct attention to some useful musical objects, hitherto in general too much overlooked; to point out some errors in the theory and practice of music; and to show the utter uselessness of pursuing the old routine of building up false theories of music, and spending years in the vain study of what is called thorough bass, and is even still considered, by too many persons, as comprehending the whole art and science of music. To attempt to make any one a composer of music by means only of dry treatises upon intervals and chords, is just as absurd as to attempt to make a poet by means of Bysshe's Art of Poetry, or other books of the kind. Genius and observation, and a careful study of the best models, are really the only things that can ever make a good poet, or a good painter, or a good composer of music. The aid of a skilful master will be of great importance, if he is not wrapped up in a theory. In the absence of a master, two or three of the best modern treatises, such as Reicha's and Cherubini's, may help the student to understand the construction of those models of composition which he ought to have constantly before him. We suppose the reader to understand musical notation, and to be able to sing, or to play upon some musical instrument. If this should be the organ, or piano-forte, so much the better for his more easy attainment of a knowledge of harmony; although he must always remember that both these instruments are out of tune, and do not produce perfect intervals or perfect harmony. If the student of musical composition would acquire a real dominion over the materials of his art, he must not trust entirely to his organ or piano-forte. He must learn to read, in silence, any piece of music in score (in partition), and to hear, "in his mind's ear," the effect of the whole; and he must learn to compose in silence, and without the aid of any instrument. All great composers have acquired these powers. This seems, to the vulgar musician, impossible. To mention only one instance of such powers among living artists; Cherubini composes all his music with the aid of no other instruments but pen, ink, and paper. We have seen him at work. An accomplished composer is able to form in his mind, with no aid from any instrument, the whole plan and details of a complicated piece of harmony, before he writes a note of it. In his "mind's eye" he sees the whole score; in his "mind's ear" he hears the effect which the piece would produce if performed. Until the student acquires this power of abstraction, he must consider himself as only on a par with those every-day musicians whom the "fatal facilities" of the organ or piano-forte raise into the ephemeral class of pseudo-composers.

Some persons consider music as a frivolous and useless art. They do not feel nor understand music, and they are not to be blamed for this when nature has denied them a musical ear, any more than a blind man is to be blamed for not admiring painting or sculpture, or a blind and deaf man for not admiring poetry. But really, when musical compositions are frivolous and useless, the fault is in the artist, not in the art. If men choose to write bad poetry, to paint bad pictures, to chisel bad sculptures, this can never prove that poetry, painting, and sculpture, are frivolous and useless arts. Every one of the fine arts may be rendered frivolous and useless by misapplication of its means; nay, some of them may be made highly dangerous and mischievous, as has often happened. No doubt all the fine arts may be considered in one point of view as superfluous things, not at all contributing to the necessaries of human existence. Food, clothing, fire, and shelter, are really all that man's mere animal existence requires to keep him alive. But if poetry and music, and painting and sculpture, cannot till the earth, nor build hovels, nor make clothing, nor kindle coal-fires, they can at least add ornaments to the structure of civilized society, and contribute to the innocent pleasures and happiness of man's transitory life. And it seems to be proved by experience, that the cultivation of these arts, how unimportant soever they may be to mere animal existence, has always tended to divert the attention of mankind from the sole indulgence of their animal appetites, and of their more dangerous passions. If so, it would not be wise to deprive man of such sources of innocent and pleasing occupation, or rather relaxation, and to reduce him to the merely animal state of the savage, who enjoys and admires nothing beyond his animal comforts, and his murderous triumphs over his rivals or his enemies.

Many persons are so constituted, or so trained, as to have no relish for poetry, or painting, or music. So much the worse for them, perhaps, since their want of feeling or imagination deprives them of sources of innocent pleasure open to others. If a mere mathematician should be dissatisfied with the works of a great poet, because these works prove nothing mathematically, a lover of poetry must not take offence at the mathematician. The lover of poetry, perhaps himself a poet, may be totally insensible to the beauties of the most profound mathematical reasonings, or the finest musical compositions. This often happens. But it rarely happens that the real lover of music is not also a lover of poetry and of painting. We have known men high in the literary and scientific world, upon whom the best music produced no other impression than that of an agreeable or a disagreeable noise. But this never made us respect them the less for their own peculiar powers of feeling and thinking. They were not so organized as to feel and think as we did. That was all. The wiser and more philosophical plan is, not to be angry with any of our fellow-creatures for not feeling and admiring as we do; but to regret that they cannot feel and admire with us, because such communion of feeling and admiration would serve to draw those persons closer to us in human fellowship. To call a man a blockhead, because he does not, or cannot, feel and think in everything exactly like ourselves, is merely to be at once ill-natured, uncharitable, and unphilosophical. It is, "not to know ourselves." Non omnia possimus omnes. We find no fault with men who cannot perceive the beauties of music. We find fault with the perversions of an art which we ourselves feel to be a fine and expressive one, too often deformed and perverted. Most treatises on this subject begin with a definition of music. To persons who already understand music thoroughly, any attempt at such a definition is unnecessary. They have already formed their own ideas of music as an art. To persons ignorant of music, any such definition is quite unintelligible. The extent, the complexity, and the mutability of the art, render all such definitions imperfect and objectionable. The best way in this, as in all others of the fine arts, is to leave the student to form his own definition, after he has thoroughly studied the art. We follow this plan.

In some of the latest and best works on music, we find a definition of it attempted in this manner: "The art of expressing an agreeable play of feelings by means of sounds." But music often expresses the most painful and tragic feelings. Another is, "The art of expressing determinate feelings by means of regulated sounds." And then follows a long description of the nature of all the various branches of music; which is just tantamount to a confession that the definition is unintelligible and useless without the lengthy description.

Leibnitz had a strange metaphysical notion of music, which he thus expressed: "Musica est exercitium arithmetice occultum nescientis se numerare animi; multa enim facit in perceptionibus confusis seu insensibilibus, quae distincta apperceptione notare nequit. Errant enim, qui nihil in anima fieri putant, cujus ipsa non sit conscia. Anima igitur etsi se numerare non sentiat, sentit tamen hujus numerationis insensibilis effectum, seu voluptatem in consonantia, molestiam in dissonantia inde resultantem. Ex multis enim congruentiis insensibilis oritur voluptas," &c. Descartes entertained similar notions; and Euler, in his Tentamen Novae Theoriae Musicae, assures us that the ear is pleasingly or unpleasingly affected by musical intervals, according to its perception of the simplicity or of the complexity of their ratios of vibration. His measures of these ratios do not agree with practice. But the absurdity consists in supposing such an auricular arithmetic, by which the ear judges of the ratios of intervals. Does the milk-maid calculate the ratios of the intervals in her untutored song, and take pleasure in it, or the reverse, according to her perception of their simplicity or complexity? In Italy we may hear persons who cannot read music, singing very agreeably in two, or three, or four parts, in harmony. Do such persons know anything of the harmonic ratios of the sounds they combine together in this way? They have no more idea that even an octave is in the ratio of 1:2, than they have of the distance between the earth and the moon. Similar false applications of mathematics have tended greatly to produce that mysterious obscurity which has hitherto been artificially thrown over the beautiful and inviting regions of musical melody and harmony. There, genius and perseverance have called the sweetest flowers; while mathematical investigations have, as yet, only groped among the soil from which these blossoms sprang.

The state of our knowledge of acoustics, one of the most subtle and difficult of sciences, is still too incomplete to permit of the formation of a perfect theory of music, even were music, as a fine art, entirely dependent upon the physico-mathematical science of acoustics, which it is not. Of late years, however, the beautiful experiments of Dr Chladni, M. Oersted, Monsieur Savart, Professor Faraday, and Professor C. Wheatstone, have thrown much light upon some of the obscurer parts of acoustics.

In another work, we have expressed ourselves in the following terms regarding proposed theories of music. "The mischievous effects of false principles have been experienced in every branch of physical science. The blind rashness of premature generalization has operated with as great absurdity in music as in any other branch of human knowledge. While music was in its infancy, and while the observations and experiments which had been made respecting it were confined within limits by much too narrow to permit the formation of just and comprehensive general principles, musicians, both practical and speculative, misled by a false philosophy, and by erroneous ideas of simplicity, attempted to establish one single principle as the sole basis of musical harmony and composition. Confounding together the essentially distinct methods proper to physical and to mathematical science, they seized upon a particular phenomenon belonging to acoustics, and endeavoured to torture it into a principle which might apply to, and explain, the whole phenomena belonging to musical composition. From a particular fact, which had no necessary connection with musical composition, they attempted, with some ingenuity, and with much sophistry and ineffectual labour, to deduce the whole system of that art; while they were not aware either of the imperfection and incompleteness of the system which then existed, or of the improper method of induction which they had adopted. They employed the synthetical method of induction proper to mathematics, instead of the analytical method of induction, which is the true guide to physical investigation. In mathematics, we make discoveries by reasoning from definitions, axioms, and postulates; in other words, by reasoning from generals to particulars; but in physics, we extend our views and consolidate our knowledge by the opposite method of reasoning from particulars to generals. In physical science, when our observations and experiments have been sufficiently numerous and extensive, we may then, but not till then, establish general laws, or first principles, and reason from these synthetically; but if, on the contrary, the facts from which we generalize have been gathered from a narrow and unenlightened survey of the field of physical science, we shall almost inevitably draw false conclusions, and form principles which involve error and absurdity in relative proportion to the obscurity and contraction belonging to our investigation of particulars.

"It was long ago observed, that a musical string, or wire, capable of rendering a grave and powerful sound when thrown into a state of vibration, produced, in that state, not only a principal sound, corresponding to its length, tension, thickness, &c., but also two audible, concomitant, and accessory sounds, related to the principal sound by the intervals of a twelfth, or double (replicate) fifth, and seventeenth major, or second replicate major third. For example, the fourth string, or largest string of the violoncello, when strongly vibrating, may produce these accessory sounds, or harmonics; which, although feeble in comparison with the principal sound, may, however, be heard by a delicate and attentive musical ear.

"Upon this acoustical phenomenon, Rameau, a French musician, attempted to found his theory of harmony. We shall afterwards quote the opinions of some of the highest authorities in Europe upon this theory, and also upon that of Tartini, to which we now proceed.

"Tartini, in his Trattato di Musica, published at Padua in 1754, informs us, that if two sustained sounds (forming, for example, a third or a fifth) are produced at once from two violins, two trumpets, &c. the result will be the generation of a harmonic third sound, distinctly perceivable by the ear. This phenomenon was observed by Rameau in 1753. Tartini seems to have mistaken the pitch of the third sound, or grave harmonic, produced in this experiment, since M. Serre of Geneva, in his Principles of Harmony, tells us that the grave harmonic sounds produced by major and minor thirds are each an octave lower than those mentioned by Tartini. This phenomenon gave rise to Tartini's theory of harmony. We now make the quotations which we promised. The first is from the works of..." the late Professor Robison, whose authority, on such a point, is of indubitable weight. He is writing of Rameau's theory. 'Rameau has made this,' the generation of acute harmonics, 'the foundation of his system of music, asserting that the pleasure of harmony results from the successful imitation of this harmony of nature.' But a little logic should convince these theorists that they must be mistaken. A little mathematics, too, or mechanics, would have convinced them. His theory is a very forced accommodation of this principle to the practice of musicians and taste of the public.' Speaking further of Rameau's theory, he says, 'It is a mere whim, proceeding on a false assumption, namely, that a musical sound is essentially accompanied by its octave, twelfth, and seventeenth, in alto. This is not true, though such accompaniment be very frequent, &c. Are these acute harmonics musical sounds or not? He surely will not deny this. Therefore they too are essentially accompanied by their harmonics, and this absolutely and necessarily ad infinitum.' Of Tartini's theory he says, 'Tartini prized this observation,' the generation of grave harmonics, 'as a most important discovery, and considered it as affording a foundation for the whole science of music.' After some farther remarks, he adds, 'The system of harmonious composition which Tartini has, with wonderful labour and address, founded on it, has, therefore, no solidity.'

'Dr Chladni, in his celebrated work Traité d'Acoustique, expresses himself as follows regarding the theories which we have just mentioned: 'It is not conformable to nature to desire, like many authors, to derive all harmony from the vibrations of a string, and especially from the co-existence of several sounds with the fundamental sound. A string is only one species of sonorous body.

'In many other sonorous bodies the general laws of vibrations, which were not known, are differently modified, consequently the laws of one sonorous body cannot be applied to that which ought to be common to all. A mono-chord cannot serve to establish the principles of harmony, but only to give an idea of the effect of ratios.' Many authors have regarded the co-existence of sounds comprised in the natural series of numbers (which, according to true principles, is nothing but a particular phenomenon) as an essential difference between a distinct sound and a noise. They have taken this quality for the basis of all harmony, believing that an interval is consonant, because the acute sound may be heard along with the fundamental sound. They do not know that, if more than one sound is heard at the same time, this is nothing more than a consequence of the existence of many species of vibrations; that in many sonorous bodies the series of possible sounds is very different from the natural series of numbers; and that we may produce each manner of vibrations, where there are nodes, without any mixture of other sounds, by touching the nodal points, or lines, which ought to be in motion in other manners of vibrating.

'According to their principles, the perfect minor chord—if one does not make use of sophisms—would not be consonant; and, on the bell of the harmonica, the ninth (4 : 9) would be the first consonance, since it is the first sound which can mingle itself with the fundamental sound, &c. Daniel Bernouilli and Lagrange have sufficiently refuted these false principles.'

With respect to Tartini's theory in particular, he says, 'Tartini pretended that this third sound was more acute by an octave than it really is. He regarded this phenomenon, combined with the pretended co-existence of the series of sounds 1, 2, 3, 4, 5, &c. in each fundamental sound, as the basis of harmony. Mr Mercadier de Belesta has very well refuted some false assertions of Tartini, in his Système de Musique, Paris, 1776.'

Choron, in his work upon composition, says, 'It has been attempted to deduce the laws of succession from the multiple resonance, or from the sub-multiple resonance. Tartini had hardly discovered this last phenomenon, when he hastened, in order to satisfy the taste of his time, to rear up upon it a system, which he gave to the world in a very unintelligible work. J. J. Rousseau, who was almost equally a stranger to geometry and to the science of composition, produced, without having even comprehended it, a very imperfect analysis of it (Tartini's system) in his shapeless dictionary, and exalted it to the utmost of his power, for the pleasure of mortifying Rameau, with whom he had some quarrel.

'With the phenomenon of the multiple resonance, of which he had considered no more than the three first terms, Rameau had propped up his system of the fundamental bass. Without entering more into detail, I shall remark, that this phenomenon has no connection with the laws of harmony. That if one absolutely would apply it to them, it would be necessary, first, in order to be consistent, to suppose, at least implicitly, that the sounds of the system are those of the series of aliquots: first absurdity. Second, That all the notes of the bass ought to be accompanied by all their aliquots, moving in a parallel manner with each other: second absurdity. Every other consequence is illegitimate, and tends, not to give a foundation in nature to the rules of harmony, but to reconcile, as one best can, the phenomena with the rules of harmony, which is a very indifferent matter.'

In 1753, M. Serre, a miniature painter at Geneva, published his Essais sur les Principes de l'Harmonie. He assumed three essential fundamentals in the scale; the tonic, the fifth, and the fourth. He described the nature and use of what he termed diacomatic intervals, or slides necessary to perfect intonation in various modulations; and he laid down as a principle, that it depended upon the nature of the intervals of a chord whether that chord should have one or two, or even three fundamentals. These opinions of M. Serre's have been of late years, and with some modifications, reproduced as new. In some works recently published, we have observed an analogy pointed out, as new, between the harmonics above mentioned and the curious phenomena of complementary colours. In Blackwood's Edinburgh Magazine for February 1823 (pp. 159-162), will be found a letter of ours in Italian, in which this analogy is particularly noticed, and a short description of some of the phenomena given. In the same letter there are some remarks upon the analogy between the harmonic series 1, 3, 5, 7, &c. and the progression of numbers 1, 3, 5, 7, ascribed by Newton to the squares of the diameters of the coloured circles produced by him on applying to the plane side of a plano-convex lens one of the convex sides of a double convex lens.

A strange error has long prevailed regarding the co-existent vibrations of a musical string. The total vibration which gives the gravest sound of the string, can by no means co-exist with the vibrations of the aliquot parts of the same string. The thing is physically impossible, as could be easily demonstrated. In fact, to assert that a vibrating string can move in a number of different and opposite directions at the same instant of time, is as absurd as to maintain that a man can run backwards and forwards, to the right and to the left, &c. all at the same moment. The following diagrams represent the three primary curves of the harmonic series 1, 2, 3. The co-existence of all these curves is a physical impossibility. For how can ACB coincide with AdefB, or with AfgkB? It is needless to go farther. There may be many co-existent vibrations of traction and torsion in the string, but not any co-existent vibrations in directions quite opposite to each other.

The musical treatises of Choron, Catel, and Momigny, &c., among the French, and of Reicha and others among the Germans, are still too much tinctured with peculiar and arbitrary theories and systems, for which there are no sufficient grounds in either acoustics or aesthetics. By this last term the Germans have long chosen to designate, not very appropriately, the theory of taste in the fine arts. It is indeed impossible, by any purely mechanical and mathematical theories, or even by any metaphysical ones, to explain all the varieties of human sensations, affections, passions, that enter into our perceptions of beauty, sublimity, &c. in poetry, painting, or music. It cannot be too often repeated, that all the rules laid down by theorists for the construction of works belonging to the fine arts, are drawn from models of art previously in existence, and relate merely to the mechanical portions of these arts.

Had the rigid rules formed for (and from) the ancient Greek drama been always adhered to, we should never have possessed Shakspeare's plays. The magnificent musical works of Haydn, Mozart, and Beethoven, not to speak of many other great German and Italian composers, were not produced by blind adherence to old rules of art, but by an enlightened view of things, far beyond what the authors of these rules contemplated. Bühle has remarked, that the mechanical rules laid down in treatises on the fine arts may be compared to telescopes, which assist the vision of those persons who already see. A remarkable instance of this is found in the case of Beethoven, who happened to be placed under a master destitute of genius for melody; but a profound harmonist, and a learned writer of fugues and canons, &c. Under this man, Beethoven laboured most industriously, and went through the whole drudgery of thorough bass, and all the rigid ancient rules of composition; but evidently with frequent misgivings as to the general truth and application of what was taught to him. But the result was, that these lessons and rules served him as a "telescope," to enable him to perceive a wide field of composition far beyond them all. In short, he was a man of first-rate musical genius, and therefore by nature a great melodist; and, fortunately for the world, his injudicious training could not extinguish his passionate feeling for melody, and his charming expression of it in his best works. In some of his works, especially among his last, we find unpleasing traces of the predominance of his early training over his native genius. But his latest works were composed when he had been for many years perfectly deaf.

Notwithstanding the laborious investigations of many eminent anatomists and physiologists, from Comparetti downwards to Magendie, the uses and functions of all the various parts that compose the human ear are by no means well understood.

The perceptive powers of the ear differ considerably among mankind, especially as regards the perception of the various qualities and relations of musical sounds. In like manner, we find that the perceptions of form, proportion, colour, &c. are by no means always the same in every human eye. Perfection of the eye is requisite to the painter; perfection of the ear to the musician. Sometimes persons are found who cannot distinguish colours, or shades of colour, from each other. Perhaps more frequently instances are met with of persons whose perceptions of the differences between musical sounds are very imperfect. We have been informed that Mr. Pond, the late astronomer royal, though a real lover of music, and capable of hearing distinctly sounds of a grave pitch, or of a middle pitch, was incapable of hearing very acute sounds, whether musical or not, which were perfectly audible to other persons; for example, the loud chirping of a number of crickets in a room, and the very piercing sound produced by turning round the ground-glass stopper of a bottle containing calomel. The stopper was turned round close to Mr. Pond's ear without producing any sensation. All this clearly proved that Mr. Pond's ear, however perfect in other respects, was incapable of conveying any perception of very acute sounds.

All vibrations sufficiently rapid and powerful to act upon the auditory organs produce the sensation of sound. To enable us to hear slow vibrations as well as more rapid ones, it would be necessary, according to Riccati, that the intensity of each simple vibration should be in proportion to its duration. For this reason, says Chladni, and on account of the different organization of each individual, and each kind of animal, there exist no absolute limits to the perceptibility of sounds.

The ear does not distinguish the very small differences of the exact ratios between sounds. Were it not for this illusion, music would have no existence. But this is not to make us seek the less for true intonation, wherever it can be obtained. Few persons are aware how great is the difference between the true intonations of a fine voice, or a violin, &c. and the false intonations of such instruments of fixed sounds as the organ, piano-forte, &c. Many singers, trained to the intonation of a piano-forte, have their ear and voice so misled that they can never afterwards learn to sing in tune. The famous Madame Mara condemned the use of the piano-forte in learning to sing. She said every singer ought to learn to play on the violin, in order to know what true intonation is.

The different quality (timbre) of a musical sound and its articulations, says Chladni, are among the most remarkable objects of audition. They do not appear to depend on the manner of vibration, nor (or very little) upon the form of the sonorous body; but rather on the matter of the sonorous body, and that of the body by which it is rubbed or struck, as well as on the matter which propagates the sound. We have not the least idea of the nature of these different characters of sound, nor of their propagation.

The limits usually assigned to musical sounds, reckoning from grave to acute, or the contrary, are as follows:

Two octaves higher than written.

Two octaves lower than written.

The lowest of these sounds will be such as is produced by an open organ-pipe of 32 feet in length, and the num- Music.

The number of vibrations of the reed will be 32 in a second of time. The next octave above will be produced by an open organ-pipe of 16 feet, and the number of vibrations in a second will be 64; the next octave above that, pipe 8 feet, and 128 vibrations; and so on. The highest sound above noted will have 16,384 vibrations in a second. This last sound is not to be taken absolutely as indicating the extreme limit of acute sounds that may be used in music, and may be appreciated by the human ear; for it has been calculated that a sound produced by 24,000 vibrations in a second is appreciable. We shall give, in a wood cut, p. 618, a copy of a very useful table of the compass of voices and instruments, published by Monsieur Choron, in his large and expensive work upon composition. As all the plates of that work were destroyed some years ago, copies are now extremely rare and valuable.

If we take a vibrating musical string or wire, perfectly uniform in thickness, and homogeneous throughout, and divide it into its aliquot parts, its half, its third, its fourth, its fifth, and so on, we shall obtain, by this division of the monochord, as it is called, a great many of the sounds belonging to our musical system. A number of these sounds can be obtained from it by lightly touching it at these divisions, as happens when we produce harmonics on the open string of a violin, &c.; and all these sounds are true, or nearly true, if the string is perfect; otherwise they are not. This frequent imperfection in the uniformity and homogeneity of strings is one great obstacle to perfect intonation. Again, if we take an organ-pipe, or a French horn, &c., and blow into it in such a manner as to produce its natural series of sounds, we shall have, beginning with the lowest, a series corresponding (in ratio of vibrations of the column of air contained in it) to the arithmetical series 1, 2, 3, 4, 5, 6, 7, 8, &c. thus:

These sounds also are true harmonics, supposing the sonorous tube properly constructed, and the force of the blast suitably regulated. If we push this harmonic generation of sounds still farther, we may obtain a number of other sounds, some of which, though apparently false as regards our artificial temperament on instruments of fixed sounds (such as the organ, piano-forte, &c.), are yet true, or nearly so, as regards the intervals which occur in true intonation.

There is no room here to enter into a discussion of this curious and intricate subject. We shall content ourselves with giving a table of the harmonics obtainable from an open cylindrical glass tube furnished with a suitable mouthpiece, and fitted to an organ-bellow. This table shows that the gravest sounds obtainable from the tube are removed from each other by wide intervals. Thus the two first sounds, C₁ and C₂, are separated by the interval of an octave. G₉ is a fifth above C₉, and C₃ is a fourth above G₃, and so on. This is the series followed by the natural sounds of such instruments as the horn, trumpet, serpent, &c.; but it is extremely difficult, or nearly impossible, to produce on these instruments the sound corresponding to C₁. Even C₂ is very difficult to produce; and the first sound that usually occurs corresponds with G₉. As the sounds become more acute, that is, as the column of air divides itself into a greater number of parts, they approximate each other more and more. By and by, chromatic intervals occur, represented by flats and sharps; and, at last, intervals so small that they cannot be represented by any of the common signs of musical notation. But these smaller intervals are necessary to perfect musical intonation, and are employed by the best singers and performers on instruments of the violin kind. In France, a number of experiments were tried with Viotti's performance, and it was ascertained that he employed a vast number of very minute intervals, in order to play perfectly in tune in all keys.

In treating of the musical sounds produced by sonorous bodies, such as vibrating strings, or wires, or springs, or columns of air in tubes, &c., it is rarely kept in view that in these, as in all mechanical phenomena, allowance must be made for the mechanical conditions which may render the actual phenomena not exactly correspondent to the mathematically calculated results. From want of attention to this, many false theories of musical intonation have been adopted. It is quite true, mathematically speaking, that if all the hypothetical conditions of a sonorous body were, as they are assumed to be, in the course of a mathematical reasoning regarding them, the physico-mathematical result deduced by such reasoning, supposing this reasoning accurate, must be perfectly correct. But, in general, such reasoning and deduction are carried on with abstraction made of some of the inevitable physical circumstances which attend the real phenomena. In this way, pure mathematical reasoning is often, in some degree, at variance with mechanical phenomena. A badly formed string, or wire, &c. will not conform to the mathematical calculations as to the sounds that it must produce when divided in such and such ways. Neither will its real vibrations agree with those mathematically calculated. In like manner, the friction, and inequalities and imperfections of any piece of machinery, will, in the real operations of the latter, produce results in some respects contradictory to the abstract mathematical theory of what the operations of the mechanism ought to be.

A musical interval consists in the difference between two given sounds, in respect to their relative acuteness and gravity. Thus it is evident that the unison is not an interval, although it is often improperly so called. Aristotle, in the tenth section of his thirty-ninth problem, very correctly designates the unison as being "only the same sound multiplied." But the slightest departure from unison, by one of the sounds becoming a little more acute, or the other a little more grave, forms an interval, though it may be so very small as not to belong to those intervals generally recognised in melody and harmony. The measure of the relative lengths, or vibrations, of two musical strings producing an interval, will be the difference of their respective logarithms, as has been remarked by Dr Smith in his "Harmonics," and by various other subsequent writers. Among these, the late Professor Robison, of Edinburgh University, pointed out some useful applications of the logarithmic subdivision of the circumference of a pasteboard circle, fitted with a moveable concentric circle, &c., as described in his article Temperament, in the present work. He adds: "Or a straight line may be so divided, and repeated thrice; then a sliding ruler, divided in the same manner, and applied to it, will answer the same purpose." We may remark, that these suggestions of Professor Robison have been employed in the construction of similar instruments, without any acknowledgment; and also, that Professor Robison's experiment, by applying a stop-cock to an organ-pipe and producing various sounds from the regular and rapid opening and shutting of the stop-cock, bears great analogy to the syren instrument recently constructed by M. Cagniard de la Tour. Professor Robison, speaking of his stop-cock apparatus, says, "The intelligent reader will see here an opening made to great additions to practical music, and the means of producing musical sounds, of which we have at present scarcely any conception," &c. We have already mentioned, very briefly, how intervals are produced by the subdivisions of a sonorous string or wire, &c., or of the column of air in a wind-instrument, or in the glass tube before described.

If we suppose such a tube to produce, as its gravest sound, \( \text{D} \), its primary harmonics will be \( \text{D} \).

viz. octave, replicate of fifth, and replicate of third. Carrying the series farther, we shall have one similar to that already given in the table of harmonics. Supposing two other such tubes, the one having for its gravest sound \( \text{D} \), and the other \( \text{D} \), the harmonics resulting from these respectively will be \( \text{D} \), and \( \text{D} \), and so on, as in the case of the first.

By bringing closer together these dispersed primary harmonics, by means of their octaves above or below, we shall obtain the following series of sounds:

\[ \begin{array}{cccc} \text{D} & \text{D} & \text{D} & \text{D} \\ \end{array} \]

and so on. If to the last of these series we add \( \text{D} \) at the top, we shall have the major diatonic scale of C.

By carrying farther the series of harmonic products of these three tubes, we shall obtain a number of other intervals (see the table), and among these the ones suitable to the scale of C minor:

\[ \begin{array}{cccc} \text{D} & \text{D} & \text{D} & \text{D} \\ \end{array} \]

The subject of intervals has been involved in frightful confusion by the number and complexity of names introduced, and the contradictory statements of various writers upon music. We have no space to devote to the clearing up of this chaos; but we may remark, in general, that in this matter, as well as in many others connected with music, there is great need of a reformation in terminology. To glance at only three or four of the misnomers in daily use, without meddling with the more abstruse terms: the fifth diatonic sound of an ascending scale is called the dominant of the scale, which signifies the ruling or governing sound; while, in fact, the tonic, or key-note, and no other, is the chief and ruling sound of the scale, the sound from which, as a common centre, all the others of the scale may diverge, or to which they may converge, like the radii of a circle. This use of the term dominant seems to have arisen from the predominance of the fifth of the key in ancient church-chants. The term subdominant is improper, too, as applied to the diatonic fourth of a scale. The terms double octave, double third, double fourth, &c., are wrong as applied to intervals, because they imply that these intervals are doubled in the unison, while it is meant to express only the acuter or graver replicates of these intervals in the octave. The same with regard to triple octave, &c. When we read of diminished or augmented sonoros, false fifths, superfluous fifths, seconds, &c., &c., we must regret the obscurity of such terms; but meantime we shall use the common terms as we find them, because to introduce new ones abruptly would only add to the confusion already existing.

### Table of Intervals in general use.

| Minor Fifth | Augmented Unison | Major Second | Minor Third | Augmented Fourth | Major Fifth | Diminished Fifth | Augmented Sixth | Minor Seventh | Augmented Eighth | |------------|-----------------|-------------|-------------|-----------------|------------|-----------------|---------------|--------------|----------------| | Minor Sixth | Augmented Seventh | Major Eighth | Minor Ninth | Augmented Tenth | Minor Eleventh | Augmented Twelfth |

### Inversions of the above Intervals.

| Major Seventh | Minor Octave | Minor Seventh | Major Sixth | Minor Fifth | Augmented Fourth | Diminished Fifth | Major Third | Minor Fourth | Minor Second | |---------------|--------------|---------------|-------------|-------------|-----------------|-----------------|-------------|--------------|--------------| | Minor Seventh | Minor Sixth | Minor Fifth | Augmented Fourth | Diminished Fifth | Major Third | Minor Fourth | Minor Second | Minor Unison |

Inversion of an interval takes place when the graver sound is carried an octave higher, or the acuter an octave lower. The effect of inversion of intervals may be represented by the following two rows of figures, where it will be seen that 1 or unison, becomes 8 or octave; 2, or second, becomes 7 or seventh, and so on.

\[ \begin{array}{cccccccc} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 \\ \end{array} \]

By looking at the above table of intervals, and their inversions, we perceive that minor intervals inverted become major, and major, minor; diminished intervals become augmented, and augmented, diminished. We have placed Db before Cs, and Eb before Ds, and so on; because, contrary to the common opinion, the Db in the above series is a graver sound than the Cs, and the Eb than the Ds, and so of the others. This is not easily understood by a mere player on the organ or piano-forte, but can be exemplified by any accomplished singer or violinist.

In writing for voices, especially in the strict or serious... style, many of these intervals are not used. The following are generally prohibited in that style: Augmented second, diminished fourth, augmented fourth, diminished fifth, augmented fifth, major sixth, diminished seventh, minor seventh, major seventh, augmented third.

Scale is the more comprehensive of these terms, since all appreciable musical sounds between the extremes of grave and acute form the general scale or system of sounds employed in melody and harmony. A mode is a certain arrangement of tones and semitones, &c., between a given sound and its octave above or below. Key properly signifies a character employed at the beginning of the staff, to fix the names of the notes; but it has long been used as nearly synonymous with scale or mode, since these terms are often employed the one for the other. What is called the key-note, or tonic, is the principal sound of a mode, or that from which we begin to reckon its degrees upwards or downwards. Suppose we take the note C as tonic, or key-note. The arrangement of notes No. 1 will form the mode or key of C major, and the arrangement of No. 2 the mode or key of C minor.

Both these are called Diatonic scales, although they are not strictly such, since they contain other intervals besides tones. The chromatic scales formed from these consist of a semitone (or so-called semitonic) series between the key-note and its octave above or below, ascending or descending. These two modes, major and minor, and their respective chromatic scales, may be considered as the types or representatives of all other major and minor modes and chromatic scales. No. 3 and No. 4 are two forms of the major and minor mode not generally adverted to, but which are very effective when skilfully used, as, for example, by Haydn in the andantino in C minor of his symphony in E flat. As an octave series or scale may be formed anywhere within the limits of appreciable musical sounds, we thus obtain a variety of scales, diatonic and chromatic, all of which, however, are to be considered as only so many fragmentary formulae, comprehended within, and belonging to the whole series of the general system. Thus we shall have the modes or scales of C flat, C sharp, major and minor; D major and minor, D flat and D sharp, major and minor, and so on with E, F, G, A, B, and their chromatic alterations, flat or sharp. The term key is usually applied to these. Thus we speak of the key of C major, of C minor, of C sharp major or minor, and so on. As concert-pitch is not one and the same in all countries, keys of the same name do not everywhere correspond exactly. The production of what is called the sharp series of keys arises from a regular succession of perfect fifths taken in ascending, or fourths in descending, beginning with C for the major ones, or A for the minor ones. Thus the first step of a 5th ascending from C brings us to G as a new key-note. G major, with one ♭ at the clef. The first step of a 5th ascending from A brings us to E as a new key-note E minor, with one ♭ at the clef. A 5th, again, ascending from G brings us to D major with two sharps at the clef; and a 5th ascending from E brings us to B minor, also with two sharps at the clef; and so on progressively with the major keys of A, E, B, with 3, 4, 5 sharps at the clef, till at last, at the twelfth 5th from C, we reach B sharp, which, when brought down by octaves towards the original C, will be found not to correspond with that C in unison or octave, but to be too sharp. The same thing will occur after a similar series of twelve perfect 5ths from A, as tonic of A minor, up to G double sharp, which last will not be in unison or octave with the original A, but will be too sharp in the same proportion as the other extreme of the series of twelve ascending 5ths from C to B sharp. We may mention here, that composers seldom go beyond the keys of F♯ or C♯ major or minor, in their notation of a piece of music, on account of the multiplicity of sharps and double sharps in the subsequent keys of G♯, D♯, A♯, E♯, B♯, and the difficulty of reading these, and of playing in tune in such keys upon musical instruments even of the most perfect kind.

What is called the flat series of keys, arises from a succession of perfect 5ths, the converse of the former. That is to say, when, beginning with C, or with A, for the major or for the minor series, each key-note, in regular succession, is a 5th in descending below, or a 4th in ascending above the key-note immediately preceding. Thus, from C to F in descending, F major with one flat at the clef; from this F to B♭ in descending, B♭ major with two flats at the clef; and so on with Eb, Ab, Db, major, and with 3, 4, 5 flats, &c., at the clef. Then, again, the minor flat series, beginning from A as tonic of minor, D minor with one flat at the clef; from D tonic to G tonic of G minor, with two flats at the clef; and so on with C minor, F minor, B flat minor, &c., with 3, 4, 5 flats, &c., at the clef. We may here remark, that what is commonly called the relative minor key of a major key, has its tonic at the interval of a minor third below the tonic of that major key, and bears at the clef the same number of sharps or of flats. Thus the relative minor of C is A, without any sharps or flats at the clef; the relative minor of G is E, with one sharp at the clef; and so on with D major and B minor, A major and F sharp minor, &c., with 2, 3 sharps, &c. The same kind of relation occurs in the flat series of relative major and minor keys. Thus C major, A minor; F major, D minor; each of the latter two with one flat at the clef; B flat major, G minor, each with two flats at the clef; and so on with the rest, 3 flats, 4 flats, &c. The remoter flat keys beyond D flat are rarely used, for reasons similar to those assigned for the infrequent use of sharp keys beyond C sharp. To render more intelligible what has been said regarding the production of the sharp and the flat series of keys, we subjoin the following explanations. Suppose a musical string to render a sound equal to the lowest C of the violoncello, and to be numerically represented by 1. If this string be divided into three equal parts, any one of these parts will (tension and other circumstances remaining the same) render a sound equal to the first octave of the 5th above that C, and will be expressed by $\frac{1}{3}$. Two of these parts taken together will render the 5th above that C, and such 5th will be expressed by $\frac{2}{3}$, and will be equivalent to the lowest G of Music. the violoncello. Taking, again, the length of the string represented by $\frac{2}{3}$ and dividing it into three equal parts, two of these parts will render a sound equivalent to D of second open string of violoncello, and this D will be expressed by $\frac{2^2}{3^2}$. By proceeding in the same manner, we shall obtain the series represented in the following diagram. With regard to the numerical expressions placed under the 5ths, it will be remarked, that at each successive 5th, the exponent of the number 3 increases by one, while that of the number 2 sometimes increases by one, sometimes by two, according as the new term is in the 5th above, or in the 4th below, the preceding one.

We shall find that the B$^\#$, the twelfth 5th of this series, will not be in unison with C$^\frac{1}{2}$, the octave above the original C1, but will be more acute than that C$^\frac{1}{2}$. If we suppose the whole string C1 divided into a number of parts equal to $2 \times 531541$, the B$^\#$ in question will have 524,288 of these, while the C$^\frac{1}{2}$ will have 531,541; and therefore the B$^\#$ will be the neuter sound of the two. In reversing the process above described, that is to say, in reckoning a series of 5ths from acute to grave, the numerical expression of the 5th will be $\frac{3}{2}$. If, then, we set out from the C represented by $\frac{1}{2}$ and carry on, from acute to grave, a series of operations similar to the former, we shall obtain the following expressions for the flat series of keys by descending 5ths.

The Db$^\flat$, the twelfth 5th from C$^\frac{1}{2}$ will be found to be a graver sound than C1, the octave below that C$^\frac{1}{2}$; for, supposing the whole string = C1 divided into 524,288 equal parts, the Db$^\flat$ would require 531,541 of these parts, which exceeds the whole length of the string, and would therefore produce a graver sound than C1. The following diagram of the scales by 5ths ascending (sharp series), and by 5ths descending (flat series), will show the relative differences in pitch between the sounds of the one series and of the other.

**Scale of Ascending Fifths.**

| C | G | D | A | E | B | F$^\#$ | C$^\#$ | G$^\#$ | D$^\#$ | A$^\#$ | E$^\#$ | B$^\#$ | |---|---|---|---|---|---|-------|-------|-------|-------|-------|-------|-------| | $\frac{2^9}{3^9}$ | $\frac{2^{11}}{3^{11}}$ | $\frac{2^{12}}{3^{12}}$ | $\frac{2^{14}}{3^{14}}$ | $\frac{2^{15}}{3^{15}}$ | $\frac{2^{17}}{3^{17}}$ | $\frac{2^{18}}{3^{18}}$ |

**Scale of Descending Fifths.**

| Db$^\flat$ | Ab$^\flat$ | Eb$^\flat$ | Bb$^\flat$ | Fb | Cb | Gb | Db | Ab | Eb | Bb | F | C | |------------|-----------|-----------|-----------|----|----|----|----|----|----|----|---|---| | $\frac{3^{11}}{2^{11}}$ | $\frac{3^{11}}{2^{11}}$ | $\frac{3^{10}}{2^{10}}$ | $\frac{3^{9}}{2^{9}}$ | $\frac{3^{8}}{2^{8}}$ | $\frac{3^{7}}{2^{7}}$ | $\frac{3^{6}}{2^{6}}$ | $\frac{3^{5}}{2^{5}}$ | $\frac{3^{4}}{2^{4}}$ | $\frac{3^{3}}{2^{3}}$ | $\frac{3^{2}}{2^{2}}$ | $\frac{3^{1}}{2^{1}}$ | $\frac{3^{0}}{2^{0}}$ |

If we compare with each other the corresponding terms of these two scales or series, we perceive that the sounds of the sharp series are more acute than those which correspond with them in the flat series, because the strings which produce the latter surpass the others in length by the difference between 524,288 and 531,541 = 7253. A slight consideration of these processes, and their results, will show the necessity of what is called temperament upon such an instrument as the organ, the piano-forte, &c. By it the fifths are rendered a little false, in order to obtain all the octaves true.

What are called the ancient ecclesiastical scales or modes, being, in reality, nothing but certain conventional scales or modifications of the common major and minor scales, and differing from these in nothing but the disposition of their semitones, it is not necessary here to notice them very particularly. The four most ancient of these were the Dorian, the Phrygian, the Lydian, and the Myxo-Lydian. The first of these was equivalent to the series d, e, f, g, a, b, c, d; the second to e, f, g, a, b, c, d, e; the third to f, g, a, b, c, d, e, f; and the fourth to g, a, b, c, d, e, f, g. The dif- different positions of the semitones is indicated by the curved line. The reader will find a full explanation of all the ecclesiastical modes, authentic and plagal, in the first part of the first volume of Padre Martini's Saggio di Contrapunto. A good many years ago, a Frenchman, Blainville, pretended to have discovered a new scale or mode, which was really nothing more than the Phrygian mode above indicated. Reicha, in his volume of thirty-six fugues, proposed what he considered as a new system of scales, harmonies, and cadences, which he considered as relative to the usual major and minor scales, &c. These relative scales, however, were merely the Dorian and others above mentioned, with the addition of the series a, b, c, d, e, f, g, a. The relative cadences were those that might be used between the assumed dominant and tonic of such scales, there being no chromatic alteration made in the sounds of the scale. For example:

Reicha says, enthusiastically, "according to this system, we should have two primitive scales, a major and a minor, and five relative ones; and, by transposition, twelve primitive minor scales, and sixty relative scales; in all eighty-four scales, and as many cadences. What resources unknown till now!" We cannot join Reicha in this burst of enthusiasm. The formulae of these scales and cadences are to be found in a great many old church chants, and even national melodies. We must not mistake these fragmentary formulae for entire and peculiar scales, independent of the general system of musical sounds. Reicha adds, "It remains for philosophers and men of genius at a future period to deduce all the consequences from this important system, as well as from the compound measures, and their use. But the subtlety of a conventional taste, the ignorance and the prejudices so fatal to the progress of the arts, and which are peculiar to narrow minds, will be long opposed to such deduction." We should rejoice if Reicha's anticipated deductions could be verified in our day; but, with all respect for that excellent musician, we rather think that he has too often suffered his reason to be led astray by the incomprehensible idealism and metaphysics, so general in Germany upon almost all subjects of art, science, and literature.

Some peculiarities that have been observed in certain national tunes, such as the omission, in some instances, of the fourth and seventh of the key, have been referred to scales of a particular kind, while it seems more reasonable to refer them merely to the imperfections of some of the musical instruments employed; for instance, the ancient flageolet, and the chalumeau, &c. Scales, seemingly anomalous, may arise from such causes, or from caprice, or conventional usage; but all such scales are only fragments of that general system of sounds which comprehends all manner of appreciable intervals, many of which last are much smaller than is commonly believed. It has been denied that the ancient Scottish music contained any semitones; but that this is an error, is proved by the Skene manuscript in the Advocates' Library, Edinburgh. In the ten Indian scales given by Sir William Jones, we find two that want the fourth and seventh of the key note, and one that wants the third and seventh. The former are the scales called Māraei and Gaudī, equivalent to e, d, e, g, a, and g, a, b, d, e; the latter is the one called Sañdhavī, equivalent to a, b, d, e, f. The Asōvēri, Bahāirāva, and Malava, correspond exactly with the Dorian, the Lydian, and the Myxolydian modes above mentioned. The Frīraga is the same as the Malava, the Todi is the same as our scale of C major, and the Varati and Bengali correspond with our scale of A minor with minor seventh. As to the Hindu, Persian, and Chinese scales, and the use of quarter tones, or other minute intervals, we refer the reader to what we published on that subject in No. iv. of the New Edinburgh Review, April 1822, pp. 521-528. We have examined a number of Chinese wind and stringed instruments brought home in June 1837, and have found semitones in all of them. Professional musicians who followed Napoleon into Egypt, remarked the frequent and dexterous use of very small intervals by some singers in that country. Dr Burney, in the second volume of his history, p. 424, mentions that the Arabian scale of music is divided into quarter tones, and that each of the twenty-four of these, into which the octave is divided, has a particular denomination.

At the head of these must be placed the human voice. Musically, the nearer any artificial instrument approaches to it in quality and power of expression, the more excellent it is. Much controversy has arisen regarding the mechanism of the vocal organs which effect the modulations or inflexions of the human voice in singing. Some physiologists have considered this mechanism as similar to that of a reed instrument; others as similar to that of a stringed instrument. It is indeed neither, according to our artificial instruments, but a mechanism of wonderful delicacy and complexity, infinitely surpassing all artificial instruments in variety of timbre, in delicacy of intonation, and in power of melodic expression. Some of the most curious inquiries into this subject were made by the late Dr Francesco Bennati, an Italian physician and surgeon, and an accomplished amateur singer, who died a very few years ago in the prime of his life. He says that phonation has hitherto been confounded with modulation; the sounds of the voice in speaking, &c., with those of the voice in singing. We would observe, that the ancient Greeks, in their writings on music, made a marked distinction in this. Dr Bennati says that the muscles of the larynx are by no means, as hitherto asserted, the only ones employed in the production of the sounds of the human voice in singing; and that from leaving out of view a number of elements which belong to the real mechanism in such production, the theories of the whole matter that have been proposed and received are erroneous. Among these omissions of real elements, he instances the muscles of the os hyoides, of the tongue, of the upper anterior and posterior part of the vocal tube, besides other anatomical parts that contribute to modify the voice. We cannot here enter into the curious details given by Dr Bennati; but may add, that he rejects the received terms of note di testa and note di petto, as conveying false ideas; and proposes to substitute for them the terms supra-laryngean and laryngean notes or sounds. His proofs of all that he asserts are drawn from his own frequent observation of the actual functions of the whole mechanism of the voice in the cases of a number of the most celebrated male and female singers, his contemporaries. Stretched strings of gut or silk, either plain or spirally covered with wire, are the sonorous bodies employed to produce musical sounds on instruments of the violin kind, or of the guitar kind, or on the harp. Stretched wires of brass or steel, &c., plain, or spirally covered with wire, produce the sounds of the pianoforte, &c. Other instruments are constructed of glass bells or rods, &c., made to sound by friction or percussion; others, again, of metal springs, made to sound by a revolving toothed barrel, as in the Geneva musical boxes; or by a current of air directed against them, as in the German toy called the mouth harmonica, or in the Æolophon, or the Accordion and Symphonion. Several other instruments of a similar kind were invented before these. It may be mentioned, that Professor Robison of Edinburgh University gave the hint for constructing instruments of this last kind.

In the year 1785, the Abbate Gattoni constructed at Como a most singular Æolian harp. He stretched fifteen iron wires, of different thicknesses, from the top of a tower fifty-two braccia in height (about ninety feet), to his dwelling-house, about 150 paces distant. This giant-harp, by its mysterious sounds while the air was calm, indicated changes of the weather. This was ascribed to electric influence. The same phenomena occurred in a similar harp constructed by Captain Haas of Basle. The effect of the vibrations of the wires in each of these giant-harps, prior to changes of weather, or during storms, is said to have been quite indescribable. The sounds swelling and dying, and combining in the wildest harmonies, were sometimes heard for miles around. Wind instruments are tubes of wood or metal, in which the vibrating body is the column of air contained in them. They are sounded either by a peculiar mouth-piece, like that of the old flute or the flageolet; or by blowing into an aperture on one side of the tube, as in the fife, German flute, &c.; or by means of a reed, as in the oboe, clarinet, bassoon, &c.; or, as in the case of the horn, the trumpet, &c., by means of a cup-shaped mouth-piece, to which the lips are applied in a particular manner, and the sounds produced by compressions and dilatations of the lips, and the regulated force of the breath, and, in some circumstances, by introducing the hand within the bell-shaped end of the instrument. Other instruments are merely pulsatile, such as triangles, cymbals, bells, gongs, drums, &c., and have their sounds fixed. The harsh and unmusical tone of the gong seems to be owing to its peculiar shape, as well as to the numerous abrupt inequalities in its thickness and density.

With reference to Choron's table of compass of voices and instruments, we have to remark in general, that the best sounds of voices and instruments are their medium sounds, and that this ought to be carefully attended to by the composer. The frequent neglect of this in modern compositions produces a detestable chaos of screaming, squeaking, and grumbling. We add the following supplementary and explanatory information, which is of importance to the student. The medium compass of voices is as follows:

| Soprano | Contr' Alto | Tenor | Bass | |---------|-------------|-------|------| | | | | |

These restrictions are, of course, not intended to apply to solo singers, who have voices of great compass, but to Parts written in songs, duets, trios, &c. for voices of ordinary compass. It should be kept in view, that in writing for voices of the same compass and quality, we can hardly go beyond a trio or a quartett without producing a poor effect. Duets, or at most trios, of this kind, are therefore best when circumstances require such combinations. But, for variety of effects, and freedom of harmonic combinations, three, four, or more voices of different compass and quality ought almost always to be preferred in vocal trios, quartetts, &c. For duets of this contrasted kind, see the operas of Cimarosa, Mozart, Cherubini, Himmel, &c. To write effective Parts in harmony for voices, requires great skill and judgment. In a vocal quartett, for example, if we throw any of the voices out of their best medium compass, and do not carry them all on in correspondence with that compass, we shall produce poor and ineffective harmonies; for instance, if we place the tenor Part too low and too near the bass, while the treble and contr' alto remain in their best medium compass. Again, we may render the principal Part in a soprano a secondary Part (to the ear), by bringing it and the contr' alto too close to the tenor and bass; and may thus render the tenor, or even the bass, the most prominent Part, when we intended the contrary. In vocal Parts for many voices, such as choruses, &c. great simplicity of structure and of performance is required to produce any good effect. In 1819 we witnessed the famous Crescentini's training of a chorus at Bologna. His ear caught in an instant the slightest defect of intonation in any of the voices; the slightest excess of disproportionate piano or forte; the slightest attempt at any embellishment, even an appoggiatura. He stopped the whole performers immediately, pointed out the fault, and made them repeat the music over and over again till he was satisfied. This was the true way to train a perfect choral band; it would be well if his example were followed in all such cases.

Its powers and compass as a solo instrument are very great, although too often misused. In orchestra music it is seldom carried above F in alt.

In writing for an orchestra, the viola is rarely used above G, two octaves and a fifth above its lowest sound C. Not unfrequently, in modern music, it crosses the second violin, and rises above it for a short time in the harmony of a quartett, even where it is not performing a solo Part. But this generally occurs for the sake of preserving a melodious progression of the Parts, or of producing some particular effect from the interweaving of the different timbres of the stringed instruments.

We must keep in view, that the German double basses have generally four strings, and that some are tuned E, A, D, G, upwards, while others have D for their lowest note. In Italy and France the double basses have only three strings, and are tuned A, D, G. In writing for the double bass, rapid passages ought to be avoided, because they produce no effect, but only a confused noise. In music for a full orchestra, the double basses are reinforced by the tenor violins and violoncellos, or by the bassoons; or by the trombones, serpent, &c.; sometimes by the horns and trumpets, by the lower notes of the clarinet or of the oboe, even by the flute in its upper octaves, or by the octave flute, though the latter combinations are often abused by some living composers. Sometimes, in a florid passage for the double bass, a good effect is produced by reinforcing it by the second violins. In orchestra music, the violoncello generally goes (an octave above) with the cello, double bass Part; but beautiful effects are often produced by giving the violoncello a principal melody, accompanied by other instruments. When the treble clef is used in passages for the violoncello, care must be taken to write them according to the real pitch of the sounds, and not an octave higher, as is too often done.

In writing for the German flute, all rapid passages in Flutes, keys having more than one or two sharps or flats should be avoided, as they are very difficult of execution. We have corrected Choron's table, by extending the compass of the flute to C downwards, as most flutes now have the C finger-key. Its compass upwards is to B flat on the fifth ledger line in alt. In modern orchestra music, the octave flute, or piccolo, is too much employed. Its shrill and piercing sounds ought to be reserved for particular effects. In military music there are other kinds of flutes used,

---

1 In this article, we use the word Part, beginning with a capital, to signify that portion of a musical composition assigned to a particular voice or instrument. Music. The piccolo in E flat, and the piccolo in F; the former being a semitone higher, and the latter a minor third higher, than the octave flute. There are also what are called third and fourth flutes, the former being a minor third, and the latter a fourth, higher than the common German flute in D. Parts for these flutes are written in Flageolets. D. There are five sorts of flageolets, in C, D, E flat, F, and G, for the sake of facilitating their performance in different keys. Double and even triple flageolets have been contrived in London by Mr Bainbridge. On the former, two parts can be played at once; on the latter, three. The oboe requires attention in writing for it. The easiest scales for it are C major, F major, G major, and D minor. In some modern oboes, there are, in the upper part of the instrument, finger-keys for F and A flat; and, in the middle part, for F sharp, E flat, and C. Some have a finger-key for the lowest C sharp. Some players have two or three upper and middle pieces, to serve for altering the pitch of the instrument to different keys, on the same principle as flutes and clarinets, &c., are made of different lengths to avoid difficulties of fingering. In orchestra music the oboe is not used beyond E flat in alt.

The English horn, or ocar humana, is an instrument of the oboe kind, having the same relation to the oboe that the viola has to the violin. It has the same number of sounds as the oboe, only the scale is a fifth lower; so that pieces of music in F are written in C for the English horn, pieces in E flat are written for it in B flat, and so on.

The clarinet, or clarionet as it is often called, is an instrument of great power and compass. We have corrected Choron's table, by extending its compass upwards to C above fifth ledger line in alt. The sweetest sounds of the clarinet are comprised between \( \frac{3}{4} \) and \( \frac{5}{4} \).

The sounds between B on third line of treble clef and C on second ledger line above are the most penetrating and brilliant. The sounds above that C are very difficult to produce without harshness of tone. It requires great skill to play in tune on this instrument, particularly in the lower part of its compass. On this account, as well as to avoid difficult fingering, clarinets of different sizes are used to suit different keys. The most common used in orchestras are those in C, in Bb, and in A. Besides these, there are used, in military bands, clarinets in D, Eb, F, and G. These changes alter the pitch of the instrument, but the fingering remains as before. Thus the pitch of a Bb clarinet becomes in its lowest sound \( \frac{3}{4} \); that is, a tone lower than the C clarinet. The pitch of the A clarinet in its lowest sound becomes \( \frac{5}{4} \), and so on.

It is the custom to consider the principal key of every clarinet, whatever that may be, as if it were C. The composer must attend to this in writing for the clarinet. The Bb clarinet serves to lessen the number of flats at the clef, and the A clarinet to lessen the number of sharps, and so of the others. When the piece of music is in Eb, the Bb clarinet plays in F. The A clarinet plays in C when the piece is in A. If the piece is in Ab, the B flat clarinet plays in Bb, and so on. An example or two will make this rather puzzling matter more clear.

A few years ago, a German instrument-maker invented a bass clarinet and a double-bass clarinet. The former is an octave lower than the C clarinet, and reaches Bb, the lowest note of the bassoon. The double bass clarinet has a compass of two octaves and a half upwards from the lowest F in bass clef. It therefore extends to a fourth below the bassoon. The union of these with common clarinets permits the formation of a clarinet quartett, and, of course, new orchestral effects.

The basset-horn is an instrument of the clarinet kind, although differing in form from a clarinet. Choron has omitted it in his table. As it is sounded and fingered like a clarinet, any clarinet-player can play upon it also. It holds a middle place between the clarinet and the bassoon. Some authors give it a compass of four octaves from \( \frac{3}{4} \) to \( \frac{5}{4} \); others a compass from \( \frac{3}{4} \) to \( \frac{5}{4} \).

As it is an instrument difficult to manage, it is generally confined to the keys of C, F, Bb, and G. Mu- Music for the bassoon is written in the bass clef for the lower sounds, and in the tenor clef for the higher ones. The easiest keys for it are C, F, Bb, and G. In general it wants the sound and the sounds are very bad, and must be avoided.

Of late years, some bassoon-players and instrument-makers have facilitated the execution of certain passages on that instrument by a new disposition of the finger-holes and the finger-keys. In orchestra music, bassoons are important instruments. They serve as a bass to the flutes, oboes, clarinets, and horns; they may fill up and enrich the harmony of the middle parts; they may go along with (in the octave or the unison, as may suit) and reinforce the double bass, the violoncello, the viola, the violin, the clarinet, the oboe, the flute, the horn; or they may perform solo passages of their own with great effect. Composers seldom put the bassoons to their proper and effective use, but too often make them a mere reinforcement to the other bass instruments.

The bass-bassoon (fagottone or contra fagotto) is an octave lower than the common bassoon. It is not mentioned by Choron in his table. The first bass-bassoon seen in England was made by Handel's orders, for the use of Lampe, an excellent bassoon-player, and author of the music of the Dragon of Wantley. Being an unwieldy instrument, sixteen feet long, it was necessary to fix it in a frame like a telescope.

The serpent is chiefly used in military music, but has of late been introduced into orchestra music to reinforce the basses. Mersenne says that a serpent played by a boy was sufficient to sustain the voices of twenty stout monks. Of late years some improvements have been made on it by the addition of keys, though it is still an imperfect instrument. Writers differ in the compass assigned to it. Some give it a compass from the lowest B-flat of the piano-forte, up to G on the second line of the treble clef, with all the semitones. Others state its compass to be from lowest C of violoncello, up to C in third space of the treble clef. One eminent writer says that its compass is four complete octaves; that is, from C an octave below the lowest C of violoncello, up to C in the third space of the treble clef. He says the lower notes, in this last compass, are very difficult to produce, and their intervals not easily appreciable. Reicha assigns to it a compass of three octaves, viz. from lowest C of violoncello, up to C in third space of treble clef. The safest compass for ordinary players is the two first of these octaves only, leaving out the highest of the three. It is a singular fact, that there exists at this day, even among many professional musicians, a great deal of misconception regarding the real compass of a number of musical instruments of the wind kind. We have often been surprised to find that a performer upon a horn, for instance, did not know its real pitch or compass, and that he even supposed these to be just what appeared from the notation in the treble clef. Now, a C horn, for example, is a tube of eight feet or so in length; and, when played upon, becomes a tube stopped at one end by the lips, and therefore may render, as its lowest possible sound, one equivalent to that produced by an organ-pipe of sixteen feet open at both ends; that is to say, = C an octave below the lowest C of the violoncello. The serpent, if a tube of the same length, will, when played on with all the finger-holes stopped, be in a condition to render (but, like the horn, with great difficulty) the same low C as the horn.

The name of this powerful brass instrument (from the Ophicleide. Greek ὀφίς and κλειδον signifies a keyed serpent. The ophicleide was invented a few years ago in Germany. It was at first used in military music only, but of late years has been introduced into orchestras. It is too noisy an instrument for any place but a large locality. There are several kinds of ophicleides, as of trombones, and music for the former is written in the same manner as for the latter. Examples of the judicious use of the ophicleide may be seen in the Gloria and subsequent movements, and Marche Religieuse of Cherubini's third solemn mass performed at the consecration of Charles X.

Whatever may be the key of the piece of music in Horn (Ital which horns are employed, their Parts are always written Corn.) in the key of C. The following is the harmonic progression of sounds producible by the horn, without any assistance from the hand introduced into the bell.

The sounds marked + are, successively, = to B flat, harmonic; G flat, ditto; and G sharp, ditto. See preceding section, Musical Sounds and Intervals. We may here remark, once for all, that the sounds called false and bad on the horn, trumpet, &c., such as the pseudo fourth and sixth and flat seventh of the scale, are true as chromatic harmonics, but do not correspond with the sounds found in the same nominal places in the diatonic scale. In treating of harmony, it will be seen that these same chromatic harmonics—called false sounds from their not belonging to the diatonic series—are frequently employed in modern harmony and melody. The dominant seventh continually occurs, and less frequently the diminished fifth and the augmented fifth, which are the other two harmonics in question. It must be observed, that if a horn in C, of eight feet tube, performs the above notes, the real sound of each is an octave lower than the notation indicates. Of late years it has been attempted to remedy the imperfections of the horn, and to render it capable of playing in a variety of different keys without difficulty. This was so far done in Italy in 1822, by means of eight finger-keys, and a sliding tube to regulate the pitch; but this improvement has not been generally adopted. Some German instrument-makers have also contrived stops, to be pressed down by the fingers, which are said to answer much better than keys. They have also applied these stops to trumpets and trombones. This has also been done in England. We shall consider only the common horns, as they are still used in some orchestras. The method generally adopted to alter the pitch of a horn, is to shorten or lengthen its tube by means of moveable bent tubes called crooks. In some few cases, horns of different sizes are used instead. Thus there are horns in C, in D, in E flat, Music in E, in F, in G, in A flat, in A, in B flat, and even in C above. There are two B flat horns, the one an octave lower than the other. The lowest B flat horn goes a tone lower than the lowest C of the C horn. In writing for the horn, it is necessary to mark at the beginning of its Part, for what key it is intended, as in the following examples. The Italian word corni (horns) is generally used in partitions.

Corni in D. Corni in Eb. Corni in A.

Real Sounds. Ditto. Ditto.

In general, in writing for an orchestra, there are two horn Parts, the first of which does not (by notation) go lower than the lowest C in the treble notation, and the second one not higher than E in the fourth space of treble clef. The compass is generally limited to the following sounds:

But in solo Parts for the horn, the compass is as follows, a number of the semitones being produced by a dexterous use of the hand within the bell of the instrument.

The notes marked + may be used in passages of some quickness, but should never be sustained. The sounds of the middle part of this compass, or at least from G on second line of treble clef to G above the fifth line, are the best. In modern orchestra music, the proper use of the horns is too often lost sight of. They are either too much employed, or used in passages quite unsuitable to their character and powers. Their best effect lies in sustained sounds, not in rapid passages. They should be used to enrich the harmony in proper places, or to sustain a principal melody, or to produce contrast by their soles judiciously introduced. By using at once three or four horns tuned to different keys, a number of rich and beautiful harmonic effects have been produced by modern composers. As the sounds of the middle compass of the horn are the best, judicious composers for that reason often make use of horns in a key different from that of the piece of music in which these take part. Sometimes, but rarely, we find horn Parts written in the bass clef, as more truly representing the compass of the instrument; but it is better to avoid difficulty in reading such notation, by conforming to the usual practice of writing horn Parts in the treble clef. Skilful horn players expend but little breath on their instrument, and thus produce its finest tone. Others not only exhaust themselves by strong blowing, but produce a harsh tone, and fill the tube with water from their condensed breath. This water contributes to spoil the quality of the tone, and to break it into gurgling sounds.

Trumpet. Trumpets in the keys of C, D, and Eb are those most commonly used; but there are also trumpets in A, Bb, E, F, and G. It must be observed, that in some of these, F and G, for example, the gravest sounds are very difficult to produce. Some very skilful performers execute all sorts of passages on the trumpet; but, in writing for an orchestra, we ought not to go beyond rapid passages of double or triple tonguing upon a reiterated sound, or certain arpeggio passages. The trumpet may be either played softly, like the horn, or loudly with tongued passages, as in military music. To perfect the trumpet, finger-keys have been applied to it by some makers, and a sliding tube by others. Whatever the key of the music, the trumpet Part is written in C. The pitch of the trumpet is an octave higher than that of the horn. Its natural scale is

The notes marked +, like those of the horn, do not correspond with the diatonic series, and should not be used in sostenuto passages. The best notes are from up to , and those higher had better be avoided.

Trumpets in D.

Trumpets in E. Trumpets, as well as horns, may be muted by introducing a pasteboard tube into the bell of the instrument. The sound then becomes extremely feeble, and the pitch is lowered a semitone. By using two trumpets in different keys (as in the case of horns), a number of harmonic combinations in minor keys may be introduced which could not otherwise be effected; also by combining together two or more horns in one key, with two or more trumpets in another. The penetrating and warlike sound of the trumpet renders it very effective in pieces of military music, and in music expressive of heroic or exulting feelings.

The trombone is a most powerful and effective instrument, but very difficult to manage correctly. In Italy the bass-trombone only is used; but in France, Germany, and England, there are three kinds of trombones, the bass, the tenor, and the counter-tenor. There is also a double-bass trombone, which goes a fifth lower than the common bass-trombone, but is not much used. The treble trombone is very rarely used; and it is better to add to the three former another counter-tenor trombone when four trombones are to be employed, than to add a treble one. In the performance of solemn religious, or warlike music, the combination of three or four trombones produces a great effect; for instance, in the statue scene in Mozart's Don Giovanni, where the supernatural voice is accompanied by three trombones, two bassoons, two clarinets, and two oboes. The effect of the chant so accompanied is terrific. Mozart borrowed the idea from that passage in Gluck's Alceste, where the voice of the oracle of Apollo is heard in the temple.

Scales of Bass, Tenor, and Countertenor Trombones.

Parts for trombones are written in the above clefs; and, as in the case of bassoon Parts, the key is marked at the beginning, or accidental sharps or flats introduced when required. It is to be noticed, that there are trombones in different keys, for different purposes: in F, C, G. Sustained sounds are most suitable to the trombone, especially in orchestral combinations. A very few players are so skilful as to be able to execute very difficult solos on the trombone; such as Schmidt, who performed on it in London in 1829. The trombone can be muted, like the horn or the trumpet, and then its effect in funeral music becomes very striking. Chromatic passages ought, in general, to be avoided on this instrument.

Kettle-drums, called Timpani in Italian, are tuned to various keys, as occasion requires. They are generally in pairs; one of them sounding the key-note of the music, and the other the 4th below, as &c.

The Part for them is always written in the key of C, whether the key of the music be C or not; but if it be another key, this is marked at the beginning, as

Drums in D. Drums in E.

&c. It has been proposed to introduce into orchestras three drums tuned to different sounds; and perhaps there might often be advantage in this. We have seen a vocal and orchestral composition for forty voices and forty-two instruments, in which eight kettle-drums were employed. They were to be played by four persons, and were tuned thus: from G upwards, A flat; A, B flat; C, D flat; D, E flat.

The roll of these drums, when executed piano, has a sombre and mysterious effect. It is usually marked tr or n over the notes. Clarinets, horns, trumpets, and drums, may be changed for others in the course of a piece of music, provided a sufficient number of bars of rest are given.

Tambourine in Italian, or vulgarly cassa grande. This is a very large drum, of the usual cylindrical shape, and is used chiefly in military bands, but occasionally in great orchestras. In Haydn's symphony, called the Surprise, it is used with startling effect. Its Part is written in the bass-clef thus:

The gong is occasionally used in theatrical music, to add to the effect of scenes where terror and confusion predominate.

The Chinese pavilion, the triangle, the common drum, Chinese and cymbals, are almost entirely confined to military mu-pavillon, sic, though they are sometimes used in theatrical orchestras. In Mozart's Die Entführung aus dem Serail, the orchestra Parts of the duett "Vivat Bacchus" contain bass-drum (tambourine grande), triangle, and cymbals (piatt). Parts for the triangle, Chinese pavilion, and cymbals, are written in the treble-clef upon C the third space.

To point out all the difficulties of the wind-instruments above mentioned, and all the particular passages that should be avoided in writing for them, would occupy a volume. We shall merely notice, that in the flute, oboe, clarinet, and bassoon, the finger-keys of these instruments often render the performance of certain legato passages impracticable, and that therefore the composer ought to make himself acquainted with all these niceties. If he do not, his music, however excellent in other respects, can never produce the effects that he intended. We have dwelt more at length upon these matters regarding voices and instruments, because they are really of great importance to the musician and the composer, and because they have been hitherto too much neglected in our British treatises upon music. What we have stated in our general view of voices and instruments will preclude the necessity of entering into details regarding most instruments under their alphabetic heads in other articles of this Encyclopedia.

The guitar, the harmonica, the harp, the organ, and the piano-forte, are mentioned in Choron's table; but we have no particular remarks to make upon them in this place. We shall have something to say of the organ and the piano-forte in speaking of accompaniment, in the course of the present article. Melody may be considered in relation to a single voice or instrument, or as accompanied by one or more voices or instruments. In the latter case it is called the principal melody. There are many simple and expressive melodies, of such a kind that they will hardly bear any accompaniment without injury to their effect. Too often such melodies are spoiled by the addition of crowded and elaborate accompaniments, having nothing in common with the melody in style or character. This is one of the great mistakes of the modern schools of music, though we have no doubt that a better taste will prevail when more study is bestowed upon melody as the most important part of musical composition. We cannot too often repeat, that harmony ought always to be considered as subordinate to melody, although we are aware that certain great and peculiar effects may be produced by harmony, independent of melody in the true sense of the latter term; for instance, such effects are heard in certain forms of solemn ecclesiastical harmony that contain hardly a vestige of melody. The effects of mere harmony are often very striking when produced by a certain combination of voices, or of instruments, or of both, and in a building sufficiently spacious and suitably constructed, or even in the open air when heard at a certain distance, and especially if they pass over an expanse of still water. In ancient ecclesiastical music, the length of the sounds and the simplicity of the harmony were well calculated to produce a great effect in large cathedral churches. In such places, rapid changes of sounds, and chromatic harmonies, never produce anything but confusion; and this ought to be kept in view by the young composer. He must calculate the effect that his music will produce in a cathedral or in a theatre, a concert-room or a private room. No one who has not observed the difference of effect produced by the same music in places of different size and construction, can understand how important it is to attend to all this. But we must not encroach here upon another section of this article.

The study of melody is by far too much neglected. Harmony has generally in these days usurped its place; and we find ten good harmonists according to rule, for one good melodist. The reason is, that a man without real musical genius may become a very good scholastic harmonist, while a great melodist must be a man of great genius. Handel was in his day one of the most remarkable musicians for general excellence in both melody and harmony; but he was a man of the highest musical genius, and his profound skill in all the harmony of his time could never altogether check the flow from the spring of melody which existed in his mind. In his oratorios and his operas that spring is never failing. It is a pity that Handel's operas are now so little known. They contain much beautiful melody, although that is often disfigured (as in his oratorios) by conventional passages of a formal kind, which must, like all other such passages, become quite antiquated after a short time, having no foundation in any thing but temporary fashion of style.

In the proper order of musical study, melody ought to precede harmony. It is from reversing this order that so many dry unimaginative harmonists have been produced—men actually rendered incapable of composing good melodies, or of appreciating their beauties when heard. The student ought to have daily before him specimens of the most beautiful and expressive melodies in all styles, and of all nations. It is much to be regretted that there has not been published any judicious and comprehensive collection of such melodies. It would be invaluable to the student.

One of the earliest writers who treated of melody was Salinas, a Spaniard, and blind, but an eminent musician, and professor of music in the university of Salamanca. His work, which is now very rare, was published in Latin in 1577, at Salamanca. The fifth, sixth, and seventh sections of it are devoted to the consideration of the nature of musical, oratorical, and poetical rhythm. There is a great deal of curious and instructive matter in these sections, and he illustrates his text by numerous fragments of melody, some of which are very interesting, being old Moorish, Spanish, or Italian melodies. We have given some of these as curiosities in Plate III. Salinas says (page 235), "In the three following books (sections) we have to treat of the rhythmical part of music, a part of it not less useful, and even more delightful, than the harmonical part."

Another of the earliest writers on melody was G. B. Doni, the Florentine musical amateur and antiquary. Among his published works (3 vols. folio, 1768) we find many sensible remarks upon melody, and some curious notices of the distinguishing characteristics of national melodies (see, in particular, his Trattato della Musica Scenica, vol. ii. of his works). Speaking of the remarkable difference in the pronunciation of Latin by the French, Spaniards, and English, as compared with its pronunciation by the Italians and Greeks, he says, "This difference arises from the diversity of the accents, and the elevations and depressions of sound."... "We may say that common speech is a kind of outlined melody; and the mode of speaking in the recitation of poems, a kind of shaded melody, half finished; while true melody, called by the Greeks ἀκοή πρὸς ἀκοής, is perfect and finished, and, as it were, completely coloured." (P. 18 of Trattato.) With regard to setting of words to music, he says, "One of the most important remarks, and one perhaps not attended to by any person at present, is, that the music should not imitate the words, but the whole sentiment of the poetry; for in this consists true musical expression." He adds, that "Mimics and buffoons adopt the other mode; and, by exaggerated looks, and gestures, and noises, attempt to enforce the words they utter, or to represent the passions they are supposed to feel. (P. 29.) "Melopoeia is the art of composing beautiful melodies, without any reference to counterpoint, which belongs to another part of music." (P. 35.) As to modulation, he says, "The moderns are too scrupulous in wishing to keep always in the same key; a custom perhaps derived from the ecclesiastical chants, but quite unsuitable to varied and scenic melody." (P. 33.) Chapter xvii. of Doni's Trattato contains a number of ideas which Reicha has borrowed and developed in his Treatise on Melody. Doni proposes the use of quinary, and even septenary measures, such as $\frac{5}{2}$, $\frac{5}{4}$, &c., or $\frac{7}{2}$, $\frac{7}{4}$, &c. Reicha has also proposed the adoption of the quinary measure, and gives a specimen of its use in a national dance-tune of the district of Kochersberg, on the Lower Rhine, in the old province of Alsace. Reicha says, from information sent to him, "The manners and customs of the inhabitants of Kochersberg distinguish them completely from the other people of Alsace. Their dances have a particular and remarkable character, and nothing in common with those of their neighbours. The tunes of these dances have a very decided measure of five times. Tradition, in the country, carries back this music to the remotest antiquity." William Shield, a clever English composer, introduced a movement in this quinary measure into one of his instrumental trios. Two or three other Englishmen, and several Germans, have attempted the same measure; but it has not been generally adopted, though there is no reason but custom and habit why it should be rejected. Doni says (p. 74 of Trattato), "If the septenary measure could be conveniently adopted, it would produce a more remarkable effect upon the ear than any other, and it would suit lachrymose and compassionate subjects. But we let this alone, because it will be no small matter if we bring the quinary measure into use."

The following passage from Doni relative to national melodies is interesting, as having been written more than two centuries ago: "Although Italian music seems the most excellent and varied of all, still let us remember that non omnis fert omnia tellus; but that one nation abounds in one thing, another in another thing, according to the different genius of each. Therefore the judicious composer may draw from French airs (which have great variety and lightness in lively subjects), good passages and spirited and pleasing melodies. From the old Spanish airs he may derive many hints regarding melody and rhythm, for grave and majestic subjects; for example, from the Pavana; and from modern airs, and those borrowed from the Moors, he may also draw beautiful and lively melodies, but more soft and effeminate. Portuguese melodies may afford him very tender and affecting passages; and, for mournful and lugubrious subjects, he may enrich his imagination with Sicilian melodies, although they have little variety; and if he will go farther, he will find in English" (Scottish? Irish? Welsh?) "and German airs something to imitate in certain bold and military conceptions; there being perceptible in these airs, especially the German, a certain manly and military character," &c. (P. 131, Trattato.) The Spanish ex-jesuit Eximeno, in his work Dell' Origine, &c. della Musica, published in 1774, says, "In Italy national airs are not common, for most of the people have so fine an ear that it is enough for them to hear the opera airs, in order to amuse themselves afterwards by singing them in the streets." However, he adds, "The country people and villagers have their songs and tunes in a simple style, but in good taste. The romanello, which they sing accompanied by the colascione, is full of good taste, and still more so the tamburo of the Trateverini. The taste for songs reigns chiefly in Venice; and although they are usually composed by professional musicians, the people learn them easily."

In Plate III. we give the tamburo, No. 1, and a beautiful Venetian air from Eximeno, No. 2. The tunes to the Spanish romances Eximeno thinks "monotonous and tiresome," and believes them to be remnants of Moorish melody, or else ancient sprouts of the Canto Fermo. "The most tasteful popular songs of Spain are the Seguidillas, of which there is an endless variety." (See Plate III., No. 4.) We have given a few other specimens of curious melody which have not before been published in Britain. Among these are (Plate IV.), No. 15, a German melody of the year 1425; No. 17, Egyptian air, performed "with all their might" by the musicians of Grand Cairo, when the principal inhabitants, headed by all the sheiks of the town, went to meet Bonaparte on his return from the Syrian expedition. It was dictated by the chief of these musicians to one of Napoleon's. The performer accompanied it on the instrument called in Arabic al oud. Hence the English name of lute, Spanish laudo, Italian liuto, French luth. No. 18 is a song and chorus of cannibals. This curiosity was written down by a Russian voyager (Councillor Tilesius) in 1804, and published in the Leipsic Musical Gazette, No. 17, in 1805. Tilesius passed a night in listening to this music among these savages, in one of the islands of St Christina. He says, "there was something frightful in this melody, which almost drove one to desperation, and seemed to make one hear his own funeral dirge." He mentions, as a curious circumstance, that the voices of these savages passed, by sliding through very small intervals, from the E to the G of this chorus, or the converse. The savages, several hundreds, men and youths, sung it in unisons, or octaves, and danced at the same time. They marked the measure by clapping their hands, and also by beating drums. Tilesius explains the meaning of this chorus. "The warriors have returned from battle. It is night. One of them perceives a distant fire on the enemy's island. He asks, 'Where is the fire?' The chorus answers, 'Upon Tanhuatah Montaniob, among our enemies! they are roasting our dead and the captives!' This renders them frantic; they call for fire immediately, and feel a pleasure in being able to use it in reprisal against the dead, and prisoners taken from the enemy, but not without compassion in thinking of the wives, the children, the relatives, who will weep at that moment. Finally, they reckon the days from the first to the tenth, indicating the time fixed for feasting upon the victims, and for solemnizing the victory." An English writer of the last century, when speaking of Scottish music in one of his essays on various subjects, says, "Who was it that threw out those dreadful wild expressions of distraction and melancholy in Lady Culross's Dream? an old composition, now, I am afraid, lost; perhaps because it was almost too terrible for the ear. I'll venture to swear that David Rizzio was as innocent as any lamb of all such frantic horrors."

The examination of the melodies Nos. 1 to 18 inclusive will suggest matter for reflection. We would point out especially the elegance of No. 2, the expressive character of No. 4, the beauty and absolutely modern modulations of No. 14 (of fifteenth century), the curious rhythm and changes of measure in No. 15, the wild and singular cast of the Egyptian air, No. 17, and the hideously lugubrious character of the cannibal chorus, No. 18. Burckhardt, Bowdich, and some others, have published curious specimens of African melodies. We can only refer to these, and to a great variety of national melodies, Russian, Danish, Swedish, Norwegian, Polish, Bohemian, Hungarian, Greek, Spanish, Italian, Sicilian, Welsh, Irish, Scottish, &c. &c. that have appeared from time to time in collections, or detached. Among foreign national airs, we may mention some rescued from obscurity among the mountains of Auvergne, by that admirable English amateur and accomplished composer, the Honourable George Onslow. He has introduced some of these interesting national tunes of Auvergne into his violin quartetts, &c.

Reicha, in his Traité de Melodie, is the latest writer upon this subject. Several valuable works upon it by Italian and German writers had preceded Reicha's treatise. Among these writers may be mentioned Pisa, Sacchi, Niethammer, Riepel, Koch, &c. A translation of Reicha's Treatise on Melody, with some judicious notes and modifications, would be a useful offering to British students of music. Before we proceed farther, we must advert to what we consider as an error in treatises on melody or harmony. We allude to what are called passing notes, or unreal notes, and which are said not to form any real part of the melody or the harmony. It appears to us very plain that this is a mere fallacy, and that every sound that is actually heard in a melody or a harmony is just as real a sound as any other can be. For example, we take the following melody:

No. 1. We shall be told that this No. 2 is only No. 1 varied, or embellished by notes of grace, passing notes, unreal notes, that do not belong to the melody. But No. 2 is a melody per se as much as No. 1; and supposing No. 1 had never existed, No. 2 would still be a real melody, and all its sounds real sounds. It would startle us were a poet to say, "Such and such words in my poem are not to be taken as real words, but merely as passing shadows of words that do not belong to the language, or melody, or harmony, or meaning of my verses." There can be no doubt that if we pre-establish a certain chord, we may say that any sound that does not form one of the sounds of that chord is not a sound belonging to it. This is easily exemplified.

No. 1.

But suppose that the notes Fz, Dz, B, Cz, in the above passage were to occur as real notes in a melody—and might they not do so?—what then becomes of their unreality? For instance,

No. 2.

Were all the sounds of the following passage (a) performed with perfect equality of intensity and duration, no strong nor weak times would be perceived; and yet it is divisible into exact measures of different kinds, producing different rhythmical effects, as at (b), (c).

Sometimes, to produce a particular effect, the accent or emphasis is thrown upon the weak times of the measure.

It is plain enough that the simplest elementary forms of musical measure are the binary and the ternary, and that the compound forms arise from a duplication, or quadruplication, &c. of the binary, or a duplication, triplication, &c. of the ternary, or by certain combinations of the binary with the ternary. In the latter case, we have quinary and septenary measures. The last of these is not in use, but the former is occasionally employed. It may be remarked, that although these quinary and septenary measures are generally avoided by composers, yet periods of melody containing five or seven measures are of frequent occurrence. In binary and quaternary measures we often meet with triplets which really belong to a measure ternary or senary, &c.

Thus (d) produces on the ear the same effect as (e), and (f) the same effect as (g); so that there would really be no impropriety in writing (e) for (d), or (g) for (f). Haydn's beautiful canzonet, O Tuneful Voice, and the larghetto movement of Beethoven's charming Adelaida, are examples of the use of compound ternary measures; while the sign C at the clef, and other circumstances of notation, lead one by the eye to infer that the measures are compound binary ones. But the effect upon the ear, from the predominance of continuous triplets in the ac- Music.

companiment, is that of compound ternary measure. A curious instance of the intermixture of different measures in melody and harmony occurs in the dance-scene near the end of the first act of Mozart's Don Juan, where there are three different orchestras, each playing a different tune, one in $\frac{3}{4}$, the other in $\frac{3}{8}$, and the third in $\frac{2}{4}$. Intermixtures of different measures were not uncommon in the works of composers of the fifteenth and sixteenth centuries, but generally produced nothing better than confusion.

The only modern music that is not divided into measures is simple recitative. It has often been desired by composers of music, that the inflexions, the varying sounds of declaimed language, could be reduced to a musical notation more delicate and accurate than the one in common use. To enable us to express such inflexions, a notation for every minute intervals, as well as for peculiar accents, would need to be contrived. The attempts to express such declamation are represented by recitatives and aria parlanti. Some of these are remarkably expressive, from their near imitation of the inflexions of the voice in declamatory and impassioned language; among others, those of Gluck and Piccini. Beethoven, among the very few remarks that he has left to us upon recitative, says, "Recitative ought to be declaimed as if it were spoken. It is a discourse sometimes accelerated, sometimes retarded, according to what is required by the impassioned expression of the words. The comma, the semicolon, the colon, the period, the sign of interrogation, and of exclamation, each require a different accent." "To compose a recitative well, it is useful, previously, to declaim the poetry to one's self, as an intelligent actor would do. Any composer who has not ability to do this, ought not to be ashamed to have recourse to some one who can aid him." The best composers of recitatives have carefully studied the declamation of the great actors of their day. The danger lies in imitating false inflexions of the voice, intended to express natural feelings or passions.

We shall now give a brief statement of some of the chief points in Reicha's Treatise on Melody, referring the reader to that work for all developments and minutiae. The treatise consists of a hundred and twenty-three quarto pages of letter-press, and seventy-five plates. "Melody is nothing but a succession of sounds; but if these sounds were placed at random, they would form no sense, that is to say, no melody. It is the same as in regard to words not connected by syntax, nor directed by the understanding. The circumstances that connect sounds together so far as to form a musical sense, are, 1. the key; 2. the measure; 3. the different durations of the sounds; 4. the slurs which connect these more closely; 5. the rhythm; 6. the perfect equality of the timbre; 7. the period in which the sense is more developed; all this being guided by feeling and taste. Ideas and periods are separated from each other by points of repose, which are cadences of different kinds. In order to see how all these objects form melodic ideas, and contribute to connect them together, it will not be superfluous to analyze here the following period:

**PERIOD.**

First Melodic Phrase, composed of three designs.

Second Melodic Phrase, composed of three designs.

(First Member. First Rhythm.) (Second Member. Second Rhythm.)

The following are Reicha's explanations of technical terms, which he uses in his treatise on melody.

"1. A quarter cadence, or a point of repose weaker than a half cadence, and which serves to separate one melodic design from another.

"2. A half cadence, which separates one member and one rhythm from another, and which ought consequently to be stronger than the preceding cadence.

"3. A three-quarter cadence, which is stronger than the half cadence, and weaker than the full cadence, but which terminates a period as well as the latter, the difference between them existing only in the key in which we end. Thus, the first period of an air of two strains which ends on the dominant, would be only a three-quarter cadence, because another period is required in order to return to the tonic.

"4. Perfect cadence, which terminates the period in a positive and indubitable manner; but which does not hinder other periods from being added, if this be thought proper.

"5. Interrupted cadences, where, instead of the final sound, we fall upon another, or else leap suddenly from the final sound to another sound.

"6. Melodic design, a short musical idea separated from another by a quarter cadence. Two or three of these designs may form a member, which last ought to form a half cadence.

"7. A member of a period is composed of one or of several designs, and ought to make up a rhythm, and form a half cadence.

"8. A period may be composed of different designs and of different members. Its cadence is final, or else a three-quarter cadence, which may be called a perfect cadence relative to the key.

"9. Rhythm is the extent or the symmetrical and comparative number of the melodic members. It may have all the cadences except the quarter cadence......Measure divides into equal parts a series of simple times, as, for example, crotchets in common time; and rhythm divides into equal parts, and consequently in a symmetrical manner, a series of measures. Hence we may say with propriety, that measures are simple times of rhythm, as the crotchets and rests are the simple times of a measure.

"10. The complement is a little melodic design that fills up the pauses which occur between the members.

"11. The supposition is a measure which, in the theory of rhythm, counts as two; 1. as final measure of the first rhythm; and, 2. as initial measure of the following rhythm.

"12. The echo is the repetition of a part of a melodic design, executed by other instruments, and which is not reckoned in the rhythm.

"13. The coda is the confirmation of the end of a piece of music. It is also sometimes employed at the end of a period, either at the beginning or in the middle of the melody; but in this case it is short. When it terminates a piece, it ought to increase the animation of the music. It is for this reason that interrupted cadences and the supposition are employed in it, and that it is often executed with an accelerated movement. As to the length of the coda, it depends upon the duration of the piece. When the coda finishes a grand piece, it may be compared to the peroration of an oratorical discourse."

We pass over Reicha's explanations of "Le Retard de..." la Cadence," and of "Le Conduit," as these relate merely to arbitrary embellishments introduced just before a final cadence, or between one period and another.

To please a vitiated public taste, most modern performers make an overwhelming use of such embellishments, as they are called. Among singers, for instance, none would be listened to who did not prepare to conclude every melody, no matter how simple and unsuited to such trappings, with a flourishing cadenza and a long shake. Pietro Verri very properly abominates all such formal shakes and cadences, and desires all rational melodies to be finished off by a simple appoggiatura. G. M. Raymond, writing in 1811 of singers of that time, says: "L'un chante avec les épaules, les bras, les coudes, le corps tout entier; l'autre pousse des cris et pratique des élans qui prouvent suffisamment ses bonnes intentions; celui-ci se livre à des mouvements convulsifs qui peignent l'excès du sentiment; celui-là à des efforts semblables à ceux qui accompagnent les nausées, et qui ne remploient pas mal les mouvements de l'âme et les accès du cœur," &c. All this applies too nearly to many of the singers of 1837.

Among most writers upon music, we find great confusion regarding feet, caesuras, phrases, clauses, sections, times, rhythms. We think that, in general, Reicha has been more successful in clearing up and simplifying these matters. His cadences come in place of the confusion of caesures, phrases, clauses, &c. He shows, by numerous examples, the nature of these melodic cadences, and of the final cadence or period; and also of melodic designs, members of periods, periods, rhythms, &c. A discrepancy occurs in what he says (above cited) regarding $\frac{1}{4}$ and $\frac{1}{2}$ cadences in melodic designs and members; and we have to object to what he says about the supposition (article 11, supra), as being a measure that counts as two in the theory of rhythm. In a matter of this kind there are really no suppositions made by the ear. It hears neither more nor less than what it hears. As to the echo (article 12) "not being reckoned in the rhythm," we conceive that it ought to be just as much so as any other passage in the melody. Reicha refers to Haydn and Mozart as models of skill in the development of a melodic subject, and we cordially agree with him. He says that a treatise upon melodic modulation is wanted; also one upon the accompaniment of melody. We refer to Plate V., No. 19, for an example of the mixture of different rhythms in a melody of Päsiello. There is an almost inexhaustible store of melodies, in all their forms, in the works of ancient and modern composers. The student who examines these works will find, that the modern melodists have, in general, little to boast of in originality. To give an instance, one of the most popular vocal compositions in England, Oh, Happy Fair, is framed in its commencement, in melody and harmony, upon a church chant of C. P. E. Bach.

Harmony has been defined by an eminent French philosopher of our day, "a succession of chords, subjected to certain laws, according to which several different melodies, governed by a common rhythm, and heard together, produce an agreeable effect to the ear." This definition is, like many other technical ones, unintelligible to every person who has not studied harmony. But we shall make only one objection to it, which is, that very frequently harmony contains little or no melody, properly so called. It must be kept in view that harmony has its own peculiar means of producing effects, independent of melody, or, at least, of any prominent melody. It is more vague in its effects than melody; and, being more complicated, is less generally relished and understood than the latter. A chorus of Handel, or a symphony of Beethoven, requires a trained ear to relish and understand it fully. The progress of both melody and harmony was slow in improvement, as the history of music shows. As the materials of each were increased, like the enrichment of a language, melody and harmony assumed new forms, and became more copious and expressive. To assign limits to what may be called improvements in melody or harmony is impossible, since the plastic nature of the human ear is such as to be capable of being trained to relish almost any peculiarities in music, as in the sounds and inflexions of language. When we find that, in ancient times, a rude, unmelodious, ecclesiastical chant, and its accompaniment by another voice in consecutive octaves, fifths, and fourths, were considered as the perfection of melody and harmony, it is hard to say what the human ear may or may not be trained to relish. Gerbert, in his work De Cantu et Musica Sacra, gives several specimens of this strange harmony of the fourteenth century. See vol. i. pp. 376, 392, 435, 6, 7, 8, and 456, 7.

But something still more curious than this is given by Franchino Gafforio in the fourteenth chapter of the third book of his work Practica Musica, published at Milan in 1496. Under the head "De Contrapuncto Falso," he says that it was anciently the custom to sing a counterpoint composed of dissonances; that is to say, of second major and minor, perfect and major fourth, seventh, and ninth; and that such counterpoint was used in the fourth century in solemn vigils, and in certain masses for the dead. He gives the following example of this horrible counterpoint, as having been sung in the cathedral of Milan, from an ancient mass for the dead. He confesses it to be hideously bad. We avoid the alto clef, for the reader's sake; so the example should be performed an octave lower than it is here written.

Doubtless the human ear was then not a different organ from what it is now, and yet we should consider such harmony as intolerable. But to many persons the noisy confusion of certain modern compositions for orchestras and voices is delightful; voices yelling and growling, and, in the orchestra, all sorts of heterogeneous instruments mingled together to make a chaos of deafening noises. When we find, in a celebrated German orchestra, musical effects attempted to be produced by cracking of whips, firing of pistols, jingling of post-horse bells, ringing of bells of all sorts and sizes, thrumming on the Russian balalaika, beat- ing of drums, and so on, and all this received with rapture by a civilized European audience, we may well be justified in saying that it is hard to tell what the human ear may or may not be trained to relish in music, or rather in noise. Such music reminds us of the pewter dish, the tongs, the bellows, and the salt-box, used as solo or concert instruments, according to No. 90 of the Babbler; or of the hog-concert, produced by order of Louis XI. Bayle gives the passage on this subject from Bouchet, *Annales d'Aquitaine*. A great number of hogs of different ages were confined in a tent covered with velvet. In front of the tent there was an apparatus with keys like an organ. These keys communicated with the hogs in the tent, and were armed with needles, so that when the performer touched the keys, the hogs were pricked by the needles, which "les faisoit crier en tel ordre et consonance, que le Roy, et ceulx qui estoient avec luy, y prirent plasir."

The opinions of theorists on the subject of chords alone, without reference to their successions and modulations, are very much at variance. Some reckon only one single fundamental chord, formed from the first harmonics of a vibrating string, and which chord, they say, contains all the other chords. Other theorists assume two fundamental chords, others seven, others twelve, others thirteen, others seventy, and so on. Another theorist reckons so many as 3600, and among these, 700 dissonant fundamental chords. Besides all this perplexity and contradiction, these theorists give no satisfactory explanation of a multitude of phenomena belonging to modulation and harmonic combination. We would advise the student to pay very little attention to theories, but a great deal to the works of the best composers. Our space permits us to make only a few occasional remarks upon some received opinions regarding harmony, which seem to us to be erroneous.

Hitherto, what is called thorough bass has been confounded with figured bass; and both, as if one and the same thing, have been ascribed to L. Viadana as their inventor, in the beginning of the seventeenth century. But it appears that Viadana was not the inventor of figured bass, and that his thorough bass (*basso continuo*) has nothing whatever to do with figured bass, or with the doctrine of the progressions of chords. This appears clearly from his Italian work published at Venice in 1603, in five volumes 4to. It contained what he called "a hundred ecclesiastical concertos for one, two, three, and four voices, with the continuous bass (*basso continuo*) to be played on the organ." He says he invented these pieces in 1597, at Rome, and that his chief reason for composing them was, that there were no pieces of the kind constructed for one, two, or three voices, with organ bass. In these concertos, the organ bass had no pauses, and was therefore called *basso continuo*, that is, continuous or thorough bass; but it was not figured. The organist played this bass, and the voice part, or parts, as they lay before him. G. Sabbatini, a contemporary of Viadana, was the inventor of the figured bass, as appears from his work published at Venice in 1628, in which all the basses are figured, and in which he claims this invention. But this invention, which might serve well enough in these days for slow and simple music, accompanied on the organ according to certain fixed rules, has been, unfortunately, brought down to our day, when it is worse than useless, although the teaching and practice of it are still persevered in, to the great disadvantage and perplexity of musical students. Besides, different composers and different nations have different ways of figuring their basses, which adds to the confusion and difficulty. This clumsy contrivance should be entirely abandoned by all modern composers, who ought to write down in the common notation, fully and exactly, the accompaniment as they wish it to be performed.

A chord, as it is called, consists of two, or three, or four, or more sounds, heard at the same time. A primary *consonant* chord consists of intervals such as those given in the following examples, No. 1, A, B, and No. 3, a, b. Examples of primary *dissonant* chords are given at No. 4, a, c. Other dissonant chords will be afterwards noticed. The tonic or key-note of every scale may be considered as the central point to which, in the course of a melody, or a harmony, the other sounds of the scale converge, or from which they diverge; in the former case producing tonic cadences or repose, and in the latter, imperfect cadences and inconclusive passages. We have already seen that the sounds of a scale, whether major or minor, may be derived from the harmonic products of three sonorous bodies, representing the tonic, the dominant, and the subdominant. In the scale of C major, for example, the simplest harmony belonging to the tonic, the dominant, and the subdominant, considered as bass sounds, will appear in the three following chords, either as they stand at A, or with a changed position, or inversion, of the two upper sounds in each, as at B.

| No. 1 | Subdominant | Tonic | Dominant | Changed Position | |-------|-------------|-------|----------|-----------------| | | Common Chord | Ditto | Ditto | |

These chords, as they stand, cannot form a harmonic succession, on account of the consecutive fifths between them. In harmony, as in melody, the intervals are reckoned from the lower sound upwards. Each of these chords is called a major common chord, and consists of lowest or fundamental sound with its major third and perfect fifth. The change of position at B makes no difference in the name of the chord, but only in its effect. The closest possible position of the intervals, as at A, is called close harmony. Their altered position at B is called extended or dispersed harmony. By making the thirds of these chords the bass sounds, we obtain the following inversions, called chords of the sixth. The lowest sound of a chord is the bass for the time being.

| No. 2 | |-------| | Diatonic or chromatic successions of chords of the sixth, with or without the third, are very frequent in harmony. If in each of the preceding common chords we make the fifth the bass, we shall have the following inversions, called chords of the sixth and fourth. |

| No. 3 | |-------| | Most writers on harmony consider the interval of the fourth as a dissonance, while in truth it is a consonance, as is clearly shown by its forming one of the intervals in the perfect common chord, which contains no dissonance of any kind. Besides these three principal chords of the major scale, with their inversions, and which are all consonant, there is an important *dissonant* chord formed by adding the minor seventh to the fifth and third of the dominant. This is named the *dominant* seventh. We subjoin it (a), and its three inversions (b). | The sounds above the bass, in each of these chords, may be placed in various positions, some of which are shown at (e) and (d). The first inversion of the chord of the dominant seventh is called the chord of the sixth, fifth, and third; the second inversion, sixth, fourth, and third; and the third inversion, sixth, fourth, and second. In particular circumstances, the second, third, sixth, and seventh sounds of the major scale may each, as a bass, bear a common chord with a minor third. See No. 5 (r), (f), (g), (h), and the inversions i, k, l, m. But harmony of this kind is generally confined to ancient music, or imitations of the ancient style.

No. 5.

(e) (f) (g) (h) (i) (k) (l) (m)

The chord at h, with imperfect fifth, is rarely used in what are called fundamental progressions.

The chord of the dominant seventh contains two primary dissonances which are the least harsh of any in use, and are therefore the most frequently employed: the interval between the bass sound and its seventh, and the interval between the third of the chord and the seventh; see n, o, p. This last is an imperfect fifth, and requires a particular resolution (as it is called) in the next succeeding chord, unless some chromatic alteration intervene to change the simple progression; see q, r, s, t. For the most common resolutions of the seventh, see u, v, w.

No. 6.

(n) (o) (p) (q) (r) (s) (t) (u) (v) (w) (x)

A good ear will be displeased by such passages as those at y and z, where the resolutions of the seventh and of the imperfect fifth are neglected.

No. 7. (y) (z)

No. 8.

Subdominant. Tonic. Dominant.

(a) (b) (c) (d) (e) or (f) (g) or

Those subordinate ones at d, e, f, and g, may be occasionally used. The same remark applies to them as to the common chords on the second, third, sixth, and seventh sounds of the major scale. Of course, all the common chords in the minor scale may be inverted in the same manner as those in the major scale, thereby producing so many chords of sixth and third, and of sixth and fourth. The positions of their intervals above the bass may also be varied in the same manner as formerly shown.

No. 9.

Besides these dissonant chords, there are many other dissonant ones, such as the chord of ninth and seventh, or ninth only; the chord of fourth and fifth; and so on.

No. 10.

It is evident that every common chord, or either of its inversions, consists of three distinct sounds only; so that in composing for four voices, for example, a gap would occur in the harmony whenever a common chord, or one of its inversions, had to be employed, unless one of these three sounds should be doubled in the unison or octave. This doubling accordingly takes place when there are more than three Parts in the harmony. Which of these sounds... it is best to double, depends entirely upon the nature of the melodic and harmonic succession of sounds in this or that particular passage, and cannot be rightly learned but by a careful study of the best compositions in four, five, six, and more Parts. The chord of the seventh, again, or any of its inversions, consists of four distinct sounds, and therefore requires no doubling of any of its sounds in wri- ting for four Parts. In other cases where the Parts are more than four, the doubling of any of the sounds (except the third, or the seventh of the primary chord) must be regulated by the circumstances of the case. The third and the seventh of the dominant chord of seventh do not bear to be doubled, because the progression of each of these sounds follows a certain course in resolution by the third rising a semitone and the seventh falling a semitone, or a tone, into the next succeeding chord, unless in the case of some chromatic alteration which interferes with the simpler progressions of these two sounds. In writing for three or for two Parts, it becomes necessary to omit one or two of the sounds belonging to the chord of seventh, or any of its inversions. Whether the third or the fifth of the primary chord should be retained along with the sev- enth, depends upon the effect intended to be produced. In the former case the effect will be more piquant, in the latter more soft and undecided. Again, in writing for two Parts, suppose a duett for two voices, it is necessary to use only two of the sounds of a common chord, or two of the sounds of a chord of seventh. In the former case none of the sounds ought to be doubled, except at the beginning, or at a close, or in preparing a cadence, when the unison or octave of the lowest sound of the primary chord, or of its fifth, may be used. In the other case (chord of seventh) there is a choice among the intervals of primary sound and seventh, third and seventh, or fifth and seventh, or the in- versions of these. The effect intended must guide the choice. In these cases none of the sounds should be dou- bled in unison or octave.

What are called the preparation, the percussion, and the resolution of dissonances, may be made sufficiently clear by the following examples of Padre Martini.

At No. 12, (a), the seventh is prepared by the previous consonance of sixth, and is resolved upon the consonance of third. At (b) the ninth is prepared by the previous con- sonance of tenth, and is resolved upon the consonance of fifth. At (c) the sevenths are both prepared by previous fifths, and resolved by the consonances of fifth in the first case, and third in the second case. At (d) the second is prepared by third, and at (e) by sixth, in the preceding chord.

At No. 13, (g), the ninth and eleventh are prepared by previous tenth and twelfth, and are resolved into eighth and tenth. At (h) the ninth and seventh are prepared by previous tenth and eighth, and are resolved into eighth and sixth. As to what is called the percussion, or striking of the dissonance, it means simply the actual occurrence of the latter. The dissonance of the dominant seventh has no need of preparation; and the diminished seventh, the ninth, and the diminished ninth, are often struck unpre- pared. The chord of the ninth, and of the di- minished ninth, are susceptible of three inver- sions. These, with their resolutions, are as follows:

In the chord of the ninth, and in its inversions, the sound forming the fifth in the direct chord is generally omitted. The ninth itself is not inverted, and care must be taken to keep the ninth in its proper interval above the lowest sound

The ninth may be used in the following manner, without any preparation:

In Hayda's beautiful canzonet, Fidelity, there are ex- amples of the use of the major seventh, the ninth, and the diminished ninth, all without preparation. In the same canzonet we find the augmented octave and augmented fifth employed very elegantly. His tenth canzonet shows a very effective use of the diminished seventh, at the word "grief;" and also, at the same passage, the skilful intro- duction of an interrupted cadence. In the second section of the first movement of Mozart's third quintett in G mi- nor there are many diminished ninths, and ninths and sev- enths, introduced very boldly without any preparation. In Italy, about 1580, Monteverde began to introduce un- prepared sevenths and ninths; but it would appear, from the following very curious passage, that Jean Mouton, a Frenchman, had used these unprepared dissonances long before. J. Mouton was born in 1461. Examples of Unprepared Sevenths and Ninths, and of both combined, about the end of the Fifteenth or beginning of the Sixteenth Century.

No. 17.

Jean Mouton.

It is worth while to remark, that, in dissonant chords, the dissonance often leaves its place and passes to some other sound of the chord, without being resolved in the way it would have been had it continued to keep its place. For example:

No. 18.

Passages of this kind often puzzle the student, as seeming to contradict the rules given for the resolution of dissonances. In a series of chords, the progression from one to another may take place by similar motion, oblique motion, or contrary motion. The latter is the most frequent and the most useful, as it gives greater variety to the harmony, and enables us to avoid displeasing consecutions of octaves and fifths.

No. 19.

Similar Motion.

Oblique Motion.

Contrary Motion.

An examination of all the possible successions of chords, consonant and dissonant, direct or inverted, diatonic or chromatic, is beyond our limits and our purpose. These successions must be learned from an extensive perusal of the best compositions. We must confine ourselves to a few examples and a few general remarks. First, with regard to common chords in succession, two or more of them are not allowed to succeed each other diatonically, or by leaps in similar progression, or what is called similar motion ascending or descending.

No. 20.

The bad effect of such progressions is much more striking in compositions for voices, or for different instruments, than it is upon such an instrument as the piano-forte, on which the progressions of the different parts are not so distinctly perceived by the ear, owing to the quality of tone or timbre of each sound being of the same kind. It ought to be remarked, that this last circumstance is too much neglected in writing for the organ or the piano-forte, and that in consequence many particular passages of harmony written for one of these instruments produce little or no effect, or even a bad effect, while the same passages, if performed by different voices or different instruments, would be good and effective. In the above successions of common chords (No. 20) there are consecutive fifths and octaves, both of which, and especially the former, are prohibited in all cases where the ear perceives them and is displeased by them. There is no other rational rule against their use. With regard to consecutive unisons or octaves, daily experience proves that they are not in themselves displeasing when they are employed in the reinforcing of some particular melody or passage of melody. Were this not so, there would be no such thing in choruses or in orchestras as ten, or twenty, or more voices or instruments, performing the same melody in unison or in octaves. Haydn said that one of the most overpowering effects he ever experienced from music, was when he heard the singing of the subjoined melody in unison by a vast number of trained children in St Paul's Cathedral at London. In a composition for two, or three, or four voices or instruments, where the intention is to interest by means of harmony, the casual occurrence of consecutive octaves is felt unpleasantly from the poorness of their effect, from the deficiency of that richness of harmonic combination generally expected in such compositions; but still only a musical and trained ear would perceive this poverty of effect, and be displeased by it. The fewer the number of Parts, down to the duett, the more perceptible would this poverty be. The bad effect of consecutive fifths also rests upon the ground of poverty and want of variety. Some modern theorists assert that the reason why two or more consecutive fifths produce a bad effect, is, that the ear supplies the major third of the lower sound of each fifth, and thereby perceives a succession of major common chords forming so many disjoined tonic chords, which give an impression of a series of different keys unrelated to each other. This hypothesis is erroneous, because the ear does really supply no such thirds, nor any other sounds. The ear, in harmony as well as in melody, supplies nothing beyond what it actually hears. It has to do with nothing but its own actual sensations. The imagination may supply or suggest what it pleases; but that is quite a different matter. Cherubini says of consecutive fifths, that "a succession of them forms a discordance, because the upper part moves in one key, while the lower part moves in another. For example, if to the scale of C major we add an upper Part moving in perfect fifths with the former, it will result from this, that one Part will be in C, while the other will be in G. It is from this double concurrence of key that the discordance arises, and consequently the prohibition to employ several fifths in succession." The best way to avoid the effect of consecutive fifths and octaves, is to employ contrary motion of the Parts. The second examples (No. 22) should never be used in music for two Parts only, or between two extreme Parts of a harmony, though they may be used in two middle Parts between the bass and the highest Part where the harmony is full.

We have seen that the three principal common chords of a scale are those of the tonic, the dominant, and the sub-dominant; and that the principal dissonant chord is the chord of the dominant seventh. We shall first examine these common chords in their simple diatonic successions, direct and inverted; and afterwards as undergoing certain chromatic changes, and other modifications. The letter T will stand for tonic chord, D for dominant chord, and S for subdominant chord.

At \(a\) and \(b\) and \(c\) we have three progressions from T to D producing three imperfect cadences (see preceding section, Melody) of harmony and melody together. At \(d\), \(e\), and \(f\), we have three other progressions from T to S, producing also imperfect cadences, but not so decidedly imperfect as those at \(a\), \(b\), and \(c\). Indeed these last might, not improperly, be called reversed cadences. At \(g\), \(h\), \(i\), we have three progressions the reverse of \(a\), \(b\), and \(c\), and forming tonic cadences more or less complete. At \(g\), the cadence is complete, from the third of dominant rising semitonically, in the upper Part, to the tonic itself. The cadence at \(h\) is less complete, from the fifth of dominant descending to tonic by a whole tone in the upper part; and at \(i\) the cadence is still less conclusive by the fifth of dominant rising by a whole tone to the third of dominant. At \(g\) and \(h\), if the dissonance of seventh were added to the dominant, the determination of the complete cadence from D to T would be more striking.

A perfect cadence from the chord of the dominant seventh may be interrupted in various ways. The following are examples.

The successions at \(k\) and \(m\), No. 23, may be considered as imperfect cadences, although in some cases, in ecclesiastical harmony, the cadence from the chord of the S to the chord of the T is used as a final cadence. The succession at \(l\) is an imperfect cadence, the most imperfect that occurs in the scale, if we except \(n\) and \(o\).

The succession at \(n\) from S to D is used in ancient and modern music; but the contrary succession at \(o\), from D to S, is very rarely attempted, on account of its harshness and striking discontinuity. No satisfactory reason has been assigned (theoretically) for the avoidance of such successions; nor why the progressions of common chords (properly managed) between the tonic and its second, ascending or descending by conjunct degrees, or between the dominant and the sixth of the scale, ascending or descending by conjunct degrees, should be frequently used with no displeasing effect. And, again, what fundamental bass can be assigned, according to received theories, to such successions as chords of sixth and third ascending or descending by conjunct degrees? Not to speak of many more successions in harmony and in melody, quite inexplicable by the system of fundamental basses, commonly received as the true one. It may be remarked, that singers, in attempting to sing the ascending major scale, always find great difficulty at first in executing, in tune, the series of sounds from the fourth upwards to the seventh.

No. 26.

This is a practical fact, not explained by any theory. If you give the learner (with a

No. 28.

At b the progression might be but such a passage is harsh in its effect, from the more natural progression of the third of the dominant being by a semitone ascending, instead of by a leap. Another harsh progression

No. 30.

might be (according to some composers) introduced at b. But such progressions ought in general to be avoided, though they sometimes occur in the free style of modern music; not, however, in the works of the best masters. It may be here remarked, that although the perfect fourth is a consonance, as we have said before, still, when it occurs between the bass and an upper Part, it requires a certain management. This is the reason why it has been erroneously called a dissonance. It would require a great many examples to show in what manner the perfect fourth should be treated when it occurs between the bass and an upper Part. We shall merely remark,

No. 31.

that, except in such successions as &c.

the fourth must, in general, descend by a semitone, or a tone, to the third of the same bass sound; or, if the bass moves upwards or downwards to the following chord by a tone or a semitone, the sound forming the original fourth must either be continued in that following chord, or must descend a semitone or a whole tone. Such are the technicalities regarding the treatment of the fourth in harmony. The quantity of printed disputations regarding the nature, &c., of the fourth is most unreasonable.

A great deal of the variety and colouring, as it is called, of the free style of modern music depends upon the use of chromatic changes of the intervals of the simple common chords, and their inversions. To make the nature of this more clear, we shall again have recourse, in the first place, to the same successions of common chords that we have already given, and show how their forms and effects can be altered by means of these chromatic changes. Of course, it is not upon every occasion that these chromatic changes are to be used. Some clever composers of the more modern schools indulge in these chromatic alterations to such excess that many of their compositions are little better than continuous lamentation, or caterwauling. By such abuses, the manly simplicity, energy, and dignity of certain styles of music are entirely destroyed. The whole practical principle of these chromatic changes is the division of a tone into two smaller intervals, ascending or descending. We do not say "into two semitones," because that is not really the case in correct intonation of such passages. In a succession of chords such as we have given, one at least of the Parts may rise or fall by a tone to one of the Parts of the next succeeding chord. It is therefore obvious that an ascending or descending tone may be divided into two smaller intervals; and this is done by the chromatic alteration—sharp in ascending, and flat in descending, as shown in Plate VI., Nos. 20 to 27 inclusive. We give these merely to show how the thing may be done. When such chromatic alterations may be introduced with good effect, is to be studied in the compositions of Haydn, Mozart, Clementi, Beethoven, and some others. All our examples of mere chords are to be considered by the student as no more than some of the dry and detached bones of a skeleton of harmony. He will find them all knitted together in their proper places, and clothed in living beauty of form and substance in the works of the best composers. It is there that he must seek for their use, and not in theories.

False relations must be avoided in melody as well as in False relation harmony. When a sound passes to its diminished or augmented octave, above or below, there is a false relation in melody; as,

No. 32.

In harmony, such octaves struck together, and prolonged for some time, would be intolerable. Such passages as the following contain false relations. In these passages, the chromatic alteration is not made in harsh effect. These examples, when corrected, will stand as follows:

No. 34.

Such passages as the following, where dissonances occur along with the chromatic alteration, are not objectionable.

No. 35.

Such as the following are permitted.

No. 36.

Dr Burney, in criticising some of Purcell's harmonic combinations, blames him severely for using the $\text{b}^6$ and $\text{#}^3$ No. 37. or $\text{b}^6$, and says that this chord is "detestable," and is "jargon at all times and in all places." It so happens that this same detestable chord is very frequently used in modern music; and, if Dr Burney had looked into the works of Emanuel Bach and Haydn, of which he speaks with unmixed commendation, he would there have found many instances of the elegant and effective use of the chord of $\text{b}^6$ and $\text{#}^3$; also in Mozart's works, both vocal and instrumental. Another chord that Dr Burney finds great fault with in Purcell, is the chord of No. 38.

$\text{b}^6$; but this chord is found in the works of the best modern composers. Among chromatic chords we shall notice only two more, of considerable importance, which frequently occur in harmony. They are the chord of the diminished seventh, and the chord of the augmented sixth.

No. 39.

Diminished Seventh.

Inversions.

Augmented Sixth.

These chords occur more frequently in minor scales than in major ones; and when they do appear in the latter, the notation is generally wrong. For example,

No. 40.

Instead of

The effect of the diminished seventh is mournful and pathetic. Among other instances, see "He was despised," in Handel's Messiah, at the words "a man of sorrows." Sometimes we meet with a series of three or four chords of diminished seventh, or their inversions, in which all the Parts ascend or descend together by semitones. With regard to the chord of the augmented sixth, it is called No. 41.

the Italian sixth when it consists of $\text{b}^6$, the French sixth when it consists of $\text{b}^6$. Of these, the Italian sixth is the most simple and elegant, and the German sixth the most powerful in its effect. The French sixth is harsh and poor. In writing for four Parts, the third of the Italian sixth is doubled:

No. 42.

German sixth when it consists of $\text{b}^6$, and its third. When in this position $\text{b}^6$, we can- not; but we may in the following position, where the diminished seventh occurs in a middle Part; and below the third

No. 46.

We have a few remarks to make upon what are called enharmonic changes of modulation, made by means of the chord of the diminished seventh, or of the chord of the German augmented sixth, or inversions of these. What is termed enharmonic, is really neither more nor less, in practice, than a change of signs in notation; which change, being merely addressed to the eye in all such pretended enharmonic transitions, leaves the sounds exactly as they were before upon all our imperfectly-tuned instruments, such as the organ and piano-forte. For example, we strike the following chord on a piano-forte

No. 47.

If we choose to alter the signs of this chord, and to write

No. 48. No. 49.

or

No. 50.

all this makes no change whatever in the sounds heard on the piano-forte. The very same sounds are produced, because the very same finger-keys are struck.

In the case of the German augmented sixth

No. 51.

At 1 we have a single suspension, that of the fourth; and at 2, a double suspension of sixth and fourth. These are two of the cases formerly alluded to, in which the perfect fourth, though a consonance, is treated as if it were a dissonance when it occurs between the bass and an upper Part. At 3 occurs a single suspension, a major seventh ascending a semitone to its resolution in the octave; at 4, a single suspension of ninth resolving downwards, as the ninth almost always does, by descending a tone or a smaller interval, according to the nature of the passage in which it occurs; at 5, a double suspension of ninth and major seventh, in which the ninth is resolved by ascending a tone, and the seventh by ascending a semitone; at 6, a double suspension of ninth and fourth; at 7, a triple suspension of ninth, b sixth, and fourth; at 8, a quadruple suspension of ninth, seventh, sixth, and fourth. Such combinations of dissonances as this last are not frequent; but they sometimes occur in the best instrumental compositions. This legato and syncopated style belongs more to the old schools of composition than to the modern. The effect of such passages is good on the organ as an accompanying instrument, or as a principal instrument, on account of its powers of producing the sostenuto and the legato; but is almost null on such an instrument as the piano-forte, from its deficiency in these powers of sostenuto and legato. Voices and wind-instruments produce great effects in this style of music. It is not so effective in music for stringed instruments. Besides a great variety of suspensions that may take place in an upper Part, there are many that may occur in the bass when its progression is by conjunct degrees ascending or descending. Of the following examples, 1 and 2 are the best, though 3 and 4 are from Beethoven. These last may be used in cases where the combinations of different voices or instruments are suitably arranged, or in the course of a rapid movement. The nature of what are called anticipations (the converse of suspensions or retardations) will be understood from the following examples.

At 1 the anticipations are in an upper part; at 2 they are in the bass. Anticipations such as those at 3 are frequent in music of the time of Handel, and before then.

We give a few examples of what are called passing notes, changing notes, transient notes, &c. which (as well as suspensions and anticipations), are said by theorists to be unessential or accidental notes.

These so-called passing notes are marked with a small zero. It is needless to multiply examples here, and we shall only refer to one remarkable instance of the use of passing notes, which occurs at the beginning of the first movement of the first quartett in Beethoven's fifty-ninth work. The violoncello begins with a fine and dignified subject (key F major), accompanied by the viola and second violin, in the following manner for six bars and a half, when the harmony changes.

The first violin comes in at the ninth bar, imitating the preceding passage of the violoncello, and accompanied by the three other instruments forming the chord of the second inversion of dominant seventh, as far as the seventeenth bar, where the following bold passage occurs.

With regard to passing notes, notes of grace, anticipations, substitutions, altered or chromatic notes, and so on, the truth seems to be, that theorists have always found them inexplicable upon their favourite principle of the fundamental bass; and that, not knowing how to account for them rationally upon that principle, they have been obliged to treat all such sounds that occur in melody and in harmony as sounds that have no foundation in the real structure of the composition; and to assign to them, by way of salvo, any names that might pass current in an obscure and erroneous terminology. But if theorists will adhere to the received systems of fundamental basses, they ought to be able to apply these systems to all the phenomena of melody and harmony. This is not the case; for it is utterly impossible to refer all the combinations of modern (or even of ancient) harmony, to the received systems of fundamental basses. Every candid and intelligent musician will admit this to be true. Among all the systems of fundamental basses, Serre's theory (formerly alluded to) seems the most plausible, although still very imperfect. He assigns to a chord, one, or two, or three fundamentals, which are to correspond to the diatonic or chromatic nature of the sounds and intervals of the chord. But other theorists have their fundamental suppositions and substitutions; their after notes; their changing notes; their passing notes; their altered notes; their appoggiature; their suspensions; their anticipations; and, in short, such a chaos of hypothetically unessential and unreal things, that it is no wonder if the study of harmony is looked upon with horror and despair by all students who are trained in the ordinary schools of composition. They meet, at every step, with contradictions as absurd and perplexing as the long established algebraical dogma that there are quantities less than nothing. A little common sense and logic might have shown that this puzzling dogma is a mere contradiction in terms. Nothing being no quantity at all, it is obvious that there can be no such thing as a quantity less than nothing, or even equal to nothing. If such absurd contradictions in terms pass so long current in the most severe and exact of all sciences—mathematics—it cannot surprise any thinking man that musical theories and systems should abound in similar ones.

It is wrong to say that the ear recognises or suggests what are called suppositions and substitutions in fundamental basses; sounds that are not heard, but are ascribed, by erroneous theory, to such and such chords. The ear hears none of these imaginary and hypothetical things. Were it otherwise, and to carry this hypothesis to the reductio ad absurdum, the ear ought to hear all the chords that can possibly be applied to the accompaniment of any given melody. In fact, if two voices, or two instruments, perform a duett, for example, the lower Part is felt to be the bass for the time being; and there is no other Part felt, or supposed, or substituted, by the ear. The imagination may suggest an additional Part below the lower Part, or above the higher Part, or intermediate; but this has nothing to do with the theory of the fundamental bass. If another lower Part is added to this same duet, then the ear feels that Part to be the bass; and supposing a fourth or a fifth Part, and so on, added still lower, then such added Part becomes the bass, in so far as the ear is concerned. If the lowest Part is overpower ed by the upper ones, then the ear pays no attention to it, but to the predominant upper or middle Part or Parts. Experiment will prove this. If a melody is performed by a single voice or instrument, or by a great number of voices or instruments in unison or in octaves, does the ear supply a fundamental bass, or any bass at all? Surely not.

As to what are called passing notes, chromatically altered notes, suspensions, anticipations, and so on, in melody or harmony; all these sounds are just as real as any other sounds that are heard in the course of the melody or of the harmony; and if theorists adhere to the received fundamental bass system, then every sound that is heard in a melody, or in any Part of a harmony, must have its own fundamental bass, just as much as any other sound that exists in the melody or the harmony. This inference is inevitable from rational logic. One of the most absurd hypotheses in musical theories is found in the attempt to explain, according to the fundamental bass system, a series of chords of 6th and 3d ascending or descending by conjunct degrees. It is said that in such passages there is an ellipse of a chord between every two chords of the series, and that the ear understands this to be the case, and supplies the omitted chords:

When musical theorists meet with passages that cannot be explained by the hypotheses advanced, such passages are called licences. Unfortunately these licences are so numerous in music, that the rules are overwhelmed by exceptions. The easy way for a puzzled system-monger to escape from the difficulties that beset him is, no doubt, to have recourse to such convenient words as licences, exceptions, and so on, which are not unwillingly received by the public as substitutes for truth. In the works of the greatest composers are found many passages of excellent effect, though prohibited by the rules of theorists. Such being the case, we would again earnestly urge the student to form an extensive acquaintance with the best models of the art, rather than trust to any theories on the subject. He ought never to give up his reason and his feelings to any theoretical authorities. If he do, he will become timid and uncertain. Every thing he meets with different from what his dry rules have taught him, will perplex and terrify him. His energies will be paralyzed, and he will be incapable of producing any thing but cold, feeble, and formal music. To escape this result, he must take a comprehensive view of the art and its accessories; devote himself to no particular composer or school of composition; study the best music of every kind and of every country; and not allow himself to be captured and manacled by any theorist. He ought to keep in view that, in music, nothing is out of rule except what offends the ear, the taste, and the judgment; but that he must not venture to imitate the freedom and the bold effects of the greatest masters, until he has acquired great knowledge and command of the materials of the art. This cannot be acquired but by a well-directed course of study. Young painters are generally ambitious of handling the brush and colours before they have learned to draw correctly with a pencil or a crayon. If they are permitted to follow this course, they never attain eminence in their art. The case of the impatient musical student is analogous. Before he has learned to write correct melody, or correct harmony for two voices or two instruments, he burns to signalize himself by writing a chorus or a symphony, an opera or an oratorio. The lamentable failure of such a premature attempt disgusts and disheartens him. He abandons study as hopeless; and, if a man of genius, deprives the world of an excellent composer by neglect of the old maxim, festina lente. It is well to remark here, that Haydn, in the height of his reputation, declared to his friends that he did not recollect having passed a day without working sixteen and sometimes eighteen hours. We may also remark, that Haydn formed his own admirable style by the indefatigable study of every good composition within his reach; by neglecting no opportunity of gaining information regarding his art; and by forming for himself his own theory and principles of musical composition. In the earlier part of his life he studied intently the works of C. P. E. Bach, a musician of the highest order of genius, and also the works of G. B. San Martini of Milan, a composer of great genius and originality, but not possessed of patience enough to cultivate his abilities to the uttermost. In Haydn's earlier works, among others, some of his Sonatas, the resemblance between his style and that of Emanuel Bach is most striking. Indeed, the two styles are hardly distinguishable. But, as his musical horizon extended, he saw that neither E. Bach, nor John Schastian Bach the father, nor G. B. San Martini, nor many more whom he studied and imitated, would suffice to make him a great and original composer. So he applied himself to the improvement of instrumental music, and to the invention of a new style of composition in instrumental quartets and symphonies. His best quartets and symphonies still remain unrivalled, for the admirable management of the subjects and modulations, the judicious employment of the different instruments, the unity of design in each movement, and the clearness of construction and of harmony. Haydn was a great advocate for melody. He used to say, "Every composition that has a fine melody is sure to please;" and experience proves the truth of Haydn's assertion. He was of opinion that the most recherché and learned harmony without melody was only an elaborate noise, which, if it did not displease the ear, excited neither the feelings nor the imagination. We shall close this part of our subject with a few remarks that may be useful to the student.

The practice of composition ought to begin with melody for a single voice, with or without a bass Part. The next step is to learn to write correctly for two voices, then for three, then for four, and so on. The custom of writing for voices will induce a habit of correctness not to be acquired by persons who begin by writing for instruments.

The proper manner of accompanying vocal music forms a difficult branch of the art, and cannot be studied with advantage till considerable skill has been acquired in vocal composition. The compass and quality (timbre) and powers of different instruments, and their effects in combination, must now occupy the student's attention. He ought to take every opportunity of hearing good instrumental music well performed, not only by orchestras, but also by military bands; and of observing attentively the various effects produced. In whatever he composes, clearness of harmony ought to be carefully preserved. Obscurity of harmony arises from the following causes: Too rapid a succession of sounds, chords, and keys; a complication of different movements that take place simultaneously in the different Parts, especially when these movements are at the same time accompanied by a series of chords that succeed each other very quickly, or by sudden modulations. Two different movements at the same time, unite easily; three not so easily; four may produce obscurity, if they are not very skilfully arranged, and especially if care is not taken, at the same time, that the chords do not suc- ceed each other, but at the distance of a bar at least. More than four different movements at once almost inevitably produce confusion. It is therefore mere waste of time to attempt to give a different movement to each of the Parts of an orchestra. Harmony for three, and especially for two Parts, is much less liable to become confused than harmony for more than three Parts. For this reason, harmony in two or three Parts should be frequently used, particularly in music written for the public. Besides clearness of harmony, there is another kind of clearness not less important. It depends on the choice of ideas, and the order in which they are connected. Wherever there is neither unity of ideas, nor proportion, nor symmetry, there is confusion.

That excellent composer Piccini, the rival of Gluck and of Sacchini, occasionally employed full and rich harmony in his orchestra, but disapproved of the common practice of keeping all the instruments continually busy. He wished to make the voice the principal Part in his operas, and that the instruments should only sustain the voice, or express what was indicated by the words, or by the action of the persons of the drama, or by the place and circumstances of the scene. He was opposed to those disegni ostinati in the accompaniment, which Jomelli brought into fashion, and which are uniformly prolonged through nearly the whole extent of a piece of music, although the words present shades of feeling or ideas which would require corresponding shades in the accompaniment. Multitudes of different instruments, continual orchestral effects, crude masses of harmony, and a perpetual affectation of dissonances, were considered by him as musical monstrosities. He said, "It is not difficult to know what can be put into a harmony. The difficulty lies in knowing what should be left out. The four Parts for stringed instruments, which form the basis of the orchestra, lend themselves almost equally to every kind of expression. This is not the case with the wind instruments, and instruments of percussion. The expression of the oboe differs from that of the clarinet, and that of the clarinet very much from that of the flute. The horns change their expression according to the key in which they are used. The bassoon, whenever it is not confounded with the bass, becomes sad and melancholy. The trombones can express nothing that is not lugubrious. The trumpet, nothing that is not warlike and brilliant. The kettle-drum is altogether military. If each of these instruments were reserved for its proper employment, we should produce varied effects, succeed in describing everything, and continually diversify our musical pictures. But we are lavish of all these means, all at once, and always. We exhaust and harden the ear. I should like to know what we shall do to awaken it when, as will soon happen, it will be accustomed to this uproar. What new diablerie shall we contrive? Perhaps we shall then wish to return to nature, and to the true means acknowledged by art; but you know what happens to persons accustomed to drink brandy." Some combinations of harmony, and treatments of dissonances, &c., not explicable by common theories, will be found in Plates VI., VII., Nos. 28 to 71.

We mentioned, in the section on Melody, that a treatise on melodic modulation is wanted; and we think that a satisfactory treatise on the modulation of harmony is also a desideratum. But neither can be written to any good purpose in the present state of the theory of music, taking the word theory in its most comprehensive sense, as applied to this art. Philosophers seldom understand music; and the greatest practical musicians have neither leisure nor inclination to attempt to analyse its nature; so that, for want of properly conducted investigation, we are likely to remain in the same "acre senza stelle" which at present darkens the depths of the art.

Modulation signifies, properly, the regular constitution of melody and of harmony in any given key, but is commonly used to express the art of conducting a melody or a harmony from one key into another, or through several successive keys. This change of key might be more properly called transition. Many persons believe that there can be no modulation where there is no change of key. But this is an error, since modulation takes place even in the simplest melody confined to one key. Transition is only one kind of modulation, and is worthless if injudiciously employed. We may make a transition from one key to another suddenly, and without any intermediate sounds; or by means of one or more intermediate chords through which we modulate into the new key.

The art of good modulation from one key to another, consists in the choice of these intermediate chords, and in their relative durations. The use of sudden transitions from one key to another, without any intermediate chords, requires attention to a variety of circumstances, in order to produce a good effect. Such transitions should be but sparingly employed in any regular composition. Every regular piece of music is composed in a particular key, in which it begins and ends, and which generally predominates over all the other keys that may happen to be introduced in the course of the piece. If the key is major, what are called its relative keys will be two major ones and three minor. If a minor key, its relative keys will be three major ones and two minor. The following tables will show what these relatives are:

| C major, principal key. | A minor, principal key. | |------------------------|------------------------| | D minor, first relative key. | G major, first relative key. | | E minor, second relative key. | D minor, second relative key. | | F major, third relative key. | E minor, third relative key. | | G major, fourth relative key. | F major, fourth relative key. | | A minor, fifth relative key. | G major, fifth relative key. |

These six keys offer, in their modulated connection, 720 combinations. The nearest related keys to a major key, taken as principal, and into either of which it may easily pass without any intermediate chord, are its dominant, its subdominant, and its sixth; thus, from C major to G major, or to F major, or to A minor.

The keys most nearly related to a minor key, are its third below or above, or its dominant, or its subdominant. It may pass into any one of these without an intermediate chord; thus, from A minor to F major, or to C major, or to E minor, or to D minor. In such cases we do not properly modulate, but make a sudden transition into a new key. In the following examples, we modulate by an intermediate chord:

No. 1

C into G. C into F. C into A.

A into E. A into D. A into C. A into F. The general rule is, that we can modulate into a relative key by means of one single intermediate chord, which chord is the dominant seventh, or some inversion of the dominant seventh, of that relative key. We may remain in the new key for some time, or we may quit it immediately, and modulate into a third key, and so on. An example of rapid modulation from key to key by means of intermediate dominant sevenths, or their inversions, occurs in what is called the "Tour du Clavier," or harmonic circle of keys. It is needless to give more of this than a fragment by way of example, since long successions of the kind are not used in modern music. Only short passages of such modulation occur in the best modern compositions.

Not unfrequently we meet with modulations into relative keys brought about by means of an intermediate common chord. For example:

In passing from one key to another, a third, a fourth, or a fifth below, without using any intermediate chord, it is proper to keep in view the following remarks:—1. Transition to third below. In this case, if the former key is major, the second should be minor. For example, C major, A minor. Here the transition is to the minor third below. A bolder and more unusual transition is from one major key to another major key, a major third below; such as from C major to A flat major. If the first key is minor, the second key should be major. Thus, from C minor to A flat major, a major third below. 2. Transition to the fourth below. The two keys ought to be both minor or both major, otherwise they will not be relative. 3. Transition to fifth below. The two keys ought to be both major or both minor, for the same reason that has just been given. To make a real change of key without intermediate chords, we must introduce at least one entire phrase or period in the new key. (See Melody, for phrase and period.) Thus, after a subject in C major, we might introduce a period in G major, in F major, or in A minor, and afterwards return to the key of the subject. Sometimes, but much more rarely, a transition is made from a given key to another a major second or a minor third above it.

The following is an instance of the first kind of transition just mentioned.

Examples of transition from the dominant common chord of a minor key, to a major key a minor second above that dominant, as at No. 6 below, may be found in the works of Haydn, Mozart, Beethoven, and other composers. An instance may be seen in the Finale to Haydn's Symphony, No.5 (about the middle of the movement), where the transition is from dominant of F sharp minor to the key of D major. In the "Trio" of the first quartett in Beethoven's Op.18 there is an example of a transition from the dominant of F major into the key of D flat major. In the sixth measure of the first movement of Beethoven's quartett, Op.95, we find a very singular transition from the dominant of the key of F minor into the key of G flat major.

In the allegretto vivace in the first quartett of Beethoven's Op.59, there are some curious transitions. Near the beginning there is a transition from the dominant of B flat major to the key of A flat major, and from the dominant of this last key a transition to the key of C flat major. Sometimes, in order to produce a powerful effect of contrast, a transition takes place directly from the tonic of a major key to the major key a semitone above, or a major third below. For example, from C major to D flat major, or to A flat major. At the beginning of the second part of the first movement in Beethoven's first sonata, Op. 12, there is an example of the second kind of transition just mentioned. It is from A major to F major. See another example about the middle of the andante in Haydn's Symphony, No. 4; transition from tonic G major to E flat major. Also another in the adagio cantabile of second quartett of Haydn's Op. 72; transition from E major to C major. All such powerful contrasts as those we have just spoken of, especially the transition from a given key to another a semitone above, ought to be very sparingly used. In dramatic music, and symphonies for an orchestra, these transitions may be very effective. The judicious composer may occasionally introduce them in music of a different description; for instance, in a cantata, or an instrumental quartett or quintett, &c. Excepting the cases we have mentioned of transitions made from one key to another without any intermediate chords, the general rule to be followed in modulating is to connect together the different keys by intermediate chords. In the proper selection of these intermediate chords consists the art of modulation taken in its widest sense. It depends entirely upon the relation or non-relation between the keys from and into which we modulate, what number of intermediate chords may be necessary to render the modulation smooth and agreeable. The manner in which these intermediate chords are to be disposed—direct or inverted, with or without dissonances or altered chromatic notes, &c.—rests with the composer's skill and imagination. One, or two, or three, or four intermediate chords may be necessary, according to circumstances; but there is hardly any modulation that cannot be effected by means of four of these.

It is necessary to observe that, in many cases, the intermediate chords used in modulating from one key to another must have a sufficient duration given to them; otherwise the effect of the modulation will be harsh and displeasing.

No. 9. From C major to D flat major. From C major to D major.

Both of these examples of modulation are harsh and unpleasing, because the intermediate chords are too few, and have not sufficient duration allowed to them; and yet they are given in a set of elaborate tables for modulation by Hudl, a German musician. Haydn never falls into errors of this kind. By taking care to prolong his intermediate chords sufficiently, he produces the smoothest and at the same time the most unexpected modulations. The following example, though not Haydn's, will illustrate this:

At A the modulation from B flat major into D flat major is gradually conducted. At B the same modulation is brought about too rapidly, and sounds harsh and unsatisfactory. Some good examples of Haydn's judgment in dwelling upon the intermediate chords when modulating, may be seen in the movement "Ecce mulier," in his "Seven last Words of the Passion." See the first nine measures of the second part of that movement, and from thirty-fourth to forty-fourth measures of same part.

A modulation frequently takes place into a key which is not a relative one to that immediately preceding, though both are related to the principal key of the piece. For example: 1. When the principal key is major, a modulation may occur from the second of the key to the third, from the third to the fourth, from the fourth to the fifth, from the second to the fifth. 2. When the principal key is minor, we may modulate from the fourth degree to the fifth, from the fifth degree to the sixth, from the sixth degree to the seventh, from the fourth degree to the seventh, and the converse of all these cases.

In modulating into a key not relative one (for instance, from G major into F major), care must be taken that the two keys are relatives to a principal key which has previously been sufficiently established; for it is only in such case that a modulation of that kind can be suitably employed. One may easily modulate from G major into F major by means of two intermediate chords in a piece of music of which the principal key is C major or A minor; but one could not do so if the principal key were D major or E minor; so that a modulation which is good in one case may become bad in another. This must always be kept in view with regard to modulations of the kind just mentioned. In order to modulate smoothly into a key more or less remote from the one we quit, we may employ two, three, or four modulations instead of one only. These may be called compound modulations. For example, to modulate from G major into F major, we may employ two modulations instead of one; the first, from G into A minor; the second, from A minor into F major.

As we can make a transition immediately from a major key to the minor key of its fifth below, so we can modulate into all the relative keys of the latter in setting out from the former; for example, into all the relative keys of F minor, beginning to modulate from C major. Again, we can modulate into all the relative keys of C minor, in setting out from C major. It is easier to modulate into keys that increase the number of their flats, than into keys that increase the number of their sharps. For instance, it is more difficult to modulate smoothly from C major into A major, than from C major into A flat major.

Sometimes, instead of using intermediate chords, a pause of some duration is employed between two keys that are not related to each other, and a modulation, or transition, effected in this way from the one key to the other. The longer the pause, the smoother the modulation in such cases. A single prolonged intermediate sound, not a chord, placed between two keys not relative, and followed by a pause, may also render the transition from the one to the other sufficiently smooth. For instance, after the chord of G minor, introduce a prolonged E flat and a pause, and then pass at once into the key of A flat major.

Towards the end of the last movement of Beethoven's third Piano-forte Trio, Op. 1, there is a curious modulation from dominant of C minor into B minor by means of two prolonged sounds, G and F#. We may modulate from one key to another far remote, by means of a series of chromatic notes performed by one Part that seems to wander uncertain in quest of something. "Or su, or giù, ed or ricirculando." The finest example that we know of this kind of modulation is in the Adagio Fantasia of Haydn's sixth Quartett, Opera 76. The whole movement is charming.

As to what are called enharmonic modulations, or transitions, we shall pass them by, since they have no real existence upon keyed instruments. We refer to what we have said on this subject in the section on Harmony. We must remark, however, that they are dangerous delusions, and are continually giving rise to a number of harsh and intolerable pseudo-modulations in the music of young composers, and even in the music of experienced composers who ought to know better. No sooner has a young composer (not wisely taught) got acquainted with the formulae of these pseudo-enharmonic transitions, than he is eager to use them on all occasions, in order, as he thinks, to display his learning. He deceives himself; for his indulging in such things only betrays his ignorance of his art. "Modulation," said Piccini, "like all the other processes of the art, ought to be employed as a means of just expression and judicious variety. To modulate for the sake of modulating, is to prove one's ignorance of the object and principles of music. It is to affect a superabundance of imagination and of knowledge, in order to conceal the want of both."

We advise the student to examine carefully the works of the best composers, Italian and German, for examples of modulation, as well as of harmony and melody. There is no other way for him to acquire even a respectable knowledge of his art. As to the books published expressly upon modulation, some of them are written by Germans, and generally contain only mere formulae of the shortest ways in which modulations can be effected. These formulae the student ought to shun, except for mere reference; because, although the study of them might render him able to modulate in a dry and formal manner, they could never teach him that grace, and freedom, and effect, without which the most elaborate modulations are worthless.

Imitation is a musical artifice, by which a Part, called Imitation, the antecedent, proposes a subject, or melody; and another Part, called the consequent, repeats the same melody, after some rests, in any given interval, and so continuing to the end.

Example. Imitation in the Unison.

No. 1.

In an imitation the consequent is not always obliged to answer to the antecedent in the whole extent of the subject proposed by the latter. It may imitate only a part of the subject, and the consequent proposing a new melody, becomes, in its turn, the antecedent.

Octave. Imitation in the fourth or the fifth is the next nearest to exact correspondence of intervals.

Imitation is called free or irregular when this exact correspondence is not observed.

Imitation is by similar motion, by contrary motion, by similar retrograde motion, by contrary retrograde motion.

The other kinds of imitation are by augmentation, by diminution, by counterpoint; interrupted, convertible, periodical, canonical, &c.

Canonical imitation is that in which the consequent answers to the antecedent, note for note, from the beginning to the end. An imitation of this kind is what is called a Music canon, and may be treated in two ways. It may end with a coda, or complete close; or it may be made what is termed an endless or circular canon, when it is so constructed that we can return from the end of the imitation to the beginning as often as we please, without stopping.

Another kind of circular canon is one which modulates through all the twelve keys.

No. 4.

A canon written upon one stave, with particular signs to indicate how and when the different parts follow each other, is called a close canon. Latin enigmatical mottos were often applied to these close canons, to direct the performer mysteriously. Padre Martini has given a list of fifty-six of these mottos. When the canon is written fully out in score, or partition, it is called an open canon.

The artifice of this kind of composition consists in combining the Parts in such a manner that they may, without inconvenience, be transposed from acute to grave if they are placed above the theme, and from grave to acute if they are placed below it, while the theme suffers no change in its melody, whether it exist in one of the extreme Parts, or in one of the intermediate.

These inversions may take place in seven ways, so that there are seven species of double counterpoint. In the ninth or second; in the tenth or third; in the eleventh or fourth; in the twelfth or fifth; in the thirteenth or sixth; in the fourteenth or seventh; and in the fifteenth or octave. Those most commonly used are in the tenth or third; in the twelfth or fifth; and in the fifteenth or octave.

In double counterpoint the Parts ought to be, as much as possible, distinguished from each other by the different lengths of their notes. The Part which forms the counterpoint ought to begin after the theme. The Parts must not be allowed to cross one another without some cogent reason. In all double counterpoints, except that in the octave, it is not only permitted, but it is necessary, to alter intervals when inverting the Parts, especially when the modulations require this.

From what has already been said regarding the inversions of intervals, the following very short examples of double counterpoints will be more easily understood. But, for full explanations, we must refer to Marpurg and others; and, above all, to the works of the great masters.

No. 1. Double Counterpoint in the Octave. Inversion of the same.

No. 2. Double Counterpoint in the Twelfth. Inversion of the same. Inversion of the same.

Here occur some of the alterations of intervals lately mentioned.

No. 3. Double Counterpoint in the Twelfth. Inversion of the same.

"Double counterpoint in the twelfth," says Cherubini, "is one of the most used, and one of the richest in resources." See his "Cours de Contrepoint et de Fugue," published in 1835. In this work he specially recommends Marpurg's Treatise on Fugue and Counterpoint, as the most complete of any. We would advise the reader to consult Cherubini's work also, as containing admirable examples of his own composition. Reicha and Cherubini seem to be at variance as to the nature of Marpurg's work. Reicha says, "il ne parle, pour ainsi dire, qu' des imitations et des canons." In the symphonies, quartetts, &c. of Haydn and Mozart, instances are frequent of the freshest and boldest melodies being used in counterpoint with the best effect; but it is only the highest genius and most consummate skill that can do this.

No. 4. Triple Counterpoint in the Octave.

There are also triple and quadruple counterpoints, susceptible of being inverted in various ways. Of these the best and most usual are in the octave, the tenth, or the twelfth.

Quadruple Counterpoint in the Octave.

In these triple and quadruple counterpoints, where the subjects are merely doubled in thirds, there is a dryness and want of variety which had better be avoided by writing, in a free style, accessory accompaniments to the counterpoint. Our limits do not permit us to enter farther into this extensive subject. We refer to Marpurg, and Reicha, and Cherubini, for full explanations.

We must add the following passage from Cherubini:

"All these examples give rise to an important remark, which is, that in spite of the denominations of triple and quadruple counterpoint, in the tenth or in the twelfth, there is no veritable triple or quadruple counterpoint, but that in the octave."

The fugue is a very complicated piece of music when it is carried to its highest pitch of artifice. It comprehends all sorts of imitations, canonical contrivances, and double counterpoints. Studied with proper views and within proper limits, so as not to interfere with the supremacy of melody and with the genius of a true composer, the fugue is extremely useful as an exercise of the student's ingenuity, and as tending to show him all the resources of artificial harmonic combination. To those who have learned to understand the artificial mechanism of fugues, and who can enjoy them on that ground, they are often very admirable things, though composers of great genius might have been better employed than in constructing them. Homer, Milton, or Shakspeare, would not have done justice to themselves, had they spent their time in writing difficult poetical puzzles, such as anagrams, acrostics, single, double, and triple poems in the shapes of crosses and triangles, or in which every word began with the same letter, as in the famous Pugna Pororum, beginning "Plaudite porcelli porosum pigra propago Progreditur," and so on for five closely printed pages. All such poetry is beyond the verge of the enchanted circle of poetical inspiration. So of all calculated artifices in music. If musical imitations, or canons of any sort, suggest themselves fluently and gracefully to a man acquainted with all the elements of the art, it is well; otherwise not; for mere dry labour ought to have no place in music. Since such artificial harmonic combinations can give pleasure to the initiated only, who have gone through a long training, there seems to be no reason why the laboured contrivances of imitation and fugue should have any preference over the simplicity of beautiful and expressive melody, and its adjunct, appropriate and effective harmony. We know well that this is all heterodox doctrine among a certain class of musicians, but do not the less adhere to our long-established opinion.

With great respect for the knowledge and ingenuity of all eminent writers of canons or of fugues, we must remark, that all these artifices arose at a time when melody was in its infancy, and had not acquired, like Hercules, the power to strangle the serpents that besieged its cradle. Among the greatest fugue writers are certainly to be reckoned G. P. Colonna, Handel, the Scarlattis, John Sebastian Bach, and his son Emanuel; and more recently Haydn, Mozart, A. Reicha, and Cherubini. Beethoven did not attempt much in this style, and what he attempted in it is not to be classed amongst his best productions. It is no wonder if a man of his towering genius and impetuous character was early disgusted by the arbitrary rules and restrictions imposed upon him by some of his unimaginative teachers, in such laboured music.

Cherubini says (we translate from the French), "The fugue, in spite of the ancient origin of the word, is, then, a creation of modern times, which was not practised in church-music until contrapuntists had freed themselves from the self-imposed obligation of working upon plain chant...........There are two kinds of fugue, from which a third kind emanates, and from this arise all the others. The two principal are, the fugue of the key, and the real fugue; the other is the fugue of imitation." All the others, children of caprice, are irregular fugues of imitation, or pieces in fugue style. The indispensable conditions of the fugue are the subject, the response or answer, the counter-subject, and the stretto. To these conditions may be added the pedal, which is almost always employed in a fugue somewhat developed........All the artifices which can be introduced into a fugue depend on the knowledge, the skill, and the choice of the composer, and at the same time on the nature of the subject and of the counterpoint, either or both of which may be more or less susceptible of yielding to these artifices. These artifices consist, in brief, 1. Of the employment of imitations in detaching, to form them, a portion either of the subject or of the counter-subject; 2. In the transposition of the subject into different keys, and in the advantage which may be derived in this respect from double counterpoints; 3. In the inversion of the subject by contrary motion; 4. In a new subject which may be introduced, and which can be combined with the first subject and the first counter-subject; 5. In the manner of introducing the stretto in several ways, by drawing closer and closer, each time, the answer to the subject; 6. In the means that may be employed to make the subject and its inversion by contrary motion be heard simultaneously; 7. In the manner of combining the subject, the counter-subject, and the stretto upon the pedal; and in the address and the taste employed in enchaining together and introducing these artifices in the course of a fugue. All these combinations, and others besides, may be employed in a studied fugue; but, in a fugue for the public, a selection must be made from them, and they must not be all employed, otherwise the fugue would be too long and tiresome."

Reicha says, "it is essential to remark, that in our days the ancient fugue (or in the rigorous style) is no longer

---

1 Reicha says, "Since fugues of the key are no longer composed, and as simple canons are not called fugues, the terms fugue of the key, real fugue, and fugue of imitation, are not really necessary, and only serve to confuse our treatises." (P. 56, 2d part.) composed quite under the same restrictions as in the time of Palestrina. At present we modulate in it a little more boldly, and employ more of dissonant chords. We sometimes introduce little chromatic phrases, and employ a greater variety in the values of the notes. We choose subjects of a more modern cast—from time to time we permit successions of notes formerly prohibited, such as the diminished fourth, the augmented fifth, diminished seventh, minor seventh—we add a coda—we compose these fugues in all kinds of measures, &c.; so that we may say there exist three kinds of fugues: 1. The fugue entirely in the ancient style; 2. the modern or free fugue; 3. the mixed fugue, which participates in these two styles." (P. 4, part ii.)

No. 1. Subject. Counter-subject.

Answer.

Octava Alta.

No. 2. Example of the Stretto, which consists in making the Answer follow the Subject as closely as possible.

Subject.

Answer.

Octava Alta.

No. 3. Example of the Pedal.

The pedal is a prolonged sound, sustained for several measures. It may be placed in the upper Part, or in a middle Part, and may occur on the key-note or the dominant; but in general it is best to place it in the lowest Part, and upon the dominant of the key.

For examples of vocal fugues, we refer the reader to Padre Martini's Saggio di Contrappunto; Paolucci's Arte pratica di Contrappunto; Choron's large work on composition, and his collection of musical classics. Clementi's collection, entitled Practical Harmony, contains a great variety of examples of instrumental fugues by different composers. Among the best of these are the fugues by Handel and the two Scarlattis, in the second volume. All Handel's fugues are excellent studies, having more melody, force, and freedom, than most others of that period. Among what are called free fugues, we would point out two beautiful specimens in Mozart's overture to the Magic Flute, and in the last movement of his first violin quartett in G.

Cherubini gives an advice which the student will do well to follow. He says, "we will add here, that in all the kinds of counterpoint of which we are to treat, as well as in the fugue, the scholar ought to write for voices, and not for instruments. He ought to write conformably to the natural compass of the different kinds of voices. By this practice he will have the advantage of learning to produce effects by voices only,—a difficult study, and one perhaps too much neglected,—and he will find himself, afterwards, much more at his ease when he writes for instruments, and consequently is no longer obliged to confine himself within the limits of voices." Speaking of modulation (after having given general rules for it), Cherubini says, "Modern composers have freed themselves in their compositions from this simple and rational method of modulating, replacing it by a manner too free, and often incoherent; but if their deviations are tolerated in modern works, it is essential, and it is even expressly enjoined, not to follow these wanderings in the case of a composition so severe as the fugue."

By imitative music we do not here mean the imitation of one melody or passage of melody by another, which has been already treated of in the section connected with canon and fugue; but the employment of music, more or less appropriately and successfully, to imitate certain natural phenomena, audible or visible. The great mystery of music lies in its power of suggesting and exciting ideas and feelings in persons endowed with a sufficient degree of sensibility and imagination. In this respect it resembles poetry, for poetry is a dead art to all who have not sensibility and imagination enough to receive and expand its suggestions. We speak of the higher poetry; not of that which attempts in vain to be minutely descriptive or imitative, and which, by so doing, loses the nobler essence of poetry, without attaining the object proposed.

There are many musical compositions that do not aim at imitation or expression of any determinate kind. Such are the great majority of pieces of instrumental music. Some fanciful persons have gone so far as to imagine a story told, or a scene described, by a quartett or a symphony, although the composer gave no indication of any such purpose, and would have transgressed the true imitative limits of his art by doing so.

One of these fanciful persons, Momigny, in his Cours Complet d'Harmonie et de Composition, has ventured to give what he calls "a picturesque and poetical analysis" of the introductory movement and succeeding allegro of Haydn's eighth Symphony in Eb, and to add words here and there, to show what the music is intended to express. Momigny has also adapted words (see his third volume) to the first movement of Mozart's second Violin Quartett in D minor, and tells us that "he thinks he has discovered that the feelings expressed by the composer were those of a loving female on the point of being abandoned by the hero whom she adores," and that this luckless woman was Dido! All this, however, is mere imagination, and every one is at liberty to exercise his own fancy in such cases. In such a composition as Beethoven's famous Pastoral Symphony, it would certainly be impossible for any person to divine, merely from hearing it played, what was meant to be expressed or imitated by the different movements of that remarkable work. Unless he were previously told that such a movement was meant to express the sensations excited by visiting a country scene; such another, those felt beside a river; another movement meant to imitate a storm, and so on; certainly his imagination might lead him to guess very wide of Beethoven's intentions. The only things that he could have no doubt of, if accustomed to such rural sounds, would be the notes of the quail and the cuckoo, introduced in the river scene. As to the nightingale, he could make nothing of it, because the notes that Beethoven uses do not express the subtle song of that bird, any more than Handel's notes do in his song "Sweet Bird," in the Penseroso. In the oratorios and operas of eminent composers are to be found many instances of attempted imitations, most of which had better have been omitted. To attempt to imitate, by music, a hail or a snow storm, the leaping or creeping of animals, the falling of walls, and so on, is to mistake the powers of the art. A particular style of music may sometimes be effectively employed to enforce the ideas conveyed by descriptive words. In Haydn's Creation, and Seasons, we have several instances of this. Among other passages, we may cite the song in the Seasons (pp. 396 to 408 of Leipzig Partition), describing the traveller wandering bewildered among the snow; and the chorus, "Oh! the tempest comes" (pp. 203, 230). In other parts of the Seasons we find passages intended to express the rustling of leaves, the running of a brook, the buzzing of flies, the crowing of a cock, the croaking of frogs, &c., but most of them unworthy of Haydn's genius. The overture to the Seasons is intended to describe the transition from winter to spring; the introduction to summer (p. 138), "the dawn of day;" the introduction to autumn (p. 252), "the husbandman's satisfaction in contemplating the abundant harvest;" the introduction to winter, "descriptive of thick fogs." All these are phenomena not susceptible of musical imitation; and the consequence is, that the fancy of the hearer might lead him to associate the pseudo-imitations with ideas totally different from those which Haydn intended to suggest. The philosopher D'Alembert says, "Si j'avais à exprimer musicalement le feu, qui dans la séparation des éléments prend sa place au plus haut lieu, pourquoi ne le pourrois-je pas jusqu'à un certain point par une suite de sons qui iraient en s'élevant avec rapidité?" and, a little after, "Si je voulais peindre le lever du soleil, pourquoi ne le pourrois-je pas par une musique dont le son aurait un progrès assez lent, mais irait tout à la fois en s'élevant et en augmentant d'éclat, précisément comme le soleil quand il se lève?" Haydn, in the representation of chaos in his Creation, and in the introduction to the recitative "In splendour bright," in the same oratorio, seems to have had D'Alembert's ideas in view.

Many striking instances of indirect musical imitation may be found in the operas of Gluck. One of them occurs in his opera of Iphigenia, in the scene where Agamemnon deplors his daughter's lot in these words: "J'entends retentir dans mon sein le cri plaintif de la nature," &c. This "plaintive cry of nature" is expressed by the wailing notes of the oboe heard at intervals,

&c. while the "oracles of destiny" are expressed by the gloomy and obstinate responses of the bassoon, &c.

This remarkable passage is given, with a criticism upon it and some others from Gluck, in the first volume of Forkel's Musikalisch-Kritische Bibliothek.

The famous painter Leonardo da Vinci, in his Treatise Musical on Painting (c. xvi.), thus expresses himself regarding the invention aids to pictorial invention that may be derived from the contemplation of confused objects: "Se riguarderai in alcuni muri imbrattati, o pietre di vari mischi, potrai qui vi vedere l'inventione e similitudine di diversi paesi, diverse battaglie, atti pronti di figure, strane arie di volti, et habiti, e infinite altre cose; perché nelle cose confuse l'ingegno si desta a nuove inventioni." A painter of such genius as Leonardo da Vinci may have his imaginative faculties thrown into action by "a blotched wall, or by stones of various colours," or by other objects that would produce no impression upon an ordinary man. So it is with the musical composer endowed with genius. To persons who feel and understand both poetry and music, poetry is well calculated to suggest musical ideas. We should think little of the musical genius of a man who could peruse the Allegro, or Penseroso, or Comus of Milton, and feel their beauties, without having his musical imagination strongly excited. To the musician of a poetical temperament (such as Beethoven), the glories of sunrise or sunset—the various gentler lights and shadows of morning or of evening—the more solemn and mysterious lights and shadows of the moonlight landscape—the wildness and vastness of mountainous scenery under all the aspects of "skyey influences"—the calm or the agitated sea—the dreary sounds of the tempest—the thrilling sublimity of the thunder-storm—will suggest musical ideas by some strange alchemy of mind yet unknown to musical theorists.

Musical invention, like poetical or pictorial, is really no more than the art of combining, in new and remarkable forms, certain elements presented to us by nature or by art. In music, vocal and instrumental, sounds are those elements; in poetry, sounds and language, signs that fluctuate in their nature and uses, and in their indications of innumerable external objects and endless shades of human feelings and passions; in painting, forms of infinite variety, and colours contrasted or combined in all the possible diversities of light and shadow. As to musical invention, or originality in melody and harmony, those who have the most extensive acquaintance with the musical compositions of the last two centuries must perceive that there is very little originality to be found in the compositions of our day. Melodic ideas and phrases, except of the most artificial kind, were nearly exhausted before the commencement of the nineteenth century. The works of Galuppi, Piccini, Sacchini, Paesiello, Sarti, and many other Italians, are now hardly known to the public; and yet from them the more modern melodists have drawn most of their best ideas of melody. The artificial combinations of harmony, and successions of modulations, had been carried to a great extent by some of the Italian composers—the Scarlattis and others—and by Handel and the Bachs and Bendas, and others among the Germans—before Haydn, Mozart, and Beethoven directed the public attention, not so much to a new style of melody and harmony, as to a freer style of both combined. They threw aside a number of fetters imposed upon composers by unreasonable rules drawn by theorists from anterior compositions of a conventional kind. Haydn, Mozart, and Beethoven—especially the two former—seem to have carried artificial music nearly as far as possible without rendering it void of pleasing melody, clear design, and intelligible harmony. Most other composers who have come after them, or who were their contemporaries, have done little more than caricature their styles. Some of the more fashionable composers who have deigned to keep any thing like melody in view, have had recourse to the older and forgotten masters, and pillaged them without mercy. But, after all, it must be confessed that no limits can be assigned to change and innovation in an art so vague and arbitrary in its general signification as music, and so dependent upon the training given to the public ear. That beauty and deformity are mere mental affections, and not existences separate from the sentient being who feels them and judges of them, is proved every day by the diversity of human opinions regarding productions of the fine arts. It is vain and absurd to argue upon these matters. The old proverb that says "there is no disputing of tastes," holds not only in things affecting the nerves of the tongue and palate, but also in things affecting the eye and the ear. It is not unworthy of remark, that the word "taste" has been so transferred from its original signification as to be applied, by common consent, to the senses of sight and hearing, and even to what may be supposed to be more intimately intellectual judgments regarding the merits of poetry and oratory. Where are we to find a perfect theory of poetry and oratory? although these arts stand at the head of all human arts. Choros writes as follows regarding musical invention: "In music, and in the arts in general, we call idea that which in a more exact language we call thought. However that may be, the musical thought or idea is usually a passage of melody which presents itself to the mind of the composer with all its suitable accessories. From this we perceive that there are many kinds of different ideas, according to the sort of effects, whether simple or compound, which they employ. We ought also to distinguish ideas into principal ideas and secondary ideas. The first are suited to form the basis or foundation of a composition; the others are applied to the development of the principal ideas. It requires art and experience to discern whether an idea belongs to the one or to the other of these classes; and also to perceive whether an idea is suited to the free or to the severe style of composition; and to be able to develop it according to the rules applicable to each of these styles. The art, or, more properly, the faculty of finding ideas, is called invention. This term sufficiently indicates that we look upon invention as almost entirely a gift of nature. No rules whatever can be laid down upon this subject. We can only offer some observations which may be useful. We distinguish two kinds of invention: invention properly so called, and invention by imitation. What we have just said applies particularly to the former kind; that kind of invention which creates new and original productions that do not resemble preceding ones, and that serve as models for succeeding productions. It is the most distinctive characteristic of genius. It is found in the details as well as in the general structure; in the manner as well as in the matter. An artist often shows as much genius in treating, in his own way, a common idea, as he could by producing new ideas. Invention by imitation consists in approximating, in peculiarities of style and manner, to some production already known. Although this seems more easy than the other, it has its dangers and difficulties. The chief objection to it is the danger we incur of falling into plagiarism; a danger which cannot be avoided if we have not enough of imagination, taste, and skill, to enrich by accessories of our own, or to disguise dexterously, the materials which we endeavour to appropriate to ourselves. On the other hand, a happy imitation may be as good as a real invention. The talent of invention is developed by a continual application of mind to the object of invention, by the study of original works, and by directing the attention to seek in all things for the relations that they may have to the art which we cultivate. A thousand things that appear indifferent or useless to an inattentive man, become very significant to him who refers every thing to a principal object. We are often astonished that artists should have been so happy in their invention, and ascribe this to superior genius. We should be much more astonished if we knew to what circumstances they owe these advantages. The greater part of their talent consists in neglecting nothing, and in perceiving in what surrounds them every thing that can have connection with

1 See Clementi's admirable preludes in imitation of the different styles of Haydn, Mozart, Dussek, &c.; and J. B. Cramer's parody of one of Dussek's Sonatas for the piano-forte; and Mozart's compositions in imitation of Handel's style. their art. If we are attentive in collecting every thing that presents itself, and take care to treasure up the ideas which occur in favourable moments, we shall soon form a rich collection of materials from which we can draw when occasion requires. Finally, we must never torture ourselves to find ideas; and must especially shun that mania of originality which induces us to reject easy and natural ideas, and to run after fantastic and perplexed ones. One may often present novelty under a guise almost common. On the contrary, as Boileau says,

Il est certains esprits dont la fougue insensée Toujours loin du droit sens va chercher leur pensée, Ils croient s'abaisser dans leurs vers monstrueux S'ils pensaient ce qu'un autre a pu penser comme eux.

And all this is often mere lost labour; for an idea which at first seems new, on account of the manner in which it is presented, is frequently reduced to nothing when it is brought back to its true expression.

"If the gift of invention is invaluable, we may say that the art of conducting and developing ideas is not less important. We might cite many authors who, though not remarkable for variety or originality, have yet acquired a great reputation by the talent which they have shown in the development of their ideas. Among such authors are Sac-

chini and Anfossi; and in the works of authors very rich in invention might be pointed out pieces that have become highly celebrated, and of which the sole merit lies in the taste and the art shown in the development of the ideas." Most of Haydn's compositions are unrivalled models of skill and judgment in the development of musical ideas, and the conduct of the melody, harmony, and modulation. The study of double counterpoint, especially that in the octave, is of essential importance to the attainment of skill in developing musical ideas. A knowledge of double counterpoint offers numerous resources to the composer of a symphony, an overture, an instrumental quartett, &c.; and, indeed, without such knowledge, it is impossible to make the most of one's musical ideas. This kind of knowledge is far remote from the dry and burdensome learning of most of the older contrapuntists; learning which generally served no better purpose than to enable them with great labour to construct music for the eye, and not for the ear. To show the advantages that a composer of symphonies may derive from a knowledge of double counterpoint, we have only to refer to Haydn, Mozart, and Beethoven. Among Haydn's symphonies, the following movements occur to us at this moment as containing examples of what we have just been discussing. We refer the reader to the Partitions.

Sym. I. Allegro.

Sym. X. Allegro.

Sym. XVI. Allegro.

Sym. XVIII. Presto.

No writer on composition has treated so fully as Reicha of the uses of double counterpoint in the development of musical ideas. (See his Traité de Haute Composition Musicale, a large and expensive work, of 596 folio pages.) It is to be regretted that Reicha, in his two large works on composition, does not give examples from the works of the best composers. He does not even give direct references to such passages in the works of these composers as might illustrate his rules and observations. A man so versed as he was in music of all kinds could have done this easily; especially as his treatises were of great extent, and could have admitted of many classical examples, instead of those which he gives composed by himself or by his pupils. He says (p. 140 of first volume), "Now-a-days, it is required that the employment of any counterpoint should be effective. If a composer has not genius enough to accomplish this, he will do well not to make use of counterpoint... In all the treatises where counterpoint is spoken of, there is a defect, inasmuch as they neglect to show, in a satisfactory manner, the true resources offered by counterpoint. This is the cause that the public has never had a just idea of invertible harmony, and of its utility. Here is an example of a double counterpoint in the octave.

"This model of four measures gives eight in reckoning its inversion. This is nearly all that is generally known. But what is to be done with eight measures, it is asked, if there are no more? These eight measures may serve as follows.

"1. To form a canon for two unequal voices—(i.e., voices of different pitch and compass).

"2. To form an entire double fugue for two, three, or four Parts.

"And, which is more important in our days, these eight measures can be employed, 3dly, in the course (chiefly in the second section) of a movement in a symphony, &c. where a very advantageous use of them may be made; as, for example, fragment of a movement in a symphony for a grand orchestra, formed entirely from the preceding counterpoint."

Reicha then proceeds to show, by a Partition on the five following pages, the use and development of this counterpoint in the fragment above alluded to. We must refer to the passage in the original work.

Accompaniment:

This term sometimes signifies the harmonic support given to a melody or to a principal voice by one or more instruments, and sometimes means that knowledge of chords which is required in playing from a figured bass, or from a Partition. Since a voice or an instrument, or several voices or several instruments, may be accompanied by one or more instruments, the variety of combinations of this kind are almost endless. Melody, which forms the most expressive part of musical language, and regulates the march of composition by different rhythms, usually occupies either the highest or the lowest Part of a piece of music, in order to become more conspicuous. But sometimes, to produce a particular effect, the melody is placed in a middle Part. When this happens, or when it occupies the lowest Part, the accompaniment must be disposed accordingly, and constructed in such a manner as to produce the best possible effect in union with the melody. Since accompaniment is always subordinate to melody, some persons have looked upon it as an accessory of little importance, and have improperly compared it to the frame of a picture, or to the pedestal of a statue. This comparison, though having an appearance of justness, is really so absurd as to merit no refutation. Other persons consider accompaniment as a purely mechanical work, which requires only patience and application. If those persons mean by such work, the adding of some insignificant chords to a melody, they are not in the wrong; but such accompaniment is not that which we find in the works of Gluck, Piccini, Sacchini, Mozart, Winter, Cherubini, and other great composers.

Organ and piano-forte:

Two of the most important instruments used in accompaniment are the organ and the piano-forte. The organ is, in reality, a collection of wind-instruments of different kinds, forming in itself a species of orchestra, but not capable of the varied expression that can be given to a number of different wind-instruments played upon by different performers. Its noble and solemn effect renders it highly appropriate for the accompaniment of church-music; and it is much to be regretted that, in more modern times, its true character and powers have been too often lost sight of by injudicious composers and organists, who have introduced a style of performance and accompaniment quite unsuitable to the organ and to sacred music. The simple and legato style of accompaniment is that most suited to the nature and powers of the organ. In a memoir upon church-music (in the Italian language) by J. P. Schulthesius, there are many sensible observations upon this subject. The organ forms the best accompaniment to choral music, and in this case the organist ought to adhere to a simple and legato style. As an effective accompaniment to other sacred compositions, such as masses, &c., the organ is too much neglected by modern composers. The organ accompaniment ought always to be written in notes as the composer intends it to be performed, and never left to be guessed at by the organist through the puzzling and uncertain signs of a mere figured bass. We refer to what we have said on the subject of thorough-bass in the section on harmony. When the organ is used along with an orchestra, as in Haydn's and Mozart's masses, and others, it would often be better for the effect, if the organ were more employed in strengthening the bass Parts than in giving the full harmony of the chords; because, in the latter case, the peculiar effects of some of the orchestra wind-instruments would be obscured or overpowered. Fine effects may be produced by a judicious use of only certain stops of the organ, even in accompanying with an orchestra. In some modern organs, the compass of the finger-keys (reckoned upwards from the eight-foot stop, or an open pipe eight feet long) is from the lowest C on the piano-forte up to F in alt, with all the intermediate semitones. In many other organs, the compass is not so extensive. There are, besides, stops of sixteen, and sometimes (in the largest organs) of thirty-two feet pipes, for the pedals. It must be observed, that in different organs the stops vary much in kind as well as in number, and that all the stops do not extend throughout the whole finger-keys, but in most organs serve for only one half of these keys. This is not the place to enter more minutely into the structure of the organ. Most foreign organs have pedals, or foot-keys, which generally extend to two octaves of the lowest sounds.

It does not appear to us that the extension, of late years, of the compass of the piano-forte, beyond its former compass of five or five and a half octaves, has been any real improvement of the instrument. The piano-forte is much used in accompanying music of various kinds, vocal or instrumental, or both. Songs, cantatas, vocal duetts, trios, quartetts in chamber or concert-room music, instrumental solos, orchestral symphonies or overtures, operatic music, and so on, are all generally accompanied by a piano-forte. If the pianist understands his instrument thoroughly, has a knowledge of composition, and is well practised in reading from Partitions, he may give important assistance to the performers whom he accompanies, even when there is a complete orchestral accompaniment besides. He may do this more especially where singers are accompanied by an orchestra. Supposing that a pianist has to accompany a piece of vocal music of the old Italian school, and with nothing but the voice Part or Parts and a figured bass before him; he must not only be a good harmonist, but also well acquainted with the peculiar style of harmony and accompaniment suitable to such compositions, and really intended by the author, although not expressed by the imperfect system of thorough-bass notation anciently employed. Among these ancient composers, who were almost all excellent harmonists, there was a method of accompaniment practised by them as appropriate, and which, from tradition and habit, was clearly understood even by means of the imperfect and conventional signs of thorough bass. But this is no longer the case; and a modern pianist who would accompany a cantata of Alessandro Scarlatti, or a duett of Clari, or a psalm of Marcello, and so on, as the composer intended, must make a particular study of the older style of accompaniment, otherwise he will fail in his attempt to accompany such compositions.

---

1 "This fragment being placed in the second section of the movement, supposes that the first or the second subject of the counterpoint, or both, have been previously heard in the first section. Without this precaution, the hearer would feel it as something foreign to the movement, as out of place, which would be a fault on the composer's part. To render this counterpoint appropriate to the movement, it is enough that the four measures form a part of the subject of the movement." He will make the harmony too full, or too thin, or dispose it in an unsuitable manner. As we have not room for examples of the style of accompaniment suitable to such music, we refer the reader to the edition of Marcello's Psalms, published in Paris some years ago by Mirecki, a pupil of Cherubini. It was revised by Cherubini himself. In that work the accompaniments are given as they ought to be, and may serve as models for the accompaniment of such music, and of much of the music of that period—the latter part of the seventeenth and the earlier part of the eighteenth centuries. The accompaniment of the compositions of that period for voices is generally attempted by modern pianists in mere dry chords read from the thorough bass figures and notes. Such an accompaniment is quite erroneous in so far as regards the composer's intention, because the accompaniment of these pieces was an accompagnamento figurato for three Parts, each of which Parts had its own melodic progression, and the whole three were so contrived as to sustain the voice or voices, and enforce the effect of these without overpowering them.

To accompany a Partition from which the pianist has to select, on the instant, those parts most important to the effect, while he leaves out others, or portions of others, requires great practice and knowledge, especially with regard to more modern Partitions. Formerly, the most important parts of a Partition were the two violins, viola, and violoncello, forming a quartett that represented the essential structure of the composition. The wind instruments were at that time employed much more sparingly and less effectively than they afterwards were in more modern music. There are other circumstances in the structure of the older Partitions which render it less difficult to accompany them than the more modern ones. But, with regard to the pianist's accompaniment of Partitions, especially modern ones, we may remark, that the attempt too often made by injudicious accompaniers to crowd into the piano-forte accompaniment all the orchestral effects that they see in a Partition, is worse than useless. The thing is impossible, from the nature and powers of the piano-forte, and its uniformity of timbre. We have already alluded to this in the section on Harmony. Where there is any particular and prominent design in the Parts of a Partition, the pianist ought to adhere to it in his accompaniment, in so far as the nature of such design and the powers of his instrument will permit. In many cases he must be content to sacrifice much of the design, and of the grace and freedom of movement, found in the Parts of the Partition, and to arrange his accompaniment in such a way as to make the most of the difficulties presented to him by the construction of the Parts. This will frequently occur to him in accompanying modern Partitions, which often contain so elaborate a construction of Parts as almost to defy any attempt to represent even a shadow of them in the piano-forte accompaniment. The best way of learning how such intricate Partitions may be suitably accompanied by the piano-forte, or how they may be arranged for the piano-forte, so as to accompany the voice Parts (for example) without any other instrument, is to study carefully the best Italian and German arrangements of the best Italian and German operas, oratorios, masses, &c. for the piano-forte, with the voice Parts; for example, Clementi's admirable arrangement of Haydn's Creation; the best French or German editions of the similarly arranged masses and operas of Mozart, Winter, Cherubini, Beethoven, &c. To render this study really useful, the accompanier must, at the same time, have before him, and consider attentively, the Partitions from which these arrangements were made. No abstract rules can teach the art of accompaniment. Nothing but talent, experience, and observation can do so; and therefore we would urge the student to go at once to the interesting fountain-head of good models, and not to waste time upon dry technicalities. Many pianists make a very easy matter of accompaniment, by reducing it to a series of dry chords (accords plaques) or else broken chords in the vulgar form of what some musicians used to term "chopped hay." For the proper piano-forte accompaniment of modern songs, duets, &c. the reader may consult the compositions of this kind by Haydn, Mozart, Cherubini, Beethoven, Hummel, &c. where the accompaniments are written by the composers themselves. The harp, although introduced of late years into orchestras, is not very effective in such a situation, unless when occasionally left nearly alone to accompany some vocal Part in an opera, or in concert-room music. It serves better for an accompaniment in chamber-music. The guitar, skilfully managed, forms a pleasing accompaniment to a single voice in songs of a certain character. Although the greater part of its sounds belong to the bass and tenor range, music for the guitar is written in the treble clef; so that the sounds heard are really each an octave lower than they are represented by the notation.

Before we conclude this section, we must advert to a fault not uncommon in the compositions of Germans for voices with orchestral accompaniments. Even Mozart himself has sometimes committed this fault. It occurs when the harmony for two or three voices is incomplete, and a succession of fourths, for example, is left to have the harmony completed by some of the instruments of the orchestra. This filling up of the harmony by the instruments does not produce the desired effect; for the imperfect harmony of the voices,—from their peculiar and prominent timbre,—is still perceived. The best modern Italian composers are more careful in this respect. They make the harmony of their voice Parts complete in itself, and independent of completion from the orchestral accompaniment.

The comparative simplicity of orchestral combinations in the works of the older composers has been adverted to music in the preceding section. Gluck, in the latter part of the eighteenth century, was one of the first composers who introduced wind instruments into the orchestra in a manner more effective than had till then been practised. Any musician who will take the trouble to examine Gluck's Partitions will perceive that they suggested to other composers many ideas of orchestral effect from the use of wind instruments,—ideas more fully developed by Haydn, Mozart, Cherubini, Mehul, Beethoven, and others. The invention of new instruments, the improvement of old ones, the introduction into orchestras of instruments formerly confined to military music, have produced a superabundance of materials for orchestral effect; a superabundance sadly abused by many modern composers. The consequence of such abuse has been too frequently nothing better than a chaotic confusion, arising from the simultaneous combination of so many heterogeneous instruments. The elaborate noise of a modern orchestra is sometimes so great as to stun all ears but those petrified by custom. Men who serve artillery get so accustomed to the din and roar of cannon that they suffer no more annoyance from such noise than other untrained persons do from the distant explosion of a spent rocket in its highest altitude. They come at last to relish the martial din that deafens a common bystander.

In the section upon voices and instruments, we have occasionally adverted to the most suitable employment of some of the latter in orchestral music. We shall here offer a few more remarks upon this subject, and upon orchestral music in general.

A complete orchestra consists of a number of stringed instruments and wind instruments, and a few instruments of percussion; the latter being generally kettle-drums. The nature and magnitude of an orchestra must be regu- lated by the locality, since a large orchestra in a small theatre or concert-room, or the converse, would be ineffective, though from different causes. The relative proportion of the instruments in an orchestra is of much importance to its effect. The orchestra of the Italian opera at Vienna is small, in order to suit the locality. It was recently as follows: one conductor, one violin obbligato for accompanying particular parts of the vocal music, one leader and five first violins, six second violins, four viole, four violoncellos, four double basses, two flutes, two oboes, two clarinets, two French horns, two bassoons, two trumpets, three trombones, one drum, one double drum, one piano-forte; in all forty-three instruments. This is about the same number and proportion as in the orchestras of Dresden, Frankfort, and the Italian opera at Paris. The orchestra of the opera at Berlin is much larger, on account of the greater size of the house. In those smaller orchestras, the wind instruments are suited in size and tone to the fewness of the stringed instruments. The double basses, too, are small sized, and have four strings, except the principal one, which has five, to facilitate the execution of difficult passages. The orchestra of the grand opera at Paris lately consisted of twenty first violins, twenty second violins, fourteen viole, thirteen violoncellos, six three-stringed double basses, three four-stringed double basses, four harps, four flutes, four oboes, four clarinets, four bassoons, three trombones, horns, trumpets, kettle-drums, one serpent. The number of performers in the orchestras of the Scala at Milan, and San Carlo at Naples, used to be, at most, about ninety-three; but their number varies, and has of late been reduced.

Trumpets, trombones, the serpent, and kettle-drums, are too noisy to be suited to a small orchestra; and the judicious composer will, in such a case, avoid them. In writing for an orchestra, the stringed instruments form, as it were, the body of the composition, or a complete harmony in four Parts among themselves. This quartett consists of first and second violin, viola, and violoncello; the double basses being employed to enforce the violoncello Part. The number of violins, viole, and violoncellos, makes no difference in the real harmony of this quartett, because if there are twenty first violins they all play the same Part, and so of the second violins, and viole and violoncellos respectively. But, for the sake of variety, the full quartett is not always continued through a whole movement, but is sometimes interrupted by harmony in two or three Parts, and by passages in unisons or octaves. Occasionally, also, but more rarely, the stringed instruments cease altogether for a short period, to allow a passage for wind instruments alone to be heard with more effect from contrast; for instance, in the trio of Beethoven's first symphony in D major, Op. 36; in the trio of his symphony in C major, Op. 21; and in the trio of his Sinfonia Eroica, Op. 55; and, passim, in the orchestral compositions of Haydn, Mozart, Cherubini, Weber, Spohr, &c. The stringed instruments of the orchestra are often employed without being accompanied by any of the wind instruments. By the addition of wind instruments of different kinds, and in different ways, to the stringed instruments, a great variety of combinations and effects take place, which open a wide field of resources to the composer. It is important to remark, that whether the stringed instruments form a quartett, a trio, or a duett, their harmony ought to be good in itself, independently of the addition of any wind instruments. The same remark applies to the harmony of a duett, trio, or quartett, formed by a combination of wind instruments. The harmony must be good and pure, independently of any filling up by the addition of stringed instruments. It is hardly necessary to say, that the uses which may be made of all these possible combinations of the wind instruments with the stringed ones, or of wind instruments with wind instruments, depend entirely for their good effect upon the skill and judgment of the composer. One of the wind instruments added to the stringed ones, may either double one of the parts of these, if its nature permit it to do so, or may have a distinctive melody given to it, and be accompanied by all, or by only one, or two, or three of these parts; and thus, in the latter case, form with them a quintett, or quartett, or a trio, or a duett for the time being. Thus, the bassoon or the horn, for example, may double the bass part of the stringed instrument quartett of the orchestra, or any of the other parts, to produce a particular effect of reinforcement; or it may have a distinctive melody, and be accompanied as before mentioned. The same remark extends to the flute, the oboe, the clarinet; with this exception, that instruments of a high pitch, like these, are not properly employed to double the bass parts of the orchestra. By this doubling of a part is to be understood the addition to it of another instrumental part, which performs the same melody in unison, or in octave higher or lower, according to the nature and compass of the added instrument. When accompanying a wind instrument of a great pitch with two violins, the accompaniment is generally above the melody. In this case, the melody should form a good bass to the accompanying harmony; and if it does not, then the orchestral basses must be employed to supply the defect. To accompany a bass instrument which has a principal melody, with other instruments of a higher pitch, often requires much dexterity in the management of the harmony.

The number of possible combinations of the different instruments in an orchestra is so great, that we cannot here enter into the subject. To study the art of orchestral combinations with most pleasure and most advantage, one must have recourse to the partitions of the best German and Italian composers of operatic and orchestral music, from Gluck and Piccinni downwards to Haydn, Mozart, Cherubini, Beethoven, Spohr, Rossini, Weber, &c. In studying the partitions of some of the latest composers, one should guard against being led away by the love of noise and the affectation of singularity too often found in them.

If what we have had space for upon a subject so extensive should be of use to the professional student, or to the amateur, our object—the advancement of music in our native country—will be so far attained. We conclude by requesting the musical student to keep in view that there is no royal road to a true knowledge of his art; and also that in music, as well as in other things, Condillac's observation holds true:—"Les règles sont comme des gardes-fous mis sur les ponts, non pas pour faire marcher les voyageurs, mais pour les empêcher de tomber."

The limits prescribed to this article necessitated the greatest possible condensation in every section of the subject. Therefore the reader is referred, for additional information, to the introduction and the appendix to this volume, published in a separate form, under the title of Essays on the Theory and Practice of Musical Composition. It is necessary to observe, that of late years various wind instruments mentioned in the article Music have received great improvements, and that some new ones have been invented. By giving additional finger-keys, &c., to flutes, oboes, and clarinets, passages that were formerly very difficult or impracticable on these instruments, are now rendered comparatively easy. Among the brass wind-instruments similar improvements have been introduced, and the semitone scales within their compass completed. Sax, of Brussels, and his son have become celebrated for the excellence of their wind-instruments, both of wood and of brass, some of the latter being new inventions. In England, France, and Germany, also, wind-instruments have been much improved. Besides, several new wood and brass instruments have been introduced into orchestras and military bands, such as the bass clarinet, the Saxophone, &c.