This word, when originally appropriated by Dr Franklin to that peculiar form or mode of musical glasses, which he himself, after a number of happy experiments, had constituted, was written Armonica. In this place, however, we have ventured to restore it to its native plentitude of sound, as we have no antipathy against the moderate use of aspirations. It is derived from the Greek word ἀρμόνιον. The radical word is ἀγορά, to suit or fit one thing to another. By the word ἀρμόνιον the Greeks expressed aptitudes of various kinds; and from the use which they made of that expression, we have reason to conclude, that it was intended to import the highest degree of refinement and delicacy in those relations which it was meant to signify. Relations or aptitudes of sound, in particular, were understood by it; and in this view, Dr Franklin could not have selected a name more expressive of its nature and genius, for the instrument which we are now to describe; as, perhaps, no musical tones can possibly be finer, nor consequently susceptible of juster concords, than those which it produces.

In an old English book, whose title we cannot at present recollect, and in which a number of various amusements were described, we remember to have seen the elements or first approaches to music by glasses. The author enjoins his pupil to choose half a dozen of such as are used in drinking; to fill each of them with water in proportion to the gravity or acuteness of the sound which he intended it should produce; and having thus adjusted them one to another, he might entertain the company with a church-tune. These, perhaps were the rude and barbarous hints which Mr Puckeridge afterwards improved. But, for a farther account of him, of the state in which he left the instrument, and of the state to which it has afterwards been carried, we must refer our readers to the following extracts from Dr Franklin's letters, and from others who have written upon the same subject.

The Doctor, in his letter to Father Beccaria, has given a minute and elegant account of the Harmonica. Nor does it appear that his successors have either more sensibly improved, or more accurately delineated, that angelic instrument. The detail of his own improvements, therefore, shall be given in his own words.

"Perhaps (says he) it may be agreeable to you, as you live in a musical country, to have an account of the new instrument lately added here to the great number that charming science was possessed of before. As it is an instrument that seems peculiarly adapted to Italian music, especially that of the soft and plaintive kind, I will endeavour to give you such a description of it, and of the manner of constructing it, that you or any of your friends may be enabled to imitate it, if you incline so to do, without being at the expense and trouble of the many experiments I have made in endeavouring to bring it to its present perfection.

"You have doubtless heard the sweet tone that is drawn from a drinking-glass, by pressing a wet finger round its brim. One Mr Puckeridge, a gentleman from Ireland, was the first who thought of playing tunes formed of these tones. He collected a number of glasses of different sizes; fixed them near each other on a table; and tuned them, by putting into them water, more or less as each note required. The tones were brought out by pressing his fingers round their brims. He was unfortunately burnt here, with his instrument, in a fire which consumed the house he lived in. Mr E. Delaval, a most ingenious member of our Royal Society, made one in imitation of it with a better choice and form of glasses, which was the first I saw or heard. Being charmed with the sweetness of its tones and the music he produced from it, I wished to see the glasses disposed in a more convenient form, and brought together in a narrower compass, so as to admit of a greater number of tones, and all within reach of hand to a person sitting before the instrument; which I accomplished, after various intermediate trials, and less commodious forms, both of glasses and construction, in the following manner:

"The glasses are blown as near as possible in the form of hemispheres, having each an open neck or socket in the middle. The thickness of the glass near the brim is about the tenth of an inch, or hardly quite so much, but thicker as it comes nearer the neck; which in the largest glasses is about an inch deep, and an inch and a half wide within; these dimensions lessening as the glasses themselves diminish in size, except that the neck of the smallest ought not to be shorter than half an inch. The largest glass is nine inches diameter, and the smallest three inches. Between these there are 23 different sizes, differing from each other a quarter of an inch in diameter. To make a single instrument there should be at least six glasses blown of each size; and out of this number one may probably pick 37 glasses (which are sufficient for three octaves with all the semitones) that will be each either the note one wants, or a little sharper than that note, and all fitting so well into each other as to taper pretty regularly from the largest to the smallest. It is true there are not 37 sizes; but it often happens that two of the same size differ a note or half a note in tone, by reason of a difference in thickness, and these may be placed one in the other without sensibly hurting the regularity of the taper form.

"The glasses being chosen, and every one marked with a diamond the note you intend it for, they are to be tuned by diminishing the thickness of those that are too sharp. This is done by grinding them round from the neck towards the brim, the breadth of one or two inches as may be required; often trying the glass by a well tuned harpsichord, comparing the note drawn from the glass by your finger with the note you want, as sounded by that string of the harpsichord." Harmonica, sichord. When you come near the matter, be careful to wipe the glass clean and dry before each trial, because the tone is something flatter when the glass is wet than it will be when dry;—and grinding a very little between each trial, you will thereby tune to great exactness. The more care is necessary in this, because if you go below your required tone, there is no sharpening it again but by grinding somewhat off the brim, which will afterwards require polishing, and thus increase the trouble.

"The glasses being thus tuned, you are to be provided with a case for them, and a spindle on which they are to be fixed. My case is about three feet long, eleven inches every way wide within at the biggest end, and five inches at the smallest end; for it tapers all the way, to adapt it better to the conical figure of the set of glasses. This case opens in the middle of its height, and the upper part turns up by hinges fixed behind. The spindle is of hard iron, lies horizontally from end to end of the box within, exactly in the middle, and is made to turn on brass gudgeons at each end. It is round, an inch diameter at the thickest end, and tapering to a quarter of an inch at the smallest. —A square shank comes from its upper end through the box, on which shank a wheel is fixed by a screw. This wheel serves as a fly to make the motion equable, when the spindle, with the glasses, is turned by the foot like a spinning-wheel. My wheel is of mahogany, 18 inches diameter, and pretty thick, so as to conceal near its circumference about 25lb. of lead.—An ivory pin is fixed in the face of this wheel, about four inches from the axis. Over the neck of this pin is put the loop of the string that comes up from the moveable step to give it motion. The case stands on a neat frame with four legs.

"To fix the glasses on the spindle, a cork is first to be fitted in each neck pretty tight, and projecting a little without the neck, that the neck of one may not touch the inside of another when put together, for that would make a jarring. These corks are to be perforated with holes of different diameters, so as to suit that part of the spindle on which they are to be fixed. When a glass is put on, by holding it stiffly between both hands, while another turns the spindle, it may be gradually brought to its place. But care must be taken that the hole be not too small, lest in forcing it up, the neck should split; nor too large, lest the glass, not being firmly fixed, should turn or move on the spindle, so as to touch or jar against its neighbouring glass. The glasses thus are placed one in another; the largest on the biggest end of the spindle, which is to the left hand: the neck of this glass is towards the wheel; and the next goes into it in the same position, only about an inch of its brim appearing beyond the brim of the first; thus proceeding, every glass when fixed shows about an inch of its brim (or three quarters of an inch, or half an inch, as they grow smaller) beyond the brim of the glass that contains it; and it is from these exposed parts of each glass that the tone is drawn, by laying a finger on one of them as the spindle and glasses turn round.

"My largest glass is G a little below the reach of a common voice, and my highest G, including three complete octaves.—To distinguish the glasses more readily to the eye, I have painted the apparent parts of the glasses within-side, every semitone white, and the other notes of the octave with the seven prismatic colours: viz. C, red; D, orange; E, yellow; F, green; G, blue; A, indigo; B, purple; and G, red again;—so that the glasses of the same colour (the white excepted) are always octaves to each other.

"This instrument is played upon by sitting before the middle of the set of glasses, as before the keys of a harpsichord, turning them with the foot, and wetting them now and then with a sponge and clean water. The fingers should be first a little soaked in water, and quite free from all greasiness; a little fine chalk upon them is sometimes useful, to make them catch the glass and bring out the tone more readily. Both hands are used, by which means different parts are played together. Observe, that the tones are best drawn out when the glasses turn from the ends of the fingers, not when they turn to them.

"The advantages of this instrument are, that its tones are incomparably sweet beyond those of any other; that they may be swelled and softened at pleasure by stronger or weaker pressures of the finger, and continued to any length; and that the instrument, being once well tuned, never again wants tuning."

Such was the state in which this learned and ingenious author found, and such the perfection to which he carried that celestial instrument of which we now treat. We call it celestial; because, in comparison with any other instrument which we know, the sounds that it produces are indeed heavenly. Some of them, however, are still constructed in the same imperfect manner as the instrument of Mr Puckeridge. They are contained in an oblong chest; their positions are either exactly or nearly rectilineal; the artificial semitones by which the full notes are divided form another parallel line; but the distances between each of them are much greater than those between the notes of the natural scale, as they take their places, not directly opposite to the notes which they are intended to heighten or depress, but in a situation between the highest and lowest, to show, that in ascending they are sharps to the one, and in descending flats to the other. This structure, however, is doubly inconvenient; for it not only increases the labour and difficulty of the performer, but renders some musical operations impracticable, which upon the Harmonica, as constituted by Dr Franklin, may be executed with ease and pleasure. In this fabric, if properly formed and accurately toned, the instrument is equally adapted to harmony and melody. But as no material structure could ever yet be brought to the perfection even of human ideas, this instrument still in some measure retains the perverse nature of its original stamina. Hence it is not without the utmost difficulty that the glasses can be tuned by grinding; and the least conceivable redundancy or defect renders the discord upon this instrument more conspicuous and intolerable than upon any other. Hence likewise that inexpressible delicacy to be observed in the manner of the friction by which the sound is produced: for if the touch be too gentle, it cannot extort the tone; and if too strong, besides the mellow and delicate sound which ought to be heard, we likewise perceive the finger jarring upon the glass, which, mingled with those softer sounds by which the senses had been soothed, gives a feeling similar to iron grating upon iron, Harmonica, iron, but more disagreeable. In wind-instruments the operation of the tongue, in harpsicords the stroke of the quill, and on the violin the motion of the bow, gives the strong and sensible interruption of sound which may be called articulation, and which renders the rhythmus or measure of an air more perceptible; but upon the glasses, the touch of the finger is too soft to divide the notes with so much force; so that, unless the mind be steadily attentive, they seem to melt one into another, by which means the idea of rhythmus is almost lost. There is no way of performing a slur but by forbearing to stop the first sound, when that which is immediately subsequent commences. Thus, when the slur is of any length, and regularly descends or rises by the interval of a second, all the notes in the slur must be heard together, and produce no disagreeable dissonance; yet if it rises or descends by perfect chords, the effect is pleasing. The open shake, or trill, is another unhappy operation upon musical glasses; which can only be performed by the alternate pulsations of two continued sounds, differing from each other only by a note or semitone. But as these pulsations thus managed cannot be distinct, the result is far from being pleasant; nor is there any succedaneum for the close shake, which in the violin is performed by alternately depressing the string to the finger-board, and suffering it to rise without entirely removing the finger from it, and which, by giving the note that tremulous sound produced by the human voice affected with grief, is a grace peculiarly adapted to pathetic and plaintive airs.

We proceed, however, to a farther account of the same instrument, extracted from the Annual Register, vol. iv. p. 149.

"Besides those tones, (says the author of that account,) which every elastic string produces by a vibrations of all its parts, it is capable of another set of tones in which only a part of the string is supposed to vibrate. These sounds are produced by the lightest touches, either by air, as in Oswald's lyre, or by rubbing the bow in the softest manner on the string of a fiddle.

"Analogous to these sounds are those produced by bells: in these last, besides those tones produced by their elliptical vibrations, there are a set of tones which may be brought by gently rubbing their edges, and in which the whole instrument does not appear to vibrate in all its parts as before.

"Take, for instance, a bell finely polished at the edges; or, what will perhaps be more convenient, a drinking-glass: let the edges be as free from anything oily as possible; then, by moistening the finger in water (I have found alum-water to be best), and rubbing it circularly round the edge of the glass, you will at length bring out the tone referred to.

"This note is possessed of infinite sweetness; it has all the excellencies of the tone of a bell without its defects. It is loud, has a sufficient body, is capable of being swelled and continued at pleasure; and, besides, has naturally that vibratory softening which musicians endeavour to imitate by mixing with the note to be played a quarter-tone from below.

"To vary these tones, nothing more is required than to procure several bells or glasses of different tones, tuned as nearly as possible, which may be done by thin-

ning the edges of either; or, for immediate satisfaction, the glasses may be tuned by pouring in water: the more water is poured in, the graver the tone will be.

"Let us suppose then a double octave of those glasses, thus tuned, to be procured. Any common tune may be executed by the fingers rubbing upon each glass successively; and this I have frequently done without the least difficulty, only choosing those tunes which are slow and easy. Here then are numbers of delicate tones, with which musicians have been till very lately unacquainted; and the only defect is, that they cannot be made to follow each other with that celerity and ease which is requisite for melody. In order to remedy this, I took a large drinking-glass, and by means of a wheel and gut, as in the electrical machine, made it to turn upon its axis with a moderately quick but equable motion; then moistening the finger as before, nothing more was required than merely to touch the glass at the edge, without any other motion, in order to bring out the tone.

"Instead of one glass only turning in this manner, if the whole number of glasses were so fixed as to keep continually turning by means of a wheel, it follows, that upon every touch of the finger a note would be expressed; and thus, by touching several glasses at once, a harmony of notes might be produced, as in a harpsichord.

"As I write rather to excite than satisfy the curious, I shall not pretend to direct the various ways this number of glasses may be contrived to turn; it may be sufficient to say, that if the glasses are placed in the segment of a circle, and then a strap, as in a cutler's wheel, be supposed to go round them all, the whole number will by this means be made to turn by means of a wheel.

"Instead of the finger, I have applied moistened leather to the edge of the glass, in order to bring out the tone: but, for want of a proper elasticity, this did not succeed. I tried cork, and this answered every purpose of the finger; but made the tone much louder than the finger could do. Instead, therefore, of the finger, if a number of corks were so contrived as to fall with a proper degree of pressure on the edge of the glass, by means of keys like the jacks of an organ, it is evident, that in such a case a new and tolerably perfect instrument would be produced; not so loud indeed as some, but infinitely more melodious than any.

"The mouths of the glasses or bells used in this experiment should not resemble the mouth of a trumpet, but should rather come forward with a perpendicular edge. The corks used in this case should be smooth, even free from those blemishes which are usually found in them, and at the same time the more elastic the better."

In the two accounts here given seems to be comprehended every thing valuable which has been said upon the subject. It remains, however, our permanent opinion, that the form and structure designed and constituted by Dr Franklin is by much the most eligible; nor can we admit, that a cork, however successfully applied, will produce the same mellowness and equality of tone in general with the finger. It appears to us, that, by this kind of voluntary attrition, a note may be sunk Harmonica sunk or swelled with much more art and propriety than by the substitution of any thing else extrinsic to the hand; and when chords are long protracted, that degree of friction, which renders every sound in the chord sensible to the ear, without harshness, must be the most agreeable. For this reason, likewise, we should recommend alum-water in preference to chalk.

From what has already been said, it will easily be perceived, that this instrument requires to be tuned with the nicest degree of delicacy which the laws of temperament will possibly admit. For these laws the reader will naturally have recourse to the article MUSIC*, in this Dictionary; where, from M. D'Alembert, is given a plain and satisfactory account, both of the method proposed by Rameau, and of that established in common practice, without anticipating the experience and taste of the reader, by dictating which of these plans is preferable. To those who have occasion to tune the instrument, it may likewise be useful to peruse the detached article TEMPERAMENT in this Work.

Without recapitulating the different rules of alteration prescribed in these accounts, we shall presuppose the reader acquainted with them; and proceed to describe how, under their influence, the Harmonica may be tuned. But it is previously expedient to observe, that the same rules which conduct the process of tuning a harpsichord, will be equally effectual in tuning the Harmonica; with this only difference, that greater delicacy in adjusting the chords should, if practicable, be attempted.

There are different notes from whence the procedure of tuning may commence. La or A, which is the key that pretty nearly divides the harpsichord, is chosen by some; this la in common spinets is 24 natural keys from the bottom, and 13 from the top; and the ut above it, or second C upon the G cliff, by others. This last we should rather advise, because we imagine those intervals which we have called seconds major to be more just through the whole octave, when the course of tuning is begun by a natural semitone. The initiate, therefore, may begin by tuning the second ut of his Harmonica, or C above the treble cliff, unison with its correspondent C upon the harpsichord or any other instrument in concert-pitch; then, descending to its octave below, adjust it with the ut above, till every pulsation if possible be lost, and the sounds rendered scarcely distinguishable when simultaneously heard. To the lowest note of this octave he must tune the sol or G immediately above it by a fifth, still observing the laws of temperament: To this G, the re, or D immediately above it, by the same chord: To the re, or D above, its octave below: To this, by a fifth, the la or A immediately above it: To la, the mi or A ascending in the same proportion: To mi, its octave below: To this, the si or B immediately above it by a fifth: To the first ut, or C, which was tuned, the fa or F immediately below by the same chord.

That the practitioner may be still more secure in the justice and propriety of his procedure, he may try the thirds of the notes already adjusted, and alter, as much as is consistent with the fifths and octaves, such among these thirds as may seem grating and disagreeable to his ear. Thus far having accomplished his operation, he may tune all the other natural notes whether above or below by octaves. His next concern is with the semi-

tones. And here it will be suggested by common sense, that as in all instruments with fixed scales, the sharp of a lower must likewise answer for the flat of a higher tone, the semitone ought as nearly as possible to divide the interval. He may begin with la or A sharp; which la in its natural state is a third minor beneath the ut or C, from whence he began in the natural scale. This semitone should correspond with the E natural immediately above by a fifth. To it may be tuned the re or D sharp immediately below by a similar chord: To D sharp, its octave above: To si or B natural, immediately above the la or A first mentioned, may be adjusted the F or fa sharp immediately above it: To this its octave below: To that octave, the C or ut sharp above by a fifth: To the C sharp, its octave below: To this, by a fifth, the G or sol sharp above. Between this G sharp and the D sharp immediately above it, the fifth will probably be too sharp; but if the others are justly tuned, that discord will not be extremely offensive; and it is a necessary consequence of temperament. The rest of the sharps and flats, like their naturals, whether ascending or descending, may be tuned by their octaves.

The notes, with their chords, may be expressed by letters and figures, thus; where, however, it must be observed, that the higher notes of any chord are marked with larger capitals. It should likewise be remarked, that the figures are not expressive of the different ratios which the notes bear to one another, considered with respect to their vibrations; but only significant of their nominal distances, according to the received denominations of the intervals. Cc cG cD dD dA AE Ee Eb Cf. The sharps and flats thus, AxFx, AxDx, DxDx, ExFx, FxFx, FXFx, CxCx, Cxcx, cGxGx. In running over the sharps and flats as the naturals, it will likewise be necessary to try the thirds, and to alter such as may offend the ear; which, if cautiously done, will not sensibly injure the other chords.

—Though this article has been protracted to a length which we did not originally intend, we have however the satisfaction to find, that it comprehends everything essential; so that any person who understands the nature of chords, and the practical principles of music as universally taught, may not only be able to tune his instrument, but to acquire its whole manoeuvre, without the least assistance from a master. On Plate CCL. is represented an instrument of this kind.

Though this topic appeared in itself complete in the former edition of this extensive work, yet having since received from Dr Edmond Cullen of Dublin the following observations, and reflecting that men of musical talents have not only different tastes, but different powers of mechanical operation, we have thought it proper to submit to the choice of our readers, either Dr Franklin's form and arrangement of the glasses, or that which was adopted by Dr Cullen; but in either case, we would recommend it to the initiate in this instrument, to distinguish by colours, according to Dr Franklin, the notes and semitones.—We likewise cannot forbear to think, that the complete bass practicable on the harmonica, is by many degrees preferable to the chords with which Dr Cullen proposed to grace every emphatic This instrument the doctor describes as consisting of 35 glasses of different sizes, answering to so many distinct sounds, and ranged in the manner hereafter to be described. They are exactly of the form of a cocoa nut when the usual quantity of the top is cut off; or the sugar-bowls made of cocoa-nut shells so much in use will give a precise idea of their figure. They are blown with plain long stalks, which are fitted to wooden feet screwed on a board at proper distances, in such a manner that the circular tops of all may be in the same horizontal plane, at the distance of about an inch asunder. Of these 35, 10 only are allotted for half tones; there remain therefore 25 for the diatonic scale. The lowest note corresponds to G in the bass cliff; hence it extends upward to the octave above C in alt. For uniformity, take the glasses which are chosen gradually and regularly diminishing in size as they ascend in tone. This, however, is not absolutely necessary, as the tone of the glass does not entirely depend upon its size, but in a great measure upon the proportion of its different parts to one another: hence the glass corresponding to one note may be smaller than a glass corresponding to a note three or four times higher; however, where it is practicable, they should always be chosen gradually diminishing as they ascend, both on account of the elegance of appearance, and that an equality in point of loudness may be preserved; for, as everybody knows, an instrument may be liable to great inequality in point of strength, though perfectly in tune. This must have a very bad effect; and therefore we find performers on the violin and other instruments of that kind very solicitous about the proportional thickness of their strings. The glasses being chosen in the best manner circumstances will permit, we proceed to arrange them. Here let me observe, that in general the diameter of the largest glass at its mouth is about seven inches, and its solid contents about five English pints, while the highest is of about one-fourth of an inch, and its contents about one-third of a gill: this, however, is arbitrary, and depends upon the pitch of the instrument. In arranging the glasses, we shall, to avoid confusion, take the diatonic scale first, and afterwards the half tones will be easily understood. The wooden feet before mentioned are to be screwed on a strong board of a proper size, and they are disposed at convenient intervals in rows perpendicular to the longest sides of the rectangular board on which they stand. In these feet the glasses are disposed in the following manner: Beginning with the lowest note G, we fix that on the foot which stands in the nearest angle of the board on the left hand, A in the next bottom in the same perpendicular line, B in the third; when we come to C, however, we do not place it in the same perpendicular line, but in the nearest bottom of the second perpendicular row to the left hand, D in the second of the same row, E in the third; F again in the nearest bottom of the third row, G in the second of the same row, A in the third; B again in the nearest bottom of the fourth row, C in the second of the same, and so on. By this contrivance it is easy to see an immense compass is obtained: so great a one indeed, that if the glasses were disposed according to the old method, regularly ascending in a line parallel to the front of the instrument, to take in the same compass, it must stretch to a considerable length, no less than a length equal to the sum of all the perpendiculums we before spoke of, which in ordinary size of the glasses would amount to upwards of 16 feet; the inconvenience of which it is unnecessary to dwell upon. As to the half tones, perhaps a more judicious and convenient arrangement may be thought of for them: but the present mode is far from inconvenient, except in some keys; and it is sufficiently commodious for performing such airs as are best suited to the nature and design of the instrument. After explaining the arrangement, we shall speak somewhat more exactly of them. Eb on the first line of the treble stave stands in the fourth bottom of the first perpendicular row to the left hand; Fg on the first space stands in the fourth place of the second row; Gg on the second line of the treble stave stands in the fourth of the third row; Ch on the third space of the same stave stands in the same manner in the fourth row, and so on, ascending Fg in the fifth row, Gg in the sixth, Ag in the seventh, Ch in the eighth. In the ninth perpendicular row, that is, the last to the right hand in the diatonic scale, stands C alone; but immediately behind is placed Bb of the middle line of the treble stave, and again behind it Db of the fourth line of the treble stave, which finishes the whole. There is something singular, and perhaps whimsical, in the distribution of the half tones: but it is found sufficiently convenient; and if a better is thought of, it may easily be adopted. In the mean time I must observe, that two of them, viz. Ch and Fg, standing immediately behind the D and G respectively above them, are singularly well fitted for performing running passages either up or down in the key of G. Ex gr. let us suppose that we have that very common A, G, Fg, E, semiquavers. Here the performer touches A, which is in the first place of the sixth row, with his left hand, G with the forefinger of his right, Fg with the middle, and E again with the left hand; in the same manner may E, D, Ch, and B, be played, or upwards by inverting the motion: Thus we can with the utmost ease run either up or down two very frequent passages, in a key which might naturally be supposed difficult upon this instrument, and that with any given rapidity. I wish as much could be said of all the other half tones, of which, by the bye, some are altogether wanting: it is obvious, however, that they may easily be added, if we can find convenient places; and I apprehend even that very practicable. Be that as it may, notwithstanding the seemingly inconvenient situation of some half tones, and the total want of others, pieces may be performed on this instrument of considerable rapidity. I myself, though very far from being an accomplished player, can with great ease go through all the parts of Fisher's celebrated rondeau; nay, I have heard the fifth concerto of Vivaldi played upon it with as much distinctness as upon a violin. The glasses are not necessarily chosen perfectly in tune, but are tuned by the help of a quantity of water. Here, however, two cautions are necessary: 1st, By no means to take a glass which is, when without water, flatter than the note you intend; as in that case you cannot remedy it, the water making Harmonica making the tone still flatter; rather let it be somewhat sharper, and you may tune it to the utmost nicety by a little water. The second caution is, not to choose a glass which is very much sharper than the note required; as in that case, so large a quantity of water will be required to tune it as will entirely smother the tone.

"This instrument is to be played somewhat in the manner of the harmonica, viz. the fingers are to be well wetted; and by the application of them to the side, assisted by a proper motion, the sound is produced. And here I would observe, that the proper motion is, to make the fingers follow the thumb, not the thumb follow the fingers, in going round the glass: it is necessary also to preserve the circular motion very exactly, as the least deviation from it produces the most horrible sound that can be conceived. It is likewise to be observed, that you must touch the smaller glasses upon the very top of the brim; and for that purpose the palm of the hand must be nearly parallel to the top of the glass: but in coming to the larger glasses, it is absolutely necessary to make the fingers touch the side, not the top of the glass; and the larger the glass, the more distant from the top must they be touched. Practice alone can determine this matter.

"From this disposition of the glasses, it is easy to see that the perfect chord of C is always most completely in our power, namely, by using different fingers to the different notes at the same time; and although a full bass cannot be executed upon this instrument, we have always a great number of accompaniments which can easily be introduced; more perhaps than upon any instrument, the organ and others of that species excepted. The thirds or fifths occasionally can be introduced; and when done with taste and judgment, will scarcely yield to a middling bass. If to this is added the thrilling softness of the tones, inimitable by any other substance, it will readily appear to be an instrument more in the true style of music, of that music which the heart acknowledges, than any that either chance or ingenuity has hitherto produced. It is indeed incapable of that whimsical subdivision to which the taste of modern composers, that sworn enemy to harmony and real music, leads; which serves no end but to exhibit the wonderful executions of a favourite performer, and to overwhelm his hearers with stupid admiration. This is not music; and upon these occasions, though I acknowledge the difficulty of doing what I see done, I lament that the honest man has taken so much pains to so little purpose. Our instrument is not capable of this (at least not in so exquisite a degree as the harpsichord, violin, and a few others): yet if the true and original intent of music is not to astonish but to please, if that instrument which most readily and pleasingly seizes the heart through the ears is the best, I have not a moment's hesitation in setting it down the first of all musical instruments. There is but one which will in any degree bear the comparison, or rather they are the same instrument, I mean Dr Franklin's harmonica: but I am inclined to think that the instrument we have been speaking of has some superiority over the harmonica. The first striking difference is in the impracticability of executing quick passages on the latter; whereas it is in most cases extremely easy on the other. Again, the very long continued vibration of the glass, inevitably must produce horrible discord, or at least confusion, except the piece played be so slow that the vibration of one glass be nearly over before the other is heard. Now, in our instrument, this may be remedied by laying pieces of sponge lightly between the glasses, so as to allow them only the proper extent of vibration. This, however, is an exceptionable method: and it is much better done by the touch of the performer's finger, which instantly stops the vibration; and the use of this may be learned by a very little practice, the motion here being entirely voluntary: But in the harmonica, the motion being partly mechanical, v.g. the rotation of the glasses, this cannot be done; and for the same reason, in the execution of the crescendo the harmonica is not so perfect as this instrument. Besides, the inconvenience of tuning the half tones, as sharps or flats, separately, is as great in the harmonica as in the harpsichord. This is a very great imperfection; as half tones, being tuned at the medium, are false both as sharps and as flats. The learned Dr Smith says, there is no less than one-fifth of the interval difference between the sharp of one note and the flat of the next above; and for this purpose proposes to have an harpsichord constructed with a stop, so as to direct the jacks to the sharps or flats according to the prevalence of either in the piece to be played: but in our instrument, from its very construction, this inconvenience is avoided. As to matters of convenience, the harmonica is exceedingly apt to be out of order; the glasses frequently break, plainly on account of the great strain upon them where they join the spindle, and are thus with much difficulty renewed; whereas with us the loss of a glass is nothing. Add to all this, that the harmonica, in point of original expense, is about five times as high as the other: although I apprehend it possesses no one advantage, except that the performer may sit at it; whereas with our instrument it is convenient, if not necessary, to stand; but he must be a lazy musician that gives himself much concern about that: And if he will sit at our instrument, he may, though at the expense of much ease in point of execution.

"Let us now consider some objections that have been made to this instrument. One is, that necessity of standing, in order to do anything capital upon it. But is not that the case in all instruments, except where the performer sits of necessity? Did ever anyone see Giardini or Fisher play a solo sitting? But for the satisfaction of these torpid gentlemen, I can faithfully assure them, I knew a lady who performed on this instrument perfectly well, though she had lost the use of both her legs. A more serious and important objection lies both to this and the harmonica, viz. the want of a shake. How this is supplied upon the harmonica, I cannot say, as I never saw it even attempted: but on our instrument, although a very perfect shake can scarcely be produced, something so like it may be done as will fairly excuse the want; and that is, by whirling the two stands round the note concerned with the shake with the utmost velocity, beginning the lower note a little sooner than the other. By this means, except in very large glasses where the vibrations are too distant in time, such an intermixture of the two sounds is produced, as extremely well imitates a fine shake, and the dexterous performer will make the best in a turned shake with a spare finger. This operation requires some dexterity; HAR

Harmony. The sense which the Greeks gave to this word in their music, is so much less easy to be determined, because, the word itself being originally a substantive proper, it has no radical words by which we might analyse it, to discover its etymology. In the ancient treatises which remain to us, harmony appears to be that department whose object is the agreeable succession of sounds, merely considered as high or low; in opposition to the two others called rhythmica and metrica, which have their principle in time and measure. This leaves our ideas concerning that aptitude of sound vague and undetermined; nor can we fix them without studying for that purpose all the rules of the art; and even after we have done so, it will be very difficult to distinguish harmony from melody, unless we add to the last the ideas of rhythmus and measure; without which, in reality, no melody can have a distinguishing character: whereas harmony is characterised by its own nature, independent of all other quantities except the chords or intervals which compose it.

It appears by a passage of Nicomachus, and by others, that they likewise gave the name of harmony to the chord of an octave, and to concerts of voices and instruments, which performed in the distance of an octave one from the other, and which is more commonly called antiphone.

Harmony, according to the moderns, is a succession of chords agreeable to the laws of modulation. For a long time this harmony had no other principle, but such rules as were almost arbitrary, or solely founded on the approbation of a practised ear, which decided concerning the agreeable or disagreeable succession of chords, and whose determinations were at last reduced to calculation. But Father Mersenne and M. Sauveur having found that every sound, however simple in appearance, was always accompanied with other sounds less sensible, which constitute with itself a perfect chord-major; with this experiment M. Rameau set out, and upon it formed the basis of his harmonic system, which he has extended to a great many volumes, and which at last M. D'Alembert has taken the trouble of explaining to the public.

Signior Tartini, taking his route from an experiment which is newer and more delicate, yet no less certain, has reached conclusions similar enough to those of Rameau, by pursuing a path whose direction seems quite opposite. According to M. Rameau, the treble is generated by the bass; Signior Tartini makes the bass result from the treble. One deduces harmony from melody, and the other supposes quite the contrary. To determine from which of the two schools the best performances are likely to proceed, no more is necessary than to investigate the end of the composer, and discover whether the air is made for the accompaniments, or the accompaniments for the air. At the word System in Rousseau's Musical Dictionary, is given a delineation of that published by Signior Tartini. Here he continues to speak of M. Rameau, whom he has followed through this whole work, as the artist of greatest authority in the country where he writes.

He thinks himself obliged, however, to declare, That this system, however ingenious it may be, is far from being founded upon nature; an affirmation which he incessantly repeats: "That it is only established upon analogies and congruities, which a man of invention may overturn to-morrow, by substituting others more natural: that, in short, of the experiments from whence he deduces it, one is detected fallacies, and the other will not yield him the consequences which he would extort from it. In reality, when this author took it in his head to dignify with the title of demonstration the reasoning upon which he established his theory, every one turned the arrogant pretence into ridicule. The Academy of Sciences loudly disapproved a title so ill founded, and so gratuitously assumed; and M. Estive, of the Royal Society, at Montpelier, has shown him, that even to begin with this proposition, That according to the law of nature, sounds are represented by their octaves, and that the octaves may be substituted for them, there was not any one thing demonstrated, or even firmly established, in his pretended demonstration." He returns to his system.

"The mechanical principle of resonance presents us, with nothing but independent and solitary chords; it neither prescribes nor establishes their succession. Yet a regular succession is necessary; a dictionary of selected words is not an oration, nor a collection of legitimate chords a piece of music: there must be a meaning, there must be connections in music as well as in language: it is necessary that what has preceded should transmit something of its nature to what is subsequent, so that all the parts conjoined may form a whole, and be stamped with the genuine character of unity.

"Now, the complex sensation which results from a perfect chord must be resolved into the simple sensation of each particular sound which composes it, and into the sensation of each particular interval which forms it, ascertained by comparison one with another. Beyond this there is nothing sensible in any chord; from whence it follows, that it is only by the relation between sounds, and by the analogy between intervals, that the connexion now in question can be established; and this is the genuine, the only source, from whence flow all the laws of harmony and modulation. If, then, the whole of harmony were only formed by a succession of perfect chords-major, it would be sufficient to proceed by intervals similar to those which compose such a chord; for then some one or more sounds of the preceding chord being necessarily protracted in that which is subsequent, all the chords would be found sufficiently connected; and the harmony would, at least in this sense, be one.

"But besides that these successions must exclude all melody by excluding the diatonic series which forms its foundation," Harmony, foundation, it would not arrive at the real end of the art; because, as music is a system of meanings like a discourse, it ought, like a discourse, to have its periods, its phrases, its suspensions, its cadences, its punctuation of every kind; and because the uniformity of a harmonical procedure implies nothing of all this, diatonic procedures require that major and minor chords should be intermixed; and the necessity of dissonances has been felt in order to distinguish the phrases, and render the cadences sensible. Now, a connected series of perfect chords-major can neither be productive of perfect chords-minor nor of dissonances, nor can sensibly mark any musical phrase, and the punctuation must there be found entirely defective.

"M. Rameau being absolutely determined, in his system, to deduce from nature all the harmony practised among us, had recourse, for this effect, to another experiment of his own invention, of which I have formerly spoken, and which by a different arrangement is taken from the first. He pretended, that any simple sound whatever afforded in it multiplies a perfect minor or flat chord, of which it was the dominant or fifth, as it furnished a perfect chord-major by the vibration of its aliquot parts, of which it is the topic or fundamental sound. He has affirmed as a certain fact, that a vocal string caused two others lower than itself to vibrate through their whole extent, yet without making them produce any sound, one to its twelfth major and the other to its seventeenth; and from this joined to the former fact, he has very ingeniously deduced not only the application of the minor mode and of dissonances in harmony, but the rules of harmonic phrases and of all modulation, such as they are found at the words Chord, Accompaniment, Fundamental Bass, Cadence, Dissonance, Modulation.

"But first (continues Rousseau), the experiment is false. It is discovered, that the strings tuned beneath the fundamental sound do not entirely vibrate when this fundamental sound is given; but that they are divided in such a manner as to return its unison alone, which of consequence can have no harmonics below. It is moreover discovered, that the property of strings in dividing themselves, is not peculiar to those which are tuned by a twelfth and seventeenth below the principal sound; but that oscillations are likewise produced in the lower strings by all its multiples. Whence it follows, that, the intervals of the twelfth and seventeenth below not being singular phenomena of their kind, nothing can be concluded in favour of the perfect minor chord which they represent.

"Though the truth of this experiment were granted, even this would by no means remove the difficulty. If, as M. Rameau alleges, all harmony is derived from the resonance of sonorous bodies, it cannot then be derived only from the vibrations of such bodies as do not resound. In reality, it is an extraordinary theory, to deduce from bodies that do not resound the principles of harmony; and it is a position in natural philosophy no less strange, that a sonorous body should vibrate without resounding, as if sound itself were anything else but the air impelled by these vibrations. Moreover, sonorous bodies do not only produce, besides the principal sound, the other tones which with itself compose a perfect chord; but an infinite number of other sounds, formed by all the aliquot parts of the bodies in vibration, which do not enter into that perfect harmony. Why then should the former sounds produce consonances, and why should the latter not produce them, since all of them equally result from nature?

"Every sound exhibits a chord truly perfect, since it is composed of all its harmonics, and since it is by them that it becomes a sound. Yet these harmonics are not heard, and nothing is distinguished but a simple sound, unless it be exceedingly strong; whence it follows, that the only good harmony is an unison; and that, as soon as the consonances can be distinguished, the natural proportion being altered, the harmony has lost its purity.

"That alteration is in this case produced two different ways. First, by causing certain harmonics to resound, and not the others, the proportions of force which ought to prevail in all of them is altered, for producing the sensation of a single sound; whence the unity of nature is destroyed. By doubling these harmonics, an effect is exhibited similar to that which would be produced by suppressing all the others; for in that case we cannot doubt, but that, along with the generating sound, the tones of the other harmonics which were permitted to sound would be heard: whereas, in leaving all of them to their natural operations, they destroy one another, and conspire together in forming and strengthening the simple sensation of the principal sound. It is the same effect which the full sound of a stop in the organ produces, when, by successively removing the stopper or register, the third and fifth are permitted to sound with the principal; for then that fifth and third, which remained absorbed in the other sounds, are separately and disagreeably distinguished by the ear.

"Moreover, the harmonics which we cause to sound have other harmonics pertaining to themselves, which cannot be such to the fundamental sound. It is by these additional harmonics that the sounds which produce them are distinguished with a more sensible degree of harshness; and these very harmonics which thus render the chord perceptible, do not enter into its harmony. This is the reason why the most perfect chords are naturally displeasing to ears whose relish for harmony is not sufficiently formed; and I have no hesitation, in thinking, that even the octave itself might be displeasing, if the mixture of male and female voices did not inure us to that interval from our infancy.

"With dissonance it is still worse, because, not only the harmonics of the sound by which the discord is produced, but even the sound itself, is excluded from the natural harmony of the fundamental; which is the cause why discord is always distinguished amongst all the other sounds in a manner shocking to the sense.

"Every key of an organ, with the stop fully opened, gives a perfect chord with its third major, which are not distinguished from the fundamental sound, if the hearer is not extremely attentive, and if he does not sound the whole stop in succession; but these harmonic sounds are never observed in the fundamental, but on account of the prodigious noise, and by such a situation of the registers as may cause the pipes which produce the fundamental sound to conceal by their force the other sounds which produce these harmonics. Now, no person observes, nor can observe, this continual proportion in a concert; since, by the manner of inverting the harmony, its greatest force must in every instant be transferred from one part to another; which is not practicable, and would destroy the whole melody.

"When we play upon the organ, every key in the bass causes to resound the perfect chord-major; but because that bass is not always fundamental, and because the music is often modulated in a perfect minor chord, this perfect chord-major is rarely struck with the right hand; so that we hear the third minor with the major, the fifth with the triton, the seventh redundant with the octave, and a thousand other cacophonies, which, however, do not much disgust our ears, because habit renders them tractable: but it is not to be imagined that an ear naturally just would prove so patient of discords, when first exposed to the test of this harmony.

"M. Rameau pretends, that trebles composed with a certain degree of simplicity naturally suggest their own basses; and that any man having a just, though unpractised ear, would spontaneously sing that bass. This is the prejudice of a musician, refuted by universal experience. Not only would he, who has never heard either bass or harmony, be of himself incapable of finding either the bass or the harmony of M. Rameau, but they would be displeasing to him if he heard them, and he would greatly prefer the simple unison.

"When we consider, that, of all the people upon earth, who have all of them some kind of music and melody, the Europeans are the only people who have a harmony consisting of chords, and who are pleased with this mixture of sounds: when we consider that the world has endured for so many ages, whilst, of all the nations which cultivated the fine arts, not one has found out this harmony; that not one animal, not one bird, not one being in nature, produces any other chord but the unison, nor any other music but melody; that the eastern languages, so sonorous, so musical; that the ears of the Greeks, so delicate, so sensible, practised and cultivated with so much art, have never conducted this people, luxurious and enamoured of pleasure as they were, towards this harmony which we imagined so natural; that without it their music produced such astonishing effects; that with it ours is so impotent; that, in short, it was reserved for the people of the north, whose gross and callous organs of sensation are more affected with the noise and clamour of voices, than with the sweetness of accents and the melody of inflections, to make this grand discovery, and to vend it as the essential principle upon which all the rules of the art were founded; when, in short, attention is paid to all these observations, it is very difficult not to suspect that all our harmony is nothing but a Gothic and barbarous invention, which would never have entered into our minds, had we been truly sensible to the genuine beauties of art, and of that music which is unquestionably natural.

"M. Rameau asserts, however, that harmony is the source of the most powerful charms in music. But this notion is contradictory both to reason and to matter of fact. To fact it is contradictory, because, since the invention of counter-point, all the wonderful effects of music have ceased, and it has lost its whole force and energy. To which may be added, that such beauties as purely result from harmony are only perceived by the learned; that they affect none with transport but such as are deeply conversant in the art; whereas the real beauties of music, resulting from nature, ought to be, and certainly are, equally obvious to the adept and the novice. To reason it is contradictory; since harmony affords us no principle of imitation by which music, in forming images and expressing sentiments, can rise above its native excellence till it becomes in some measure dramatic or imitative, which is the highest pitch of elevation and energy to which the art can aspire; since all the pleasures which we can receive from the mere mechanical influence of sounds are extremely limited, and have very little power over the human heart."

Thus far we have heard M. Rousseau, in his observations on harmony, with patience; and we readily grant, that the system of harmony by M. Rameau is neither demonstrated, nor capable of demonstration. But it will not follow, that any man of invention can so easily and so quickly subvert those aptitudes and analogies on which the system is founded. Every hypothesis is admitted to possess a degree of probability proportioned to the number of phenomena for which it offers a satisfactory solution. The first experiment of M. Rameau is, that every sonorous body, together with its principal sound and its octave, gives likewise its twelfth and seventeenth major above; which being approximated as much as possible, even to the chords immediately represented by them, return to the third, fifth, and octave, or, in other words, produce perfect harmony. This is what nature, when solicited, spontaneously gives; this is what the human ear, unprepared and uncultivated, imbibes with ineffable avidity and pleasure. Could anything which claims a right to our attention and acceptance from nature, be impressed with more genuine or more legible signatures of her sanction than this? We do not contend for the truth of M. Rameau's second experiment. Nor is it necessary we should. The first, expanded and carried into all its consequences, resolves the phenomena of harmony in a manner sufficient to establish its authenticity and influence. The difficulties for which it affords no solution are too few and too trivial either to merit the regard of an artist, or a philosopher, as M. D'Alembert in his elements has clearly shown. The facts with which M. Rousseau confronts this principle, the armies of multiplied harmonics generated in infinitum, which he draws up in formidable array against it, only show the thin partitions which sometimes may divide philosophy from whim. For, as bodies are infinitely divisible, according to the philosophy now established, or as, according to every philosophy, they must be indefinitely divisible, each infinitesimal of any given mass, which are only harmonics to other principal sounds, must have fundamental tones and harmonics peculiar to themselves: so that, if the reasoning of Rousseau has any force against M. Rameau's experiment, the ear must be continually distracted with a chaos of inappretable harmonics, and melody itself must be lost in the confusion. But the truth of the matter is, that by the wise institution of nature, there is such a conformity established between our senses and their proper objects, as must prevent all these disagreeable Harmony. Rousseau and his opponent are agreed in this, that the harmonies conspire to form one predominant sound; and are not to be detected but by the nicest organs, applied with the deepest attention. It is equally obvious, that, in an artificial harmony, by a proper management of this wise precaution of nature, dissonances themselves may be either entirely concealed or considerably softened. So that, since by nature sonorous bodies in actual vibration are predisposed to exhibit perfect harmony; and since the human ear is, by the same wise regulation, fabricated in such a manner as to perceive it; the harmonical chaos of M. Rousseau may be left to operate on his own brain, where it will probably meet with the warmest reception it can expect to find. Nor does it avail him to pretend, that before the harmonics can be distinguished, sonorous bodies must be impelled with a force which alters the chords, and destroys the purity of the harmony; for this position is equally false both in theory and practice;—in theory, because an impulse, however forcible, must proportionally operate on all the parts of any sonorous body, so far as it extends; in practice, because the human ear actually perceives the harmony to be pure. What effects his various manoeuvres upon the organ may have, we leave to such as have leisure and curiosity enough to try the experiments; but it is apprehended, that when tried, their results will leave the system of Rameau, particularly as remodelled by D'Alembert, in its full force.

Of all the whims and paradoxes maintained by this philosopher, none is more extravagant than his assertion, that every chord, except the simple unison, is displeasing to the human ear; nay, that we are only reconciled to octaves themselves by being inured to hear them from our infancy. Strange, that nature should have fixed this invariable proportion between male and female voices, whilst at the same time she inspired the hearers with such violent prepossessions against it as were invincible but by long and confirmed habit! The translator of D'Alembert's Elements, as given under the article Music in this Dictionary, has been at peculiar pains to investigate his earliest recollections upon this subject; and has had such opportunities, both of attending to his original perceptions, and of recognising the fidelity of his memory, as are not common. He can remember, even from a period of early childhood, to have been pleased with the simplest kinds of artificial harmony; to have distinguished the harmonics of sonorous bodies with delight; and to have been struck with horror at the sound of such bodies as, by their structure, or by the cohesion of their parts, exhibited these harmonics false. This is the chief, if not the only cause, of the tremendous and disagreeable sensation which we feel from the sound of the Chinese ghong. The same horrible cacophony is frequently, in some degree, produced by a drum unequally braced: from this sound the translator often remembers to have started and screamed, when carried through the streets of the town in which he was born in the arms of his nursery-maid; and as he is conscious, that the acoustic organs of many are as exquisite as his own, he cannot doubt but they may have had the same sensations, though perhaps they do not recollect the facts. So early and so nicely may the sensations of harmony and discord be distinguished. But after all, it seems that harmony is no more than a modern invention, and even at this late period only known to the Europeans. We should, however, be glad to know, from what oracle our philosopher learned that harmony was not known to antiquity. From what remains of their works, no proof of his position can be derived; and we have at least mentioned one probability against it in our notes to the Preliminary Discourse to the article Music, (see note B). But though Rousseau's mighty objections were granted, that harmony can only be endured by such ears as are habitually formed and cultivated; that the period of its prevalence has been short, and the extent of its empire limited to Europe; still his conclusion, that it is a Gothic and barbarous invention, is not fairly deducible even from these premises. Must we affirm, that epic poetry has no foundation in nature, because, during the long interval which happened from the beginning of the world to the destruction of Troy, no epic poem seems to have appeared? Or because a natural and mellifluous versification is less relished by an unpolished taste, than the uncouth rhimes of a common ballad, shall we infer, that the power of numbers is merely supposititious and arbitrary? On the contrary, we will venture to affirm, that though harmony cannot, as Rameau supposes, be mathematically demonstrated from the nature and vibrations of sonorous bodies; yet the idea of its constituent parts, and of their coalescence, is no less established, no less precise and definite, than any mode or property of space or quantity to be investigated by geometrical researches or algebraical calculations. It is certain, that the mimetic or imitative power of music chiefly consists in melody; but from this truth, however evident, it cannot be fairly deduced that harmony is absolutely unsusceptible of imitation. Perhaps every musical sound, even to the most simple, and all modulations of sound, are more or less remotely connected with some sentiment or passion of the human heart. We know, that there are instinctive expressions of pain or pleasure in their various modes and degrees, which, when uttered by any sensitive, and perceived by any conscious being, excite in the mind of the percipient a feeling sympathetic with that by which they are prompted. We likewise know from experience, that all artificial sounds modulated in the same manner, have similar, though not equal, effects. We have seen that, in order to render harmony compatible with itself, the melody of each part must be congenial; and, for that reason, one kindred melody results from the whole. So far, therefore, as any composer has it in his power to render the general melody homogeneous, so far the imitation may be preserved, and even heightened: for such objects as are majestic and august, or the feelings which they excite, are more aptly expressed by a composition of kindred sounds, than by any simple tone whatever. Those who suppose the mimetic powers of music to be consummated in the imitation of mere unmeaning sounds or degrees of motion, must entertain limited and unworthy ideas of its province. It is naturally a representative almost of every sentiment or affection of the soul; and, when this end is gained, the art must have reached its highest perfection, and produced its noblest effects. But these effects, however sensible among the ancients, may in us be superseded by other causes which remain yet unexplored. Theatrical performances are likewise, by them, said to have produced the most wonderful effects; yet these we do not recognise amongst ourselves, though we have dramatic entertainments perhaps not inferior to theirs.

Rousseau proceeds to tell us, that among the ancients the enharmonic species of music was sometimes called harmony.

Direct Harmony, is that in which the bass is fundamental, and in which the upper parts preserve among themselves, and with that fundamental bass, the natural and original order which ought to subsist in each of the chords that compose this harmony.

Inverted Harmony, is that in which the fundamental or generating sound is placed in some of the upper parts, and when some other sound of the chord is transferred to the bass beneath the others.