in anatomy, the lowest part of the intestinum rectum, called by anatomists the anus. See ANATOMY, no. 93.

in general, something that serves as a base or foundation for another.

music. A fundamental sound is that which forms the lowest note of the chord, and from whence are deduced the harmonical relations of the rest; or, which serves for a key to the tone*. The fundamental bass is that which serves for a foundation to the harmony. A fundamental chord is that whose bass is fundamental, and in which the sounds are ranged in the same order as when they are generated, according to the experiment so often repeated by M. d'Alembert, in his Preliminary Discourse and Elements of Music†. But as this order removes the parts to an extreme distance one from the other, they must be approximated by combinations or inversions; but if the bass remains the same, the chord does not for this reason cease to bear the name of fundamental. Such an example is this chord, ut mi sol, included in the interval of a fifth; whereas, in the order of its generation, ut sol mi, it includes a tenth, and even a seventeenth; since the fundamental ut is not the fifth of sol, but the octave of that fifth.

FUNDAMENTAL Bass. This part in music is, according to Rousseau, and indeed according to all authors who have proceeded upon M. Rameau's experiment, in its primary idea, that bass which is formed by the fundamental notes of every perfect chord that constitutes the harmony of the piece; so that under each chord it causes to be heard, or understood, the fundamental sound of that particular chord; that is to say, the sound from whence it is derived by the rules of harmony. From whence we may see, that the fundamental bass can have no other contexture than that of a regular and fundamental succession, without which the procedure of the upper parts would be illegitimate.

To understand this well, it is necessary to be known, that, according to the system of Rameau, which Rousseau has followed in his Dictionary, every chord, the composed of several sounds, can only have one which is its fundamental, viz., that which produces this chord, and which is its bass according to the direct and natural order. Now, the bass which prevails under all the other parts, does not always express the fundamental foundations of the chords: for amongst all the sounds which form a chord, the composer is at liberty to transfer to the bass that which he thinks preferable; regard being had to the procedure of that bass, to the beauty of the melody, and above all to the expression, as may afterwards be explained. In this case the real fundamental sound, instead of retaining its natural position, which is in the bass, will either be transferred to some of the other parts, or perhaps even entirely suppressed, and such a chord is called an inverted chord.

In reality, says Rameau, a chord inverted does not differ from the chord in its direct and natural order from which it was produced: but as these sounds form different combinations, these combinations have long been taken for fundamental chords; different names have been given them, (which may be seen at the word Accord, in Rousseau's Dictionary). These names, by the persons who bestowed them, were thought to create and sanctify their distinctions; as if a difference in names could really produce a difference in the species.

M. Rameau in his Treatise of Harmony has shown, and M. d'Alcambert in his Elements of Music has still more clearly evinced, that many of these pretendedly different chords were no more than inversions of one single chord. Thus the chord of the sixth is no more than the perfect chord of the third transferred to the bass; by adding a fifth, we shall have the chord of the fifth and fourth. Here there are three combinations of a chord, which only consists of three sounds; those which contain four sounds are susceptible of four combinations, since each of these sounds may be transferred to the bass. But in adding beneath this another bass which, under all the combinations of one and the same chord, always presents the fundamental sound; it is evident, that consonant chords are reduced to the number three, and the number of dissonant chords to four. Add to this all the chords by supposition, which may likewise be reduced to the same fundamentals, and you will find harmony brought to a degree of simplicity in which no person could ever hope to see it whilst its rules remained in that state of confusion where M. Rameau found them. It is certainly, as that author observes, an astonishing occurrence, that the practice of this art could be carried so far as it really was, without knowing its foundation; and that all the rules were so exactly found, without having discovered the principle on which they depended.

After having shown what is the fundamental bass beneath the chords, let us now speak of its procedure, and of the manner in which it connects these chords among themselves. Upon this point the precepts of the art may be reduced to the six following rules.

1. The fundamental bass ought never to sound any other notes than those of the series or tone in which the composer finds himself, or at least those of the series or tone to which he chooses to make a transition. This of all the rules for the fundamental bass is the first and most indispensible.

2. By the second, its procedure ought to be so implicitly subjected to the laws of modulation, as never to suffer the idea of a former mode to be lost till that of a subsequent one can be legitimately assumed; that is to say, that the fundamental bass ought never to be de- very properly observes, intended for the judgment, and Fundamen- not for the ear. It would at least produce a monotony extremely nauseous by frequent returns of the same chord, which they disguise and vary more agreeably by combining it in different manners upon the conti- nued basis, without reckoning upon the different inver- sions of harmony, which furnish a thousand means of adding new beauties to the music and new energy to the expression. See Chord, Inversion.

But it will be objected, If the fundamental basis is not useful in composing good music, if it must even be retrenched in practice, what good purpose, then, can it serve? We answer, that, in the first place, it serves for a rule to scholars, upon which they may learn to form a regular harmony, and to give to all the parts such a diatonic and elementary procedure as is pre- scribed them by that fundamental basis. It does more, as we have already said: it proves whether a harmony already formed be just and regular; for all harmony which cannot be subjected to the test of a fundamental basis, must according to all rules be bad. Finally, it serves for the investigation of a continued basis under a given air: though, in reality, he who cannot directly form a continued basis, will scarcely be able to form a fundamental basis, which is better; and much less still will he be able to transform that fundamental basis into a legitimate continued basis. These which follow are, however, the principal rules which M. Rameau prescribes for finding the fundamental basis of a given air.

1. To ascertain with precision the mode in which the composer begins, and those through which he passes. There are also rules for investigating the modes; but so long, so vague, so incomplete, that with respect to this, the ear may be formed long before the rules are acquired; and the dunce who should try to use them, would gain no improvement but the habit of proceeding always note by note, without even knowing where he is.

2. To try in succession under each note the princi- pal chords of the mode, beginning by those which are most analogous, and passing even to the most remote, when the composer sees himself under a necessity of doing so.

3. To consider whether the chord chosen can suit the upper part in what precedes and in what follows, by a just fundamental succession; and when this is im- practicable, to return the way he came.

4. Not to change the note of the fundamental basis till after having exhausted all the notes which are al- lowed in succession in the upper part, and which can enter into its chord; or till some syncopated note in the air may be susceptible of two or a greater number of notes in the basis, to prepare the dissonance which may be afterwards resolved according to rule.

5. To study the intertexture of the phrases; the possible succession of cadences, whether full or avoided; and above all, the pauses which for ordinary return at the end of every four, or of every two bars, so that they may always fall upon perfect and regular cadences.

6. In short, to observe all the rules formerly given for the composition of the fundamental basis.—These are the principal observations to be made for finding one under any given air; for there are sometimes fever-

The fundamental basis, which they add for no other reason than to serve as a proof of the harmony, must be retrenched in execution, and often in practice it would have a very bad effect; for it is, as M. Rameau FUN

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rad different ones which may be investigated. But, whatever may be said to the contrary, if the air has accent and character, there is only one just fundamental basis which can be adapted to it.

After having given a summary explication of the manner in which a fundamental basis should be composed, it should remain to suggest the means of transforming it into a continued basis; and this would be easy, if it were only necessary to regard the diatonic procedure and the agreeable air of this basis. But let us not imagine that the basis, which is the guide and support of the harmony, the soul, and as it were the interpreter, of the air, should be limited to rules so simple: there are others which depend upon principles more certain and more radical; fruitful, but latent principles, which have been felt by every artist of genius, without having been detected by any one. Rousseau hopes, that in his letter upon French music he intimated this principle. For those who understand him, he imagines he has said enough concerning it, and can never say enough of it for those who do not. See Rousseau's Miscellanies, Vol. II. p. 1.

He does not here mention the ingenious system by M. Serre of Geneva, nor his double fundamental basis; because the principles which, with a facility meritorious of praise, he had half detected, have afterwards been unfolded by M. Tartini, in a work of which Rousseau has given an account in his article System.