sounds of nature, readily detects the relations of minuter divisions, and discovers the more pleasing degrees which occur between any two of them. The subdivisions of the octave, according to their greater or less minuteness, constitute the diatonic, or chromatic, or enharmonic scale: the diatonic being the system of eight tones and semitones, as they constantly occur in nature; the chromatic, the division of the same series into semitones; and the enharmonic, a very unusual further division of the semitone. The diatonic scale is also arranged in two ways, as the major and minor modes. They are both equally natural, and, although differing in several essential effects, are fundamentally to be distinguished only by the place of the semitones.

The relation of notes to each other in the scale is strictly mathematical. In the major mode, the number of vibrations necessary to produce the respective notes are to each other as 1, 8, 4, 3, 3, 3, 5, 2; and the length of the string producing them 1, §, 3, 4, 3,

9 5 4

5 15

4

2 3

8

In other words, suppose the number of vibrations giving the fundamental note C, to be represented by 1, then 1 will be the number giving the second note, D, 11 the number giving E, etc., and the string, which in its whole length sounds C, in order to make D must be diminished by, to make E, by, and so on. Accordingly, if thirty-two strokes in a second produce the fundamental note, then thirty-two and one-eighth of thirtytwo, that is, thirty-six strokes in a second, will produce D, thirty-two and one-quarter of thirty-two, that is

32+8=40, will produce E, and so, for the other notes, 32+103=423 will give F, 32+16=48 will give G, 32+211-531 will give A, 32+28-60 will give B, and 32+32=64 the octave.

Again, if these notes are arranged in groups, occupying precisely similar times, and these groups or measures into strains, holding an exact arithmetical correspondence to each other, to the expression of some idea of melody, we have the foundation of musical science.

Artificial as this may seem, it is as truly natural as the law whereby we see, through an equal medium, only in straight lines. The principles of music have grown up from the unchanging laws of the material world, to which the human ear has been created to correspond. Its mathematical basis extends to every essential element of the art. The primary charm wielded by sounds over the human spirit is the precise division of time by waves of air, to which harmony gives additional richness and power, and varying degrees of intensity give expression; while the field of the art is greatly enlarged by the endless diversity of quality in voices and instruments, a particular which no research has, as yet, satisfactorily explained.

But the relations of human life, and association with its changing phases in joy and sorrow, convey to the same sounds an auxiliary power, often transcending that which they possess in their own right. And when the results of faithful science are made fully subservient

to the demands of human emotion, the highest effects of musical art are attained.

Why it is, that "there is in souls a sympathy with sounds," it may be impossible to determine; but the fact is most obvious that music, though more subtile and evanescent than any of its sister arts, is more promptly, more profoundly, and more generally felt. In all ages its power over the feelings has been proved by triumphs which need to be repeated to secure credence. The warm imagination of antiquity, and the cool arithmetic of modern times, have equally been taken captive by it. The mythological wonders of Orpheus and Amphion might almost be taken for figurative prophecies of the real wonders wrought by the violin of Paganini, and the voice of Jenny Lind.

In spite of that law whereby human feelings revolt from the abstract, music addresses them successfully without personification. When the painter has delineated his idea on the canvas, he has given it a body and expression once for all: so the polished marble retains and will express, as long as it endures, the thought with which the sculptor has imbued it; but music refuses to assume any material body. Its written signs are only a system of marks to guide one artist in reproducing what another has conceivedresembling those of literature, but differing in as far as the written word does not need to be uttered in order to convey the writer's thought, whereas musical notation is in itself no expression of the composer's

ideas at all. Writing can answer the end of its being without the aid of oral reading, but music has no existence except in sound. To read the notes silently, is only to learn what they will be when performed. Music reveals herself only in the symmetrical relations of evanescent sound-not of continuous sound which might be made permanent; but of sounds as they pass away and give place to others, and in the measured lapse of time during which they begin and end. This immateriality constitutes a distinctive feature of the art, and, if a disadvantage in one point of view, is a safeguard in another.

All who address the public are liable to be misunderstood; but the musical composer is subject to the additional inconvenience of being misrepresented. For he has to utter himself, for the most part, through the instrumentality of others, and if his performers are either ill prepared or ill natured, his idea may not only be ruined, but something entirely at variance therewith expressed. And when we consider the defects of voices, and the limited power of instruments, and the changing effects of atmosphere upon wood, and cord, and metal, and the thousand accidents operating upon the human mind and body, and thereby upon the style of the singer, we shall find abundant reason to believe that many ideas of the greatest masters seldom find any adequate expression.

On the other hand, advantages of incalculable value

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flow from this peculiarity, tending to render music one of the most effective coadjutors of religion. Of these the most noticeable is its perfect freedom from all inherent taint of moral wrong. A musical tone is as perfectly free from stain as the falling flake of snow, and no combination of tones, unassociated with other things, can be made to convey a vicious idea. You may unite them to words expressive of vice, or with improper gestures, looks, or signs, and thereby pollute your own associations with the music; but these are external defilements entirely foreign to the concord of sweet sounds. In itself considered, music has no congeniality with any form of vice, although often employed to conceal the monster's deformity. All beauty is essentially holy and can be polluted only externally by contact with meaner things; but on account of its immateriality, music is less liable to permanent contamination than the other arts. If a beautiful air is sometimes degraded by being connected with a vulgar song, the evil exists in that contiguity; to all who never heard the song, the music is as pure as if it had been composed for the harp of an angel. If those who have been accustomed to hear or to sing it with its vicious associations still think of it as something morally wrong, the fault is entirely in their own minds. I do not say that for them it will ever be a proper vehicle of pure thought; nor do I mean to say that every tune is capable of expressing just the same kind of holy