the sound of the string in such case is the octave to its fundamental. E. g.

H

Fig. 49.

L

K

1092. The next mode is that in which a string vibrates triply in equal parts simultaneously, having two nodes, M M, and the sound of the string in this case is the fifth to the fundamental. E. g.

Fig. 50.

M

M

H

K

1093. In like manner, a string vibrating in five equal parts has four nodes, N N N N, and yields the sound of the third to its fundamental, e. g. &c.

And the three latter, or three former sounds, each constitute the common chord, or notes CEG of the Diatonic scale, being the primary triad of the

musician.

1094. Every perfect sound, note, or tone, is a system of these three primaries, the third, the fifth, and the octave to the fundamental, in the manner

of colours; and as the secondary colours are mediates or compounds of the primaries, so are the other notes of the musical octave mediates or concurrents of the common chord or primary triad of the musician, as illustrated in the above experiment, and the preceding analogous scale of sounds and colours; ascending and descending within limits which are determined only to observation by the perceptive powers of the two senses of vision and hearing. The same may be asserted of all other possible scales and modes of harmonic science.

1095. In such manner is produced and constituted, by derivation or composition, all that infinite variety of sounds which nature and art present to the ear, whether in the melodies and harmonies of natural and artificial music-the numbers, rhythms, and cadences of poetry-the articulations of languages-the cries of animals-in noises or slurred sounds, as distinguished from notes or musical intervals, or in other broken sounds, however produced; equally also in the hum of an insect and the thunder of the storm, and all various as the hues and shades which distinguish visual objects. So much for sound in general, whether it be harmonious, significant, or promiscuous.

1096. Notes or sounds, like colours, have by analogy the three dimensions of figures, length, height, and depth. The measure of length in musical sounds is time, height is acuteness, and

depth is gravity; to the two last of which belong tone and tune.

1097. The ratio of division in both time and tone is also geometrical, the length of notes being as 1, 2, 4, 8, &c., or, conversely, 1,,,, &c. And, as intervals of height or depth, they are whole, half, or quarter tones: to express which relations of sound, the musician employs his peculiar well-known characters and notation, wherein there is much indication of triple relation.

1098. In regard to the length of musical sounds, simple sounds are significantly denoted by a point, thus,, which is called a crotchet, to which a tail is generally appended downward or upward, thus,

If the note be longer than a crotchet it is

called a minim, and marked thus,

ثم

and is

equivalent to two crotchets. If it be still longer, it is called a semibreve; is equal to four crotchets, and is marked thus, o, advancing in duplicate ratio.

1099. On the other hand, if the note be shorter than a crotchet, it is distinguished by a hook, thus, and called a quaver, and is equal to of a crotchet; if it be still shorter, it is double-hooked, thus, and is called a semi

quaver, equal to of a crotchet; and if a note be yet shorter, it is called a demisemiquaver, is treble

hooked, thus,, and is equal to of a crotchet :

the whole being in subduplicate ratio.

1100. Silence, or pause, is measured, in like manner, by equivalent rests of the same denomination, thus distinguished as longer or shorter than the crotchet: -- Semibreve,

- Crotchet; quaver, &c.

L

Quaver,

Semiquaver,

Minim, Demisemi

1101. Besides time, as belonging to note and rest, there is compound time, or motion, as applied to musical composition, denoted by the terms Adagio, Largo, and Allegro, which are equally referred to common and triple time.

1102. Height and depth of musical sounds, or acuteness and gravity of note or tone, are denoted by the place or position of their characters as high or low, with respect to certain parallel lines called a Stave, formed thus: And all the variety

of note or tone, as determined by nature, and derived from the primary musical triad, is comprehended in the diatonic octave, named after the first letters of the alphabet, A BCDEFG, and are characterized and posited upon the stave in the scale or gamut of the musician thus:

GA B C D E F G,

&c.

1103. As this scale, or series of note succeeding note, may be continued upward or downward simply by the repetition of the same relations of sound, musicians have extended this scale by octave above octave, and stave above stave, distinguishing their position, or relation of acuteness and gravity, by characters called Claves, Clefs, or Clifs, formed as follow:

the first of which is called the G or treble clef, or soprano; the second, the C tenor, or mean; and the last the F, or bass clef.

1104. The relations of these in the principal scale of the musician may be represented in the following figure, as ascending and descending from the mean:

or in a single series, as in the analogical scale of sounds and colours in the preceding chapter.

1105. It is worthy of remark, that these relations of height and depth, or acuteness and gravity,