606. Speaking trumpets confine and give a limited direction to sound, independently of the mechanical effects of their reflection.

The human voice is produced by the expulsion of air from the lungs, and by the vibrations excited in that air, by a very small membrane called the glottis, in its passage through the trachia or windpipe; and by the subtle modifications of the mouth, tongue, and lips.

Singing is performed by a very delicate enlargement or contraction of the glottis, aided likewise by the mouth and tongue for articulation.

607. The natural music of birds, and the power of singing or producing agreeable notes by the human voice, led, in the course of ages, to the contrivance of stringed instruments, as the harp, lyre, &c.; and to the invention of wind-instruments, as the pipe, &c.

In stringed instruments, the air is struck by the string, and the vibrations of the air produce a corresponding sound in the ear; but, in pipes, the air is forced against the sides by the breath, and its vibrations or tones are produced by the re-action of the sides.

608. Sound is varied by the rapidity and momentum of the vibrating body; and this depends on the length, tension, and size of the string.

A short string vibrates quicker than a long one, and therefore produces the sharpest and highest tones: and a short and small pipe, from a like cause, produces sharp notes; and large pipes, grave and deep ones.

Savages discovered this; and they made, and

still make, instruments which please themselves and their wild companions; but art and science go further; they ascertain the causes of their pleasure, and direct them so as to increase it.

609. Hence, it was long since found, that if two strings of a harp were of equal lengths, they produced the same tone, or vibrated together, or in unison.

They produce the same number of vibrations exactly in the same time; their vibrations, if struck together, accord; hence, they produce the same sound to the ear.

610. It was, afterwards, found, that if one of these strings were equally divided, the vibrations became half the length of the vibrations of the whole, and the note twice as acute; but as every other vibration of the half-string corresponds with every vibration of the whole one, there is a constant unison or concordance between them: they harmonize or vibrate together for once in the long string, or twice in the short one.

Hence, there is no jarring or discord; but they are said to be in concord; and, in regard to intervening subdivisions, have been called oc

taves.

611. But as a harp, composed of strings of only two lengths, would produce little variety of sound, it was justly considered, that if other strings could be contrived, whose vibrations corresponded even with less frequency than the octave, the compass and variety would be increased without discord.

Hence, as the number of vibrations of a string are 1, while that of its octave is 2; the next best

division would be, to produce a string, which, while the original vibrated 2, the next should vibrate 3; this was done; and this note, which is two-thirds of the original, is called a fifth.

Obs.-If, then, the original string was 120 parts, the octave would be 60, and the fifths 80, or two-thirds.

612. In like manner, another string might be divided, so as to correspond with every fourth vibration of the original; and this would be of three-fourths of its length, or 90 parts of 120, and is called a fourth.

So on with others, whose vibrations accord 5 for every 4, and 6 for every 5; also 5 for every 3, and 5 for every 8, till seven melodious or according vibrations are made of the original chord.

A harp, constructed of strings, divided in this manner, produces an agreeable melody; the vibrations according and agreeing with one another at equal intervals, although the tones are dif

ferent.

613. If a string consist of 120 parts (inches, or barley-corns,) the octave will be 2 vibrations to 1, or 60 parts of 120.

The fifth, 3 vibrations to 2, or 80 parts.

The fourth, 4 vibrations to 3, or 90 parts. The major third, 5 vibrations to 4, or 96 parts. The minor third, 6 vibrations to 5, or 100 parts.

The major sixth, 10 vibrations to 6 (or 5 to 3,) or 72 parts.

And the minor sixth, 16 vibrations to 10 (or 8 to 5,) or 75 parts.

Obs. These divisions of a string, constitute the diatonic scale; the sole and simple object of which, is to

produce the greatest variety of tones with unisons of vibration, or an exact recurrence of vibrations after the nearest intervals.

614. The strings of a piano-forte, harp, or violin, are brought into accordance or successive octaves, or recurring tones, by the accuracy of the

ear.

In the harp, &c., their lengths are exactly proportioned to the scale by the maker, but as the strings vary in their tension, owing to the weather and other causes; and as they cannot all have the same precise bulk, it is necessary, from time to time, to tone them; which means nothing more, than making each perform its proper number of vibrations in relation to the other strings.

615. These seven notes, then, are the basis of all music; and, with the addition of five half tones, are the alphabet of music, and fill all the concordant intervals of one octave.

Octaves may, however, rise upon each other in successive ratios or degrees, as in the piano-forte, which has 5 and even 7 octaves; or 5 sets of natural notes as above, and 5 semi-tones, or flats and sharps to each octave.

616. For the purpose of obtaining further variety in composing tunes or melodies, these several tones may be played shorter or longer; and, in this respect, are divided as under:— 2 minums make 1 semi-breve;

2 crochets make 1 minum:

2 quavers make 1 crochet;

2 semi-quavers make 1 quaver;

2 demi-semi-quavers make 1 semi-quaver;

A a

32 demi-semi-quavers are to be played in the time of one semi-breve.

Again, in regard to the tune itself, there are also two sorts of time, slow and quick, as common time and treble time.

617. When an agreeable succession of simple notes, having a perfect beginning and ending, is played or sung, it is called a tune, an air, or melody; as a song, hymn, dance, or march, according to its several purposes.

When these notes, forming an air, are combined with corresponding notes, in different octaves, or on other instruments, and the whole is scientifically made to produce a concordant and agreeable effect, it is called Harmony.

The bass and treble of a piano-forte played at the same time with the left and right hand, constitute the most common practice of harmony.

Some of Handel's pieces have been played by 1000 instruments and voices, all sounding harmoniously together.

Obs.-The human soul may be moved in all its passions by music: and as a soother of the mind, and a source of exquisite pleasure, the practice on some instrument cannot be too strongly recommended as a branch of liberal education to children of both sexes.

XXVIII. Of Physics; or, the General Properties of Matter.

618. All existence is, what it appears to be to the powers of our senses; and is, therefore, relative, or comparative, to those powers.