_Mrs. B._ Certainly. The quicker a sonorous body vibrates, the more acute, or sharp, is the sound produced; and the slower the vibrations, the more grave will be the note. _Caroline._ But if I strike any one note of the piano-forte, repeatedly, whether quickly or slowly, it always gives the same tone. _Mrs. B._ Because the vibrations of the same string, at the same degree of tension, are always of a similar duration. The quickness, or slowness of the vibrations, relate to the single tones, not to the various sounds which they may compose, by succeeding each other. Striking the note in quick succession, produces a more frequent repetition of the tone, but does not increase the velocity of the vibrations of the string. The duration of the vibrations of strings, or wires, depends upon their length, their thickness, or weight, and their degree of tension: thus, you find, the low bass notes are produced by long, thick, loose strings; and the high treble notes by short, small, and tight strings. _Caroline._ Then, the different length, and size, of the strings of musical instruments, serve to vary the duration of the vibrations, and consequently, the acuteness or gravity of the notes? _Mrs. B._ Yes. Among the variety of tones, there are some which, sounded together, please the ear, producing what we call harmony, or concord. This arises from the agreement of the vibrations of the two sonorous bodies; so that some of the vibrations of each, strike upon the ear at the same time. Thus, if the vibrations of two strings are performed in equal times, the same tone is produced by both, and they are said to be in unison. _Emily._ Now, then, I understand why, when I tune my harp, in unison with the piano-forte, I draw the strings tighter, if it is too low, or loosen them, if it is too high a pitch: it is in order to bring them to vibrate, in equal times, with the strings of the piano-forte. _Mrs. B._ But concord, you know, is not confined to unison; for two different tones, harmonize in a variety of cases. When the vibrations of one string (or other sonorous body) vibrate in double the time of another, the second vibration of the latter, will strike upon the ear, at the same instant, as the first vibration of the former; and this is the concord of an octave. If the vibrations of two strings are as two to three, the second vibration of the first, corresponds with the third vibration of the latter, producing the harmony called, a fifth. _Caroline._ So, then, when I strike the key-note with its fifth, I hear every second vibration of one, and every third of the other, at the same time? _Mrs. B._ Yes; and the key-note, struck with the fourth, is likewise a concord, because the vibrations, are as three to four. The vibrations of a major third, with the key-note, are as four to five; and those of a minor third, as five to six.