|Key of C          |C   |D   |E   |F   |G   |A    |B   |C’  |
|No. of vibrations |    |    |    |    |    |     |    |    |
|per sec.          |256 |288 |320 |341 |384 |427  |480 |512 |
|Interval          |9/8 |5/4 |4/3 |3/2 |5/3 |15/8 |2   |    |

The intervals of F and A are not strictly 4/3 and 5/3, but are nearly so; if F made 341.3 vibrations per second instead of 341; and if A made 426.6 instead of 427, then the intervals would be exactly 4/3 and 5/3.  Since the real difference is so slight, we can assume the simpler ratios without appreciable error.

Any eight notes whose frequencies are in the ratio of 9/8, 5/4, etc., will when played in succession give the familiar musical scale; for example, the deepest bass voice starts a musical scale whose notes have the frequencies 80, 90, 100, 107, 120, 133, 150, 160, but the intervals here are identical with those of a higher scale; the interval between C and D, 80 and 90, is 9/8, just as it was before when the frequencies were much greater; that is, 256 and 288.  In singing “Home, Sweet Home,” for example, a bass voice may start with a note vibrating only 132 times a second; while a tenor may start at a higher pitch, with a note vibrating 198 times per second, and a soprano would probably take a much higher range still, with an initial frequency of 528 vibrations per second.  But no matter where the voices start, the intervals are always identical.  The air as sung by the bass voice would be represented by A.  The air as sung by the tenor voice would be represented by B.  The air as sung by the soprano voice would be represented by C.

[Illustration:  FIG. 178.—­A song as sung by three voices of different pitch.]

CHAPTER XXVIII

MUSICAL INSTRUMENTS

265.  Musical instruments maybe divided into three groups according to the different ways in which their tones are produced:—­

First. The stringed instruments in which sound is produced by the vibration of stretched strings, as in the piano, violin, guitar, mandolin.

Second. The wind instruments in which sound is produced by the vibrations of definite columns of air, as in the organ, flute, cornet, trombone.

Third. The percussion instruments, in which sound is produced by the motion of stretched membranes, as in the drum, or by the motion of metal disks, as in the tambourines and cymbals.

266.  Stringed Instruments.  If the lid of a piano is opened, numerous wires are seen within; some long, some short, some coarse, some fine.  Beneath each wire is a small felt hammer connected with the keys in such a way that when a key is pressed, a string is struck by a hammer and is thrown into vibration, thereby producing a tone.

If we press the lowest key, that is, the key giving forth the lowest pitch, we see that the longest wire is struck and set into vibration; if we press the highest key, that is, the key giving the highest pitch, we see that the shortest wire is struck.  In addition, it is seen that the short wires which produce the high tones are fine, while the long wires which produce the low tones are coarse.  The shorter and finer the wire, the higher the pitch of the tone produced.  The longer and coarser the wire, the lower the pitch of the tone produced.