pitch. If the speed of the disk is increased so that
the puffs become more frequent, the pitch of the resulting note rises;
and at very high speeds the notes produced become so shrill and
piercing as to be disagreeable to the ear. If the speed of the disk is
lessened, the pitch falls correspondingly; and if the speed again
becomes so low that less than 16 puffs are formed per second, the
sustained sound disappears and a series of intermittent noises is
produced.

263. The Pitch of a Note. By means of an apparatus called the siren,
it is possible to calculate the number of vibrations producing any
given musical note, such, for example, as middle C on the piano. If
air is forced continuously against the disk as it rotates, a series of
puffs will be heard (Fig. 177).

If the disk turns fast enough, the puffs blend into a musical sound,
whose pitch rises higher and higher as the disk moves faster and
faster, and produces more and more puffs each second.

The instrument is so constructed that clockwork at the top registers
the number of revolutions made by the disk in one second. The number
of holes in the disk multiplied by the number of revolutions a second
gives the number of puffs of air produced in one second. If we wish to
find the number of vibrations which correspond to middle C on the
piano, we increase the speed of the disk until the note given forth by
the siren agrees with middle C as sounded on the piano, as nearly as
the ear can judge; we then calculate the number of puffs of air which
took place each second at that particular speed of the disk. In this
way we find that middle C is due to about 256 vibrations per second;
that is, a piano string must vibrate 256 times per second in order for
the resultant note to be of pitch middle C. In a similar manner we
determine the following frequencies:--

|do |re |mi |fa |sol |la |si |do |
|C |D |E |F |G |A |B |C' |
|256 |288 |320 |341 |384 |427 |480 |512 |

[Illustration: FIG. 177.--A siren.]

The pitch of pianos, from the lowest bass note to the very highest
treble, varies from 27 to about 3500 vibrations per second. No human
voice, however, has so great a range of tone; the highest soprano
notes of women correspond to but 1000 vibrations a second, and the
deepest bass of men falls but to 80 vibrations a second.

While the human voice is limited in its production of sound,--rarely
falling below 80 vibrations a second and rarely exc