eeding 1000
vibrations a second,--the ear is by no means limited to that range in
hearing. The chirrup of a sparrow, the shrill sound of a cricket, and
the piercing shrieks of a locomotive are due to far greater
frequencies, the number of vibrations at times equaling 38,000 per
second or more.

264. The Musical Scale. When we talk, the pitch of the voice changes
constantly and adds variety and beauty to conversation; a speaker
whose tone, or pitch, remains too constant is monotonous and dull, no
matter how brilliant his thoughts may be.

While the pitch of the voice changes constantly, the changes are
normally gradual and slight, and the different tones merge into each
other imperceptibly. In music, however, there is a well-defined
interval between even consecutive notes; for example, in the musical
scale, middle C (do) with 256 vibrations is followed by D (re) with
288 vibrations, and the interval between these notes is sharp and well
marked, even to an untrained ear. The interval between two notes is
defined as the ratio of the frequencies; hence, the interval between C
and D (do and re) is 288/256, or 9/8. Referring to Section 263, we see
that the interval between C and E is 320/256, or 5/4, and the interval
between C and C' is 512/256, or 2; the interval between any note and
its octave is 2.

The successive notes in one octave of the musical scale are related as
follows:--

|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,