The Musical Scale

Sound:
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 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.

FIG. - A song as sung by three voices of different pitch.