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II. § 34.] MEASURES OF INTERVALS. 67
same time for the graver sound. Accordingly we have the following result:—
When two sounds differ by a single Octave, the higher sound makes exactly twice as many vibrations in any assigned time as the lower.
Next let a row of 12 holes be punched in the disc of the Syren. Taking this row with the 8-hole row, and proceeding as in the last instance, we find that the more acute sound forms a Fifth with the graver one. The numbers of discharges in any given time are here as 12 to 8, i.e. as 3 to 2. The result therefore is as follows :—
When two sounds differ by a Fifth, the higher sound makes exactly three vibrations during the time in which the lower sound makes two.
If we take the 16-hole and 12-hole rows together, the interval amounts to a Fourth; accordingly, when two sounds differ by a Fourth, the higher sound makes exactly four vibrations during the time in which the lower sound makes three.
34. The results just obtained admit of being somewhat more concisely stated. During one second of time the upper of two sounds differing by an Octave makes a number of vibrations which is to the number made by the lower sound as 2 to 1. For a Fifth the ratio is 3 to 2. For a Fourth it is 4 to 3. Remembering, then, the definition of the vibration-number