HANDBOOK OF ACOUSTICS - online book

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226
CHAPTER XVIII.
Temperament.
In Chap. V, we saw how, by means of Helmholtz's Syren, it may be proved, that, for two tones to be at the interval of a Fifth, it is requisite that their vibration numbers be in the ratio of 3:2; and that for two tones to form the interval of a Major Third, their vibration numbers must be as 5 : 4.
In Chap. XV we have seen the reason for this; the vibration numbers must be exactly in these ratios, in order to avoid beats, between Overtones on the one hand, and Combination Tones on the other.
numbers of all the tones of the diatonic scale can be readily calculated on any given basis, after the manner shown in Chap. V (which the student is recommended to read again, before proceeding with the present chapter). There, 288 having been chosen as the vibration number of d, the vibration numbers of the other notes were found to be as follows :