# HANDBOOK OF ACOUSTICS - online book

### A complete view of Acoustical Science & its bearings on music, for musicians & music students.

 132                    HAND-BOOK OF ACOUSTICS. sounded, we proceed as before. For example, let the two generators be jS. The relative rates of vibration being J J , the relative vibration rate of the differential of the first order = 5 — 4 = 1. Subtracting this from the generators 5 and 4 we obtain the relative vibration rates of the differentials of the second order viz. 5 — 1 = 4 and 4 — 1 = 3, this latter only being a new tone. Again, subtracting this 3 from the higher generator, we get another new tone 5 — 3 = 2, a differential of the third order. Thus, omitting duplicate tones we have— generators f J ~ 4 Differential of 1st order, d| = 1 (= 5 — 4) 2nd „ s = 3 (= 4 - 1) 3rd „ d =2 (=5-3) The 2nd, 3rd, 4th, and 5th columns of the following table show the differentials of the 1st, 2nd, 3rd, and 4th order which may be pro­duced by the tones in the 1st column. •Nearly.