MELODIG RELATIONS OF SOUNDS OF THE SCALE. 51 

It may be shown, by means of this instrument, that the vibration numbers of the three tones of a Major Triad, in its normal position
Starting from this experimental foundation, the vibration numbers of all the tones of the modern scale can readily be calculated on any basis; and from these results, the vibration ratio of any interval used in modern music may be obtained.
Vibration ratios must never be added or subtracted.
To find the vibration ratio of the sum of two or more intervals, multiply their vibration ratios together.
To find the vibration ratio of the difference of two intervals, divide the vibration ratio of the greater interval by that of th.e smaller.
The vibration ratios of the principal intervals of the modem musical scale are as follows:— 




