MELODIC RELATIONS OF SOUNDS OF THE SCALE. 47 

must take particular care not to subtract or add vibration numbers, in order to find the interval between them; thus the difference between the vibration numbers of t and n in the second scale is 375 — 250 = 125, but this does not express the interval between them, viz., a Fifth, but merely the difference between the vibration numbers of these particular sounds. To make this clearer, take the difference between the vibration numbers of d and s in the second table = 300 — 200 = 100, and between d and s in the first = 432 — 288 = 144. Here we have different results, although the interval is the same. Take the ratio, however, and we shall get the same in each case for 







aao _. a and ±aa
2 00 2 2 88
We shall now proceed to ascertain the vibration ratios of the intervals between the successive sounds of the scale, using the first of the two scales given on the preceding page :— 








