In the same general manner, may be found the best system of intervals, for a scale confined to a less number of degrees than that of the complete Enharmonic scale. In such an investigation, the numbers in Table IV. expressing the frequency of all such adjacent degrees as have but one sound in the given scale, must be united; and the temperaments m, n, &c. of the theorem, when belonging to concords whose terminating degrees are united to those adjacent, must be taken, not what they were in the complete scale, but what they become, considering them as terminated by the substituted adjacent degree.
If, for example, the best temperaments were required for a scale of 15 degrees to the octave, such as is that of some European organs, or in other words, having no Enharmonic intervals except D
E
, and G
A
,—the numbers in Table IV. belonging to C