Ramsay
In just such a manner, only by more obvious leaps, the middle of the dominant in the advancing major scales is raised a sharp - i.e., four commas. When D27, the dominant top of the key of C, is multiplied by 5, it generates F#135; so, taking it one octave lower, F64 in C major is F#67 1/2 in the key of G. C96 in the key of G is C#101 1/4 in the key of D; G72 in the key of D is G#151 7/8 in the key of A. And this raising of the middle of the dominant goes on through all the twelve major keys.[Scientific Basis and Build of Music, page 62]
The root of the subdominant is F, in the key of C major; and the top of the dominant is D. The difference between these two notes at the top and bottom of the chord-scale, is the quantity which two octaves is more than three fifths; it is the ratio of 27 to 30, a comma less than the minor third whose ratio is 5 to 6. [Scientific Basis and Build of Music, page 76]
See Also