Ramsay
There are 32 notes required for each octave for the 13 major and the 13 minor mathematical scales. These 32 notes are by the law of duality arranged symmetrically from D as a center upwards to G#, and downwards to A?. D itself serves for 2 of the 32 on the piano. The first black keys on each side of D serve for nominally 3 notes each = 6. The first white key above and the first below D serve for 2 notes each = 4. The second white key above and the second below serve each for 3 notes = 6. The second black keys above and below D serve each for 3 notes = 6. The third black key above D is G#, the third below is A?; this key, for it is one, serves for 2 of the 32. There is a comma of difference between D minor and D major. Six fifths below the minor D26 2/3 is A?, the root of the subdominant of the key of E? minor; and six fifths above the major D27 is G#, the top of the dominant of F# major. The difference between this minor A? and this major G# is two commas and [Scientific Basis and Build of Music, page 85]