When the major and minor scales are generated to be shown the one half in #s and the other half in ?s, it is not necessary to carry the mathematical process through the whole 24, as when the majors are all in #s and the minors all in ?s; because when six majors have been generated in #s, they furnish the new notes needed by the six relative minors; and when six minors have been generated in ?s, they furnish the new notes for the six relative majors. This plate begins with the major in C and the minor in A. The notes of these two are all identical except the D, which is the sexual note, in which each is not the other, the D of the minor being a comma lower than the D of the major. Going round by the keys in sharp, we come first to E minor and G major. G major has been mathematically generated, and the relative minor E gets its F# from it; but the D of C major must also be [Scientific Basis and Build of Music, page 112]
given to this scale, as the D of A minor would be a comma too low; it would make a 9-comma interval between D and E, the seventh and eighth, where the minor mode has an 8-comma one. So its two new notes are thus found in the relative and sub-relative majors. This is the way of their mutual providing in the region of the #s; the # seventh of the major is given to be the # second of the minor, and the comma-higher second of the sub-relative becomes the seventh of the minor; and then we have a true written representation of what Nature has done. [Scientific Basis and Build of Music, page 113]
Starting again at C major and A minor and going round by the keys in ?s, we come first to D minor and F major. The major gets its ? fourth from the ? sixth of the relative minor; and as the interval between D-E, the major sixth and seventh, must be a 9-comma interval, and its own D-E is only an 8-comma one, it must take the D of A minor, which is a comma lower, and this will correctly show the 9-comma interval between D and E. This is the way of their mutual providing in the region of ?s; the ? sixth of the minor is given to be the ? fourth of the relative major; and the comma-lower fourth of the sub-relative minor becomes the correct sixth of the major. The arrows indicate the source from which, and the place to which; the new notes come and go. [Scientific Basis and Build of Music, page 113]
The signature of major and relative minor is always the same whether in #s or ?s; but in the keys with #s in the plate the signature is only given on the major stave, to indicate that generating upwards is its natural way; and in the keys with ?s the signature is only placed in the minor stave, to indicate that generating downward is the natural way for the minor mode. [Scientific Basis and Build of Music, page 113]
See Also
Ramsay - Duality in the Genesis of Music's Scales
Ramsay - The Natural Way of the Genesis Major and Minor