Ramsay
It must be noted that the two new notes needed for each new scale are quite a different affair from the sexual note, that is the note which is different in major and minor, e.g., the two D's in major C and minor A. The [Scientific Basis and Build of Music, page 90]
sexual note in the scales of G major and E minor are the two A's; in D major and B minor, the two E's; in A major and F# minor, the two B's; in E major and C# minor, the two F's; in B major and G# minor, the two C's; and in F# major and D# minor, the two G's. These two last scales being the beginning of a second cycle of twelve scales when the scales are written half in flats and half in sharps, as we have done them in this case. Turning to the other half of our circle, those which we have, and which usually in music books are, written in flats, in F major and D minor the sexual notes are the two G's; in B? and G, the two C's, in E? and C, the two F's; in A? and F, the two B's; in D? and B?, the two E's; and in G? and E?, the two A's. [Scientific Basis and Build of Music, page 91]
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 #s, 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]
This is a twofold mathematical table of the masculine and feminine modes of the twelve scales, the so-called major and relative minor. The minor is set a minor third below the major in every pair, so that the figures in which they are the same may be beside each other; and in this arrangement, in the fourth column in which the figures of the major second stand over the minor fourth, is shown in each pair the sexual note, the minor being always a comma lower than the major. An index finger points to this distinctive note. The note, however, which is here seen as the distinction of the feminine mode, is found in the sixth of the preceding masculine scale in every case, except in the first, where the note is D26 2/3. D is the Fourth of the octave scale of A minor, and the Second of the octave scale of C major. It is only on this note that the two modes differ; the major Second and the minor Fourth are the sexual notes in which each is itself, and not the other. Down this column of seconds and fourths will be seen this sexual distinction through all the twelve scales, they being in this table wholly developed upward by sharps. The minor is always left this comma behind by the comma-advance of the major. The major A in the key of C is 40, but in the key of G it has been advanced to 40 1/2; while in the key of E, this relative minor to G, the A is still 40, a comma lower, and thus it is all the way through the relative scales. This note is found by her own downward genesis from B, the top of the feminine dominant. But it will be remembered that this same B is the middle of the dominant of the masculine, and so the whole feminine mode is seen to be not a terminal, but a lateral outgrowth from the masculine. Compare Plate II., where the whole twofold yet continuous genesis is seen. The mathematical numbers in which the vibration-ratios are expressed are not those of concert pitch, but those in which they appear in the genesis of the scale which begins from F1, for the sake of having the simplest expression of numbers; and it is this series of numbers which is used, for the most part, in this work. It must not be supposed, however, by the young student that there is any necessity for this arrangement. The unit from which to begin may be any number; it may, if he chooses, be the concert-pitch-number of F. But let him take good heed that when he has decided what his unit will be there is no more coming and going, no more choosing by him; Nature comes in [Scientific Basis and Build of Music, page 117]
See Also