Ramsay
There are joinings, however, though at a wilder limit. The system of music is not a spiral line. The minor scale is developed from the major by the law of Duality; and when this is done, D26 2/3, the root of the subdominant minor, is so near to D27, the top of the dominant major, that one note may be made to serve for both; and this joins the one extreme of the major and minor systems in this note D, which has thus duality in itself. The only other place where the dual system of major and minor stands open is at the other extreme of the two modes, between B, the top of the dominant minor, and F the root of the subdominant major; and these unjoined ends reach away till at three fifths below F, namely A?, and at three fifths above [Scientific Basis and Build of Music, page 38]
Moreover, it is only from one to five, that is from C to G in ascending, which is its proper direction in the genesis, that the major in being harmonized does not admit of minor chords, but if we descend this same natural major scale of the fifth from five to one, that is from G to C, the first chord is C E G; the next chord is F A C; if this is succeeded by the minor chord A C E, there are two notes in common and one semitonic progression, as very facile step in harmony; and the following two notes are most naturally harmonized as minor chords. So modulation into the minor, even in this major scale, is very easy in descending, which is the proper direction of the minor genesis.2 In a similar way, it is only from five to one, that is from E to A in descending, which is its proper genetic direction, that the minor in being harmonized does not admit of major chords; but if we ascend this same minor scale of the fifth from one to five, the first chord is A C E, the next is E G B, and if this chord be followed by the major C E G, there are here again two notes in common and one semitonic progression; and the two notes following are then most naturally harmonized as major chords. So modulation into the major, even in this minor scale, is very natural and easy in ascending, which is the proper direction of the major genesis.3 The dominant minor and the tonic major are, like the subdominant major and the tonic minor, very intimately related in having two notes in common and one semitonic progression. [Scientific Basis and Build of Music, page 65]
Fig. 4 is a setting of the minor and the major chord-scales, showing how they stand linked by notes in common in their direct sequence from dominant minor to dominant major. To each of the six chords is placed the first chromatic chord, showing how it resolves in its three-fold manner by 1, 2, and 3 semitonic progressions in each mode, and by 1 and 2 notes in common variously in each mode; and here again the law of duality is seen in its always symmetrical adjustments. Duality, when once clearly and familiarly come into possession of musicians, will be sure to become an operative rule and test-agent in composition. [Scientific Basis and Build of Music, page 121]
See Also