Ramsay
being also the center of the diatonic triplet, B, D, F, which is the diatonic germ of the chromatic system. Four minor thirds upward or downward from C# we have a second chromatic chord, its central note being G. The dual1 of C# is E?; and there is the same order of keys on the keyboard2 below C# as there is above E?. Four minor thirds from E? upward or downward forms a third chromatic chord, the central note of which is A. The dual A, the center of the third chromatic, is G, the center of the second; and these two notes, by their duality, and by the duality of the two chords throughout, balance each other exactly on the keyboard on either side of the first chromatic chord, which contains all its own duals, and by this self-duality sits in the center, like the tonic chord among the diatonic three. [Scientific Basis and Build of Music, page 57]
Hughes
In the progression of harmonies these are always closely linked into each other. If any key-note is taken as central, its root will be the fifth note of its harmony below, and it becomes in its turn the root of the fifth note above. If we add the silent notes, the root of the central note is the eighth below, and becomes the root of the eighth above. To explain the lower series of the notes sounding the six tones from within themselves, the only plan appeared to be to write the tones as notes in musical clef. By reference to Chapter V., we see that the lowest series still sound their tones, and lead the ear to the higher series of a key-note, and the six notes of its harmony, as they follow each other in trinities. [Harmonies of Tones and Colours, Diagram III - The Major Keynotes Developing by Sevens, page 25a]
ON a keyed instrument only twelve are major key-notes, but as the double tones C#-D? and F#-G? are roots, there are fourteen different chords. The fourteen that are roots are written in musical clef. As an example of the major chords in the different keys, we may examine those in the key of C. A major fifth includes five out of the seven of its key; with the third or central note it is the threefold chord, or fourfold when the octave note is added. Including the silent key-notes, a threefold chord embraces eight, or, counting the double tones, not including E#, eleven. The first and second chords of the seven of the harmony are perfect major chords in the key of C; the central note of the third chord, being #C-?D, is a discord. The first pair of fifths in the scale, with its central note, is a chord of the key; if we include the octave, the last pair of fifths, with its central note, is the same chord an octave higher than the lowest chord of the seven. Of the chords written in musical clef of the twelve keys, the octave chord is only written to C, the seven of each having two chords and the scale one, thirty-six in all, or forty-eight if the octave chords are added. Notice how the chords of each seven and the chord of its scale are altered. [Harmonies of Tones and Colours, Diagram V - The Chords of the Twelve Major Keys, page 27a]
In the development of the key-notes, the sharp or flat is written to each note, but not to the keys. The reversal of the three and four notes of each seven of the twelve key-notes and their trinities meeting by fifths having been traced, we will now examine the twelve scales meeting by fifths, and the results arising from the reversal of the three and four notes of each fifth lower scale in the fifth higher. Take as an example the scale of C: C D E F G A B, and that of G: G A B C D E F#. The four lowest notes of the seven of C are the four highest, an octave higher, in G; F, the central and isolated note of the seven of C, having risen a tone higher than the octave in the scale of G. The twelve scales thus modulate into each other by fifths, which sound the same harmonies as the key-notes and their trinities. Refer to the twelve scales written in musical clef ascending by fifths, and strike them, beginning at the lowest C in the bass clef; this scale sounds no intermediate tones, but these must be struck as required for all the scales to run on in fifths. After striking the seven notes of C, if we fall back three, and repeat them with the next four notes of the seven; or strike the seven and octave of C, and fall back four, repeating them and striking the next four, the four last notes of each scale will be found to be always in the harmony of the four first of the fifth higher scale. When the twelve scales ascending have been thus gained, as we trace them also on the table, they may be struck descending by following them as written in musical clef upwards, and [Harmonies of Tones and Colours, Diagram VII - The Modulating Gamut of the Twelve Keys2, page 30]
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