twice twelve-fold family of keys

"Of these three chords, which constitute a scale or key, Nature next proceeds to generate, in a similar way, a family of scales or keys, and these in two lines, the Major and the Minor. The twice twelve-fold family of keys is brought forth in much the same way as were the chords which constitute them, and as were the notes which constitute the chords. There is a beautiful growth-like continuity in the production of all." [Scientific Basis and Build of Music, page 20]

The number of Chromatic Chords. Three chromatic chords exhaust the semitonic 12-foldness of the octave. The chromatic scale is a much more even thing than the diatonic; contrast is not its feature, and we may expect [Scientific Basis and Build of Music, page 72]

One purpose of this plate is to show that twelve times the interval of a fifth divides the octave into twelve semitones; and each of these twelve notes is the first note of a major and a minor scale. When the same note has two names, the one has sharps and the other has flats. The number of sharps and flats taken together is always twelve. In this plate will also be observed an exhibition of the omnipresence of the chromatic chords among the twice twelve scales. The staff in the center of the plate is also used as to show the whole 24 scales. Going from the major end, the winding line, advancing by fifths, goes through all the twelve keys notes; but in order to keep all within the staff, a double expedient is resorted to. Instead of starting from C0, the line starts from the subdominant F0, that is, one key lower, and then following the line we have C1, G2, etc., B6 proceeds to G♭ instead of F#, but the signature-number continues still to indicate as if the keys went on in sharps up to F12, where the winding line ends. Going from the minor end, the line starts from E0 instead of A0 - that is, it starts from the dominant of A0, or one key in advance. Then following the line we have B1, F#2, etc. When we come to D#5, we proceed to B♭ instead of A#6, but the signature-number continues as if still in sharps up [Scientific Basis and Build of Music, page 114]

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Created by Dale Pond. Last Modification: Thursday December 31, 2020 05:55:49 MST by Dale Pond.