User:Unque/Chord interlacing (scale building method)
Chord Interlacing is a method of building scales out of a chord.
Scale Formation
Building a scale via chord interlacing requires only a single chord; this chord can be in pure JI or it can be tempered. Two instances of this chord are arranged such that one instance begins on the root pitch, and the other terminates on the period (usually an octave, though other periods are possible).
Chord Interlace scales are so named due to the interlacing of the notes that the scale provides if the chord terminates higher than half of the period; for instance, 5/3 is more than half of an octave, so a chord that terminates on 5/3 will interlace with its counterpart. Note that, in spite of the name, not all chords will interlace when constructing a scale in this manner.
Ancient Greek Genera
The Ancient Greek genera can be interpreted as Chord Interlace scales. A five-limit shade of the Genus Diatonic, for instance, can be created using the chord 10/9 - 5/4 - 4/3 (with step sizes 10/9 - 9/8 - 16/15), and a seven-limit shade can be created with the chord 8/7 - 9/7 - 4/3 (with step sizes 8/7 - 9/8 - 28/27). Scales of the other genera can be similarly created by interlacing the tetrachords thereof.
Similarly, the modern equal-tempered tuning of the Diatonic scale can be created with the 12-EDO chord 2 - 4 - 5, with step sizes 2 - 2 - 1.
Other Applications
Chord Interlace scales can be used to approximate other musical traditions, such as the Arabic Ajnas and Maqamat. If we interpret Jins Rast as a 9::12 tetrachord, for instance, then the Chord Interlace scale built from this tetrachord provides a convincing Maqam Rast.
Additionally, chord interlace scales can provide a useful structure for a JI or tempered scale. Any and all chords can be used to generate the scale - this includes overtone segments, undertone segments, generator patterns, DR chords, or any other arbitrarily-chosen chords the composer may want to use.