User:Unque/Chord interlacing (scale building method)

Chord Interlacing is a method of building scales out of a chord.

Scale Formation

An example of a Chord Interlace scale, built using the harmonic segment 7::10. Note how the first instance of the chord (shown in red) begins on the root pitch, and the other instance (shown in blue) ends on the octave.

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.

The modern equal-tempered tunings of the Diatonic scale can be similarly created using the 12-EDO chord 2 - 4 - 5, with step sizes 2 - 2 - 1; this can also be extended to other tunings thereof, such as 17-EDO (with the chord 3 - 6 - 7), 19-EDO (with the chord 3 - 6 - 8), 31-EDO (with the chord 5 - 10 - 13), and any other desired shade of the diatonic scale.

Maqamat and Ajnas

The Arabic Maqamat are built using chords called Ajnas. For instance, Maqam Rast is created using two copies of Jins Rast. If we take an approximation of this Rast chord, such as the 9::12 tetrachord, we can use a Chord Interlace scale to create a reasonable approximation of Maqam Rast. This can also be done for other Maqamat whose Jins are identical or nearly so, such as 'Ajam and Hijazkar.

Keep in mind that while the generated scales might sound similar to the traditional maqamat, this method of approximation is extremely crude, and a very poor representation of the actual traditions.

Other Applications

Chord interlace scales can provide a useful structure for any JI or tempered scale. Any and all chords can be used to generate such a scale - this includes overtone segments, undertone segments, generator patterns, DR chords, or any other arbitrarily-chosen chords the composer may want to use.