Modeless interchange

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

Modeless interchange, is a technique or a chord progression that consists of crossing over the Triad present in the 7-note MOS scale. In particular, an EDO in which all six types of 7-note MOSs are possible is called Interchangable, and an EDO in which all triad 0-2-4 on all those 7-note MOSes are Delta-rational chords is called Perfectly Interchangable.

Theory

As you know, there are six different 7-tone MOS scales, 1L 6s, 2L 5s, 3L 4s, 4L 3s, 5L 2s and 6L 1s. Of course, all of which are based on different group of EDOs. However, as mentioned above, there are EDOs in which all of these scales are simultaneously valid. Taking 19edo as an example, there is a subset of this scale: 6L 1s (L:s=3:1), 4L 3s (L:s=4:1), 3L 4s (L:s=5:1), 2L 5s (L:s=7:1), and 1L 6s (L:s=7:2). Naturally, a further subset of these scales could be the 0-2-4 triad, but not all of them sound beautiful. More specifically, it is currently assumed as that the simply ratio of the frequency difference of the triad is the Just Intonation ratio, i.e., that the triad is a Delta-rational.

Thankfully, since generators are known to produce many Delta-rational Chords when tuned close to the stock ratio, and since the 5/4 (major third, generator of 3L 4s) and 6/5 (minor third, generator of 4L 3s) approximations in 19EDO mean are as close to the JI ratio as possible, we can expect at least two modeless interchanges to be possible for the 4L 3s and 3L 4s. If you wish to use other averages, the following table will be helpful:

	1L 6s	2L 5s	3L 4s	4L 3s	5L 2s	6L 1s
Ideal Δ-ratio	+2+3, +5+6, +1+1 (L:s≒√2:1)	+2+3, +4+5, +1+1 (L:s≒3:2)	+1+2, +5+6, +1+5 (L:s≒4:1)	+1+2, +5+6, +3+1 (L:s≒7:2)	+2+3, +5+6, +1+1 (L:s≒8:5)	+2+3, +5+6, +1+1 (L:s≒3:2)
in 19edo	+4+1, +1+3, +1+1 (L:s=7:2)	+5+1, +3+10, +1+1 (L:s=7:1)	+5+1, +4+5, +5+4 (L:s=5:1)	+1+2, +4+5, +6+5 (L:s=4:1)	+2+3, +5+6, +1+1 (L:s≒3:2)	+5:9, +4+5, +1+1 (L:s≒3:1)

Todo: expand expand and refactor this table

Usage

This technique is still in its infancy and information is drying up, but it should be used like a modal interchange.

Todo: expand