Modeless Interchange

Modeless interchange is a technique used for chord progression, that consists of modulating over different types of 7-note MOS scale. In particular, an EDO in which all six types of 7-note MOSes can be realized is called interchangable, and an EDO in which all 0-2-4 triads on all those 7-note MOSes are delta-rational is called perfectly interchangable.

Theory

There are six different 7-tone MOS scales, 1L 6s, 2L 5s, 3L 4s, 4L 3s, 5L 2s and 6L 1s. Each MOS is realized by a different set of EDOs, and not all EDOs can realize all of these MOSes. However, as mentioned above, there are EDOs in which all of these scales are simultaneously valid. Taking 19edo as an example:

7-note MOSes in 19edo

MOS	6L 1s	5L 2s	4L 3s	3L 4s	2L 5s	1L 6s
L:s	3:1	3:2	4:1	5:1	7:1	7:2

Naturally, the 0-2-4 scale step pattern of these scales could be the fundamental triad, but not all of them sound beautiful. Therefore, it is currently assumed as that the frequency differences of the two consecutive intervals in the triad form a simple integer ratio, i.e., that the triad is delta-rational, since these chords tend to sound consonant.

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.

Generalizations

Modeless interchange can be applied to MOSes with any number of notes, not just heptatonic ones.

Todo: expand