Mathematical research of superimpositions took a great deal of time. 8 basic types of seventh chord were combined with each other, one of them – static (basic chord), another – varying trough chromatic scale (possible superimposition). In total 768 pairs. Great part of them misfit, some results were rejected because they contained avoid tones.
Here you could see and test a part of final list I`ve got. For full version contact me directly firstname.lastname@example.org
Any basic chord could fit with several scales and modes at once, whose have identical 1st, 3rd, 5th and 7th`s. Further list shows what scales / modes and seventh chords have common degrees.
Because superimpositions add modal 2nd`s, 4th`s and 6th`s to arpeggio of basic chord, they could be interpreted as modal. We could list and use them in groups – each group for each mode, with root of basic chord.
For instance, we could define what superimpositions update Cm7 chord up to C dorian #4 mode (add 2, #4 and 6 to basic arpeggio). Let`s see and hear it.
Next is the partial list of superimpositions organized mode by mode. Because some modes have plenty of avoid tones, they are not represented there at all.
If basic chord could not be extended vertically, it may be used in pair with other diatonic chord, which contains missing modal tones. Such one could not be considered as a superimposition.
For instance, Cm7 (C, Eb, G, Bb) has only one stable vertical tension in C phrygian context: it`s 4th (F). Unstable tones (Db and Ab) could be successfully represented by Dbmaj7 chord (Db, F, Ab, C), but this is subject of another study.
Notice that superimpositions also could be extended, according to modal context they belong. Next to each available superimposition, brackets contain the name of diatonically correct mode for it and numbers of degrees – what tones in basic chord are actually hit.