Two Tetrad Chords

Here are some two triad chords. Most of these are only true enharmonically in 12-TET.

: .m7b5

C.m11b5b9 = C.dim + Bb.m
C.m11b5 = C.dim + Bb.maj
C.m7b5b9 = C.dim + Gb.maj

:: .m7

C.m11b9 = C.m + Bb.m
C.m11 = C.m + Bb.maj
C.m7#11 = C.m + Eb.m
C.m7b9 = C.m + G.dim
C.m9 = C.m + G.m
C.m7b9#11 = C.m + Gb.maj

:: .7

C.7b9 = C.maj + Bb.dim
C.11b9 = C.maj + Bb.m
C.11 = C.maj + Bb.maj
C.7#9#11 = C.maj + Eb.m
C.7#9 = C.maj + Eb.maj
C.7b9 = C.maj + G.dim
C.9 = C.maj + G.m
C.7b9#11 = C.maj + Gb.maj

: .maj7

C.maj7#9b13 = C.maj + Ab.m
C.maj11 = C.maj + B.dim
C.maj7#9#11 = C.maj + B.maj
C.maj7b13 = C.maj + E.maj

Here's a are some chords made of a (tetrad) and another (triad or tetrad):

:: .m7b5:

C.m7b5b13 = C.m7b5 + (Ab.maj or Ab.7)

C.m11b5b13 = C.m7b5 + (D.dim or D.m7b5)

C.m13b5 = C.m7b5 + (D.m or D.m7)

C.m13b5#11 = C.m7b5 + (D.maj or D.7)

C.m11b5b9b13 = C.m7b5 + (Db.maj or Db.maj7)

:: .m7:

C.m7b13 = C.m7 + (Ab.maj or Ab.maj7)

C.m11b9b13 = C.m7 + (Db.maj or Db.maj7)

C.m11b13 = C.m7 + (D.dim or D.m7b5)

C.m13 = C.m7 + (D.m or D.m7)

C.m13#11 = C.m7 + (D.maj or D.7)

:: .7:

C.11b9b13 = C.7 + (Db.maj or Db.maj7)

C.11b13 = C.7 + (D.dim or D.m7b5)

C.13 = C.7 + (D.m or D.m7)

C.13#11 = C.7 + (D.maj or D.7)

:: maj7:

C.maj11b9b13 = C.maj7 + (Db.maj or Db.maj7)

C.maj11b13 = C.maj7 + (D.dim or D.m7b5)

C.maj13 = C.maj7 + (D.m or D.m7)

C.maj13#11 = C.maj7 + (D.maj or D.7)

I like those a lot. I think they're all true exactly, instead of just enharmonically, at least in rank-2 interval space.

Here's an even larger set. Probably too long to be useful. I should compress it or filter or something. But maybe someone will like it.

  : .m7b5

C.m11b5 = C.m7b5 + Bb.maj

C.m11b5b9 = C.m7b5 + Bb.m

C.m11b5b9 = C.m7b5 + Gb.maj7

C.m13b5 = C.m7b5 + Bb.maj7

C.m7b5b9 = C.m7b5 + Eb.m7

C.m7b5b9 = C.m7b5 + Gb.maj

:: .m7

C.m11 = C.m7 + Bb.maj

C.m11 = C.m7 + G.m7

C.m11b9 = C.m7 + Bb.m

C.m11b9 = C.m7 + G.m7b5

C.m13 = C.m7 + Bb.maj7

C.m13#11 = C.m7 + D.7

C.m13#11 = C.m7 + D.maj

C.m13#9#11 = C.m7 + C.dim7

C.m13#9#11 = C.m7 + Eb.dim

C.m13#9#11 = C.m7 + Eb.dim7

C.m13#9#11 = C.m7 + Gb.dim

C.m13b9#11 = C.m7 + Eb.m7b5

C.m13b9#11 = C.m7 + Gb.m

C.m7#11 = C.m7 + Eb.m

C.m7#11b13 = C.m7 + Ab.7

C.m7b13 = C.m7 + Ab.maj

C.m7b13 = C.m7 + Ab.maj7

C.m7b9 = C.m7 + Eb.7

C.m7b9 = C.m7 + G.dim

C.m7b9#11 = C.m7 + Eb.m7

C.m7b9#11 = C.m7 + Gb.maj

C.m9 = C.m7 + Eb.maj7

C.m9 = C.m7 + G.m

:: .7

C.11 = C.7 + Bb.maj

C.11 = C.7 + G.m7

C.11#9b13 = C.7 + F.m7

C.11b13 = C.7 + Bb.7

C.11b13 = C.7 + D.dim

C.11b13 = C.7 + D.m7b5

C.11b9 = C.7 + Bb.m

C.11b9 = C.7 + G.m7b5

C.11b9b13 = C.7 + Bb.m7

C.13 = C.7 + Bb.maj7

C.13 = C.7 + D.m

C.13 = C.7 + D.m7

C.13#11 = C.7 + D.7

C.13#11 = C.7 + D.maj

C.13#9 = C.7 + F.7

C.13#9#11 = C.7 + C.dim7

C.13#9#11 = C.7 + Eb.dim

C.13#9#11 = C.7 + Eb.dim7

C.13b9#11 = C.7 + Gb.m

C.13b9#11 = C.7 + Gb.m7

C.7#9 = C.7 + Eb.maj

C.7#9#11 = C.7 + Eb.m

C.7#9#11b13 = C.7 + Ab.7

C.7#9b13 = C.7 + Ab.maj

C.7#9b13 = C.7 + Ab.maj7

C.7b9 = C.7 + Bb.dim

C.7b9 = C.7 + E.dim7

C.7b9 = C.7 + G.dim

C.7b9 = C.7 + G.dim7

C.7b9#11 = C.7 + Gb.7

C.7b9#11 = C.7 + Gb.maj

C.7b9b13 = C.7 + Bb.m7b5

C.9 = C.7 + E.m7b5

C.9 = C.7 + G.m

: .maj7

C.maj11 = C.maj7 + B.dim

C.maj11 = C.maj7 + G.7

C.maj11#9b13 = C.maj7 + F.m7

C.maj11#9b13 = C.maj7 + F.m7b5

C.maj13#9 = C.maj7 + F.7

C.maj13b9#11 = C.maj7 + Gb.m

C.maj13b9#11 = C.maj7 + Gb.m7

C.maj7#9#11 = C.maj7 + B.maj

C.maj7#9#11b13 = C.maj7 + Ab.7

C.maj7#9#11b13 = C.maj7 + Ab.m7

C.maj7#9b13 = C.maj7 + Ab.m

C.maj7#9b13 = C.maj7 + Ab.maj

C.maj7#9b13 = C.maj7 + Ab.maj7

C.maj7#9b13 = C.maj7 + E.maj7

C.maj7b13 = C.maj7 + E.maj