Heptatonic Sevenths and Triads Infodump

I'm told many people enjoy it when I can't sleep and do one of these "here's some data, you sort it out" posts. If you're one of those people, this is your lucky day.

First I decided to take every common seventh chord and try to fit in a common triad to make a heptatonic scale. Here are the not-especially-surprising results:

• Maj7 + b2Maj = 1 b2 3 4 5 b6 7 (mode of Rasikapriya)
• Maj7 + 2Maj = 1 2 3 b5 5 6 7 (mode of Ionian)
• Maj7 + b5Maj = 1 b2 3 b5 5 b7 7 (mode of Vishwambari)
• Maj7 + b7Maj = 1 2 3 4 5 b7 7 (mode of Naganandini)
• Maj7 + b2Aug = 1 b2 3 4 5 6 7 (mode of Suryakantam)
• Maj7 + 2Aug = 1 2 3 b5 5 b7 7 (mode of Sulini)
• Maj7 + 2Dim = 1 2 3 4 5 b6 7 (mode of Harmonic Major)
• Maj7 + b3Dim = 1 b3 3 b5 5 6 7 (mode of Harmonic Minor)
• Maj7 + b5Min = 1 b2 3 b5 5 6 7 (mode of Superaugmented)
• Maj7 + b7Min = 1 b2 3 4 5 b7 7 (mode of Hatakambari)
• Min7 + b2Maj = 1 b2 b3 4 5 b6 b7 (mode of Ionian)
• Min7 + 2Maj = 1 2 b3 b5 5 6 b7 (mode of Harmonic Minor)
• Min7 + 3Maj = 1 b3 3 5 b6 b7 7 (mode of Gayakapriya)
• Min7 + 6Maj = 1 b2 b3 3 5 6 b7 (mode of Ramapriya)
• Min7 + b2Aug = 1 b2 b3 4 5 6 b7 (mode of Melodic Minor)
• Min7 + 4Dim = 1 b3 4 5 b6 b7 7 (mode of Melodic Minor b4)
• Min7 + b6Dim = 1 2 b3 5 b6 b7 7 (mode of 1maj+b2maj)
• Min7 + 7Dim = 1 2 b3 4 5 b7 7 (mode of Varunapriya)
• Min7 + b2Min = 1 b2 b3 3 5 b6 b7 (mode of Harmonic Major)
• Min7 + b5Min = 1 b2 b3 b5 5 6 b7 (mode of Augmented Minor)
• Min7 + 7Min = 1 2 b3 b5 5 b7 7 (mode of Neetimati)
• Dom7 + b2Maj = 1 b2 3 4 5 b6 b7 (mode of Harmonic Minor)
• Dom7 + 2Maj = 1 2 3 b5 5 6 b7 (mode of Melodic Minor)
• Dom7 + 7Maj = 1 b3 3 b5 5 b7 7 (mode of Rasikapriya)
• Dom7 + b2Aug = 1 b2 3 4 5 6 b7 (mode of Harmonic Major)
• Dom7 + b3Dim = 1 b3 3 b5 5 6 b7 (mode of Augmented Minor)
• Dom7 + 4Dim = 1 3 4 5 b6 b7 7 (mode of Navaneetam)
• Dom7 + b6Dim = 1 2 3 5 b6 b7 7 (mode of Jyoti Swarupini)
• Dom7 + 7Dim = 1 2 3 4 5 b7 7 (mode of Naganandini)
• Dom7 + 2Min = 1 2 3 4 5 6 b7 (mode of Ionian)
• Dom7 + b5Min = 1 b2 3 b5 5 6 b7 (mode of Ramapriya)
• Dom7 + b6Min = 1 b3 3 5 b6 b7 7 (mode of Gayakapriya)
• Dom7 + 7Min = 1 2 3 b5 5 b7 7 (mode of Sulini)
• m7b5 + b2Maj = 1 b2 b3 4 b5 b6 b7 (mode of Ionian)
• m7b5 + 3Maj = 1 b3 3 b5 b6 b7 7 (mode of Suryakantam)
• m7b5 + 5Maj = 1 2 b3 b5 5 b7 7 (mode of Neetimati)
• m7b5 + 6Maj = 1 b2 b3 3 b5 6 b7 (mode of Augmented Minor)
• m7b5 + b2Aug = 1 b2 b3 4 b5 6 b7 (mode of Harmonic Minor)
• m7b5 + b2Dim = 1 b2 b3 3 b5 5 b7 (mode of Ramapriya)
• m7b5 + 2Dim = 1 2 b3 4 b5 b6 b7 (mode of Melodic Minor)
• m7b5 + 4Dim = 1 b3 4 b5 b6 b7 7 (mode of Superaugmented)
• m7b5 + b6Dim = 1 2 b3 b5 b6 b7 7 (mode of Melodic Minor b2 b4)
• m7b5 + 7Dim = 1 2 b3 4 b5 b7 7 (mode of b7maj+nat7maj)
• m7b5 + 2Min = 1 2 b3 4 b5 6 b7 (mode of Harmonic Major)
• m7b5 + 3Min = 1 b3 3 b5 5 b7 7 (mode of Rasikapriya)
• Dim7 + b2Maj = 1 b2 b3 4 b5 b6 6 (mode of Harmonic Major)
• Dim7 + b2Dim = 1 b2 b3 3 b5 5 6 (mode of Augmented Minor)
• Dim7 + 2Dim = 1 2 b3 4 b5 b6 6 (mode of Ramapriya)
• Dim7 + b2Min = 1 b2 b3 3 b5 b6 6 (mode of Harmonic Minor)

Some common themes in here that might be worth digging into, but blah. Then I thought I'd try two sevenths, and unsurprisingly I got more:

• Maj7 + 2Dim = 1 2 3 4 5 b6 7 (mode of Harmonic Major)
• Maj7 + b3Dim = 1 b3 3 b5 5 6 7 (mode of Harmonic Minor)
• Maj7 + 2Min7 = 1 2 3 4 5 6 7 (mode of Ionian)
• Maj7 + 4Min7 = 1 b3 3 4 5 b6 7 (mode of Neetimati)
• Maj7 + b5Min7 = 1 b2 3 b5 5 6 7 (mode of Superaugmented)
• Maj7 + 5Min7 = 1 2 3 4 5 b7 7 (mode of Naganandini)
• Maj7 + b6Min7 = 1 b3 3 b5 5 b6 7 (mode of Gayakapriya)
• Maj7 + b2Maj7 = 1 b2 3 4 5 b6 7 (mode of Rasikapriya)
• Maj7 + b3Maj7 = 1 2 b3 3 5 b7 7 (mode of Yagapriya)
• Maj7 + b3Dom7 = 1 b2 b3 3 5 b7 7 (mode of UNIDENTIFIED)
• Maj7 + 4Dom7 = 1 b3 3 4 5 6 7 (mode of Sulini)
• Maj7 + b5Dom7 = 1 b2 3 b5 5 b7 7 (mode of Vishwambari)
• Maj7 + 5m7b5 = 1 b2 3 4 5 b7 7 (mode of Hatakambari)
• Maj7 + b6m7b5 = 1 2 3 b5 5 b6 7 (mode of Suryakantam)
• Maj7 + b7m7b5 = 1 b2 3 5 b6 b7 7 (mode of Sucharitra)
• Min7 + 2Min7 = 1 2 b3 4 5 6 b7 (mode of Ionian)
• Min7 + 3Min7 = 1 2 b3 3 5 b7 7 (mode of Yagapriya)
• Min7 + 3Maj7 = 1 b3 3 5 b6 b7 7 (mode of Gayakapriya)
• Min7 + 4Maj7 = 1 b3 3 4 5 6 b7 (mode of Naganandini)
• Min7 + b5Maj7 = 1 b2 b3 4 b5 5 b7 (mode of Superaugmented)
• Min7 + 5Maj7 = 1 2 b3 b5 5 b7 7 (mode of Neetimati)
• Min7 + 2Dom7 = 1 2 b3 b5 5 6 b7 (mode of Harmonic Minor)
• Min7 + b5Dom7 = 1 b2 b3 3 b5 5 b7 (mode of Ramapriya)
• Min7 + 5Dom7 = 1 2 b3 4 5 b7 7 (mode of Varunapriya)
• Min7 + 7Dom7 = 1 b3 b5 5 6 b7 7 (mode of Sucharitra)
• Min7 + b2m7b5 = 1 b2 b3 3 5 b7 7 (mode of UNIDENTIFIED)
• Min7 + b3m7b5 = 1 b2 b3 b5 5 6 b7 (mode of Augmented Minor)
• Min7 + 4m7b5 = 1 b3 4 5 b6 b7 7 (mode of Melodic Minor b4)
• Min7 + b7m7b5 = 1 b2 b3 3 5 b6 b7 (mode of Harmonic Major)
• Dom7 + b3Dim = 1 b3 3 b5 5 6 b7 (mode of Augmented Minor)
• Dom7 + b2Min7 = 1 b2 3 5 b6 b7 7 (mode of Sucharitra)
• Dom7 + 2Min7 = 1 2 3 4 5 6 b7 (mode of Ionian)
• Dom7 + b3Min7 = 1 b2 b3 3 b5 5 b7 (mode of Ramapriya)
• Dom7 + 4Min7 = 1 b3 3 4 5 b6 b7 (mode of Varunapriya)
• Dom7 + b7Min7 = 1 b2 3 4 5 b6 b7 (mode of Harmonic Minor)
• Dom7 + 3Maj7 = 1 b3 3 5 b6 b7 7 (mode of Gayakapriya)
• Dom7 + b5Maj7 = 1 b2 3 4 b5 5 b7 (mode of Vishwambari)
• Dom7 + 5Maj7 = 1 2 3 b5 5 b7 7 (mode of Sulini)
• Dom7 + 6Maj7 = 1 b2 3 5 b6 6 b7 (mode of UNIDENTIFIED)
• Dom7 + 7Maj7 = 1 b3 3 b5 5 b7 7 (mode of Rasikapriya)
• Dom7 + 2Dom7 = 1 2 3 b5 5 6 b7 (mode of Melodic Minor)
• Dom7 + 3Dom7 = 1 2 3 5 b6 b7 7 (mode of Jyoti Swarupini)
• Dom7 + 4Dom7 = 1 b3 3 4 5 6 b7 (mode of Naganandini)
• m7b5 + b2Dim = 1 b2 b3 3 b5 5 b7 (mode of Ramapriya)
• m7b5 + 2Min7 = 1 2 b3 4 b5 6 b7 (mode of Harmonic Major)
• m7b5 + b5Min7 = 1 b2 b3 3 b5 6 b7 (mode of Augmented Minor)
• m7b5 + 5Min7 = 1 2 b3 4 b5 5 b7 (mode of Melodic Minor b4)
• m7b5 + b7Min7 = 1 b2 b3 4 b5 b6 b7 (mode of Ionian)
• m7b5 + 7Min7 = 1 2 b3 b5 6 b7 7 (mode of UNIDENTIFIED)
• m7b5 + 2Maj7 = 1 b2 2 b3 b5 6 b7 (mode of Sucharitra)
• m7b5 + 3Maj7 = 1 b3 3 b5 b6 b7 7 (mode of Suryakantam)
• m7b5 + 4Maj7 = 1 b3 3 4 b5 6 b7 (mode of Hatakambari)
• m7b5 + 5Maj7 = 1 2 b3 b5 5 b7 7 (mode of Neetimati)
• m7b5 + b7Dom7 = 1 2 b3 4 b5 b6 b7 (mode of Melodic Minor)
• m7b5 + 3m7b5 = 1 2 b3 3 b5 5 b7 (mode of Melodic Minor b2 b4)
• m7b5 + 4m7b5 = 1 b3 4 b5 b6 b7 7 (mode of Superaugmented)
• Dim7 + b2Maj7 = 1 b2 b3 4 b5 b6 6 (mode of Harmonic Major)
• Dim7 + b3Maj7 = 1 2 b3 b5 5 6 b7 (mode of Harmonic Minor)
• Dim7 + b3Dom7 = 1 b2 b3 b5 5 6 b7 (mode of Augmented Minor)
• Dim7 + 2m7b5 = 1 2 b3 4 b5 b6 6 (mode of Ramapriya)

But wait -- what's that UNIDENTIFIED scale that crops up for four out of the five commonest seventh chords? This thing contains a Maj 7, a Min 7, a Dom 7 and a m7b5, so why haven't we heard of it? Well, actually that's sort of obvious: it contains all these four chord qualities at the root, because the notes are all crammed down that end of the scale. Still, it might be worth investigating a bit.

Other than that, I guess I'm slightly interested in two things: the scales that appear in the second batch but not the first, and whether we can get any sense out of the altered-note heptatonics that aren't in either list, if there are any. My gut says there might be, but my brain says I should get some sleep now and think about it in the morning.

Incidentally, I used Python to put this together. Rather than pasting my code here I'm going to tidy it up and stick it on github or somewhere similar. It needs more work first though.