Weird dissonant chords can be given musical functions through resolution; you follow the weird chord with a pretty one through tight voice leading, and the dissonances become setups for the consonances in the punch line. There's a baroque prescription of preparing your dissonances by consonant suspension from the previous chord and then resolving them downward by to consonances in the next chord, and this is a beautiful idiom that composers should become skilled in, but in non-baroque music, it can be beautiful to just introduce some crazy bullshit and then follow it with whatever resolution your ear likes, not requiring preparation or downward resolution.
Anyway, most chords can be given musical function, so it doesn't make sense for a person to give a list of all the useable chords. Almost any chord should be usable. But it might be good to have a list of pretty chords - the ones you can resolve to, the ones that make sense of the weird ones, the punch lines.
I haven't trained my ear well enough to compose well in just intonation, and so I often look for theoretical shortcuts to finding good chords. I've done this in interval space a lot. I can't recall if I've written it up here, but that's a topic for another day. I've also looked for consonant chord identification heuristics in frequency space a little bit: see "Odd Harmonics Sound Great". In this post, I'm going to share a new heuristic for making pretty chords in frequency space, chords with moderately high prime limits.
Here's the trick: I start with a justly tuned harmonic seventh chord, which has the otonal representation [4, 5, 6, 7]. Now I make a new chord from that. Each voice in the chord has to move up or down by one of these steps:
[1/1, 3/2, 4/3, 5/3, 5/4, 6/5, 7/4, 7/6, 8/5, 8/7, 9/8, 10/9, 11/4, 11/8, 12/7, 12/8, 13/8]
There's nothing magical about that list, it's just one of the first things I tried and liked. It has super particular ratios, some reduced harmonics, and some octave complements of those, and also the unison. I call them the tridecimal fluid steps.
Next we check if the chord made this way has good adjacent harmony, i.e. if there is good harmony between each pair of adjacent voices. I used a similar but slightly different set of frequency ratios for the blessed set of good harmonies:
[2/1, 3/2, 4/3, 5/3, 5/4, 6/5, 7/4, 7/6, 8/5, 8/7, 9/8, 10/9, 11/10, 12/7, 12/11, 13/12, 14/13, 15/14, 16/15]
This one has the octave instead of the unison, and more high-limit super particular ratios than the previous list. Again, nothing magic, it's just the first thing that I tried and liked.
So we make make a new chord that flows from the harmonic seventh chord. And then we repeat, basing off the most recent new chord each time.
Most chords that follow as fluid transitions won't also have good adjacent harmony. Sometimes I had to do like 8000 loops of (chord construction and checking) to get the next chord. And not every chord made in this way will sound amazing. But a large proportion of them sound good. I don't know why it works, but I'm glad that it does. It doesn't even seem to me that the chords get reliably worse as you go farther from the initial chord in the generative chain. You can definitely get chords with larger integers in their otonal representations, but the quality doesn't really degrade much, in my estimation.
I do confess that the chords sound worse at higher prime limits. So maybe I'll focus on figuring predictive principles for which 7-limit and higher-limit chords sound good next. But also the generative sequence weaves into and then back out of high-prime limit chords, so the sequences you get are still overall pretty good.
So here below are about 500 chords I found by this procedure. I haven't filtered out the bad sounding ones, because I haven't decided which ones sound bad for all 500 yet, and also because I don't want to present only the good ones: I'm showing you what my procedure makes, and there is work left to do to figure out why a few of these chords sound bad - there's is more aesthetic formalization that I want to do that should start with this data.
[2, 3, 4, 6], # 3-limit
[3, 6, 12, 16], # 3-limit
[4, 6, 9, 12], # 3-limit
[4, 6, 9, 18], # 3-limit
[6, 8, 9, 12], # 3-limit
[6, 8, 9, 18], # 3-limit
[8, 9, 12, 16], # 3-limit
[8, 9, 18, 24], # 3-limit
[8, 16, 18, 27], # 3-limit
[8, 16, 24, 27], # 3-limit
[9, 12, 16, 32], # 3-limit
[16, 18, 27, 36], # 3-limit
[1, 2, 3, 5], # 5-limit
[2, 3, 5, 10], # 5-limit
[2, 4, 5, 10], # 5-limit
[3, 4, 6, 10], # 5-limit
[3, 5, 8, 10], # 5-limit
[3, 6, 10, 16], # 5-limit
[4, 5, 6, 8], # 5-limit
[4, 5, 6, 10], # 5-limit
[4, 5, 8, 9], # 5-limit
[4, 5, 8, 16], # 5-limit
[4, 5, 10, 15], # 5-limit
[4, 5, 10, 16], # 5-limit
[4, 5, 10, 20], # 5-limit
[5, 6, 9, 10], # 5-limit
[5, 6, 9, 12], # 5-limit
[5, 6, 9, 18], # 5-limit
[5, 6, 10, 15], # 5-limit
[5, 6, 12, 15], # 5-limit
[5, 8, 9, 10], # 5-limit
[5, 8, 10, 12], # 5-limit
[5, 8, 12, 15], # 5-limit
[5, 8, 12, 24], # 5-limit
[5, 8, 16, 32], # 5-limit
[5, 10, 16, 20], # 5-limit
[5, 10, 16, 24], # 5-limit
[6, 10, 15, 20], # 5-limit
[6, 12, 15, 20], # 5-limit
[9, 10, 12, 16], # 5-limit
[9, 10, 15, 20], # 5-limit
[9, 10, 16, 24], # 5-limit
[9, 10, 20, 32], # 5-limit
[9, 12, 20, 40], # 5-limit
[9, 15, 16, 18], # 5-limit
[9, 15, 16, 32], # 5-limit
[9, 15, 18, 20], # 5-limit
[9, 15, 20, 24], # 5-limit
[9, 15, 20, 32], # 5-limit
[9, 15, 30, 40], # 5-limit
[9, 18, 30, 40], # 5-limit
[10, 12, 15, 20], # 5-limit
[10, 12, 24, 27], # 5-limit
[10, 15, 16, 20], # 5-limit
[10, 15, 18, 24], # 5-limit
[10, 15, 18, 36], # 5-limit
[10, 15, 24, 30], # 5-limit
[10, 15, 24, 36], # 5-limit
[10, 15, 24, 40], # 5-limit
[10, 16, 24, 27], # 5-limit
[12, 15, 20, 30], # 5-limit
[12, 15, 20, 32], # 5-limit
[12, 15, 20, 40], # 5-limit
[12, 20, 25, 30], # 5-limit
[15, 16, 18, 24], # 5-limit
[15, 16, 20, 40], # 5-limit
[15, 16, 24, 30], # 5-limit
[15, 16, 24, 40], # 5-limit
[15, 16, 32, 64], # 5-limit
[15, 18, 24, 32], # 5-limit
[15, 18, 24, 40], # 5-limit
[15, 18, 30, 32], # 5-limit
[15, 18, 36, 40], # 5-limit
[15, 20, 24, 27], # 5-limit
[15, 20, 24, 30], # 5-limit
[15, 20, 24, 32], # 5-limit
[15, 20, 30, 32], # 5-limit
[15, 20, 30, 36], # 5-limit
[15, 20, 32, 40], # 5-limit
[15, 20, 32, 64], # 5-limit
[15, 24, 30, 50], # 5-limit
[15, 24, 32, 40], # 5-limit
[15, 24, 36, 40], # 5-limit
[15, 24, 40, 50], # 5-limit
[15, 24, 40, 64], # 5-limit
[15, 30, 32, 48], # 5-limit
[15, 30, 36, 40], # 5-limit
[15, 30, 40, 64], # 5-limit
[15, 30, 48, 64], # 5-limit
[16, 20, 25, 40], # 5-limit
[16, 20, 30, 45], # 5-limit
[16, 20, 40, 45], # 5-limit
[16, 24, 27, 30], # 5-limit
[18, 20, 30, 45], # 5-limit
[18, 27, 36, 40], # 5-limit
[18, 30, 40, 45], # 5-limit
[18, 30, 45, 50], # 5-limit
[18, 30, 50, 75], # 5-limit
[18, 36, 40, 45], # 5-limit
[20, 24, 27, 45], # 5-limit
[20, 24, 27, 54], # 5-limit
[20, 24, 40, 45], # 5-limit
[20, 30, 45, 54], # 5-limit
[20, 40, 45, 72], # 5-limit
[24, 40, 45, 75], # 5-limit
[25, 30, 32, 36], # 5-limit
[25, 30, 36, 60], # 5-limit
[25, 30, 36, 72], # 5-limit
[25, 30, 45, 54], # 5-limit
[25, 30, 48, 64], # 5-limit
[25, 30, 48, 72], # 5-limit
[25, 30, 48, 80], # 5-limit
[25, 30, 60, 64], # 5-limit
[25, 30, 60, 72], # 5-limit
[25, 40, 48, 64], # 5-limit
[25, 40, 64, 128], # 5-limit
[25, 40, 80, 128], # 5-limit
[25, 50, 80, 128], # 5-limit
[27, 30, 40, 60], # 5-limit
[27, 30, 45, 50], # 5-limit
[27, 36, 40, 60], # 5-limit
[27, 36, 40, 64], # 5-limit
[27, 45, 60, 64], # 5-limit
[27, 45, 72, 80], # 5-limit
[30, 40, 45, 72], # 5-limit
[30, 45, 60, 64], # 5-limit
[32, 40, 45, 90], # 5-limit
[32, 40, 50, 75], # 5-limit
[36, 45, 48, 80], # 5-limit
[36, 45, 60, 80], # 5-limit
[40, 45, 48, 64], # 5-limit
[40, 45, 54, 60], # 5-limit
[40, 45, 60, 64], # 5-limit
[40, 45, 90, 108], # 5-limit
[40, 64, 72, 81], # 5-limit
[45, 54, 60, 100], # 5-limit
[45, 72, 80, 128], # 5-limit
[45, 72, 96, 128], # 5-limit
[45, 72, 96, 160], # 5-limit
[50, 75, 90, 108], # 5-limit
[50, 75, 120, 128], # 5-limit
[60, 75, 120, 128], # 5-limit
[64, 72, 81, 135], # 5-limit
[64, 72, 120, 135], # 5-limit
[64, 80, 120, 135], # 5-limit
[75, 80, 160, 192], # 5-limit
[75, 90, 120, 128], # 5-limit
[75, 120, 160, 256], # 5-limit
[80, 90, 108, 135], # 5-limit
[80, 96, 108, 135], # 5-limit
[81, 90, 96, 128], # 5-limit
[81, 108, 144, 160], # 5-limit
[128, 160, 180, 225], # 5-limit
[135, 144, 240, 256], # 5-limit
[135, 144, 240, 320], # 5-limit
[135, 180, 240, 256], # 5-limit
[144, 180, 225, 250], # 5-limit
[225, 240, 480, 512], # 5-limit
[375, 600, 640, 768], # 5-limit
[2, 3, 6, 7], # 7-limit
[2, 4, 7, 12], # 7-limit
[3, 4, 7, 12], # 7-limit
[4, 6, 7, 14], # 7-limit
[4, 7, 8, 14], # 7-limit
[4, 7, 12, 15], # 7-limit
[4, 7, 14, 28], # 7-limit
[5, 8, 14, 16], # 7-limit
[6, 7, 8, 9], # 7-limit
[6, 7, 12, 14], # 7-limit
[6, 7, 12, 18], # 7-limit
[6, 7, 14, 28], # 7-limit
[6, 9, 12, 14], # 7-limit
[7, 8, 9, 12], # 7-limit
[7, 8, 9, 18], # 7-limit
[7, 8, 12, 16], # 7-limit
[7, 8, 14, 16], # 7-limit
[7, 8, 14, 28], # 7-limit
[7, 8, 16, 24], # 7-limit
[7, 12, 14, 24], # 7-limit
[7, 12, 15, 24], # 7-limit
[7, 12, 16, 20], # 7-limit
[7, 12, 16, 28], # 7-limit
[7, 12, 18, 21], # 7-limit
[7, 12, 20, 32], # 7-limit
[7, 14, 16, 18], # 7-limit
[7, 14, 24, 42], # 7-limit
[7, 14, 28, 48], # 7-limit
[8, 9, 12, 14], # 7-limit
[8, 10, 12, 21], # 7-limit
[8, 12, 21, 42], # 7-limit
[8, 14, 28, 35], # 7-limit
[9, 10, 16, 28], # 7-limit
[9, 10, 20, 35], # 7-limit
[9, 15, 20, 35], # 7-limit
[9, 18, 21, 28], # 7-limit
[10, 12, 14, 15], # 7-limit
[10, 12, 21, 36], # 7-limit
[10, 15, 24, 42], # 7-limit
[12, 14, 21, 24], # 7-limit
[12, 15, 16, 28], # 7-limit
[12, 15, 24, 28], # 7-limit
[12, 16, 18, 21], # 7-limit
[12, 21, 28, 32], # 7-limit
[14, 15, 18, 21], # 7-limit
[14, 15, 24, 36], # 7-limit
[14, 15, 25, 30], # 7-limit
[14, 21, 24, 27], # 7-limit
[14, 21, 24, 30], # 7-limit
[14, 21, 36, 40], # 7-limit
[14, 21, 36, 54], # 7-limit
[14, 21, 36, 60], # 7-limit
[15, 18, 21, 28], # 7-limit
[15, 18, 24, 28], # 7-limit
[15, 20, 24, 42], # 7-limit
[15, 24, 28, 42], # 7-limit
[15, 24, 28, 49], # 7-limit
[15, 30, 48, 56], # 7-limit
[16, 24, 28, 35], # 7-limit
[16, 24, 28, 49], # 7-limit
[16, 28, 35, 56], # 7-limit
[16, 28, 42, 49], # 7-limit
[16, 28, 56, 63], # 7-limit
[18, 20, 30, 35], # 7-limit
[18, 20, 35, 60], # 7-limit
[18, 24, 30, 35], # 7-limit
[18, 30, 35, 60], # 7-limit
[18, 36, 42, 49], # 7-limit
[20, 35, 40, 48], # 7-limit
[20, 35, 56, 70], # 7-limit
[21, 24, 28, 32], # 7-limit
[21, 24, 28, 56], # 7-limit
[21, 24, 32, 40], # 7-limit
[21, 24, 32, 56], # 7-limit
[21, 24, 32, 64], # 7-limit
[21, 24, 40, 48], # 7-limit
[21, 28, 42, 45], # 7-limit
[21, 28, 48, 56], # 7-limit
[21, 28, 48, 96], # 7-limit
[21, 35, 56, 60], # 7-limit
[21, 35, 56, 64], # 7-limit
[21, 35, 60, 75], # 7-limit
[21, 36, 60, 80], # 7-limit
[21, 42, 72, 80], # 7-limit
[24, 28, 35, 56], # 7-limit
[24, 30, 35, 60], # 7-limit
[25, 30, 35, 42], # 7-limit
[27, 30, 35, 70], # 7-limit
[27, 30, 60, 70], # 7-limit
[27, 36, 42, 56], # 7-limit
[27, 36, 63, 70], # 7-limit
[28, 35, 40, 64], # 7-limit
[28, 35, 40, 70], # 7-limit
[28, 35, 60, 70], # 7-limit
[28, 42, 45, 50], # 7-limit
[28, 42, 45, 60], # 7-limit
[30, 35, 40, 48], # 7-limit
[30, 35, 40, 64], # 7-limit
[32, 36, 63, 84], # 7-limit
[32, 56, 60, 105], # 7-limit
[32, 56, 63, 105], # 7-limit
[35, 40, 45, 72], # 7-limit
[35, 40, 60, 96], # 7-limit
[35, 40, 70, 84], # 7-limit
[35, 42, 48, 60], # 7-limit
[35, 42, 63, 108], # 7-limit
[35, 42, 70, 120], # 7-limit
[35, 42, 72, 96], # 7-limit
[35, 56, 60, 72], # 7-limit
[35, 56, 63, 108], # 7-limit
[35, 56, 64, 80], # 7-limit
[35, 56, 64, 96], # 7-limit
[35, 56, 64, 112], # 7-limit
[35, 56, 70, 120], # 7-limit
[35, 56, 84, 90], # 7-limit
[35, 56, 84, 96], # 7-limit
[35, 56, 96, 144], # 7-limit
[35, 70, 80, 96], # 7-limit
[35, 70, 112, 128], # 7-limit
[35, 70, 112, 192], # 7-limit
[36, 40, 70, 105], # 7-limit
[36, 42, 56, 63], # 7-limit
[36, 45, 60, 70], # 7-limit
[36, 48, 56, 63], # 7-limit
[40, 45, 48, 84], # 7-limit
[42, 45, 48, 56], # 7-limit
[42, 45, 60, 80], # 7-limit
[42, 49, 84, 90], # 7-limit
[42, 63, 70, 80], # 7-limit
[45, 48, 64, 112], # 7-limit
[45, 60, 64, 112], # 7-limit
[45, 72, 96, 112], # 7-limit
[48, 56, 60, 75], # 7-limit
[48, 56, 60, 105], # 7-limit
[48, 56, 63, 84], # 7-limit
[48, 80, 140, 175], # 7-limit
[48, 84, 140, 175], # 7-limit
[49, 56, 96, 192], # 7-limit
[49, 84, 144, 180], # 7-limit
[49, 84, 144, 240], # 7-limit
[54, 60, 100, 175], # 7-limit
[54, 63, 70, 140], # 7-limit
[54, 63, 84, 112], # 7-limit
[54, 63, 105, 140], # 7-limit
[56, 60, 105, 112], # 7-limit
[56, 60, 105, 210], # 7-limit
[56, 63, 105, 120], # 7-limit
[56, 63, 108, 126], # 7-limit
[56, 63, 108, 135], # 7-limit
[56, 70, 75, 120], # 7-limit
[56, 70, 120, 135], # 7-limit
[56, 96, 168, 189], # 7-limit
[60, 105, 112, 192], # 7-limit
[63, 70, 105, 120], # 7-limit
[63, 70, 105, 180], # 7-limit
[63, 70, 112, 192], # 7-limit
[63, 70, 120, 210], # 7-limit
[63, 70, 140, 240], # 7-limit
[63, 72, 80, 96], # 7-limit
[63, 72, 80, 100], # 7-limit
[63, 72, 80, 140], # 7-limit
[63, 72, 84, 140], # 7-limit
[63, 72, 96, 128], # 7-limit
[63, 84, 140, 150], # 7-limit
[63, 105, 120, 160], # 7-limit
[63, 108, 120, 128], # 7-limit
[63, 108, 120, 160], # 7-limit
[63, 126, 144, 160], # 7-limit
[64, 112, 120, 135], # 7-limit
[70, 84, 126, 135], # 7-limit
[70, 105, 126, 216], # 7-limit
[70, 105, 168, 180], # 7-limit
[72, 80, 90, 105], # 7-limit
[81, 90, 120, 140], # 7-limit
[84, 140, 150, 175], # 7-limit
[98, 105, 120, 210], # 7-limit
[100, 175, 210, 252], # 7-limit
[105, 112, 140, 150], # 7-limit
[105, 112, 140, 160], # 7-limit
[105, 112, 140, 240], # 7-limit
[105, 112, 192, 256], # 7-limit
[105, 112, 192, 288], # 7-limit
[105, 112, 224, 256], # 7-limit
[105, 120, 128, 224], # 7-limit
[105, 120, 140, 168], # 7-limit
[105, 120, 144, 160], # 7-limit
[105, 126, 140, 240], # 7-limit
[105, 126, 144, 160], # 7-limit
[105, 140, 160, 192], # 7-limit
[105, 168, 224, 384], # 7-limit
[105, 168, 280, 300], # 7-limit
[105, 180, 210, 224], # 7-limit
[108, 120, 150, 175], # 7-limit
[112, 120, 135, 225], # 7-limit
[112, 120, 140, 175], # 7-limit
[112, 126, 135, 144], # 7-limit
[112, 168, 180, 315], # 7-limit
[112, 168, 189, 216], # 7-limit
[120, 140, 168, 189], # 7-limit
[120, 210, 245, 294], # 7-limit
[128, 224, 252, 441], # 7-limit
[135, 216, 252, 280], # 7-limit
[147, 252, 280, 320], # 7-limit
[150, 175, 210, 224], # 7-limit
[160, 180, 315, 336], # 7-limit
[168, 280, 300, 525], # 7-limit
[175, 200, 240, 288], # 7-limit
[175, 210, 240, 256], # 7-limit
[175, 210, 360, 432], # 7-limit
[175, 280, 480, 576], # 7-limit
[175, 300, 360, 576], # 7-limit
[180, 210, 245, 294], # 7-limit
[189, 210, 240, 280], # 7-limit
[189, 210, 360, 400], # 7-limit
[189, 216, 288, 320], # 7-limit
[189, 252, 288, 320], # 7-limit
[189, 315, 350, 400], # 7-limit
[216, 240, 280, 315], # 7-limit
[224, 252, 315, 540], # 7-limit
[245, 280, 448, 768], # 7-limit
[245, 294, 336, 576], # 7-limit
[245, 420, 448, 768], # 7-limit
[245, 420, 672, 768], # 7-limit
[245, 420, 672, 1152], # 7-limit
[270, 315, 336, 560], # 7-limit
[270, 315, 420, 448], # 7-limit
[280, 315, 504, 540], # 7-limit
[300, 525, 560, 672], # 7-limit
[315, 336, 384, 512], # 7-limit
[315, 336, 560, 640], # 7-limit
[315, 360, 384, 640], # 7-limit
[315, 420, 448, 768], # 7-limit
[315, 504, 560, 600], # 7-limit
[315, 504, 560, 960], # 7-limit
[336, 560, 630, 675], # 7-limit
[343, 392, 420, 720], # 7-limit
[441, 504, 560, 640], # 7-limit
[441, 504, 560, 960], # 7-limit
[525, 560, 960, 1152], # 7-limit
[735, 784, 1344, 2304], # 7-limit
[784, 882, 945, 1080], # 7-limit
[11, 12, 16, 18], # 11-limit
[11, 12, 18, 24], # 11-limit
[11, 12, 20, 32], # 11-limit
[11, 12, 24, 27], # 11-limit
[11, 22, 33, 36], # 11-limit
[15, 18, 20, 22], # 11-limit
[18, 30, 33, 55], # 11-limit
[20, 25, 30, 33], # 11-limit
[20, 40, 44, 55], # 11-limit
[22, 33, 36, 48], # 11-limit
[24, 40, 44, 55], # 11-limit
[25, 40, 80, 88], # 11-limit
[25, 50, 55, 66], # 11-limit
[30, 33, 55, 110], # 11-limit
[33, 36, 63, 70], # 11-limit
[33, 36, 72, 80], # 11-limit
[33, 44, 88, 96], # 11-limit
[33, 55, 60, 70], # 11-limit
[33, 55, 60, 72], # 11-limit
[33, 55, 60, 90], # 11-limit
[33, 55, 66, 72], # 11-limit
[33, 55, 110, 120], # 11-limit
[35, 40, 60, 66], # 11-limit
[35, 60, 66, 110], # 11-limit
[44, 48, 56, 63], # 11-limit
[44, 48, 72, 81], # 11-limit
[44, 55, 60, 70], # 11-limit
[44, 66, 72, 81], # 11-limit
[45, 50, 60, 66], # 11-limit
[45, 60, 80, 88], # 11-limit
[50, 60, 66, 99], # 11-limit
[54, 90, 99, 110], # 11-limit
[55, 88, 96, 168], # 11-limit
[55, 88, 110, 120], # 11-limit
[66, 77, 84, 147], # 11-limit
[66, 99, 110, 120], # 11-limit
[66, 110, 120, 135], # 11-limit
[66, 110, 165, 180], # 11-limit
[77, 84, 96, 192], # 11-limit
[77, 84, 144, 216], # 11-limit
[77, 132, 231, 252], # 11-limit
[88, 110, 120, 135], # 11-limit
[88, 110, 165, 180], # 11-limit
[99, 108, 180, 200], # 11-limit
[99, 110, 120, 128], # 11-limit
[99, 110, 120, 192], # 11-limit
[99, 110, 165, 180], # 11-limit
[121, 242, 264, 288], # 11-limit
[125, 200, 220, 352], # 11-limit
[165, 176, 192, 384], # 11-limit
[165, 220, 240, 384], # 11-limit
[175, 300, 330, 396], # 11-limit
[200, 225, 270, 297], # 11-limit
[200, 240, 264, 297], # 11-limit
[220, 385, 616, 672], # 11-limit
[231, 252, 280, 480], # 11-limit
[231, 385, 440, 480], # 11-limit
[363, 605, 660, 720], # 11-limit
[440, 495, 540, 864], # 11-limit
[605, 968, 1056, 1152], # 11-limit
[847, 924, 1056, 1152], # 11-limit
[847, 968, 1056, 1152], # 11-limit
[1815, 1936, 2112, 2304], # 11-limit
[24, 26, 52, 91], # 13-limit
[60, 65, 78, 91], # 13-limit
[60, 65, 78, 130], # 13-limit
[65, 70, 105, 168], # 13-limit
[65, 70, 140, 168], # 13-limit
[108, 117, 130, 260], # 13-limit
[117, 126, 140, 168], # 13-limit
[117, 126, 140, 280], # 13-limit
[144, 156, 195, 260], # 13-limit
[144, 156, 273, 455], # 13-limit
[168, 182, 195, 260], # 13-limit
[180, 195, 260, 312], # 13-limit
[195, 210, 245, 294], # 13-limit
[240, 260, 455, 728], # 13-limit
[288, 312, 364, 637], # 13-limit
[324, 351, 468, 520], # 13-limit
[360, 390, 455, 728], # 13-limit
[420, 455, 520, 624], # 13-limit
[420, 455, 780, 936], # 13-limit
[1188, 1287, 1430, 1560], # 13-limit
[1456, 1638, 1755, 1890], # 13-limit
When composing music generatively in frequency space, I think a person could do a lot worse than to bless all of these chords as good, then see what they can produce for chord progressions using these chords, and then decide yay or nay for each little generated progression, instead of having to decide yay or nay for each chord. And then you can do whatever you like given your harmonic skeleton - a four voice chorale, a wandering chromatic solo over a waltz figure, some cocktail piano comping, whatever.
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