7-limit note groups

Two generator groups:

I found 42 of these generated by consonances in the octave; the
octave-containing groups are [2, c] for c a consonance, and the full
list is:

{{5/3, 7/4}, {8/5, 12/7}, {3/2, 5/2}, {16/7, 4/3}, {3, 7/4},
{8/7, 6/5}, {8/7, 4/3}, {3/2, 7/4}, {2, 7/3}, {6/5, 7/4}, {4/3, 7/4},
{8/7, 5/4}, {8/5, 4/3}, {2, 3}, {8/5, 7/4}, {2, 7/5}, {5/4, 4/3},
{3/2, 7/5}, {5/4, 7/4}, {2, 5/3}, {3/2, 8/7}, {2, 7}, {8/5, 8/3},
{5/3, 7/3}, {5/3, 8/7}, {2, 5}, {12/5, 12/7}, {7/6, 5/4}, {5/4, 12/7},
{6/5, 12/7}, {5/3, 12/7}, {3/2, 10/7}, {7/6, 6/5}, {16/7, 8/5},
{7/5, 4/3}, {5/2, 7/4}, {5/3, 7/6}, {4/3, 10/7}, {8/5, 8/7},
{8/5, 3/2}, {8/5, 7/6}, {3/2, 5/4}}

Three generator groups:

There are 35 of thise:

{{16/7, 8/5, 8/3}, {8/5, 4/3, 7/4}, {2, 5/3, 7/3}, {16/7, 5/4, 4/3},
{16/7, 16/5, 4/3}, {2, 5, 7}, {3, 5/2, 7/4}, {2, 3, 7/5},
{8/5, 32/7, 8/3}, {3/2, 5/2, 7/2}, {8/5, 8/7, 4/3}, {3/2, 5/4, 7/4},
{2, 5, 7/3}, {2, 3, 5}, {8/5, 8/3, 7/4}, {8/5, 3/2, 8/7}, {2, 3, 7},
{16/7, 8/5, 4/3}, {8/5, 3/2, 7/4}, {5/4, 4/3, 7/4}, {3/2, 5/2, 8/7},
{4, 5/3, 7/3}, {3, 8/5, 7/4}, {8/5, 8/7, 8/3}, {4, 7, 10},
{2, 7, 5/3}, {8/7, 5/4, 4/3}, {3, 5/4, 7/4}, {3/2, 5/2, 7/4},
{5/2, 4/3, 7/4}, {3, 5, 7/4}, {3, 4, 7}, {3/2, 8/7, 5/4}, {4, 6, 10},
{16/7, 8/5, 3/2}}

Four generator groups:

{{2, 3, 5, 7}, {4, 6, 7, 10}, {3, 4, 5, 7}, {4, 6, 10, 14},
{3, 4, 7, 10}, {3, 5, 8, 14}}

There's a lot of unexplored territory here, and the four generator
groups seem particular noteworthy from that point of view. One way to
get subgroups one might find interesting is to take as generators a
chord you like; that way you are sure of having at least that chord in
your repertoire. For instance, if you are fond of 12:14:17:24, the
subgroup generated by {7/6, 17/12, 2} has TM basis {2, 5/3, 17/3},
adding a 3 or 3/2 to the mix gives {2,3,7,17}, with 17-limit diminised
seventh chords and subminor and supermajor triads both. Nonoctave
groups can be abundently supplied with chords as well; if you like a
closed chord you could try {5/4, 3/2, 7/4}, or you might prefer {3/2,
7/4, 5/2}, etc.