User:FloraC/Sequence of equal temperaments by error/Supplement

For a method to iterate thru all GPVs, see Patent val/Properties. GPVs starting with a zero are excluded as they would meddle with the results.

The tier of an equal temperament is defined as the number of GPVs before it that is tuned more efficient than it.

3-limit

Tier-0: 1b, 1, 2, 5, 12, 41, 53, 306, 665, 15601, 31867…

Tier-1: 3, 7, 17, 24, 29, 94, 106, 253, 359, 971, 1330…

Tier-2: 2bb, 4, 10, 147, 159, 200, 612, 1636, 1995…

5-limit

Tier-0: 1bcc, 1b, 1c, 2c, 2, 3, 7, 12, 19, 34, 53, 118, 441, 559, 612, 1171, 1783, 2513, 4296…

Tier-1: 1, 4, 5, 171, 730, 6809…

Tier-2: 15, 31, 99, 106, 1342, 3684…

7-limit

Tier-0: 1bccddd, 1bccd, 1bd, 1c, 2cd, 3d, 4, 5, 10, 12, 19, 31, 72, 99, 171, 3125, 11664, 18355…

Tier-1: 1b, 1, 2, 41, 270, 441, 2954…

Tier-2: 2d, 3, 7d, 8d, 9, 15, 22, 53, 130, 342, 612, 2019, 3566…

11-limit

Tier-0: 1ce, 2cde, 2, 3de, 5, 7, 8d, 9, 12, 22, 31, 72, 270, 342, 1848, 6079, 6691…

13-limit

Tier-0: 2cde, 2f, 3, 3de, 3def, 4ef, 5e, 7, 8d, 9, 12f, 19e, 19, 27e, 31, 41, 53, 58, 72, 224, 270, 494, 1506, 2190, 2684, 5585, 6079, 14618…

17-limit

Tier-0: 4ef, 5eg, 8d, 10, 19eg, 22, 26, 27eg, 31, 46, 72, 494, 1506, 3395, 7033, 16808, 20203…

19-limit

Tier-0: 7, 8d, 8dhh, 9g, 9, 12f, 19egh, 26, 27eg, 46, 72, 217, 270, 581, 742, 1178, 1578, 2000, 2460, 3395, 8269, 8539, 16808, 20203…

23-limit

Tier-0: 14cf, 15g, 26i, 29g, 46, 94, 190g, 193, 217, 270, 282, 311, 581, 1578, 2460, 8269, 11664, 16808…

29-limit

Tier-0: 26i, 46, 58hi, 80, 140, 159, 183, 243e, 311, 954hj, 1578, 16808…

31-limit

Tier-0: 46, 99efk, 103h, 183, 190g, 217, 311, 954hj, 4501, 16808…

7-limit

Tier-0: 80k, 99efk, 103hl, 270, 270i, 311, 1395, 1920, 4501, 16808…

sqrt (2).sqrt (3).5.7.11.13 subgroup

Tier-0: 10e, 10, 34d, 58, 72, 270, 2684, 13112…

sqrt (2).sqrt (3).5.7.11.13.17 subgroup

Tier-0: 10e, 10, 34d, 58, 72, 742, 954, 2000, 2684, 10356, 10427, 16808…