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

1b, 1, 2, 5, 12, 41, 53, 306, 665, 15601, 31867…

5-limit

1, 1c, 2c, 2, 3, 7, 12, 19, 34, 53, 118, 441, 559, 612, 1171, 1783, 2513, 4296…

7-limit

1bd, 1c, 2cd, 3d, 4, 5, 10, 12, 19, 31, 72, 99, 171, 3125, 11664, 18355…

11-limit

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

13-limit

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

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

19-limit

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

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

29-limit

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

31-limit

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

7-limit

80k, 99efk, 103hl, 270, 270i, 311, 1395, 1920, 4501, 16808…

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

10e, 10, 34d, 58, 72, 270, 2684, 13112…

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

10e, 10, 34d, 58, 72, 742, 954, 2000, 2684, 10356, 10427, 16808…