User:FloraC/Sequence of equal temperaments by error/Supplement: Difference between revisions
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; 3-limit: | ; 3-limit: | ||
: {{EDOs| 1b, 1, 2, 5, 12, 41, 53, 306, 665, 15601, 31867 }}… | : Tier-0: {{EDOs| 1b, 1, 2, 5, 12, 41, 53, 306, 665, 15601, 31867 }}… | ||
: Tier-1: {{EDOs| 3, 7, 17, 24, 29, 94, 106, 253, 359, 971, 1330 }}… | |||
: Tier-2: {{EDOs| 2bb, 4, 10, 147, 159, 200, 612, 1636, 1995 }}… | |||
; 5-limit: | ; 5-limit: | ||
: {{EDOs| | : Tier-0: {{EDOs| 1bcc, 1b, 1c, 2c, 2, 3, 7, 12, 19, 34, 53, 118, 441, 559, 612, 1171, 1783, 2513, 4296 }}… | ||
: Tier-1: {{EDOs| 1, 4, 5, 171, 730, 6809 }}… | |||
: Tier-2: {{EDOs| 15, 31, 99, 106, 1342, 3684 }}… | |||
; 7-limit: | ; 7-limit: | ||
: {{EDOs| 1bd, 1c, 2cd, 3d, 4, 5, 10, 12, 19, 31, 72, 99, 171, 3125, 11664, 18355 }}… | : Tier-0: {{EDOs| 1bccddd, 1bccd, 1bd, 1c, 2cd, 3d, 4, 5, 10, 12, 19, 31, 72, 99, 171, 3125, 11664, 18355 }}… | ||
: Tier-1: {{EDOs| 1b, 1, 2, 41, 270, 441, 2954 }}… | |||
: Tier-2: {{EDOs| 2d, 3, 7d, 8d, 9, 15, 22, 53, 130, 342, 612, 2019, 3566 }}… | |||
; 11-limit: | ; 11-limit: | ||
: {{EDOs| 1ce, 2cde, 2, 3de, 5, 7, 8d, 9, 12, 22, 31, 72, 270, 342, 1848, 6079, 6691 }}… | : Tier-0: {{EDOs| 1ce, 2cde, 2, 3de, 5, 7, 8d, 9, 12, 22, 31, 72, 270, 342, 1848, 6079, 6691 }}… | ||
; 13-limit: | ; 13-limit: | ||
: {{EDOs| 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 }}… | : Tier-0: {{EDOs| 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: | ; 17-limit: | ||
: {{EDOs| 4ef, 5eg, 8d, 10, 19eg, 22, 26, 27eg, 31, 46, 72, 494, 1506, 3395, 7033, 16808, 20203 }}… | : Tier-0: {{EDOs| 4ef, 5eg, 8d, 10, 19eg, 22, 26, 27eg, 31, 46, 72, 494, 1506, 3395, 7033, 16808, 20203 }}… | ||
; 19-limit: | ; 19-limit: | ||
: {{EDOs| 7, 8d, 8dhh, 9g, 9, 12f, 19egh, 26, 27eg, 46, 72, 217, 270, 581, 742, 1178, 1578, 2000, 2460, 3395, 8269, 8539, 16808, 20203 }}… | : Tier-0: {{EDOs| 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: | ; 23-limit: | ||
: {{EDOs| 14cf, 15g, 26i, 29g, 46, 94, 190g, 193, 217, 270, 282, 311, 581, 1578, 2460, 8269, 11664, 16808 }}… | : Tier-0: {{EDOs| 14cf, 15g, 26i, 29g, 46, 94, 190g, 193, 217, 270, 282, 311, 581, 1578, 2460, 8269, 11664, 16808 }}… | ||
; 29-limit: | ; 29-limit: | ||
: {{EDOs| 26i, 46, 58hi, 80, 140, 159, 183, 243e, 311, 954hj, 1578, 16808 }}… | : Tier-0: {{EDOs| 26i, 46, 58hi, 80, 140, 159, 183, 243e, 311, 954hj, 1578, 16808 }}… | ||
; 31-limit: | ; 31-limit: | ||
: {{EDOs| 46, 99efk, 103h, 183, 190g, 217, 311, 954hj, 4501, 16808 }}… | : Tier-0: {{EDOs| 46, 99efk, 103h, 183, 190g, 217, 311, 954hj, 4501, 16808 }}… | ||
; 7-limit: | ; 7-limit: | ||
: {{EDOs| 80k, 99efk, 103hl, 270, 270i, 311, 1395, 1920, 4501, 16808 }}… | : Tier-0: {{EDOs| 80k, 99efk, 103hl, 270, 270i, 311, 1395, 1920, 4501, 16808 }}… | ||
; sqrt (2).sqrt (3).5.7.11.13 subgroup: | ; sqrt (2).sqrt (3).5.7.11.13 subgroup: | ||
: {{EDOs| 10e, 10, 34d, 58, 72, 270, 2684, 13112 }}… | : Tier-0: {{EDOs| 10e, 10, 34d, 58, 72, 270, 2684, 13112 }}… | ||
; sqrt (2).sqrt (3).5.7.11.13.17 subgroup: | ; sqrt (2).sqrt (3).5.7.11.13.17 subgroup: | ||
: {{EDOs| 10e, 10, 34d, 58, 72, 742, 954, 2000, 2684, 10356, 10427, 16808 }}… | : Tier-0: {{EDOs| 10e, 10, 34d, 58, 72, 742, 954, 2000, 2684, 10356, 10427, 16808 }}… | ||
Revision as of 02:16, 9 June 2022
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…
- 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…