User:FloraC/Sequence of equal temperaments by error/Supplement: Difference between revisions

Revision as of 16:56, 24 November 2022

For a method to iterate thru all GPVs, see Patent val/Properties.

The tier of an equal temperament is defined as the number of GPVs before it that is tuned more efficient than it. Efficiency can be determined in various ways, but the most common way is the TE relative error.

GPVs starting with 0 are not accounted as they would meddle with the results. For readability reasons, results are shown in the range of 5 and 16808.

3-limit: Tier-0: 5, 12, 41, 53, 306, 665, 15601…; Tier-1: 7, 17, 24, 29, 94, 106, 253, 359, 971, 1330, 14936, 16266…; Tier-2: 10, 147, 159, 200, 612, 1636, 1995, 14271…; Tier-3: 65, 2301, 2660, 13606…; Tier-4: 8, 9, 19, 36, 82, 412, 1024, 2966, 3325, 12941…; Tier-5: 6b, 6, 14, 22, 212, 559, 718, 1277, 3631, 3990, 12276…

5-limit: Tier-0: 7, 12, 19, 34, 53, 118, 441, 559, 612, 1171, 1783, 2513, 4296…; Tier-1: 5, 171, 730, 6809, 8592, 16572…; Tier-2: 15, 31, 99, 106, 1342, 3684, 11105, 12276…; Tier-3: 10, 22, 46, 152, 236, 270, 289, 3125, 5467, 7980…; Tier-4: 8, 9, 41, 224, 323, 494, 2954…; Tier-5: 5c, 24, 27, 87, 205, 388, 1224, 1901, 9763, 12888…

7-limit: Tier-0: 5, 10, 12, 19, 31, 72, 99, 171, 3125, 11664…; Tier-1: 41, 270, 441, 2954, 6691, 14789…; Tier-2: 7d, 8d, 9, 15, 22, 53, 130, 342, 612, 2019, 3566…; Tier-3: 7, 27, 140, 1848, 3296, 11835…; Tier-4: 14c, 46, 152, 301, 323, 3395, 6520…; Tier-5: 5, 58, 118, 494, 513, 783, 1106, 3737, 4973, 5144, 6250, 9816, 15230…

11-limit: Tier-0: 5, 7, 8d, 9, 12, 22, 31, 72, 270, 342, 1848, 6079, 6691…; Tier-1: 7, 14c, 15, 27e, 41, 152, 1578, 8269, 14618, 14960…; Tier-2: 19, 46, 58, 118, 224, 494, 612, 5585, 12276, 12770…; Tier-3: 5e, 10, 19e, 130, 1106, 1236, 2190, 6349, 7927…; Tier-4: 53, 80, 87, 311, 764, 836, 2684, 4843, 6421…; Tier-5: 99e, 183, 400, 472, 684, 742, 8539…

13-limit: Tier-0: 5e, 7, 8d, 9, 12f, 19e, 19, 27e, 31, 41, 53, 58, 72, 224, 270, 494, 1506, 2190, 2684, 5585, 6079, 14618…; Tier-1: 5, 7d, 15, 87, 130, 8269, 8539…; Tier-2: 10, 34d, 46, 198, 311, 684, 954, 1236…; Tier-3: 7df, 29, 103, 581, 1178, 3395, 7033…; Tier-4: 5f, 10e, 14cf, 111, 121, 140, 190, 764, 1448, 2460, 11664, 13112…; Tier-5: 22, 26, 152f, 183, 373, 422, 742, 1012, 2954…

17-limit: Tier-0: 5eg, 8d, 10, 19eg, 22, 26, 27eg, 31, 46, 72, 494, 1506, 3395, 7033, 16808, 20203…; Tier-1: 5g, 7dg, 7, 9, 12f, 41, 58, 111, 140, 183, 270, 581, 742, 764, 954, 1178, 1236, 1578, 2460, 8539, 14348…; Tier-2: 7dfg, 9g, 22f, 29g, 94, 103, 121, 224, 311, 1817, 5855, 8269…; Tier-3: 14cf, 15g, 17cg, 50, 53, 87, 217, 422, 460, 814, 2000, 2684, 4573, 10428…; Tier-4: 7g, 12, 34d, 400, 6079…; Tier-5: 10e, 15, 282, 354, 1889, 9033…

19-limit: Tier-0: 5egh, 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-1: 7dfgh, 10h, 14cf, 15g, 24, 29g, 31, 41, 53, 58h, 94, 111, 311…; Tier-2: 7dgh, 12, 50, 103h, 121, 140, 183, 354, 422, 11934…; Tier-3: 22fh, 72h, 99ef, 190g, 193, 243e, 460, 935, 6961, 11664…; Tier-4: 5cf, 5g, 5eg, 10, 15, 34dh, 118f, 282, 954h, 1889, 4349, 6079…; Tier-5: 22, 43, 80, 87, 130, 224, 373g, 400, 643, 3178, 3920, 4501…

23-limit: Tier-0: 14cf, 15g, 26i, 29g, 46, 94, 190g, 193, 217, 270, 282, 311, 581, 1578, 2460, 8269, 11664, 16808…; Tier-1: 15, 27egi, 31, 50, 72i, 130, 183, 243e, 373g, 422, 954h, 1889…; Tier-2: 22fh, 34dh, 53, 72, 80, 111, 140, 152fg, 159, 525, 935, 1920, 2000, 3178, 8539…; Tier-3: 19eghi, 58hi, 99ef, 121i, 624, 814, 4038, 4349, 6079, 6269…; Tier-4: 27eg, 68, 718, 742i, 14348…; Tier-5: 19egh, 19, 24, 41i, 43, 3395i, 7315…

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…

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

2.3.5.11 subgroup: Tier-0: 7, 65, 152, 342, 494, 1171, 11105, 12276…; Tier-1: 5, 5e, 8, 9, 12e, 12, 15, 22, 31, 53, 72, 87, 118, 270, 677, 1665, 2342, 9934…; Tier-2: 19, 34, 183, 407, 559, 5520, 6691…; Tier-3: 14, 24, 335, 612, 829, 901, 1513, 2836, 3513, 13347…; Tier-4: 41, 46, 159, 224, 2684, 7862, 8763…; Tier-5: 10, 19e, 137, 217, 836, 1019, 2072, 3855…

sqrt (2).sqrt (3).5.7.11.13 subgroup: Tier-0: 10e, 10, 34d, 58, 72, 270, 2684, 13112…; Tier-1: 14cf, 130, 954, 10428, 16808…; Tier-2: 24, 38df, 68, 198, 742, 814, 2000, 2954, 14124…; Tier-3: 62, 140, 612, 1012, 1730…; Tier-4: 14c, 34, 96d, 1084, 3696, 3768, 10158, 10356, 12158, 13040…; Tier-5: 10f, 24d, 202, 212, 342f, 13854…

sqrt (2).sqrt (3).5.7.11.13.17 subgroup: Tier-0: 10e, 10, 34d, 58, 72, 742, 954, 2000, 2684, 10356, 10428, 16808…; Tier-1: 14cf, 24, 68, 130, 140, 270, 814…; Tier-2: 38df, 212g, 400, 2414, 3638, 12842…; Tier-3: 10eg, 14c, 34, 58g, 130g, 328, 414, 684, 11170, 12428, 13112, 13170…; Tier-4: 14cfgg, 62, 96d, 198g, 342f, 882…; Tier-5: …

@@ Line 58: / Line 58: @@
 : Tier-2: {{EDOs| 7dgh, 12, 50, 103h, 121, 140, 183, 354, 422, 11934 }}…
 : Tier-3: {{EDOs| 22fh, 72h, 99ef, 190g, 193, 243e, 460, 935, 6961, 11664 }}…
-: Tier-4: {{EDOs| 5cf, 5g, 5eg, 10, 15, 34dh, 118f, 282, 954, 1889, 4349, 6079 }}…
+: Tier-4: {{EDOs| 5cf, 5g, 5eg, 10, 15, 34dh, 118f, 282, 954h, 1889, 4349, 6079 }}…
 : Tier-5: {{EDOs| 22, 43, 80, 87, 130, 224, 373g, 400, 643, 3178, 3920, 4501 }}…
 ; 23-limit:
 : Tier-0: {{EDOs| 14cf, 15g, 26i, 29g, 46, 94, 190g, 193, 217, 270, 282, 311, 581, 1578, 2460, 8269, 11664, 16808 }}…
+: Tier-1: {{EDOs| 15, 27egi, 31, 50, 72i, 130, 183, 243e, 373g, 422, 954h, 1889 }}…
+: Tier-2: {{EDOs| 22fh, 34dh, 53, 72, 80, 111, 140, 152fg, 159, 525, 935, 1920, 2000, 3178, 8539 }}…
+: Tier-3: {{EDOs| 19eghi, 58hi, 99ef, 121i, 624, 814, 4038, 4349, 6079, 6269 }}…
+: Tier-4: {{EDOs| 27eg, 68, 718, 742i, 14348 }}…
+: Tier-5: {{EDOs| 19egh, 19, 24, 41i, 43, 3395i, 7315 }}…
 ; 29-limit:

User:FloraC/Sequence of equal temperaments by error/Supplement: Difference between revisions

Revision as of 16:56, 24 November 2022

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