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

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; 2.3.5.7.11.13.19 subgroup
; 2.3.5.7.11.13.19 subgroup
: {{EDOs| 22fh, 24*, 26*, '''27e''', 31, 34dh, 38df, 41f*, '''41''', 50, '''53''', 58h, '''72''', 87, 94, 103h, 111, 121, '''130''', '''152f''', 190, 217, 224, '''270''', 552, 581, 684h, 742, 935, 954h, 1012, 1178, 1308, 1448, 1578, 1730, 2000, '''2190''', 3125, 3395, 3768, 4079, 4190, 4349, 4771, 5585, '''6079''', '''8269''', '''8539''', 14618, 16808, … }}.  
: {{EDOs| '''27e''', 31, 34dh*, 38df*, 41f*, '''41''', 50*, '''53''', 58h, '''72''', 87, 94, 103h, 111, 121, '''130''', '''152f''', 190, 217, 224, '''270''', 552, 581, 684h, 742, 935, 954h, 1012, 1178, 1308, 1448, 1578, 1730, 2000, '''2190''', 3125, 3395, 3768, 4079, 4190, 4349, 4771, 5585, '''6079''', '''8269''', '''8539''', 14618, 16808, 20203, 28472, 35999, 44538, 46355, 47663, 47933, 52434, 56202, 58973, 60973, 69242, 85255, 89445, 94972, '''115175''', 128215, '''148418''', '''176148''', '''184417''', … }}.  


: {{Databox|Exotemperaments*| 5cf, 5f, 5, '''5eh''', 7dfh, 7dh, '''7''', 8d, 8dhh, '''9''', 12e, 12, 12f, 14cf, '''15''', 19eh, 22 }}
: {{Databox|Exotemperaments*| 5cf, 5f, 5, '''5eh''', 7dfh, 7dh, '''7''', 8d, 8dhh, '''9''', 12e, 12, 12f, 14cf, '''15''', 19eh, 22, 22fh, 24, 26 }}
: <nowiki>*</nowiki> Monotonicity considered for {1, 3, 5, 7, 9, 11, 13, 15, 19}  
: <nowiki>*</nowiki> Monotonicity considered for {1, 3, 5, 7, 9, 11, 13, 15, 19, 21}  


; 2.3.5.7.11.13.17.23 subgroup
; 2.3.5.7.11.13.17.23 subgroup
: {{EDOs| '''31''', 34d*, 39dfgi*, 41g* 41* 41i*, 43*, '''46''', 58i, 68*, '''72i'''* (72), 94, 103, 111, 121i, 130, '''140''', 159, '''183''', 217, 224, 243e, 270, '''311''', 373g, 422, '''494''', 581, 684, 742i, '''764''', 814, 954, 1075, 1236, 1506i, '''1578''', 1889, 2414, '''2460''', 3696, 3809, 3855, 3992, 4038, 4349, 4573, 5455, 6079, '''7033''', 11664, 13112, 14348, '''16808''', … }}.  
: {{EDOs| '''31''', 34d, 39dfgi*, 41g* 41* 41i*, 43*, '''46''', 58i, 68, '''72i'''* (72), 94, 103, 111, 121i, 130, '''140''', 159, '''183''', 217, 224, 243e, 270, '''311''', 373g, 422, '''494''', 581, 684, 742i, '''764''', 814, 954, 1075, 1236, 1506i, '''1578''', 1889, 2414, '''2460''', 3696, 3809, 3855, 3992, 4038, 4349, 4573, 5455, 6079, '''7033''', 11664, 13112, 14348, '''16808''', 29053, 29236, 31156, 32231, 35132, 35505, 36269, 38189, 41584, 45861, 49039, 51940, 58973, 68748, 75781, 85749, 88209, '''102557''', 161530, 178338, … }}.  


: {{Databox|Exotemperaments*| 5cfi, 5, 5g, '''5eg''', 7dfgi, 7dgi, 7, 8d, '''8di''', 10e, '''10''', 12e, 12, 12f, 12fi, 14cf, 15, 15g, 16, 17cg, 19egi, 19, 22i, 22, '''22f''', '''26i''', 27egi, '''29g''' }}
: {{Databox|Exotemperaments*| 5cfi, 5, 5g, '''5eg''', 7dfgi, 7dgi, 7, 8d, '''8di''', 10e, '''10''', 12e, 12, 12f, 12fi, 14cf, 15, 15g, 16, 17cg, 19egi, 19, 22i, 22, '''22f''', '''26i''', 27egi, '''29g''' }}
: <nowiki>*</nowiki> Monotonicity considered for {1, 3, 5, 7, 9, 11, 13, 15, 17, 21, 23}  
: <nowiki>*</nowiki> Monotonicity considered for {1, 3, 5, 7, 9, 11, 13, 15, 17, 23}  


----
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Revision as of 16:36, 23 May 2026

< Sequence of equal temperaments by error
2.3.5.11 subgroup
7, 12, 15, 19, 22, 31, 34, 41, 46, 53, 65, 87, 118, 152, 224, 270, 335, 342, 494, 677, 1019, 1171, 3855, 4349, 5026, 5520, 6691, 7862, 8763, 9934, 11105, 12276, 35657, 41177, 42348, 53453, 54624, 66900, 121524, 149931, 161036, 173312, 192279, …
Exotemperaments*
5c, 5, 5e
* Monotonicity considered for {1, 3, 5, 9, 11}
2.3.7.11 subgroup
5, 9, 10, 12, 14, 17, 31, 41, 58, 63, 72, 94, 118, 130, 135, 342, 477, 670, 701, 836, 877, 1012, 1506, 1713, 1848, 4573, 4708, 6556, 11264, 17478, 19326, 22186, 24034, 28742, 35298, 59332, 64040, 94630, 123372, 158670, …
* Monotonicity considered for {1, 3, 7, 9, 11}
2.3.5.13 subgroup
5, 7, 10, 12, 15, 19, 34, 53, 130, 140, 164, 183, 217, 270, 354, 388, 407, 441, 494, 848, 901, 1289, 1342, 2901, 3395, 3802, 4243, 4737, 5638, 6079, 11717, 15960, 17302, 22039, 23381, 35098, 45420, 57137, 80518, 137655, 143734, 189154, …
Exotemperaments*
5f
* Monotonicity considered for {1, 3, 5, 9, 13}
2.3.7.13 subgroup
5, 7, 9, 10, 17, 26, 27, 36, 77, 94, 130, 207, 234, 270, 347, 364, 441, 477, 571, 1048, 1412, 1983, 5144, 6079, 6556, 7127, 8539, 9110, 20203, 49516, 58055, 67165, 69148, 78258, 87368, 98461, 107571, 127774, 179750, 190843, …
Exotemperaments*
5f
* Monotonicity considered for {1, 3, 7, 9, 13}
2.3.5.7.11.13.19 subgroup
27e, 31, 34dh*, 38df*, 41f*, 41, 50*, 53, 58h, 72, 87, 94, 103h, 111, 121, 130, 152f, 190, 217, 224, 270, 552, 581, 684h, 742, 935, 954h, 1012, 1178, 1308, 1448, 1578, 1730, 2000, 2190, 3125, 3395, 3768, 4079, 4190, 4349, 4771, 5585, 6079, 8269, 8539, 14618, 16808, 20203, 28472, 35999, 44538, 46355, 47663, 47933, 52434, 56202, 58973, 60973, 69242, 85255, 89445, 94972, 115175, 128215, 148418, 176148, 184417, ….
Exotemperaments*
5cf, 5f, 5, 5eh, 7dfh, 7dh, 7, 8d, 8dhh, 9, 12e, 12, 12f, 14cf, 15, 19eh, 22, 22fh, 24, 26
* Monotonicity considered for {1, 3, 5, 7, 9, 11, 13, 15, 19, 21}
2.3.5.7.11.13.17.23 subgroup
31, 34d, 39dfgi*, 41g* 41* 41i*, 43*, 46, 58i, 68, 72i* (72), 94, 103, 111, 121i, 130, 140, 159, 183, 217, 224, 243e, 270, 311, 373g, 422, 494, 581, 684, 742i, 764, 814, 954, 1075, 1236, 1506i, 1578, 1889, 2414, 2460, 3696, 3809, 3855, 3992, 4038, 4349, 4573, 5455, 6079, 7033, 11664, 13112, 14348, 16808, 29053, 29236, 31156, 32231, 35132, 35505, 36269, 38189, 41584, 45861, 49039, 51940, 58973, 68748, 75781, 85749, 88209, 102557, 161530, 178338, ….
Exotemperaments*
5cfi, 5, 5g, 5eg, 7dfgi, 7dgi, 7, 8d, 8di, 10e, 10, 12e, 12, 12f, 12fi, 14cf, 15, 15g, 16, 17cg, 19egi, 19, 22i, 22, 22f, 26i, 27egi, 29g
* Monotonicity considered for {1, 3, 5, 7, 9, 11, 13, 15, 17, 23}
2.3.5.7.11.13.19.29 subgroup
41, 53*, 58h, 72, 77, 80, 87* (94), 99ef, 103h* (113, 118f, 118), 121, 130, 140, 152fj, 159, 183, 190, 198, 217, 224, 243e, 270j*, 270, 422, 472, 494, 494h, 552, 590, 612, 684h, 692, 742, 795, 908, 935, 954hj, 1106, 1205, 1308, 1448, 1578, 1920, 2000, 2190, 3395, 4190, 4501, 5585, 6079, 6539, 7527, 8539, 10729, 11934, 12618, 13040, 14124, 14618, 16808, ….
Exotemperaments*
5cf, 5f, 5, 5ehj, 7deefhjj, 7dfhjj, 7dh, 7, 8d, 8dhhjj, 9j, 10h, 12e, 12, 12f, 12fj, 14cfjj, 15, 19eh, 22, 22fh, 24, 26, 27ej, 31j, 31, 34dhj, 38dfj, 41f
* Monotonicity considered for {1, 3, 5, 7, 9, 11, 13, 15, 19, 21, 27, 29} (omission of 25 is intentional)
2.3.5.7.11.13.19.29.31 subgroup
58hk, 72*, 77*, 80k*, 87*, 99efk, 103h* (118), 121k, 130j*, 130, 152fj, 159k* (159), 166*, 183, 190, 217, 224, 270k*, 270, 311, 422, 525, 540, 552, 612, 692k, 718, 742, 908, 954hj, 1178, 1205, 1308, 1759, 1817h, 1920, 2159, 2190, 2684, 2901, 3125, 3395k, 4190, 4501, 5809, 6539, 7527, 8539, 11664j, 12307, 12618, 14124, 16066, 16808, …
Exotemperaments*
5cfk, 5f, 5, 5ehj, 7deeefhjjk, 7dfhjjk, 7k, 7, 8d, 9jk, 10h, 12e, 12fk, 12fjk, 14cfjj, 15, 15k, 19ehkk, 19eh, 19, 22, 22fh, 24, 26k, 27e, 27ej, 31, 34dhk, 34dhjk, 38dfj, 41f, 41, 53k
* Monotonicity considered for {1, 3, 5, 7, 9, 11, 13, 15, 19, 21, 25, 27, 29, 31}
sqrt (2).sqrt (3).5.7.11.13 subgroup
Relative: 10e, 10, 34d, 58, 72, 270, 2684, 13112, ….
sqrt (2).sqrt (3).5.7.11.13.17 subgroup
Relative: 10e, 10, 34d, 58, 72, 742, 954, 2000, 2684, 10356, 10428, 16808, ….
sqrt (2).sqrt (3).5.7.11.13.17.19.23 subgroup
Relative: 14cf, 34dh, 58hi, 72i, 130, 270, 718, 742i, 814, 954h, 2000, 4038, 12770, 16808, ….
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