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

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-Below are the sequences of [[equal temperament]]s in various [[subgroup]]s by [[TE error|TE absolute error]] (and [[TE relative error]], in '''bold'''), searched up to [[196608edo|196608]]. [[GPV]]s starting with 0 are skipped as they would meddle with the results otherwise. For readability reasons, equal temperaments smaller than 5 are not shown.
+Below are the sequences of [[equal temperament]]s in various [[subgroup]]s by [[TE error|TE absolute error]] (and [[TE relative error]], in '''bold'''), searched up to [[196608edo|196608]]. These sequences are obtained with the [https://github.com/FloraCanou/temperament_evaluator Temperament Evaluator]. For a method to iterate thru all GPVs, see [[Patent val/Properties]].
-These sequences are obtained with the [https://github.com/FloraCanou/temperament_evaluator Temperament Evaluator]. For a method to iterate thru all GPVs, see [[Patent val/Properties]].
+[[GPV]]s starting with 0 are ignored as they would otherwise meddle with the results. GPVs starting with 1, 2, 3, and 4 may be regarded as trivial, and are not shown.
+(WIP) While looking at these sequences, an important consideration is whether a temperament tunes the relevant intervals [[monotonic]]. If a temperament is meant to be used in the [[harmonic limit|''p''-prime-limit]], it is reasonable to request that the order of size for the [[odd limit|''p''-odd-limit]] should at least be kept. For this reason and for the sake of readability, each main sequence starts with the first temperament that passes the monotonicity test, with the entries before that point relegated to the exotemperaments databox below it. There are usually some more entries in the main sequence that fail the monotonicity test. These are noted with an apostrophe.
 ; 3-limit
@@ Line 10: / Line 12: @@
 ; 7-limit
-: {{EDOs| '''5''', 7d, 8d, 9, '''10''', '''12''', '''19''', 27, '''31''', 41, 53, '''72''', '''99''', '''171''', 441, 612, 935, 1106, 1277, 1407, 1547, 1578, 1718, 1848, 2019, 2684, 2783, 2954, '''3125''', 6520, 6691, 9816, '''11664''', 14789, '''18355''', 33144, 51499, 51670, 63334, 70025, 81689, '''84814''', '''103169''', … }}.
+: {{EDOs| '''5''', 7d*, 8d, 9, '''10''', '''12''', '''19''', 27, '''31''', 41, 53, '''72''', '''99''', '''171''', 441, 612, 935, 1106, 1277, 1407, 1547, 1578, 1718, 1848, 2019, 2684, 2783, 2954, '''3125''', 6520, 6691, 9816, '''11664''', 14789, '''18355''', 33144, 51499, 51670, 63334, 70025, 81689, '''84814''', '''103169''', … }}.
 ; 11-limit
-: {{EDOs| 5c, '''5''', '''7d''', '''8d''', '''9''', 10, 12e, '''12''', 15, 19e, 19, '''22''', 27e, '''31''', 41, 53, 58, '''72''', 118, 130, 152, 224, '''270''', '''342''', 612, 836, 1084, 1106, 1236, 1506, 1578, '''1848''', 2684, 3395, 3737, 4007, 4501, 4843, 5585, '''6079''', '''6691''', 12276, 12770, 14618, 14960, 21309, 25046, 26894, 33315, 39664, '''40006''', 47933, '''54624''', 81860, 94630, 96478, '''121524''', 176148, … }}.
+: {{EDOs| '''12''', 15, 19e*, 19, '''22''', 27e, '''31''', 41, 53, 58, '''72''', 118, 130, 152, 224, '''270''', '''342''', 612, 836, 1084, 1106, 1236, 1506, 1578, '''1848''', 2684, 3395, 3737, 4007, 4501, 4843, 5585, '''6079''', '''6691''', 12276, 12770, 14618, 14960, 21309, 25046, 26894, 33315, 39664, '''40006''', 47933, '''54624''', 81860, 94630, 96478, '''121524''', 176148, … }}.
+: {{Databox|Exotemperaments| 5c, '''5''', '''7d''', '''8d''', '''9''', 10, 12e }}
 ; 13-limit
-: {{EDOs| 5cf, 5f, 5, '''5e''', 7df, 7d, '''7''', '''8d''', '''9''', 10, 12, '''12f''', 14cf, 15, 17c, '''19e''', '''19''', 22, 26, '''27e''', 29, 31f, '''31''', '''41''', 46, '''53''', '''58''', '''72''', 87, 103, 111, 121, 130, 183, 190, 198, '''224''', '''270''', '''494''', 684, 764, 935, 954, 1178, 1236, 1448, '''1506''', '''2190''', '''2684''', 3395, 4079, 4349, 4843, '''5585''', '''6079''', 8269, 8539, 11664, 13112, 14348, '''14618''', 20203, 22887, 27236, 33315, 40276, 41584, 46355, 63163, 65062, 66558, 69242, '''73591''', '''81860''', '''87939''', '''96478''', 161530, 184417, … }}.
+: {{EDOs| 15, 17c, '''19e'''*, '''19''', 22*, 26, '''27e''', 29, 31f*, '''31''', '''41''', 46, '''53''', '''58''', '''72''', 87, 103, 111, 121, 130, 183, 190, 198, '''224''', '''270''', '''494''', 684, 764, 935, 954, 1178, 1236, 1448, '''1506''', '''2190''', '''2684''', 3395, 4079, 4349, 4843, '''5585''', '''6079''', 8269, 8539, 11664, 13112, 14348, '''14618''', 20203, 22887, 27236, 33315, 40276, 41584, 46355, 63163, 65062, 66558, 69242, '''73591''', '''81860''', '''87939''', '''96478''', 161530, 184417, … }}.
+: {{Databox|Exotemperaments| 5cf, 5f, 5, '''5e''', 7df, 7d, '''7''', '''8d''', '''9''', 10, 12, '''12f''', 14cf }}
 ; 17-limit
-: {{EDOs| 5cf, 5f, 5, 5g, '''5eg''', 7dfg, 7dg, 7, '''8d''', 9, 10e, '''10''', 12, 12f, 14cf, 15, 15g, 16, 17cg, '''19eg''', '''22''', '''26''', '''27eg''', 29g, '''31''', 38df, 41g, 41, '''46''', 58, '''72''', 103, 111, 121, 140, 171, 183, 217, 224, 270, 311, 354, 400, 422, 460, '''494''', 581, 742, 764, 814, 935, 954, 1178, 1236, 1395, '''1506''', 2000, 2414, 2460, '''3395''', 4573, 5455, 5809, 5855, 6079, '''7033''', 8539, 10428, 11934, 14348, '''16808''', '''20203''', 27236, 41584, 51940, 58973, 60973, 76275, 79176, 82354, 88209, '''102557''', 128215, 129793, 155451, 161530, 169799, 181733, … }}.
+: {{EDOs| '''31''', 38df, 41g*, 41, '''46''', 58, '''72''', 103, 111, 121, 140, 171, 183, 217, 224, 270, 311, 354, 400, 422, 460, '''494''', 581, 742, 764, 814, 935, 954, 1178, 1236, 1395, '''1506''', 2000, 2414, 2460, '''3395''', 4573, 5455, 5809, 5855, 6079, '''7033''', 8539, 10428, 11934, 14348, '''16808''', '''20203''', 27236, 41584, 51940, 58973, 60973, 76275, 79176, 82354, 88209, '''102557''', 128215, 129793, 155451, 161530, 169799, 181733, … }}.
+: {{Databox|Exotemperaments| 5cf, 5f, 5, 5g, '''5eg''', 7dfg, 7dg, 7, '''8d''', 9, 10e, '''10''', 12, 12f, 14cf, 15, 15g, 16, 17cg, '''19eg''', '''22''', '''26''', '''27eg''', 29g }}
 ; 19-limit
-: {{EDOs| 5cf, 5g, 5eg, '''5egh''', 7deefgh, 7dfgh, '''7''', '''8d''', '''8dhh''', '''9g''', '''9''', 10, 10h, 12e, 12, '''12f''', 14cf, 15, 15g, 17cgh, '''19egh''', 22, 22fh, 24, '''26''', '''27eg''', 29g, 31, 34dh, 38df, 41g, 41, '''46''', 50, 53, 58h, 68, 72h, '''72''', 94, 103h, 111, 121, 130, 140, 152fg, 159, 161, 183, 190g, 193, 212gh, '''217''', 243e, '''270''', 311, 400, 422, 460, 525, '''581''', '''742''', 935, 954h, '''1178''', '''1578''', 1889, '''2000''', '''2460''', 3178, '''3395''', 4349, 4501, 5498, 5527, 5809, 6079, 6961, 7527, '''8269''', '''8539''', 11934, 14348, 15854, 16066, '''16808''', '''20203''', 36269, 37011, 40770, 49039, 50434, 52434, 58973, 60973, 79176, 95984, 99162, 111407, 119365, 119946, '''128215''', 178338, … }}.
+: {{EDOs| 34dh, 38df, 41g*, 41, '''46'''*, 50, 53, 58h, 68, 72h*, '''72''', 94, 103h, 111, 121, 130, 140, 152fg, 159, 161, 183, 190g, 193, 212gh, '''217''', 243e, '''270''', 311, 400, 422, 460, 525, '''581''', '''742''', 935, 954h, '''1178''', '''1578''', 1889, '''2000''', '''2460''', 3178, '''3395''', 4349, 4501, 5498, 5527, 5809, 6079, 6961, 7527, '''8269''', '''8539''', 11934, 14348, 15854, 16066, '''16808''', '''20203''', 36269, 37011, 40770, 49039, 50434, 52434, 58973, 60973, 79176, 95984, 99162, 111407, 119365, 119946, '''128215''', 178338, … }}.
+: {{Databox|Exotemperaments| 5cf, 5g, 5eg, '''5egh''', 7deefgh, 7dfgh, '''7''', '''8d''', '''8dhh''', '''9g''', '''9''', 10, 10h, 12e, 12, '''12f''', 14cf, 15, 15g, 17cgh, '''19egh''', 22, 22fh, 24, '''26''', '''27eg''', 29g, 31 }}
 ; 23-limit
-: {{EDOs| 5cfi, 5g, 5eg, '''5egh''', 7deefghi, 7dfghi, 7, 8d, 8di, '''8dhhi''', 9gi, 9i, 9, 10e, 10, '''10h''', 12e, 12, 12f, '''12fi''', '''14cf''', 15, '''15g''', 18ehi, 19eghi, 22i, 22fh, 24, '''26i''', 27egi, '''29g''', 31, 34dh, 38dfi, 39dfgi, 41g, 41, 41i, 43, '''46''', 50, 53, 58hi, 62, 68, 72hi, 72i, 80, 87, '''94''', 111, 121i, 130, 140, 152fg, 159, 183, '''190g''', '''193''', '''217''', 243e, '''270''', '''282''', '''311''', 373g, 422, 525, 566g, '''581''', 718, 742i, 814, 935, 954h, 1106, 1178, 1308, 1323, 1395, 1506hi, '''1578''', 1889, 2000, '''2460''', 3178, 4038, 4349, 5144, 5395, 5638, 5783, 5958, 6079, 6269, 7315, '''8269''', 8539, 10539, '''11664''', 14348, '''16808''', 28472, 28742, 29053, 32231, 36269, 38189, 44907, 45861, 49039, 58973, 75781, 81176, 95242, 102557, 119365, 140149, '''148418''', 178338, … }}.
+: {{EDOs| 58hi, 62, 68*, 72hi*, 72i*, 80*, 87*, '''94''', 111, 121i, 130, 140, 152fg, 159, 183, '''190g''', '''193''', '''217''', 243e, '''270''', '''282''', '''311''', 373g, 422, 525, 566g, '''581''', 718, 742i, 814, 935, 954h, 1106, 1178, 1308, 1323, 1395, 1506hi, '''1578''', 1889, 2000, '''2460''', 3178, 4038, 4349, 5144, 5395, 5638, 5783, 5958, 6079, 6269, 7315, '''8269''', 8539, 10539, '''11664''', 14348, '''16808''', 28472, 28742, 29053, 32231, 36269, 38189, 44907, 45861, 49039, 58973, 75781, 81176, 95242, 102557, 119365, 140149, '''148418''', 178338, … }}.
+: {{Databox|Exotemperaments| 5cfi, 5g, 5eg, '''5egh''', 7deefghi, 7dfghi, 7, 8d, 8di, '''8dhhi''', 9gi, 9i, 9, 10e, 10, '''10h''', 12e, 12, 12f, '''12fi''', '''14cf''', 15, '''15g''', 18ehi, 19eghi, 22i, 22fh, 24, '''26i''', 27egi, '''29g''', 31, 34dh, 38dfi, 39dfgi, 41g, 41, 41i, 43, '''46''', 50, 53 }}
+----
 ; 29-limit