Sequence of equal temperaments by error: Difference between revisions

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Below are the sequences of [[equal temperament]]s by [[TE error|TE absolute error]] (and [[TE relative error]], in '''bold''') in various [[subgroup]]s, 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 [[GPV]]s, see [[Patent val/Properties]].  
Below are the sequences of [[equal temperament]]s by [[TE error|TE absolute error]] (and [[TE relative error]], in '''bold''') in various [[subgroup]]s, searched up to [[196608edo|196608]]. These sequences are obtained with the [https://github.com/FloraCanou/temperament_evaluator Temperament Evaluator]. For a method to iterate through all [[GPV]]s, see [[Patent val/Properties]].  


GPVs 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.  
GPVs 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.  


While looking at these sequences, an important consideration is whether a temperament tunes the relevant intervals [[diamond monotone|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.  
While looking at these sequences, an important consideration is whether a temperament tunes the relevant intervals [[diamond monotone|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, which are noted with an apostrophe. Alternatives that pass the test but have a higher error than a previous entry are noted in parentheses.  


; 3-limit
; 3-limit
Line 19: Line 19:


; 13-limit
; 13-limit
: {{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, … }}.  
: {{EDOs| (14c), 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 }}
: {{Databox|Exotemperaments| 5cf, 5f, 5, '''5e''', 7df, 7d, '''7''', '''8d''', '''9''', 10, 12, '''12f''', 14cf }}


; 17-limit
; 17-limit
: {{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, … }}.  
: {{EDOs| (19), '''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, … }}.  
: {{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 }}
: {{Databox|Exotemperaments| 5cf, 5f, 5, 5g, '''5eg''', 7dfg, 7dg, 7, '''8d''', 9, 10e, '''10''', 12, 12f, 14cf, 15, 15g, 16, 17cg, '''19eg''' }}


; 19-limit
; 19-limit
Line 31: Line 31:


; 23-limit
; 23-limit
: {{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, … }}.  
: {{EDOs| (53e), 58hi, 62, 68* (68e), 72hi* 72i* (72), 80*, (84), 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 }}
: {{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
; 29-limit
: {{EDOs| 99ef, 103h*, 113*, 118, 121i, 130, 140h*, '''140''', 152fgj, '''159''', '''183''', 217, '''243e''', 270, 282, '''311''', 422, 472, 494h, 525, 535, 540, 554e, 566gj, 571, 581, 581j, 624j, 653, 692i, 718, 742i, 814, 882, 908, '''954hj''', 1106, 1282, 1308, 1323, 1395, '''1578''', 1920, 2000, 2460, 2742, 3041, 3178, 3395i, 4038j, 4190g, 4349, 4501, 5395, 5783, 6079, 6893, 7315, 7361, 7527, 7847j, 8269, 8539, 9204, 9447, 9934, 10729, 11664j, 11934, 12245, 13112, 14066, 15230, '''16808''', 28742, 29053, 36269, 45861, 48945, 52704, 53077, 56513, 58392, 58973, 60973, 65322, 67242, 69512, 78716, 81176j, 83096, 87445, 92782, 102557, 119365, '''148418''', … }}.  
: {{EDOs| 72, 77, '''80'''*, 87*, 94j* 94*, 99ef, 103h*, 113*, 118, 121i, 130, 140h*, '''140''', 152fgj, '''159''', '''183''', 217, '''243e''', 270, 282, '''311''', 422, 472, 494h, 525, 535, 540, 554e, 566gj, 571, 581, 581j, 624j, 653, 692i, 718, 742i, 814, 882, 908, '''954hj''', 1106, 1282, 1308, 1323, 1395, '''1578''', 1920, 2000, 2460, 2742, 3041, 3178, 3395i, 4038j, 4190g, 4349, 4501, 5395, 5783, 6079, 6893, 7315, 7361, 7527, 7847j, 8269, 8539, 9204, 9447, 9934, 10729, 11664j, 11934, 12245, 13112, 14066, 15230, '''16808''', 28742, 29053, 36269, 45861, 48945, 52704, 53077, 56513, 58392, 58973, 60973, 65322, 67242, 69512, 78716, 81176j, 83096, 87445, 92782, 102557, 119365, '''148418''', … }}.  
: {{Databox|Exotemperaments| 5cfi, 5egj, '''5eghj''', 7deefghijj, 7dfghijj, 7, 8di, 8dhhijj, 9gij, 9, 10ej, 10, '''10h''', 12de, 12e, '''12fij''', '''14cfjj''', '''15''', '''15g''', 17cgh, 18ehij, 19eghi, 22i, 22h, 22fh, '''26i''', 29gj, 29g, 31j, 31, 34dh, 34dhj, 38dfij, 39dfgij, 41g, 41, 43, '''46''', 50, 53, '''58hi''', 62, 68j, 72hij, 72ij, 72, 77, '''80''', 87, 94j, 94 }}
: {{Databox|Exotemperaments| 5cfi, 5egj, '''5eghj''', 7deefghijj, 7dfghijj, 7, 8di, 8dhhijj, 9gij, 9, 10ej, 10, '''10h''', 12de, 12e, '''12fij''', '''14cfjj''', '''15''', '''15g''', 17cgh, 18ehij, 19eghi, 22i, 22h, 22fh, '''26i''', 29gj, 29g, 31j, 31, 34dh, 34dhj, 38dfij, 39dfgij, 41g, 41, 43, '''46''', 50, 53, '''58hi''', 62, 68j, 72hij, 72ij }}


; 31-limit
; 31-limit
: {{EDOs| '''99efk''', '''103h'''*, 121ik, 130j*, 130, 140k*, 140, 149, 152fgj, 159k*, 167hijk*, 181*, 183k*, '''183''', '''190g''', '''217''', 243ek*, 270, '''311''', 388, 422, 525, 566gj, 571, 624jk, 639hj, 643ijk, 653, 692ik, 718, 742i, 863efgjk, 882, 908, '''954hj''', 1205g, 1289, 1308, 1395, 1578, 1920, 2311, 2460j, 2460, 2684, 2742k, 2901, 3041, 3323, 3395ik, 3759, 4038j, 4349, '''4501''', 5395, 5455, 5809, 6079, 6219, 6893, 7315, 7361, 7527, 8539, 9447, 9934, 11353, 11664j, 12245, 13823, 14066k, 14348, 15112, '''16808''', 29053, 31920, 32231, 34691, 36269, 40078, 47309, 48514, 48945, 50434, 51499, 52704, 58973, 64368, 65322, 67242, 78716, 81176j, 83096, 92782, 109590, 119365, 131610, '''148418''', … }}.  
: {{EDOs| '''99efk''', '''103h'''*, 121ik, 130j*, 130, 140k*, 140, 149, 152fgj, 159k* (159), 167hijk*, 181*, 183k*, '''183''', '''190g''', '''217''', 243ek* (243e), 270, '''311''', 388, 422, 525, 566gj, 571, 624jk, 639hj, 643ijk, 653, 692ik, 718, 742i, 863efgjk, 882, 908, '''954hj''', 1205g, 1289, 1308, 1395, 1578, 1920, 2311, 2460j, 2460, 2684, 2742k, 2901, 3041, 3323, 3395ik, 3759, 4038j, 4349, '''4501''', 5395, 5455, 5809, 6079, 6219, 6893, 7315, 7361, 7527, 8539, 9447, 9934, 11353, 11664j, 12245, 13823, 14066k, 14348, 15112, '''16808''', 29053, 31920, 32231, 34691, 36269, 40078, 47309, 48514, 48945, 50434, 51499, 52704, 58973, 64368, 65322, 67242, 78716, 81176j, 83096, 92782, 109590, 119365, 131610, '''148418''', … }}.  
: {{Databox|Exotemperaments| 5cfijjk, 5cfik, 5g, 5gj, 5egj, '''5eghj''', 7deefghijjk, 7dfghijjk, '''7''', 8d, 8di, 9gijk, 10ejk, 10h, 12de, 12e, '''12fijk''', '''14cfjj''', 15, 15k, '''15gk''', 17cghk, 18ehijk, 19eghikk, 19eghi, 19egh, 19, 22i, 22h, '''22fh''', 24, '''26ik''', 27egij, 29gjk, '''31''', 34dhk, 34dhjk, 38dfij, '''39dfgijk''', 41g, '''41''', '''43''', '''46''', 58hi, 58hik, 62, 68, 68j, 72hijk, 77, 80k, 87, 94 }}
: {{Databox|Exotemperaments| 5cfijjk, 5cfik, 5g, 5gj, 5egj, '''5eghj''', 7deefghijjk, 7dfghijjk, '''7''', 8d, 8di, 9gijk, 10ejk, 10h, 12de, 12e, '''12fijk''', '''14cfjj''', 15, 15k, '''15gk''', 17cghk, 18ehijk, 19eghikk, 19eghi, 19egh, 19, 22i, 22h, '''22fh''', 24, '''26ik''', 27egij, 29gjk, '''31''', 34dhk, 34dhjk, 38dfij, '''39dfgijk''', 41g, '''41''', '''43''', '''46''', 58hi, 58hik, 62, 68, 68j, 72hijk, 77, 80k, 87, 94 }}


; 37-limit
; 37-limit
: {{EDOs| 152fgj, 159k*, 181*, 183k*, 183*, 190gl*, 198gl, 212ghj*, 212gh, 217*, 217l, 224, 239*, 243ekl*, 248h, 270l*, '''270''', '''270i''', 296, 311k*, '''311''', 388, 422l, 487, 525, 566gjl, 571, 597ik, 624jk, 643ijkl, 653, 692ik, 718, 742il, 814k, 814, 863efgjk, 882, 908, 954hjl, 1106, 1164fi, 1205gl, 1224, 1289, 1308, '''1395''', 1578l, 1600, 1696, 1821efk, '''1920''', 2460j, 2460, 2684, 2742kl, 2901, 3041, 3395ik, 3759, 3949i, 3992, 4190g, 4349, '''4501''', 6219, 6349, 6893, 7033, 7361, 7847jkl, 8269, 8893, 9281, 9934, 10652, 10729k, 11025, 11353, 12245, 13823, 14066k, 14348, 15854j, '''16808''', 20567, 23270, 25347, '''26742''', 31920, 32231, 34691, 40078, 47309, 48945, 52704, 53077, 57578, '''58973''', '''65322''', '''67242''', 81176j, '''83096''', 95524, 109590, 131610, '''148418''', … }}.  
: {{EDOs| 152fgj, 159k*, 181*, 183k* 183*, 190gl* (190g), 198gl, 212ghj*, 212gh, 217*, 217l, 224, 239*, 243ekl*, 248h, 270l*, '''270''', '''270i''', 296, 311k*, '''311''', 388, 422l, 487, 525, 566gjl, 571, 597ik, 624jk, 643ijkl, 653, 692ik, 718, 742il, 814k, 814, 863efgjk, 882, 908, 954hjl, 1106, 1164fi, 1205gl, 1224, 1289, 1308, '''1395''', 1578l, 1600, 1696, 1821efk, '''1920''', 2460j, 2460, 2684, 2742kl, 2901, 3041, 3395ik, 3759, 3949i, 3992, 4190g, 4349, '''4501''', 6219, 6349, 6893, 7033, 7361, 7847jkl, 8269, 8893, 9281, 9934, 10652, 10729k, 11025, 11353, 12245, 13823, 14066k, 14348, 15854j, '''16808''', 20567, 23270, 25347, '''26742''', 31920, 32231, 34691, 40078, 47309, 48945, 52704, 53077, 57578, '''58973''', '''65322''', '''67242''', 81176j, '''83096''', 95524, 109590, 131610, '''148418''', … }}.  
: {{Databox|Exotemperaments| 5cfijjkll, 5cfikll, 5cfik, 5, 5g, 5egj, '''5eghj''', '''5eghjl''', 6fhijl, 7deefghijjkll, 7dfghijjkll, '''7dfghijjk''', 7l, 8d, '''8di''', 9gijkl, 10ejk, '''10h''', 12del, 12el, '''12fijk''', 14cfjjl, 15, 15gk, 15gkl, 16j, 17cgk, 17cghk, 19eghikkl, 19eghil, 19egh, 19gh, 19g, '''19''', 22il, 22i, 22, 22h, '''22fh''', 24, '''26ik''', 27egij, 29gjk, 29gk, 31fghjk, 31l, 34dhk, 34dhjkl, 38dfijkkl, 38dfijl, '''39dfgijkl''', '''43''', 46l, '''46''', 50jk, 50k, 53, 53j, 58hik, '''58hikl''', 60el, 62, 65d, 68, 68j, 68jl, 72hijkll, 72hijk, 72ijk, 72, '''77''', '''80k''', 94, 99ek, '''99efk''', '''103hl''', 121ikl, 130j, 140k, 149 }}
: {{Databox|Exotemperaments| 5cfijjkll, 5cfikll, 5cfik, 5, 5g, 5egj, '''5eghj''', '''5eghjl''', 6fhijl, 7deefghijjkll, 7dfghijjkll, '''7dfghijjk''', 7l, 8d, '''8di''', 9gijkl, 10ejk, '''10h''', 12del, 12el, '''12fijk''', 14cfjjl, 15, 15gk, 15gkl, 16j, 17cgk, 17cghk, 19eghikkl, 19eghil, 19egh, 19gh, 19g, '''19''', 22il, 22i, 22, 22h, '''22fh''', 24, '''26ik''', 27egij, 29gjk, 29gk, 31fghjk, 31l, 34dhk, 34dhjkl, 38dfijkkl, 38dfijl, '''39dfgijkl''', '''43''', 46l, '''46''', 50jk, 50k, 53, 53j, 58hik, '''58hikl''', 60el, 62, 65d, 68, 68j, 68jl, 72hijkll, 72hijk, 72ijk, 72, '''77''', '''80k''', 94, 99ek, '''99efk''', '''103hl''', 121ikl, 130j, 140k, 149 }}


; 41-limit
; 41-limit
: {{EDOs| 224, 248h, '''270'''*, '''270i''', 311k*, '''311''', 388, 422*, 422l, 525*, 540, 566gjl, 597ik, 624jk, 639hjm, 653, 692ikm, 718, 764, 764j, 814k, 814, 863efgjk, 908m, 954hjl, 1012, 1147i, 1164fim, 1178, 1205gl, 1289, 1385k, 1395, 1578l, 1696, 1817hi, '''1920''', 2159, 2270il, 2460jm, 2460m, 2460, 2554, 2581ij, 2703, 2742klm, 3041, 3084, 3337, 3395ik, 3759, 3992, 4349, '''4501m''', 5144, 5638, 5809, 6151, 6349, 7204, 7216, '''7361''', 7847jklm, 8893, 9717, 9934, 10729k, 11353, 11534, 12245, 12428, 13584, 14066k, '''14348''', '''15854j''', 16808, '''17461''', 19933, 20203, 20567, 23270, 25347, 27730, 28414hjk, 28742, '''29053''', 31920, '''34691''', 40078, 42052, 44268, 47309, 49256, 51176, 53077, 53612, 56354m, 57578, 58392, '''58973''', '''65322''', 81176j, '''95524''', 109590, 133431, '''148418''', 165226 … }}.  
: {{EDOs| 224, 248h, '''270'''*, '''270i''', 311k*, '''311''', 388, 422*, 422l, 525* (525j), 540, 566gjl, 597ik, 624jk, 639hjm, 653, 692ikm, 718, 764, 764j, 814k, 814, 863efgjk, 908m, 954hjl, 1012, 1147i, 1164fim, 1178, 1205gl, 1289, 1385k, 1395, 1578l, 1696, 1817hi, '''1920''', 2159, 2270il, 2460jm, 2460m, 2460, 2554, 2581ij, 2703, 2742klm, 3041, 3084, 3337, 3395ik, 3759, 3992, 4349, '''4501m''', 5144, 5638, 5809, 6151, 6349, 7204, 7216, '''7361''', 7847jklm, 8893, 9717, 9934, 10729k, 11353, 11534, 12245, 12428, 13584, 14066k, '''14348''', '''15854j''', 16808, '''17461''', 19933, 20203, 20567, 23270, 25347, 27730, 28414hjk, 28742, '''29053''', 31920, '''34691''', 40078, 42052, 44268, 47309, 49256, 51176, 53077, 53612, 56354m, 57578, 58392, '''58973''', '''65322''', 81176j, '''95524''', 109590, 133431, '''148418''', 165226 … }}.  
: {{Databox|Exotemperaments| 5cfijjkllm, 5cfikllm, 5cfikm, 5f, 5, 5g, 5egj, '''5eghj''', '''5eghjl''', 6fhijlm, 7dfghijjkllmmm, 7dfghijjkllm, '''7dfghijjkm''', 7l, 8d, 8di, 9gijklmm, 9gijkl, '''10h''', 12del, 12el, '''12fijkm''', 14cfjjlmm, 15, 15km, 15gkm, 15gklm, 16jm, 17cghk, 17cghkm, 18ehijkm, 19eghikklm, 19eghilm, '''19''', 22il, 22i, 22, 22h, '''22fh''', 24, '''26ik''', 27egij, 29gjk, 29gk, 31, 31l, 34dhjklm, 38dfijkklm, 38dfijlm, 39dfgijklmm, 41, 41i, 43, 43m, 46l, 46, 49fghjl, 50km, 50k, 53gk, 53k, 53, 53j, 58hik, '''58hikl''', 60ehl, 60el, 62, 72hijkllm, 72hijkm, 72, 77m, 80, '''80k''', 99ekm, 99efkm, 118fikl, 121iklm, 130j, 137, 140hk, 140k, 149, 159k, 166gl, 171, 181, 183k, 183, 188egijklm, 193, 193l, 198l, 198gl, 217, 217l }}
: {{Databox|Exotemperaments| 5cfijjkllm, 5cfikllm, 5cfikm, 5f, 5, 5g, 5egj, '''5eghj''', '''5eghjl''', 6fhijlm, 7dfghijjkllmmm, 7dfghijjkllm, '''7dfghijjkm''', 7l, 8d, 8di, 9gijklmm, 9gijkl, '''10h''', 12del, 12el, '''12fijkm''', 14cfjjlmm, 15, 15km, 15gkm, 15gklm, 16jm, 17cghk, 17cghkm, 18ehijkm, 19eghikklm, 19eghilm, '''19''', 22il, 22i, 22, 22h, '''22fh''', 24, '''26ik''', 27egij, 29gjk, 29gk, 31, 31l, 34dhjklm, 38dfijkklm, 38dfijlm, 39dfgijklmm, 41, 41i, 43, 43m, 46l, 46, 49fghjl, 50km, 50k, 53gk, 53k, 53, 53j, 58hik, '''58hikl''', 60ehl, 60el, 62, 72hijkllm, 72hijkm, 72, 77m, 80, '''80k''', 99ekm, 99efkm, 118fikl, 121iklm, 130j, 137, 140hk, 140k, 149, 159k, 166gl, 171, 181, 183k, 183, 188egijklm, 193, 193l, 198l, 198gl, 217, 217l }}


; 43-limit
; 43-limit
: {{EDOs| 236dghin, 239*, 243eklmn*, 248h*, 270*, '''270i''', 296, '''311n'''*, '''311''', 373g, 388, 422*, 422l, 525*, 540, 566gjl, 597ik, 624jk, 639hjmn, 653, 711, 718, 764hj, 814k, 814, 863efgjk, 882, 908m, 954hjln, 1065, 1164fimn, 1178j, 1178, 1205gl, 1323, 1323k, 1357efhijlmn, 1385k, 1395, 1578kln, 1578ln, 1578l, '''1600''', 1696, 1817hi, '''1920''', 2159, 2270il, 2554n, 2581ijn, 2684m, 2684, 2703, 2742klm, 3041, 3084, 3337, 3395ik, 3759, 3949i, 3976j, 4132k, 4349, 4380, '''4501m''', 5395, 5638, 5809, 5927fk, 6349, 6597, 7033, 7204, 7216, '''7361''', 8893, 9717, 10729k, 11664jm, 12245, 12428, 12999, 13112, 14066kn, '''14348''', 16066i, 17461, 19933, 20203, '''20567''', 23270, 26742m, 26742, 28742, 29053, 32231, 34691, 36269, 37592, 37946, 40649, 44268, 47309, 52704m, 53612, 54997, 55407, 56354m, '''58973''', 73815, 81176jn, 83096, 95524, '''109590''', 135800g, 148418, 157865, 159070, '''165226''', … }}.  
: {{EDOs| 236dghin, 239*, 243eklmn*, 248h*, 270*, '''270i''', 296, '''311n'''* '''311'''*, (320ij), (354), 373g, 388, 422*, 422l, 525* (525j), 540, 566gjl, 597ik, 624jk, 639hjmn, 653, 711, 718, 764hj, 814k, 814, 863efgjk, 882, 908m, 954hjln, 1065, 1164fimn, 1178j, 1178, 1205gl, 1323, 1323k, 1357efhijlmn, 1385k, 1395, 1578kln, 1578ln, 1578l, '''1600''', 1696, 1817hi, '''1920''', 2159, 2270il, 2554n, 2581ijn, 2684m, 2684, 2703, 2742klm, 3041, 3084, 3337, 3395ik, 3759, 3949i, 3976j, 4132k, 4349, 4380, '''4501m''', 5395, 5638, 5809, 5927fk, 6349, 6597, 7033, 7204, 7216, '''7361''', 8893, 9717, 10729k, 11664jm, 12245, 12428, 12999, 13112, 14066kn, '''14348''', 16066i, 17461, 19933, 20203, '''20567''', 23270, 26742m, 26742, 28742, 29053, 32231, 34691, 36269, 37592, 37946, 40649, 44268, 47309, 52704m, 53612, 54997, 55407, 56354m, '''58973''', 73815, 81176jn, 83096, 95524, '''109590''', 135800g, 148418, 157865, 159070, '''165226''', … }}.  
: {{Databox|Exotemperaments| 5cfijjkllmnn, 5cfikllmnn, 5cfikllm, 5cfikm, 5f, 5, 5g, 5eghj, '''5eghjn''', '''5eghjln''', 6fhijlm, 7dfghijjkllmmmn, 7dfghijjkllmn, '''7dfghijjkmn''', 7l, 8dn, 8din, 9gijkln, 10egjkm, 10ejkm, 10h, 12del, '''12el''', '''12fijkmn''', 14cfjjkklmmn, '''14cfjjlmmn''', 15mn, 15kmn, '''15gkmn''', '''15gklmn''', 17cghkn, 17cghkmn, 18ehijkm, 19eghikklmnn, 19g, '''19''', 22il, 22i, 22, 22h, 22hn, '''22fhn''', 24, 26iknn, '''26ik''', 27egj, '''27egij''', 29gjk, 29gk, 31l, 34dhkn, 34dhjkmn, 34dhjklmn, 38dfijkklmnn, 38dfijlmnn, 38dfijlm, 39dfgijkl, 39dfgijklmm, 41in, 43, 43m, 43mn, 46ln, 49fghjlnn, 50jkm, 50km, 50k, 53, 53j, 58hi, '''58hik''', '''58hikl''', 60ehln, 60eln, 62, 72hijkllmn, 72hijkmn, 77m, 80, '''80k''', 84, 87, 94, 99efkm, '''99efkmn''', 111jln, 113l, 113, 118fikl, '''121iklm''', 140kn, 140k, 140, 145jkl, 149n, 152fgjm, 171, 181, 183k, 183, 193, 198ln, 198gln, 217n, 217ln }}
: {{Databox|Exotemperaments| 5cfijjkllmnn, 5cfikllmnn, 5cfikllm, 5cfikm, 5f, 5, 5g, 5eghj, '''5eghjn''', '''5eghjln''', 6fhijlm, 7dfghijjkllmmmn, 7dfghijjkllmn, '''7dfghijjkmn''', 7l, 8dn, 8din, 9gijkln, 10egjkm, 10ejkm, 10h, 12del, '''12el''', '''12fijkmn''', 14cfjjkklmmn, '''14cfjjlmmn''', 15mn, 15kmn, '''15gkmn''', '''15gklmn''', 17cghkn, 17cghkmn, 18ehijkm, 19eghikklmnn, 19g, '''19''', 22il, 22i, 22, 22h, 22hn, '''22fhn''', 24, 26iknn, '''26ik''', 27egj, '''27egij''', 29gjk, 29gk, 31l, 34dhkn, 34dhjkmn, 34dhjklmn, 38dfijkklmnn, 38dfijlmnn, 38dfijlm, 39dfgijkl, 39dfgijklmm, 41in, 43, 43m, 43mn, 46ln, 49fghjlnn, 50jkm, 50km, 50k, 53, 53j, 58hi, '''58hik''', '''58hikl''', 60ehln, 60eln, 62, 72hijkllmn, 72hijkmn, 77m, 80, '''80k''', 84, 87, 94, 99efkm, '''99efkmn''', 111jln, 113l, 113, 118fikl, '''121iklm''', 140kn, 140k, 140, 145jkl, 149n, 152fgjm, 171, 181, 183k, 183, 193, 198ln, 198gln, 217n, 217ln }}


; 47-limit
; 47-limit
: {{EDOs| '''270i''', 296*, 311n*, '''311'''*, '''311o'''*, 320ij, 354, 364i*, 383ij*, 388, 422*, '''422l''', 472, 487, 525*, 566gjl, 597ik, 639hjmno, 653, 711, 718, 764hj, 814k, 814, 863efgjk, 908mo, 954hjln, 1065, 1121, 1164fimn, '''1178''', 1289n, 1323k, 1357efhijlmn, '''1385k''', 1578kln, 1578ln, 1578l, 1646, 1696o, 1817h, '''1817hi''', '''1920''', 2072, 2132ehln, 2159, 2270il, 2554n, 2581ijno, , 2619l, 2684o, 2703, '''2742klm''', 3084o, 3224, 3337o, 3395ik, 3889, 3949i, 4038j, 4132ko, 4349, '''4380''', 4973, 5091, 4387ho, 5395, 5455l, 5809, 5927fk, 6151, 6219, 6349, 7204, 7216, 7315m, 7361, '''7361o''', 8269, 8539l, 8539, '''8893''', 9717, 10257, 10729k, 11664jm, 12245, 13823, 14124, '''14348''', 16066i, 17461o, 17883, 19381jm, 19849, 20567, '''23270''', 28742, 30631, 31243, 32137, 32231, 36269, 37592, 40649, 44268o, 45861, 47309, 52704m, 53077, 55407, '''58973''', 73815, 81176jno, 83096, 89023, '''95524''', '''109590''', 136173, 148418, 157865, 166431, 182687, 191580, … }}.  
: {{EDOs| '''270i''', 296*, 311n* '''311'''* '''311o'''*, 320ij, 354, 364i* (364), 383ij*, 388, 422*, '''422l''', 472, 487, 525* (525j), 566gjl, 597ik, 639hjmno, 653, 711, 718, 764hj, 814k, 814, 863efgjk, 908mo, 954hjln, 1065, 1121, 1164fimn, '''1178''', 1289n, 1323k, 1357efhijlmn, '''1385k''', 1578kln, 1578ln, 1578l, 1646, 1696o, 1817h, '''1817hi''', '''1920''', 2072, 2132ehln, 2159, 2270il, 2554n, 2581ijno, , 2619l, 2684o, 2703, '''2742klm''', 3084o, 3224, 3337o, 3395ik, 3889, 3949i, 4038j, 4132ko, 4349, '''4380''', 4973, 5091, 4387ho, 5395, 5455l, 5809, 5927fk, 6151, 6219, 6349, 7204, 7216, 7315m, 7361, '''7361o''', 8269, 8539l, 8539, '''8893''', 9717, 10257, 10729k, 11664jm, 12245, 13823, 14124, '''14348''', 16066i, 17461o, 17883, 19381jm, 19849, 20567, '''23270''', 28742, 30631, 31243, 32137, 32231, 36269, 37592, 40649, 44268o, 45861, 47309, 52704m, 53077, 55407, '''58973''', 73815, 81176jno, 83096, 89023, '''95524''', '''109590''', 136173, 148418, 157865, 166431, 182687, 191580, … }}.  
: {{Databox|Exotemperaments| 5cfijjkllmnno, 5cfikllmnno, 5cfikllmo, 5cfikmo, 5f, 5, 5g, 5eghj, 5eghjn, '''5eghjln''', 6fhijlmo, 7dfghijjkllmmmno, 7dfghijjkllmno, '''7dfghijjkmno''', 7l, 8dno, 8dino, 9gijklno, 9k, 9, 10egjkmo, 10ejkmo, 10h, 12delo, 12elo, 12fijkm, '''12fijkmn''', 14cfjjkklmmno, '''14cfjjlmmno''', 15gkmno, '''15gklmno''', 17cghkno, 17cghkmno, 19eghikklmnno, 19eghilmnno, 19eghmo, 19go, 19o, 22ilm, 22il, 22i, '''22fhn''', '''22fhno''', 24, 26iknn, '''26ik''', 29gjk, 29gk, 31l, 34dhkn, 34dhjklmn, 38dfijkklmnnoo, 38dfijlmnnoo, 39dfgijkl, 39dfgijklmm, 41in, 43, 43m, 43mn, 46lno, 49fghjlnno, 50jkmo, 50kmo, 50ko, 53gkn, 53, 53j, 53jo, 56, 58hik, 58hiko, '''58hiklo''', '''60ehln''', '''60eln''', '''62''', 72hijkllmno, 72hijkmno, 72, 77m, 80o, 80ko, 87, 94jklm, 94m, 99efkm, '''99efkmn''', 103hl, 111ln, 111jln, 118fikl, 121iklm, '''121iklmo''', 130j, 140, 145jklo, 149no, 152fgjmo, 167hijkn, 171i, 171, 181, 183k, 183, 188egijklmno, 193, 198ln, '''198gln''', 212ghjmo, 217ln, 217lno, 224, 224n, 236dghino, 243eklmno, '''248h''', '''270''' }}
: {{Databox|Exotemperaments| 5cfijjkllmnno, 5cfikllmnno, 5cfikllmo, 5cfikmo, 5f, 5, 5g, 5eghj, 5eghjn, '''5eghjln''', 6fhijlmo, 7dfghijjkllmmmno, 7dfghijjkllmno, '''7dfghijjkmno''', 7l, 8dno, 8dino, 9gijklno, 9k, 9, 10egjkmo, 10ejkmo, 10h, 12delo, 12elo, 12fijkm, '''12fijkmn''', 14cfjjkklmmno, '''14cfjjlmmno''', 15gkmno, '''15gklmno''', 17cghkno, 17cghkmno, 19eghikklmnno, 19eghilmnno, 19eghmo, 19go, 19o, 22ilm, 22il, 22i, '''22fhn''', '''22fhno''', 24, 26iknn, '''26ik''', 29gjk, 29gk, 31l, 34dhkn, 34dhjklmn, 38dfijkklmnnoo, 38dfijlmnnoo, 39dfgijkl, 39dfgijklmm, 41in, 43, 43m, 43mn, 46lno, 49fghjlnno, 50jkmo, 50kmo, 50ko, 53gkn, 53, 53j, 53jo, 56, 58hik, 58hiko, '''58hiklo''', '''60ehln''', '''60eln''', '''62''', 72hijkllmno, 72hijkmno, 72, 77m, 80o, 80ko, 87, 94jklm, 94m, 99efkm, '''99efkmn''', 103hl, 111ln, 111jln, 118fikl, 121iklm, '''121iklmo''', 130j, 140, 145jklo, 149no, 152fgjmo, 167hijkn, 171i, 171, 181, 183k, 183, 188egijklmno, 193, 198ln, '''198gln''', 212ghjmo, 217ln, 217lno, 224, 224n, 236dghino, 243eklmno, '''248h''', '''270''' }}
[[Category:EDO theory pages]]
[[Category:Regular temperament theory]]
[[Category:Lists]]

Latest revision as of 09:59, 6 September 2025

Below are the sequences of equal temperaments by TE absolute error (and TE relative error, in bold) in various subgroups, searched up to 196608. These sequences are obtained with the Temperament Evaluator. For a method to iterate through all GPVs, see Patent val/Properties.

GPVs 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.

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 p-prime-limit, it is reasonable to request that the order of size for the 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, which are noted with an apostrophe. Alternatives that pass the test but have a higher error than a previous entry are noted in parentheses.

3-limit
5, 7, 12, 29, 41, 53, 200, 253, 306, 359, 665, 8286, 8951, 9616, 10281, 10946, 11611, 12276, 12941, 13606, 14271, 14936, 15601, 31867, 79335, 111202, 190537, … (OEIS: A060528).
5-limit
5, 7, 12, 19, 31, 34, 46, 53, 118, 171, 289, 323, 388, 441, 559, 612, 1171, 1783, 2513, 3684, 4296, 12276, 16572, 20868, 25164, 46032, 48545, 52841, 73709, 78005, 151714, ….
7-limit
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
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, ….
Exotemperaments
5c, 5, 7d, 8d, 9, 10, 12e
13-limit
(14c), 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, ….
Exotemperaments
5cf, 5f, 5, 5e, 7df, 7d, 7, 8d, 9, 10, 12, 12f, 14cf
17-limit
(19), 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, ….
Exotemperaments
5cf, 5f, 5, 5g, 5eg, 7dfg, 7dg, 7, 8d, 9, 10e, 10, 12, 12f, 14cf, 15, 15g, 16, 17cg, 19eg
19-limit
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, ….
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
(53e), 58hi, 62, 68* (68e), 72hi* 72i* (72), 80*, (84), 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, ….
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
72, 77, 80*, 87*, 94j* 94*, 99ef, 103h*, 113*, 118, 121i, 130, 140h*, 140, 152fgj, 159, 183, 217, 243e, 270, 282, 311, 422, 472, 494h, 525, 535, 540, 554e, 566gj, 571, 581, 581j, 624j, 653, 692i, 718, 742i, 814, 882, 908, 954hj, 1106, 1282, 1308, 1323, 1395, 1578, 1920, 2000, 2460, 2742, 3041, 3178, 3395i, 4038j, 4190g, 4349, 4501, 5395, 5783, 6079, 6893, 7315, 7361, 7527, 7847j, 8269, 8539, 9204, 9447, 9934, 10729, 11664j, 11934, 12245, 13112, 14066, 15230, 16808, 28742, 29053, 36269, 45861, 48945, 52704, 53077, 56513, 58392, 58973, 60973, 65322, 67242, 69512, 78716, 81176j, 83096, 87445, 92782, 102557, 119365, 148418, ….
Exotemperaments
5cfi, 5egj, 5eghj, 7deefghijj, 7dfghijj, 7, 8di, 8dhhijj, 9gij, 9, 10ej, 10, 10h, 12de, 12e, 12fij, 14cfjj, 15, 15g, 17cgh, 18ehij, 19eghi, 22i, 22h, 22fh, 26i, 29gj, 29g, 31j, 31, 34dh, 34dhj, 38dfij, 39dfgij, 41g, 41, 43, 46, 50, 53, 58hi, 62, 68j, 72hij, 72ij
31-limit
99efk, 103h*, 121ik, 130j*, 130, 140k*, 140, 149, 152fgj, 159k* (159), 167hijk*, 181*, 183k*, 183, 190g, 217, 243ek* (243e), 270, 311, 388, 422, 525, 566gj, 571, 624jk, 639hj, 643ijk, 653, 692ik, 718, 742i, 863efgjk, 882, 908, 954hj, 1205g, 1289, 1308, 1395, 1578, 1920, 2311, 2460j, 2460, 2684, 2742k, 2901, 3041, 3323, 3395ik, 3759, 4038j, 4349, 4501, 5395, 5455, 5809, 6079, 6219, 6893, 7315, 7361, 7527, 8539, 9447, 9934, 11353, 11664j, 12245, 13823, 14066k, 14348, 15112, 16808, 29053, 31920, 32231, 34691, 36269, 40078, 47309, 48514, 48945, 50434, 51499, 52704, 58973, 64368, 65322, 67242, 78716, 81176j, 83096, 92782, 109590, 119365, 131610, 148418, ….
Exotemperaments
5cfijjk, 5cfik, 5g, 5gj, 5egj, 5eghj, 7deefghijjk, 7dfghijjk, 7, 8d, 8di, 9gijk, 10ejk, 10h, 12de, 12e, 12fijk, 14cfjj, 15, 15k, 15gk, 17cghk, 18ehijk, 19eghikk, 19eghi, 19egh, 19, 22i, 22h, 22fh, 24, 26ik, 27egij, 29gjk, 31, 34dhk, 34dhjk, 38dfij, 39dfgijk, 41g, 41, 43, 46, 58hi, 58hik, 62, 68, 68j, 72hijk, 77, 80k, 87, 94
37-limit
152fgj, 159k*, 181*, 183k* 183*, 190gl* (190g), 198gl, 212ghj*, 212gh, 217*, 217l, 224, 239*, 243ekl*, 248h, 270l*, 270, 270i, 296, 311k*, 311, 388, 422l, 487, 525, 566gjl, 571, 597ik, 624jk, 643ijkl, 653, 692ik, 718, 742il, 814k, 814, 863efgjk, 882, 908, 954hjl, 1106, 1164fi, 1205gl, 1224, 1289, 1308, 1395, 1578l, 1600, 1696, 1821efk, 1920, 2460j, 2460, 2684, 2742kl, 2901, 3041, 3395ik, 3759, 3949i, 3992, 4190g, 4349, 4501, 6219, 6349, 6893, 7033, 7361, 7847jkl, 8269, 8893, 9281, 9934, 10652, 10729k, 11025, 11353, 12245, 13823, 14066k, 14348, 15854j, 16808, 20567, 23270, 25347, 26742, 31920, 32231, 34691, 40078, 47309, 48945, 52704, 53077, 57578, 58973, 65322, 67242, 81176j, 83096, 95524, 109590, 131610, 148418, ….
Exotemperaments
5cfijjkll, 5cfikll, 5cfik, 5, 5g, 5egj, 5eghj, 5eghjl, 6fhijl, 7deefghijjkll, 7dfghijjkll, 7dfghijjk, 7l, 8d, 8di, 9gijkl, 10ejk, 10h, 12del, 12el, 12fijk, 14cfjjl, 15, 15gk, 15gkl, 16j, 17cgk, 17cghk, 19eghikkl, 19eghil, 19egh, 19gh, 19g, 19, 22il, 22i, 22, 22h, 22fh, 24, 26ik, 27egij, 29gjk, 29gk, 31fghjk, 31l, 34dhk, 34dhjkl, 38dfijkkl, 38dfijl, 39dfgijkl, 43, 46l, 46, 50jk, 50k, 53, 53j, 58hik, 58hikl, 60el, 62, 65d, 68, 68j, 68jl, 72hijkll, 72hijk, 72ijk, 72, 77, 80k, 94, 99ek, 99efk, 103hl, 121ikl, 130j, 140k, 149
41-limit
224, 248h, 270*, 270i, 311k*, 311, 388, 422*, 422l, 525* (525j), 540, 566gjl, 597ik, 624jk, 639hjm, 653, 692ikm, 718, 764, 764j, 814k, 814, 863efgjk, 908m, 954hjl, 1012, 1147i, 1164fim, 1178, 1205gl, 1289, 1385k, 1395, 1578l, 1696, 1817hi, 1920, 2159, 2270il, 2460jm, 2460m, 2460, 2554, 2581ij, 2703, 2742klm, 3041, 3084, 3337, 3395ik, 3759, 3992, 4349, 4501m, 5144, 5638, 5809, 6151, 6349, 7204, 7216, 7361, 7847jklm, 8893, 9717, 9934, 10729k, 11353, 11534, 12245, 12428, 13584, 14066k, 14348, 15854j, 16808, 17461, 19933, 20203, 20567, 23270, 25347, 27730, 28414hjk, 28742, 29053, 31920, 34691, 40078, 42052, 44268, 47309, 49256, 51176, 53077, 53612, 56354m, 57578, 58392, 58973, 65322, 81176j, 95524, 109590, 133431, 148418, 165226 ….
Exotemperaments
5cfijjkllm, 5cfikllm, 5cfikm, 5f, 5, 5g, 5egj, 5eghj, 5eghjl, 6fhijlm, 7dfghijjkllmmm, 7dfghijjkllm, 7dfghijjkm, 7l, 8d, 8di, 9gijklmm, 9gijkl, 10h, 12del, 12el, 12fijkm, 14cfjjlmm, 15, 15km, 15gkm, 15gklm, 16jm, 17cghk, 17cghkm, 18ehijkm, 19eghikklm, 19eghilm, 19, 22il, 22i, 22, 22h, 22fh, 24, 26ik, 27egij, 29gjk, 29gk, 31, 31l, 34dhjklm, 38dfijkklm, 38dfijlm, 39dfgijklmm, 41, 41i, 43, 43m, 46l, 46, 49fghjl, 50km, 50k, 53gk, 53k, 53, 53j, 58hik, 58hikl, 60ehl, 60el, 62, 72hijkllm, 72hijkm, 72, 77m, 80, 80k, 99ekm, 99efkm, 118fikl, 121iklm, 130j, 137, 140hk, 140k, 149, 159k, 166gl, 171, 181, 183k, 183, 188egijklm, 193, 193l, 198l, 198gl, 217, 217l
43-limit
236dghin, 239*, 243eklmn*, 248h*, 270*, 270i, 296, 311n* 311*, (320ij), (354), 373g, 388, 422*, 422l, 525* (525j), 540, 566gjl, 597ik, 624jk, 639hjmn, 653, 711, 718, 764hj, 814k, 814, 863efgjk, 882, 908m, 954hjln, 1065, 1164fimn, 1178j, 1178, 1205gl, 1323, 1323k, 1357efhijlmn, 1385k, 1395, 1578kln, 1578ln, 1578l, 1600, 1696, 1817hi, 1920, 2159, 2270il, 2554n, 2581ijn, 2684m, 2684, 2703, 2742klm, 3041, 3084, 3337, 3395ik, 3759, 3949i, 3976j, 4132k, 4349, 4380, 4501m, 5395, 5638, 5809, 5927fk, 6349, 6597, 7033, 7204, 7216, 7361, 8893, 9717, 10729k, 11664jm, 12245, 12428, 12999, 13112, 14066kn, 14348, 16066i, 17461, 19933, 20203, 20567, 23270, 26742m, 26742, 28742, 29053, 32231, 34691, 36269, 37592, 37946, 40649, 44268, 47309, 52704m, 53612, 54997, 55407, 56354m, 58973, 73815, 81176jn, 83096, 95524, 109590, 135800g, 148418, 157865, 159070, 165226, ….
Exotemperaments
5cfijjkllmnn, 5cfikllmnn, 5cfikllm, 5cfikm, 5f, 5, 5g, 5eghj, 5eghjn, 5eghjln, 6fhijlm, 7dfghijjkllmmmn, 7dfghijjkllmn, 7dfghijjkmn, 7l, 8dn, 8din, 9gijkln, 10egjkm, 10ejkm, 10h, 12del, 12el, 12fijkmn, 14cfjjkklmmn, 14cfjjlmmn, 15mn, 15kmn, 15gkmn, 15gklmn, 17cghkn, 17cghkmn, 18ehijkm, 19eghikklmnn, 19g, 19, 22il, 22i, 22, 22h, 22hn, 22fhn, 24, 26iknn, 26ik, 27egj, 27egij, 29gjk, 29gk, 31l, 34dhkn, 34dhjkmn, 34dhjklmn, 38dfijkklmnn, 38dfijlmnn, 38dfijlm, 39dfgijkl, 39dfgijklmm, 41in, 43, 43m, 43mn, 46ln, 49fghjlnn, 50jkm, 50km, 50k, 53, 53j, 58hi, 58hik, 58hikl, 60ehln, 60eln, 62, 72hijkllmn, 72hijkmn, 77m, 80, 80k, 84, 87, 94, 99efkm, 99efkmn, 111jln, 113l, 113, 118fikl, 121iklm, 140kn, 140k, 140, 145jkl, 149n, 152fgjm, 171, 181, 183k, 183, 193, 198ln, 198gln, 217n, 217ln
47-limit
270i, 296*, 311n* 311* 311o*, 320ij, 354, 364i* (364), 383ij*, 388, 422*, 422l, 472, 487, 525* (525j), 566gjl, 597ik, 639hjmno, 653, 711, 718, 764hj, 814k, 814, 863efgjk, 908mo, 954hjln, 1065, 1121, 1164fimn, 1178, 1289n, 1323k, 1357efhijlmn, 1385k, 1578kln, 1578ln, 1578l, 1646, 1696o, 1817h, 1817hi, 1920, 2072, 2132ehln, 2159, 2270il, 2554n, 2581ijno, , 2619l, 2684o, 2703, 2742klm, 3084o, 3224, 3337o, 3395ik, 3889, 3949i, 4038j, 4132ko, 4349, 4380, 4973, 5091, 4387ho, 5395, 5455l, 5809, 5927fk, 6151, 6219, 6349, 7204, 7216, 7315m, 7361, 7361o, 8269, 8539l, 8539, 8893, 9717, 10257, 10729k, 11664jm, 12245, 13823, 14124, 14348, 16066i, 17461o, 17883, 19381jm, 19849, 20567, 23270, 28742, 30631, 31243, 32137, 32231, 36269, 37592, 40649, 44268o, 45861, 47309, 52704m, 53077, 55407, 58973, 73815, 81176jno, 83096, 89023, 95524, 109590, 136173, 148418, 157865, 166431, 182687, 191580, ….
Exotemperaments
5cfijjkllmnno, 5cfikllmnno, 5cfikllmo, 5cfikmo, 5f, 5, 5g, 5eghj, 5eghjn, 5eghjln, 6fhijlmo, 7dfghijjkllmmmno, 7dfghijjkllmno, 7dfghijjkmno, 7l, 8dno, 8dino, 9gijklno, 9k, 9, 10egjkmo, 10ejkmo, 10h, 12delo, 12elo, 12fijkm, 12fijkmn, 14cfjjkklmmno, 14cfjjlmmno, 15gkmno, 15gklmno, 17cghkno, 17cghkmno, 19eghikklmnno, 19eghilmnno, 19eghmo, 19go, 19o, 22ilm, 22il, 22i, 22fhn, 22fhno, 24, 26iknn, 26ik, 29gjk, 29gk, 31l, 34dhkn, 34dhjklmn, 38dfijkklmnnoo, 38dfijlmnnoo, 39dfgijkl, 39dfgijklmm, 41in, 43, 43m, 43mn, 46lno, 49fghjlnno, 50jkmo, 50kmo, 50ko, 53gkn, 53, 53j, 53jo, 56, 58hik, 58hiko, 58hiklo, 60ehln, 60eln, 62, 72hijkllmno, 72hijkmno, 72, 77m, 80o, 80ko, 87, 94jklm, 94m, 99efkm, 99efkmn, 103hl, 111ln, 111jln, 118fikl, 121iklm, 121iklmo, 130j, 140, 145jklo, 149no, 152fgjmo, 167hijkn, 171i, 171, 181, 183k, 183, 188egijklmno, 193, 198ln, 198gln, 212ghjmo, 217ln, 217lno, 224, 224n, 236dghino, 243eklmno, 248h, 270
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