Sequence of equal temperaments by error - Revision history

Z4wr: the edos that fail the monotonicity test are marked by an asterisk, not an apostrophe, yet it said apostrophe, so i changed it

2026-05-14T03:23:12Z

the edos that fail the monotonicity test are marked by an asterisk, not an apostrophe, yet it said apostrophe, so i changed it

← Older revision		Revision as of 03:23, 14 May 2026
Line 3:		Line 3:
	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, which are noted with an ~~apostrophe~~. Alternatives that pass the test but have a higher error than a previous entry are noted in parentheses.		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 asterisk. Alternatives that pass the test but have a higher error than a previous entry are noted in parentheses.

	; 3-limit		; 3-limit

Overthink: + category

2025-11-03T01:04:46Z

+ category

← Older revision		Revision as of 01:04, 3 November 2025
Line 58:		Line 58:
	: {{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:Pages with mostly numerical content]]
	[[Category:EDO theory pages]]		[[Category:EDO theory pages]]
	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
	[[Category:Lists]]		[[Category:Lists]]

FloraC: Style

2025-09-06T09:59:46Z

Style

← Older revision		Revision as of 09:59, 6 September 2025
Line 1:		Line 1:
	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.

FloraC: Some corrections and add alternatives that pass the monotonicity test but have a higher error

2025-08-20T16:15:24Z

Some corrections and add alternatives that pass the monotonicity test but have a higher error

Show changes

FloraC: FloraC moved page Sequence of ETs by error to Sequence of equal temperaments by error without leaving a redirect: Avoid the acronym when there's no need

2025-08-08T07:52:35Z

FloraC moved page Sequence of ETs by error to Sequence of equal temperaments by error without leaving a redirect: Avoid the acronym when there's no need

← Older revision	Revision as of 07:52, 8 August 2025
(No difference)

FloraC: + categories

2025-08-07T12:28:06Z

+ categories

← Older revision		Revision as of 12:28, 7 August 2025
Line 57:		Line 57:
	: {{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, 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, … }}.
	: {{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]]

FloraC: FloraC moved page User:FloraC/Sequence of ETs by error to Sequence of ETs by error without leaving a redirect: Reference material for everyone to use

2025-08-07T12:20:08Z

FloraC moved page User:FloraC/Sequence of ETs by error to Sequence of ETs by error without leaving a redirect: Reference material for everyone to use

← Older revision	Revision as of 12:20, 7 August 2025
(No difference)

FloraC at 12:10, 7 August 2025

2025-08-07T12:10:37Z

← Older revision		Revision as of 12:10, 7 August 2025
Line 1:		Line 1:
	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]].		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]].

	~~[[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.		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 [[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. These are noted with an apostrophe.

	; 3-limit		; 3-limit

FloraC: Split page

2025-08-07T12:00:18Z

Split page

New page

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]].

[[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.

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
: {{EDOs| '''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
: {{EDOs| 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
: {{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| '''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| 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| '''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| 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| 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
: {{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''', … }}.
: {{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 }}

; 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''', … }}.
: {{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
: {{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''', … }}.
: {{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
: {{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 … }}.
: {{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
: {{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''', … }}.
: {{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
: {{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, … }}.
: {{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''' }}