Sequence of equal temperaments by error: Difference between revisions

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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

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: {{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:Regular temperament theory]]

[[Category:Lists]]

@@ 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.
-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
@@ 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''' }}
+[[Category:Pages with mostly numerical content]]
 [[Category:EDO theory pages]]
 [[Category:Regular temperament theory]]
 [[Category:Lists]]