58edo: Difference between revisions

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== Theory ==

~~58et tempers out [[2048/2025]], [[126/125]], [[1728/1715]], [[144/143]], [[176/175]], [[896/891]], [[243/242]], [[5120/5103]], [[351/350]], [[364/363]], [[441/440]], and [[540/539]], and~~ is a strong system in the [[11-limit|11]]-, [[13-limit|13]]- and [[17-limit]]. It is the smallest [[edo]] which is [[consistent]] through the [[17-odd-limit]], and is also the smallest ~~uniquely~~ consistent in the [[11-odd-limit]] (the first equal temperament to map the entire 11-limit [[tonality diamond]] to distinct scale steps), and hence the first et which can define a version of the famous 43-note [[Harry Partch related scales|Genesis scale]] of [[Harry Partch]]. It [[support]]s [[hemififths]], [[myna]], [[diaschismic]], [[harry]], [[mystery]], [[buzzard]] and [[thuja]] [[Regular temperament|temperament]]s, and supplies the [[optimal patent val]] for 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank-3 temperaments [[thrush]], [[bluebird]], [[aplonis]] and [[jofur]].

58edo is a strong system in the [[11-limit|11]]-, [[13-limit|13]]- and [[17-limit]]. It is the smallest [[edo]] which is [[consistent]] through the [[17-odd-limit]], and is also the smallest distinctly consistent in the [[11-odd-limit]] (the first equal temperament to map the entire 11-odd-limit [[tonality diamond]] to distinct scale steps), and hence the first which can define a tempered version of the famous 43-note [[Harry Partch related scales|Genesis scale]] of [[Harry Partch]].

While the 17th harmonic is a cent and a half flat, the harmonics below it are all a little sharp, giving it the sound of a sharp system~~. 58 = 2 × 29, and 58 shares the same excellent fifth with [[29edo]]~~.

58et tempers out [[2048/2025]], [[126/125]], [[1728/1715]], [[144/143]], [[176/175]], [[896/891]], [[243/242]], [[5120/5103]], [[351/350]], [[364/363]], [[441/440]], and [[540/539]]. It [[support]]s [[hemififths]], [[myna]], [[diaschismic]], [[harry]], [[mystery]], [[buzzard]] and [[thuja]] [[Regular temperament|temperament]]s, and supplies the [[optimal patent val]] for the 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank-3 temperaments [[thrush]], [[bluebird]], [[aplonis]] and [[jofur]].

While the 17th harmonic is a cent and a half flat, the harmonics below it are all a little sharp, giving it the sound of a sharp system.

=== Prime harmonics ===

=== Subsets and supersets ===

58 = 2 × 29, and 58edo shares the same excellent fifth with [[29edo]].

== Intervals ==

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 == Theory ==
-et tempers out [[2048/2025]], [[126/125]], [[1728/1715]], [[144/143]], [[176/175]], [[896/891]], [[243/242]], [[5120/5103]], [[351/350]], [[364/363]], [[441/440]], and [[540/539]], and is a strong system in the [[11-limit|11]]-, [[13-limit|13]]- and [[17-limit]]. It is the smallest [[edo]] which is [[consistent]] through the [[17-odd-limit]], and is also the smallest uniquely consistent in the [[11-odd-limit]] (the first equal temperament to map the entire 11-limit [[tonality diamond]] to distinct scale steps), and hence the first et which can define a version of the famous 43-note [[Harry Partch related scales|Genesis scale]] of [[Harry Partch]]. It [[support]]s [[hemififths]], [[myna]], [[diaschismic]], [[harry]], [[mystery]], [[buzzard]] and [[thuja]] [[Regular temperament|temperament]]s, and supplies the [[optimal patent val]] for 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank-3 temperaments [[thrush]], [[bluebird]], [[aplonis]] and [[jofur]].
+edo is a strong system in the [[11-limit|11]]-, [[13-limit|13]]- and [[17-limit]]. It is the smallest [[edo]] which is [[consistent]] through the [[17-odd-limit]], and is also the smallest distinctly consistent in the [[11-odd-limit]] (the first equal temperament to map the entire 11-odd-limit [[tonality diamond]] to distinct scale steps), and hence the first which can define a tempered version of the famous 43-note [[Harry Partch related scales|Genesis scale]] of [[Harry Partch]].
-While the 17th harmonic is a cent and a half flat, the harmonics below it are all a little sharp, giving it the sound of a sharp system. 58 = 2 × 29, and 58 shares the same excellent fifth with [[29edo]].
+et tempers out [[2048/2025]], [[126/125]], [[1728/1715]], [[144/143]], [[176/175]], [[896/891]], [[243/242]], [[5120/5103]], [[351/350]], [[364/363]], [[441/440]], and [[540/539]]. It [[support]]s [[hemififths]], [[myna]], [[diaschismic]], [[harry]], [[mystery]], [[buzzard]] and [[thuja]] [[Regular temperament|temperament]]s, and supplies the [[optimal patent val]] for the 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank-3 temperaments [[thrush]], [[bluebird]], [[aplonis]] and [[jofur]].
+While the 17th harmonic is a cent and a half flat, the harmonics below it are all a little sharp, giving it the sound of a sharp system.
 === Prime harmonics ===
 {{Harmonics in equal|58}}
+=== Subsets and supersets ===
+= 2 × 29, and 58edo shares the same excellent fifth with [[29edo]].
 == Intervals ==