58edo: Difference between revisions
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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]]. | 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 [[17/1|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, | While the [[17/1|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. Since {{nowrap|58 {{=}} 2 × 29}}, 58edo shares the same excellent fifth with [[29edo]]. | ||
As an equal temperament, 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]], [[thuja]] [[regular temperament|temperament]]s plus a number of [[gravity family]] extensions, 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]]. | As an equal temperament, 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]], [[thuja]] [[regular temperament|temperament]]s plus a number of [[gravity family]] extensions, 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]]. | ||
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{{Sharpness-sharp6-qt}} | {{Sharpness-sharp6-qt}} | ||
=== Ivan Wyschnegradsky's notation === | |||
Since a sharp raises by six steps, Wyschnegradsky accidentals borrowed from [[72edo]] can also be used: | |||
{{Sharpness-sharp6-iw}} | |||
=== Sagittal notation === | === Sagittal notation === | ||
==== Evo flavor ==== | |||
====Evo flavor==== | |||
<imagemap> | <imagemap> | ||
File:58-EDO_Evo_Sagittal.svg | File:58-EDO_Evo_Sagittal.svg | ||
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</imagemap> | </imagemap> | ||
====Revo flavor==== | ==== Revo flavor ==== | ||
<imagemap> | <imagemap> | ||
File:58-EDO_Revo_Sagittal.svg | File:58-EDO_Revo_Sagittal.svg | ||
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</imagemap> | </imagemap> | ||
====Evo-SZ flavor==== | ==== Evo-SZ flavor ==== | ||
<imagemap> | <imagemap> | ||
File:58-EDO_Evo-SZ_Sagittal.svg | File:58-EDO_Evo-SZ_Sagittal.svg | ||
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default [[File:58-EDO_Evo-SZ_Sagittal.svg]] | default [[File:58-EDO_Evo-SZ_Sagittal.svg]] | ||
</imagemap> | </imagemap> | ||
=== Hemipyth notation === | === Hemipyth notation === | ||