159th-octave temperaments: Difference between revisions
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{{ | {{Infobox fractional-octave|159}} | ||
[[159edo]] is a notable [[17-limit]] system. It first contains [[53edo]], tempering out Mercator's comma. | [[159edo]] is a notable [[17-limit]] system. It first contains [[53edo]], tempering out Mercator's comma. | ||
159edo has attracted a lot of attention from prominent microtonalists like [[Ozan Yarman]], [[Dawson Berry]] (also known as [[Aura]]), [[Gene Ward Smith]]. In addition, some of its multiples have large consistency limits as well, and this naturally commends itself to 159th-octave temperaments. | 159edo has attracted a lot of attention from prominent microtonalists like [[Ozan Yarman]], [[Dawson Berry]] (also known as [[Aura]]), [[Gene Ward Smith]]. In addition, some of its multiples have large consistency limits as well, and this naturally commends itself to 159th-octave temperaments. | ||
This page collects temperaments that are of theoretical interest specific to 159edo, beyond just [[53edo]]. | |||
== Auric == | == Auric == | ||
''Auric'', named after [[Aura]], is defined by setting the 2.3.5.11 mapping to that of 159edo and the generator for the prime 7 being independent. | ''Auric'', named after [[Aura]], is defined by setting the 2.3.5.11 mapping to that of 159edo and the generator for the prime 7 being independent. | ||
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''Aemilic'' is described as the 159 & 954 temperament in the 17-limit and is named after the minor planet [[wikipedia:159 Aemilia|159 Aemilia]]. | ''Aemilic'' is described as the 159 & 954 temperament in the 17-limit and is named after the minor planet [[wikipedia:159 Aemilia|159 Aemilia]]. | ||
In the 7-limit, aemilic tempers out the [[landscape comma]] alongisde the [[Mercator comma]], and also {{monzo|-76 41 12 -6}}. | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 250047/250000, {{monzo|-84 53}} | |||
{{Mapping|legend=1|159 252 0 -292|0 0 1 2}} | |||
: mapping generators: ~225/224 = 1\159, ~5 | |||
[[Optimal tuning]] ([[CTE]]): ~5/4 = 386.303 | |||
[[Support]]ing [[ET]]s: {{EDOs|159, 795, 954, 1749, 2544, 2703}} | |||
=== 11-limit === | |||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: 3025/3024, 160083/160000, {{monzo|34 19 8 4 -1}} | |||
{{Mapping|legend=1|159 252 0 -292 550|0 0 1 2 0}} | |||
: mapping generators: ~225/224 = 1\159, ~5 | |||
[[Optimal tuning]] ([[CTE]]): ~5/4 = 386.303 | |||
[[Support]]ing [[ET]]s: {{EDOs|159, 795, 954}} | |||
=== 13-limit === | |||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: 3025/3024, 123201/123200, 160083/160000, 4100625/4100096 | |||
{{Mapping|legend=1|159 252 0 -292 550 -150|0 0 1 2 0 2}} | |||
: mapping generators: ~225/224 = 1\159, ~5 | |||
[[Optimal tuning]] ([[CTE]]): ~5/4 = 386.303 | |||
[[Support]]ing [[ET]]s: {{EDOs|159, 795, 954}} | |||
=== 17-limit === | |||
[[Subgroup]]: 2.3.5.7.11.13.17 | [[Subgroup]]: 2.3.5.7.11.13.17 | ||
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[[Support]]ing [[ET]]s: {{EDOs|159, 795g, 954}} | [[Support]]ing [[ET]]s: {{EDOs|159, 795g, 954}} | ||
{{Navbox fractional-octave}} | |||