Luna family: Difference between revisions
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=== Overview to extensions === | === Overview to extensions === | ||
[[Hemimean clan #Hemithirds|Hemithirds]], a strong extension of [[didacus]] that tempers out [[1029/1024]] alongside [[3136/3125]], might be considered the main [[7-limit]] extension to luna of practical interest, as [[7/4]] is found at only 5 generators. However, luna is an undoubted microtemperament of the [[5-limit]] in its own right, supported by systems like [[118edo]] and [[441edo]], and therefore merits consideration of other extensions to the 7-limit, which are documented on this page. Though of very high complexity, they continue the level of accuracy of 5-limit luna. | [[Hemimean clan #Hemithirds|Hemithirds]] (25 & 31), a strong extension of [[didacus]] that tempers out [[1029/1024]] alongside [[3136/3125]], might be considered the main [[7-limit]] extension to luna of practical interest, as [[7/4]] is found at only 5 generators. However, luna is an undoubted microtemperament of the [[5-limit]] in its own right, supported by systems like [[118edo]] and [[441edo]], and therefore merits consideration of other extensions to the 7-limit, which are documented on this page. Though of very high complexity, they continue the level of accuracy of 5-limit luna. | ||
Weak extensions of luna include hemiluna (87 & 323), semiluna (118 & 292), and subneutral (31 & 441). | |||
Temperaments discussed elsewhere include: | Temperaments discussed elsewhere include: | ||
* [[Hemithirds]] (+3136/3125) → [[Hemimean clan #Hemithirds|Hemimean clan]] | * [[Hemithirds]] (+3136/3125) → [[Hemimean clan #Hemithirds|Hemimean clan]] | ||
The rest are considered below. | |||
== Lunatic == | == Lunatic == | ||
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[[Badness]] (Sintel): 4.54 | [[Badness]] (Sintel): 4.54 | ||
== Semiluna == | == Semiluna == | ||
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Badness (Sintel): 2.24 | Badness (Sintel): 2.24 | ||
== Subneutral == | |||
Subneutral tempers out 2401/2400, the [[breedsma]], and may be described as the {{nowrap| 31 & 441 }} temperament. Despite the name, the generator is only about 3 cents flat of the exact neutral third. | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 2401/2400, 274877906944/274658203125 | |||
{{Mapping|legend=1| 1 -41 8 -5 | 0 60 -8 11 }} | |||
: mapping generators: ~2, ~46875/28672 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1199.9998{{c}}, ~46875/28672 = 851.6994{{c}} (~57344/46875 = 348.3005{{c}}) | |||
: [[error map]]: {{val| -0.000 +0.013 +0.090 -0.132 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~46875/28672 = 851.6995{{c}} (~57344/46875 = 348.3005{{c}}) | |||
: error map: {{val| 0.000 +0.014 +0.090 -0.132 }} | |||
{{Optimal ET sequence|legend=1| 31, …, 348, 379, 410, 441, 1354, 1795, 2236 }} | |||
[[Badness]] (Sintel): 1.16 | |||
[[Category:Luna family| ]] <!-- main article --> | |||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category: | [[Category:Catalogs of rank-2 temperaments]] | ||