Immunity family: Difference between revisions
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== Immunity == | == Immunity == | ||
The head of this family is immunity, which splits the perfect twelfth in halves, and [[5/4]] is found in 13 generator steps. Its [[ploidacot]] is alpha-dicot. It is a member of the [[syntonic–limmic equivalence continuum]] with equivalence number ''n'' = 2, meaning the [[Pythagorean limma]] is equated with a stack of two [[syntonic comma]]s. | |||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
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[[Badness]] (Sintel): 4.33 | [[Badness]] (Sintel): 4.33 | ||
=== Overview to extensions === | === Overview to extensions === | ||
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* Immunized adds [[64/63]]; | * Immunized adds [[64/63]]; | ||
* Immune adds [[225/224]]. | * Immune adds [[225/224]]. | ||
The immunity family boasts a very remarkable extension to the [[2.3.5.13 subgroup]], discussed in [[#Subgroup extensions]]. | |||
== Septimal immunity == | == Septimal immunity == | ||
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Comma list: 49/48, 55/54, 896/891 | Comma list: 49/48, 55/54, 896/891 | ||
{{Mapping|legend=0| 1 0 -8 2 9 | 0 2 13 1 -7 }} | |||
Optimal tunings: | Optimal tunings: | ||
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Comma list: 49/48, 55/54, 91/90, 896/891 | Comma list: 49/48, 55/54, 91/90, 896/891 | ||
{{Mapping|legend=0| 1 0 -8 2 9 -9 | 0 2 13 1 -7 16 }} | |||
Optimal tunings: | Optimal tunings: | ||
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Comma list: 49/48, 100/99, 1232/1215 | Comma list: 49/48, 100/99, 1232/1215 | ||
{{Mapping|legend=0| 1 0 -8 2 -14 | 0 2 13 1 22 }} | |||
Optimal tunings: | Optimal tunings: | ||
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Comma list: 49/48, 91/90, 100/99, 352/351 | Comma list: 49/48, 91/90, 100/99, 352/351 | ||
{{Mapping|legend=0| 1 0 -8 2 -14 -9 | 0 2 13 1 22 16 }} | |||
Optimal tunings: | Optimal tunings: | ||
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Comma list: 64/63, 99/98, 1944/1925 | Comma list: 64/63, 99/98, 1944/1925 | ||
{{Mapping|legend=0| 1 0 -8 6 13 | 0 2 13 -4 -12 }} | |||
Optimal tunings: | Optimal tunings: | ||
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Comma list: 100/99, 225/224, 1331/1323 | Comma list: 100/99, 225/224, 1331/1323 | ||
{{Mapping|legend=0| 1 2 5 9 8 | 0 -2 -13 -30 -22 }} | |||
Optimal tunings: | Optimal tunings: | ||
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Comma list: 100/99, 169/168, 225/224, 275/273 | Comma list: 100/99, 169/168, 225/224, 275/273 | ||
{{Mapping|legend=0| 1 2 5 9 8 7 | 0 -2 -13 -30 -22 -16 }} | |||
Optimal tunings: | Optimal tunings: | ||
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Badness (Sintel): 1.18 | Badness (Sintel): 1.18 | ||
== Subgroup extensions == | |||
=== Immunity (2.3.5.13) === | |||
Immunity is naturally a [[2.3.5.13 subgroup|2.3.5.13-subgroup]] temperament as the generator serves as ~[[26/15]] (or its [[octave complement]] ~[[15/13]]), tempering out [[676/675]]. | |||
Subgroup: 2.3.5.13 | |||
Comma list: 676/675, 3200/3159 | |||
{{Mapping|legend=2| 1 0 -8 -9 | 0 2 13 16 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1198.8955{{c}}, ~26/15 = 952.0049{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 952.7890{{c}} | |||
{{Optimal ET sequence|legend=0| 5, …, 29, 34 }} | |||
Badness (Sintel): 0.858 | |||
[[Category:Immunity family| ]] <!-- Main article --> | [[Category:Immunity family| ]] <!-- Main article --> | ||