Syntonic–limmic equivalence continuum: Difference between revisions
Expand (ultrapyth and rodan) |
Move 5-limit superpyth here cuz it's simpler and many are more familiar with the syntonic comma and diatonic semitone than anything about the 22-comma |
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| 11/2 = 5.5 || 11/9 = 1.{{overline|2}} || 5 & 137 || {{monzo| -60 54 -11 }} | | 11/2 = 5.5 || 11/9 = 1.{{overline|2}} || 5 & 137 || {{monzo| -60 54 -11 }} | ||
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== Superpyth (5-limit) == | |||
: ''For extensions, see [[Archytas clan #Superpyth]] and [[Jubilismic clan #Bipyth]].'' | |||
In the 5-limit, superpyth tempers out [[20480/19683]]. It has a fifth generator of ~3/2 = ~710¢ and ~5/4 is found at +9 generator steps, as an augmented second (C–D#). It corresponds to ''n'' = 1, meaning that the syntonic comma is equated with the diatonic semitone. | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: 20480/19683 | |||
{{Mapping|legend=1| 1 0 -12 | 0 1 9 }} | |||
: mapping generators: ~2, ~3 | |||
[[Optimal tuning]]s: | |||
* [[CTE]]: ~2 = 1200.000, ~3/2 = 709.393 | |||
: [[error map]]: {{val| 0.000 +7.438 -1.774 }} | |||
* [[POTE]]: ~2 = 1200.000, ~3/2 = 710.078 | |||
: error map: {{val| 0.000 +8.123 +4.385 }} | |||
{{Optimal ET sequence|legend=1| 5, 17, 22, 49, 120b, 169bbc }} | |||
[[Badness]] (Smith): 0.135141 | |||
== Uncle (5-limit) == | == Uncle (5-limit) == | ||