Syntonic–diatonic equivalence continuum: Difference between revisions
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 |
+dirt |
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| −1/2 = −0.5 || 1/3 = 0.{{overline|3}} || [[Uncle]] || {{monzo| 12 -6 -1 }} | | −1/2 = −0.5 || 1/3 = 0.{{overline|3}} || [[Uncle]] || {{monzo| 12 -6 -1 }} | ||
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| 1/3 = 0.{{overline|3}} || −1/2 = −0.5 || [[Dirt]] || {{monzo| 28 -19 1 }} | |||
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| 5/2 = 2.5 || 5/3 = 1.{{overline|6}} || [[Counterpental]] || {{monzo| 36 -30 5 }} | | 5/2 = 2.5 || 5/3 = 1.{{overline|6}} || [[Counterpental]] || {{monzo| 36 -30 5 }} | ||
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: ''For extensions, see [[Archytas clan #Ultrapyth]].'' | : ''For extensions, see [[Archytas clan #Ultrapyth]].'' | ||
The 5-limit version of ultrapyth tempers out the [[ultrapyth comma]]. It is generated by a perfect fifth. The interval class of 5 is found at +14 fifths as a double augmented unison (C–Cx). It corresponds to {{nowrap|''m'' {{=}} -1}} and {{nowrap|''n'' {{=}} 1/2}}. | The 5-limit version of ultrapyth tempers out the [[ultrapyth comma]]. It is generated by a perfect fifth. The interval class of 5 is found at +14 fifths as a double-augmented unison (C–Cx). It corresponds to {{nowrap|''m'' {{=}} -1}} and {{nowrap|''n'' {{=}} 1/2}}. | ||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
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[[Badness]] (Smith): 0.795243 | [[Badness]] (Smith): 0.795243 | ||
== Dirt == | |||
{{Main| Dirt }} | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: {{monzo| 28 -19 1 }} | |||
{{Mapping|legend=1| 1 0 -28 | 0 1 19 }} | |||
: mapping generators: ~2, ~3 | |||
[[Optimal tuning]]s: | |||
* [[CTE]]: ~2 = 1200.000, ~3/2 = 714.992 | |||
: [[error map]]: {{val| 0.000 +13.037 -1.473 }} | |||
* [[CWE]]: ~2 = 1200.000, ~3/2 = 715.341 | |||
: error map: {{val| 0.000 +13.386 +5.157 }} | |||
{{Optimal ET sequence|legend=1| 5, 42c, 47b, 52b, 109bbc }} | |||
[[Badness]] (Smith): 2.36 | |||
== Rodan (5-limit) == | == Rodan (5-limit) == | ||