Syntonic–chromatic equivalence continuum: Difference between revisions
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| 11/2 = 5.5 || 11/9 = 1.{{overline|2}} || [[Undetrita]] || {{monzo| -22 30 -11 }} | | 11/2 = 5.5 || 11/9 = 1.{{overline|2}} || [[Undetrita]] || {{monzo| -22 30 -11 }} | ||
|} | |} | ||
== Deeptone a.k.a. tragicomical == | |||
{{Main| Deeptone }} | |||
Deeptone is generated by a fifth, which is typically sharper than in [[7edo]] but flatter than in [[flattone]]. The ~5/4 is reached by eleven fifths octave-reduced, which is an augmented third (C–E♯). | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: 177147/163840 | |||
{{Mapping|legend=1| 1 0 -15 | 0 1 11 }} | |||
: mapping generators: ~2, ~3 | |||
[[Optimal tuning]]s: | |||
* [[CTE]]: ~2/1 = 1\1, ~3/2 = 689.8791 | |||
* [[CWE]]: ~2/1 = 1\1, ~3/2 = 689.3122 | |||
{{Optimal ET sequence|legend=1| 7, 33, 40, 47, 87b }} | |||
[[Badness]]: 0.403 | |||
== Shallowtone (5-limit) == | |||
: ''For extensions, see [[Mint temperaments #Shallowtone]].'' | |||
Shallowtone is generated by a fifth, which is typically sharper than in [[mavila]] but flatter than in [[7edo]]. The ~5/4 is reached by minus ten fifths octave-reduced, which is an augmented third (C-E𝄪) in melodic [[2L 5s|antidiatonic]] notation and a diminished third (C-E𝄫) in harmonic antidiatonic notation. | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: 295245/262144 | |||
{{Mapping|legend=1| 1 0 18 | 0 1 -10 }} | |||
: mapping generators: ~2, ~3 | |||
[[Optimal tuning]]s: | |||
* [[CTE]]: ~2 = 1\1, ~3/2 = 681.8012 | |||
* [[CWE]]: ~2 = 1\1, ~3/2 = 682.6617 | |||
{{Optimal ET sequence|legend=1| 7, 30b, 37b, 44b, 51b, 58bc, 65bbc }} | |||
[[Badness]]: 0.666 | |||
== Nethertone == | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: 14348907/13107200 | |||
{{Mapping|legend=1| 1 1 -1 | 0 2 15 }} | |||
: mapping generators: ~2, ~2560/2187 | |||
[[Optimal tuning]]s: | |||
* [[CTE]]: ~2 = 1\1, ~2560/2187 = 345.9462 | |||
* [[CWE]]: ~2 = 1\1, ~2560/2187 = 345.5992 | |||
{{Optimal ET sequence|legend=1| 7, 38c, 45c, 52, 59b, 66b }} | |||
[[Badness]]: 0.828 | |||
== Enipucrop == | == Enipucrop == | ||
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[[Badness]]: 0.1439 | [[Badness]]: 0.1439 | ||
== Nadir == | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: 1162261467/1048576000 | |||
{{Mapping|legend=1| 1 2 5 | 0 -3 -19 }} | |||
: mapping generators: ~2, ~729/640 | |||
[[Optimal tuning]]s: | |||
* [[CTE]]: ~2 = 1\1, ~729/640 = 168.9826 | |||
* [[CWE]]: ~2 = 1\1, ~729/640 = 169.2234 | |||
{{Optimal ET sequence|legend=1| 7, 57c, 64, 71b, 78b, 85b }} | |||
[[Badness]]: 1.47 | |||
== Sixix (5-limit) == | == Sixix (5-limit) == | ||
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[[Badness]]: 0.341202 | [[Badness]]: 0.341202 | ||
== Sevond (5-limit) == | == Sevond (5-limit) == | ||
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[[Badness]]: 0.4377 | [[Badness]]: 0.4377 | ||
== | == Artoneutral (5-limit) == | ||
: ''For extensions, see [[Hemifamity temperaments #Artoneutral]].'' | |||
5-limit artoneutral is generated by ~243/200 (or ~400/243), same as that of [[amity]] but sharper. This corresponds to {{nowrap|''n'' {{=}} 9/2}} and {{nowrap|''m'' {{=}} 9/7}} and can be described as the 80 & 87 temperament, though [[94edo]] is a notable tuning not appearing in the optimal ET sequence. | |||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
[[Comma list]]: | [[Comma list]]: {{monzo| 14 -22 9 }} | ||
{{Mapping|legend=1| 1 0 - | {{Mapping|legend=1| 1 8 18 | 0 -9 -22 }} | ||
: mapping generators: ~2, ~ | : mapping generators: ~2, ~400/243 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 | * [[CTE]]: ~2 = 1\1, ~400/243 = 855.2127 | ||
* [[CWE]]: ~2 | * [[CWE]]: ~2 = 1\1, ~400/243 = 855.1959 | ||
{{Optimal ET sequence|legend=1| 7, | {{Optimal ET sequence|legend=1| 7, … 73, 80, 87 }} | ||
[[Badness]]: 0. | [[Badness]]: 0.348 | ||
[[Category:7edo]] | [[Category:7edo]] | ||
[[Category:Equivalence continua]] | [[Category:Equivalence continua]] | ||