Syntonic–chromatic equivalence continuum: Difference between revisions
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{{Main| Deeptone }} | {{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 ( | 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 | [[Subgroup]]: 2.3.5 | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2/1 = | * [[CTE]]: ~2/1 = 1200.000, ~3/2 = 689.879 | ||
* [[CWE]]: ~2/1 = | * [[CWE]]: ~2/1 = 1200.000, ~3/2 = 689.312 | ||
{{Optimal ET sequence|legend=1| 7, 33, 40, 47, 87b }} | {{Optimal ET sequence|legend=1| 7, 33, 40, 47, 87b }} | ||
[[Badness]]: 0.403 | [[Badness]] (Smith): 0.403 | ||
== Shallowtone (5-limit) == | == Shallowtone (5-limit) == | ||
: ''For extensions, see [[Mint temperaments #Shallowtone]].'' | : ''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- | 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 | [[Subgroup]]: 2.3.5 | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1200.000, ~3/2 = 681.801 | ||
* [[CWE]]: ~2 = | * [[CWE]]: ~2 = 1200.000, ~3/2 = 682.662 | ||
{{Optimal ET sequence|legend=1| 7, 30b, 37b, 44b, 51b, 58bc, 65bbc }} | {{Optimal ET sequence|legend=1| 7, 30b, 37b, 44b, 51b, 58bc, 65bbc }} | ||
[[Badness]]: 0.666 | [[Badness]] (Smith): 0.666 | ||
== Nethertone == | == Nethertone == | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1200.000, ~2560/2187 = 345.946 | ||
* [[CWE]]: ~2 = | * [[CWE]]: ~2 = 1200.000, ~2560/2187 = 345.599 | ||
{{Optimal ET sequence|legend=1| 7, 38c, 45c, 52, 59b, 66b }} | {{Optimal ET sequence|legend=1| 7, 38c, 45c, 52, 59b, 66b }} | ||
[[Badness]]: 0.828 | [[Badness]] (Smith): 0.828 | ||
== Enipucrop == | == Enipucrop == | ||
Enipucrop corresponds to {{nowrap|''n'' {{=}} 3/2}} and {{nowrap|''m'' {{=}} 3}}, and can be described as the 6b & | Enipucrop corresponds to {{nowrap|''n'' {{=}} 3/2}} and {{nowrap|''m'' {{=}} 3}}, and can be described as the 6b & 7 temperament. Its name is ''porcupine'' spelled backwards, because that is what this temperament is – it is porcupine, with the generator sharp of 2\7 such that the major and minor thirds switch places. The fifths are very flat, meaning that this is more of a melodic temperament than a harmonic one. | ||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1200.000, ~16/15 = 170.671 | ||
* [[POTE]]: ~2 = | * [[POTE]]: ~2 = 1200.000, ~16/15 = 173.101 | ||
{{Optimal ET sequence|legend=1| 6b, 7 }} | {{Optimal ET sequence|legend=1| 6b, 7 }} | ||
[[Badness]]: 0.1439 | [[Badness]] (Smith): 0.1439 | ||
== Nadir == | == Nadir == | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1200.000, ~729/640 = 168.983 | ||
* [[CWE]]: ~2 = | * [[CWE]]: ~2 = 1200.000, ~729/640 = 169.223 | ||
{{Optimal ET sequence|legend=1| 7, 57c, 64, 71b, 78b, 85b }} | {{Optimal ET sequence|legend=1| 7, 57c, 64, 71b, 78b, 85b }} | ||
[[Badness]]: 1.47 | [[Badness]] (Smith): 1.47 | ||
== Sixix (5-limit) == | == Sixix (5-limit) == | ||
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: ''For extensions, see [[Porwell temperaments #Absurdity]].'' | : ''For extensions, see [[Porwell temperaments #Absurdity]].'' | ||
Absurdity corresponds to {{nowrap|''n'' {{=}} 7}}, and can be described as the | Absurdity corresponds to {{nowrap|''n'' {{=}} 7}}, and can be described as the 77 & 84 temperament, so named because it truly is an absurd temperament. The generator is ~81/80 and the period is ~800/729, which is (10/9)/(81/80). | ||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~800/729 = | * [[CTE]]: ~800/729 = 171.429, ~3/2 = 700.538 (~81/80 = 14.824) | ||
* [[POTE]]: ~800/729 = | * [[POTE]]: ~800/729 = 171.429, ~3/2 = 700.187 (~81/80 = 14.473) | ||
{{Optimal ET sequence|legend=1| 7, …, 70, 77, 84, 329, 413b, 497b }} | {{Optimal ET sequence|legend=1| 7, …, 70, 77, 84, 329, 413b, 497b }} | ||
[[Badness]]: 0.341202 | [[Badness]] (Smith): 0.341202 | ||
== Sevond (5-limit) == | == Sevond (5-limit) == | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~10/9 = | * [[CTE]]: ~10/9 = 171.429, ~3/2 = 705.526 (~250/243 = 19.812) | ||
* [[POTE]]: ~10/9 = | * [[POTE]]: ~10/9 = 171.429, ~3/2 = 706.288 (~250/243 = 20.574) | ||
{{Optimal ET sequence|legend=1| 7, 42, 49, 56, 119 }} | {{Optimal ET sequence|legend=1| 7, 42, 49, 56, 119 }} | ||
[[Badness]]: 0.339335 | [[Badness]] (Smith): 0.339335 | ||
== Seville == | == Seville == | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~125/108 = | * [[CTE]]: ~125/108 = 171.429, ~3/2 = 710.606 (~25/24 = 24.891) | ||
* [[POTE]]: ~125/108 = | * [[POTE]]: ~125/108 = 171.429, ~3/2 = 706.410 (~25/24 = 20.696) | ||
{{Optimal ET sequence|legend=1| 7, 35b, 42c }} | {{Optimal ET sequence|legend=1| 7, 35b, 42c }} | ||
[[Badness]]: 0.4377 | [[Badness]] (Smith): 0.4377 | ||
== Artoneutral (5-limit) == | == Artoneutral (5-limit) == | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1200.000, ~400/243 = 855.213 | ||
* [[CWE]]: ~2 = | * [[CWE]]: ~2 = 1200.000, ~400/243 = 855.196 | ||
{{Optimal ET sequence|legend=1| 7, … 73, 80, 87 }} | {{Optimal ET sequence|legend=1| 7, … 73, 80, 87 }} | ||
[[Badness]]: 0.348 | [[Badness]] (Smith): 0.348 | ||
[[Category:7edo]] | [[Category:7edo]] | ||
[[Category:Equivalence continua]] | [[Category:Equivalence continua]] | ||