Syntonic–31 equivalence continuum: Difference between revisions
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Examples of temperaments with fractional values of ''n'': | Examples of temperaments with fractional values of ''n'': | ||
* 31 & 70c (''n'' = 11/2 = 5.5) | * 31 & 70c (''n'' = 11/2 = 5.5) | ||
* [[Marvel temperaments#Slender|Slender]] (''n'' = 13/2 = 6.5) | * [[Marvel temperaments #Slender|Slender]] (''n'' = 13/2 = 6.5) | ||
* [[Breedsmic temperaments#Tertiaseptal|Tertiaseptal]] (''n'' = 22/3 = 7.{{overline|3}}) | * [[Mirkwai clan #Eris|Eris]] (''n'' = 29/4 = 7.25) | ||
* [[Luna family#Luna|Luna]] (''n'' = 15/2 = 7.5) | * [[Breedsmic temperaments #Tertiaseptal|Tertiaseptal]] (''n'' = 22/3 = 7.{{overline|3}}) | ||
* [[Luna family #Luna|Luna]] (''n'' = 15/2 = 7.5) | |||
* [[Breedsmic temperaments #Quasiorwell|Quasiorwell]] (''n'' = 38/5 = 7.6) | |||
* [[Mirkwai clan #Grendel|Grendel]] (''n'' = 23/3 = 7.{{overline|6}}) | * [[Mirkwai clan #Grendel|Grendel]] (''n'' = 23/3 = 7.{{overline|6}}) | ||
* [[31-comma temperaments#Birds|Birds]] (''n'' = 31/4 = 7.75) | * [[31-comma temperaments #Birds|Birds]] (''n'' = 31/4 = 7.75) | ||
* [[Porwell temperaments|Countermiracle]] (''n'' = 25/3 = 8.{{overline|3}}) | * [[Porwell temperaments #Countermiracle|Countermiracle]] (''n'' = 25/3 = 8.{{overline|3}}) | ||
* [[Hemimean clan#Semisept|Semisept]] (''n'' = 17/2 = 8.5) | * [[Hemimean clan #Semisept|Semisept]] (''n'' = 17/2 = 8.5) | ||
* [[Casablanca | * [[Starling temperaments #Casablanca|Casablanca]] (''n'' = 19/2 = 9.5) | ||
== Quadlayo (31 & 12c) == | == Quadlayo (31 & 12c) == | ||
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Mapping: [{{val| 1 2 -9 }}, {{val| 0 -1 27 }}] | Mapping: [{{val| 1 2 -9 }}, {{val| 0 -1 27 }}] | ||
POTE generator: ~4/3 = 503. | POTE generator: ~4/3 = 503.050 | ||
Vals: {{Val list| 12c, 19c, 31, 43c, 50c }} | Vals: {{Val list| 12c, 19c, 31, 43c, 50c }} | ||
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[http://x31eq.com/cgi-bin/rt.cgi?ets=31_12c&limit=5 The temperament finder - 5-limit 31 & 12c] | [http://x31eq.com/cgi-bin/rt.cgi?ets=31_12c&limit=5 The temperament finder - 5-limit 31 & 12c] | ||
== Quadlaleyo (31 & 70c) == | |||
Comma list: {{monzo| -54 18 11 }} = 18917016064453125/18014398509481984 | |||
Mapping: [{{val| 1 3 0 }}, {{val| 0 -11 18 }}] | |||
POTE generator: ~32768/30375 = 154.597 | |||
Vals: {{Val list| 8c, 23c, 31, 39c, 132, 163 }} | |||
Badness: 2.067160 | |||
[http://x31eq.com/cgi-bin/rt.cgi?ets=31_70c&limit=5 The temperament finder - 5-limit 31 & 70c] | |||
== Ampersand (31 & 41) == | |||
{{See also|Gamelismic clan #Miracle}} | |||
Comma list: {{monzo| -25 7 6 }} = 34171875/33554432 | |||
Mapping: [{{val| 1 1 3 }}, {{val| 0 6 -7 }}] | |||
POTE generator: ~16/15 = 116.673 | |||
Vals: {{Val list| 10, 21, 31, 41, 72 }} | |||
Badness: 0.165755 | |||
== Lalasepbigu (31 & 13c) == | == Lalasepbigu (31 & 13c) == | ||
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Mapping: [{{val| 1 7 12 }}, {{val| 0 -14 -25 }}] | Mapping: [{{val| 1 7 12 }}, {{val| 0 -14 -25 }}] | ||
POTE generator: ~25000/19683 = 464. | POTE generator: ~25000/19683 = 464.423 | ||
Vals: {{Val list| 13c, 18bc, 31, 44c, 49bc, 75c, 80bc }} | Vals: {{Val list| 13c, 18bc, 31, 44c, 49bc, 75c, 80bc }} | ||
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[http://x31eq.com/cgi-bin/rt.cgi?ets=31_13c&limit=5 The temperament finder - 5-limit 31 & 13c] | [http://x31eq.com/cgi-bin/rt.cgi?ets=31_13c&limit=5 The temperament finder - 5-limit 31 & 13c] | ||
[[Category:31edo]] | [[Category:31edo]] | ||