Syntonic–31 equivalence continuum: Difference between revisions
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| [[31-comma temperaments|31 & 31c]] | | [[31-comma temperaments|31 & 31c]] | ||
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| {{monzo|-49 31}} | | {{monzo|-49 31}} | ||
|- | |- | ||
| 1 | | 1 | ||
| 31 & 12c | | 31 & 12c | ||
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| {{monzo|-45 27 1}} | | {{monzo|-45 27 1}} | ||
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| [[Würschmidt]] | | [[Würschmidt]] | ||
| 393216/390625 | | 393216/390625 | ||
| {{monzo| | | {{monzo|17 1 -8}} | ||
|- | |- | ||
| 9 | | 9 | ||
| [[Valentine]] | | [[Valentine]] | ||
| 1990656/1953125 | | 1990656/1953125 | ||
| {{monzo| | | {{monzo|13 5 -9}} | ||
|- | |- | ||
| 10 | | 10 | ||
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| 14 | | 14 | ||
| 31 & 13c | | 31 & 13c | ||
| 847288609443/781250000000 | | 847288609443/781250000000 | ||
| {{monzo|-7 25 -14}} | | {{monzo|-7 25 -14}} | ||
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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}}) | |||
* [[Luna family#Luna|Luna]] (''n'' = 15/2 = 7.5) | * [[Luna family#Luna|Luna]] (''n'' = 15/2 = 7.5) | ||
* [[Mirkwai clan #Grendel|Grendel]] (''n'' = 23/3 = 7.{{overline|6}}) | |||
* [[31-comma temperaments#Birds|Birds]] (''n'' = 31/4 = 7.75) | |||
* [[Porwell temperaments|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 node|Casablanca]] (''n'' = 19/2 = 9.5) | * [[Casablanca node|Casablanca]] (''n'' = 19/2 = 9.5) | ||
== 31 & 12c == | == Quadlayo (31 & 12c) == | ||
In fifths notation, 5/4 is mapped to the quadruple-diminished fifth. | In fifths notation, 5/4 is mapped to the quadruple-diminished fifth. | ||
Comma list: {{monzo| -45 27 1 }} = 38127987424935/35184372088832 | Comma list: {{monzo| -45 27 1 }} = 38127987424935/35184372088832 | ||
Mapping: [{{val| 1 2 -9 }}, {{val| 0 -1 27 }}] | |||
POTE generator: ~4/3 = 503.0504 | POTE generator: ~4/3 = 503.0504 | ||
Vals: {{Val list| 12c, 19c, 31, 43c, 50c }} | |||
Badness: 2.993628 | |||
[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] | ||
== 31 & 13c == | == Lalasepbigu (31 & 13c) == | ||
Comma list: {{monzo| -7 25 -14 }} = 847288609443/781250000000 | |||
Mapping: [{{val| 1 7 12 }}, {{val| 0 -14 -25 }}] | |||
POTE generator: 464.4231 | POTE generator: ~25000/19683 = 464.4231 | ||
Vals: {{Val list| 13c, 18bc, 31, 44c, 49bc, 75c, 80bc }} | |||
Badness: 2.094918 | |||
[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] | ||
== 31 & 70c == | == Quadlaleyo (31 & 70c) == | ||
Comma list: {{monzo| -54 18 11 }} = 18917016064453125/18014398509481984 | |||
Mapping: [{{val| 1 3 0 }}, {{val| 0 -11 18 }}] | |||
POTE generator: 154.5972 | POTE generator: ~32768/30375 = 154.5972 | ||
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] | [http://x31eq.com/cgi-bin/rt.cgi?ets=31_70c&limit=5 The temperament finder - 5-limit 31 & 70c] | ||