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Syntonic–diatonic equivalence continuum: Difference between revisions

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Line 27: Line 27:
| -2
| -2
| -3
| -3
| [[Laconic family#Laconic|Laconic]]
| [[Gamelismic clan #Gorgo|Laconic]]
| [[2187/2000]]
| [[2187/2000]]
| {{monzo| -4 7 -3 }}
| {{monzo| -4 7 -3 }}
Line 77: Line 77:
| [[Pental family|Pental]]
| [[Pental family|Pental]]
|  
|  
| {{monzo| 28 -25 5 }}
| {{monzo| -28 25 -5 }}
|-
|-
| 7
| 7
Line 83: Line 83:
| [[Hemiseven]]
| [[Hemiseven]]
|  
|  
| {{monzo| 32 -29 6 }}
| {{monzo| -32 29 -6 }}
|-
|-
| …
| …
Line 100: Line 100:
* [[University temperament|University]] (''n'' = -1.5)
* [[University temperament|University]] (''n'' = -1.5)
* [[Uncle]] (''n'' = -0.5)
* [[Uncle]] (''n'' = -0.5)
* 5 & 32p (''n'' = 0.5)
* 5 & 32 (''n'' = 0.5)
* 5 & 56 (''n'' = 1.5)
* 5 & 56 (''n'' = 1.5)
* Counterpental (''n'' = 2.5)
* Counterpental (''n'' = 2.5)
* [[Septiquarter]] (''n'' = 3.5)
* [[Septiquarter]] (''n'' = 3.5)
* 2513 & 559 (''n'' = 4.2)
* 2513 & 559 (''n'' = 4.2)
* 5 & 118 (''n'' = 4.5)
* 5 & 118 (''n'' = 4.5)
* 5 & 137 (''n'' = 5.5)


== Hemiseven (5-limit) ==
== Hemiseven (5-limit) ==
{{See also|Gamelismic clan #Hemiseven}}


Comma: {{Monzo|32 -29 6}}
Comma: {{Monzo|32 -29 6}}


POTE generator: 483.2474 cents
Mapping: [{{val|1 4 14}}, {{val|0 -6 -29}}]


Map: [<1 4 14|, <0 -6 -29|]
POTE generator: ~320/243 = 483.2474 cents


EDOs: {{EDOs| 5, 10c, 67c, 72, 77, 82c, 139c, 144, 149, 154 }}
Vals: {{Val list| 5, 62c, 67c, 72, 149, 221, 370, 591b, 961bb }}
 
Badness: 0.720465


[http://x31eq.com/cgi-bin/rt.cgi?ets=72_5&limit=5 The temperament finder - 5-limit 5 & 72]
[http://x31eq.com/cgi-bin/rt.cgi?ets=72_5&limit=5 The temperament finder - 5-limit 5 & 72]


== 5 & 32p ==
== Sasayo (5 & 32) ==
Comma: {{Monzo|20 -14 1}} = 5242880/4782969


Comma: {{Monzo|20 -14 1}} (5242880/4782969)
Mapping: [{{val|1 2 8}}, {{val|0 -1 -14}}]


POTE generator: ~4/3 = 486.1713 cents
POTE generator: ~4/3 = 486.1713 cents


Map: [<1 2 8|, <0 -1 -14|]
Vals: {{Val list| 5, 27c, 32, 37, 79bc, 116bbc }}


EDOs: {{EDOs| 5, 32, 37, 42 }}
Badness: 0.795243


[http://x31eq.com/cgi-bin/rt.cgi?ets=5_32p&limit=5 The temperament finder - 5-limit 5 & 32p]
[http://x31eq.com/cgi-bin/rt.cgi?ets=5_32p&limit=5 The temperament finder - 5-limit 5 & 32p]


== 5 & 56 ==
== Trisatriyo (5 & 56) ==
Comma: {{Monzo|28 -22 3}} = 33554432000/31381059609


Comma: {{Monzo|28 -22 3}} (33554432000/31381059609)
Mapping: [{{val|1 1 -2}}, {{val|0 3 22}}]


POTE generator: 235.8673 cents
POTE generator: ~2560/2187 = 235.8673 cents


Map: [<1 1 -2|, <0 3 22|]
Vals: {{Val list| 5, 56, 61 }}


EDOs: {{EDOs| 5, 56, 61 }}
Badness: 1.323443


[http://x31eq.com/cgi-bin/rt.cgi?ets=5_56&limit=5 The temperament finder - 5-limit 5 & 56]
[http://x31eq.com/cgi-bin/rt.cgi?ets=5_56&limit=5 The temperament finder - 5-limit 5 & 56]


== Counterpental ==
== Counterpental ==
Comma: {{Monzo|36 -30 5}}


Comma: {{Monzo|36 -30 5}}
Mapping: [{{val|5 8 12}}, {{val|0 -1 -6}}]


POTE generator: 15.4278 cents
POTE generator: 15.4278 cents


Map: [<5 8 12|, <0 -1 -6|]
Vals: {{Val list| 5, 75, 80 }}


EDOs: {{EDOs| 5, 75, 80 }}
Badness: 1.500224


[http://x31eq.com/cgi-bin/rt.cgi?ets=5_75&limit=5 The temperament finder - 5-limit 5 & 75]
[http://x31eq.com/cgi-bin/rt.cgi?ets=5_75&limit=5 The temperament finder - 5-limit 5 & 75]


== Septiquarter (5-limit) ==
== Septiquarter (5-limit) ==
{{See also|Hemifamity temperaments #Septiquarter}}


Comma: {{Monzo|44 -38 7}}
Comma: {{Monzo|44 -38 7}}


POTE generator: 242.4567 cents
Mapping: [{{val|1 3 10}}, {{val|0 -7 -38}}]
 
POTE generator: ~204800/177147 = 242.4567 cents


Map: [<1 3 10|, <0 -7 -38|]
Vals: {{Val list| 5, 89c, 94, 99, 193, 292, 391 }}


EDOs: {{EDOs| 5, 94, 99, 193, 198, 292, 297 }}
Badness: 0.971284


[http://x31eq.com/cgi-bin/rt.cgi?ets=99_94&limit=5 The temperament finder - 5-limit 99 & 94]
[http://x31eq.com/cgi-bin/rt.cgi?ets=99_94&limit=5 The temperament finder - 5-limit 99 & 94]


== 2513 & 559 ==
== 559 & 2513 ==
Comma: {{Monzo|-124 109 -21}}


Comma: {{Monzo|-124 109 -21}}
Mapping: [{{val|1 10 46}}, {{val|0 -21 -109}}]
 
POTE generator: ~3355443200000/2541865828329 = 480.8595 cents
 
Vals: {{Val list| 5, 267c, 272c, 277, 559, 1395, 1954, 2513, 40767, 43280, 45793, 48306, 50819, 53332, 55845, 58358, 60871, 63384, 65897, 68410, 70923, 73436, 75949, 78462 }}
 
Badness: 0.134523
 
[http://x31eq.com/cgi-bin/rt.cgi?ets=2513_559&limit=5 The temperament finder - 5-limit 2513 & 559]
 
== Quinla-tritrigu (5 & 118) ==
Comma: {{Monzo|-52 46 -9}}


POTE generator: 480.8595 cents
Mapping: [{{val|1 -2 -16}}, {{val|0 9 46}}]


Map: [<1 10 46|, <0 -21 -109|]
POTE generator: ~320/243 = 477.9609 cents


EDOs: {{EDOs| 559, 1118, 1395, 1954, 2513, 3072, 3631, 4467, 5026, 5585 }}
Vals: {{Val list| 5, 108c, 113, 118, 1057, 1175, 1293, 1411, 1529, 1647, 1765, 1883, 2001b, 3884b }}


[http://x31eq.com/cgi-bin/rt.cgi?ets=2513_559&limit=5 The temperament finder - 5-limit 2153 & 559]
Badness: 0.617683


== 5 & 137 ==
== Tribilalegu (5 & 137) ==
Comma: {{Monzo|-60 54 -11}}


Comma: {{Monzo|60 -54 11}}
Mapping: [{{val|1 6 24}}, {{val|0 -11 -54}}]


POTE generator: 481.7421 cents
POTE generator: ~320/243 = 481.7421 cents


Map: [<1 6 24|, <0 -11 -54|]
Vals: {{Val list| 5, 127c, 132, 137, 553, 690b, 827b, 964b }}


EDOs: {{EDOs| 5, 132, 137, 142, 274, 279 }}
Badness: 3.620981


[http://x31eq.com/cgi-bin/rt.cgi?ets=5_137&limit=5 The temperament finder - 5-limit 5 & 137]
[http://x31eq.com/cgi-bin/rt.cgi?ets=5_137&limit=5 The temperament finder - 5-limit 5 & 137]
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