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Syntonic–kleismic equivalence continuum: Difference between revisions

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|-
|-
| 1
| 1
| Lalayo
| 7c & 12c
| [[71744535/67108864]]
| [[71744535/67108864]]
| {{monzo|-26 15 1}}
| {{monzo|-26 15 1}}
|-
|-
| 2
| 2
| [[High badness temperaments#Hogzilla|Hogzilla]]
| [[High badness temperaments #Hogzilla|Hogzilla]]
| [[4428675/4194304]]
| [[4428675/4194304]]
| {{monzo|-22 11 2}}
| {{monzo|-22 11 2}}
|-
|-
| 3
| 3
| [[High badness temperaments#Stump|Stump]]
| [[High badness temperaments #Stump|Stump]]
| [[273375/262144]]
| [[273375/262144]]
| {{monzo|-18 7 3}}
| {{monzo|-18 7 3}}
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Examples of temperaments with fractional values of ''k'':
Examples of temperaments with fractional values of ''k'':


* 19 & 8c (''k'' = 3.5)
* 8c & 11 (''n'' = 3.5)
* [[High badness temperaments#Unsmate|Unsmate]] (''k'' = 4.5)
* [[High badness temperaments#Unsmate|Unsmate]] (''n'' = 4.5)
* [[Sycamore family#Sycamore|Sycamore]] (''k'' = 5.5)
* [[Sycamore family#Sycamore|Sycamore]] (''n'' = 5.5)
* [[Counterhanson]] (''k'' = 25/4 = 6.25)
* [[Counterhanson]] (''n'' = 25/4 = 6.25)
* [[Enneadecal]] (''k'' = 19/3 = 6.{{overline|3}})
* [[Enneadecal]] (''n'' = 19/3 = 6.{{overline|3}})
* [[Very high accuracy temperaments#Egads|Egads]] (''k'' = 51/8 = 6.375)
* [[Very high accuracy temperaments#Egads|Egads]] (''n'' = 51/8 = 6.375)
* [[Acrokleismic]] (''k'' = 32/5 = 6.4)
* [[Acrokleismic]] (''n'' = 32/5 = 6.4)
* 19 & 506 (''k'' = 58/9 = 6.{{overline|4}})
* [[Parakleismic]] (''n'' = 6.5)
* [[Parakleismic]] (''k'' = 6.5)
* [[Countermeantone]] (''n'' = 20/3 = 6.{{overline|6}})
* [[Countermeantone]] (''k'' = 20/3 = 6.{{overline|6}})
* [[Mowgli]] (''n'' = 7.5)
* [[Mowgli]] (''k'' = 7.5)


== Lalayo ==
== Lalasepyo (8c & 11) ==
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -26 15 1 }} = 71744535/67108864
 
[[Mapping]]: [{{val| 1 2 -4 }}, {{val| 0 -1 15 }}]
 
[[POTE generator]]: ~4/3 = 505.348 cents
 
{{Val list|legend=1| 7c, 12c, 19 }}
 
[[Badness]]: 0.803397
 
== Lalasepyo (8c & 19) ==
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


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[[Badness]]: 0.317551
[[Badness]]: 0.317551
== 19 & 506 ==
[[Subgroup]]: 2.3.5
[[Comma list]]: {{monzo| 38 61 -58 }}
[[Mapping]]: [{{val| 1 26 28 }}, {{val| 0 -58 -61 }}]
[[Optimal tuning]] ([[POTE]]): ~{{monzo| -12 -20 19 }} = 505.1394
{{Val list|legend=1| 19, 468, 487, 506, 1031 }}
[[Badness]]: 2.105450
[http://x31eq.com/cgi-bin/rt.cgi?ets=19_506&limit=5 The temperament finder - 5-limit 19 & 506]


== Countermeantone ==
== Countermeantone ==
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