Catalog of rank-4 temperaments: Difference between revisions
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== Semiporwellismic (16384/16335) == | == Semiporwellismic (16384/16335) == | ||
See [[Semiporwellismic clan #Semiporwellismic]]. | See [[Semiporwellismic clan #Semiporwellismic]]. | ||
== Symbiotic (19712/19683) == | |||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: 19712/19683 | |||
[[Mapping]]: [{{val| 1 0 0 0 -8 }}, {{val| 0 1 0 0 9 }}, {{val| 0 0 1 0 0 }}, {{val| 0 0 0 1 -1 }}] | |||
Mapping generators: ~2, ~3, ~5, ~7 | |||
[[Optimal tuning]] ([[POTE]]): ~3/2 = 702.2681, ~5/4 = 386.4785, ~7/4 = 968.9552 | |||
{{Val list|legend=1| 17c, 19e, 24, 34d, 41, 53, 58, 94, 99e, 118, 152, 270, 581, 733, 851, 1003, 1273, 1854, 2124b }} | |||
[[Badness]]: 0.120 × 10<sup>-6</sup> | |||
=== Tridecimal symbiotic === | |||
[[Subgroup]]: 2.3.5.7.11.13 | |||
[[Comma list]]: 2080/2079, 19712/19683 | |||
[[Mapping]]: [{{val| 1 0 0 0 -8 -13 }}, {{val| 0 1 0 0 9 12 }}, {{val| 0 0 1 0 0 -1 }}, {{val| 0 0 0 1 -1 0 }}] | |||
[[Optimal tuning]] ([[POTE]]): ~3/2 = 702.2721, ~5/4 = 386.4790, ~7/4 = 968.9705 | |||
{{Val list|legend=1| 17c, 34dff, 36ce, 41, 53, 58, 94, 111, 152f, 212, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 3127bf }} | |||
[[Badness]]: 3.31 × 10<sup>-6</sup> | |||
== Olympic (131072/130977) == | == Olympic (131072/130977) == | ||
[[Subgroup]]: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: 131072/130977 | [[Comma list]]: [[131072/130977]] | ||
[[Mapping]]: [{{val| 1 0 0 0 17 }}, {{val| 0 1 0 0 -5 }}, {{val| 0 0 1 0 0 }}, {{val| 0 0 0 1 -2 }}] | [[Mapping]]: [{{val| 1 0 0 0 17 }}, {{val| 0 1 0 0 -5 }}, {{val| 0 0 1 0 0 }}, {{val| 0 0 0 1 -2 }}] | ||