Marvel–sensamagic equivalence continuum: Difference between revisions
Created page with "{{Mathematical interest}} The '''marvel–sensamagic equivalence continuum''' is a continuum of 7-limit temperament families which equate a number of marvel commas (225/224) with a sensamagic comma (245/243). This continuum is theoretically interesting in that these are all 7-limit temperament families supported by septimal magic temperament. All temperaments in the continuum satisfy {{..." Tags: Mobile edit Mobile web edit |
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* 19 & 41 & 359 ({{nowrap|''n'' {{=}} {{frac|5|3}} {{=}} 1.666…}}) | * 19 & 41 & 359 ({{nowrap|''n'' {{=}} {{frac|5|3}} {{=}} 1.666…}}) | ||
* 19 & 41 & 511 ({{nowrap|''n'' {{=}} {{frac|7|4}} {{=}} 1.75}}) | * 19 & 41 & 511 ({{nowrap|''n'' {{=}} {{frac|7|4}} {{=}} 1.75}}) | ||
== 19 & 41 & 69 == | |||
[[Comma list]]: 234375/229376 | |||
{{Mapping|legend=1| 1 0 0 -15 | 0 1 0 1 | 0 0 1 7 }} | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1201.118¢, ~3 = 1901.764¢, ~5 = 2783.489¢ | |||
* [[CWE]]: ~2 = 1200.000¢, ~3 = 1900.566¢, ~5 = 2780.998¢ | |||
{{Optimal ET sequence|legend=1| 3d, 6b, 9d, 13, 16d, 19, 22, 41 }} | |||
[[Badness]] (Sintel): 16.808 | |||
== Breeze == | |||
[[Comma list]]: 2460375/2458624 | |||
{{Mapping|legend=1| 1 0 2 -1 | 0 1 1 3 | 0 0 -4 -3 }} | |||
: Mapping generators: ~2, ~3, ~56/45 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1200.026¢, ~3 = 1901.897¢, ~56/45 = 378.919¢ | |||
* [[CWE]]: ~2 = 1200.000¢, ~3 = 1900.867¢, ~56/45 = 378.908¢ | |||
{{Optimal ET sequence|legend=1| 19, 22, 41, 89, 111, 130, 152, 171 }} | |||
[[Badness]] (Sintel): 0.520 | |||
[[Category:Magic]] | [[Category:Magic]] | ||
[[Category:Equivalence continua]] | [[Category:Equivalence continua]] | ||