Starling–sensamagic equivalence continuum: Difference between revisions
Created page with "{{Mathematical interest}} The '''starling–sensamagic equivalence continuum''' is a continuum of 7-limit temperament families which equate a number of starling commas (126/125) with a sensamagic comma (245/243). This continuum is theoretically interesting in that these are all 7-limit temperament families supported by septimal sensi temperament. All temperaments in the continuum sa..." Tags: Mobile edit Mobile web edit |
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Examples of temperaments with fractional values of ''n'': | Examples of temperaments with fractional values of ''n'': | ||
* | * [[#Sensibeta|Sensibeta]] ({{nowrap|''n'' {{=}} {{frac|1|2}} {{=}} 0.5}}) | ||
* 19 & 46 & 193 ({{nowrap|''n'' {{=}} {{frac|2|3}} {{=}} 0.666…}}) | * 19 & 46 & 193 ({{nowrap|''n'' {{=}} {{frac|2|3}} {{=}} 0.666…}}) | ||
* 19 & 46 & 265 ({{nowrap|''n'' {{=}} {{frac|3|4}} {{=}} 0.75}}) | * 19 & 46 & 265 ({{nowrap|''n'' {{=}} {{frac|3|4}} {{=}} 0.75}}) | ||
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* 19 & 46 & 255 ({{nowrap|''n'' {{=}} {{frac|4|3}} {{=}} 1.333…}}) | * 19 & 46 & 255 ({{nowrap|''n'' {{=}} {{frac|4|3}} {{=}} 1.333…}}) | ||
* 19 & 46 & 183 ({{nowrap|''n'' {{=}} {{frac|3|2}} {{=}} 1.5}}) | * 19 & 46 & 183 ({{nowrap|''n'' {{=}} {{frac|3|2}} {{=}} 1.5}}) | ||
== Sensibeta == | |||
{{See also| Sensibeta comma }} | |||
[[Comma list]]: 1071875/1062882 | |||
{{Mapping|legend=1| 1 0 2 -3 | 0 1 0 4 | 0 0 3 -5 }} | |||
: Mapping generators: ~2, ~3, ~175/162 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1200.025¢, ~3 = 1902.728¢, ~175/162 = 128.524¢ | |||
* [[CWE]]: ~2 = 1200.000¢, ~3 = 1902.709¢, ~175/162 = 128.530¢ | |||
{{Optimal ET sequence|legend=1| 19, 27, 46, 94, 113, 121, 140 }} | |||
[[Badness]] (Sintel): 7.973 | |||
[[Category:Sensi]] | [[Category:Sensi]] | ||
[[Category:Equivalence continua]] | [[Category:Equivalence continua]] | ||