Orwell extensions: Difference between revisions
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Undo revision 225002 by VectorGraphics (talk). Here only 22 and 31 are used with different warts for ease of comparison between these extensions. Plus 9 isn't a reasonable tuning for orwell. Tag: Undo |
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[[Orwell]] has multiple competing [[extension]]s to the [[13-limit]]. This is evidenced by the fact that its [[support]]ing [[equal temperament]]s, [[22edo|22]] and [[31edo|31]], do less well in the 13-limit. The extensions are: | [[Orwell]] has multiple competing [[extension]]s to the [[13-limit]]. This is evidenced by the fact that its [[support]]ing [[equal temperament]]s, [[22edo|22]] and [[31edo|31]], do less well in the 13-limit. The extensions are: | ||
* '''Tridecimal orwell''' ({{nowrap| 22 & 31 }}) – tempering out 99/98, 121/120, 176/175, and 275/273 | * '''Tridecimal orwell''' ({{nowrap| 22 & 31 }}) – tempering out 99/98, 121/120, 176/175, and 275/273 | ||
* '''Blair''' ( | * '''Blair''' ({{nowrap| 22 & 31f }}) – tempering out 65/64, 78/77, 91/90, and 99/98 | ||
* '''Winston''' ( | * '''Winston''' ({{nowrap| 22f & 31 }}) – tempering out 66/65, 99/98, 105/104, and 121/120 | ||
The most important of these is tridecimal orwell, which tempers out [[352/351]] and may also be characterized by tempering out [[275/273]] instead. Supported by [[53edo|53]], it has the highest accuracy in its approximation of 13/8, but also the highest complexity. The other two extensions have lower complexity, but also lower accuracy. In winston, ~13/8 is conflated with ~18/11 and is generally tuned worse than in 31edo as a result of an improved ~18/11. In blair, ~13/8 is conflated with ~8/5 and is generally tuned worse than in 22edo as a result of an improved ~8/5. | The most important of these is tridecimal orwell, which tempers out [[352/351]] and may also be characterized by tempering out [[275/273]] instead. Supported by [[53edo|53]], it has the highest accuracy in its approximation of 13/8, but also the highest complexity. The other two extensions have lower complexity, but also lower accuracy. In winston, ~13/8 is conflated with ~18/11 and is generally tuned worse than in 31edo as a result of an improved ~18/11. In blair, ~13/8 is conflated with ~8/5 and is generally tuned worse than in 22edo as a result of an improved ~8/5. | ||