Orwell extensions: Difference between revisions

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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:

* '''Tridecimal orwell''' (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''' (22 & 31f) – tempering out 65/64, 78/77, 91/90, and 99/98

* '''Blair''' {{nowrap|(22 & 31f)}} – tempering out 65/64, 78/77, 91/90, and 99/98

* '''Winston''' (22f & 31) – tempering out 66/65, 99/98, 105/104, and 121/120

* '''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, ~~the~~ ~13/8 is conflated with ~~the~~ ~18/11 and is generally tuned worse than in 31edo as a result of an improved ~18/11. In blair, ~~the~~ ~13/8 is conflated with ~~the~~ ~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.

Another possible path which relates a sense of compromise is to temper out [[169/168]], leading to [[doublethink]]. This has the effect of slicing the generator in two, and is supported by [[44edo|44]], 53, and [[62edo|62]].

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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:
-* '''Tridecimal orwell''' (22 & 31) – tempering out 99/98, 121/120, 176/175, and 275/273
+* '''Tridecimal orwell''' {{nowrap|(22 &amp; 31)}} – tempering out 99/98, 121/120, 176/175, and 275/273
-* '''Blair''' (22 & 31f) – tempering out 65/64, 78/77, 91/90, and 99/98
+* '''Blair''' {{nowrap|(22 & 31f)}} – tempering out 65/64, 78/77, 91/90, and 99/98
-* '''Winston''' (22f & 31) – tempering out 66/65, 99/98, 105/104, and 121/120
+* '''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, the ~13/8 is conflated with the ~18/11 and is generally tuned worse than in 31edo as a result of an improved ~18/11. In blair, the ~13/8 is conflated with the ~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.
 Another possible path which relates a sense of compromise is to temper out [[169/168]], leading to [[doublethink]]. This has the effect of slicing the generator in two, and is supported by [[44edo|44]], 53, and [[62edo|62]].