59edo: Difference between revisions

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59edo’s approximations of 3/1, 7/1 and 11/1 are improved by [[93edt]], a [[Octave stretch|stretched-octave]] version of 59edo. The trade-off is a slightly worse 2/1 and 5/1. The tunings [[203ed11]] or [[ed257/128#59ed257/128|59ed257/128]] could also be used as they are near identical to 93edt.

There are also some nearby [[Zeta peak index]] (ZPI) tunings which can be used ~~for this same purpose~~: 293zpi, 294zpi, 295zpi, 296zpi and 297zpi. The main Zeta peak index page details all five tunings.

If one prefers ''[[Octave shrinking|compressed octaves]]'', then [[166ed7]] is a viable option. It improves upon 59edo’s 3/1, 7/1 and 13/1 at the cost of a slightly worse 2/1 and 5/1, but substantially worse 11/1. It is a more accurate choice than 93edt in the [[7-limit]] or no-11s [[13-limit]] due to its better 2/1, but less accurate than 93edt in the [[11-limit]] due to its heavily damaged 11/1.

There are also some nearby [[Zeta peak index]] (ZPI) tunings which can be used to improve 59edo’s JI approximations: 293zpi, 294zpi, 295zpi, 296zpi and 297zpi. The main Zeta peak index page details all five tunings.

=== Subsets and supersets ===

59edo is the 17th [[prime edo]], following [[53edo]] and before [[61edo]].

== Intervals ==

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 edo’s approximations of 3/1, 7/1 and 11/1 are improved by [[93edt]], a [[Octave stretch|stretched-octave]] version of 59edo. The trade-off is a slightly worse 2/1 and 5/1. The tunings [[203ed11]] or [[ed257/128#59ed257/128|59ed257/128]] could also be used as they are near identical to 93edt.
-There are also some nearby [[Zeta peak index]] (ZPI) tunings which can be used for this same purpose: 293zpi, 294zpi, 295zpi, 296zpi and 297zpi. The main Zeta peak index page details all five tunings.
+If one prefers ''[[Octave shrinking|compressed octaves]]'', then [[166ed7]] is a viable option. It improves upon 59edo’s 3/1, 7/1 and 13/1 at the cost of a slightly worse 2/1 and 5/1, but substantially worse 11/1. It is a more accurate choice than 93edt in the [[7-limit]] or no-11s [[13-limit]] due to its better 2/1, but less accurate than 93edt in the [[11-limit]] due to its heavily damaged 11/1.
+There are also some nearby [[Zeta peak index]] (ZPI) tunings which can be used to improve 59edo’s JI approximations: 293zpi, 294zpi, 295zpi, 296zpi and 297zpi. The main Zeta peak index page details all five tunings.
 === Subsets and supersets ===
 edo is the 17th [[prime edo]], following [[53edo]] and before [[61edo]].
 == Intervals ==