41edo: Difference between revisions

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Whether there is intonational improvement from [[stretched and compressed tuning|octave stretch or compression]] depends on which [[subgroup]] of [[JI]] we are focusing on.

For the 5-, 7-, ~~29- or 31~~-limit, ~~a moderately stretched 41edo tuning~~ is advised, ~~such as~~ the ~~7-limit [[WE]] or [[TE]] tuning for 41et.~~

For the 5-, 7-, and 11-limit, stretch is advised, though in the case of the 11-limit the stretch should be milder. A tuning that does that is [[ZPI|184zpi]]. For the 13-limit and in particular the 17-limit, little to no stretch or even compression may be suitable for balancing out the sharp and flat tuning tendencies, as is demonstrated in tunings such as [[65edt]], [[106ed6]], and [[147ed12]]. 41edo additionally approximates primes 19, 29, and 31, which all tend flat, so stretching will serve again as we take that into account, especially if we use the temperament in any no-17 or no-13 no-17 settings.

~~For~~ the 11~~- or 23~~-limit~~, a slightly stretched 41edo~~ tuning is ~~advised, such as~~ [[~~zpi~~|184zpi]].

For the 13~~- or 19~~-limit~~, pure-octaves 41edo is advised.~~

~~For~~ the 17-limit, ~~a slightly compressed 41edo~~ tuning is ~~advised,~~ such as ~~[[24edf]],~~ [[65edt]], [[106ed6]] or [[147ed12]].

== Scales and modes ==

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 Whether there is intonational improvement from [[stretched and compressed tuning|octave stretch or compression]] depends on which [[subgroup]] of [[JI]] we are focusing on.
-For the 5-, 7-, 29- or 31-limit, a moderately stretched 41edo tuning is advised, such as the 7-limit [[WE]] or [[TE]] tuning for 41et.
+For the 5-, 7-, and 11-limit, stretch is advised, though in the case of the 11-limit the stretch should be milder. A tuning that does that is [[ZPI|184zpi]]. For the 13-limit and in particular the 17-limit, little to no stretch or even compression may be suitable for balancing out the sharp and flat tuning tendencies, as is demonstrated in tunings such as [[65edt]], [[106ed6]], and [[147ed12]]. 41edo additionally approximates primes 19, 29, and 31, which all tend flat, so stretching will serve again as we take that into account, especially if we use the temperament in any no-17 or no-13 no-17 settings.
-For the 11- or 23-limit, a slightly stretched 41edo tuning is advised, such as [[zpi|184zpi]].
-For the 13- or 19-limit, pure-octaves 41edo is advised.
-For the 17-limit, a slightly compressed 41edo tuning is advised, such as [[24edf]], [[65edt]], [[106ed6]] or [[147ed12]].
 == Scales and modes ==