User:Overthink/Draft edits: Difference between revisions

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As an equal temperament, 56et most notably tempers out [[2048/2025]], the diaschisma, as well as the [[shibboleth comma]] in the [[5-limit]]. Using the patent val, it tempers out [[686/675]], [[875/864]], and [[1029/1024]] in the [[7-limit]], [[100/99]], [[245/242]], and [[385/384]] in the [[11-limit]], and [[91/90]] and [[169/168]] in the 13-limit. It supports 7- and 11-limit keen, and its 13- and 17-limit extension [[keenic]]. It also supports [[hemithirds]], [[superkleismic]], and [[sycamore]] in various limits, being an especially optimal tuning for sycamore in the 11-, and 13-limits. It is also a very sharp tuning of [[slendric]], mapping 7/6 to a wide semifourth of 257.1{{c}}, and 9/7 inconsistently to a 450{{c}} [[Interseptimal interval|naiadic]].

Another interesting val to consider is 56d ({{Val|56 89 130 '''158'''}}), which maps 7/4 sharply to around 986{{c}}. This mapping tempers out [[50/49]] and [[64/63]], providing an alternative to [[22edo]] for [[pajara]]. It improves accuracy of the 3rd harmonic and makes the 5th harmonic basically just, especially improving [[6/5]] and [[10/9]], which are quite out of tune in 22edo. Its 7th harmonic is sharper than 22edo's, and combined with the fact that the 3rd harmonic is sharp, one may want to [[Octave stretch|compress the octave]], using tunings such as [[145ed6]] or [[201ed12]]. It is also an excellent tuning for the 11-limit version of pajara, which tempers out [[99/98]] and [[100/99]]. Finally, it gives an excellent tuning to the no-fives [[supra]] temperament tempering out [[64/63]] and [[99/98]].

Another interesting val to consider is 56d ({{Val|56 89 130 '''158'''}}), which maps 7/4 sharply to around 986{{c}}. This mapping tempers out [[50/49]] and [[64/63]], providing an alternative to [[22edo]] for [[pajara]]. It improves accuracy of the 3rd harmonic and makes the 5th harmonic basically just, especially improving [[6/5]] and [[10/9]], which are quite out of tune in 22edo. Its 7th harmonic is sharper than 22edo's, and combined with the fact that the 3rd harmonic is sharp, one may want to [[Octave stretch|compress the octave]], using tunings such as [[145ed6]] or [[201ed12]]. It is also an excellent tuning for the 11-limit version of pajara, which tempers out [[99/98]] and [[100/99]]. Finally, it gives an excellent tuning for the no-fives [[supra]] temperament tempering out [[64/63]] and [[99/98]].

=== Subsets and supersets ===

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 As an equal temperament, 56et most notably tempers out [[2048/2025]], the diaschisma, as well as the [[shibboleth comma]] in the [[5-limit]]. Using the patent val, it tempers out [[686/675]], [[875/864]], and [[1029/1024]] in the [[7-limit]], [[100/99]], [[245/242]], and [[385/384]] in the [[11-limit]], and [[91/90]] and [[169/168]] in the 13-limit. It supports 7- and 11-limit keen, and its 13- and 17-limit extension [[keenic]]. It also supports [[hemithirds]], [[superkleismic]], and [[sycamore]] in various limits, being an especially optimal tuning for sycamore in the 11-, and 13-limits. It is also a very sharp tuning of [[slendric]], mapping 7/6 to a wide semifourth of 257.1{{c}}, and 9/7 inconsistently to a 450{{c}} [[Interseptimal interval|naiadic]].
-Another interesting val to consider is 56d ({{Val|56 89 130 '''158'''}}), which maps 7/4 sharply to around 986{{c}}. This mapping tempers out [[50/49]] and [[64/63]], providing an alternative to [[22edo]] for [[pajara]]. It improves accuracy of the 3rd harmonic and makes the 5th harmonic basically just, especially improving [[6/5]] and [[10/9]], which are quite out of tune in 22edo. Its 7th harmonic is sharper than 22edo's, and combined with the fact that the 3rd harmonic is sharp, one may want to [[Octave stretch|compress the octave]], using tunings such as [[145ed6]] or [[201ed12]]. It is also an excellent tuning for the 11-limit version of pajara, which tempers out [[99/98]] and [[100/99]]. Finally, it gives an excellent tuning to the no-fives [[supra]] temperament tempering out [[64/63]] and [[99/98]].
+Another interesting val to consider is 56d ({{Val|56 89 130 '''158'''}}), which maps 7/4 sharply to around 986{{c}}. This mapping tempers out [[50/49]] and [[64/63]], providing an alternative to [[22edo]] for [[pajara]]. It improves accuracy of the 3rd harmonic and makes the 5th harmonic basically just, especially improving [[6/5]] and [[10/9]], which are quite out of tune in 22edo. Its 7th harmonic is sharper than 22edo's, and combined with the fact that the 3rd harmonic is sharp, one may want to [[Octave stretch|compress the octave]], using tunings such as [[145ed6]] or [[201ed12]]. It is also an excellent tuning for the 11-limit version of pajara, which tempers out [[99/98]] and [[100/99]]. Finally, it gives an excellent tuning for the no-fives [[supra]] temperament tempering out [[64/63]] and [[99/98]].
 === Subsets and supersets ===