64edo: Difference between revisions
m →Theory: (''See regular temperament for more about what all this means and how to use it.'') Tag: Reverted |
m →Octave stretch: temporary improvement until the roll out |
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Still, the patent val [[tempering out|tempers out]] [[648/625]] in the 5-limit and [[225/224]] in the 7-limit, plus [[66/65]], [[121/120]] and [[441/440]] in the 11-limit and [[144/143]] in the 13-limit. It provides the optimal patent val in the 7-, 11- and 13-limits for the 16&64 temperament. | Still, the patent val [[tempering out|tempers out]] [[648/625]] in the 5-limit and [[225/224]] in the 7-limit, plus [[66/65]], [[121/120]] and [[441/440]] in the 11-limit and [[144/143]] in the 13-limit. It provides the optimal patent val in the 7-, 11- and 13-limits for the 16&64 temperament. | ||
64be val is a tuning for the [[beatles]] temperament and for the [[rank-3]] temperaments [[heimlaug]] and [[vili]] in the 17-limit. 64bccc tunes [[dichotic]], although that is an [[exotemperament]]. 64cdf is a tuning for [[vibhu]]. | 64be val is a tuning for the [[beatles]] temperament and for the [[rank-3]] temperaments [[heimlaug]] and [[vili]] in the 17-limit. 64bccc tunes [[dichotic]], although that is an [[exotemperament]]. 64cdf is a tuning for [[vibhu]]. | ||
The patent val of 64edo is the first patent val to represent the intervals 5/4, 81/64, 14/11, 9/7, 13/10, 21/16, and 4/3 distinctly, although in 64edo they are not in the correct order. | |||
=== Odd harmonics === | === Odd harmonics === | ||
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If one prefers a ''[[Octave stretch|stretched-octave]]'', 64edo's approximations of 3/1, 5/1, 11/1 and 17/1 are improved by [[221ed11]], a stretched version of 64edo. The trade-off is a slightly worse 2/1 and 13/1. | If one prefers a ''[[Octave stretch|stretched-octave]]'', 64edo's approximations of 3/1, 5/1, 11/1 and 17/1 are improved by [[221ed11]], a stretched version of 64edo. The trade-off is a slightly worse 2/1 and 13/1. | ||
[[ | [[47ed5/3]] can also be used: it is similar to 221ed11 but both the improvements and shortcomings are amplified. Most notably its 2/1 is not as accurate as 221ed11's. | ||
There are also some nearby [[zeta peak index]] (ZPI) tunings which can be used to improve 64edo's JI approximations: 326zpi, 327zpi, 328zpi and 329zpi. The main Zeta peak index page details all four tunings. | There are also some nearby [[zeta peak index]] (ZPI) tunings which can be used to improve 64edo's JI approximations: 326zpi, 327zpi, 328zpi and 329zpi. The main Zeta peak index page details all four tunings. | ||
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default [[File:64b_Evo-SZ_Sagittal.svg]] | default [[File:64b_Evo-SZ_Sagittal.svg]] | ||
</imagemap> | </imagemap> | ||
== Instruments == | |||
* [[Lumatone mapping for 64edo]] | |||
== Music == | |||
; [[Bryan Deister]] | |||
* [https://www.youtube.com/shorts/ag1FbgAuR6I ''microtonal improvisation in 64edo''] (2025) | |||