64edo: Difference between revisions

(3 intermediate revisions by 3 users not shown)

Line 8:

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 ===

Line 19:

Line 21:

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.

[[~~Ed257~~/~~128#64ed257/128|64ed257/128~~]] 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.

[[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.

Line 96:

Line 98:

default [[File:64b_Evo-SZ_Sagittal.svg]]

</imagemap>

== Instruments ==

* [[Lumatone mapping for 64edo]]

== Music ==

; [[Bryan Deister]]

* [https://www.youtube.com/shorts/ag1FbgAuR6I ''microtonal improvisation in 64edo''] (2025)

@@ Line 8: / Line 8: @@
 be 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 ===
@@ Line 19: / Line 21: @@
 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.
-[[Ed257/128#64ed257/128|64ed257/128]] 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.
+[[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.
@@ Line 96: / Line 98: @@
 default [[File:64b_Evo-SZ_Sagittal.svg]]
 </imagemap>
+== Instruments ==
+* [[Lumatone mapping for 64edo]]
+== Music ==
+; [[Bryan Deister]]
+* [https://www.youtube.com/shorts/ag1FbgAuR6I ''microtonal improvisation in 64edo''] (2025)