64edo: Difference between revisions

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=== Odd harmonics ===

=== Octave stretch ===

64edo’s approximations of 3/1, 5/1, 7/1, 11/1 and 17/1 are improved by [[180ed7]], a [[Octave shrinking|compressed-octave]] version of 64edo. The trade-off is a slightly worse 2/1 and 13/1.

[[149ed5]] can also be used: it is ~~very~~ similar to 180ed7 but both the improvements and shortcomings are amplified.

[[149ed5]] can also be used: it is similar to 180ed7 but both the improvements and shortcomings are amplified. Most notably its 2/1 isn’t as accurate as 180ed7’s.

If one prefers a ''stretched'' octave, 64edo's approximations of 3/1, 5/1, 11/1 and 17/1 are improved by [[221ed11]], a [[Octave stretch|stretched-octave]] version of 64edo. The trade-off is a slightly worse 2/1 and 13/1.

~~If one prefers a ''stretched'' octave, 64edo's approximations of 3/1, 5/1 and 11/1 are improved by~~ [[ed257/128#64ed257/128|64ed257/128]]~~, a [[Octave stretch|stretched-octave]] version of 64edo. The trade-off~~ is ~~a slightly worse 2/1~~. ~~The stretched~~ 2/1 ~~is more inaccurate than the compressed 2/1 from the previously mentioned tunings~~.

[[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 isn’t 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.

=== Subsets and supersets ===

64edo is the 6th power of two edo, and it has subset edos {{EDOs| 2, 4, 8, 16, 32 }}. [[128edo]], which doubles it, corrects its approximation to many of the lower harmonics.

== Intervals ==

@@ Line 10: / Line 10: @@
 === Odd harmonics ===
-{{Harmonics in equal|64}}
+{{Harmonics in equal|64|intervals=prime}}
+{{Harmonics in equal|221|11|1|intervals=prime}}
+{{Harmonics in equal|101|3|1|intervals=prime}}
+{{Harmonics in equal|64|257|128|intervals=prime}}
 === Octave stretch ===
 edo’s approximations of 3/1, 5/1, 7/1, 11/1 and 17/1 are improved by [[180ed7]], a [[Octave shrinking|compressed-octave]] version of 64edo. The trade-off is a slightly worse 2/1 and 13/1.
-[[149ed5]] can also be used: it is very similar to 180ed7 but both the improvements and shortcomings are amplified.
+[[149ed5]] can also be used: it is similar to 180ed7 but both the improvements and shortcomings are amplified. Most notably its 2/1 isn’t as accurate as 180ed7’s.
+If one prefers a ''stretched'' octave, 64edo's approximations of 3/1, 5/1, 11/1 and 17/1 are improved by [[221ed11]], a [[Octave stretch|stretched-octave]] version of 64edo. The trade-off is a slightly worse 2/1 and 13/1.
-If one prefers a ''stretched'' octave, 64edo's approximations of 3/1, 5/1 and 11/1 are improved by [[ed257/128#64ed257/128|64ed257/128]], a [[Octave stretch|stretched-octave]] version of 64edo. The trade-off is a slightly worse 2/1. The stretched 2/1 is more inaccurate than the compressed 2/1 from the previously mentioned tunings.
+[[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 isn’t 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.
 === Subsets and supersets ===
 edo is the 6th power of two edo, and it has subset edos {{EDOs| 2, 4, 8, 16, 32 }}. [[128edo]], which doubles it, corrects its approximation to many of the lower harmonics.
 == Intervals ==
 {{Interval table}}