66edo: Difference between revisions

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In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.

== Octave stretch or compression ==

66edo tunes multiple-of-3 [[harmonic]]s quite sharp, but most other simple harmonics quite flat.

Slight [[octave stretching]] turns 66edo into a [[dual-fifth]] tuning, sharing error near-equally between its two [[mapping]]s of 3, while improving most other simple harmonics. Slightly stretched tunings of 66edo include [[zpi|340zpi]], [[equal tuning|219ed10]] & [[equal tuning|209ed9]].

Substantial octave stretching will flip the mapping of many harmonics including 3, but will reduce the error of most of them. Though it will introduce more mapping inconsistencies. Such tunings of 66edo include [[zpi|338zpi]] and [[104edt]].

Moderate ''[[octave shrinking]]'' will instead improve upon 66edo's best mapping of prime 3 dramatically. It reduce the error on most other simple harmonics. It flips the mapping of many of them, but introduces less internal mapping inconsistencies than stretching by the same amount. Moderately octave-compressed tunings for 66edo include [[105edt]] and [[zpi|342zpi]].

== Instruments ==

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31/16: string 2 fret 9

== Music ==

; [[Bryan Deister]]

* [https://www.youtube.com/shorts/jHwtQg0aR14 ''Spring Yard Zone (microtonal version in 66edo) - Sonic The Hedgehog''] (2022)

* [https://www.youtube.com/shorts/Cn28RJSSgQ0 ''microtonal improvisation in 66edo''] (2025)

@@ Line 49: / Line 49: @@
 In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.
+== Octave stretch or compression ==
+edo tunes multiple-of-3 [[harmonic]]s quite sharp, but most other simple harmonics quite flat.
+Slight [[octave stretching]] turns 66edo into a [[dual-fifth]] tuning, sharing error near-equally between its two [[mapping]]s of 3, while improving most other simple harmonics. Slightly stretched tunings of 66edo include [[zpi|340zpi]], [[equal tuning|219ed10]] & [[equal tuning|209ed9]].
+Substantial octave stretching will flip the mapping of many harmonics including 3, but will reduce the error of most of them. Though it will introduce more mapping inconsistencies. Such tunings of 66edo include [[zpi|338zpi]] and [[104edt]].
+Moderate ''[[octave shrinking]]'' will instead improve upon 66edo's best mapping of prime 3 dramatically. It reduce the error on most other simple harmonics. It flips the mapping of many of them, but introduces less internal mapping inconsistencies than stretching by the same amount. Moderately octave-compressed tunings for 66edo include  [[105edt]] and [[zpi|342zpi]].
 == Instruments ==
@@ Line 80: / Line 89: @@
 /16: string 2 fret 9
+== Music ==
+; [[Bryan Deister]]
+* [https://www.youtube.com/shorts/jHwtQg0aR14 ''Spring Yard Zone (microtonal version in 66edo) - Sonic The Hedgehog''] (2022)
+* [https://www.youtube.com/shorts/Cn28RJSSgQ0 ''microtonal improvisation in 66edo''] (2025)