66edo: Difference between revisions

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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]], [[~~ed10~~|219ed10]] & [[~~ed9~~|209ed9]].

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 mapping inconsistencies than stretching. Moderately octave-compressed tunings for 66edo include [[105edt]] and [[zpi|342zpi]].

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 53: / Line 53: @@
 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]], [[ed10|219ed10]] & [[ed9|209ed9]].
+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 mapping inconsistencies than stretching. Moderately octave-compressed tunings for 66edo include  [[105edt]] and [[zpi|342zpi]].
+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 ==