60edo: Difference between revisions

Line 1:

The '''60 equal divisions of the octave''' ('''60edo'''), or the '''60-tone equal temperament''' ('''60tet'''), '''60 equal temperament''' ('''60et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 60 [[equal]] parts of ~~about {{#expr:(1200/60) round 3}}~~ [[cent]]s each.

The '''60 equal divisions of the octave''' ('''60edo'''), or the '''60-tone equal temperament''' ('''60tet'''), '''60 equal temperament''' ('''60et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 60 [[equal]] parts of exactly 20 [[cent]]s each.

== Theory ==

Since 60 = 5×12, 60edo belongs to the family of edos which contain [[12edo]], and like the other small edos of this kind, it tempers out the [[Pythagorean comma]], 531441/524288 = {{monzo|-19 12}}. In the [[5-limit]], it tempers out both the [[magic comma]], 3125/3072, and the [[amity comma]], 1600000/1594323, and supplies the optimal patent val for 5-limit [[magic]], tempering out 3125/3072. In the [[7-limit]] it tempers out [[875/864]], [[245/243]], [[225/224]] and [[10976/10935]], and [[support]]s [[magic]], [[compton]] and [[tritonic]] temperaments. In the [[11-limit]], the 60e [[val]] scores lower in [[badness]] than the [[patent val]], and makes for an excellent tritonic tuning. It tempers out [[121/120]] and [[441/440]], whereas the patent val tempers out [[100/99]], [[385/384]] and [[540/539]]. The tuning of 13 is superb at half a cent flat, and the 60e val also works excellently for [[13-limit]] tritonic. As a no-fives val, it is also excellent for the 2.3.7.11.13 [[Chromatic_pairs#Bleu|bleu temperament]].

@@ Line 1: / Line 1: @@
-The '''60 equal divisions of the octave''' ('''60edo'''), or the '''60-tone equal temperament''' ('''60tet'''), '''60 equal temperament''' ('''60et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 60 [[equal]] parts of about {{#expr:(1200/60) round 3}} [[cent]]s each.
+The '''60 equal divisions of the octave''' ('''60edo'''), or the '''60-tone equal temperament''' ('''60tet'''), '''60 equal temperament''' ('''60et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 60 [[equal]] parts of exactly 20 [[cent]]s each.
 == Theory ==
 Since 60 = 5×12, 60edo belongs to the family of edos which contain [[12edo]], and like the other small edos of this kind, it tempers out the [[Pythagorean comma]], 531441/524288 = {{monzo|-19 12}}. In the [[5-limit]], it tempers out both the [[magic comma]], 3125/3072, and the [[amity comma]], 1600000/1594323, and supplies the optimal patent val for 5-limit [[magic]], tempering out 3125/3072. In the [[7-limit]] it tempers out [[875/864]], [[245/243]], [[225/224]] and [[10976/10935]], and [[support]]s [[magic]], [[compton]] and [[tritonic]] temperaments. In the [[11-limit]], the 60e [[val]] scores lower in [[badness]] than the [[patent val]], and makes for an excellent tritonic tuning. It tempers out [[121/120]] and [[441/440]], whereas the patent val tempers out [[100/99]], [[385/384]] and [[540/539]]. The tuning of 13 is superb at half a cent flat, and the 60e val also works excellently for [[13-limit]] tritonic. As a no-fives val, it is also excellent for the 2.3.7.11.13 [[Chromatic_pairs#Bleu|bleu temperament]].