67edo: Difference between revisions

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== Theory ==

67edo tempers out 81/80, [[support~~|supporting~~]] meantone ~~temperament~~, with a tuning which is approximately [[1/~~6_syntonic_comma_meantone~~|1/6 comma]] (the tuning favored by Mozart and contemporaries), or 0.16 comma, meantone. In the 7-limit the patent val tempers out [[1029/1024]] and [[1728/1715]], so that it supports [[~~Meantone_family|~~mothra ~~temperament~~]]. In the 11-limit it tempers out [[176/175]] and [[540/539]], supporting mosura, an alternative 11-limit mothra. In the 13-limit it tempers out [[144/143]] and [[196/195]], supporting 13-limit mosura. It tempers out the orgonisma, and on the 2.7.11 subgroup it supports [[~~Orgonia|~~orgone ~~temperament~~]].

67edo [[tempering out|tempers out]] [[81/80]], [[support]]ing [[meantone]], with a tuning which is approximately [[1/6-comma meantone|1/6-comma]] (the tuning favored by {{w|Wolfgang Amadeus Mozart|Mozart}} and contemporaries), or 0.16-comma meantone. In the 7-limit the [[patent val]] tempers out [[1029/1024]] and [[1728/1715]], so that it supports [[mothra]]. In the 11-limit it tempers out [[176/175]] and [[540/539]], supporting [[mosura]], an alternative 11-limit mothra. In the 13-limit it tempers out [[144/143]] and [[196/195]], supporting 13-limit mosura. It tempers out the [[orgonisma]], and on the 2.7.11 subgroup it supports the [[orgone]] temperament.

A promising tuning which has, as many relatively large equal temperaments do, a variety of tonal resources: it is the first edo to have both meantone (26 could be called meantone, but it's more of a flattone) ~~and an orgone temperament~~. It has relatively good approximations of the 3rd, 7th, 11th, 13th, 15th, 17th ~~harmonics~~, although the 5th, 9th, and 19th as well as certain higher ones are workable as well. 33+34 can be used to construct this temperament explaining some of its properties. It does well on the 2.3.7.11.13.17.23.31.37.41 ~~subgroup.~~

It is a promising tuning which has, as many relatively large equal temperaments do, a variety of tonal resources: it is the first edo to have both meantone and an orgone temperament ([[26edo]] could be called meantone, but it is more of a [[flattone]]). It has relatively good approximations of the [[3/1|3rd]], [[7/1|7th]], [[11/1|11th]], [[13/1|13th]], [[15/1|15th]], [[17/1|17th]] [[harmonic]]s, although the [[5/1|5th]], [[9/1|9th]], and [[19/1|19th]] as well as certain higher ones are workable as well. 33 + 34 can be used to construct this temperament explaining some of its properties. It does well on the 2.3.7.11.13.17.23.31.37.41 [[subgroup]].

~~67edo is the 19th~~ [[~~prime EDO~~]].

=== Prime harmonics ===

=== Subsets and supersets ===

67edo is the 19th [[prime edo]], following [[61edo]] and before [[71edo]].

== Intervals==

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== Scales ==

=== Subsets of Negri ===

* Bustling Docks (original/default tuning): 14 14 11 14 14

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-{{Infobox ET}}{{EDO intro|67}}
+{{Infobox ET}}
+{{EDO intro}}
 == Theory ==
-edo tempers out 81/80, [[support|supporting]] meantone temperament, with a tuning which is approximately [[1/6_syntonic_comma_meantone|1/6 comma]] (the tuning favored by Mozart and contemporaries), or 0.16 comma, meantone. In the 7-limit the patent val tempers out [[1029/1024]] and [[1728/1715]], so that it supports [[Meantone_family|mothra temperament]]. In the 11-limit it tempers out [[176/175]] and [[540/539]], supporting mosura, an alternative 11-limit mothra. In the 13-limit it tempers out [[144/143]] and [[196/195]], supporting 13-limit mosura. It tempers out the orgonisma, and on the 2.7.11 subgroup it supports [[Orgonia|orgone temperament]].
+edo [[tempering out|tempers out]] [[81/80]], [[support]]ing [[meantone]], with a tuning which is approximately [[1/6-comma meantone|1/6-comma]] (the tuning favored by {{w|Wolfgang Amadeus Mozart|Mozart}} and contemporaries), or 0.16-comma meantone. In the 7-limit the [[patent val]] tempers out [[1029/1024]] and [[1728/1715]], so that it supports [[mothra]]. In the 11-limit it tempers out [[176/175]] and [[540/539]], supporting [[mosura]], an alternative 11-limit mothra. In the 13-limit it tempers out [[144/143]] and [[196/195]], supporting 13-limit mosura. It tempers out the [[orgonisma]], and on the 2.7.11 subgroup it supports the [[orgone]] temperament.
-A promising tuning which has, as many relatively large equal temperaments do, a variety of tonal resources: it is the first edo to have both meantone (26 could be called meantone, but it's more of a flattone) and an orgone temperament. It has relatively good approximations of the 3rd, 7th, 11th, 13th, 15th, 17th harmonics, although the 5th, 9th, and 19th as well as certain higher ones are workable as well. 33+34 can be used to construct this temperament explaining some of its properties. It does well on the 2.3.7.11.13.17.23.31.37.41 subgroup.
+It is a promising tuning which has, as many relatively large equal temperaments do, a variety of tonal resources: it is the first edo to have both meantone and an orgone temperament ([[26edo]] could be called meantone, but it is more of a [[flattone]]). It has relatively good approximations of the [[3/1|3rd]], [[7/1|7th]], [[11/1|11th]], [[13/1|13th]], [[15/1|15th]], [[17/1|17th]] [[harmonic]]s, although the [[5/1|5th]], [[9/1|9th]], and [[19/1|19th]] as well as certain higher ones are workable as well. 33 + 34 can be used to construct this temperament explaining some of its properties. It does well on the 2.3.7.11.13.17.23.31.37.41 [[subgroup]].
-edo is the 19th [[prime EDO]].
 === Prime harmonics ===
 {{Harmonics in equal|67|columns=13}}
+=== Subsets and supersets ===
+edo is the 19th [[prime edo]], following [[61edo]] and before [[71edo]].
 == Intervals==
@@ Line 15: / Line 17: @@
 == Scales ==
 === Subsets of Negri ===
 * Bustling Docks (original/default tuning): 14 14 11 14 14