Meantone: Difference between revisions

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[[Meantone intervals|Intervals in meantone]] have standard names based on the number of steps of the diatonic scale they span (this corresponds to the [[val]] {{val| 7 11 16 }}), with a modifier {…"double diminished", "diminished", "minor", "major", "augmented", "double augmented"…} that tells you the specific interval in increments of a chromatic semitone. Note that in a general meantone system, all of these intervals are distinct. For example, a diminished fourth is a different interval from a major third.

== ~~Meantone temperaments~~ ==

== Tunings ==

~~The common~~ meantone temperaments ~~(''recte''~~ tunings~~) include:~~

Common meantone tunings include various [[eigenmonzo]] tunings such as the [[quarter-comma meantone]], edo tunings like [[31edo]], and otherwise optimized tunings like the POTE tuning, shown below. For a more complete list, see [[#Spectrum of meantone tunings by eigenmonzos]]. These different tunings are referred to as "temperaments" in traditional terms.

* [[1/2 syntonic comma meantone]]

* [[~~33edo~~]]

; Eigenmonzo tunings

* [[~~26edo~~]]

* [[1/2 syntonic comma meantone]] – with eigenmonzo [[10/9]]

* [[2/5 syntonic comma meantone]]

* [[1/3 syntonic comma meantone]] – with eigenmonzo [[5/3]]

* [[~~45edo~~]]

* [[2/7 syntonic comma meantone]] – with eigenmonzo [[25/24]]

* [[1/3 syntonic comma meantone]]

* [[Quarter-comma meantone|1/4 syntonic comma meantone]] – with eigenmonzo [[5/4]]

* [[19edo]]

* [[1/5 syntonic comma meantone]] – with eigenmonzo [[15/8]]

* [[1/6 syntonic comma meantone]] – with eigenmonzo [[45/32]]

; Edo tunings

* [[33edo|19\33]]

* [[26edo|15\26]]

* [[45edo|26\45]]

* [[19edo|11\19]]

* [[50edo|29\50]]

* [[31edo|18\31]]

* [[105edo|61\105]]

* [[43edo|25\43]]

* [[55edo|32\55]]

* [[12edo|7\12]]

; POTE tunings

* ~3/2 = 696.239¢ – 5-limit meantone

* ~3/2 = 696.495¢ – 7-limit meantone

; Other optimized tunings

* [[Golden meantone]]

* [[~~2/7 syntonic comma~~ meantone]]

* [[Tungsten meantone]]

* [[50edo]]

* [[Quarter-comma meantone|1/4 syntonic comma meantone]]

* [[31edo]]

* [[1/5 syntonic comma meantone]]

* [[43edo]]

* [[105edo]]

* [[1/6 syntonic comma meantone]]

* [[55edo]]

* [[12edo]]

* [[Lucy tuning]]

* [[Tungsten meantone]]

== Scales ==

@@ Line 9: / Line 9: @@
 [[Meantone intervals|Intervals in meantone]] have standard names based on the number of steps of the diatonic scale they span (this corresponds to the [[val]] {{val| 7 11 16 }}), with a modifier {…"double diminished", "diminished", "minor", "major", "augmented", "double augmented"…} that tells you the specific interval in increments of a chromatic semitone. Note that in a general meantone system, all of these intervals are distinct. For example, a diminished fourth is a different interval from a major third.
-== Meantone temperaments ==
+== Tunings ==
-The common meantone temperaments (''recte'' tunings) include:
+Common meantone tunings include various [[eigenmonzo]] tunings such as the [[quarter-comma meantone]], edo tunings like [[31edo]], and otherwise optimized tunings like the POTE tuning, shown below. For a more complete list, see [[#Spectrum of meantone tunings by eigenmonzos]]. These different tunings are referred to as "temperaments" in traditional terms.
-* [[1/2 syntonic comma meantone]]
-* [[33edo]]
+; Eigenmonzo tunings
-* [[26edo]]
+* [[1/2 syntonic comma meantone]] – with eigenmonzo [[10/9]]
-* [[2/5 syntonic comma meantone]]
+* [[1/3 syntonic comma meantone]] – with eigenmonzo [[5/3]]
-* [[45edo]]
+* [[2/7 syntonic comma meantone]] – with eigenmonzo [[25/24]]
-* [[1/3 syntonic comma meantone]]
+* [[Quarter-comma meantone|1/4 syntonic comma meantone]] – with eigenmonzo [[5/4]]
-* [[19edo]]
+* [[1/5 syntonic comma meantone]] – with eigenmonzo [[15/8]]
+* [[1/6 syntonic comma meantone]] – with eigenmonzo [[45/32]]
+; Edo tunings
+* [[33edo|19\33]]
+* [[26edo|15\26]]
+* [[45edo|26\45]]
+* [[19edo|11\19]]
+* [[50edo|29\50]]
+* [[31edo|18\31]]
+* [[105edo|61\105]]
+* [[43edo|25\43]]
+* [[55edo|32\55]]
+* [[12edo|7\12]]
+; POTE tunings
+* ~3/2 = 696.239¢ – 5-limit meantone
+* ~3/2 = 696.495¢ – 7-limit meantone
+; Other optimized tunings
 * [[Golden meantone]]
-* [[2/7 syntonic comma meantone]]
+* [[Tungsten meantone]]
-* [[50edo]]
-* [[Quarter-comma meantone|1/4 syntonic comma meantone]]
-* [[31edo]]
-* [[1/5 syntonic comma meantone]]
-* [[43edo]]
-* [[105edo]]
-* [[1/6 syntonic comma meantone]]
-* [[55edo]]
-* [[12edo]]
 * [[Lucy tuning]]
-* [[Tungsten meantone]]
 == Scales ==