Meantone: Difference between revisions

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== Tunings ==

Common meantone tunings can be classified into [[eigenmonzo]] (unchanged-interval) tunings, edo tunings, prime-optimized tunings and others. In eigenmonzo tunings such as the [[quarter-comma meantone]], a certain interval is tuned pure and certain others are equally off. Edo tunings like [[31edo]] have rational size relationship between steps, and happen to send an additional comma to unison. Prime-optimized tunings are optimized for all intervals. For a more complete list, see the table below. These different tunings are referred to as "temperaments" in traditional terms.

Common meantone tunings can be classified into [[Eigenmonzo|eigenmonzo (unchanged-interval)]] tunings, edo tunings, prime-optimized tunings and others. In eigenmonzo tunings such as the [[quarter-comma meantone]], a certain interval is tuned pure and certain others are equally off. Edo tunings like [[31edo]] have rational size relationship between steps, and happen to send an additional comma to unison. Prime-optimized tunings are optimized for all intervals. For a more complete list, see the table below. These different tunings are referred to as "temperaments" in traditional terms.

; Notable eigenmonzo (unchanged-interval) tunings

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

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

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

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

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

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

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

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

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

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

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

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

* [[Ratwolf|Ratwolf tuning]]

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| Tenney-Weil || CTWE ~3/2 = 696.6512¢

|-

| Equilateral || CEE ~3/2 = 696.8947¢ [[Eigenmonzo basis]] ([[unchanged-interval basis]]): 2.1875 (4/17-comma tuning)

| Equilateral || CEE ~3/2 = 696.8947¢ [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.1875 (4/17-comma tuning)

|-

| Equilateral-Weil || CEWE ~3/2 = 696.4534¢ Eigenmonzo ~~basis~~ (unchanged-interval basis): 2.48828125/3 (11/43-comma tuning)

| Equilateral-Weil || CEWE ~3/2 = 696.4534¢ Eigenmonzo (unchanged-interval) basis: 2.48828125/3 (11/43-comma tuning)

|-

| Benedetti || CBE ~3/2 = 697.3738¢ Eigenmonzo ~~basis~~ (unchanged-interval basis): 2.{{monzo| 0 25 36 }} (36/169-comma tuning)

| Benedetti || CBE ~3/2 = 697.3738¢ Eigenmonzo (unchanged-interval) basis: 2.{{monzo| 0 25 36 }} (36/169-comma tuning)

|-

| Benedetti-Weil || CBWE ~3/2 = 696.7868¢ Eigenmonzo ~~basis~~ (unchanged-interval basis): 2.{{monzo| 0 5 31 }} (31/129-comma tuning)

| Benedetti-Weil || CBWE ~3/2 = 696.7868¢ Eigenmonzo (unchanged-interval) basis: 2.{{monzo| 0 5 31 }} (31/129-comma tuning)

|}

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| Tenney-Weil || CTWE ~3/2 = 696.6562¢

|-

| Equilateral || CEE ~3/2 = 696.8843¢ Eigenmonzo ~~basis~~ (unchanged-interval basis): 2.{{monzo| 0 1 4 10 }}

| Equilateral || CEE ~3/2 = 696.8843¢ Eigenmonzo (unchanged-interval) basis: 2.{{monzo| 0 1 4 10 }}

|-

| Equilateral-Weil || CEWE ~3/2 = 696.7248¢ Eigenmonzo ~~basis~~ (unchanged-interval basis): 2.4117715/9

| Equilateral-Weil || CEWE ~3/2 = 696.7248¢ Eigenmonzo (unchanged-interval) basis: 2.4117715/9

|-

| Benedetti || CBE ~3/2 = 697.0147¢ Eigenmonzo ~~basis~~ (unchanged-interval basis): 2.{{monzo| 0 1225 1764 2250 }}

| Benedetti || CBE ~3/2 = 697.0147¢ Eigenmonzo (unchanged-interval) basis: 2.{{monzo| 0 1225 1764 2250 }}

|-

| Benedetti-Weil || CBWE ~3/2 = 696.6306¢ Eigenmonzo ~~basis~~ (unchanged-interval basis): 2.{{monzo| 0 -3290 3171 7215 }}

| Benedetti-Weil || CBWE ~3/2 = 696.6306¢ Eigenmonzo (unchanged-interval) basis: 2.{{monzo| 0 -3290 3171 7215 }}

|}

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|-

! Edo Generator

! [[Eigenmonzo|Eigenmonzo (~~unchanged~~-interval)]]

! [[Eigenmonzo|Eigenmonzo (Unchanged-interval)]]

! Generator (¢)

! Comments

@@ Line 48: / Line 48: @@
 == Tunings ==
-Common meantone tunings can be classified into [[eigenmonzo]] (unchanged-interval) tunings, edo tunings, prime-optimized tunings and others. In eigenmonzo tunings such as the [[quarter-comma meantone]], a certain interval is tuned pure and certain others are equally off. Edo tunings like [[31edo]] have rational size relationship between steps, and happen to send an additional comma to unison. Prime-optimized tunings are optimized for all intervals. For a more complete list, see the table below. These different tunings are referred to as "temperaments" in traditional terms.
+Common meantone tunings can be classified into [[Eigenmonzo|eigenmonzo (unchanged-interval)]] tunings, edo tunings, prime-optimized tunings and others. In eigenmonzo tunings such as the [[quarter-comma meantone]], a certain interval is tuned pure and certain others are equally off. Edo tunings like [[31edo]] have rational size relationship between steps, and happen to send an additional comma to unison. Prime-optimized tunings are optimized for all intervals. For a more complete list, see the table below. These different tunings are referred to as "temperaments" in traditional terms.
 ; Notable eigenmonzo (unchanged-interval) tunings
-* [[1/2 syntonic comma meantone]] – with eigenmonzo [[10/9]]
+* [[1/2-comma meantone]] – with eigenmonzo [[10/9]]
-* [[1/3 syntonic comma meantone]] – with eigenmonzo [[5/3]]
+* [[1/3-comma meantone]] – with eigenmonzo [[5/3]]
-* [[2/7 syntonic comma meantone]] – with eigenmonzo [[25/24]]
+* [[2/7-comma meantone]] – with eigenmonzo [[25/24]]
-* [[Quarter-comma meantone|1/4 syntonic comma meantone]] – with eigenmonzo [[5/4]]
+* [[Quarter-comma meantone|1/4-comma meantone]] – with eigenmonzo [[5/4]]
-* [[1/5 syntonic comma meantone]] – with eigenmonzo [[15/8]]
+* [[1/5-comma meantone]] – with eigenmonzo [[15/8]]
-* [[1/6 syntonic comma meantone]] – with eigenmonzo [[45/32]]
+* [[1/6-comma meantone]] – with eigenmonzo [[45/32]]
 * [[Ratwolf|Ratwolf tuning]]
@@ Line 76: / Line 76: @@
 | Tenney-Weil || CTWE<br>~3/2 = 696.6512¢
 |-
-| Equilateral || CEE<br>~3/2 = 696.8947¢<br>[[Eigenmonzo basis]] ([[unchanged-interval basis]]): 2.1875 (4/17-comma tuning)
+| Equilateral || CEE<br>~3/2 = 696.8947¢<br>[[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.1875 (4/17-comma tuning)
 |-
-| Equilateral-Weil || CEWE<br>~3/2 = 696.4534¢<br>Eigenmonzo basis (unchanged-interval basis): 2.48828125/3 (11/43-comma tuning)
+| Equilateral-Weil || CEWE<br>~3/2 = 696.4534¢<br>Eigenmonzo (unchanged-interval) basis: 2.48828125/3 (11/43-comma tuning)
 |-
-| Benedetti || CBE<br>~3/2 = 697.3738¢<br>Eigenmonzo basis (unchanged-interval basis): 2.{{monzo| 0 25 36 }} (36/169-comma tuning)
+| Benedetti || CBE<br>~3/2 = 697.3738¢<br>Eigenmonzo (unchanged-interval) basis: 2.{{monzo| 0 25 36 }} (36/169-comma tuning)
 |-
-| Benedetti-Weil || CBWE<br>~3/2 = 696.7868¢<br>Eigenmonzo basis (unchanged-interval basis): 2.{{monzo| 0 5 31 }} (31/129-comma tuning)
+| Benedetti-Weil || CBWE<br>~3/2 = 696.7868¢<br>Eigenmonzo (unchanged-interval) basis: 2.{{monzo| 0 5 31 }} (31/129-comma tuning)
 |}
@@ Line 94: / Line 94: @@
 | Tenney-Weil || CTWE<br>~3/2 = 696.6562¢
 |-
-| Equilateral || CEE<br>~3/2 = 696.8843¢<br>Eigenmonzo basis (unchanged-interval basis): 2.{{monzo| 0 1 4 10 }}
+| Equilateral || CEE<br>~3/2 = 696.8843¢<br>Eigenmonzo (unchanged-interval) basis: 2.{{monzo| 0 1 4 10 }}
 |-
-| Equilateral-Weil || CEWE<br>~3/2 = 696.7248¢<br>Eigenmonzo basis (unchanged-interval basis): 2.4117715/9
+| Equilateral-Weil || CEWE<br>~3/2 = 696.7248¢<br>Eigenmonzo (unchanged-interval) basis: 2.4117715/9
 |-
-| Benedetti || CBE<br>~3/2 = 697.0147¢<br>Eigenmonzo basis (unchanged-interval basis): 2.{{monzo| 0 1225 1764 2250 }}
+| Benedetti || CBE<br>~3/2 = 697.0147¢<br>Eigenmonzo (unchanged-interval) basis: 2.{{monzo| 0 1225 1764 2250 }}
 |-
-| Benedetti-Weil || CBWE<br>~3/2 = 696.6306¢<br>Eigenmonzo basis (unchanged-interval basis): 2.{{monzo| 0 -3290 3171 7215 }}
+| Benedetti-Weil || CBWE<br>~3/2 = 696.6306¢<br>Eigenmonzo (unchanged-interval) basis: 2.{{monzo| 0 -3290 3171 7215 }}
 |}
@@ Line 107: / Line 107: @@
 |-
 ! Edo<br>Generator
-! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]
+! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]]
 ! Generator<br>(¢)
 ! Comments

Meantone: Difference between revisions

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