Meantone: Difference between revisions

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* [[Meantone7]] – diatonic scale in 19edo and 31edo

* [[Meantone12]] – chromatic scale in 31edo

; Eigenmonzo tunings

; Eigenmonzo (unchanged-interval) tunings

* [[Meanwoo12]] – chromatic scale in 5/4.7-eigenmonzo tuning

* [[Meanwoo19]] – enharmonic scale in 5/4.7-eigenmonzo tuning

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== Tunings ==

Common meantone tunings can be classified into eigenmonzo 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]] (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 tunings

; Notable eigenmonzo (unchanged-interval) tunings

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

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

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

|-

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

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

|-

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

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

|-

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

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

|-

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

| Benedetti-Weil || CBWE ~3/2 = 696.7868¢ Eigenmonzo basis (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: 2.{{monzo| 0 1 4 10 }}

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

|-

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

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

|-

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

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

|-

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

| Benedetti-Weil || CBWE ~3/2 = 696.6306¢ Eigenmonzo basis (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 39: / Line 39: @@
 * [[Meantone7]] – diatonic scale in 19edo and 31edo
 * [[Meantone12]] – chromatic scale in 31edo
-; Eigenmonzo tunings
+; Eigenmonzo (unchanged-interval) tunings
 * [[Meanwoo12]] – chromatic scale in 5/4.7-eigenmonzo tuning
 * [[Meanwoo19]] – enharmonic scale in 5/4.7-eigenmonzo tuning
@@ Line 48: / Line 48: @@
 == Tunings ==
-Common meantone tunings can be classified into eigenmonzo 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]] (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 tunings
+; Notable eigenmonzo (unchanged-interval) tunings
 * [[1/2 syntonic comma meantone]] – with eigenmonzo [[10/9]]
 * [[1/3 syntonic comma meantone]] – with eigenmonzo [[5/3]]
@@ Line 76: / Line 76: @@
 | Tenney-Weil || CTWE<br>~3/2 = 696.6512¢
 |-
-| Equilateral || CEE<br>~3/2 = 696.8947¢<br>Eigenmonzo basis: 2.1875 (4/17-comma tuning)
+| Equilateral || CEE<br>~3/2 = 696.8947¢<br>[[Eigenmonzo basis]] ([[unchanged-interval basis]]): 2.1875 (4/17-comma tuning)
 |-
-| Equilateral-Weil || CEWE<br>~3/2 = 696.4534¢<br>Eigenmonzo basis: 2.48828125/3 (11/43-comma tuning)
+| Equilateral-Weil || CEWE<br>~3/2 = 696.4534¢<br>Eigenmonzo basis (unchanged-interval basis): 2.48828125/3 (11/43-comma tuning)
 |-
-| Benedetti || CBE<br>~3/2 = 697.3738¢<br>Eigenmonzo basis: 2.{{monzo| 0 25 36 }} (36/169-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-Weil || CBWE<br>~3/2 = 696.7868¢<br>Eigenmonzo basis: 2.{{monzo| 0 5 31 }} (31/129-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)
 |}
@@ Line 94: / Line 94: @@
 | Tenney-Weil || CTWE<br>~3/2 = 696.6562¢
 |-
-| Equilateral || CEE<br>~3/2 = 696.8843¢<br>Eigenmonzo basis: 2.{{monzo| 0 1 4 10 }}
+| Equilateral || CEE<br>~3/2 = 696.8843¢<br>Eigenmonzo basis (unchanged-interval basis): 2.{{monzo| 0 1 4 10 }}
 |-
-| Equilateral-Weil || CEWE<br>~3/2 = 696.7248¢<br>Eigenmonzo basis: 2.4117715/9
+| Equilateral-Weil || CEWE<br>~3/2 = 696.7248¢<br>Eigenmonzo basis (unchanged-interval basis): 2.4117715/9
 |-
-| Benedetti || CBE<br>~3/2 = 697.0147¢<br>Eigenmonzo basis: 2.{{monzo| 0 1225 1764 2250 }}
+| Benedetti || CBE<br>~3/2 = 697.0147¢<br>Eigenmonzo basis (unchanged-interval basis): 2.{{monzo| 0 1225 1764 2250 }}
 |-
-| Benedetti-Weil || CBWE<br>~3/2 = 696.6306¢<br>Eigenmonzo basis: 2.{{monzo| 0 -3290 3171 7215 }}
+| Benedetti-Weil || CBWE<br>~3/2 = 696.6306¢<br>Eigenmonzo basis (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