Subgroup temperaments: Difference between revisions

Line 906:

[[Subgroup]]: 2.5/3.7.11

[[Comma list]]: 100/99 = {{monzo| 2 2 0 -1 }}, 385/384 = {{monzo| -7 1 1 1 }}

[[Comma list]]: 100/99 ({{monzo| 2 2 0 -1 }}), 385/384 ({{monzo| -7 1 1 1 }})

Line 922:

<nowiki />* Wart for 5/3

<nowiki/>* Wart for 5/3

[[Tp tuning #T2 tuning|RMS error]]: 1.206 cents

Line 929:

Starlingtet, the 4 &~~amp;~~ 15 temperament in the 2.5/3.7/3 subgroup, is related to [[starling]] as well as to [[myna]]. The tonic and the first three generator steps make a [[starling tetrad]], hence the name.

Starlingtet, the {{nowrap| 4 & 15 }} temperament in the 2.5/3.7/3 subgroup, is related to [[starling]] as well as to [[myna]]. The tonic and the first three generator steps make a [[starling tetrad]], hence the name.

[[Subgroup]]: 2.5/3.7/3

[[Comma list]]: [[126/125]] = {{monzo| 1 -3 1 }}

[[Comma list]]: [[126/125]] ({{monzo| 1 -3 1 }})

Line 958:

[[Subgroup]]: 2.5/3.7/3.11/3

[[Comma list]]: 121/120 = {{monzo| -3 -1 0 2 }}, 126/125 = {{monzo| 1 -3 1 }}

[[Comma list]]: 121/120 ({{monzo| -3 -1 0 2 }}), 126/125 ({{monzo| 1 -3 1 }})

Line 972:

<nowiki />* Wart for 11/3

<nowiki/>* Wart for 11/3

[[Tp tuning#T2 tuning|RMS error]]: 1.034 cents

[[Tp tuning #T2 tuning|RMS error]]: 1.034 cents

==== Skateboard ====

Line 983:

[[Subgroup]]: 2.5/3.7/3.11.13/9

[[Comma list]]: 56/55 = {{monzo| 3 -1 1 -1 }}, 91/90 = {{monzo| -1 -1 1 0 1 }}, 100/99 = {{monzo| 2 2 0 -1 }}

[[Comma list]]: 56/55 ({{monzo| 3 -1 1 -1 }}), 91/90 ({{monzo| -1 -1 1 0 1 }}), 100/99 ({{monzo| 2 2 0 -1 }})

Line 1,005:

Gariberttet can be described as the 4 &~~amp;~~ 29 temperament in the 2.5/3.7/3.13/11 subgroup.

Gariberttet can be described as the {{nowrap| 4 & 29 }} temperament in the 2.5/3.7/3.13/11 subgroup.

[[Subgroup]]: 2.5/3.7/3.13/11

[[Comma list]]: [[275/273]] = {{monzo| 0 2 -1 -1 }}, [[847/845]] = {{monzo| 0 -1 1 -2 }}

[[Comma list]]: [[275/273]] ({{monzo| 0 2 -1 -1 }}), [[847/845]] ({{monzo| 0 -1 1 -2 }})

Line 1,022:

{{Optimal ET sequence|legend=1| 29, 33, 37, 41, 45, 49, 78, 94, 143* }}

<nowiki />* Wart for 13/11

<nowiki/>* Wart for 13/11

[[Tp tuning #T2 tuning|RMS error]]: 0.6914 cents

Line 1,029:

Indium can be described as the 8 &~~amp;~~ 33 temperament in the 2.5/3.7/3.11/3 subgroup.

Indium can be described as the {{nowrap| 8 & 33 }} temperament in the 2.5/3.7/3.11/3 subgroup.

[[Subgroup]]: 2.5/3.7/3.11/3

[[Comma list]]: [[3025/3024]] = {{monzo| -4 2 -1 2 }}, [[3125/3087]] = {{monzo| 0 5 -3 }}

[[Comma list]]: [[3025/3024]] ({{monzo| -4 2 -1 2 }}), [[3125/3087]] ({{monzo| 0 5 -3 }})

Line 1,047:

{{Optimal ET sequence|legend=1| 8, 33, 41, 49, 204*† }}

<nowiki />* Wart for 7/3

<nowiki/>* Wart for 7/3

† Wart for 11/3

Line 1,056:

Semidim can be described as the 8 &~~amp;~~ 29 temperament in the 2.5/3.7/3.11/3.13/3 subgroup. It extends [[tridec]], and is related to [[ammonite]]. It is generated by a semidiminished fourth, hence the name.

Semidim can be described as the {{nowrap| 8 & 29 }} temperament in the 2.5/3.7/3.11/3.13/3 subgroup. It extends [[tridec]], and is related to [[ammonite]]. It is generated by a semidiminished fourth, hence the name.

[[Subgroup]]: 2.5/3.7/3.11/3.13/3

[[Comma list]]: [[121/120]] = {{monzo| -3 -1 0 2 }}, [[169/168]] = {{monzo| -3 0 -1 0 2 }}, [[275/273]] = {{monzo| 0 2 -1 1 -1 }}

[[Comma list]]: [[121/120]] ({{monzo| -3 -1 0 2 }}), [[169/168]] ({{monzo| -3 0 -1 0 2 }}), [[275/273]] ({{monzo| 0 2 -1 1 -1 }})

Line 1,079:

Sentry, the 3 &~~amp;~~ 5 temperament in the 2.5/3.9/7 subgroup, is related to [[sensi]].

Sentry, the {{nowrap| 3 & 5 }} temperament in the 2.5/3.9/7 subgroup, is related to [[sensi]].

[[Subgroup]]: 2.5/3.9/7

[[Comma list]]: [[245/243]] = {{monzo| 0 1 -2 }}

[[Comma list]]: [[245/243]] ({{monzo| 0 1 -2 }})

Line 1,092:

[[Optimal tuning]]s:

* [[Tp tuning|subgroup]] [[CTE]] and [[POTE]]: ~2 = ~~1\1~~, ~9/7 = 440.902

* [[Tp tuning|subgroup]] [[CTE]] and [[POTE]]: ~2 = 1200.000, ~9/7 = 440.902

{{Optimal ET sequence|legend=1| 8, 11, 19, 30, 41, 49, 52, 145*, 166†, 197*†, 215†, 264*† }}

<nowiki />* Wart for 5/3

<nowiki/>* Wart for 5/3

† Wart for 9/7

Line 1,105:

Marveltwintri can be described as the 3 &~~amp;~~ 4 temperament in the 2.5/3.13/9 subgroup. The tonic and the first two generator steps make a [[marveltwin triad]], hence the name.

Marveltwintri can be described as the {{nowrap| 3 & 4 }} temperament in the 2.5/3.13/9 subgroup. The tonic and the first two generator steps make a [[marveltwin triad]], hence the name.

[[Subgroup]]: 2.5/3.13/9

[[Comma list]]: [[325/324]] = {{monzo| -2 2 1 }}

[[Comma list]]: [[325/324]] ({{monzo| -2 2 1 }})

@@ Line 906: / Line 906: @@
 [[Subgroup]]: 2.5/3.7.11
-[[Comma list]]: 100/99 = {{monzo| 2 2 0 -1 }}, 385/384 = {{monzo| -7 1 1 1 }}
+[[Comma list]]: 100/99 ({{monzo| 2 2 0 -1 }}), 385/384 ({{monzo| -7 1 1 1 }})
 {{Mapping|legend=2| 1 0 5 2 | 0 1 -3 2 }}
@@ Line 922: / Line 922: @@
 {{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 67, 93* }}
-<nowiki />* Wart for 5/3
+<nowiki/>* Wart for 5/3
 [[Tp tuning #T2 tuning|RMS error]]: 1.206 cents
@@ Line 929: / Line 929: @@
 {{See also | Chromatic pairs #Starlingtet }}
-Starlingtet, the 4 &amp; 15 temperament in the 2.5/3.7/3 subgroup, is related to [[starling]] as well as to [[myna]]. The tonic and the first three generator steps make a [[starling tetrad]], hence the name.
+Starlingtet, the {{nowrap| 4 & 15 }} temperament in the 2.5/3.7/3 subgroup, is related to [[starling]] as well as to [[myna]]. The tonic and the first three generator steps make a [[starling tetrad]], hence the name.
 [[Subgroup]]: 2.5/3.7/3
-[[Comma list]]: [[126/125]] = {{monzo| 1 -3 1 }}
+[[Comma list]]: [[126/125]] ({{monzo| 1 -3 1 }})
 {{Mapping|legend=2| 1 0 -1 | 0 1 3 }}
@@ Line 958: / Line 958: @@
 [[Subgroup]]: 2.5/3.7/3.11/3
-[[Comma list]]: 121/120 = {{monzo| -3 -1 0 2 }}, 126/125 = {{monzo| 1 -3 1 }}
+[[Comma list]]: 121/120 ({{monzo| -3 -1 0 2 }}), 126/125 ({{monzo| 1 -3 1 }})
 {{Mapping|legend=2| 1 1 2 2 | 0 -2 -6 -1 }}
@@ Line 972: / Line 972: @@
 {{Optimal ET sequence|legend=1| 8, 15, 23, 54, 77, 100, 131* }}
-<nowiki />* Wart for 11/3
+<nowiki/>* Wart for 11/3
-[[Tp tuning#T2 tuning|RMS error]]: 1.034 cents
+[[Tp tuning #T2 tuning|RMS error]]: 1.034 cents
 ==== Skateboard ====
@@ Line 983: / Line 983: @@
 [[Subgroup]]: 2.5/3.7/3.11.13/9
-[[Comma list]]: 56/55 = {{monzo| 3 -1 1 -1 }}, 91/90 = {{monzo| -1 -1 1 0 1 }}, 100/99 = {{monzo| 2 2 0 -1 }}
+[[Comma list]]: 56/55 ({{monzo| 3 -1 1 -1 }}), 91/90 ({{monzo| -1 -1 1 0 1 }}), 100/99 ({{monzo| 2 2 0 -1 }})
 {{Mapping|legend=2| 1 0 -1 2 2 | 0 1 3 2 -2 }}
@@ Line 1,005: / Line 1,005: @@
 {{See also | Chromatic pairs #Gariberttet }}
-Gariberttet can be described as the 4 &amp; 29 temperament in the 2.5/3.7/3.13/11 subgroup.
+Gariberttet can be described as the {{nowrap| 4 & 29 }} temperament in the 2.5/3.7/3.13/11 subgroup.
 [[Subgroup]]: 2.5/3.7/3.13/11
-[[Comma list]]: [[275/273]] = {{monzo| 0 2 -1 -1 }}, [[847/845]] = {{monzo| 0 -1 1 -2 }}
+[[Comma list]]: [[275/273]] ({{monzo| 0 2 -1 -1 }}), [[847/845]] ({{monzo| 0 -1 1 -2 }})
 {{Mapping|legend=2| 1 0 0 0 | 0 3 5 1 }}
@@ Line 1,022: / Line 1,022: @@
 {{Optimal ET sequence|legend=1| 29, 33, 37, 41, 45, 49, 78, 94, 143* }}
-<nowiki />* Wart for 13/11
+<nowiki/>* Wart for 13/11
 [[Tp tuning #T2 tuning|RMS error]]: 0.6914 cents
@@ Line 1,029: / Line 1,029: @@
 {{See also | Chromatic pairs #Indium }}
-Indium can be described as the 8 &amp; 33 temperament in the 2.5/3.7/3.11/3 subgroup.
+Indium can be described as the {{nowrap| 8 & 33 }} temperament in the 2.5/3.7/3.11/3 subgroup.
 [[Subgroup]]: 2.5/3.7/3.11/3
-[[Comma list]]: [[3025/3024]] = {{monzo| -4 2 -1 2 }}, [[3125/3087]] = {{monzo| 0 5 -3 }}
+[[Comma list]]: [[3025/3024]] ({{monzo| -4 2 -1 2 }}), [[3125/3087]] ({{monzo| 0 5 -3 }})
 {{Mapping|legend=2| 1 0 0 2 | 0 6 10 -1 }}
@@ Line 1,047: / Line 1,047: @@
 {{Optimal ET sequence|legend=1| 8, 33, 41, 49, 204*<sup>†</sup> }}
-<nowiki />* Wart for 7/3
+<nowiki/>* Wart for 7/3
 <sup>†</sup> Wart for 11/3
@@ Line 1,056: / Line 1,056: @@
 {{See also| Chromatic pairs #Semidim }}
-Semidim can be described as the 8 &amp; 29 temperament in the 2.5/3.7/3.11/3.13/3 subgroup. It extends [[tridec]], and is related to [[ammonite]]. It is generated by a semidiminished fourth, hence the name.
+Semidim can be described as the {{nowrap| 8 & 29 }} temperament in the 2.5/3.7/3.11/3.13/3 subgroup. It extends [[tridec]], and is related to [[ammonite]]. It is generated by a semidiminished fourth, hence the name.
 [[Subgroup]]: 2.5/3.7/3.11/3.13/3
-[[Comma list]]: [[121/120]] = {{monzo| -3 -1 0 2 }}, [[169/168]] = {{monzo| -3 0 -1 0 2 }}, [[275/273]] = {{monzo| 0 2 -1 1 -1 }}
+[[Comma list]]: [[121/120]] ({{monzo| -3 -1 0 2 }}), [[169/168]] ({{monzo| -3 0 -1 0 2 }}), [[275/273]] ({{monzo| 0 2 -1 1 -1 }})
 {{Mapping|legend=2| 1 3 5 3 4 | 0 -6 -10 -3 -5 }}
@@ Line 1,079: / Line 1,079: @@
 {{See also | Chromatic pairs #Sentry }}
-Sentry, the 3 &amp; 5 temperament in the 2.5/3.9/7 subgroup, is related to [[sensi]].
+Sentry, the {{nowrap| 3 & 5 }} temperament in the 2.5/3.9/7 subgroup, is related to [[sensi]].
 [[Subgroup]]: 2.5/3.9/7
-[[Comma list]]: [[245/243]] = {{monzo| 0 1 -2 }}
+[[Comma list]]: [[245/243]] ({{monzo| 0 1 -2 }})
 {{Mapping|legend=2| 1 0 0 | 0 2 1 }}
@@ Line 1,092: / Line 1,092: @@
 [[Optimal tuning]]s:
-* [[Tp tuning|subgroup]] [[CTE]] and [[POTE]]: ~2 = 1\1, ~9/7 = 440.902
+* [[Tp tuning|subgroup]] [[CTE]] and [[POTE]]: ~2 = 1200.000, ~9/7 = 440.902
 {{Optimal ET sequence|legend=1| 8, 11, 19, 30, 41, 49, 52, 145*, 166<sup>†</sup>, 197*<sup>†</sup>, 215<sup>†</sup>, 264*<sup>†</sup> }}
-<nowiki />* Wart for 5/3
+<nowiki/>* Wart for 5/3
 <sup>†</sup> Wart for 9/7
@@ Line 1,105: / Line 1,105: @@
 {{See also| Chromatic pairs #Marveltwintri }}
-Marveltwintri can be described as the 3 &amp; 4 temperament in the 2.5/3.13/9 subgroup. The tonic and the first two generator steps make a [[marveltwin triad]], hence the name.
+Marveltwintri can be described as the {{nowrap| 3 & 4 }} temperament in the 2.5/3.13/9 subgroup. The tonic and the first two generator steps make a [[marveltwin triad]], hence the name.
 [[Subgroup]]: 2.5/3.13/9
-[[Comma list]]: [[325/324]] = {{monzo| -2 2 1 }}
+[[Comma list]]: [[325/324]] ({{monzo| -2 2 1 }})
 {{Mapping|legend=2| 1 0 2 | 0 1 -2 }}