Sengic family: Difference between revisions

Line 14:

: mapping generators: ~2, ~3, ~15/14

[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.7873{{c}}, ~15/14 = 129.6451{{c}}

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.7533{{c}}, ~3/2 = 704.0092{{c}}, ~15/14 = 129.7976{{c}}

: [[error map]]: {{val| -0.247 +1.808 +2.586 -5.715 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.9671{{c}}, ~15/14 = 129.7330{{c}}

: error map: {{val| 0.000 +2.012 +2.885 -5.393 }}

[[Badness]] (~~Smith~~): 0.~~320 × 10-3~~

[[Badness]] (Sintel): 1.41

[[Projection pair]]s: ~5 = 3375/686, ~7 = 675/98 to 2.3.7/5

Line 27:

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Comma list: 91/90, 169/168

~~Sval~~ mapping: {{mapping| 1 0 2 1 2 | 0 1 0 1 1 | 0 0 3 2 1 }}

Subgroup-val mapping: {{mapping| 1 0 2 1 2 | 0 1 0 1 1 | 0 0 3 2 1 }}

Optimal ~~tuning (~~CTE): ~2 = 1200.0000{{c}}, ~3/2 = 704.5918{{c}}, ~14/13 = 129.7585{{c}}

Optimal tunings:

* WE: ~2 = 1200.3448{{c}}, ~3/2 = 704.1998{{c}}, ~14/13 = 129.5253{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2688{{c}}, ~14/13 = 129.6115{{c}}

{{Optimal ET sequence|legend=0| 8d, 9, 10, 17c, 19, 27, 46, 111df, 121df }}

Badness (~~Smith~~): 0.~~320 × 10-3~~

Badness (Sintel): 0.425

== Demeter ==

Line 44:

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[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3/2 = 705.518{{c}}, ~15/14 = 130.039{{c}}

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.4002{{c}}, ~3/2 = 705.1652{{c}}, ~15/14 = 129.9738{{c}}

: [[error map]]: {{val| -0.600 +2.610 +2.408 -4.913 -1.283 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 705.2789{{c}}, ~15/14 = 129.8330{{c}}

: error map: {{val| 0.000 +3.324 +3.185 -3.881 -0.369 }}

{{Optimal ET sequence|legend=1| 10, 17c, 19e, 27e, 46, 102, 148 }}

[[Badness]] (~~Smith~~): 1.~~32 × 10-3~~

[[Badness]] (Sintel): 1.58

[[Projection pair]]s: ~5 = 2725888/531441, ~7 = 15488/2187 to 2.3.11

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Mapping: {{mapping| 1 0 2 1 -3 2 | 0 1 0 1 4 1 | 0 0 3 2 1 1 }}

Optimal ~~tuning (~~POTE): ~2 = 1200.000{{c}}, ~3/2 = 705.113{{c}}, ~14/13 = 129.673{{c}}

Optimal tunings:

* WE: ~2 = 1200.0393{{c}}, ~3/2 = 705.1360{{c}}, ~14/13 = 129.6770{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 705.1277{{c}}, ~14/13 = 129.6854{{c}}

{{Optimal ET sequence|legend=0| 10, 17c, 19e, 27e, 29, 46, 102, 148f }}

Badness (~~Smith~~): 0.~~977 × 10-3~~

Badness (Sintel): 0.913

Projection pairs: ~5 = 2725888/531441, ~7 = 15488/2187, ~13 = 352/27 to 2.3.11

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Mapping: {{mapping| 1 0 2 1 -3 2 -1 | 0 1 0 1 4 1 3 | 0 0 3 2 1 1 3 }}

Optimal ~~tuning (~~POTE): ~2 = 1200.000{{c}}, ~3/2 = 705.147{{c}}, ~14/13 = 129.700{{c}}

Optimal tunings:

* WE: ~2 = 1200.0255{{c}}, ~3/2 = 705.1616{{c}}, ~14/13 = 129.7024{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 705.1553{{c}}, ~14/13 = 129.7071{{c}}

{{Optimal ET sequence|legend=0| 10, 17cg, 19eg, 27eg, 29g, 46, 102, 148f }}

Badness (~~Smith~~): 0.~~830 × 10-3~~

Badness (Sintel): 0.789

Projection pairs: ~5 = 2725888/531441, ~7 = 15488/2187, ~13 = 352/27, ~17 = 340736/19683 to 2.3.11

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[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3/2 = 705.978{{c}}, ~12/11 = 132.544{{c}}

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1197.0576{{c}}, ~3/2 = 704.2467{{c}}, ~15/14 = 132.2189{{c}}

: [[error map]]: {{val| -2.942 -0.651 +4.458 -6.026 +11.883 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.6964{{c}}, ~15/14 = 131.8166{{c}}

: error map: {{val| 0.000 +1.741 +9.136 -1.496 +20.562 }}

{{Optimal ET sequence|legend=1| 8d, 9, 10, 17c, 19, 27e, 63cee }} *

[[Badness]] (~~Smith~~): 0.~~856 × 10-3~~

<nowiki/>* [[optimal patent val]]: [[36edo|36]]

[[Badness]] (Sintel): 1.03

[[Projection pair]]s: ~5 = 6912/1331, ~7 = 854/121 to 2.3.11

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Mapping: {{mapping| 1 0 2 1 2 2 | 0 1 0 1 1 1 | 0 0 3 2 -1 1 }}

Optimal ~~tuning (~~POTE): ~2 = 1200.000{{c}}, ~3/2 = 706.029{{c}}, ~14/13 = 132.428{{c}}

Optimal tunings:

* WE: ~2 = 1197.6484{{c}}, ~3/2 = 704.6450{{c}}, ~14/13 = 132.1686{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.1616{{c}}, ~14/13 = 131.8445{{c}}

{{Optimal ET sequence|legend=0| 8d, 9, 10, 17c, 19, 27e }} *

~~{{Optimal ET sequence~~|~~legend=0| 8d, 9, 10, 17c, 19, 27e,~~ 36 }}

<nowiki/>* optimal patent val: [[36edo|36]]

Badness (~~Smith~~): 0.~~727 × 10-3~~

Badness (Sintel): 0.680

Projection pairs: ~5 = 6912/1331, ~7 = 854/121, ~13 = 144/11 to 2.3.11

@@ Line 14: / Line 14: @@
 : mapping generators: ~2, ~3, ~15/14
-[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.7873{{c}}, ~15/14 = 129.6451{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.7533{{c}}, ~3/2 = 704.0092{{c}}, ~15/14 = 129.7976{{c}}
+: [[error map]]: {{val| -0.247 +1.808 +2.586 -5.715 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.9671{{c}}, ~15/14 = 129.7330{{c}}
+: error map: {{val| 0.000 +2.012 +2.885 -5.393 }}
+<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.7873{{c}}, ~15/14 = 129.6451{{c}} -->
 {{Optimal ET sequence|legend=1| 8d, 9, 10, 17c, 19, 27, 46 }}
-[[Badness]] (Smith): 0.320 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 1.41
 [[Projection pair]]s: ~5 = 3375/686, ~7 = 675/98 to 2.3.7/5
@@ Line 27: / Line 32: @@
 Comma list: 91/90, 169/168
-Sval mapping: {{mapping| 1 0 2 1 2 | 0 1 0 1 1 | 0 0 3 2 1 }}
+Subgroup-val mapping: {{mapping| 1 0 2 1 2 | 0 1 0 1 1 | 0 0 3 2 1 }}
-Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~3/2 = 704.5918{{c}}, ~14/13 = 129.7585{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.3448{{c}}, ~3/2 = 704.1998{{c}}, ~14/13 = 129.5253{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2688{{c}}, ~14/13 = 129.6115{{c}}
+<!-- * CTE: ~2 = 1200.0000{{c}}, ~3/2 = 704.5918{{c}}, ~14/13 = 129.7585{{c}} -->
 {{Optimal ET sequence|legend=0| 8d, 9, 10, 17c, 19, 27, 46, 111df, 121df }}
-Badness (Smith): 0.320 × 10<sup>-3</sup>
+Badness (Sintel): 0.425
 == Demeter ==
@@ Line 44: / Line 52: @@
 {{Mapping|legend=1| 1 0 2 1 -3 | 0 1 0 1 4 | 0 0 3 2 1 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3/2 = 705.518{{c}}, ~15/14 = 130.039{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.4002{{c}}, ~3/2 = 705.1652{{c}}, ~15/14 = 129.9738{{c}}
+: [[error map]]: {{val| -0.600 +2.610 +2.408 -4.913 -1.283 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 705.2789{{c}}, ~15/14 = 129.8330{{c}}
+: error map: {{val| 0.000 +3.324 +3.185 -3.881 -0.369 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 705.518{{c}}, ~15/14 = 130.039{{c}} -->
 {{Optimal ET sequence|legend=1| 10, 17c, 19e, 27e, 46, 102, 148 }}
-[[Badness]] (Smith): 1.32 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 1.58
 [[Projection pair]]s: ~5 = 2725888/531441, ~7 = 15488/2187 to 2.3.11
@@ Line 59: / Line 72: @@
 Mapping: {{mapping| 1 0 2 1 -3 2 | 0 1 0 1 4 1 | 0 0 3 2 1 1 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 705.113{{c}}, ~14/13 = 129.673{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.0393{{c}}, ~3/2 = 705.1360{{c}}, ~14/13 = 129.6770{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 705.1277{{c}}, ~14/13 = 129.6854{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 705.113{{c}}, ~14/13 = 129.673{{c}} -->
 {{Optimal ET sequence|legend=0| 10, 17c, 19e, 27e, 29, 46, 102, 148f }}
-Badness (Smith): 0.977 × 10<sup>-3</sup>
+Badness (Sintel): 0.913
 Projection pairs: ~5 = 2725888/531441, ~7 = 15488/2187, ~13 = 352/27 to 2.3.11
@@ Line 74: / Line 90: @@
 Mapping: {{mapping| 1 0 2 1 -3 2 -1 | 0 1 0 1 4 1 3 | 0 0 3 2 1 1 3 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 705.147{{c}}, ~14/13 = 129.700{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.0255{{c}}, ~3/2 = 705.1616{{c}}, ~14/13 = 129.7024{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 705.1553{{c}}, ~14/13 = 129.7071{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 705.147{{c}}, ~14/13 = 129.700{{c}} -->
 {{Optimal ET sequence|legend=0| 10, 17cg, 19eg, 27eg, 29g, 46, 102, 148f }}
-Badness (Smith): 0.830 × 10<sup>-3</sup>
+Badness (Sintel): 0.789
 Projection pairs: ~5 = 2725888/531441, ~7 = 15488/2187, ~13 = 352/27, ~17 = 340736/19683 to 2.3.11
@@ Line 89: / Line 108: @@
 {{Mapping|legend=1| 1 0 2 1 2 | 0 1 0 1 1 | 0 0 3 2 -1 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3/2 = 705.978{{c}}, ~12/11 = 132.544{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1197.0576{{c}}, ~3/2 = 704.2467{{c}}, ~15/14 = 132.2189{{c}}
+: [[error map]]: {{val| -2.942 -0.651 +4.458 -6.026 +11.883 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.6964{{c}}, ~15/14 = 131.8166{{c}}
+: error map: {{val| 0.000 +1.741 +9.136 -1.496 +20.562 }}
+<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 705.978{{c}}, ~12/11 = 132.544{{c}} -->
-{{Optimal ET sequence|legend=1| 8d, 9, 10, 17c, 19, 27e, 36 }}
+{{Optimal ET sequence|legend=1| 8d, 9, 10, 17c, 19, 27e, 63cee }} *
-[[Badness]] (Smith): 0.856 × 10<sup>-3</sup>
+<nowiki/>* [[optimal patent val]]: [[36edo|36]]
+[[Badness]] (Sintel): 1.03
 [[Projection pair]]s: ~5 = 6912/1331, ~7 = 854/121 to 2.3.11
@@ Line 104: / Line 130: @@
 Mapping: {{mapping| 1 0 2 1 2 2 | 0 1 0 1 1 1 | 0 0 3 2 -1 1 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 706.029{{c}}, ~14/13 = 132.428{{c}}
+Optimal tunings:
+* WE: ~2 = 1197.6484{{c}}, ~3/2 = 704.6450{{c}}, ~14/13 = 132.1686{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.1616{{c}}, ~14/13 = 131.8445{{c}}
+<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 706.029{{c}}, ~14/13 = 132.428{{c}} -->
+{{Optimal ET sequence|legend=0| 8d, 9, 10, 17c, 19, 27e }} *
-{{Optimal ET sequence|legend=0| 8d, 9, 10, 17c, 19, 27e, 36 }}
+<nowiki/>* optimal patent val: [[36edo|36]]
-Badness (Smith): 0.727 × 10<sup>-3</sup>
+Badness (Sintel): 0.680
 Projection pairs: ~5 = 6912/1331, ~7 = 854/121, ~13 = 144/11 to 2.3.11