Keemic family: Difference between revisions

Line 16:

: Angle (6/5, 3/2) = 77.834

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.8733{{c}}, ~5/4 = 380.4684{{c}}

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1201.0490{{c}}, ~3/2 = 702.4868{{c}}, ~5/4 = 380.8010{{c}}

: [[error map]]: {{val| +1.049 +1.581 -3.415 -1.670 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.8060{{c}}, ~5/4 = 381.0536{{c}}

: error map: {{val| 0.000 +0.851 -5.260 -3.569 }}

[[Minimax tuning]]:

Line 25:

Line 30:

{{Optimal ET sequence|legend=1| 7, 12d, 15, 19, 41, 142cd, 183cd, 224ccd }}

[[Badness]] (~~Smith~~): 0.~~212 × 10-3~~

[[Badness]] (Sintel): 0.937

[[Projection pair]]: 7 864/125

Line 40:

Line 45:

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 704.1985{{c}}, ~5/4 = 381.5394{{c}}

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9868{{c}}, ~3/2 = 704.1908{{c}}, ~5/4 = 381.5352{{c}}

: [[error map]]: {{val| -0.013 +2.223 -4.805 -0.885 +3.318 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.1922{{c}}, ~5/4 = 381.5339{{c}}

: error map: {{val| 0.000 +2.237 -4.780 -0.851 +3.365 }}

[[Badness]] (~~Smith~~): 0.~~641 × 10-3~~

[[Badness]] (Sintel): 0.770

Scales: [[supermagic15]]

Line 56:

Line 66:

: mapping generators: ~2, ~5, ~11

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~5/4 = 380.3520{{c}}, ~11/8 = 547.5758{{c}}

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1201.0786{{c}}, ~5/4 = 380.6939{{c}}, ~11/8 = 548.0690{{c}}

: [[error map]]: {{val| +1.079 +1.514 -3.463 -1.578 -0.013 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 380.4576{{c}}, ~11/8 = 548.8962{{c}}

: error map: {{val| 0.000 +0.333 -5.856 -3.335 -2.422 }}

{{Optimal ET sequence|legend=1| 19, 22, 38d, 41, 60e, 101cd, 164c, 224ccde * }}

{{Optimal ET sequence|legend=1| 19, 22, 38d, 41, 60e, 101cd, 164c, 224ccde }} *

<nowiki>*</nowiki> [[optimal patent val]]: [[104edo|104]]

[[Badness]] (~~Smith~~): 0.~~888 × 10-3~~

[[Badness]] (Sintel): 1.07

=== 13-limit ===

Line 71:

Line 86:

Mapping: {{mapping| 1 0 2 -1 0 -2 | 0 5 1 12 0 18 | 0 0 0 0 1 0 }}

Optimal ~~tuning (~~POTE): ~2 = 1200.0000{{c}}, ~5/4 = 380.0401{{c}}, ~11/8 = 546.6672{{c}}

Optimal tunings:

* WE: ~2 = 1201.3389{{c}}, ~5/4 = 380.4641{{c}}, ~11/8 = 547.2772{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.1532{{c}}, ~11/8 = 548.2678{{c}}

{{Optimal ET sequence|legend=1| 19, 22f, 38df, 41, 60e, 79d, 101cd }}

Badness (~~Smith~~): 1.~~14 × 10-3~~

Badness (Sintel): 1.07

[[Category:Temperament families]]

@@ Line 16: / Line 16: @@
 : Angle (6/5, 3/2) = 77.834
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.8733{{c}}, ~5/4 = 380.4684{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1201.0490{{c}}, ~3/2 = 702.4868{{c}}, ~5/4 = 380.8010{{c}}
+: [[error map]]: {{val| +1.049 +1.581 -3.415 -1.670 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.8060{{c}}, ~5/4 = 381.0536{{c}}
+: error map: {{val| 0.000 +0.851 -5.260 -3.569 }}
+<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8733{{c}}, ~5/4 = 380.4684{{c}} -->
 [[Minimax tuning]]:
@@ Line 25: / Line 30: @@
 {{Optimal ET sequence|legend=1| 7, 12d, 15, 19, 41, 142cd, 183cd, 224ccd }}
-[[Badness]] (Smith): 0.212 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.937
 [[Projection pair]]: 7 864/125
@@ Line 40: / Line 45: @@
 {{Mapping|legend=1| 1 0 0 5 2 | 0 1 0 3 -2 | 0 0 1 -3 2 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 704.1985{{c}}, ~5/4 = 381.5394{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9868{{c}}, ~3/2 = 704.1908{{c}}, ~5/4 = 381.5352{{c}}
+: [[error map]]: {{val| -0.013 +2.223 -4.805 -0.885 +3.318 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.1922{{c}}, ~5/4 = 381.5339{{c}}
+: error map: {{val| 0.000 +2.237 -4.780 -0.851 +3.365 }}
+<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.1985{{c}}, ~5/4 = 381.5394{{c}} -->
 {{Optimal ET sequence|legend=1| 7, 15, 19, 22, 37, 41, 104 }}
-[[Badness]] (Smith): 0.641 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.770
 Scales: [[supermagic15]]
@@ Line 56: / Line 66: @@
 : mapping generators: ~2, ~5, ~11
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~5/4 = 380.3520{{c}}, ~11/8 = 547.5758{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1201.0786{{c}}, ~5/4 = 380.6939{{c}}, ~11/8 = 548.0690{{c}}
+: [[error map]]: {{val| +1.079 +1.514 -3.463 -1.578 -0.013 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 380.4576{{c}}, ~11/8 = 548.8962{{c}}
+: error map: {{val| 0.000 +0.333 -5.856 -3.335 -2.422 }}
+<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~5/4 = 380.3520{{c}}, ~11/8 = 547.5758{{c}} -->
-{{Optimal ET sequence|legend=1| 19, 22, 38d, 41, 60e, 101cd, 164c, 224ccde * }}
+{{Optimal ET sequence|legend=1| 19, 22, 38d, 41, 60e, 101cd, 164c, 224ccde }} *
 <nowiki>*</nowiki> [[optimal patent val]]: [[104edo|104]]
-[[Badness]] (Smith): 0.888 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 1.07
 === 13-limit ===
@@ Line 71: / Line 86: @@
 Mapping: {{mapping| 1 0 2 -1 0 -2 | 0 5 1 12 0 18 | 0 0 0 0 1 0 }}
-Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~5/4 = 380.0401{{c}}, ~11/8 = 546.6672{{c}}
+Optimal tunings:
+* WE: ~2 = 1201.3389{{c}}, ~5/4 = 380.4641{{c}}, ~11/8 = 547.2772{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.1532{{c}}, ~11/8 = 548.2678{{c}}
+<!-- * POTE: ~2 = 1200.0000{{c}}, ~5/4 = 380.0401{{c}}, ~11/8 = 546.6672{{c}} -->
 {{Optimal ET sequence|legend=1| 19, 22f, 38df, 41, 60e, 79d, 101cd }}
-Badness (Smith): 1.14 × 10<sup>-3</sup>
+Badness (Sintel): 1.07
 [[Category:Temperament families]]