Octagar family: Difference between revisions

Line 12:

: Mapping generators: ~2, ~3, ~63/40

Line 21:

Line 20:

: Angle (63/50, 21/20) = 97.743 degrees

[[Optimal tuning]] (POTE): ~3/2 = 703.6224, ~21/20 = 89.3227

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.6224{{c}}, ~21/20 = 89.3227{{c}}

[[Minimax tuning]]:

* [[7-odd-limit]]

: {{monzo list| 1 0 0 0 | 5/6 1/3 1/2 -1/3 | 0 0 1 0 | 5/6 -2/3 1/2 2/3 }}

: [[~~Eigenmonzo~~ basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7/3

: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7/3

* [[9-odd-limit]]

: {{monzo list| 1 0 0 0 | 5/8 1/2 3/8 -1/4 | 0 0 1 0 | 5/4 -1 3/4 1/2 }}

: [[~~Eigenmonzo~~ basis|unchanged-interval (eigenmonzo) basis]]: 2.5.9/7

: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.9/7

{{Optimal ET sequence|legend=1| 12, 26, 27, 39d, 41, 53, 80, 94, 121, 174d, 215, 295d, 336d }}

[[Badness]]: 0.216 × 10-3

[[Badness]] (Smith): 0.216 × 10-3

[[Projection pair]]s: 5 - 3969/800, 7 - 27783/4000 to 2.3.7/5

[[Projection pair]]s: <code>5 3969/800 7 27783/4000</code> to 2.3.7/5

{{Databox|[[Hobbit|Hobbit bases]]|

Line 57:

Line 56:

: Angle (11/7, 22/21) = 97.747 degrees

[[Optimal tuning]] (POTE): ~3/2 = 703.8837, ~21/20 = 87.8919

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.8837{{c}}, ~21/20 = 87.8919{{c}}

[[Badness]]: 0.539 × 10-3

[[Badness]] (Smith): 0.539 × 10-3

[[Projection pair]]s: 5 - 242/49, 7 - 21296/3087, 11 - 234256/21609 to 2.3.11/7

[[Projection pair]]s: <code>5 242/49 7 21296/3087 11 234256/21609</code> to 2.3.11/7

[[Associated temperament]]: [[octacot]]

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Mapping: {{mapping| 1 0 1 4 4 2 | 0 1 0 -2 -2 -1 | 0 0 2 3 4 5 }}

Optimal tuning (POTE): ~3/2 = 701.8881, ~21/20 = 87.4143

Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 701.8881{{c}}, ~21/20 = 87.4143{{c}}

~~Optimal ET sequence:~~ {{Optimal ET sequence| 12f, 14cf, 15, 26, 29, 41 }}

== Octasand ==

Line 87:

Line 86:

[[Optimal tuning]] (POTE): ~3/2 = 703.5501, ~21/20 = 89.3956

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.5501{{c}}, ~21/20 = 89.3956{{c}}

{{Optimal ET sequence|legend=1| 12e, 14c, 27e, 41, 53, 80, 94, 121 }}

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Line 97:

Mapping: {{mapping| 1 0 1 4 -5 0 | 0 1 0 -2 7 4 | 0 0 2 3 -4 -4 }}

Optimal tuning (POTE): ~3/2 = 703.5688, ~21/20 = 89.4032

Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 703.5688{{c}}, ~21/20 = 89.4032{{c}}

~~Optimal ET sequence:~~ {{Optimal ET sequence| 12e, 14c, 27e, 41, 53, 80, 94, 121 }}

{{Optimal ET sequence|legend=0| 12e, 14c, 27e, 41, 53, 80, 94, 121 }}

[[Category:Temperament families]]

[[Category:Octagar family| ]]

~~[[Category:Octagar| ]] ~~

[[Category:Rank 3]]

@@ Line 12: / Line 12: @@
 {{Mapping|legend=1| 1 0 1 4 | 0 1 0 -2 | 0 0 2 3 }}
 : Mapping generators: ~2, ~3, ~63/40
@@ Line 21: / Line 20: @@
 : Angle (63/50, 21/20) = 97.743 degrees
-[[Optimal tuning]] (POTE): ~3/2 = 703.6224, ~21/20 = 89.3227
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.6224{{c}}, ~21/20 = 89.3227{{c}}
 [[Minimax tuning]]:
 * [[7-odd-limit]]
 : {{monzo list| 1 0 0 0 | 5/6 1/3 1/2 -1/3 | 0 0 1 0 | 5/6 -2/3 1/2 2/3 }}
-: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7/3
+: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7/3
 * [[9-odd-limit]]
 : {{monzo list| 1 0 0 0 | 5/8 1/2 3/8 -1/4 | 0 0 1 0 | 5/4 -1 3/4 1/2 }}
-: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.9/7
+: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.9/7
 {{Optimal ET sequence|legend=1| 12, 26, 27, 39d, 41, 53, 80, 94, 121, 174d, 215, 295d, 336d }}
-[[Badness]]: 0.216 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.216 × 10<sup>-3</sup>
-[[Projection pair]]s: 5 - 3969/800, 7 - 27783/4000 to 2.3.7/5
+[[Projection pair]]s: <code>5 3969/800 7 27783/4000</code> to 2.3.7/5
 {{Databox|[[Hobbit|Hobbit bases]]|
@@ Line 57: / Line 56: @@
 : Angle (11/7, 22/21) = 97.747 degrees
-[[Optimal tuning]] (POTE): ~3/2 = 703.8837, ~21/20 = 87.8919
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.8837{{c}}, ~21/20 = 87.8919{{c}}
 {{Optimal ET sequence|legend=1| 12, 15, 26, 27e, 41, 109e }}
-[[Badness]]: 0.539 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.539 × 10<sup>-3</sup>
-[[Projection pair]]s: 5 - 242/49, 7 - 21296/3087, 11 - 234256/21609 to 2.3.11/7
+[[Projection pair]]s: <code>5 242/49 7 21296/3087 11 234256/21609</code> to 2.3.11/7
 [[Associated temperament]]: [[octacot]]
@@ Line 76: / Line 75: @@
 Mapping: {{mapping| 1 0 1 4 4 2 | 0 1 0 -2 -2 -1 | 0 0 2 3 4 5 }}
-Optimal tuning (POTE): ~3/2 = 701.8881, ~21/20 = 87.4143
+Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 701.8881{{c}}, ~21/20 = 87.4143{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 12f, 14cf, 15, 26, 29, 41 }}
+{{Optimal ET sequence|legend=0| 12f, 14cf, 15, 26, 29, 41 }}
 == Octasand ==
@@ Line 87: / Line 86: @@
 {{Mapping|legend=1| 1 0 1 4 -5 | 0 1 0 -2 7 | 0 0 2 3 -4 }}
-[[Optimal tuning]] (POTE): ~3/2 = 703.5501, ~21/20 = 89.3956
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.5501{{c}}, ~21/20 = 89.3956{{c}}
 {{Optimal ET sequence|legend=1| 12e, 14c, 27e, 41, 53, 80, 94, 121 }}
@@ Line 98: / Line 97: @@
 Mapping: {{mapping| 1 0 1 4 -5 0 | 0 1 0 -2 7 4 | 0 0 2 3 -4 -4 }}
-Optimal tuning (POTE): ~3/2 = 703.5688, ~21/20 = 89.4032
+Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 703.5688{{c}}, ~21/20 = 89.4032{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 12e, 14c, 27e, 41, 53, 80, 94, 121 }}
+{{Optimal ET sequence|legend=0| 12e, 14c, 27e, 41, 53, 80, 94, 121 }}
 [[Category:Temperament families]]
 [[Category:Octagar family| ]] <!-- main article -->
-[[Category:Octagar| ]] <!-- key article -->
 [[Category:Rank 3]]