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Octagar family: Difference between revisions

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m Units & misc. cleanup. - redundant category
Switch to Sintel's badness, WE & CWE tunings
Line 20: Line 20:
: Angle (63/50, 21/20) = 97.743 degrees
: Angle (63/50, 21/20) = 97.743 degrees


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.6224{{c}}, ~21/20 = 89.3227{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.5353{{c}}, ~3/2 = 703.3499{{c}}, ~63/40 = 792.6380{{c}}
: [[error map]]: {{val| -0.465 +0.930 -1.502 +1.459 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.3764{{c}}, ~63/40 = 792.6299{{c}}
: error map: {{val| 0.000 +1.421 -1.054 +2.311 }}
<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.6224{{c}}, ~21/20 = 89.3227{{c}} -->


[[Minimax tuning]]:
[[Minimax tuning]]:
Line 32: Line 37:
{{Optimal ET sequence|legend=1| 12, 26, 27, 39d, 41, 53, 80, 94, 121, 174d, 215, 295d, 336d }}
{{Optimal ET sequence|legend=1| 12, 26, 27, 39d, 41, 53, 80, 94, 121, 174d, 215, 295d, 336d }}


[[Badness]] (Smith): 0.216 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.951


[[Projection pair]]s: <code>5 3969/800 7 27783/4000</code> to 2.3.7/5
[[Projection pair]]s: <code>5 3969/800 7 27783/4000</code> to 2.3.7/5
Line 56: Line 61:
: Angle (11/7, 22/21) = 97.747 degrees
: Angle (11/7, 22/21) = 97.747 degrees


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.8837{{c}}, ~21/20 = 87.8919{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.6137{{c}}, ~3/2 = 703.6571{{c}}, ~11/7 = 791.5207{{c}}
: [[error map]]: {{val| -0.386 +1.316 -3.659 -2.351 +6.678 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.6783{{c}}, ~11/7 = 791.5168{{c}}
: error map: {{val| 0.000 +1.723 -3.280 -1.632 +7.393 }}
<!-- * [[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 }}
{{Optimal ET sequence|legend=1| 12, 15, 26, 27e, 41, 109e }}


[[Badness]] (Smith): 0.539 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.647


[[Projection pair]]s: <code>5 242/49 7 21296/3087 11 234256/21609</code> to 2.3.11/7
[[Projection pair]]s: <code>5 242/49 7 21296/3087 11 234256/21609</code> to 2.3.11/7
Line 75: Line 85:
Mapping: {{mapping| 1 0 1 4 4 2 | 0 1 0 -2 -2 -1 | 0 0 2 3 4 5 }}
Mapping: {{mapping| 1 0 1 4 4 2 | 0 1 0 -2 -2 -1 | 0 0 2 3 4 5 }}


Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 701.8881{{c}}, ~21/20 = 87.4143{{c}}
Optimal tunings:
* WE: ~2 = 1200.5397{{c}}, ~3/2 = 702.2038{{c}}, ~11/7 = 789.6574{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0977{{c}}, ~11/7 = 789.5686{{c}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8881{{c}}, ~21/20 = 87.4143{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 14cf, 15, 26, 29, 41 }}
{{Optimal ET sequence|legend=0| 12f, 14cf, 15, 26, 29, 41 }}
Badness (Sintel): 0.832


== Octasand ==
== Octasand ==
Line 86: Line 101:
{{Mapping|legend=1| 1 0 1 4 -5 | 0 1 0 -2 7 | 0 0 2 3 -4 }}
{{Mapping|legend=1| 1 0 1 4 -5 | 0 1 0 -2 7 | 0 0 2 3 -4 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.5501{{c}}, ~21/20 = 89.3956{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.5255{{c}}, ~3/2 = 703.2719{{c}}, ~63/40 = 792.6321{{c}}
: [[error map]]: {{val| -0.475 +0.842 -1.524 +1.578 +0.108 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.2662{{c}}, ~63/40 = 792.6212{{c}}
: error map: {{val| 0.000 +1.311 -1.071 +2.505 +1.061 }}
<!-- * [[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 }}
{{Optimal ET sequence|legend=1| 27e, 39d, 41, 53, 80, 94, 121, 174d, 215, 295d }}
 
[[Badness]] (Sintel): 1.20


=== 13-limit ===
=== 13-limit ===
Line 97: Line 119:
Mapping: {{mapping| 1 0 1 4 -5 0 | 0 1 0 -2 7 4 | 0 0 2 3 -4 -4 }}
Mapping: {{mapping| 1 0 1 4 -5 0 | 0 1 0 -2 7 4 | 0 0 2 3 -4 -4 }}


Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 703.5688{{c}}, ~21/20 = 89.4032{{c}}
Optimal tunings:
* WE: ~2 = 1199.5112{{c}}, ~3/2 = 703.2823{{c}}, ~63/40 = 792.6491{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 703.3684{{c}}, ~63/40 = 792.7875{{c}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 703.5688{{c}}, ~21/20 = 89.4032{{c}} -->
 
{{Optimal ET sequence|legend=0| 27e, 41, 53, 80, 94, 121, 174d, 215, 295d, 336def }}


{{Optimal ET sequence|legend=0| 12e, 14c, 27e, 41, 53, 80, 94, 121 }}
Badness (Sintel): 1.03


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Octagar family| ]] <!-- main article -->
[[Category:Octagar family| ]] <!-- main article -->
[[Category:Rank 3]]
[[Category:Rank 3]]
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