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Canopic family: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings
Line 5: Line 5:
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 16875/16807 (canopus)
[[Comma list]]: 16875/16807


[[Mapping]]: [{{val| 1 0 0 0 }}, {{val| 0 1 3 3 }}, {{val| 0 0 -5 -4 }}]
{{Mapping|legend=1| 1 0 -5 -4 | 0 1 3 3 | 0 0 5 4 }}
: Mapping generators: ~2, ~3, ~10/7


Mapping generators: ~2, ~3, ~7/5
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9999{{c}}, ~3/2 = 701.7827{{c}}, ~10/7 = 616.0944{{c}}
: [[error map]]: {{val| -0.000 -0.172 -0.493 +0.900 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7827{{c}}, ~10/7 = 616.0945{{c}}
: error map: {{val| 0.000 -0.172 -0.493 +0.900 }}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit]]
* [[7-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 0 4/7 -4/7 5/7 }}, {{monzo| 0 -3/7 3/7 5/7 }}, {{monzo| 0 0 0 1 }}]
: {{monzo list| 1 0 0 0 | 0 4/7 -4/7 5/7 | 0 -3/7 3/7 5/7 | 0 0 0 1 }}
: [[Eigenmonzo]]s (unchanged-intervals): 2, 8/7, 6/5
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5/3.7
* [[9-odd-limit]]
* [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 0 8/11 -4/11 5/11 }}, {{monzo| 0 -6/11 3/11 10/11 }}, {{monzo| 0 0 0 1 }}]
: {{monzo list| 1 0 0 0 | 0 8/11 -4/11 5/11 | 0 -6/11 3/11 10/11 | 0 0 0 1 }}
: [[Eigenmonzo]]s (unchanged-intervals): 2, 10/9, 8/7
: eigenmonzo (unchanged-interval) basis: 2.9/5.7


{{Optimal ET sequence|legend=1| 31, 41, 72, 152, 224 }}
{{Optimal ET sequence|legend=1| 31, 41, 72, 152, 224 }}


[[Badness]]: 0.342 × 10<sup>-3</sup>
[[Badness]] (Sintel): 1.51


[[Projection pair]]s: 5 84375/16807 7 16875/2401 to 2.3.7/5
[[Projection pair]]s: <code>5 84375/16807 7 16875/2401</code> to 2.3.7/5


== Indra ==
== Indra ==
Line 30: Line 35:
[[Comma list]]: 540/539, 1375/1372
[[Comma list]]: 540/539, 1375/1372


[[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 3 3 0 }}, {{val| 0 0 -5 -4 3 }}]
{{Mapping| 1 0 -5 -4 5 | 0 1 3 3 0 | 0 0 5 4 -3 }}
 
: Mapping generators: ~2, ~3, ~10/7
Mapping generators: ~2, ~3, ~7/5


[[Mapping to lattice]]: [{{val| 0 2 1 2 3 }}, {{val| 0 -1 2 1 -3 }}]
[[Mapping to lattice]]: [{{val| 0 2 1 2 3 }}, {{val| 0 -1 2 1 -3 }}]
Line 39: Line 43:
: 15/14 length = 0.6184, 55/36 length = 0.7585
: 15/14 length = 0.6184, 55/36 length = 0.7585
: Angle (15/14, 55/36) = 68.1048 deg
: Angle (15/14, 55/36) = 68.1048 deg
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9693{{c}}, ~3/2 = 701.7444{{c}}, ~10/7 = 616.1152{{c}}
: [[error map]]: {{val| -0.031 -0.241 -0.443 +0.899 +0.183 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7342{{c}}, ~10/7 = 616.1422{{c}}
: error map: {{val| 0.000 -0.221 -0.400 +0.946 +0.256 }}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[11-odd-limit]]
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 10 10 -3 0 -5 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 6 6 -1 0 -3 }}, {{monzo| 20 18 -6 0 -9 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 10 10 -3 0 -5 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 6 6 -1 0 -3 }}, {{monzo| 20 18 -6 0 -9 }}]
: [[Eigenmonzo]]s (unchanged-intervals): 2, 11/9, 5/4
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5.11/9


{{Optimal ET sequence|legend=1| 31, 41, 72, 152, 224, 631d, 855d }}
{{Optimal ET sequence|legend=1| 31, 41, 72, 152, 224, 631d, 855d }}


[[Badness]]: 0.266 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.320


[[Projection pair]]s: 5 84375/16807 7 16875/2401 11 1372/125 to 2.3.7/5
[[Projection pair]]s: <code>5 84375/16807 7 16875/2401 11 1372/125</code> to 2.3.7/5


Scales: [[indra31]]
Scales: [[indra31]]
Line 58: Line 68:
Comma list: 540/539, 729/728, 1375/1372
Comma list: 540/539, 729/728, 1375/1372


Mapping: [{{val| 1 0 0 0 2 -3 }}, {{val| 0 1 3 3 0 3 }}, {{val| 0 0 -5 -4 4 }}]
Mapping: {{mapping| 1 0 -5 -4 5 1 | 0 1 3 3 0 3 | 0 0 5 4 -3 -4 }}


{{Optimal ET sequence|legend=1| 31f, 39df, 41, 72, 111, 152f, 183, 224, 631d, 855d }}
Optimal tunings:
* WE: ~2 = 1199.9762{{c}}, ~3/2 = 701.7232{{c}}, ~10/7 = 616.1317{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7261{{c}}, ~10/7 = 616.1467{{c}}


Badness: 0.721 × 10<sup>-3</sup>
{{Optimal ET sequence|legend=0| 31f, 39df, 41, 72, 111, 152f, 183, 224, 631d, 855d }}
 
Badness (Sintel): 0.674


=== Yajna ===
=== Yajna ===
Line 69: Line 83:
Comma list: 540/539, 625/624, 1375/1372
Comma list: 540/539, 625/624, 1375/1372


Mapping: [{{val| 1 0 0 0 2 -4 }}, {{val| 0 1 3 3 0 11 }}, {{val| 0 0 -5 -4 3 -20 }}]
Mapping: {{mapping| 1 0 -5 -4 5 -24 | 0 1 3 3 0 11 | 0 0 5 4 -3 20 }}


Mapping generators: ~2, ~3, ~7/5
Optimal tunings:
* WE: ~2 = 1200.0073{{c}}, ~3/2 = 701.7067{{c}}, ~10/7 = 616.1052{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7089{{c}}, ~10/7 = 616.0986{{c}}


Minimax tuning:  
Minimax tuning:  
* 13-odd-limit  
* 13-odd-limit  
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 4/5 6/5 -4/5 0 0 1/5 }}, {{monzo| 8/5 2/5 -3/5 0 0 2/5 }}, {{monzo| 44/25 26/25 -24/25 0 0 11/25 }}, {{monzo| 62/25 48/25 -27/25 0 0 3/25 }}, {{monzo| 8/5 2/5 -8/5 0 0 7/5 }}]
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 4/5 6/5 -4/5 0 0 1/5 }}, {{monzo| 8/5 2/5 -3/5 0 0 2/5 }}, {{monzo| 44/25 26/25 -24/25 0 0 11/25 }}, {{monzo| 62/25 48/25 -27/25 0 0 3/25 }}, {{monzo| 8/5 2/5 -8/5 0 0 7/5 }}]
: [[Eigenmonzo]]s (unchanged-intervals): 2, 10/9, 13/10
: eigenmonzo (unchanged-interval) basis: 2.9/5.13/5
* 15-odd-limit minimax
* 15-odd-limit
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 0 1 0 0 0 0 }}, {{monzo| 5/4 1/2 0 -5/16 0 5/16 }}, {{monzo| 1 1 0 -1/4 0 1/4 }}, {{monzo| 5/4 3/2 0 3/16 0 -3/16 }}, {{monzo| 1 1 0 -5/4 0 5/4 }}]
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 0 1 0 0 0 0 }}, {{monzo| 5/4 1/2 0 -5/16 0 5/16 }}, {{monzo| 1 1 0 -1/4 0 1/4 }}, {{monzo| 5/4 3/2 0 3/16 0 -3/16 }}, {{monzo| 1 1 0 -5/4 0 5/4 }}]
: [[Eigenmonzo]]s (unchanged-intervals): 2, 14/13, 4/3
: eigenmonzo (unchanged-interval) basis: 2.3.13/7


{{Optimal ET sequence|legend=1| 31, 49f, 72, 103, 121, 152f, 193, 224 }}
{{Optimal ET sequence|legend=0| 31, 49f, 72, 103, 121, 152f, 193, 224 }}


Badness: 0.700 × 10<sup>-3</sup>
Badness (Sintel): 0.655


=== Vibhu ===
=== Vibhu ===
Line 90: Line 106:
Comma list: 351/350, 540/539, 1375/1372
Comma list: 351/350, 540/539, 1375/1372


Mapping: [{{val| 1 0 0 0 2 1 }}, {{val| 0 1 3 3 0 6 }}, {{val| 0 0 -5 -4 3 -14 }}]
Mapping: {{mapping| 1 0 -5 -4 5 -13 | 0 1 3 3 0 6 | 0 0 5 4 -3 14 }}


{{Optimal ET sequence|legend=1| 31, 64cdf, 72, 103, 111, 152, 175f, 183, 469f }}
Optimal tunings:
* WE: ~2 = 1200.1587{{c}}, ~3/2 = 701.2394{{c}}, ~10/7 = 616.6507{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.2689{{c}}, ~10/7 = 616.5306{{c}}


Badness: 0.826 × 10<sup>-3</sup>
{{Optimal ET sequence|legend=0| 31, 64cdf, 72, 103, 111, 152, 175f, 183, 469f }}
 
Badness (Sintel): 0.772


=== Vish ===
=== Vish ===
Line 101: Line 121:
Comma list: 325/324, 364/363, 540/539
Comma list: 325/324, 364/363, 540/539


Mapping: [{{val| 1 0 0 0 2 2 }}, {{val| 0 1 3 3 0 -2 }}, {{val| 0 0 -5 -4 3 10 }}]
Mapping: {{mapping| 1 0 0 0 2 2 | 0 1 3 3 0 -2 | 0 0 5 4 -3 -10 }}
 
Optimal tunings:
* WE: ~2 = 1199.9463{{c}}, ~3/2 = 702.3912{{c}}, ~10/7 = 615.5733{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.3742{{c}}, ~10/7 = 615.6198{{c}}


{{Optimal ET sequence|legend=1| 31f, 41, 72, 121, 193 }}
{{Optimal ET sequence|legend=0| 31f, 41, 72, 121, 193 }}


Badness: 0.930 × 10<sup>-3</sup>
Badness (Sintel): 0.870


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