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Cataharry family: Difference between revisions

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Comma list: 351/350, 540/539, 676/675
Comma list: 351/350, 540/539, 676/675


Mapping: {{mapping| 1 0 0 -2 6 -1 | 0 2 0 9 -12 3 | 0 0 1 -1 3 1 }}
{{Mapping|legend=0| 1 0 0 -2 6 -1 | 0 2 0 9 -12 3 | 0 0 1 -1 3 1 }}


[[Mapping to lattice]]: [{{val| 0 -2 -3 -6 3 -6 }}, {{val| 0 0 -1 1 -3 -1 }}]
[[Mapping to lattice]]: [{{val| 0 -2 -3 -6 3 -6 }}, {{val| 0 0 -1 1 -3 -1 }}]
Line 78: Line 78:


Badness (Sintel): 0.524
Badness (Sintel): 0.524
Complexity spectrum: 15/13, 4/3, 13/10, 10/9, 6/5, 9/7, 18/13, 9/8, 5/4, 7/6, 13/12, 15/14, 16/15, 14/13, 8/7, 7/5, 16/13, 11/10, 15/11, 11/8, 12/11, 13/11, 11/9, 14/11


Projection pairs: <code>3 676/225 7 1357375919744/192216796875 11 16218292236328125/1491077447838784 13 8788/675</code> to 2.5.13/3
Projection pairs: <code>3 676/225 7 1357375919744/192216796875 11 16218292236328125/1491077447838784 13 8788/675</code> to 2.5.13/3
Line 107: Line 105:
Comma list: 351/350, 441/440, 676/675
Comma list: 351/350, 441/440, 676/675


Mapping: {{mapping| 1 0 0 -2 -7 -1 | 0 2 0 9 22 3 | 0 0 1 -1 -3 1 }}
{{Mapping|legend=0| 1 0 0 -2 -7 -1 | 0 2 0 9 22 3 | 0 0 1 -1 -3 1 }}


Optimal tunings:  
Optimal tunings:  
Line 117: Line 115:
Badness (Sintel): 0.735
Badness (Sintel): 0.735


== Hagrid ==
== Draco ==
[[Subgroup]]: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 243/242, 9801/9800
[[Comma list]]: 176/175, 19683/19600


{{Mapping|legend=1| 2 0 0 -4 -1 | 0 2 0 9 5 | 0 0 1 -1 0 }}
{{Mapping|legend=1| 1 0 0 -2 -6 | 0 2 0 9 9 | 0 0 1 -1 1 }}
: mapping generators: ~99/70, ~140/81, ~5


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~99/70 = 600.0301{{c}}, ~140/81 = 950.5810{{c}}, ~5/4 = 386.1803{{c}}
* [[WE]]: ~2 = 1199.3870{{c}}, ~140/81 = 950.8204{{c}}, ~5/4 = 389.4825{{c}}
: [[error map]]: {{val| +0.060 -0.793 -0.013 -0.019 +1.557 }}
: [[error map]]: {{val| -0.613 -0.314 +1.943 +1.527 -2.000 }}
* [[CWE]]: ~99/70 = 600.0000{{c}}, ~140/81 = 950.5516{{c}}, ~5/4 = 386.2351{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~140/81 = 951.2120{{c}}, ~5/4 = 389.3756{{c}}
: error map: {{val| 0.000 -0.852 -0.079 -0.096 +1.440 }}
: error map: {{val| 0.000 +0.469 +3.062 +2.706 -1.035 }}


{{Optimal ET sequence|legend=1| 24, 34d, 48, 58, 72, 130, 202 }}
{{Optimal ET sequence|legend=1| 19e, 24, 34d, 53, 58, 111, 280cd }}


[[Badness]] (Sintel): 1.34
[[Badness]] (Sintel): 2.32


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 243/242, 351/350, 364/363
Comma list: 176/175, 351/350, 676/675


Mapping: {{mapping| 2 0 0 -4 -1 -2 | 0 2 0 9 5 3 | 0 0 1 -1 0 1 }}
{{Mapping|legend=0| 1 0 0 -2 -6 -1 | 0 2 0 9 9 3 | 0 0 1 -1 1 1 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~55/39 = 599.9896{{c}}, ~26/15 = 950.6467{{c}}, ~5/4 = 387.0194{{c}}
* WE: ~2 = 1199.3551{{c}}, ~26/15 = 950.7982{{c}}, ~5/4 = 389.3905{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~26/15 = 950.6571{{c}}, ~5/4 = 387.0028{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.2095{{c}}, ~5/4 = 389.2432{{c}}


{{Optimal ET sequence|legend=0| 24, 34d, 58, 72, 130 }}
{{Optimal ET sequence|legend=0| 19e, 24, 34d, 53, 58, 111, 280cdf }}


Badness (Sintel): 0.819
Badness (Sintel): 0.934


== Draco ==
== Hagrid ==
[[Subgroup]]: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 176/175, 19683/19600
[[Comma list]]: 243/242, 9801/9800


{{Mapping|legend=1| 1 0 0 -2 -6 | 0 2 0 9 9 | 0 0 1 -1 1 }}
{{Mapping|legend=1| 2 0 0 -4 -1 | 0 2 0 9 5 | 0 0 1 -1 0 }}
: mapping generators: ~99/70, ~140/81, ~5


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.3870{{c}}, ~140/81 = 950.8204{{c}}, ~5/4 = 389.4825{{c}}
* [[WE]]: ~99/70 = 600.0301{{c}}, ~140/81 = 950.5810{{c}}, ~5/4 = 386.1803{{c}}
: [[error map]]: {{val| -0.613 -0.314 +1.943 +1.527 -2.000 }}
: [[error map]]: {{val| +0.060 -0.793 -0.013 -0.019 +1.557 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~140/81 = 951.2120{{c}}, ~5/4 = 389.3756{{c}}
* [[CWE]]: ~99/70 = 600.0000{{c}}, ~140/81 = 950.5516{{c}}, ~5/4 = 386.2351{{c}}
: error map: {{val| 0.000 +0.469 +3.062 +2.706 -1.035 }}
: error map: {{val| 0.000 -0.852 -0.079 -0.096 +1.440 }}


{{Optimal ET sequence|legend=1| 19e, 24, 34d, 53, 58, 111, 280cd }}
{{Optimal ET sequence|legend=1| 24, 34d, 48, 58, 72, 130, 202 }}


[[Badness]] (Sintel): 2.32
[[Badness]] (Sintel): 1.34


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 176/175, 351/350, 676/675
Comma list: 243/242, 351/350, 364/363


Mapping: {{mapping| 1 0 0 -2 -6 -1 | 0 2 0 9 9 3 | 0 0 1 -1 1 1 }}
{{Mapping|legend=0| 2 0 0 -4 -1 -2 | 0 2 0 9 5 3 | 0 0 1 -1 0 1 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.3551{{c}}, ~26/15 = 950.7982{{c}}, ~5/4 = 389.3905{{c}}
* WE: ~55/39 = 599.9896{{c}}, ~26/15 = 950.6467{{c}}, ~5/4 = 387.0194{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.2095{{c}}, ~5/4 = 389.2432{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~26/15 = 950.6571{{c}}, ~5/4 = 387.0028{{c}}


{{Optimal ET sequence|legend=0| 19e, 24, 34d, 53, 58, 111, 280cdf }}
{{Optimal ET sequence|legend=0| 24, 34d, 58, 72, 130 }}


Badness (Sintel): 0.934
Badness (Sintel): 0.819


[[Category:Cataharry family| ]] <!-- main article -->
[[Category:Cataharry family| ]] <!-- main article -->
[[Category:Cataharry| ]] <!-- key article -->
[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Catalogs of rank-3 temperaments]]
[[Category:Catalogs of rank-3 temperaments]]
Retrieved from "https://en.xen.wiki/w/Cataharry_family"