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Aberschismic family: Difference between revisions

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m Units & misc. cleanup
Switch to Sintel's badness, WE & CWE tunings, per community consensus (1/)
Line 21: Line 21:
: Angle (3/2, 10/9) = 82.112 degrees
: Angle (3/2, 10/9) = 82.112 degrees


[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.7918{{c}}, ~5/4 = 386.0144{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.7172{{c}}, ~3/2 = 702.6636{{c}}, ~5/4 = 386.7266{{c}}
: [[error map]]: {{val| -0.283 +0.426 -0.153 +0.222 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.8166{{c}}, ~5/4 = 386.5465{{c}}
: error map: {{val| 0.000 +0.862 +0.233 +0.821 }}
<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.7918{{c}}, ~5/4 = 386.0144{{c}} -->


[[Minimax tuning]]: c = 5120/5103
[[Minimax tuning]]: c = 5120/5103
* [[7-odd-limit]]: 3 and 7 1/7c sharp, 5 just
* [[7-odd-limit]]: 3 and 7 1/7c sharp, 5 just
: {{monzo list| 1 0 0 0 | 10/7 1/7 1/7 -1/7 | 0 0 1 0 | 10/7 -6/7 1/7 6/7 }}
: {{monzo list| 1 0 0 0 | 10/7 1/7 1/7 -1/7 | 0 0 1 0 | 10/7 -6/7 1/7 6/7 }}
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7/3
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7/3
* [[9-odd-limit]]: 3 1/8c sharp, 5 just, 7 1/4c sharp
* [[9-odd-limit]]: 3 1/8c sharp, 5 just, 7 1/4c sharp
: {{monzo list| 1 0 0 0 | 5/4 1/4 1/8 -1/8 | 0 0 1 0 | 5/2 -3/2 1/4 3/4 }}
: {{monzo list| 1 0 0 0 | 5/4 1/4 1/8 -1/8 | 0 0 1 0 | 5/2 -3/2 1/4 3/4 }}
: [[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| 41, 53, 87, 94, 99, 239, 251, 292, 391, 881bd, 1272bcdd }}
{{Optimal ET sequence|legend=1| 41, 53, 87, 94, 99, 239, 251, 292, 391, 881bd, 1272bcdd }}


[[Badness]] (Smith): 0.153 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.675


[[Projection pair]]s: 7 5120/729
[[Projection pair]]s: 7 5120/729
Line 61: Line 66:
Mapping: {{mapping| 1 0 0 10 -6 | 0 1 0 -6 5 | 0 0 1 1 1 }}
Mapping: {{mapping| 1 0 0 10 -6 | 0 1 0 -6 5 | 0 0 1 1 1 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~3/2 = 702.6411{{c}}, ~5/4 = 385.4452{{c}}
Optimal tunings:
* WE: ~2 = 1199.6953{{c}}, ~3/2 = 702.5169{{c}}, ~5/4 = 386.2648{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6771{{c}}, ~5/4 = 386.0544{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6411{{c}}, ~5/4 = 385.4452{{c}} -->


{{Optimal ET sequence|legend=0| 12, 29, 41, 53, 94, 99, 140, 152, 292h, 444dh }}
{{Optimal ET sequence|legend=0| 12, 29, 41, 53, 94, 99, 140, 152, 292h, 444dh }}


Badness (Smith): 0.212 × 10<sup>-3</sup>
Badness (Sintel): 0.347


== Pele ==
== Pele ==
Line 83: Line 91:
: Angle(3/2, 56/55) = 90.4578 degrees
: Angle(3/2, 56/55) = 90.4578 degrees


[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.2829{{c}}, ~5/4 = 386.5647{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.5424{{c}}, ~3/2 = 703.0109{{c}}, ~5/4 = 387.6427{{c}}
: [[error map]]: {{val| -0.458 +0.598 +0.414 -1.995 +2.097 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.2804{{c}}, ~5/4 = 387.3911{{c}}
: error map: {{val| 0.000 +1.325 +1.077 -1.117 +3.269 }}
<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.2829{{c}}, ~5/4 = 386.5647{{c}} -->


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 92: Line 105:
{{Optimal ET sequence|legend=1| 29, 41, 58, 87, 99e, 145, 186e }}
{{Optimal ET sequence|legend=1| 29, 41, 58, 87, 99e, 145, 186e }}


[[Badness]] (Smith): 0.648 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.779


[[Projection pair]]s: 7 5120/729 11 655360/59049
[[Projection pair]]s: 7 5120/729 11 655360/59049
Line 103: Line 116:
Mapping: {{mapping| 1 0 0 10 17 22 | 0 1 0 -6 -10 -13 | 0 0 1 1 1 1 }}
Mapping: {{mapping| 1 0 0 10 17 22 | 0 1 0 -6 -10 -13 | 0 0 1 1 1 1 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~3/2 = 703.4398{{c}}, ~5/4 = 386.8933{{c}}
Optimal tunings:
* WE: ~2 = 1199.4965{{c}}, ~3/2 = 703.1192{{c}}, ~5/4 = 388.0342{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 703.4225{{c}}, ~5/4 = 387.7761{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~3/2 = 703.4398{{c}}, ~5/4 = 386.8933{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 111: Line 127:
{{Optimal ET sequence|legend=0| 29, 41, 46, 58, 87, 145, 232 }}
{{Optimal ET sequence|legend=0| 29, 41, 46, 58, 87, 145, 232 }}


Badness (Smith): 0.703 × 10<sup>-3</sup>
Badness (Sintel): 0.658


=== 17-limit ===
=== 17-limit ===
Line 120: Line 136:
Mapping: {{mapping| 1 0 0 10 17 22 8 | 0 1 0 -6 -10 -13 -1 | 0 0 1 1 1 1 -1 }}
Mapping: {{mapping| 1 0 0 10 17 22 8 | 0 1 0 -6 -10 -13 -1 | 0 0 1 1 1 1 -1 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~3/2 = 703.5544{{c}}, ~5/4 = 387.9654{{c}}
Optimal tunings:
* WE: ~2 = 1199.3960{{c}}, ~3/2 = 703.0725{{c}}, ~5/4 = 388.4246{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 703.4518{{c}}, ~5/4 = 388.4909{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~3/2 = 703.5544{{c}}, ~5/4 = 387.9654{{c}} -->


{{Optimal ET sequence|legend=0| 29, 41, 46, 58, 87, 99ef, 145 }}
{{Optimal ET sequence|legend=0| 29, 41, 46, 58, 87, 99ef, 145 }}


Badness (Smith): 0.930 × 10<sup>-3</sup>
Badness (Sintel): 0.884


== Laka ==
== Laka ==
Line 144: Line 163:
{{Mapping|legend=1| 1 0 0 10 -18 | 0 1 0 -6 15 | 0 0 1 1 -1 }}
{{Mapping|legend=1| 1 0 0 10 -18 | 0 1 0 -6 15 | 0 0 1 1 -1 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.5133{{c}}, ~5/4 = 385.5563{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.6201{{c}}, ~3/2 = 702.4416{{c}}, ~5/4 = 386.6781{{c}}
: [[error map]]: {{val| -0.380 +0.107 -0.395 +0.924 +0.527 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.6175{{c}}, ~5/4 = 386.4170{{c}}
: error map: {{val| 0.000 +0.663 +0.103 +1.886 +1.528 }}
<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.5133{{c}}, ~5/4 = 385.5563{{c}} -->


[[Minimax tuning]]
[[Minimax tuning]]
Line 153: Line 177:
{{Optimal ET sequence|legend=1| 41, 53, 58, 94, 99e, 152, 497de, 555dee, 707ddee, 859bddee }}
{{Optimal ET sequence|legend=1| 41, 53, 58, 94, 99e, 152, 497de, 555dee, 707ddee, 859bddee }}


[[Badness]] (Smith): 0.825 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.992


[[Projection pair]]s: 5120/729 11 14348907/1310720
[[Projection pair]]s: 5120/729 11 14348907/1310720
Line 164: Line 188:
Mapping: {{mapping| 1 0 0 10 -18 -13 | 0 1 0 -6 15 12 | 0 0 1 1 -1 -1 }}
Mapping: {{mapping| 1 0 0 10 -18 -13 | 0 1 0 -6 15 12 | 0 0 1 1 -1 -1 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~3/2 = 702.4078{{c}}, ~5/4 = 385.5405{{c}}
Optimal tunings:
* WE: ~2 = 1199.4742{{c}}, ~3/2 = 702.3385{{c}}, ~5/4 = 387.0965{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.5780{{c}}, ~5/4 = 386.7718{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~3/2 = 702.4078{{c}}, ~5/4 = 385.5405{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 171: Line 198:
: unchanged-interval (eigenmonzo) basis: 2.11.13/7
: unchanged-interval (eigenmonzo) basis: 2.11.13/7


{{Optimal ET sequence|legend=0| 41, 53, 58, 94, 111, 152f, 415dff }}*
{{Optimal ET sequence|legend=0| 41, 53, 58, 94, 111, 152f, 415dff }} *


<nowiki>*</nowiki> optimal patent val: [[205edo|205]]
<nowiki>*</nowiki> optimal patent val: [[205edo|205]]


Badness (Smith): 0.822 × 10<sup>-3</sup>
Badness (Sintel): 0.769


=== 2.3.5.7.11.13.19 subgroup ===
=== 2.3.5.7.11.13.19 subgroup ===
Line 184: Line 211:
Mapping: {{mapping| 1 0 0 10 -18 -13 -6 | 0 1 0 -6 15 12 5 | 0 0 1 1 -1 -1 1 }}
Mapping: {{mapping| 1 0 0 10 -18 -13 -6 | 0 1 0 -6 15 12 5 | 0 0 1 1 -1 -1 1 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~3/2 = 702.4062{{c}}, ~5/4 = 385.5254{{c}}
Optimal tunings:
* WE: ~2 = 1199.4881{{c}}, ~3/2 = 702.3224{{c}}, ~5/4 = 386.8881{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.5613{{c}}, ~5/4 = 386.6230{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~3/2 = 702.4062{{c}}, ~5/4 = 385.5254{{c}} -->


{{Optimal ET sequence|legend=0| 41, 53, 58h, 94, 111, 152f, 415dffhh }}*
{{Optimal ET sequence|legend=0| 41, 53, 58h, 94, 111, 152f, 415dffhh }} *


<nowiki>*</nowiki> optimal patent val: [[205edo|205]]
<nowiki>*</nowiki> optimal patent val: [[205edo|205]]


Badness (Smith): 0.661 × 10<sup>-3</sup>
Badness (Sintel): 0.647


=== 17-limit ===
=== 17-limit ===
Line 198: Line 228:


Mapping: {{mapping| 1 0 0 10 -18 -13 32 | 0 1 0 -6 15 12 -22 | 0 0 1 1 -1 -1 3 }}
Mapping: {{mapping| 1 0 0 10 -18 -13 32 | 0 1 0 -6 15 12 -22 | 0 0 1 1 -1 -1 3 }}
Optimal tunings:
* WE: ~2 = 1199.6101{{c}}, ~3/2 = 702.3391{{c}}, ~5/4 = 387.1022{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.5253{{c}}, ~5/4 = 386.8488{{c}}


Minimax tuning:  
Minimax tuning:  
Line 206: Line 240:
{{Optimal ET sequence|legend=0| 58, 94, 111, 152f, 205, 263df }}
{{Optimal ET sequence|legend=0| 58, 94, 111, 152f, 205, 263df }}


Badness (Smith): 1.19 × 10<sup>-3</sup>
Badness (Sintel): 1.13


== Akea ==
== Akea ==
Line 218: Line 252:
{{Mapping|legend=1| 1 0 0 10 -3 | 0 1 0 -6 7 | 0 0 1 1 -2 }}
{{Mapping|legend=1| 1 0 0 10 -3 | 0 1 0 -6 7 | 0 0 1 1 -2 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.8909{{c}}, ~5/4 = 385.3273{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.1396{{c}}, ~3/2 = 702.9241{{c}}, ~5/4 = 385.1817{{c}}
: [[error map]]: {{val| +0.140 +1.109 -0.853 -0.351 -1.213 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.8511{{c}}, ~5/4 = 385.1712{{c}}
: error map: {{val| 0.000 +0.896 -1.143 -0.761 -1.703 }}
<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.8909{{c}}, ~5/4 = 385.3273{{c}} -->


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[11-odd-limit]]
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 5/3 0 1/6 -1/6 0 }}, {{monzo| 26/9 0 13/18 -7/18 -1/3 }}, {{monzo| 26/9 0 -5/18 11/18 -1/3 }}, {{monzo| 26/9 0 -5/18 -7/18 2/3 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 5/3 0 1/6 -1/6 0 }}, {{monzo| 26/9 0 13/18 -7/18 -1/3 }}, {{monzo| 26/9 0 -5/18 11/18 -1/3 }}, {{monzo| 26/9 0 -5/18 -7/18 2/3 }}]
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11/5
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11/5


{{Optimal ET sequence|legend=1| 34, 41, 53, 87, 140, 181, 321 }}
{{Optimal ET sequence|legend=1| 34, 41, 53, 87, 140, 181, 321 }}


[[Badness]] (Smith): 0.998 × 10<sup>-3</sup>
[[Badness]] (Sintel): 1.20


=== 13-limit ===
=== 13-limit ===
Line 242: Line 281:
Mapping to lattice: [{{val| 0 1 3 -3 1 -2 }}, {{val| 0 0 -1 -1 2 2 }}]
Mapping to lattice: [{{val| 0 1 3 -3 1 -2 }}, {{val| 0 0 -1 -1 2 2 }}]


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~3/2 = 702.9018{{c}}, ~5/4 = 385.4158{{c}}
Optimal tunings:
* WE: ~2 = 1200.0943{{c}}, ~3/2 = 702.9377{{c}}, ~5/4 = 385.4278{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.8853{{c}}, ~5/4 = 385.4002{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~3/2 = 702.9018{{c}}, ~5/4 = 385.4158{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 251: Line 293:
{{Optimal ET sequence|legend=0| 34, 41, 46, 53, 87, 140, 321, 461e }}
{{Optimal ET sequence|legend=0| 34, 41, 46, 53, 87, 140, 321, 461e }}


Badness (Smith): 0.822 × 10<sup>-3</sup>
Badness (Sintel): 0.769


Scales: [[akea46_13]]
Scales: [[akea46_13]]
Line 262: Line 304:
{{Mapping|legend=1| 1 0 0 10 6 | 0 1 0 -6 -6 | 0 0 1 1 3 }}
{{Mapping|legend=1| 1 0 0 10 6 | 0 1 0 -6 -6 | 0 0 1 1 3 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.8941{{c}}, ~5/4 = 388.5932{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.3368{{c}}, ~3/2 = 702.5643{{c}}, ~5/4 = 389.5319{{c}}
: [[error map]]: {{val| -0.663 -0.054 +1.892 +1.341 -2.088 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.9356{{c}}, ~5/4 = 389.4076{{c}}
: error map: {{val| 0.000 +0.981 +3.094 +2.968 -0.708 }}
<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.8941{{c}}, ~5/4 = 388.5932{{c}} -->


{{Optimal ET sequence|legend=1| 46, 53, 58, 99, 111, 268cd }}
{{Optimal ET sequence|legend=1| 46, 53, 58, 99, 111, 268cd }}


[[Badness]] (Smith): 1.18 × 10<sup>-3</sup>
[[Badness]] (Sintel): 1.41


=== 13-limit ===
=== 13-limit ===
Line 275: Line 322:
Mapping: {{mapping| 1 0 0 10 6 11 | 0 1 0 -6 -6 -9 | 0 0 1 1 3 3 }}
Mapping: {{mapping| 1 0 0 10 6 11 | 0 1 0 -6 -6 -9 | 0 0 1 1 3 3 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~3/2 = 702.8670{{c}}, ~5/4 = 388.6277{{c}}
Optimal tunings:
* WE: ~2 = 1199.3329{{c}}, ~3/2 = 702.5519{{c}}, ~5/4 = 389.5508{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.9205{{c}}, ~5/4 = 389.4341{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~3/2 = 702.8670{{c}}, ~5/4 = 388.6277{{c}} -->


{{Optimal ET sequence|legend=0| 46, 53, 58, 99, 104c, 111, 268cd }}
{{Optimal ET sequence|legend=0| 46, 53, 58, 99, 104c, 111, 268cd }}


Badness (Smith): 0.908 × 10<sup>-3</sup>
Badness (Sintel): 0.850


== Kapo ==
== Kapo ==
Retrieved from "https://en.xen.wiki/w/Aberschismic_family"