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Sensipent family: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings, per community consensus (3/)
Switch to Sintel's badness, WE & CWE tunings, per community consensus (4/4)
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== Bison ==
== Bison ==
Bison has a 1/2-octave period. Its ploidacot is diploid delta-heptacot (pergen (P8/2, ccP5/7)). Related page: [[Bison/Eliora's Approach]].  
Bison has a 1/2-octave period. Its ploidacot is diploid delta-heptacot (pergen (P8/2, ccP5/7)). Related page: [[Bison/Eliora's Approach]].


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 594: Line 594:
[[Comma list]]: 6144/6125, 78732/78125
[[Comma list]]: 6144/6125, 78732/78125


[[Mapping]]:  
[[Mapping]]:
* common form: {{mapping| 2 -2 -2 13 | 0 7 9 -10}}
* common form: {{mapping| 2 -2 -2 13 | 0 7 9 -10}}
:: mapping generators: ~567/400, ~162/125
:: mapping generators: ~567/400, ~162/125
Line 600: Line 600:
:: mapping generators: ~567/400, ~35/32
:: mapping generators: ~567/400, ~35/32


[[Optimal tuning]]s:  
[[Optimal tuning]]s:
* [[POTE]]: ~567/400 = 600.000{{c}}, ~162/125 = 443.075{{c}} (~35/32 = 156.925{{c}})
* [[WE]]: ~567/400 = 599.9413{{c}}, ~162/125 = 443.0320{{c}} (~35/32 = 156.9093{{c}})
: [[error map]]: {{val| -0.117 -0.613 +1.092 +0.091 }}
* [[CWE]]: ~567/400 = 1200.0000{{c}}, ~162/125 = 443.0728{{c}} (~35/32 = 156.9272{{c}})
: error map: {{val| 0.000 -0.446 +1.341 +0.446 }}
<!-- * [[POTE]]: ~567/400 = 600.000{{c}}, ~162/125 = 443.075{{c}} (~35/32 = 156.925{{c}}) -->


{{Optimal ET sequence|legend=1| 8, 38, 46, 84, 130 }}
{{Optimal ET sequence|legend=1| 8, 38, 46, 84, 130 }}


[[Badness]] (Smith): 0.070375
[[Badness]] (Sintel): 1.78


=== 11-limit ===
=== 11-limit ===
Line 612: Line 616:
Comma list: 441/440, 6144/6125, 8019/8000
Comma list: 441/440, 6144/6125, 8019/8000


Mapping:  
Mapping:
* common form: {{mapping| 2 -2 -2 13 18 | 0 7 9 -10 -15}}
* common form: {{mapping| 2 -2 -2 13 18 | 0 7 9 -10 -15 }}
:: mapping generators: ~567/400, ~162/125
:: mapping generators: ~567/400, ~162/125
* mingen form: {{mapping| 2 5 7 3 3 | 0 -7 -9 10 15 }}
* mingen form: {{mapping| 2 5 7 3 3 | 0 -7 -9 10 15 }}
:: mapping generators: ~567/400, ~35/32
:: mapping generators: ~567/400, ~35/32


Optimal tunings:  
Optimal tunings:
* POTE: ~99/70 = 600.000{{c}}, ~162/125 = 443.117{{c}} (~35/32 = 156.883{{c}})
* WE: ~99/70 = 599.8776{{c}}, ~162/125 = 443.0265{{c}} (~35/32 = 156.8511{{c}})
* CWE: ~99/70 = 600.0000{{c}}, ~162/125 = 443.1166{{c}} (~35/32 = 156.8834{{c}})
<!-- * POTE: ~99/70 = 600.000{{c}}, ~162/125 = 443.117{{c}} (~35/32 = 156.883{{c}}) -->


{{Optimal ET sequence|legend=0| 46, 84, 130, 306, 436ce }}
{{Optimal ET sequence|legend=0| 38e, 46, 84, 130, 306, 436ce }}


Badness (Smith): 0.037132
Badness (Sintel): 1.23


=== 13-limit ===
=== 13-limit ===
Line 630: Line 636:
Comma list: 351/350, 364/363, 441/440, 10985/10976
Comma list: 351/350, 364/363, 441/440, 10985/10976


Mapping:  
Mapping:
* common form: {{mapping| 2 -2 -2 13 18 17 | 0 7 9 -10 -15 -13 }}
* common form: {{mapping| 2 -2 -2 13 18 17 | 0 7 9 -10 -15 -13 }}
:: mapping generators: ~55/39, ~162/125
:: mapping generators: ~55/39, ~162/125
Line 636: Line 642:
:: mapping generators: ~55/39, ~35/32
:: mapping generators: ~55/39, ~35/32


Optimal tunings:  
Optimal tunings:
* POTE: ~55/39 = 600.000{{c}}, ~162/125 = 443.096{{c}} (~35/32 = 156.904{{c}})
* WE: ~55/39 = 599.9161{{c}}, ~162/125 = 443.0343{{c}} (~35/32 = 156.8817{{c}})
* CWE: ~55/39 = 600.0000{{c}}, ~162/125 = 443.0973{{c}} (~35/32 = 156.9027{{c}})
<!-- * POTE: ~55/39 = 600.000{{c}}, ~162/125 = 443.096{{c}} (~35/32 = 156.904{{c}}) -->


{{Optimal ET sequence|legend=0| 46, 84, 130, 566ce, 596cef }}
{{Optimal ET sequence|legend=0| 38e, 46, 84, 130, 566ce, 596cef }}


Badness (Smith): 0.023504
Badness (Sintel): 0.971


== Subpental ==
== Subpental ==
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[[Comma list]]: 3136/3125, 19683/19600
[[Comma list]]: 3136/3125, 19683/19600


{{Mapping|legend=1| 1 6 8 17 | 0 -14 -18 -45 }}
{{Mapping|legend=1| 1 -8 -10 -28 | 0 14 18 45 }}


: mapping generators: ~2, ~56/45
: mapping generators: ~2, ~45/28


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000{{c}}, ~56/45 = 378.467{{c}}
* [[WE]]: ~2 = 1199.9261{{c}}, ~45/28 = 821.4823{{c}}
: [[error map]]: {{val| -0.074 -0.611 +1.107 -0.052 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~45/28 = 821.5303{{c}}
: error map: {{val| 0.000 -0.531 +1.231 +0.036 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~45/28 = 821.533{{c}} -->


{{Optimal ET sequence|legend=1| 19, 111, 130, 929c, 1059c, 1189bc, 1319bc }}
{{Optimal ET sequence|legend=1| 19, …, 111, 130 }}


[[Badness]] (Smith): 0.054303
[[Badness]] (Sintel): 1.37


=== 11-limit ===
=== 11-limit ===
Line 666: Line 678:
Comma list: 540/539, 3136/3125, 8019/8000
Comma list: 540/539, 3136/3125, 8019/8000


Mapping: {{mapping| 1 6 8 17 -6 | 0 -14 -18 -45 30 }}
Mapping: {{mapping| 1 -8 -10 -28 24 | 0 14 18 45 -30 }}


Optimal tunings:  
Optimal tunings:  
* POTE: ~2 = 1200.000{{c}}, ~56/45 = 378.440{{c}}
* WE: ~2 = 1199.6571{{c}}, ~45/28 = 821.3249{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~45/28 = 821.5560{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~45/28 = 821.560{{c}} -->


{{Optimal ET sequence|legend=0| 19, 111, 130, 241, 371ce, 501cde, 872cde }}
{{Optimal ET sequence|legend=0| 19, 111, 130, 241, 371ce, 501cde }}


Badness (Smith): 0.045352
Badness (Sintel): 1.50


=== 13-limit ===
=== 13-limit ===
Line 680: Line 694:
Comma list: 351/350, 540/539, 676/675, 3136/3125
Comma list: 351/350, 540/539, 676/675, 3136/3125


Mapping: {{mapping| 1 6 8 17 -6 16 | 0 -14 -18 -45 30 -39 }}
Mapping: {{mapping| 1 -8 -10 -28 24 -23 | 0 14 18 45 -30 39 }}


Optimal tunings:  
Optimal tunings:  
* POTE: ~2 = 1200.000{{c}}, ~56/45 = 378.437{{c}}
* WE: ~2 = 1199.6819{{c}}, ~45/28 = 821.3451{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~45/28 = 821.5591{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~45/28 = 821.563{{c}} -->


{{Optimal ET sequence|legend=0| 19, 111, 130, 241, 371ce }}
{{Optimal ET sequence|legend=0| 19, 111, 130, 241, 371ce }}


Badness (Smith): 0.023940
Badness (Sintel): 0.989


== Heinz ==
== Heinz ==
Line 696: Line 712:
[[Comma list]]: 1029/1024, 78732/78125
[[Comma list]]: 1029/1024, 78732/78125


{{Mapping|legend=1| 1 -8 -10 6| 0 21 27 -7 }}
{{Mapping|legend=1| 1 -8 -10 6 | 0 21 27 -7 }}


: mapping generators: ~2, ~48/35
: mapping generators: ~2, ~48/35


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000{{c}}, ~48/35 = 546.815{{c}}
* [[WE]]: ~2 = 1200.4250{{c}}, ~48/35 = 547.8379{{c}}
: [[error map]]: {{val| +0.425 -0.758 +1.061 -1.141 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~48/35 = 547.6528{{c}}
: error map: {{val| 0.000 -1.247 +0.311 -2.395 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~48/35 = 546.815{{c}} -->


{{Optimal ET sequence|legend=1| 46, 103, 149, 699bdd }}
{{Optimal ET sequence|legend=1| 46, 103, 149, 699bdd }}


[[Badness]] (Smith): 0.115385
[[Badness]] (Sintel): 2.92


=== 11-limit ===
=== 11-limit ===
Line 717: Line 737:


Optimal tunings:  
Optimal tunings:  
* POTE: ~2 = 1200.000{{c}}, ~11/8 = 547.631{{c}}
* WE: ~2 = 1200.6094{{c}}, ~11/8 = 547.9095{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 547.6413{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~11/8 = 547.631{{c}} -->


{{Optimal ET sequence|legend=0| 46, 103, 149, 252e, 401bdee }}
{{Optimal ET sequence|legend=0| 46, 103, 149, 252e, 401bdee }}


Badness (Smith): 0.042412
Badness (Sintel): 1.40


=== 13-limit ===
=== 13-limit ===
Line 731: Line 753:


Optimal tunings:  
Optimal tunings:  
* POTE: ~2 = 1200.000{{c}}, ~11/8 = 547.629{{c}}
* WE: ~2 = 1200.6343{{c}}, ~11/8 = 547.9182{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 547.6345{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~11/8 = 547.629{{c}} -->


{{Optimal ET sequence|legend=0| 46, 103, 149, 252ef, 401bdeef }}
{{Optimal ET sequence|legend=0| 46, 103, 149, 252ef, 401bdeef }}


Badness (Smith): 0.025779
Badness (Sintel): 1.07


=== 17-limit ===
=== 17-limit ===
Line 745: Line 769:


Optimal tunings:  
Optimal tunings:  
* POTE: ~2 = 1200.000{{c}}, ~11/8 = 547.635{{c}}
* WE: ~2 = 1200.5351{{c}}, ~11/8 = 547.8790{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 547.6388{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~11/8 = 547.635{{c}} -->


{{Optimal ET sequence|legend=0| 46, 103, 149, 252ef, 401bdeef }}
{{Optimal ET sequence|legend=0| 46, 103, 149, 252ef }}


Badness (Smith): 0.018479
Badness (Sintel): 0.941


=== 19-limit ===
=== 19-limit ===
Line 759: Line 785:


Optimal tunings:  
Optimal tunings:  
* POTE: ~2 = 1200.000{{c}}, ~11/8 = 547.614{{c}}
* WE: ~2 = 1200.7181{{c}}, ~11/8 = 547.9418{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 547.6175{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~11/8 = 547.614{{c}} -->


{{Optimal ET sequence|legend=0| 46, 103h, 149h, 252efhh }}
{{Optimal ET sequence|legend=0| 46, 103h, 149h }}


Badness (Smith): 0.019005
Badness (Sintel): 1.16


== Trisensory ==
== Trisensory ==
Line 777: Line 805:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~63/50 = 400.000{{c}}, ~36/35 = 43.147{{c}}
* [[WE]]: ~63/50 = 399.8117{{c}}, ~36/35 = 43.1270{{c}}
: [[error map]]: {{val| -0.565 -0.819 +0.700 +2.176 }}
* [[CWE]]: ~63/50 = 400.0000{{c}}, ~36/35 = 43.0852{{c}}
: error map: {{val| 0.000 -0.359 +1.453 +3.515 }}
<!-- * [[POTE]]: ~63/50 = 400.000{{c}}, ~36/35 = 43.147{{c}} -->


{{Optimal ET sequence|legend=1| 27, 57, 84, 111, 195d, 306d }}
{{Optimal ET sequence|legend=1| 27, 57, 84, 111, 195d, 306d }}


[[Badness]] (Smith): 0.089740
[[Badness]] (Sintel): 2.27


=== 11-limit ===
=== 11-limit ===
Line 791: Line 823:


Optimal tunings:  
Optimal tunings:  
* POTE: ~63/50 = 400.000{{c}}, ~36/35 = 43.292{{c}}
* WE: ~63/50 = 399.7341{{c}}, ~36/35 = 43.2633{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~36/35 = 43.2290{{c}}
<!-- * POTE: ~63/50 = 400.000{{c}}, ~36/35 = 43.292{{c}} -->


{{Optimal ET sequence|legend=0| 27e, 84e, 111 }}
{{Optimal ET sequence|legend=0| 27e, 84e, 111, 360ccdde }}


Badness (Smith): 0.058413
Badness (Sintel): 1.93


=== 13-limit ===
=== 13-limit ===
Line 807: Line 841:


Optimal tunings:  
Optimal tunings:  
* POTE: ~49/39 = 400.000{{c}}, ~36/35 = 43.288{{c}}
* WE: ~49/39 = 399.7403{{c}}, ~36/35 = 43.2602{{c}}
* CWE: ~49/39 = 400.0000{{c}}, ~36/35 = 43.2415{{c}}
<!-- * POTE: ~49/39 = 400.000{{c}}, ~36/35 = 43.288{{c}} -->


{{Optimal ET sequence|legend=0| 27e, 84e, 111 }}
{{Optimal ET sequence|legend=0| 27e, 84e, 111, 360ccddef }}


Badness (Smith): 0.034829
Badness (Sintel): 1.44


=== 17-limit ===
=== 17-limit ===
Line 821: Line 857:


Optimal tunings:  
Optimal tunings:  
* POTE: ~49/39 = 400.000{{c}}, ~36/35 = 43.276{{c}}
* WE: ~49/39 = 399.7422{{c}}, ~36/35 = 43.2480{{c}}
* CWE: ~49/39 = 400.0000{{c}}, ~36/35 = 43.2305{{c}}
<!-- * POTE: ~49/39 = 400.000{{c}}, ~36/35 = 43.276{{c}} -->


{{Optimal ET sequence|legend=0| 27eg, 84e, 111 }}
{{Optimal ET sequence|legend=0| 27eg, 84e, 111 }}


Badness (Smith): 0.024120
Badness (Sintel): 1.23


=== 19-limit ===
=== 19-limit ===
Line 835: Line 873:


Optimal tunings:  
Optimal tunings:  
* POTE: ~49/39 = 400.000{{c}}, ~36/35 = 43.292{{c}}
* WE: ~49/39 = 399.7059{{c}}, ~36/35 = 43.2600{{c}}
* CWE: ~49/39 = 400.0000{{c}}, ~36/35 = 43.2433{{c}}
<!-- * POTE: ~49/39 = 400.000{{c}}, ~36/35 = 43.292{{c}} -->


{{Optimal ET sequence|legend=0| 27eg, 84e, 111 }}
{{Optimal ET sequence|legend=0| 27eg, 84e, 111 }}


Badness (Smith): 0.018466
Badness (Sintel): 1.12


[[Category:Temperament families]]
[[Category:Temperament families]]
Retrieved from "https://en.xen.wiki/w/Sensipent_family"