Xenharmonic Wiki

Varunismic temperaments: Difference between revisions

← Older editNewer edit →
VisualWikitext
Sort links by ploidacot. Sort main entries by badness
Switch to Sintel's badness, WE & CWE tunings
Line 26: Line 26:
: mapping generators: ~160/147, ~350/243
: mapping generators: ~160/147, ~350/243


[[Optimal tuning]] ([[POTE]]): ~160/147 = 150.000{{c}}, ~350/243 = 633.738{{c}} (~49/48 = 33.738{{c}})
[[Optimal tuning]]s:
* [[WE]]: ~160/147 = 150.0317{{c}}, ~350/243 = 633.8714{{c}} (~49/48 = 33.7447{{c}})
: [[error map]]: {{val| +0.253 -0.341 +0.438 -0.640 }}
* [[CWE]]: ~160/147 = 150.0000{{c}}, ~350/243 = 633.7791{{c}} (~49/48 = 33.7791{{c}})
: error map: {{val| 0.000 -0.618 +0.140 -1.268 }}


{{Optimal ET sequence|legend=1| 32c, 72, 176, 248, 320 }}
{{Optimal ET sequence|legend=1| 32c, 72, 176, 248, 320 }}


[[Badness]] (Smith): 0.102295
[[Badness]] (Sintel): 2.59


=== 11-limit ===
=== 11-limit ===
Line 39: Line 43:
Mapping: {{mapping| 8 0 -11 14 15 | 0 3 7 2 3 }}
Mapping: {{mapping| 8 0 -11 14 15 | 0 3 7 2 3 }}


Optimal tuning (POTE): ~12/11 = 150.000{{c}}, ~121/84 = 633.755{{c}} (~49/48 = 33.755{{c}})
Optimal tunings:
* WE: ~12/11 = 150.0233{{c}}, ~121/84 = 633.8533{{c}} (~49/48 = 33.7602{{c}})
* CWE: ~12/11 = 150.0000{{c}}, ~121/84 = 633.7841{{c}} (~49/48 = 33.7841{{c}})


{{Optimal ET sequence|legend=0| 32c, 72, 176, 248, 320 }}
{{Optimal ET sequence|legend=0| 32c, 72, 176, 248, 320 }}


Badness (Smith): 0.030159
Badness (Sintel): 0.997


==== 13-limit ====
==== 13-limit ====
Line 52: Line 58:
Mapping: {{mapping| 8 0 -11 14 15 -38 | 0 3 7 2 3 16 }}
Mapping: {{mapping| 8 0 -11 14 15 -38 | 0 3 7 2 3 16 }}


Optimal tuning (POTE): ~12/11 = 150.000{{c}}, ~75/52 = 633.742{{c}} (~49/48 = 33.742{{c}})
Optimal tunings:
* WE: ~12/11 = 150.0247{{c}}, ~75/52 = 633.8469{{c}} (~49/48 = 33.7480{{c}})
* CWE: ~12/11 = 150.000{{c}}, ~75/52 = 633.7616{{c}} (~49/48 = 33.7616{{c}})


{{Optimal ET sequence|legend=0| 72, 176f, 248, 320 }}
{{Optimal ET sequence|legend=0| 72, 176f, 248, 320 }}


Badness (Smith): 0.027632
Badness (Sintel): 1.14


==== Octowerckis ====
==== Octowerckis ====
Line 65: Line 73:
Mapping: {{mapping| 8 0 -11 14 15 0 | 0 3 7 2 3 7 }}
Mapping: {{mapping| 8 0 -11 14 15 0 | 0 3 7 2 3 7 }}


Optimal tuning (POTE): ~12/11 = 150.000{{c}}, ~13/9 = 633.8370{{c}} (~49/48 = 33.8370{{c}})
Optimal tunings:
* WE: ~12/11 = 150.0289{{c}}, ~13/9 = 633.9590{{c}} (~49/48 = 33.8435{{c}})
* CWE: ~12/11 = 150.0000{{c}}, ~13/9 = 633.8739{{c}} (~49/48 = 33.8739{{c}})


{{Optimal ET sequence|legend=0| 32cf, 72, 176, 248f }}
{{Optimal ET sequence|legend=0| 32cf, 72, 176, 248f }}


Badness (Smith): 0.030192
Badness (Sintel): 1.25


== Essence ==
== Essence ==
Line 78: Line 88:
[[Comma list]]: 321489/320000, 823543/820125
[[Comma list]]: 321489/320000, 823543/820125


{{Mapping|legend=1| 2 10 27 23 | 0 -11 -36 -28 }}
{{Mapping|legend=1| 2 -1 -9 -5 | 0 11 36 28 }}
: mapping generators: ~567/400, ~243/196
: mapping generators: ~567/400, ~343/300


[[Optimal tuning]] ([[POTE]]): ~567/400 = 600.000{{c}}, ~243/196 = 372.597{{c}} (~343/300 = 227.403{{c}})
[[Optimal tuning]]s:
* [[WE]]: ~567/400 = 600.0984{{c}}, ~343/300 = 227.4405{{c}}
: [[error map]]: {{val| +0.197 -0.208 +0.659 -0.984 }}
* [[CWE]]: ~567/400 = 600.0000{{c}}, ~343/300 = 227.4104{{c}}
: error map: {{val| 0.000 -0.441 +0.460 -1.335 }}


{{Optimal ET sequence|legend=1| 58, 132d, 190, 248, 438d, 686d }}
{{Optimal ET sequence|legend=1| 58, 132d, 190, 248, 438d, 686d }}


[[Badness]] (Smith): 0.173565
[[Badness]] (Sintel): 4.39


=== 11-limit ===
=== 11-limit ===
Line 92: Line 106:
Comma list: 441/440, 8019/8000, 456533/455625
Comma list: 441/440, 8019/8000, 456533/455625


Mapping: {{mapping| 2 10 27 23 33 | 0 -11 -36 -28 -42 }}
Mapping: {{mapping| 2 -1 -9 -5 -9 | 0 11 36 28 42 }}


Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~150/121 = 372.599{{c}} (~154/135 = 227.401{{c}})
Optimal tunings:
* WE: ~99/70 = 600.0988{{c}}, ~154/135 = 227.4386{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~154/135 = 227.4084{{c}}


{{Optimal ET sequence|legend=0| 58, 132de, 190, 248, 438d }}
{{Optimal ET sequence|legend=0| 58, 132de, 190, 248, 438d }}


Badness (Smith): 0.046447
Badness (Sintel): 1.54


=== 13-limit ===
=== 13-limit ===
Line 105: Line 121:
Comma list: 441/440, 729/728, 847/845, 1001/1000
Comma list: 441/440, 729/728, 847/845, 1001/1000


Mapping: {{mapping| 2 10 27 23 33 31 | 0 -11 -36 -28 -42 -38 }}
Mapping: {{mapping| 2 -1 -9 -5 -9 -7 | 0 11 36 28 42 38 }}


Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~26/21 = 372.602{{c}} (~154/135 = 227.398{{c}})
Optimal tunings:
* WE: ~99/70 = 600.0805{{c}}, ~154/135 = 227.4285{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~154/135 = 227.4040{{c}}


{{Optimal ET sequence|legend=0| 58, 132de, 190, 248, 438d }}
{{Optimal ET sequence|legend=0| 58, 132de, 190, 248, 438d }}


Badness (Smith): 0.026107
Badness (Sintel): 1.08


[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Varunismic temperaments| ]] <!-- main article -->
[[Category:Varunismic temperaments| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Varunismic_temperaments"