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Porwell temperaments: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings (2/)
Switch to Sintel's badness, WE & CWE tunings (3/)
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:''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Untriton]].''  
:''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Untriton]].''  


Also named by [[Petr Pařízek]] in 2011, ''aufo'' refers to the augmented fourth, which is a generator of this temperament<ref name="petr's long post"/>.  
Also named by [[Petr Pařízek]] in 2011, ''aufo'' refers to the augmented fourth, which is a generator of this temperament<ref name="petr's long post"/>. The functional generator however is the [[64/45]] diminished fifth, and like its [[untriton]] variant, nine generator steps give the [[interval class]] of [[3/1|3]]. The [[ploidacot]] for this temperament is delta-enneacot.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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[[Comma list]]: 6144/6125, 177147/175616
[[Comma list]]: 6144/6125, 177147/175616


{{Mapping|legend=1| 1 6 -7 19 | 0 -9 19 -33 }}
{{Mapping|legend=1| 1 -3 12 -14 | 0 9 -19 33 }}
: mapping generators: ~2, ~45/32
: mapping generators: ~2, ~64/45


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~45/32 = 588.782{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9758{{c}}, ~64/45 = 611.2055{{c}}
: [[error map]]: {{val| -0.024 -1.303 +0.491 +1.295 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~64/45 = 611.2177{{c}}
: error map: {{val| 0.000 -0.996 +0.551 +1.357 }}


{{Optimal ET sequence|legend=1| 53, 161, 214 }}
{{Optimal ET sequence|legend=1| 53, 161, 214 }}


[[Badness]] (Smith): 0.121428
[[Badness]] (Sintel): 3.07


=== 11-limit ===
=== 11-limit ===
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Comma list: 121/120, 176/175, 177147/175616
Comma list: 121/120, 176/175, 177147/175616


Mapping: {{mapping| 1 6 -7 19 1 | 0 -9 19 -33 5 }}
Mapping: {{mapping| 1 -3 12 -14 6 | 0 9 -19 33 -5 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~45/32 = 588.811{{c}}
Optimal tunings:
* WE: ~2 = 1200.4500{{c}}, ~64/45 = 611.4185{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~64/45 = 611.1918{{c}}


{{Optimal ET sequence|legend=0| 53, 108e, 161e }}
{{Optimal ET sequence|legend=0| 53, 108e, 161e }}


Badness (Smith): 0.088631
Badness (Sintel): 2.93


==== 13-limit ====
==== 13-limit ====
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Comma list: 121/120, 176/175, 351/350, 58806/57967
Comma list: 121/120, 176/175, 351/350, 58806/57967


Mapping: {{mapping| 1 6 -7 19 1 -12 | 0 -9 19 -33 5 32 }}
Mapping: {{mapping| 1 -3 12 -14 6 20 | 0 9 -19 33 -5 -32 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~45/32 = 588.788{{c}}
Optimal tunings:
* WE: ~2 = 1200.3134{{c}}, ~64/45 = 611.3715{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~64/45 = 611.2118{{c}}


{{Optimal ET sequence|legend=0| 53, 108e, 161e, 214ee }}
{{Optimal ET sequence|legend=0| 53, 108e }}


Badness (Smith): 0.058507
Badness (Sintel): 2.42


=== Aufic ===
=== Aufic ===
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Comma list: 540/539, 5632/5625, 72171/71680
Comma list: 540/539, 5632/5625, 72171/71680


Mapping: {{mapping| 1 6 -7 19 -25 | 0 -9 19 -33 58 }}
Mapping: {{mapping| 1 -3 12 -14 33 | 0 9 -19 33 -58 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~45/32 = 588.800{{c}}
Optimal tunings:
* WE: ~2 = 1200.0668{{c}}, ~64/45 = 611.2342{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~64/45 = 611.2000{{c}}


{{Optimal ET sequence|legend=0| 53, 108, 161, 214, 375 }}
{{Optimal ET sequence|legend=0| 53, 108, 161, 214, 375 }}


Badness (Smith): 0.075149
Badness (Sintel): 2.48


==== 13-limit ====
==== 13-limit ====
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Comma list: 351/350, 540/539, 847/845, 4096/4095
Comma list: 351/350, 540/539, 847/845, 4096/4095


Mapping: {{mapping| 1 6 -7 19 -25 -12 | 0 -9 19 -33 58 32 }}
Mapping: {{mapping| 1 -3 12 -14 33 20 | 0 9 -19 33 -58 -32 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~45/32 = 588.796{{c}}
Optimal tunings:
* WE: ~2 = 1200.0177{{c}}, ~64/45 = 611.2130{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~64/45 = 611.2039{{c}}


{{Optimal ET sequence|legend=0| 53, 108, 161, 214, 375, 589be }}
{{Optimal ET sequence|legend=0| 53, 108, 161, 214, 375 }}


Badness (Smith): 0.039050
Badness (Sintel): 1.61


== Whoops ==
== Whoops ==
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[[Comma list]]: 6144/6125, 244140625/243045684
[[Comma list]]: 6144/6125, 244140625/243045684


{{Mapping|legend=1| 1 17 14 -7 | 0 -33 -25 21 }}
{{Mapping|legend=1| 1 -16 -11 14 | 0 33 25 -21 }}
: mapping generators: ~2, ~441/320
: mapping generators: ~2, ~640/441


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~441/320 = 560.519{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.5944{{c}}, ~640/441 = 639.2648{{c}}
: [[error map]]: {{val| -0.406 +0.272 -0.233 +0.936 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~640/441 = 639.4769{{c}}
: error map: {{val| 0.000 +0.783 +0.609 +2.159 }}


{{Optimal ET sequence|legend=1| 15, 122d, 137, 152, 608d, 623bd, 775bcd }}
{{Optimal ET sequence|legend=1| 15, 122d, 137, 152, 623bdd, 775bcdd, 927bcddd, 1079bcddd }}


[[Badness]] (Smith): 0.175840
[[Badness]] (Sintel): 4.45


=== 11-limit ===
=== 11-limit ===
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Comma list: 3025/3024, 4000/3993, 6144/6125
Comma list: 3025/3024, 4000/3993, 6144/6125


Mapping: {{mapping| 1 17 14 -7 10 | 0 -33 -25 21 -14 }}
Mapping: {{mapping| 1 -16 -11 14 -4 | 0 33 25 -21 14 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~242/175 = 560.519{{c}}
Optimal tunings:
* WE: ~2 = 1199.5936{{c}}, ~175/121 = 639.264{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~175/121 = 639.4770{{c}}


{{Optimal ET sequence|legend=0| 15, 122d, 137, 152, 608de, 623bde, 775bcde }}
{{Optimal ET sequence|legend=0| 15, 122d, 137, 152, 623bdde, 775bcdde, 927bcdddee, 1079bcdddee }}


Badness (Smith): 0.043743
Badness (Sintel): 1.45


== Polypyth ==
== Polypyth ==
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: mapping generators: ~2, ~3
: mapping generators: ~2, ~3


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3/2 = 704.174{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.3465{{c}}, ~3/2 = 703.7905{{c}}
: [[error map]]: {{val| -0.654 +1.182 -0.177 -0.056 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.1749{{c}}
: error map: {{val| 0.000 +2.220 +1.359 +1.752 }}


{{Optimal ET sequence|legend=1| 46, 121, 167, 288b, 455bcd, 743bcd }}
{{Optimal ET sequence|legend=1| 46, 121, 167, 288b, 455bcd }}


[[Badness]] (Smith): 0.137995
[[Badness]] (Sintel): 3.49


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 0 -31 52 59 | 0 1 21 -31 -35 }}
Mapping: {{mapping| 1 0 -31 52 59 | 0 1 21 -31 -35 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 704.177{{c}}
Optimal tunings:
* WE: ~2 = 1199.3335{{c}}, ~3/2 = 703.7856{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.1812{{c}}


{{Optimal ET sequence|legend=0| 46, 121, 167, 288be, 455bcde }}
{{Optimal ET sequence|legend=0| 46, 121, 167, 288be, 455bcde }}


Badness (Smith): 0.051131
Badness (Sintel): 1.69


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 0 -31 52 59 64 | 0 1 21 -31 -35 -38 }}
Mapping: {{mapping| 1 0 -31 52 59 64 | 0 1 21 -31 -35 -38 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 704.168{{c}}
Optimal tunings:
* WE: ~2 = 1199.3768{{c}}, ~3/2 = 703.8018{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.1731{{c}}


{{Optimal ET sequence|legend=0| 46, 121, 167, 288be }}
{{Optimal ET sequence|legend=0| 46, 75e, 121, 167, 288be }}


Badness (Smith): 0.030292
Badness (Sintel): 1.25


=== 17-limit ===
=== 17-limit ===
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Mapping: {{mapping| 1 0 -31 52 59 64 39 | 0 1 21 -31 -35 -38 -22 }}
Mapping: {{mapping| 1 0 -31 52 59 64 39 | 0 1 21 -31 -35 -38 -22 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 704.168{{c}}
Optimal tunings:
* WE: ~2 = 1199.3518{{c}}, ~3/2 = 703.7880{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.1747{{c}}


{{Optimal ET sequence|legend=0| 46, 121, 167, 288beg }}
{{Optimal ET sequence|legend=0| 46, 75e, 121, 167, 288beg }}


Badness (Smith): 0.019051
Badness (Sintel): 0.971


== Icositritonic ==
== Icositritonic ==
Retrieved from "https://en.xen.wiki/w/Porwell_temperaments"