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Buzzardsmic clan: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings, per community consensus (1/)
Switch to Sintel's badness, WE & CWE tunings, per community consensus (2/2)
Line 241: Line 241:
[[Comma list]]: 225/224, 51200/50421
[[Comma list]]: 225/224, 51200/50421


{{Mapping|legend=1| 1 4 -1 1 | 0 -8 11 6 }}
{{Mapping|legend=1| 1 -4 10 7 | 0 8 -11 -6 }}
: mapping generators: ~2, ~49/40
: mapping generators: ~2, ~80/49


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~49/40 = 362.255{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.7399{{c}}, ~80/49 = 837.5637{{c}}
: [[error map]]: {{val| -0.260 -0.405 -2.116 +3.971 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~80/49 = 837.7471{{c}}
: error map: {{val| 0.000 +0.022 -1.532 +4.691 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~80/49 = 837.745{{c}} -->


{{Optimal ET sequence|legend=1| 10, 33, 43, 53 }}
{{Optimal ET sequence|legend=1| 10, 33, 43, 53 }}


[[Badness]] (Smith): 0.060533
[[Badness]] (Sintel): 1.53


==== 2.3.5.7.13 subgroup ====
==== 2.3.5.7.13 subgroup ====
Line 259: Line 264:
Comma list: 169/168, 225/224, 640/637
Comma list: 169/168, 225/224, 640/637


Mapping: {{mapping| 1 4 -1 1 4 | 0 -8 11 6 -1 }}
Mapping: {{mapping| 1 -4 10 7 3 | 0 8 -11 -6 1 }}


Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~16/13 = 362.242{{c}}
Optimal tunings:
* WE: ~2 = 1199.9444{{c}}, ~13/8 = 837.7178{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/8 = 837.7569{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~13/8 = 837.758{{c}} -->


{{Optimal ET sequence|legend=0| 10, 33, 43, 53 }}
{{Optimal ET sequence|legend=0| 10, 33, 43, 53 }}
Line 274: Line 282:
Comma list: 225/224, 385/384, 6655/6561
Comma list: 225/224, 385/384, 6655/6561


Mapping: {{mapping| 1 4 -1 1 11 | 0 -8 11 6 -25 }}
Mapping: {{mapping| 1 -4 10 7 -14 | 0 8 -11 -6 25 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~27/22 = 362.101{{c}}
Optimal tunings:
* WE: ~2 = 1200.0666{{c}}, ~44/27 = 837.9460{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~44/27 = 837.9000{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~44/27 = 837.899{{c}} -->


{{Optimal ET sequence|legend=0| 10, 43e, 53, 116, 169de, 285cde }}
{{Optimal ET sequence|legend=0| 10, 43e, 53, 116 }}


Badness (Smith): 0.050582
Badness (Sintel): 1.67


==== 13-limit ====
==== 13-limit ====
Line 287: Line 298:
Comma list: 169/168, 225/224, 275/273, 385/384
Comma list: 169/168, 225/224, 275/273, 385/384


Mapping: {{mapping| 1 4 -1 1 11 4 | 0 -8 11 6 -25 -1 }}
Mapping: {{mapping| 1 -4 10 7 -14 3 | 0 8 -11 -6 25 1 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~16/13 = 362.105{{c}}
Optimal tunings:
* WE: ~2 = 1200.1769{{c}}, ~13/8 = 838.0187{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/8 = 837.8965{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~13/8 = 837.895{{c}} -->


{{Optimal ET sequence|legend=0| 10, 43e, 53, 116, 169de, 285cdef }}
{{Optimal ET sequence|legend=0| 10, 43e, 53, 116 }}


Badness (Smith): 0.027689
Badness (Sintel): 1.14


=== Interpental ===
=== Interpental ===
Line 300: Line 314:
Comma list: 99/98, 176/175, 51200/50421
Comma list: 99/98, 176/175, 51200/50421


Mapping: {{mapping| 1 4 -1 1 -5 | 0 -8 11 6 28 }}
Mapping: {{mapping| 1 -4 10 7 23 | 0 8 -11 -6 -28 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~49/40 = 362.418{{c}}
Optimal tunings:
* WE: ~2 = 1199.9381{{c}}, ~80/49 = 838.5389{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~80/49 = 837.5832{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~80/49 = 837.582{{c}} -->


{{Optimal ET sequence|legend=0| 43, 53, 96, 149d }}
{{Optimal ET sequence|legend=0| 43, 53, 96 }}


Badness (Smith): 0.051806
Badness (Sintel): 1.71


==== 13-limit ====
==== 13-limit ====
Line 313: Line 330:
Comma list: 99/98, 169/168, 176/175, 640/637
Comma list: 99/98, 169/168, 176/175, 640/637


Mapping: {{mapping| 1 4 -1 1 -5 4 | 0 -8 11 6 28 -1 }}
Mapping: {{mapping| 1 -4 10 7 23 3 | 0 8 -11 -6 -28 1 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~16/13 = 362.402{{c}}
Optimal tunings:
* WE: ~2 = 1200.1048{{c}}, ~13/8 = 837.6710{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/8 = 837.5964{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~16/13 = 362.402{{c}} -->


{{Optimal ET sequence|legend=0| 43, 53, 96, 149d }}
{{Optimal ET sequence|legend=0| 43, 53, 96 }}


Badness (Smith): 0.029680
Badness (Sintel): 1.23


== Thuja ==
== Thuja ==
Line 331: Line 351:
: mapping generators: ~2, ~175/128
: mapping generators: ~2, ~175/128


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~175/128 = 558.605{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1198.7356{{c}}, ~175/128 = 558.0168{{c}}
: [[error map]]: {{val| -1.264 -0.696 +3.770 +0.172 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~175/128 = 558.5795{{c}}
: error map: {{val| 0.000 +0.999 +6.584 +3.959 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~175/128 = 558.605{{c}} -->


{{Optimal ET sequence|legend=1| 15, 43, 58 }}
{{Optimal ET sequence|legend=1| 15, 43, 58 }}


[[Badness]] (Smith): 0.088441
[[Badness]] (Sintel): 2.24


=== 11-limit ===
=== 11-limit ===
Line 344: Line 369:
Mapping: {{mapping| 1 -4 0 7 3 | 0 12 5 -9 1 }}
Mapping: {{mapping| 1 -4 0 7 3 | 0 12 5 -9 1 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/8 = 558.620{{c}}
Optimal tunings:
* WE: ~2 = 1198.5470{{c}}, ~11/8 = 557.9433{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 558.5942{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~11/8 = 558.620{{c}} -->


{{Optimal ET sequence|legend=0| 15, 43, 58 }}
{{Optimal ET sequence|legend=0| 15, 43, 58 }}


Badness (Smith): 0.033078
Badness (Sintel): 1.09


=== 13-limit ===
=== 13-limit ===
Line 357: Line 385:
Mapping: {{mapping| 1 -4 0 7 3 -7 | 0 12 5 -9 1 23 }}
Mapping: {{mapping| 1 -4 0 7 3 -7 | 0 12 5 -9 1 23 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/8 = 558.589{{c}}
Optimal tunings:
* WE: ~2 = 1198.5083{{c}}, ~11/8 = 557.8942{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 558.5565{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~11/8 = 558.589{{c}} -->


{{Optimal ET sequence|legend=0| 15, 43, 58 }}
{{Optimal ET sequence|legend=0| 15, 43, 58 }}


Badness (Smith): 0.022838
Badness (Sintel): 0.944


=== 17-limit ===
=== 17-limit ===
Line 370: Line 401:
Mapping: {{mapping| 1 -4 0 7 3 -7 12 | 0 12 5 -9 1 23 -17 }}
Mapping: {{mapping| 1 -4 0 7 3 -7 12 | 0 12 5 -9 1 23 -17 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/8 = 558.509{{c}}
Optimal tunings:
* WE: ~2 = 1198.8533{{c}}, ~11/8 = 557.9750{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 558.4979{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~11/8 = 558.509{{c}} -->


{{Optimal ET sequence|legend=0| 15, 43, 58 }}
{{Optimal ET sequence|legend=0| 15, 43, 58, 101e, 159cdef }}


Badness (Smith): 0.022293
Badness (Sintel): 1.14


=== 19-limit ===
=== 19-limit ===
Line 383: Line 417:
Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 | 0 12 5 -9 1 23 -17 7 }}
Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 | 0 12 5 -9 1 23 -17 7 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/8 = 558.504{{c}}
Optimal tunings:
* WE: ~2 = 1198.6460{{c}}, ~11/8 = 557.8736{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 558.4905{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~11/8 = 558.504{{c}} -->


{{Optimal ET sequence|legend=0| 15, 43, 58h }}
{{Optimal ET sequence|legend=0| 15, 43, 58h, 101eh }}


Badness (Smith): 0.018938
Badness (Sintel): 1.15


=== 23-limit ===
=== 23-limit ===
Line 396: Line 433:
Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 5 | 0 12 5 -9 1 23 -17 7 -1 }}
Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 5 | 0 12 5 -9 1 23 -17 7 -1 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/8 = 558.522{{c}}
Optimal tunings:
* WE: ~2 = 1198.4488{{c}}, ~11/8 = 557.7999{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 558.5086{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~11/8 = 558.522{{c}} -->


{{Optimal ET sequence|legend=0| 15, 43, 58hi }}
{{Optimal ET sequence|legend=0| 15, 43, 58hi }}


Badness (Smith): 0.016581
Badness (Sintel): 1.19


=== 29-limit ===
=== 29-limit ===
Line 411: Line 451:
Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 5 3 | 0 12 5 -9 1 23 -17 7 -1 4 }}
Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 5 3 | 0 12 5 -9 1 23 -17 7 -1 4 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/8 = 558.520{{c}}
Optimal tunings:
* WE: ~2 = 1198.5114{{c}}, ~11/8 = 557.8276{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 558.5079{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~11/8 = 558.520{{c}} -->


{{Optimal ET sequence|legend=0| 15, 43, 58hi }}
{{Optimal ET sequence|legend=0| 15, 43, 58hi }}


Badness (Smith): 0.013762
Badness (Sintel): 1.15


== Anthoine ==
== Anthoine ==
Anthoine is generated by [[5/4]] and tempers out [[3125/3087]] in addition to the buzzardsma, so that 32/21 is found at 5 generators up. It is most notable as the {{nowrap| 25 & 28 }} temperament and as the chain of 5/4's present in 53edo.
Anthoine is generated by [[5/4]] and tempers out [[3125/3087]] in addition to the buzzardsma, so that 32/21 is found at 5 generators up. It is most notable as the {{nowrap| 25 & 28 }} temperament and as the chain of 5/4's present in 53edo.


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Comma list: 3125/3087, 65536/64827
[[Comma list]]: 3125/3087, 65536/64827


Mapping: {{mapping| 1 8 2 -2 | 0 -20 1 15 }}
{{Mapping|legend=1| 1 -12 3 13 | 0 20 -1 -15 }}
: mapping generators: ~2, ~5/4
: mapping generators: ~2, ~8/5


Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~5/4 = 384.856{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.6282{{c}}, ~8/5 = 814.9050{{c}}
: [[error map]]: {{val| -0.372 +0.605 -2.334 +2.767 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/5 = 815.1546{{c}}
: error map: {{val| 0.000 +1.138 -1.468 +3.854 }}
<!-- * CTE: ~2 = 1200.000{{c}}, ~8/5 = 815.144{{c}} -->


{{Optimal ET sequence|legend=0| 25, 53, 184, 237d, 290d, 343dd }}
{{Optimal ET sequence|legend=1| 25, 53, 184, 237d }}


Badness (Sintel): 4.571
[[Badness]] (Sintel): 4.57


[[Category:Temperament clans]]
[[Category:Temperament clans]]
Retrieved from "https://en.xen.wiki/w/Buzzardsmic_clan"