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Canopic clan: Difference between revisions

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- grendel (moved to porwell temps)
Switch to Sintel's badness, WE & CWE tunings (1/)
Line 9: Line 9:
[[Comma list]]: 16875/16807
[[Comma list]]: 16875/16807


{{Mapping|legend=2| 1 3 3 | 0 -5 -4 }}
{{Mapping|legend=2| 1 -2 -1 | 0 5 4 }}
: mapping generators: ~3, ~7/5
: mapping generators: ~3, ~15/7


[[Optimal tuning]] ([[POTE]]): ~3 = 1901.9550{{c}}, ~7/5 = 583.9584{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~3 = 1901.7826{{c}}, ~15/7 = 1317.8771{{c}}
: [[error map]]: {{val| +1.785 -0.771 -2.248 }}
* [[CWE]]: ~3 = 1901.9550{{c}}, ~15/7 = 1317.9686{{c}}
: error map: {{val| 0.000 -0.381 +1.093 }}


[[Optimal ET sequence]]: [[13edt|b13]], [[62edt|b62]], [[75edt|b75]], [[88edt|b88]], [[101edt|b101]], [[114edt|b114]], [[355edt|b355]], [[469edt|b469]], [[583edt|b583]], [[697edt|b697]]
[[Optimal ET sequence]]: [[13edt|b13]], [[62edt|b62]], [[75edt|b75]], [[88edt|b88]], [[101edt|b101]], [[114edt|b114]], [[355edt|b355]], [[469edt|b469]], [[583edt|b583]], [[697edt|b697]]
[[Badness]] (Sintel): 0.0996


=== Overview to extensions ===
=== Overview to extensions ===
Line 44: Line 50:


== Mirkat ==
== Mirkat ==
Mirkat tempers out 19683/19600, the [[cataharry comma]], as well as 250047/250000, the [[landscape comma]], and may be described as the {{nowrap| 72 & 111 }} temperament with a [[ploidacot]] signature of triploid alpha-hexacot.
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Line 49: Line 57:


{{Mapping|legend=1| 3 2 1 2 | 0 6 13 14 }}
{{Mapping|legend=1| 3 2 1 2 | 0 6 13 14 }}
: mapping generators: ~63/50, ~10/9


[[Optimal tuning]] ([[POTE]]): ~63/50 = 400.000{{c}}, ~10/9 = 183.539{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~63/50 = 400.0277{{c}}, ~10/9 = 183.5515{{c}}
: [[error map]]: {{val| +0.083 -0.591 -0.117 +0.950 }}
* [[CWE]]: ~63/50 = 400.0000{{c}}, ~10/9 = 183.5470{{c}}
: error map: {{val| 0.000 -0.673 -0.203 +0.831 }}


{{Optimal ET sequence|legend=1| 39d, 72, 111, 183, 255 }}
{{Optimal ET sequence|legend=1| 39d, 72, 111, 183, 255 }}


[[Badness]] (Smith): 0.059376
[[Badness]] (Sintel): 1.50


=== 11-limit ===
=== 11-limit ===
Line 63: Line 76:
Mapping: {{mapping| 3 2 1 2 9 | 0 6 13 14 3 }}
Mapping: {{mapping| 3 2 1 2 9 | 0 6 13 14 3 }}


Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~10/9 = 183.528{{c}}
Optimal tunings:
* WE: ~63/50 = 400.0463{{c}}, ~10/9 = 183.5496{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~10/9 = 183.5391{{c}}


{{Optimal ET sequence|legend=0| 39d, 72, 111, 183, 255 }}
{{Optimal ET sequence|legend=0| 39d, 72, 111, 183, 255 }}


Badness (Smith): 0.022126
Badness (Sintel): 0.731


=== 13-limit ===
=== 13-limit ===
Line 76: Line 91:
Mapping: {{mapping| 3 2 1 2 9 1 | 0 6 13 14 3 22 }}
Mapping: {{mapping| 3 2 1 2 9 1 | 0 6 13 14 3 22 }}


Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~10/9 = 183.577{{c}}
Optimal tunings:
* WE: ~63/50 = 400.0245{{c}}, ~10/9 = 183.5885{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~10/9 = 183.5825{{c}}


{{Optimal ET sequence|legend=0| 39df, 72, 111, 183 }}
{{Optimal ET sequence|legend=0| 39df, 72, 111, 183 }}


Badness (Smith): 0.018632
Badness (Sintel): 0.770


=== 17-limit ===
=== 17-limit ===
Line 89: Line 106:
Mapping: {{mapping| 3 2 1 2 9 1 4 | 0 6 13 14 3 22 18 }}
Mapping: {{mapping| 3 2 1 2 9 1 4 | 0 6 13 14 3 22 18 }}


Optimal tuning (POTE): ~34/27 = 400.000{{c}}, ~10/9 = 183.579{{c}}
Optimal tunings:
* WE: ~34/27 = 400.0257{{c}}, ~10/9 = 183.5906{{c}}
* CWE: ~34/27 = 400.0000{{c}}, ~10/9 = 183.5843{{c}}


{{Optimal ET sequence|legend=0| 39dfg, 72, 111, 183 }}
{{Optimal ET sequence|legend=0| 39dfg, 72, 111, 183 }}


Badness (Smith): 0.011775
Badness (Sintel): 0.600


== Eris ==
== Eris ==
The [[2.5.7 subgroup]] restriction of this temperament is [[exodia]].
Eris tempers out 65625/65536, the [[horwell comma]], and may be described as the {{nowrap| 31 & 224 }} temperament. The [[2.5.7-subgroup|2.5.7 subgroup]] restriction of this temperament is [[exodia]].


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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[[Comma list]]: 16875/16807, 65625/65536
[[Comma list]]: 16875/16807, 65625/65536


{{Mapping|legend=1| 1 10 0 6 | 0 -29 8 -11 }}
{{Mapping|legend=1| 1 -19 8 -5 | 0 29 -8 11 }}
: mapping generators: ~2, ~49/30


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~60/49 = 348.216{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0256{{c}}, ~49/30 = 851.8023{{c}}
: [[error map]]: {{val| +0.026 -0.173 -0.528 +0.872 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/30 = 851.7845{{c}}
: error map: {{val| 0.000 -0.204 -0.590 +0.804 }}


{{Optimal ET sequence|legend=1| 31, 131, 162, 193, 224, 1823cd, 2271cd }}
{{Optimal ET sequence|legend=1| 31, 131, 162, 193, 224 }}


[[Badness]] (Smith): 0.074719
[[Badness]] (Sintel): 1.89


=== 11-limit ===
=== 11-limit ===
Line 115: Line 139:
Comma list: 540/539, 1375/1372, 65625/65536
Comma list: 540/539, 1375/1372, 65625/65536


Mapping: {{mapping| 1 10 0 6 20 | 0 -29 8 -11 -57 }}
Mapping: {{mapping| 1 -19 8 -5 -37 | 0 29 -8 11 57 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/9 = 348.219{{c}}
Optimal tunings:
* WE: ~2 = 1200.0218{{c}}, ~18/11 = 851.7963{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~18/11 = 851.7812{{c}}


{{Optimal ET sequence|legend=0| 31, 193, 224, 703, 927d, 1151cd }}
{{Optimal ET sequence|legend=0| 31, …, 193, 224, 703, 927d }}


Badness (Smith): 0.027621
Badness (Sintel): 0.913


=== 13-limit ===
=== 13-limit ===
Line 128: Line 154:
Comma list: 540/539, 625/624, 1375/1372, 4096/4095
Comma list: 540/539, 625/624, 1375/1372, 4096/4095


Mapping: {{mapping| 1 10 0 6 20 -14 | 0 -29 8 -11 -57 61 }}
Mapping: {{mapping| 1 -19 8 -5 -37 47 | 0 29 -8 11 57 -61 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/9 = 348.213{{c}}
Optimal tuning:  
* WE ~2 = 1199.9623{{c}}, ~18/11 = 851.7598{{c}}
* CWE ~2 = 1200.0000{{c}}, ~18/11 = 851.7865{{c}}


{{Optimal ET sequence|legend=0| 31, 193, 224 }}
{{Optimal ET sequence|legend=0| 31, 193, 224 }}


Badness (Smith): 0.025137
Badness (Sintel): 1.04


== Subsemifourth ==
== Subsemifourth ==
Line 141: Line 169:
[[Comma list]]: 16875/16807, 26873856/26796875
[[Comma list]]: 16875/16807, 26873856/26796875


{{Mapping|legend=1| 1 39 27 45 | 0 -47 -31 -53 }}
{{Mapping|legend=1| 1 -8 -4 -8 | 0 47 31 53 }}
: mapping generators: ~2, ~125/72
: mapping generators: ~2, ~144/125


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~144/125 = 244.719{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9182{{c}}, ~144/125 = 244.7020{{c}}
: [[error map]]: {{val| -0.082 -0.305 -0.223 +1.037 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~144/125 = 244.7172{{c}}
: error map: {{val| 0.000 -0.248 -0.082 +1.184 }}


{{Optimal ET sequence|legend=1| 49, 103, 152, 255, 407 }}
{{Optimal ET sequence|legend=1| 49, 103, 152, 255, 407 }}


[[Badness]] (Smith): 0.135173
[[Badness]] (Sintel): 3.42


=== 11-limit ===
=== 11-limit ===
Line 155: Line 187:
Comma list: 540/539, 1375/1372, 234375/234256
Comma list: 540/539, 1375/1372, 234375/234256


Mapping: {{mapping| 1 39 27 45 56 | 0 -47 -31 -53 -66 }}
Mapping: {{mapping| 1 -8 -4 -8 -10 | 0 47 31 53 66 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~121/105 = 244.719{{c}}
Optimal tunings:
* WE: ~2 = 1199.9229{{c}}, ~121/105 = 244.7033{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~121/105 = 244.7175{{c}}


{{Optimal ET sequence|legend=0| 49, 103, 152, 255, 407, 966d }}
{{Optimal ET sequence|legend=0| 49, 103, 152, 255, 407 }}


Badness (Smith): 0.034276
Badness (Sintel): 1.13


=== 13-limit ===
=== 13-limit ===
Line 168: Line 202:
Comma list: 540/539, 847/845, 1375/1372, 1575/1573
Comma list: 540/539, 847/845, 1375/1372, 1575/1573


Mapping: {{mapping| 1 39 27 45 56 65 | 0 -47 -31 -53 -66 -77 }}
Mapping: {{mapping| 1 -8 -4 -8 -10 -12 | 0 0 47 31 53 66 77 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/13 = 244.714{{c}}
Optimal tunings:
* WE: ~2 = 1199.9003{{c}}, ~15/13 = 244.6932{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/13 = 244.7116{{c}}


{{Optimal ET sequence|legend=0| 49f, 103, 152f, 255, 407f, 662df }}
{{Optimal ET sequence|legend=0| 49f, 103, 152f, 255, 407f }}


Badness (Smith): 0.028387
Badness (Sintel): 1.17


== Septendesemi ==
== Septendesemi ==
The name ''septendesemi'' means a septendecimal semitone ([[17/16]]). The septendesemi temperament (80 & 103) tempers out the mirkwai comma and 1959552/1953125 (''parkleiness'' comma, zotritrigu) in the 7-limit. [[183edo]] provides an excellent tuning for 7-, 11-, 13-, and 17-limit septendesemi.
The name ''septendesemi'' means a septendecimal semitone ([[17/16]]). The septendesemi temperament (80 & 103) tempers out the mirkwai comma and 1959552/1953125 (parkleiness comma) in the 7-limit. [[183edo]] provides an excellent tuning for 7-, 11-, 13-, and 17-limit septendesemi.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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[[Comma list]]: 16875/16807, 1959552/1953125
[[Comma list]]: 16875/16807, 1959552/1953125


{{Mapping|legend=1| 1 39 37 53 | 0 -41 -38 -55 }}
{{Mapping|legend=1| 1 -2 -1 -2 | 0 41 38 55 }}
: mapping generators: ~2, ~648/343
: mapping generators: ~2, ~343/324


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~343/324 = 104.916{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.8649{{c}}, ~343/324 = 104.9046{{c}}
: [[error map]]: {{val| -0.135 -0.597 +0.195 +1.196 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~343/324 = 104.9134{{c}}
: error map: {{val| 0.000 -0.506 +0.395 +1.410 }}


{{Optimal ET sequence|legend=0| 80, 103, 183 }}
{{Optimal ET sequence|legend=0| 80, 103, 183 }}


[[Badness]] (Smith): 0.146795
[[Badness]] (Sintel): 3.71


=== 11-limit ===
=== 11-limit ===
Line 197: Line 237:
Comma list: 540/539, 1375/1372, 43923/43750
Comma list: 540/539, 1375/1372, 43923/43750


Mapping: {{mapping| 1 39 37 53 50 | 0 -41 -38 -55 -51 }}
Mapping: {{mapping| 1 -2 -1 -2 -1 | 0 41 38 55 51 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~35/33 = 104.916{{c}}
Optimal tunings:
* WE: ~2 = 1199.9327{{c}}, ~35/33 = 104.9100{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~35/33 = 104.9144{{c}}


{{Optimal ET sequence|legend=0| 80, 103, 183 }}
{{Optimal ET sequence|legend=0| 80, 103, 183 }}


Badness (Smith): 0.041554
Badness (Sintel): 1.37


=== 13-limit ===
=== 13-limit ===
Line 210: Line 252:
Comma list: 351/350, 540/539, 1375/1372, 4225/4224
Comma list: 351/350, 540/539, 1375/1372, 4225/4224


Mapping: {{mapping| 1 39 37 53 50 11 | 0 -41 -38 -55 -51 -8 }}
Mapping: {{mapping| 1 -2 -1 -2 -1 3 | 0 41 38 55 51 8 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~35/33 = 104.908{{c}}
Optimal tunings:
* WE: ~2 = 1200.1082{{c}}, ~35/33 = 104.9170{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~35/33 = 104.9094{{c}}


{{Optimal ET sequence|legend=0| 80, 103, 183, 469f, 652def }}
{{Optimal ET sequence|legend=0| 80, 103, 183, 469f }}


Badness (Smith): 0.027908
Badness (Sintel): 1.15


=== 17-limit ===
=== 17-limit ===
Line 223: Line 267:
Comma list: 351/350, 540/539, 561/560, 715/714, 4225/4224
Comma list: 351/350, 540/539, 561/560, 715/714, 4225/4224


Mapping: {{mapping| 1 39 37 53 50 11 5 | 0 -41 -38 -55 -51 -8 -1 }}
Mapping: {{mapping| 1 -2 -1 -2 -1 3 4 | 0 41 38 55 51 8 1 }}
 
Optimal tunings:
* WE: ~2 = 1200.0758{{c}}, ~17/16 = 104.9158{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~17/16 = 104.9101{{c}}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~17/16 = 104.909{{c}}
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~17/16 = 104.909{{c}}


{{Optimal ET sequence|legend=0| 80, 103, 183, 469f, 652def }}
{{Optimal ET sequence|legend=0| 80, 103, 183, 469f }}


Badness (Smith): 0.020128
Badness (Sintel): 1.03


== Gaster ==
== Gaster ==
Retrieved from "https://en.xen.wiki/w/Canopic_clan"