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Canopic clan: Difference between revisions

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{{Technical data page}}
{{Technical data page}}
The '''mirkwai clan''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[mirkwai comma]] ({{monzo|legend=1| 0 3 4 -5 }}, [[ratio]]: 16875/16807), a no-twos comma.  
The '''canopic clan''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[canopic comma]] ({{monzo|legend=1| 0 3 4 -5 }}, [[ratio]]: 16875/16807), a no-twos comma.  


== Canopus ==
== Canopus ==
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 31: Line 37:
* ''[[Pluto]]'' (+4000/3969) → [[Octagar temperaments #Pluto|Octagar temperaments]]
* ''[[Pluto]]'' (+4000/3969) → [[Octagar temperaments #Pluto|Octagar temperaments]]
* ''[[Bohpier]]'' (+245/243) → [[Sensamagic clan #Bohpier|Sensamagic clan]]
* ''[[Bohpier]]'' (+245/243) → [[Sensamagic clan #Bohpier|Sensamagic clan]]
* ''[[Subsedia]]'' (+65536/64827) → [[Buzzardsmic clan #Subsedia|Buzzardsmic clan]]
* ''[[Semisept]]'' (+1728/1715 or 3136/3125) → [[Hemimean clan #Semisept|Hemimean clan]]
* ''[[Semisept]]'' (+1728/1715 or 3136/3125) → [[Hemimean clan #Semisept|Hemimean clan]]
* ''[[Grendel]]'' (+6144/6125) → [[Porwell temperaments #Grendel|Porwell temperaments]]
* ''[[Grendel]]'' (+6144/6125) → [[Porwell temperaments #Grendel|Porwell temperaments]]
Line 41: Line 48:
For ''no-twos'' extensions, see [[No-twos subgroup temperaments #Canopus]].
For ''no-twos'' extensions, see [[No-twos subgroup temperaments #Canopus]].


Considered below are mirkat, eris, subsemifourth, septendesemi, gaster, subsedia, hemiseptisix, browser, and grazer.  
Considered below are mirkat, eris, subsemifourth, septendesemi, gaster, hemiseptisix, browser, and grazer, in the order of increasing [[badness]].  


== 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 58:


{{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 77:
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 92:
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 107:
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
Line 102: Line 122:
[[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 140:
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 155:
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 170:
[[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 188:
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 203:
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.
Septendesemi tempers out the mirkwai comma and 1959552/1953125 (parkleiness comma) in the 7-limit, and may be described as the {{nowrap| 80 & 103 }} temperament. [[183edo]] provides an excellent tuning for 7-, 11-, 13-, and 17-limit septendesemi. Septendesemi was named by [[Xenllium]] in 2021; the name ''septendesemi'' refers to a septendecimal semitone ([[17/16]]).  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 183: Line 220:
[[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 238:
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 253:
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 268:
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 ==
Line 235: Line 284:
{{Main| Gaster temperament }}
{{Main| Gaster temperament }}


The gaster temperament (111 & 113) tempers out {{monzo| -70 72 -19 }} (quadbila-negu) in the 5-limit; mirkwai comma (16875/16807) and [[scheme comma]] (14348907/14336000) in the 7-limit. The word "[[Wiktionary: gaster|gaster]]" means [[Wiktionary: abdomen|abdomen]] or [[Wiktionary: stomach|stomach]], but also a restructuring of the words "gassormic tritone", which is a generator of this temperament. This temperament is sufficient to obtain high prime limit harmonics like a stomach, so that patent vals [[111edo|111]], [[113edo|113]] and [[224edo|224]] support it even in the 41-limit.
Gaster tempers out {{monzo| -70 72 -19 }} in the 5-limit, mirkwai comma (16875/16807) and [[scheme comma]] (14348907/14336000) in the 7-limit, and may be described as the {{nowrap| 111 & 113 }} temperament.  
 
It was named by [[Xenllium]] in 2022; the word "[[Wiktionary: gaster|gaster]]" means [[Wiktionary: abdomen|abdomen]] or [[Wiktionary: stomach|stomach]], but also a restructuring of the words "gassormic tritone", which is a generator of this temperament. This temperament is sufficient to obtain high prime limit harmonics like a stomach, so that patent vals [[111edo|111]], [[113edo|113]] and [[224edo|224]] support it even in the 41-limit.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 241: Line 292:
[[Comma list]]: 16875/16807, 14348907/14336000
[[Comma list]]: 16875/16807, 14348907/14336000


{{Mapping|legend=1| 1 11 38 37 | 0 -19 -72 -69 }}
{{Mapping|legend=1| 1 -8 -34 -32 | 0 19 72 69 }}
: mapping generators: ~2, ~567/400


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~800/567 = 594.641{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9920{{c}}, ~567/400 = 605.3546{{c}}
: [[error map]]: {{val| -0.008 -0.152 -0.506 +0.902 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~567/400 = 605.3586{{c}}
: error map: {{val| 0.000 -0.142 -0.497 +0.915 }}


{{Optimal ET sequence|legend=1| 111, 224 }}
{{Optimal ET sequence|legend=1| 111, 224 }}


[[Badness]] (Smith): 0.154521
[[Badness]] (Sintel): 3.91


=== 11-limit ===
=== 11-limit ===
Line 254: Line 310:
Comma list: 540/539, 1375/1372, 14348907/14336000
Comma list: 540/539, 1375/1372, 14348907/14336000


Mapping: {{mapping| 1 11 38 37 -1 | 0 -19 -72 -69 9 }}
Mapping: {{mapping| 1 -8 -34 -32 8 | 0 19 72 69 -9 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~512/363 = 594.639{{c}}
Optimal tunings:
* WE: ~2 = 1199.9387{{c}}, ~363/256 = 605.3300{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~363/256 = 605.3603{{c}}


{{Optimal ET sequence|legend=0| 111, 224, 783d, 1007d, 1231dd }}
{{Optimal ET sequence|legend=0| 111, 224, 783d }}


Badness (Smith): 0.054060
Badness (Sintel): 1.79


=== 13-limit ===
=== 13-limit ===
Line 267: Line 325:
Comma list: 540/539, 729/728, 1375/1372, 2200/2197
Comma list: 540/539, 729/728, 1375/1372, 2200/2197


Mapping: {{mapping| 1 11 38 37 -1 26 | 0 -19 -72 -69 9 -45 }}
Mapping: {{mapping| 1 -8 -34 -32 8 -19 | 0 19 72 69 -9 45 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~55/39 = 594.639{{c}}
Optimal tunings:
* WE: ~2 = 1199.9154{{c}}, ~78/55 = 605.3183{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~78/55 = 605.3601{{c}}


{{Optimal ET sequence|legend=0| 111, 224, 783df, 1007df, 1231ddf }}
{{Optimal ET sequence|legend=0| 111, 224, 783df }}


Badness (Smith): 0.024882
Badness (Sintel): 1.03


=== 17-limit ===
=== 17-limit ===
Line 280: Line 340:
Comma list: 540/539, 715/714, 729/728, 936/935, 2200/2197
Comma list: 540/539, 715/714, 729/728, 936/935, 2200/2197


Mapping: {{mapping| 1 11 38 37 -1 26 14 | 0 -19 -72 -69 9 -45 -20 }}
Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 | 0 19 72 69 -9 45 20 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~24/17 = 594.636{{c}}
Optimal tunings:
* WE: ~2 = 1199.8076{{c}}, ~17/12 = 605.2674{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3626{{c}}


{{Optimal ET sequence|legend=0| 111, 224, 559dgg }}
{{Optimal ET sequence|legend=0| 111, 224, 559dgg }}


Badness (Smith): 0.021436
Badness (Sintel): 1.09


=== 19-limit ===
=== 19-limit ===
Line 293: Line 355:
Comma list: 324/323, 400/399, 495/494, 540/539, 715/714, 1445/1444
Comma list: 324/323, 400/399, 495/494, 540/539, 715/714, 1445/1444


Mapping: {{mapping| 1 11 38 37 -1 26 14 32 | 0 -19 -72 -69 9 -45 -20 -56 }}
Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 | 0 19 72 69 -9 45 20 56 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~24/17 = 594.636{{c}}
Optimal tunings:
* WE: ~2 = 1199.7542{{c}}, ~17/12 = 605.2674{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3613{{c}}


{{Optimal ET sequence|legend=0| 111, 224 }}
{{Optimal ET sequence|legend=0| 111, 224 }}


Badness (Smith): 0.018370
Badness (Sintel): 1.12


=== 23-limit ===
=== 23-limit ===
Line 306: Line 370:
Comma list: 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714
Comma list: 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714


Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 | 0 -19 -72 -69 9 -45 -20 -56 -5 }}
Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 | 0 19 72 69 -9 45 20 56 5 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~24/17 = 594.641{{c}}
Optimal tunings:
* WE: ~2 = 1199.8733{{c}}, ~17/12 = 605.2946{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3575{{c}}


{{Optimal ET sequence|legend=0| 111, 224 }}
{{Optimal ET sequence|legend=0| 111, 224 }}


Badness (Smith): 0.017619
Badness (Sintel): 1.26


=== 29-limit ===
=== 29-limit ===
Line 319: Line 385:
Comma list: 290/289, 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714
Comma list: 290/289, 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714


Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 -11 | 0 -19 -72 -69 9 -45 -20 -56 -5 32 }}
Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 21 | 0 19 72 69 -9 45 20 56 5 -32 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~24/17 = 594.646{{c}}
Optimal tunings:
* WE: ~2 = 1199.9442{{c}}, ~17/12 = 605.3263{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3541{{c}}


{{Optimal ET sequence|legend=0| 111, 113, 224 }}
{{Optimal ET sequence|legend=0| 111, 113, 224 }}


Badness (Smith): 0.016815
Badness (Sintel): 1.41


=== 31-limit ===
=== 31-limit ===
Line 332: Line 400:
Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 715/714
Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 715/714


Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 -11 0 | 0 -19 -72 -69 9 -45 -20 -56 -5 32 10 }}
Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 | 0 19 72 69 -9 45 20 56 5 -32 -10 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~24/17 = 594.644{{c}}
Optimal tunings:
* WE: ~2 = 1199.9100{{c}}, ~17/12 = 605.3107{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3556{{c}}


{{Optimal ET sequence|legend=0| 111, 113, 224 }}
{{Optimal ET sequence|legend=0| 111, 113, 224 }}


Badness (Smith): 0.014790
Badness (Sintel): 1.42


=== 37-limit ===
=== 37-limit ===
Line 345: Line 415:
Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 667/666, 715/714
Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 667/666, 715/714


Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 -11 0 -27 | 0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65 }}
Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 38 | 0 19 72 69 -9 45 20 56 5 -32 -10 -65 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~24/17 = 594.644{{c}}
Optimal tunings:
* WE: ~2 = 1199.9087{{c}}, ~17/12 = 605.3101{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3559{{c}}


{{Optimal ET sequence|legend=0| 111, 113, 224 }}
{{Optimal ET sequence|legend=0| 111, 113, 224 }}


Badness (Smith): 0.014377
Badness (Sintel): 1.56


=== 41-limit ===
=== 41-limit ===
Line 358: Line 430:
Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 533/532, 540/539, 575/574, 667/666
Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 533/532, 540/539, 575/574, 667/666


Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 -11 0 -27 45 | 0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65 -80 }}
Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 38 -35 | 0 19 72 69 -9 45 20 56 5 -32 -10 -65 80 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~24/17 = 594.643{{c}}
Optimal tunings:
* WE: ~2 = 1199.9179{{c}}, ~17/12 = 605.3156{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3567{{c}}


{{Optimal ET sequence|legend=0| 111, 113, 224 }}
{{Optimal ET sequence|legend=0| 111, 113, 224 }}


Badness (Smith): 0.012858
Badness (Sintel): 1.57
 
== Subsedia ==
The generator for subsedia (10 & 111) is 0.5 cents flat of [[15/14]]-wide semitone and tempers out the mirkwai comma and [[buzzardsma]]. In this temperament, three generators makes ~[[16/13]], five of them equals ~[[24/17]], twelve of them equals ~[[16/7]], sixteen of them equals ~[[3/1]], and 45 of them equals ~22/1.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 16875/16807, 65536/64827
 
{{Mapping|legend=1| 1 0 5 4 | 0 16 -27 -12 }}
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~15/14 = 118.965{{c}}
 
{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232d }}
 
[[Badness]] (Smith): 0.157658
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 540/539, 1375/1372, 65536/64827
 
Mapping: {{mapping| 1 0 5 4 -1 | 0 16 -27 -12 45 }}
 
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/14 = 118.968{{c}}
 
{{Optimal ET sequence|legend=0| 10, 101, 111, 121, 232d }}
 
Badness (Smith): 0.066838
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 352/351, 540/539, 676/675, 1375/1372
 
Mapping: {{mapping| 1 0 5 4 -1 4 | 0 16 -27 -12 45 -3 }}
 
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/14 = 118.968{{c}}
 
{{Optimal ET sequence|legend=0| 10, 101, 111, 121, 232d }}
 
Badness (Smith): 0.031635
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 256/255, 352/351, 442/441, 540/539, 715/714
 
Mapping: {{mapping| 1 0 5 4 -1 4 3 | 0 16 -27 -12 45 -3 11 }}
 
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/14 = 118.968{{c}}
 
{{Optimal ET sequence|legend=0| 10, 101, 111, 121, 232dg }}
 
Badness (Smith): 0.019707
 
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 256/255, 352/351, 400/399, 442/441, 456/455, 715/714
 
Mapping: {{mapping| 1 0 5 4 -1 4 3 10 | 0 16 -27 -12 45 -3 11 -58 }}
 
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/14 = 118.964{{c}}
 
{{Optimal ET sequence|legend=0| 10, 101h, 111, 121, 232dg }}
 
Badness (Smith): 0.017935


== Hemiseptisix ==
== Hemiseptisix ==
The name ''hemiseptisix'' means a half of septimal major sixth ([[12/7]]). The hemiseptisix temperament (103 & 121) tempers out the mirkwai comma and 95703125/95551488 (''pontiqak'' comma, lazozotritriyo) in the 7-limit. [[224edo]] provides an excellent tuning for 7-, 11-, and 13-limit hemiseptisix.
Hemiseptisix tempers out the mirkwai comma and 95703125/95551488 (pontiqak comma) in the 7-limit, and may be described as the {{nowrap| 103 & 121 }} temperament. [[224edo]] provides an excellent tuning for 7-, 11-, and 13-limit hemiseptisix. Hemiseptisix was named by [[Xenllium]] in 2021; the name ''hemiseptisix'' refers to a half of septimal major sixth ([[12/7]]).  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 440: Line 447:
[[Comma list]]: 16875/16807, 95703125/95551488
[[Comma list]]: 16875/16807, 95703125/95551488


{{Mapping|legend=1| 1 34 17 34 | 0 -53 -24 -51 }}
{{Mapping|legend=1| 1 -19 -7 -17 | 0 53 24 51 }}
: mapping generators: ~2, ~75/49
: mapping generators: ~2, ~98/75


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~98/75 = 466.071{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.2693{{c}}, ~98/75 = 466.0801{{c}}
: [[error map]]: {{val| +0.023 -0.149 -0.553 +0.866 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~98/75 = 466.0715{{c}}
: error map: {{val| 0.000 -0.167 -0.598 +0.819 }}


{{Optimal ET sequence|legend=1| 103, 121, 224 }}
{{Optimal ET sequence|legend=1| 103, 121, 224 }}


[[Badness]] (Smith): 0.162826
[[Badness]] (Sintel): 4.12


=== 11-limit ===
=== 11-limit ===
Line 454: Line 465:
Comma list: 540/539, 1375/1372, 2734375/2725888
Comma list: 540/539, 1375/1372, 2734375/2725888


Mapping: {{mapping| 1 34 17 34 53 | 0 -53 -24 -51 -81 }}
Mapping: {{mapping| 1 -19 -7 -17 -28 | 0 53 24 51 81 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~55/42 = 466.070{{c}}
Optimal tunings:
* WE: ~2 = 1200.0183{{c}}, ~55/42 = 466.0767{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~55/42 = 466.0699{{c}}


{{Optimal ET sequence|legend=0| 103, 121, 224 }}
{{Optimal ET sequence|legend=0| 103, 121, 224 }}


Badness (Smith): 0.043381
Badness (Sintel): 1.43


=== 13-limit ===
=== 13-limit ===
Line 467: Line 480:
Comma list: 540/539, 625/624, 1375/1372, 2200/2197
Comma list: 540/539, 625/624, 1375/1372, 2200/2197


Mapping: {{mapping| 1 34 17 34 53 30 | 0 -53 -24 -51 -81 -43 }}
Mapping: {{mapping| 1 -19 -7 -17 -28 -13 | 0 53 24 51 81 43 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~55/42 = 466.071{{c}}
Optimal tunings:
* WE: ~2 = 1199.9784{{c}}, ~55/42 = 466.0622{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~55/42 = 466.0703{{c}}


{{Optimal ET sequence|legend=0| 103, 121, 224 }}
{{Optimal ET sequence|legend=0| 103, 121, 224 }}


Badness (Smith): 0.021127
Badness (Sintel): 0.873


=== 17-limit ===
=== 17-limit ===
Line 480: Line 495:
Comma list: 375/374, 540/539, 625/624, 715/714, 2200/2197
Comma list: 375/374, 540/539, 625/624, 715/714, 2200/2197


Mapping: {{mapping| 1 34 17 34 53 30 31 | 0 -53 -24 -51 -81 -43 -44 }}
Mapping: {{mapping| 1 -19 -7 -17 -28 -13 -13 | 0 53 24 51 81 43 44 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~17/13 = 466.074{{c}}
Optimal tunings:
* WE: ~2 = 1199.8544{{c}}, ~17/13 = 466.0174{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~17/13 = 466.0718{{c}}


{{Optimal ET sequence|legend=0| 103, 121, 224 }}
{{Optimal ET sequence|legend=0| 103, 121, 224 }}


Badness (Smith): 0.018611
Badness (Sintel): 0.948


== Browser ==
== Browser ==
{{See also| Sensipent family }}
{{See also| Sensipent family }}


This can also be considered a [[non-over-1 temperament]], with considerable scope for harmony in the 2.5/3.7/3.11/3.13/3.17/3 subgroup with MOSes of 8, 15, 23, and 31 notes despite no harmonics from the root. It can be considered a detemperament of 8et, with a generator very slightly sharp of 1\8.
Named by [[Xenllium]] in 2022, browser may be described as the {{nowrap| 103 & 111 }} temperament.
 
This can also be considered a [[non-over-1 temperament]], with considerable scope for harmony in the 2.5/3.7/3.11/3.13/3.17/3 subgroup with mos scales of 8, 15, 23, and 31 notes despite no harmonics from the root. It can be considered a detemperament of 8d-et, with a generator very slightly flat of 7\8.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 497: Line 516:
[[Comma list]]: 16875/16807, 78732/78125
[[Comma list]]: 16875/16807, 78732/78125


{{Mapping|legend=1| 1 6 8 10 | 0 -35 -45 -57 }}
{{Mapping|legend=1| 1 -29 -37 -47 | 0 35 45 57 }}
: mapping generators: ~2, ~90/49


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~49/45 = 151.399{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9313{{c}}, ~90/49 = 1048.5414{{c}}
: [[error map]]: {{val| -0.069 -1.013 +0.592 +1.264 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~90/49 = 1048.5998{{c}}
: error map: {{val| 0.000 -0.962 +0.677 +1.362 }}


{{Optimal ET sequence|legend=1| 103, 111, 214 }}
{{Optimal ET sequence|legend=1| 103, 111, 214 }}


[[Badness]] (Smith): 0.180645
[[Badness]] (Sintel): 4.57


=== 11-limit ===
=== 11-limit ===
Line 510: Line 534:
Comma list: 540/539, 1375/1372, 78732/78125
Comma list: 540/539, 1375/1372, 78732/78125


Mapping: {{mapping| 1 6 8 10 8 | 0 -35 -45 -57 -36 }}
Mapping: {{mapping| 1 -29 -37 -47 -28 | 0 35 45 57 36 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 151.405{{c}}
Optimal tunings:
* WE: ~2 = 1200.1344{{c}}, ~11/6 = 1048.7124{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/6 = 1048.5981{{c}}


{{Optimal ET sequence|legend=0| 103, 214 }}
{{Optimal ET sequence|legend=0| 103, 214 }}


Badness (Smith): 0.057634
Badness (Sintel): 1.91


=== 13-limit ===
=== 13-limit ===
Line 523: Line 549:
Comma list: 351/350, 540/539, 847/845, 1375/1372
Comma list: 351/350, 540/539, 847/845, 1375/1372


Mapping: {{mapping| 1 6 8 10 8 9 | 0 -35 -45 -57 -36 -42 }}
Mapping: {{mapping| 1 -29 -37 -47 -28 -33 | 0 35 45 57 36 42 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 151.403{{c}}
Optimal tunings:
* WE: ~2 = 1200.1344{{c}}, ~11/6 = 1048.7124{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/6 = 1048.5984{{c}}


{{Optimal ET sequence|legend=0| 103, 111, 214 }}
{{Optimal ET sequence|legend=0| 103, 111, 214 }}


Badness (Smith): 0.028822
Badness (Sintel): 1.19


=== 17-limit ===
=== 17-limit ===
Line 536: Line 564:
Comma list: 351/350, 540/539, 561/560, 715/714, 847/845
Comma list: 351/350, 540/539, 561/560, 715/714, 847/845


Mapping: {{mapping| 1 6 8 10 8 9 8 | 0 -35 -45 -57 -36 -42 -31 }}
Mapping: {{mapping| 1 -29 -37 -47 -28 -33 -23 | 0 35 45 57 36 42 31 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 151.397{{c}}
Optimal tunings:
* WE: ~2 = 1199.9191{{c}}, ~11/6 = 1048.5324{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/6 = 1048.6014{{c}}


{{Optimal ET sequence|legend=0| 103, 111, 214 }}
{{Optimal ET sequence|legend=0| 103, 111, 214 }}


Badness (Smith): 0.020384
Badness (Sintel): 1.04


=== 19-limit ===
=== 19-limit ===
Line 549: Line 579:
Comma list: 324/323, 351/350, 456/455, 495/494, 540/539, 715/714
Comma list: 324/323, 351/350, 456/455, 495/494, 540/539, 715/714


Mapping: {{mapping| 1 6 8 10 8 9 8 18 | 0 -35 -45 -57 -36 -42 -31 -109 }}
Mapping: {{mapping| 1 -29 -37 -47 -28 -33 -23 -91 | 0 35 45 57 36 42 31 109 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 151.396{{c}}
Optimal tunings:
* WE: ~2 = 1199.9145{{c}}, ~11/6 = 1048.5290{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/6 = 1048.6021{{c}}


{{Optimal ET sequence|legend=0| 103h, 111, 214 }}
{{Optimal ET sequence|legend=0| 103h, 111, 214 }}


Badness (Smith): 0.017570
Badness (Sintel): 1.07


== Grazer ==
== Grazer ==
Named by [[Xenllium]] in 2022, grazer may be described as the {{nowrap| 113 & 121 }} temperament.
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 16875/16807, 1071875/1062882
[[Comma list]]: 16875/16807, 1071875/1062882


{{Mapping|legend=1| 1 34 47 58 | 0 -37 -51 -63 }}
{{Mapping|legend=1| 1 -3 -4 -5 | 0 37 51 63 }}
: mapping generators: ~2, ~90/49
: mapping generators: ~2, ~49/45


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~49/45 = 148.719{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0310{{c}}, ~49/45 = 148.7229{{c}}
: [[error map]]: {{val| +0.031 +0.700 -1.561 +0.563 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/45 = 148.7198{{c}}
: error map: {{val| 0.000 +0.676 -1.606 +0.519 }}


{{Optimal ET sequence|legend=1| 113, 121, 234 }}
{{Optimal ET sequence|legend=1| 113, 121, 234 }}


[[Badness]] (Smith): 0.217166
[[Badness]] (Sintel): 5.50


=== 11-limit ===
=== 11-limit ===
Line 576: Line 614:
Comma list: 540/539, 1375/1372, 218750/216513
Comma list: 540/539, 1375/1372, 218750/216513


Mapping: {{mapping| 1 34 47 58 35 | 0 -37 -51 -63 -36 }}
Mapping: {{mapping| 1 -3 -4 -5 -1 | 0 37 51 63 36 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 148.729{{c}}
Optimal tunings:
* WE: ~2 = 1199.7242{{c}}, ~12/11 = 148.6946{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 148.7230{{c}}


{{Optimal ET sequence|legend=0| 113, 121, 234, 355e, 589cee }}
{{Optimal ET sequence|legend=0| 113, 121, 234 }}


Badness (Smith): 0.076062
Badness (Sintel): 2.51


=== 13-limit ===
=== 13-limit ===
Line 589: Line 629:
Comma list: 325/324, 364/363, 540/539, 2200/2197
Comma list: 325/324, 364/363, 540/539, 2200/2197


Mapping: {{mapping| 1 34 47 58 35 44 | 0 -37 -51 -63 -36 -46 }}
Mapping: {{mapping| 1 -3 -4 -5 -1 -2 | 0 37 51 63 36 46 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 148.729{{c}}
Optimal tunings:
* WE: ~2 = 1199.7257{{c}}, ~12/11 = 148.6947{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 148.7230{{c}}


{{Optimal ET sequence|legend=0| 113, 121, 234, 355e, 589cee }}
{{Optimal ET sequence|legend=0| 113, 121, 234 }}


Badness (Smith): 0.036248
Badness (Sintel): 1.50


=== 17-limit ===
=== 17-limit ===
Line 602: Line 644:
Comma list: 325/324, 364/363, 540/539, 595/594, 2000/1989
Comma list: 325/324, 364/363, 540/539, 595/594, 2000/1989


Mapping: {{mapping| 1 34 47 58 35 44 33 | 0 -37 -51 -63 -36 -46 -33 }}
Mapping: {{mapping| 1 -3 -4 -5 -1 -2 0 | 0 37 51 63 36 46 33 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 148.735{{c}}
Optimal tunings:
* WE: ~2 = 1199.5690{{c}}, ~12/11 = 148.6815{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 148.7267{{c}}


{{Optimal ET sequence|legend=0| 113, 121, 234g, 355eg }}
{{Optimal ET sequence|legend=0| 113, 121, 234g }}


Badness (Smith): 0.025410
Badness (Sintel): 1.29


=== 19-limit ===
=== 19-limit ===
Line 615: Line 659:
Comma list: 325/324, 364/363, 400/399, 540/539, 595/594, 665/663
Comma list: 325/324, 364/363, 400/399, 540/539, 595/594, 665/663


Mapping: {{mapping| 1 34 47 58 35 44 33 6 | 0 -37 -51 -63 -36 -46 -33 -2 }}
Mapping: {{mapping| 1 -3 -4 -5 -1 -2 0 4 | 0 37 51 63 36 46 33 2 }}
 
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 148.727{{c}}


{{Optimal ET sequence|legend=0| 113, 121, 234g, 355eg, 589ceegg }}
Optimal tunings:
* WE: ~2 = 1199.7269{{c}}, ~12/11 = 148.6928{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 148.7227{{c}}


Badness (Smith): 0.022574
{{Optimal ET sequence|legend=0| 113, 121, 234g }}


== References ==
Badness (Sintel): 1.37


[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Mirkwai clan| ]] <!-- main article -->
[[Category:Mirkwai clan| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Canopic_clan"