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The generator for [[amity]] temperament is the acute minor third, which means an ordinary 6/5 minor third raised by an 81/80 comma to 243/200, and from this it derives its name. It tempers out the 5-limit amity comma, 1600000/1594323. It can also be described as the 46&53 temperament, which tempers out [[4375/4374]] and [[5120/5103]] in the 7-limit. [[99edo|99EDO]] is a good tuning for amity, with generator 28/99, and MOS of 11, 18, 25, 32, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you.
{{Technical data page}}
The '''amity family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[amity comma]] ({{monzo|legend=1| 9 -13 15 }}, [[ratio]]: 1600000/1594323).  


Temperaments not discussed here include [[Breedsmic temperaments|amicable]] and [[Hemimage temperaments|chromat]].
== Amity ==
{{Main| Amity }}


= Amity =
The [[generator]] for the amity temperament is the acute minor third, which means the [[6/5]] just minor third raised by a [[syntonic comma]] to [[243/200]], and from this it derives its name. If you are looking for a different kind of neutral third, this could be the temperament for you. However its functional generator is the [[octave complement]] thereof, five of which stack to the [[12/1|12th harmonic]]. Its [[ploidacot]] is thus gamma-pentacot.
{{see also|Amity}}
{{see also|Ragismic microtemperaments #Amity}}


[[Comma]]: 1600000/1594323
It is a member of the [[syntonic–chromatic equivalence continuum]] with {{nowrap| ''n'' {{=}} 5 }}, so it equates an apotome with a stack of five syntonic commas. It is also in the [[schismic–Mercator equivalence continuum]] with {{nowrap| ''n'' {{=}} 5 }}, so unless 53edo is used as a tuning, the schisma is always observed.


[[Mapping]]: [<1 3 6|, <0 -5 -13|]
Amity is a genuine [[microtemperament]] in the 5-limit, with 58\205 being a possible tuning. Another good choice is (64/5)<sup>1/13</sup>, which gives a pure classical major third. [[Mos scale]]s of 11, 18, 25, 32, 39, 46 or 53 notes are available.


[[POTE tuning|POTE generator]]: ~243/200 = 339.519
[[Subgroup]]: 2.3.5


[[EDO|Vals]]: {{Val list| 7, 39, 46, 53, 152, 205, 463, 668, 873 }}
[[Comma list]]: 1600000/1594323


[[Badness]]: 0.021960
{{Mapping|legend=1| 1 -2 -7 | 0 5 13 }}
: mapping generators: ~2, ~400/243
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9135{{c}}, ~400/243 = 860.4191{{c}}
: [[error map]]: {{val| -0.087 +0.314 -0.259 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~400/243 = 860.4726{{c}}
: error map: {{val| 0.000 +0.408 -0.169 }}
 
{{Optimal ET sequence|legend=1| 7, 32c, 39, 46, 53, 152, 205, 463, 668, 873 }}
 
[[Badness]] (Sintel): 0.515
 
=== Overview to extensions ===
The second comma to extend 5-limit amity include [[4375/4374]] for septimal amity, [[65625/65536]] for paramity, [[126/125]] for accord, and [[225/224]] for houborizic. Those all use the same generator as the 5-limit temperament.
 
Bamity adds [[245/243]] with a 1/2-octave period. Hamity adds [[2430/2401]] and splits the generator in two. Gamity adds [[1029/1024]]. Chromat adds [[10976/10935]]. Trinity adds [[703125/702464]]. Those split the generator in three. Amicable adds [[2401/2400]], splitting the generator in four. Witcher adds [[420175/419904]]. Calamity adds [[2100875/2097152]]. Familia adds [[16875/16807]]. Those split the generator in five.
 
== Septimal amity ==
{{Main| Amity }}
 
Septimal amity can be described as the {{nowrap| 46 & 53 }} temperament, which tempers out [[4375/4374]] and [[5120/5103]] in the 7-limit. [[99edo]] is a good tuning, with generator 28\99.
 
[[Subgroup]]: 2.3.5.7


== 7-limit ==
[[Comma list]]: 4375/4374, 5120/5103
[[Comma list]]: 4375/4374, 5120/5103


[[Mapping]]: [&lt;1 3 6 -2|, &lt;0 -5 -13 17|]
{{Mapping|legend=1| 1 -2 -7 15 | 0 5 13 -17 }}


[[Wedgie]]: &lt;&lt;5 13 -17 9 -41 -76||
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.6100{{c}}, ~105/64 = 860.2881{{c}}
: [[error map]]: {{val| -0.390 +0.266 +0.162 +0.426 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~105/64 = 860.5650{{c}}
: error map: {{val| 0.000 +0.870 +1.032 +1.568 }}


[[POTE tuning|POTE generator]]: ~128/105 = 339.432
{{Optimal ET sequence|legend=1| 7, 39, 46, 53, 99, 152, 251, 350, 601cd, 905bcdd }}


[[EDO|Vals]]: {{Val list| 7, 39, 46, 53, 99, 251, 350, 601cd, 951bcdd }}
[[Badness]] (Sintel): 0.598


[[Badness]]: 0.023649
=== 11-limit ===
Subgroup: 2.3.5.7.11


== 11-limit ==
Comma list: 540/539, 4375/4374, 5120/5103
Comma list: 540/539, 4375/4374, 5120/5103


Mapping: [&lt;1 3 6 -2 21|, &lt;0 -5 -13 17 -62|]
Mapping: {{mapping| 1 -2 -7 15 -41 | 0 5 13 -17 62 }}
 
Optimal tunings:
* WE: ~2 = 1199.5961{{c}}, ~105/64 = 860.2460{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~105/64 = 860.5314{{c}}
 
{{Optimal ET sequence|legend=0| 46e, 53, 99e, 152, 555dee, 707ddee, 859bddee }}
 
Badness (Sintel): 1.04
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 352/351, 540/539, 625/624, 729/728
 
Mapping: {{mapping| 1 -2 -7 15 -41 -30 | 0 5 13 -17 62 47 }}
 
Optimal tunings:
* WE: ~2 = 1199.5437{{c}}, ~105/64 = 860.1922{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~105/64 = 860.5140{{c}}
 
{{Optimal ET sequence|legend=0| 46ef, 53, 99ef, 152f }} *


POTE generator: ~128/105 = 339.464
<nowiki/>* optimal patent val: 205


Vals: {{Val list| 53, 99e, 152, 555dee, 707ddee, 859bddee }}
Badness (Sintel): 1.16


Badness: 0.031506
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17


=== 13-limit ===
Comma list: 256/255, 352/351, 375/374, 540/539, 729/728
Comma list: 352/351, 540/539, 625/624, 847/845
 
Mapping: {{mapping| 1 -2 -7 15 -41 -30 17 | 0 5 13 -17 62 47 -18 }}
 
Optimal tunings:
* WE: ~2 = 1199.3376{{c}}, ~28/17 = 860.0617{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~28/17 = 860.5317{{c}}
 
{{Optimal ET sequence|legend=0| 46ef, 53, 99ef, 152fg }}
 
Badness (Sintel): 1.33
 
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 256/255, 324/323, 352/351, 375/374, 400/399, 456/455
 
Mapping: {{mapping| 1 -2 -7 15 -41 -30 17 -23 | 0 5 13 -17 62 47 -18 38 }}


Mapping: [&lt;1 3 6 -2 21 17|, &lt;0 -5 -13 17 -62 -47|]
Optimal tunings:  
* WE: ~2 = 1199.3361{{c}}, ~28/17 = 860.0605{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~28/17 = 860.5310{{c}}


POTE generator: ~128/105 = 339.481
{{Optimal ET sequence|legend=0| 46efh, 53, 99ef, 152fg }}


Vals: {{Val list| 53, 99ef, 152f }}
Badness (Sintel): 1.14


Badness: 0.028008
=== Hitchcock ===
Subgroup: 2.3.5.7.11


== Hitchcock ==
Comma list: 121/120, 176/175, 2200/2187
Comma list: 121/120, 176/175, 2200/2187


Mapping: [&lt;1 3 6 -2 6|, &lt;0 -5 -13 17 -9|]
Mapping: {{mapping| 1 -2 -7 15 -3 | 0 5 13 -17 9 }}


POTE generator: ~11/9 = 339.390
Optimal tunings:
* WE: ~2 = 1199.9979{{c}}, ~18/11 = 860.6089{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~18/11 = 860.6104{{c}}


Vals: {{Val list| 7, 39, 46, 53, 99 }}
{{Optimal ET sequence|legend=0| 7, 39, 46, 53, 99 }}


Badness: 0.035187
Badness (Sintel): 1.16
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


=== 13-limit ===
Comma list: 121/120, 169/168, 176/175, 325/324
Comma list: 121/120, 169/168, 176/175, 325/324


Mapping: [&lt;1 3 6 -2 6 2|, &lt;0 -5 -13 17 -9 6|]
Mapping: {{mapping| 1 -2 -7 15 -3 8 | 0 5 13 -17 9 -6 }}
 
Optimal tunings:
* WE: ~2 = 1200.2037{{c}}, ~18/11 = 860.5820{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~18/11 = 860.7268{{c}}
 
{{Optimal ET sequence|legend=0| 7, 39, 46, 53, 99 }}
 
Badness (Sintel): 0.928
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 121/120, 154/153, 169/168, 176/175, 273/272
 
Mapping: {{mapping| 1 -2 -7 15 -3 8 17 | 0 5 13 -17 9 -6 -18 }}
 
Optimal tunings:
* WE: ~2 = 1200.0179{{c}}, ~18/11 = 860.6472{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~18/11 = 860.6344{{c}}
 
{{Optimal ET sequence|legend=0| 7, 39, 46, 99 }}
 
Badness (Sintel): 0.988
 
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 121/120, 154/153, 169/168, 171/170, 176/175, 190/189
 
Mapping: {{mapping| 1 -2 -7 15 -3 8 17 15 | 0 5 13 -17 9 -6 -18 -15 }}
 
Optimal tunings:
* WE: ~2 = 1200.1977{{c}}, ~18/11 = 860.7343{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~18/11 = 860.5917{{c}}
 
{{Optimal ET sequence|legend=0| 7, 46, 53, 99h }}
 
Badness (Sintel): 1.07
 
=== Stalagmite ===
The stalagmite temperament (46 & 99ef) tempers out 441/440 ([[werckisma]]) and 896/891 ([[pentacircle comma]]) in the 11-limit; [[196/195]], [[352/351]] and [[364/363]] in the 13-limit. "-mite" in the name references amity, and stalagmites being found in caves underground references how it is ''down'' from amity.


POTE generator: ~11/9 = 339.419
Subgroup: 2.3.5.7.11


Vals: {{Val list| 7, 39, 46, 53, 99 }}
Comma list: 441/440, 896/891, 4375/4374


Badness: 0.022448
Mapping: {{mapping| 1 -2 -7 15 30 | 0 5 13 -17 -37 }}
 
Optimal tunings:
* WE: ~2 = 1199.3915{{c}}, ~105/64 = 860.2240{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~105/64 = 860.6649{{c}}
 
{{Optimal ET sequence|legend=0| 46, 99e, 145, 244e }}
 
Badness (Sintel): 1.35
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 196/195, 352/351, 364/363, 4375/4374
 
Mapping: {{mapping| 1 -2 -7 15 30 41 | 0 5 13 -17 -37 -52 }}
 
Optimal tunings:
* WE: ~2 = 1199.3577{{c}}, ~105/64 = 860.2259{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~105/64 = 860.6929{{c}}
 
{{Optimal ET sequence|legend=0| 46, 99ef, 145 }}
 
Badness (Sintel): 1.41
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 196/195, 256/255, 352/351, 364/363, 1156/1155
 
Mapping: {{mapping| 1 -2 -7 15 30 41 17 | 0 5 13 -17 -37 -52 -18 }}
 
Optimal tunings:
* WE: ~2 = 1199.3555{{c}}, ~28/17 = 860.2244{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~28/17 = 860.6932{{c}}
 
{{Optimal ET sequence|legend=0| 46, 99ef, 145 }}
 
Badness (Sintel): 1.08
 
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 196/195, 256/255, 343/342, 352/351, 364/363, 476/475
 
Mapping: {{mapping| 1 -2 -7 15 30 41 17 48 | 0 5 13 -17 -37 -52 -18 -61 }}
 
Optimal tunings:
* WE: ~2 = 1199.3599{{c}}, ~28/17 = 860.2161{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~28/17 = 860.6820{{c}}
 
{{Optimal ET sequence|legend=0| 46, 99ef, 145 }}
 
Badness (Sintel): 1.15
 
=== Hemiamity ===
Subgroup: 2.3.5.7.11


== Hemiamity ==
Comma list: 3025/3024, 4375/4374, 5120/5103
Comma list: 3025/3024, 4375/4374, 5120/5103


Mapping: [&lt;2 1 -1 13 13|, &lt;0 5 13 -17 -14|]
Mapping: {{mapping| 2 1 -1 13 13 | 0 5 13 -17 -14 }}
: mapping generators: ~99/70, ~64/55
 
Optimal tunings:
* WE: ~99/70 = 599.8218{{c}}, ~64/55 = 260.4833{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~64/55 = 260.5615{{c}}
 
{{Optimal ET sequence|legend=0| 46, 106, 152, 350, 502d, 852bcdde }}
 
Badness (Sintel): 1.04
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


POTE generator: ~64/55 = 339.439
Comma list: 352/351, 847/845, 1716/1715, 3025/3024


Vals: {{Val list| 14cde, 46, 106, 152, 350, 502d }}
Mapping: {{mapping| 2 1 -1 13 13 20 | 0 5 13 -17 -14 -29 }}


Badness: 0.031307
Optimal tunings:
* WE: ~99/70 = 599.7965{{c}}, ~64/55 = 260.4951{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~64/55 = 260.5872{{c}}
 
{{Optimal ET sequence|legend=0| 46, 106f, 152f, 198, 350f, 548cdff }}
 
Badness (Sintel): 1.07
 
== Accord ==
Accord tempers out [[126/125]], the starling comma, and may be described as the {{nowrap| 39d & 46 }} temperament.
 
[[Subgroup]]: 2.3.5.7


= Accord =
[[Comma list]]: 126/125, 100352/98415
[[Comma list]]: 126/125, 100352/98415


[[Mapping]]: [&lt;1 3 6 11|, &lt;0 -5 -13 -29|]
{{Mapping|legend=1| 1 -2 -7 -18 | 0 5 13 29 }}


[[Wedgie]]: &lt;&lt;5 13 29 9 32 31||
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1198.7458{{c}}, ~224/135 = 860.1071{{c}}
: [[error map]]: {{val| -1.254 +1.089 +3.858 -3.144 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~224/135 = 860.9433{{c}}
: error map: {{val| 0.000 +2.761 +5.949 -1.471 }}


[[POTE tuning|POTE generator]]: ~243/200 = 338.993
{{Optimal ET sequence|legend=1| 7d, …, 39d, 46, 131c }}


[[EDO|Vals]]: {{Val list| 7d, 46, 131c, 177c }}
[[Badness]] (Sintel): 2.42


[[Badness]]: 0.095612
=== 11-limit ===
Subgroup: 2.3.5.7.11


== 11-limit ==
Comma list: 121/120, 126/125, 896/891
Comma list: 121/120, 126/125, 896/891


Mapping: [&lt;1 3 6 11 6|, &lt;0 -5 -13 -29 -9|]
Mapping: {{mapping| 1 -2 -7 -18 -3 | 0 5 13 29 9 }}


POTE generator: ~11/9 = 339.047
Optimal tunings:
* WE: ~2 = 1199.3576{{c}}, ~18/11 = 860.4919{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~18/11 = 860.9224{{c}}


Vals: {{Val list| 7d, 46, 177c, 223bc, 269bce }}
{{Optimal ET sequence|legend=0| 7d, 39d, 46 }}


Badness: 0.042468
Badness (Sintel): 1.40


= Bamity =
== Houborizic ==
Bamity has a period of half octave and tempers out the sensamagic comma, [[245/243]]. The name "bamity" is a play on the words "bi-" and "amity".
Houborizic tempers out 225/224, the [[marvel comma]], and may be described as the {{nowrap| 53 & 60 }} temperament. It was named by [[Xenllium]] in 2021 for its close relation to the ''houboriz tuning'' (generator: 339.774971 cents).
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 1250000/1240029
 
{{Mapping|legend=1| 1 -2 -7 -23 | 0 5 13 36 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.4959{{c}}, ~400/243 = 860.5922{{c}}
: [[error map]]: {{val| +0.496 +0.014 -2.086 +1.090 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~400/243 = 860.2558{{c}}
: error map: {{val| 0.000 -0.676 -2.989 +0.382 }}
 
{{Optimal ET sequence|legend=1| 7d, …, 46d, 53, 113, 166 }}
 
[[Badness]] (Sintel): 1.69
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 385/384, 1250000/1240029
 
Mapping: {{mapping| 1 -2 -7 -23 35 | 0 5 13 36 -44 }}
 
Optimal tunings:
* WE: ~2 = 1200.4973{{c}}, ~400/243 = 860.5930{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~400/243 = 860.2386{{c}}
 
{{Optimal ET sequence|legend=0| 53, 113, 166 }}
 
Badness (Sintel): 2.24
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 225/224, 325/324, 385/384, 2200/2197
 
Mapping: {{mapping| 1 -2 -7 -23 35 8 | 0 5 13 36 -44 -6 }}
 
Optimal tunings:
* WE: ~2 = 1200.5022{{c}}, ~64/39 = 860.5964{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~64/39 = 860.2378{{c}}
 
{{Optimal ET sequence|legend=0| 53, 113, 166 }}
 
Badness (Sintel): 1.36
 
=== Houbor ===
Subgroup: 2.3.5.7.11
 
Comma list: 121/120, 225/224, 2200/2187
 
Mapping: {{mapping| 1 -2 -7 -23 -3 | 0 5 13 36 9 }}
 
Optimal tunings:
* WE: ~2 = 1201.1684{{c}}, ~18/11 = 861.0240{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~18/11 = 860.2273{{c}}
 
{{Optimal ET sequence|legend=0| 7d, 53, 60e, 113e }}
 
Badness (Sintel): 1.49
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 121/120, 225/224, 275/273, 325/324
 
Mapping: {{mapping| 1 -2 -7 -23 -3 8 | 0 -5 -13 -36 -9 6 }}
 
Optimal tunings:
* WE: ~2 = 1200.9339{{c}}, ~18/11 = 860.8859{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~18/11 = 860.2376{{c}}
 
{{Optimal ET sequence|legend=0| 7d, 53, 113e }}
 
Badness (Sintel): 1.29
 
== Paramity ==
Paramity tempers out the [[horwell comma]] (65625/65536) and [[garischisma]] (33554432/33480783), and may be described as the {{nowrap| 53 & 311 }} temperament. It was named by [[Xenllium]] in 2021, with the prefix ''para-'' signifying its relation to amity.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 65625/65536, 1600000/1594323
 
{{Mapping|legend=1| 1 -2 -7 53 | 0 5 13 -70 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0199{{c}}, ~400/243 = 860.4612{{c}}
: [[error map]]: {{val| +0.020 +0.311 -0.458 -0.055 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~400/243 = 860.4468{{c}}
: error map: {{val| 0.000 +0.279 -0.505 -0.103 }}
 
{{Optimal ET sequence|legend=1| 53, 205d, 258, 311, 675, 986, 1297c }}
 
[[Badness]] (Sintel): 2.88
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 6250/6237, 19712/19683, 41503/41472
 
Mapping: {{mapping| 1 -2 -7 53 -79 | 0 5 13 -70 115 }}
 
Optimal tunings:
* WE: ~2 = 1200.0139{{c}}, ~400/243 = 860.4562{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~400/243 = 860.4462{{c}}
 
{{Optimal ET sequence|legend=0| 53, 258, 311, 675, 986 }}
 
Badness (Sintel): 2.14
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 625/624, 2080/2079, 2200/2197, 19712/19683
 
Mapping: {{mapping| 1 -2 -7 53 -79 -30 | 0 5 13 -70 115 47 }}
 
Optimal tunings:
* WE: ~2 = 1199.9945{{c}}, ~385/234 = 860.4417{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~385/234 = 860.4456{{c}}
 
{{Optimal ET sequence|legend=0| 53, 258, 311, 675, 986 }}
 
Badness (Sintel): 1.25
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 625/624, 1225/1224, 2080/2079, 2200/2197, 2431/2430
 
Mapping: {{mapping| 1 -2 -7 53 -79 -30 93 | 0 5 13 -70 115 47 -124 }}
 
Optimal tunings:
* WE: ~2 = 1200.0026{{c}}, ~385/234 = 860.4468{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~385/234 = 860.4450{{c}}
 
{{Optimal ET sequence|legend=0| 53, 311, 675 }}
 
Badness (Sintel): 1.23
 
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 625/624, 1225/1224, 1540/1539, 1729/1728, 2080/2079, 2200/2197
 
Mapping: {{mapping| 1 -2 -7 53 -79 -30 93 -23 | 0 5 13 -70 115 47 -124 38 }}
 
Optimal tunings:
* WE: ~2 = 1200.0196{{c}}, ~208/171 = 860.4594{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~208/171 = 860.4454{{c}}
 
{{Optimal ET sequence|legend=0| 53, 311, 675, 986 }}
 
Badness (Sintel): 1.06
 
== Bamity ==
Bamity has a period of half octave and tempers out the sensamagic comma, [[245/243]]. The name ''bamity'' is a contraction of ''bi-'' and ''amity''.
 
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 245/243, 64827/64000
[[Comma list]]: 245/243, 64827/64000


[[Mapping]]: [&lt;2 1 -1 3|, &lt;0 5 13 6|]
{{Mapping|legend=1| 2 1 -1 3 | 0 5 13 6 }}
: mapping generators: ~343/240, ~7/6


[[Wedgie]]: &lt;&lt;10 26 12 18 -9 -45||
[[Optimal tuning]]s:
* [[WE]]: ~343/240 = 600.3379{{c}}, ~7/6 = 260.5488{{c}}
: [[error map]]: {{val| +0.676 +1.127 +0.483 -4.519 }}
* [[CWE]]: ~343/240 = 600.0000{{c}}, ~7/6 = 260.4686{{c}}
: error map: {{val| 0.000 +0.388 -0.222 -6.014 }}


[[POTE tuning|POTE generator]]: ~7/6 = 260.402
{{Optimal ET sequence|legend=1| 14c, 32c, 46, 60, 106d }}


[[EDO|Vals]]: {{Val list| 46, 60, 106d }}
[[Badness]] (Sintel): 2.12


[[Badness]]: 0.083601
=== 11-limit ===
Subgroup: 2.3.5.7.11


== 11-limit ==
Comma list: 121/120, 245/243, 441/440
Comma list: 121/120, 245/243, 441/440


Mapping: [&lt;2 1 -1 3 3|, &lt;0 5 13 6 9|]
Mapping: {{mapping| 2 1 -1 3 3 | 0 5 13 6 9 }}


POTE generator: ~7/6 = 260.393
Optimal tunings:
* WE: ~99/70 = 600.5039{{c}}, ~7/6 = 260.6119{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~7/6 = 260.4948{{c}}


Vals: {{Val list| 14c, 46, 60e, 106de }}
{{Optimal ET sequence|legend=0| 14c, 32c, 46, 60e, 106de }}


Badness: 0.035504
Badness (Sintel): 1.17
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


== 13-limit ==
Comma list: 91/90, 121/120, 245/243, 441/440
Comma list: 91/90, 121/120, 245/243, 441/440


Mapping: [&lt;2 1 -1 3 3 0|, &lt;0 5 13 6 9 17|]
Mapping: {{mapping| 2 1 -1 3 3 0 | 0 5 13 6 9 17 }}


POTE generator: ~7/6 = 260.618
Optimal tunings:
* WE: ~55/39 = 600.3896{{c}}, ~7/6 = 260.7874{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~7/6 = 260.6927{{c}}


Vals: {{Val list| 46, 106def, 152def }}
{{Optimal ET sequence|legend=0| 14cf, 32cf, 46, 106deff }}


Badness: 0.030885
Badness (Sintel): 1.28


= Hamity =
== Hamity ==
Hamity has a generator of about 430 cents which represents [[9/7]]. It is also generated by half of acute minor "tenth" (acute minor third of 243/200 plus an octave), and its name is a play on the words "half" and "acute minor tenth".
Hamity has a generator of about 430 cents which represents [[9/7]]. It is also generated by half of acute minor "tenth" (acute minor third of 243/200 plus an octave), and its name is a contraction of ''half'' and ''amity''.
 
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 2430/2401, 4000/3969  
[[Comma list]]: 2430/2401, 4000/3969  


[[Mapping]]: [&lt;1 8 19 15|, &lt;0 -10 -26 -19|]
{{Mapping|legend=1| 1 -2 -7 -4 | 0 10 26 19 }}
: mapping generators: ~2, ~9/7


[[Wedgie]]: &lt;&lt;10 26 19 18 2 -29||
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.5499{{c}}, ~9/7 = 430.0579{{c}}
: [[error map]]: {{val| -0.450 -0.476 -1.657 +4.075 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~9/7 = 430.1958{{c}}
: error map: {{val| 0.000 +0.003 -1.222 +4.895 }}


[[POTE tuning|POTE generator]]: ~9/7 = 430.219
{{Optimal ET sequence|legend=1| 14c, 39d, 53 }}


[[EDO|Vals]]: {{Val list| 14c, 39d, 53 }}
[[Badness]] (Sintel): 1.87


[[Badness]]: 0.073956
=== 11-limit ===
Subgroup: 2.3.5.7.11


== 11-limit ==
Comma list: 99/98, 121/120, 2200/2187
Comma list: 99/98, 121/120, 2200/2187


Mapping: [&lt;1 8 19 15 15|, &lt;0 -10 -26 -19 -18|]
Mapping: {{mapping| 1 -2 -7 -4 -3 | 0 10 26 19 18 }}
 
Optimal tunings:
* WE: ~2 = 1200.2215{{c}}, ~9/7 = 430.2713{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~9/7 = 430.2036{{c}}


POTE generator: ~9/7 = 430.192
{{Optimal ET sequence|legend=0| 14c, 39d, 53 }}


Vals: {{Val list| 14c, 39d, 53 }}
Badness (Sintel): 1.42


Badness: 0.042947
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


== 13-limit ==
Comma list: 99/98, 121/120, 275/273, 572/567
Comma list: 99/98, 121/120, 275/273, 572/567


Mapping: [&lt;1 8 19 15 15 30|, &lt;0 -10 -26 -19 -18 -41|]
Mapping: {{mapping| 1 8 19 15 15 30 | 0 -10 -26 -19 -18 -41 }}


POTE generator: ~9/7 = 430.216
Optimal tunings:
* WE: ~2 = 1200.1379{{c}}, ~9/7 = 430.2658{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~9/7 = 430.2227{{c}}


Vals: {{Val list| 14cf, 53 }}
{{Optimal ET sequence|legend=0| 14cf, 39df, 53 }}


Badness: 0.029753
Badness (Sintel): 1.23


= Houborizic =
== Gamity ==
The ''houborizic'' temperament (53&amp;113, named by [[User:Xenllium|Xenllium]]) tempers out the [[marvel comma]], 225/224. It is so named because it is closely related to the '''houboriz tuning''' (generator: 339.774971 cents).
Gamity tempers out 1029/1024, the [[gamelisma]], and may be described as the {{nowrap| 46 & 113 }} temperament. It splits the interval of the grave major sixth in three. It was named by [[Xenllium]] in 2021 as a contraction of ''gamelismic'' and ''amity''.  


[[Comma list]]: 225/224, 1250000/1240029
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 1029/1024, 1071875/1062882


[[Mapping]]: [&lt;1 3 6 13|, &lt;0 -5 -13 -36|]
{{Mapping|legend=1| 1 -2 -7 4 | 0 15 39 -5 }}
: mapping generators: ~2, ~189/160


[[Wedgie]]: &lt;&lt;5 13 36 9 43 47||
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.4434{{c}}, ~189/160 = 286.8930{{c}}
: [[error map]]: {{val| +0.443 +0.553 -0.591 -1.571 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~189/160 = 286.7955{{c}}
: error map: {{val| 0.000 -0.022 -1.288 -2.804 }}


[[POTE tuning|POTE generator]]: ~243/200 = 339.763
{{Optimal ET sequence|legend=1| 46, 113, 159 }}


[[EDO|Vals]]: {{Val list| 7d, 46d, 53, 113, 166 }}
[[Badness]] (Sintel): 3.18


[[Badness]]: 0.066638
=== 11-limit ===
Subgroup: 2.3.5.7.11


== 11-limit ==
Comma list: 385/384, 441/440, 1071875/1062882
Comma list: 225/224, 385/384, 1250000/1240029


Mapping: [&lt;1 3 6 13 -9|, &lt;0 -5 -13 -36 44|]
Mapping: {{mapping| 1 -2 -7 4 8 | 0 15 39 -5 -19 }}


POTE generator: ~243/200 = 339.763
Optimal tunings:
* WE: ~2 = 1200.3315{{c}}, ~33/28 = 286.8764{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~33/28 = 286.8002{{c}}


Vals: {{Val list| 53, 113, 166 }}
{{Optimal ET sequence|legend=0| 46, 113, 159 }}


Badness: 0.067891
Badness (Sintel): 1.69


=== 13-limit ===
=== 13-limit ===
Comma list: 225/224, 325/324, 385/384, 2200/2197
Subgroup: 2.3.5.7.11.13
 
Comma list: 325/324, 364/363, 385/384, 10985/10976
 
Mapping: {{mapping| 1 -2 -7 4 8 8 | 0 15 39 -5 -19 -18 }}
 
Optimal tunings:
* WE: ~2 = 1200.4248{{c}}, ~13/11 = 286.8906{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/11 = 286.7912{{c}}
 
{{Optimal ET sequence|legend=0| 46, 113, 159, 364df, 523ddff }}
 
Badness (Sintel): 1.25
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 273/272, 325/324, 364/363, 385/384, 3773/3757
 
Mapping: {{mapping| 1 -2 -7 4 8 8 6 | 0 15 39 -5 -19 -18 -8 }}
 
Optimal tunings:
* WE: ~2 = 1200.3287{{c}}, ~13/11 = 286.8731{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/11 = 286.7957{{c}}
 
{{Optimal ET sequence|legend=0| 46, 113, 159 }}
 
Badness (Sintel): 1.12
 
== Trinity ==
Trinity tempers out 703125/702464, the [[meter]], and may be described as the {{nowrap| 152 & 159 }} temperament. [[311edo|178\311]] is a recommendable generator. It was named by [[Xenllium]] in 2022 for the fact that it splits amity's generator in three.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 703125/702464, 1600000/1594323
 
{{Mapping|legend=1| 1 -7 -20 -55 | 0 15 39 101 }}
: mapping generators: ~2, ~125/84


Mapping: [&lt;1 3 6 13 -9 2|, &lt;0 -5 -13 -36 44 6|]
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9474{{c}}, ~125/84 = 686.7921{{c}}
: [[error map]]: {{val| -0.053 +0.295 -0.369 +0.071 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~125/84 = 686.8215{{c}}
: error map: {{val| 0.000 +0.367 -0.276 +0.144 }}


POTE generator: ~39/32 = 339.764
{{Optimal ET sequence|legend=1| 7d, …, 152, 311, 463, 774 }}


Vals: {{Val list| 53, 113, 166 }}
[[Badness]] (Sintel): 3.02


Badness: 0.032996
=== 11-limit ===
Subgroup: 2.3.5.7.11


== Houbor ==
Comma list: 3025/3024, 4000/3993, 19712/19683
Comma list: 121/120, 225/224, 2200/2187


Mapping: [&lt;1 3 6 13 6|, &lt;0 -5 -13 -36 -9|]
Mapping: {{mapping| 1 -7 -20 -55 -16 | 0 15 39 101 34 }}


POTE generator: ~11/9 = 339.814
Optimal tunings:
* WE: ~2 = 1199.9090{{c}}, ~125/84 = 686.7710{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~125/84 = 686.8218{{c}}


Vals: {{Val list| 7d, 46d, 53, 60e, 113e }}
{{Optimal ET sequence|legend=0| 7d, …, 152, 311, 463, 774, 1237e }}


Badness: 0.045232
Badness (Sintel): 1.03


=== 13-limit ===
=== 13-limit ===
Comma list: 121/120, 225/224, 275/273, 325/324
Subgroup: 2.3.5.7.11.13
 
Comma list: 625/624, 1575/1573, 2080/2079, 13720/13689
 
Mapping: {{mapping| 1 -7 -20 -55 -16 -77 | 0 15 39 101 34 141 }}
 
Optimal tunings:
* WE: ~2 = 1199.9531{{c}}, ~52/35 = 686.7909{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~52/35 = 686.8172{{c}}
 
{{Optimal ET sequence|legend=0| 7df, …, 152f, 311 }}
 
Badness (Sintel): 1.09
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 595/594, 625/624, 833/832, 1575/1573, 8624/8619
 
Mapping: {{mapping| 1 -7 -20 -55 -16 -77 39 | 0 15 39 101 34 141 -61 }}
 
Optimal tunings:
* WE: ~2 = 1200.0347{{c}}, ~52/35 = 686.8342{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~52/35 = 686.8146{{c}}
 
{{Optimal ET sequence|legend=0| 152f, 159, 311, 1092cdg }}
 
Badness (Sintel): 1.30
 
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 595/594, 625/624, 833/832, 969/968, 1216/1215, 1575/1573
 
Mapping: {{mapping| 1 -7 -20 -55 -16 -77 39 -61 | 0 15 39 101 34 141 -61 114 }}
 
Optimal tunings:
* WE: ~2 = 1200.0406{{c}}, ~52/35 = 686.8382{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~52/35 = 686.8152{{c}}
 
{{Optimal ET sequence|legend=0| 152f, 159, 311 }}
 
Badness (Sintel): 1.12
 
=== 23-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23
 
Comma list: 595/594, 625/624, 760/759, 833/832, 875/874, 969/968, 1105/1104
 
Mapping: {{mapping| 1 -7 -20 -55 -16 -77 39 -61 -55 | 0 15 39 101 34 141 -61 114 104 }}
 
Optimal tunings:
* WE: ~2 = 1200.0311{{c}}, ~52/35 = 686.8324{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~52/35 = 686.8148{{c}}
 
{{Optimal ET sequence|legend=0| 152f, 159, 311 }}
 
Badness (Sintel): 1.03
 
=== 29-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23.29
 
Comma list: 595/594, 625/624, 760/759, 784/783, 833/832, 875/874, 969/968, 1045/1044
 
Mapping: {{mapping| 1 -7 -20 -55 -16 -77 39 -61 -55 -85 | 0 15 39 101 34 141 -61 114 104 157 }}
 
Optimal tunings:
* WE: ~2 = 1200.0311{{c}}, ~52/35 = 686.8318{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~52/35 = 686.8142{{c}}
 
{{Optimal ET sequence|legend=0| 152fj, 159, 311, 781dh }}
 
Badness (Sintel): 1.01
 
== Chromat ==
Chromat has a period of 1/3 octave and tempers out the [[hemimage comma]] (10976/10935) and the [[triwellisma]].
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 10976/10935, 235298/234375
 
{{Mapping|legend=1| 3 4 5 6 | 0 5 13 16 }}
: mapping generators: ~63/50, ~28/27
 
[[Optimal tuning]]s:
* [[WE]]: ~63/50 = 399.9549{{c}}, ~28/27 = 60.5216{{c}}
: [[error map]]: {{val| -0.135 +0.473 +0.241 -0.751 }}
* [[CWE]]: ~63/50 = 400.0000{{c}}, ~28/27 = 60.5162{{c}}
: error map: {{val| 0.000 +0.626 +0.397 -0.567 }}
 
{{Optimal ET sequence|legend=1| 39d, 60, 99, 258, 357, 456 }}
 
[[Badness]] (Sintel): 1.46
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 441/440, 4375/4356, 10976/10935
 
Mapping: {{mapping| 3 4 5 6 6 | 0 5 13 16 29 }}
 
Optimal tunings:
* WE: ~44/35 = 400.0359{{c}}, ~28/27 = 60.4357{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~28/27 = 60.4375{{c}}
 
{{Optimal ET sequence|legend=0| 60e, 99e, 159, 258 }}
 
Badness (Sintel): 1.67
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 364/363, 441/440, 625/624, 10976/10935
 
Mapping: {{mapping| 3 4 5 6 6 4 | 0 5 13 16 29 47 }}
 
Optimal tunings:
* WE: ~44/35 = 400.0382{{c}}, ~28/27 = 60.4342{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~28/27 = 60.4331{{c}}
 
{{Optimal ET sequence|legend=0| 60eff, 99ef, 159, 258, 417d }}
 
Badness (Sintel): 1.90
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 364/363, 375/374, 441/440, 595/594, 3773/3757
 
Mapping: {{mapping| 3 4 5 6 6 4 10 | 0 5 13 16 29 47 15 }}
 
Optimal tunings:
* WE: ~44/35 = 399.9982{{c}}, ~28/27 = 60.4374{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~28/27 = 60.4375{{c}}
 
{{Optimal ET sequence|legend=0| 99ef, 159, 258, 417dg }}
 
Badness (Sintel): 1.61
 
==== Catachrome ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 325/324, 441/440, 1001/1000, 10976/10935
 
Mapping: {{mapping| 3 4 5 6 6 12 | 0 5 13 16 29 -6 }}
 
Optimal tunings:
* WE: ~44/35 = 400.1386{{c}}, ~28/27 = 60.3986{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~28/27 = 60.3929{{c}}
 
{{Optimal ET sequence|legend=0| 60e, 99e, 159 }}
 
Badness (Sintel): 1.81
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 273/272, 325/324, 375/374, 441/440, 4928/4913
 
Mapping: {{mapping| 3 4 5 6 6 12 10 | 0 5 13 16 29 -6 15 }}
 
Optimal tunings:
* WE: ~44/35 = 400.1115{{c}}, ~28/27 = 60.3935{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~28/27 = 60.3893{{c}}
 
{{Optimal ET sequence|legend=0| 60e, 99e, 159 }}
 
Badness (Sintel): 1.54
 
==== Chromic ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 196/195, 352/351, 729/728, 1875/1859
 
Mapping: {{mapping| 3 4 5 6 6 9 | 0 5 13 16 29 14 }}
 
Optimal tunings:
* WE: ~44/35 = 399.9082{{c}}, ~28/27 = 60.4425{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~28/27 = 60.4380{{c}}
 
{{Optimal ET sequence|legend=0| 60e, 99ef, 159f }}
 
Badness (Sintel): 2.06
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 170/169, 196/195, 352/351, 375/374, 595/594
 
Mapping: {{mapping| 3 4 5 6 6 9 10 | 0 5 13 16 29 14 15 }}
 
Optimal tunings:
* WE: ~44/35 = 399.8948{{c}}, ~28/27 = 60.4435{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~28/27 = 60.4385{{c}}
 
{{Optimal ET sequence|legend=0| 60e, 99ef, 159f }}
 
Badness (Sintel): 1.58
 
=== Hemichromat ===
Subgroup: 2.3.5.7.11
 
Comma list: 3025/3024, 10976/10935, 102487/102400
 
Mapping: {{mapping| 3 4 5 6 10 | 0 10 26 32 5 }}
 
Optimal tunings:
* WE: ~63/50 = 399.9750{{c}}, ~55/54 = 30.2568{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~55/54 = 30.2561{{c}}
 
{{Optimal ET sequence|legend=0| 39d, 120cd, 159, 198, 357, 912b }}
 
Badness (Sintel): 2.22
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 676/675, 1001/1000, 3025/3024, 10976/10935
 
Mapping: {{mapping| 3 4 5 6 10 8 | 0 10 26 32 5 41 }}
 
Optimal tunings:
* WE: ~63/50 = 399.9741{{c}}, ~55/54 = 30.2584{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~55/54 = 30.2577{{c}}
 
{{Optimal ET sequence|legend=0| 39df, 120cdff, 159, 198, 357, 912b }}
 
Badness (Sintel): 1.38
 
== Amicable ==
Amicable tempers out the [[breedsma]] as well as the [[canousma]], and may be described as the {{nowrap| 99 & 311 }} temperament.
 
There are multiple reasonable places for primes 11 and 13 in the interval chain. Amorous (99ef & 311) has these primes placed on the same side of the interval chain so it blends smarter with the lower harmonics. Amical (99 & 311) shows a slightly more accurate but much more complex alternative. Pseudoamorous (99ef & 113) and pseudoamical (99 & 113) are the corresponding low-complexity interpretations. Floral (198 & 212) shares the semi-octave period and the ~21/20 generator with [[harry]], but in a complementary style, including a characteristic flat 11. Finally, humorous (198 & 311) is one of the best extensions out there and it splits the generator in two.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 2401/2400, 1600000/1594323
 
{{Mapping|legend=1| 1 -17 -46 -26 | 0 20 52 31 }}
: mapping generators: ~2, ~40/21
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9463{{c}}, ~40/21 = 1115.0701{{c}}
: [[error map]]: {{val| -0.054 +0.361 -0.195 -0.254 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1187{{c}}
: error map: {{val| 0.000 +0.419 -0.142 -0.146 }}
 
{{Optimal ET sequence|legend=1| 14c, …, 85c, 99, 212, 311, 410, 1131, 1541b }}
 
[[Badness]] (Sintel): 1.15
 
=== Amorous ===
Subgroup: 2.3.5.7.11
 
Comma list: 2401/2400, 6250/6237, 19712/19683
 
Mapping: {{mapping| 1 -17 -46 -26 -135 | 0 20 52 31 149 }}
 
Optimal tunings:
* WE: ~2 = 1200.0380{{c}}, ~40/21 = 1115.1458{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1109{{c}}
 
{{Optimal ET sequence|legend=0| 99e, 212, 311, 1145c, 1456cd }}
 
Badness (Sintel): 1.62
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 625/624, 2080/2079, 2401/2400, 10648/10647
 
apping: {{mapping| 1 -17 -46 -26 -135 -171 | 0 20 52 31 149 188 }}
 
Optimal tunings:
* WE: ~2 = 1200.0543{{c}}, ~40/21 = 1115.1594{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1095{{c}}
 
{{Optimal ET sequence|legend=0| 99ef, 212, 311, 834, 1145c }}
 
Badness (Sintel): 1.43
 
=== Amical ===
Subgroup: 2.3.5.7.11
 
Comma list: 2401/2400, 131072/130977, 1600000/1594323
 
Mapping: {{mapping| 1 -17 -46 -26 154 | 0 20 52 31 -162 }}
 
Optimal tunings:
* WE: ~2 = 1200.0008{{c}}, ~40/21 = 1115.1165{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1157{{c}}
 
{{Optimal ET sequence|legend=0| 99, 212e, 311, 721, 1032, 1343 }}
 
Badness (Sintel): 3.33
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 2080/2079, 2401/2400, 4096/4095, 741125/739206
 
Mapping: {{mapping| 1 -17 -46 -26 154 118 | 0 20 52 31 -162 -123 }}
 
Optimal tunings:
* WE: ~2 = 1199.9926{{c}}, ~40/21 = 1115.1094{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1162{{c}}
 
{{Optimal ET sequence|legend=0| 99, 212ef, 311, 721, 1032 }}
 
Badness (Sintel): 2.06
 
=== Pseudoamorous ===
Subgroup: 2.3.5.7.11
 
Comma list: 243/242, 441/440, 980000/970299
 
Mapping: {{mapping| 1 -17 -46 -26 -43 | 0 20 52 31 50 }}
 
Optimal tunings:
* WE: ~2 = 1199.8269{{c}}, ~21/11 = 1114.9475{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/11 = 1115.1038{{c}}
 
{{Optimal ET sequence|legend=0| 99e, 212e }} *
 
<nowiki/>* optimal patent val: [[113edo|113]]
 
Badness (Sintel): 1.87
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 243/242, 364/363, 441/440, 1875/1859
 
Mapping: {{mapping| 1 -17 -46 -26 -43 -79 | 0 20 52 31 50 89 }}
 
Optimal tunings:
* WE: ~2 = 1200.0182{{c}}, ~40/21 = 1115.1005{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.0840{{c}}
 
{{Optimal ET sequence|legend=0| 99ef, 113, 212ef }}
 
Badness (Sintel): 1.77
 
=== Pseudoamical ===
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 1375/1372, 1600000/1594323
 
Mapping: {{mapping| 1 -17 -46 -26 62 | 0 20 52 31 -63 }}
 
Optimal tunings:
* WE: ~2 = 1200.3436{{c}}, ~40/21 = 1115.4102{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.0925{{c}}
 
{{Optimal ET sequence|legend=0| 99, 113, 212, 961ccdeee }}
 
Badness (Sintel): 2.84
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 325/324, 385/384, 1375/1372, 19773/19712
 
Mapping: {{mapping| 1 -17 -46 -26 62 26 | 0 20 52 31 -63 -24 }}
 
Optimal tunings:
* WE: ~2 = 1200.4212{{c}}, ~40/21 = 1115.4787{{c}}
* CWE: ~2 = 1200.0000{{c}}, 40/21 = 1115.0885{{c}}
 
{{Optimal ET sequence|legend=0| 99, 113, 212, 537cdeff, 749ccdeefff }}
 
Badness (Sintel): 1.94
 
=== Floral ===
Subgroup: 2.3.5.7.11
 
Comma list: 2401/2400, 9801/9800, 14641/14580
 
Mapping: {{mapping| 2 -14 -40 -21 -30 | 0 20 52 31 43 }}
: mapping generators: ~99/70, ~66/49
 
Optimal tunings:
* WE: ~99/70 = 600.0052{{c}}, ~66/49 = 515.1257{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~66/49 = 515.1215{{c}}
 
{{Optimal ET sequence|legend=0| 14c, … 198, 212, 410 }}
 
Badness (Sintel): 2.15
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 676/675, 1001/1000, 1716/1715, 14641/14580
 
Mapping: {{mapping| 2 -14 -40 -21 -30 -63 | 0 20 52 31 43 82 }}
 
Optimal tunings:
* WE: ~99/70 = 599.9923{{c}}, ~66/49 = 515.1184{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~66/49 = 515.1246{{c}}
 
{{Optimal ET sequence|legend=0| 14cf, …, 198, 410 }}
 
Badness (Sintel): 1.53
 
=== Humorous ===
Subgroup: 2.3.5.7.11
 
Comma list: 2401/2400, 3025/3024, 1600000/1594323
 
Mapping: {{mapping| 1 -37 -98 -57 16 | 0 40 104 62 -13 }}
: mapping generators: ~2, ~3993/2048
 
Optimal tunings:
* WE: ~2 = 1199.9189{{c}}, ~3993/2048 = 1157.4826{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3993/2048 = 1157.5602{{c}}
 
{{Optimal ET sequence|legend=0| 85c, 113, 198, 311, 509, 820 }}
 
Badness (Sintel): 1.93
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 2080/2079, 2200/2197, 2401/2400, 3025/3024
 
Mapping: {{mapping| 1 -37 -98 -57 16 -59 | 0 40 104 62 -13 65 }}
 
Optimal tunings:
* WE: ~2 = 1199.8903{{c}}, ~39/20 = 1157.4551{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~39/20 = 1157.5600{{c}}
 
{{Optimal ET sequence|legend=0| 85c, 113, 198, 311, 509, 820f }}
 
Badness (Sintel): 1.17
 
== Witcher ==
Witcher tempers out 420175/419904, the [[wizma]], and may be described as the {{nowrap| 99 & 166 }} temperament.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 420175/419904, 1600000/1594323
 
{{Mapping|legend=1| 1 -7 -20 -2 | 0 25 65 14 }}
: mapping generators: ~2, ~80/63
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.8698{{c}}, ~80/63 = 412.0531{{c}}
: [[error map]]: {{val| -0.130 +0.283 -0.260 +0.178 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~80/63 = 412.0956{{c}}
: error map: {{val| 0.000 +0.435 -0.100 +0.512 }}
 
{{Optimal ET sequence|legend=1| 32c, 67c, 99, 265, 364, 463, 562, 1025 }}
 
[[Badness]] (Sintel): 2.04
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 540/539, 4375/4356, 1240029/1239040
 
Mapping: {{mapping| 1 -7 -20 -2 -35 | 0 25 65 14 112 }}
 
Optimal tunings:
* WE: ~2 = 1199.9909{{c}}, ~80/63 = 412.0758{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~80/63 = 412.0788{{c}}
 
{{Optimal ET sequence|legend=0| 99e, 166, 265 }}
 
Badness (Sintel): 2.73
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 540/539, 729/728, 4375/4356, 10648/10647
 
Mapping: {{mapping| 1 -7 -20 -2 -35 -43 | 0 25 65 14 112 136 }}
 
Optimal tunings:
* WE: ~2 = 1200.0660{{c}}, ~33/26 = 412.0928{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~33/26 = 412.0709{{c}}
 
{{Optimal ET sequence|legend=0| 99ef, 166, 265 }}
 
Badness (Sintel): 2.40
 
=== Semiwitcher ===
Subgroup: 2.3.5.7.11
 
Comma list: 9801/9800, 41503/41472, 585640/583443
 
Mapping: {{mapping| 2 -14 -40 -4 -13 | 0 25 65 14 29 }}
: mapping generators: ~99/70, ~80/63
 
Optimal tunings:
* WE: ~99/70 = 599.9717{{c}}, ~80/63 = 412.0766{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~80/63 = 412.0951{{c}}
 
{{Optimal ET sequence|legend=0| 32c, 166, 198, 364, 562, 926 }}
 
Badness (Sintel): 2.92
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 1716/1715, 2080/2079, 2200/2197, 17303/17280
 
Mapping: {{mapping| 2 11 25 10 16 24 | 0 25 65 14 29 53 }}
 
Optimal tunings:
* WE: ~99/70 = 599.9666{{c}}, ~33/26 = 412.0726{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~33/26 = 412.0944{{c}}
 
{{Optimal ET sequence|legend=0| 32cf, 166, 198, 364, 562, 926 }}
 
Badness (Sintel): 1.57
 
=== Hitch ===
Subgroup: 2.3.5.7.11
 
Comma list: 3025/3024, 117649/117612, 1600000/1594323
 
Mapping: {{mapping| 1 -32 -85 -16 31 | 0 50 130 28 -41 }}
: mapping generators: ~2, ~891/560
 
Optimal tunings:
* WE: ~2 = 1199.8455{{c}}, ~891/560 = 805.9457{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~891/560 = 806.0488{{c}}
 
{{Optimal ET sequence|legend=0| 67c, 198, 463, 661, 1124bde }}
 
Badness (Sintel): 3.09
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 676/675, 1716/1715, 3025/3024, 1600000/1594323
 
Mapping: {{mapping| 1 -32 -85 -16 31 -134 | 0 50 130 28 -41 205 }}
 
Optimal tunings:
* WE: ~2 = 1199.8415{{c}}, ~891/560 = 805.9451{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~891/560 = 806.0508{{c}}
 
{{Optimal ET sequence|legend=0| 198, 463, 661 }}
 
Badness (Sintel): 2.51
 
==== Hitcher ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 2080/2079, 3025/3024, 13720/13689, 28672/28561
 
Mapping: {{mapping| 1 -32 -85 -16 31 -1 | 0 50 130 28 -41 7 }}
 
Optimal tunings:
* WE: ~2 = 1199.7690{{c}}, ~78/49 = 805.8958{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~78/49 = 806.0500{{c}}
 
{{Optimal ET sequence|legend=0| 67c, 198, 463f, 661ff }}
 
Badness (Sintel): 2.46
 
== Calamity ==
Named by [[Flora Canou]] in 2023, calamity tempers out 2100875/2097152, the [[rainy comma]], and may be described as the {{nowrap| 46 & 311 }} temperament. It splits the interval of grave major sixth plus an octave into five.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 1600000/1594323, 2100875/2097152
 
{{Mapping|legend=1| 1 -12 -33 24 | 0 25 65 -39 }}
: mapping generators: ~2, ~35/24
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0332{{c}}, ~35/24 = 652.1081{{c}}
: [[error map]]: {{val| +0.033 +0.348 -0.387 -0.243 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~35/24 = 652.0902{{c}}
: error map: {{val| 0.000 +0.300 -0.452 -0.343 }}
 
{{Optimal ET sequence|legend=1| 46, 219c, 265, 311 }}
 
[[Badness]] (Sintel): 5.01
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 3025/3024, 12005/11979, 131072/130977
 
Mapping: {{mapping| 1 -12 -33 24 29 | 0 25 65 -39 -47 }}
 
Optimal tunings:
* WE: ~2 = 1199.9938{{c}}, ~35/24 = 652.0887{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~35/24 = 652.0920{{c}}
 
{{Optimal ET sequence|legend=0| 46, 219c, 265, 311, 979, 1290 }}


Mapping: [&lt;1 3 6 13 6 2|, &lt;0 -5 -13 -36 -9 6|]
Badness (Sintel): 2.00


POTE generator: ~11/9 = 339.784
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Vals: {{Val list| 7d, 46d, 53, 60e, 113e }}
Comma list: 2080/2079, 3025/3024, 4096/4095, 12005/11979


Badness: 0.031331
Mapping: {{mapping| 1 -12 -33 24 29 45 | 0 25 65 -39 -47 -76 }}


= Gamity =
Optimal tunings:
The ''gamity'' temperament (46&amp;113, named by [[User:Xenllium|Xenllium]]) tempers out the [[1029/1024|gamelisma]], 1029/1024.
* WE: ~2 = 1199.9742{{c}}, ~35/24 = 652.0794{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~35/24 = 652.0934{{c}}


[[Comma list]]: 1029/1024, 1071875/1062882
{{Optimal ET sequence|legend=0| 46, 265, 311, 668, 979, 1290 }}


[[Mapping]]: [&lt;1 -2 -7 4|, &lt;0 15 39 -5|]
Badness (Sintel): 1.39


[[Wedgie]]: &lt;&lt;15 39 -5 27 -50 -121||
== Familia ==
Named by [[Xenllium]] in 2021, familia tempers out 16875/16807, the [[mirkwai comma]], and may be described as the {{nowrap| 113 & 152 }} temperament. It is generated by a major sixth, five of which octave reduced make the original generator of amity.


[[POTE tuning|POTE generator]]: ~189/160 = 286.787
[[Subgroup]]: 2.3.5.7


[[EDO|Vals]]: {{Val list| 46, 113, 159 }}
[[Comma list]]: 16875/16807, 1600000/1594323


[[Badness]]: 0.125733
{{Mapping|legend=1| 1 -17 -46 -47 | 0 25 65 67 }}
: mapping generators: ~2, ~6561/3920


== 11-limit ==
[[Optimal tuning]]s:
Comma list: 385/384, 441/440, 1071875/1062882
* [[WE]]: ~2 = 1199.9165{{c}}, ~6561/3920 = 892.0267{{c}}
: [[error map]]: {{val| -0.084 +0.132 -0.736 +0.888 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~6561/3920 = 892.0871{{c}}
: error map: {{val| 0.000 +0.224 -0.649 +1.013 }}


Mapping: [&lt;1 -2 -7 4 8|, &lt;0 15 39 -5 -19|]
{{Optimal ET sequence|legend=1| 39d, 74cd, 113, 152, 265, 417 }}


POTE generator: ~33/28 = 286.797
[[Badness]] (Sintel): 3.66


Vals: {{Val list| 46, 113, 159 }}
=== 11-limit ===
Subgroup: 2.3.5.7.11


Badness: 0.051111
Comma list: 540/539, 1375/1372, 1600000/1594323


== 13-limit ==
Mapping: {{mapping| 1 -17 -46 -47 -1 | 0 25 65 67 6 }}
Comma list: 325/324, 364/363, 385/384, 10985/10976


Mapping: [&lt;1 -2 -7 4 8 8|, &lt;0 15 39 -5 -19 -18|]
Optimal tunings:
* WE: ~2 = 1199.7927{{c}}, ~2673/1600 = 891.9397{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~2673/1600 = 892.0909{{c}}


POTE generator: ~13/11 = 286.789
{{Optimal ET sequence|legend=0| 39d, 74cd, 113, 152, 417, 569de, 721de }}


Vals: {{Val list| 46, 113, 159 }}
Badness (Sintel): 1.71


Badness: 0.030297
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


== 17-limit ==
Comma list: 540/539, 729/728, 1375/1372, 2205/2197
Comma list: 273/272, 325/324, 364/363, 385/384, 3773/3757


Mapping: [&lt;1 -2 -7 4 8 8 6|, &lt;0 15 39 -5 -19 -18 -8|]
Mapping: {{mapping| 1 -17 -46 -47 -1 -58 | 0 25 65 67 6 83 }}


POTE generator: ~13/11 = 286.795
Optimal tunings:
* WE: ~2 = 1199.7844{{c}}, ~240/143 = 892.9268{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~240/143 = 892.0839{{c}}


Vals: {{Val list| 46, 113, 159 }}
{{Optimal ET sequence|legend=0| 39df, 74cdf, 113, 152f, 265 }}


Badness: 0.022036
Badness (Sintel): 1.59


[[Category:Theory]]
[[Category:Temperament families]]
[[Category:Temperament family]]
[[Category:Amity family| ]] <!-- main article -->
[[Category:Amity family| ]] <!-- main article -->
[[Category:Amity|#]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Amity_family"