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Amity family: Difference between revisions

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{{Main| Amity }}
{{Main| 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. Its [[ploidacot]] is gamma-pentacot. 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.  
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.  
 
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.  


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.  
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.  
Line 13: Line 15:
[[Comma list]]: 1600000/1594323
[[Comma list]]: 1600000/1594323


{{Mapping|legend=1| 1 3 6 | 0 -5 -13 }}
{{Mapping|legend=1| 1 -2 -7 | 0 5 13 }}
: mapping generators: ~2, ~243/200
: mapping generators: ~2, ~400/243


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~243/200 = 339.537{{c}}
* [[WE]]: ~2 = 1199.9135{{c}}, ~400/243 = 860.4191{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~243/200 = 339.519{{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, 258, 1085, 1343, 1601, 1859b, 2117bc }}
{{Optimal ET sequence|legend=1| 7, 32c, 39, 46, 53, 152, 205, 463, 668, 873 }}


[[Badness]] (Smith): 0.021960
[[Badness]] (Sintel): 0.515


=== Overview to extensions ===
=== Overview to extensions ===
Line 42: Line 46:
[[Comma list]]: 4375/4374, 5120/5103
[[Comma list]]: 4375/4374, 5120/5103


{{Mapping|legend=1| 1 3 6 -2 | 0 -5 -13 17 }}
{{Mapping|legend=1| 1 -2 -7 15 | 0 5 13 -17 }}


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~128/105 = 339.446{{c}}
* [[WE]]: ~2 = 1199.6100{{c}}, ~105/64 = 860.2881{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~128/105 = 339.432{{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 }}


{{Optimal ET sequence|legend=1| 7, 32cd, 39, 46, 53, 99, 152, 251, 905bcdd }}
{{Optimal ET sequence|legend=1| 7, 39, 46, 53, 99, 152, 251, 350, 601cd, 905bcdd }}


[[Badness]] (Smith): 0.023649
[[Badness]] (Sintel): 0.598


=== 11-limit ===
=== 11-limit ===
Line 57: Line 63:
Comma list: 540/539, 4375/4374, 5120/5103
Comma list: 540/539, 4375/4374, 5120/5103


Mapping: {{mapping| 1 3 6 -2 21 | 0 -5 -13 17 -62 }}
Mapping: {{mapping| 1 -2 -7 15 -41 | 0 5 13 -17 62 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000{{c}}, ~128/105 = 339.485{{c}}
* WE: ~2 = 1199.5961{{c}}, ~105/64 = 860.2460{{c}}
* POTE: ~2 = 1200.000{{c}}, ~128/105 = 339.464{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~105/64 = 860.5314{{c}}


{{Optimal ET sequence|legend=0| 46e, 53, 99e, 152, 357d, 509dd, 661dd }}
{{Optimal ET sequence|legend=0| 46e, 53, 99e, 152, 555dee, 707ddee, 859bddee }}


Badness (Smith): 0.031506
Badness (Sintel): 1.04


==== 13-limit ====
==== 13-limit ====
Line 72: Line 78:
Comma list: 352/351, 540/539, 625/624, 729/728
Comma list: 352/351, 540/539, 625/624, 729/728


Mapping: {{mapping| 1 3 6 -2 21 17 | 0 -5 -13 17 -62 -47 }}
Mapping: {{mapping| 1 -2 -7 15 -41 -30 | 0 5 13 -17 62 47 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000{{c}}, ~128/105 = 339.508{{c}}
* WE: ~2 = 1199.5437{{c}}, ~105/64 = 860.1922{{c}}
* POTE: ~2 = 1200.000{{c}}, ~128/105 = 339.481{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~105/64 = 860.5140{{c}}


{{Optimal ET sequence|legend=0| 46ef, 53, 99ef, 152f, 205 }}
{{Optimal ET sequence|legend=0| 46ef, 53, 99ef, 152f }} *


Badness (Smith): 0.028008
<nowiki/>* optimal patent val: 205
 
Badness (Sintel): 1.16


==== 17-limit ====
==== 17-limit ====
Line 87: Line 95:
Comma list: 256/255, 352/351, 375/374, 540/539, 729/728
Comma list: 256/255, 352/351, 375/374, 540/539, 729/728


Mapping: {{mapping| 1 3 6 -2 21 17 -1 | 0 -5 -13 17 -62 -47 18 }}
Mapping: {{mapping| 1 -2 -7 15 -41 -30 17 | 0 5 13 -17 62 47 -18 }}


Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~17/14 = 339.496{{c}}
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, 205gg }}
{{Optimal ET sequence|legend=0| 46ef, 53, 99ef, 152fg }}


Badness (Smith): 0.026201
Badness (Sintel): 1.33


==== 19-limit ====
==== 19-limit ====
Line 100: Line 110:
Comma list: 256/255, 324/323, 352/351, 375/374, 400/399, 456/455
Comma list: 256/255, 324/323, 352/351, 375/374, 400/399, 456/455


Mapping: {{mapping| 1 3 6 -2 21 17 -1 15 | 0 -5 -13 17 -62 -47 18 -38 }}
Mapping: {{mapping| 1 -2 -7 15 -41 -30 17 -23 | 0 5 13 -17 62 47 -18 38 }}


Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~17/14 = 339.501{{c}}
Optimal tunings:
* WE: ~2 = 1199.3361{{c}}, ~28/17 = 860.0605{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~28/17 = 860.5310{{c}}


{{Optimal ET sequence|legend=0| 46efh, 53, 99ef, 152fg, 205gg }}
{{Optimal ET sequence|legend=0| 46efh, 53, 99ef, 152fg }}


Badness (Smith): 0.018782
Badness (Sintel): 1.14


=== Hitchcock ===
=== Hitchcock ===
Line 113: Line 125:
Comma list: 121/120, 176/175, 2200/2187
Comma list: 121/120, 176/175, 2200/2187


Mapping: {{mapping| 1 3 6 -2 6 | 0 -5 -13 17 -9 }}
Mapping: {{mapping| 1 -2 -7 15 -3 | 0 5 13 -17 9 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000{{c}}, ~11/9 = 339.390{{c}}
* WE: ~2 = 1199.9979{{c}}, ~18/11 = 860.6089{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/9 = 339.390{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~18/11 = 860.6104{{c}}


{{Optimal ET sequence|legend=0| 7, 25cdde, 32cd, 39, 46, 53, 99 }}
{{Optimal ET sequence|legend=0| 7, 39, 46, 53, 99 }}


Badness (Smith): 0.035187
Badness (Sintel): 1.16


==== 13-limit ====
==== 13-limit ====
Line 128: Line 140:
Comma list: 121/120, 169/168, 176/175, 325/324
Comma list: 121/120, 169/168, 176/175, 325/324


Mapping: {{mapping| 1 3 6 -2 6 2 | 0 -5 -13 17 -9 6 }}
Mapping: {{mapping| 1 -2 -7 15 -3 8 | 0 5 13 -17 9 -6 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000{{c}}, ~11/9 = 339.411{{c}}
* WE: ~2 = 1200.2037{{c}}, ~18/11 = 860.5820{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/9 = 339.419{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~18/11 = 860.7268{{c}}


{{Optimal ET sequence|legend=0| 7, 25cddef, 32cd, 39, 46, 53, 99 }}
{{Optimal ET sequence|legend=0| 7, 39, 46, 53, 99 }}


Badness (Smith): 0.022448
Badness (Sintel): 0.928


==== 17-limit ====
==== 17-limit ====
Line 143: Line 155:
Comma list: 121/120, 154/153, 169/168, 176/175, 273/272
Comma list: 121/120, 154/153, 169/168, 176/175, 273/272


Mapping: {{mapping| 1 3 6 -2 6 2 -1 | 0 -5 -13 17 -9 6 18 }}
Mapping: {{mapping| 1 -2 -7 15 -3 8 17 | 0 5 13 -17 9 -6 -18 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000{{c}}, ~11/9 = 339.366{{c}}
* WE: ~2 = 1200.0179{{c}}, ~18/11 = 860.6472{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/9 = 339.366{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~18/11 = 860.6344{{c}}


{{Optimal ET sequence|legend=0| 7, 25cddefgg, 32cdg, 39, 46, 99 }}
{{Optimal ET sequence|legend=0| 7, 39, 46, 99 }}


Badness (Smith): 0.019395
Badness (Sintel): 0.988


==== 19-limit ====
==== 19-limit ====
Line 158: Line 170:
Comma list: 121/120, 154/153, 169/168, 171/170, 176/175, 190/189
Comma list: 121/120, 154/153, 169/168, 171/170, 176/175, 190/189


Mapping: {{mapping| 1 3 6 -2 6 2 -1 0 | 0 -5 -13 17 -9 6 18 15 }}
Mapping: {{mapping| 1 -2 -7 15 -3 8 17 15 | 0 5 13 -17 9 -6 -18 -15 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000{{c}}, ~11/9 = 339.415{{c}}
* WE: ~2 = 1200.1977{{c}}, ~18/11 = 860.7343{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/9 = 339.407{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~18/11 = 860.5917{{c}}


{{Optimal ET sequence|legend=0| 7, 25cddefgghh, 32cdgh, 39h, 46, 53, 99h }}
{{Optimal ET sequence|legend=0| 7, 46, 53, 99h }}


Badness (Smith): 0.017513
Badness (Sintel): 1.07


=== Stalagmite ===
=== Stalagmite ===
The stalagmite temperament (46 & 99ef) tempers out 441/440 (werckisma) and 896/891 (pentacircle) 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.  
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.  


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 175: Line 187:
Comma list: 441/440, 896/891, 4375/4374
Comma list: 441/440, 896/891, 4375/4374


Mapping: {{mapping| 1 3 6 -2 -7 | 0 -5 -13 17 37 }}
Mapping: {{mapping| 1 -2 -7 15 30 | 0 5 13 -17 -37 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000{{c}}, ~128/105 = 339.314{{c}}
* WE: ~2 = 1199.3915{{c}}, ~105/64 = 860.2240{{c}}
* POTE: ~2 = 1200.000{{c}}, ~128/105 = 339.340{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~105/64 = 860.6649{{c}}


{{Optimal ET sequence|legend=0| 46, 99e, 145 }}
{{Optimal ET sequence|legend=0| 46, 99e, 145, 244e }}


Badness (Smith): 0.040976
Badness (Sintel): 1.35


==== 13-limit ====
==== 13-limit ====
Line 190: Line 202:
Comma list: 196/195, 352/351, 364/363, 4375/4374
Comma list: 196/195, 352/351, 364/363, 4375/4374


Mapping: {{mapping| 1 3 6 -2 -7 -11 | 0 -5 -13 17 37 52 }}
Mapping: {{mapping| 1 -2 -7 15 30 41 | 0 5 13 -17 -37 -52 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000{{c}}, ~128/105 = 339.277{{c}}
* WE: ~2 = 1199.3577{{c}}, ~105/64 = 860.2259{{c}}
* POTE: ~2 = 1200.000{{c}}, ~128/105 = 339.313{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~105/64 = 860.6929{{c}}


{{Optimal ET sequence|legend=0| 46, 99ef, 145, 191c, 336cef, 527bccef }}
{{Optimal ET sequence|legend=0| 46, 99ef, 145 }}


Badness (Smith): 0.034215
Badness (Sintel): 1.41


==== 17-limit ====
==== 17-limit ====
Line 205: Line 217:
Comma list: 196/195, 256/255, 352/351, 364/363, 1156/1155
Comma list: 196/195, 256/255, 352/351, 364/363, 1156/1155


Mapping: {{mapping| 1 3 6 -2 -7 -11 -1 | 0 -5 -13 17 37 52 18 }}
Mapping: {{mapping| 1 -2 -7 15 30 41 17 | 0 5 13 -17 -37 -52 -18 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000{{c}}, ~17/14 = 339.272{{c}}
* WE: ~2 = 1199.3555{{c}}, ~28/17 = 860.2244{{c}}
* POTE: ~2 = 1200.000{{c}}, ~17/14 = 339.313{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~28/17 = 860.6932{{c}}


{{Optimal ET sequence|legend=0| 46, 99ef, 145, 191c }}
{{Optimal ET sequence|legend=0| 46, 99ef, 145 }}


Badness (Smith): 0.021193
Badness (Sintel): 1.08


==== 19-limit ====
==== 19-limit ====
Line 220: Line 232:
Comma list: 196/195, 256/255, 343/342, 352/351, 364/363, 476/475
Comma list: 196/195, 256/255, 343/342, 352/351, 364/363, 476/475


Mapping: {{mapping| 1 3 6 -2 -7 -11 -1 -13 | 0 -5 -13 17 37 52 18 61 }}
Mapping: {{mapping| 1 -2 -7 15 30 41 17 48 | 0 5 13 -17 -37 -52 -18 -61 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000{{c}}, ~17/14 = 339.282{{c}}
* WE: ~2 = 1199.3599{{c}}, ~28/17 = 860.2161{{c}}
* POTE: ~2 = 1200.000{{c}}, ~17/14 = 339.325{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~28/17 = 860.6820{{c}}


{{Optimal ET sequence|legend=0| 46, 99ef, 145, 191c, 336cefg }}
{{Optimal ET sequence|legend=0| 46, 99ef, 145 }}


Badness (Smith): 0.018864
Badness (Sintel): 1.15


=== Hemiamity ===
=== Hemiamity ===
Line 239: Line 251:


Optimal tunings:
Optimal tunings:
* CTE: ~99/70 = 600.000{{c}}, ~64/55 = 260.566{{c}}
* WE: ~99/70 = 599.8218{{c}}, ~64/55 = 260.4833{{c}}
* POTE: ~99/70 = 600.000{{c}}, ~64/55 = 260.561{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~64/55 = 260.5615{{c}}


{{Optimal ET sequence|legend=0| 14cde, 32cde, 46, 106, 152, 350 }}
{{Optimal ET sequence|legend=0| 46, 106, 152, 350, 502d, 852bcdde }}


Badness (Smith): 0.031307
Badness (Sintel): 1.04


==== 13-limit ====
==== 13-limit ====
Line 254: Line 266:


Optimal tunings:
Optimal tunings:
* CTE: ~99/70 = 600.000{{c}}, ~64/55 = 260.607{{c}}
* WE: ~99/70 = 599.7965{{c}}, ~64/55 = 260.4951{{c}}
* POTE: ~99/70 = 600.000{{c}}, ~64/55 = 260.583{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~64/55 = 260.5872{{c}}


{{Optimal ET sequence|legend=0| 46, 106f, 152f, 198 }}
{{Optimal ET sequence|legend=0| 46, 106f, 152f, 198, 350f, 548cdff }}


Badness (Smith): 0.025784
Badness (Sintel): 1.07


== Accord ==
== Accord ==
Line 266: Line 278:
[[Comma list]]: 126/125, 100352/98415
[[Comma list]]: 126/125, 100352/98415


{{Mapping|legend=1| 1 3 6 11 | 0 -5 -13 -29 }}
{{Mapping|legend=1| 1 -2 -7 -18 | 0 5 13 29 }}


Optimal tunings:
[[Optimal tuning]]s:
* CTE: ~2 = 1200.000{{c}}, ~243/200 = 339.154{{c}}
* [[WE]]: ~2 = 1198.7458{{c}}, ~224/135 = 860.1071{{c}}
* POTE: ~2 = 1200.000{{c}}, ~243/200 = 338.993{{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 }}


{{Optimal ET sequence|legend=1| 7d, 25cddd, 32cdd, 39d, 46 }}
{{Optimal ET sequence|legend=1| 7d, …, 39d, 46, 131c }}


[[Badness]] (Smith): 0.095612
[[Badness]] (Sintel): 2.42


=== 11-limit ===
=== 11-limit ===
Line 281: Line 295:
Comma list: 121/120, 126/125, 896/891
Comma list: 121/120, 126/125, 896/891


Mapping: {{mapping| 1 3 6 11 6 | 0 -5 -13 -29 -9 }}
Mapping: {{mapping| 1 -2 -7 -18 -3 | 0 5 13 29 9 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000{{c}}, ~11/9 = 339.136{{c}}
* WE: ~2 = 1199.3576{{c}}, ~18/11 = 860.4919{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/9 = 339.047{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~18/11 = 860.9224{{c}}


{{Optimal ET sequence|legend=0| 7d, 25cddde, 32cdd, 39d, 46 }}
{{Optimal ET sequence|legend=0| 7d, 39d, 46 }}


Badness (Smith): 0.042468
Badness (Sintel): 1.40


== Houborizic ==
== Houborizic ==
Houborizic tempers out 225/224, the [[marvel comma]], and may be described as the {{nowrap| 53 & 60 }} temperament. It is so named because it is closely related to the '''houboriz tuning''' (generator: 339.774971 cents).
Houborizic tempers out 225/224, the [[marvel comma]], and may be described as the {{nowrap| 53 & 60 }} temperament. It is so named because it is closely related to the ''houboriz tuning'' (generator: 339.774971 cents).


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 298: Line 312:
[[Comma list]]: 225/224, 1250000/1240029
[[Comma list]]: 225/224, 1250000/1240029


{{Mapping|legend=1| 1 3 6 13 | 0 -5 -13 -36 }}
{{Mapping|legend=1| 1 -2 -7 -23 | 0 5 13 36 }}


Optimal tunings:
[[Optimal tuning]]s:
* CTE: ~2 = 1200.000{{c}}, ~243/200 = 339.711{{c}}
* [[WE]]: ~2 = 1200.4959{{c}}, ~400/243 = 860.5922{{c}}
* POTE: ~2 = 1200.000{{c}}, ~243/200 = 339.763{{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, 32cdddd, 39ddd, 46d, 53, 166, 219c, 272c }}
{{Optimal ET sequence|legend=1| 7d, …, 46d, 53, 113, 166 }}


[[Badness]] (Smith): 0.066638
[[Badness]] (Sintel): 1.69


=== 11-limit ===
=== 11-limit ===
Line 313: Line 329:
Comma list: 225/224, 385/384, 1250000/1240029
Comma list: 225/224, 385/384, 1250000/1240029


Mapping: {{mapping| 1 3 6 13 -9 | 0 -5 -13 -36 44 }}
Mapping: {{mapping| 1 -2 -7 -23 35 | 0 5 13 36 -44 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000{{c}}, ~243/200 = 339.751{{c}}
* WE: ~2 = 1200.4973{{c}}, ~400/243 = 860.5930{{c}}
* POTE: ~2 = 1200.000{{c}}, ~243/200 = 339.763{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~400/243 = 860.2386{{c}}


{{Optimal ET sequence|legend=0| 53, 113, 166, 551ccee }}
{{Optimal ET sequence|legend=0| 53, 113, 166 }}


Badness (Smith): 0.067891
Badness (Sintel): 2.24


==== 13-limit ====
==== 13-limit ====
Line 328: Line 344:
Comma list: 225/224, 325/324, 385/384, 2200/2197
Comma list: 225/224, 325/324, 385/384, 2200/2197


Mapping: {{mapping| 1 3 6 13 -9 2 | 0 -5 -13 -36 44 6 }}
Mapping: {{mapping| 1 -2 -7 -23 35 8 | 0 5 13 36 -44 -6 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000{{c}}, ~39/32 = 339.754{{c}}
* WE: ~2 = 1200.5022{{c}}, ~64/39 = 860.5964{{c}}
* POTE: ~2 = 1200.000{{c}}, ~39/32 = 339.764{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~64/39 = 860.2378{{c}}


{{Optimal ET sequence|legend=0| 53, 113, 166 }}
{{Optimal ET sequence|legend=0| 53, 113, 166 }}


Badness (Smith): 0.032996
Badness (Sintel): 1.36


=== Houbor ===
=== Houbor ===
Line 343: Line 359:
Comma list: 121/120, 225/224, 2200/2187
Comma list: 121/120, 225/224, 2200/2187


Mapping: {{mapping| 1 3 6 13 6 | 0 -5 -13 -36 -9 }}
Mapping: {{mapping| 1 -2 -7 -23 -3 | 0 5 13 36 9 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000{{c}}, ~11/9 = 339.680{{c}}
* WE: ~2 = 1201.1684{{c}}, ~18/11 = 861.0240{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/9 = 339.814{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~18/11 = 860.2273{{c}}


{{Optimal ET sequence|legend=0| 7d, 32cdddd, 39ddd, 46d, 53 }}
{{Optimal ET sequence|legend=0| 7d, 53, 60e, 113e }}


Badness (Smith): 0.045232
Badness (Sintel): 1.49


==== 13-limit ====
==== 13-limit ====
Line 358: Line 374:
Comma list: 121/120, 225/224, 275/273, 325/324
Comma list: 121/120, 225/224, 275/273, 325/324


Mapping: {{mapping| 1 3 6 13 6 2 | 0 -5 -13 -36 -9 6 }}
Mapping: {{mapping| 1 -2 -7 -23 -3 8 | 0 -5 -13 -36 -9 6 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000{{c}}, ~11/9 = 339.685{{c}}
* WE: ~2 = 1200.9339{{c}}, ~18/11 = 860.8859{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/9 = 339.784{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~18/11 = 860.2376{{c}}


{{Optimal ET sequence|legend=0| 7d, 32cdddd, 39ddd, 46d, 53 }}
{{Optimal ET sequence|legend=0| 7d, 53, 113e }}


Badness (Smith): 0.031331
Badness (Sintel): 1.29


== Paramity ==
== Paramity ==
Line 375: Line 391:
[[Comma list]]: 65625/65536, 1600000/1594323
[[Comma list]]: 65625/65536, 1600000/1594323


{{Mapping|legend=1| 1 3 6 -17 | 0 -5 -13 70 }}
{{Mapping|legend=1| 1 -2 -7 53 | 0 5 13 -70 }}


Optimal tunings:
[[Optimal tuning]]s:
* CTE: ~2 = 1200.000{{c}}, ~243/200 = 339.554{{c}}
* [[WE]]: ~2 = 1200.0199{{c}}, ~400/243 = 860.4612{{c}}
* POTE: ~2 = 1200.000{{c}}, ~243/200 = 339.553{{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 }}
{{Optimal ET sequence|legend=1| 53, 205d, 258, 311, 675, 986, 1297c }}


[[Badness]] (Smith): 0.113655
[[Badness]] (Sintel): 2.88


=== 11-limit ===
=== 11-limit ===
Line 390: Line 408:
Comma list: 6250/6237, 19712/19683, 41503/41472
Comma list: 6250/6237, 19712/19683, 41503/41472


Mapping: {{mapping| 1 3 6 -17 36 | 0 -5 -13 70 -115 }}
Mapping: {{mapping| 1 -2 -7 53 -79 | 0 5 13 -70 115 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000{{c}}, ~243/200 = 339.554{{c}}
* WE: ~2 = 1200.0139{{c}}, ~400/243 = 860.4562{{c}}
* POTE: ~2 = 1200.000{{c}}, ~243/200 = 339.554{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~400/243 = 860.4462{{c}}


{{Optimal ET sequence|legend=0| 53, 205de, 258, 311, 675, 986 }}
{{Optimal ET sequence|legend=0| 53, 258, 311, 675, 986 }}


Badness (Smith): 0.064853
Badness (Sintel): 2.14


=== 13-limit ===
=== 13-limit ===
Line 405: Line 423:
Comma list: 625/624, 2080/2079, 2200/2197, 19712/19683
Comma list: 625/624, 2080/2079, 2200/2197, 19712/19683


Mapping: {{mapping| 1 3 6 -17 36 17 | 0 -5 -13 70 -115 -47 }}
Mapping: {{mapping| 1 -2 -7 53 -79 -30 | 0 5 13 -70 115 47 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000{{c}}, ~243/200 = 339.554{{c}}
* WE: ~2 = 1199.9945{{c}}, ~385/234 = 860.4417{{c}}
* POTE: ~2 = 1200.000{{c}}, ~243/200 = 339.554{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~385/234 = 860.4456{{c}}


{{Optimal ET sequence|legend=0| 53, 205de, 258, 311, 675, 986, 1661cf }}
{{Optimal ET sequence|legend=0| 53, 258, 311, 675, 986 }}


Badness (Smith): 0.030347
Badness (Sintel): 1.25


=== 17-limit ===
=== 17-limit ===
Line 420: Line 438:
Comma list: 625/624, 1225/1224, 2080/2079, 2200/2197, 2431/2430
Comma list: 625/624, 1225/1224, 2080/2079, 2200/2197, 2431/2430


Mapping: {{mapping| 1 3 6 -17 36 17 -31 | 0 -5 -13 70 -115 -47 124 }}
Mapping: {{mapping| 1 -2 -7 53 -79 -30 93 | 0 5 13 -70 115 47 -124 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000{{c}}, ~243/200 = 339.555{{c}}
* WE: ~2 = 1200.0026{{c}}, ~385/234 = 860.4468{{c}}
* POTE: ~2 = 1200.000{{c}}, ~243/200 = 339.555{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~385/234 = 860.4450{{c}}


{{Optimal ET sequence|legend=0| 53, 205deg, 258g, 311, 675, 1661cf, 2336bccf, 3011bccf }}
{{Optimal ET sequence|legend=0| 53, 311, 675 }}


Badness (Smith): 0.024118
Badness (Sintel): 1.23


=== 19-limit ===
=== 19-limit ===
Line 435: Line 453:
Comma list: 625/624, 1225/1224, 1540/1539, 1729/1728, 2080/2079, 2200/2197
Comma list: 625/624, 1225/1224, 1540/1539, 1729/1728, 2080/2079, 2200/2197


Mapping: {{mapping| 1 3 6 -17 36 17 -31 15 | 0 -5 -13 70 -115 -47 124 -38 }}
Mapping: {{mapping| 1 -2 -7 53 -79 -30 93 -23 | 0 5 13 -70 115 47 -124 38 }}


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000{{c}}, ~208/171 = 339.555{{c}}
* WE: ~2 = 1200.0196{{c}}, ~208/171 = 860.4594{{c}}
* POTE: ~2 = 1200.000{{c}}, ~208/171 = 339.555{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~208/171 = 860.4454{{c}}


{{Optimal ET sequence|legend=0| 53, 205deg, 258g, 311, 675, 986, 1661cfh }}
{{Optimal ET sequence|legend=0| 53, 311, 675, 986 }}


Badness (Smith): 0.017420
Badness (Sintel): 1.06


== Bamity ==
== Bamity ==
Retrieved from "https://en.xen.wiki/w/Amity_family"