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Amity family: Difference between revisions

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The '''amity family''' tempers out the 5-limit [[amity comma]], 1600000/1594323. The generator for the [[amity]] temperament is the acute minor third, which means the 6/5 just minor third raised by an 81/80 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.
{{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).  


== Amity ==
== Amity ==
{{Main| Amity }}
{{Main| Amity }}


In the 5-limit amity is a genuine [[microtemperament]], 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.  
The [[generator]] for the amity temperament is the acute minor third, which means the [[6/5]] just minor third raised by a [[81/80|syntonic comma]] 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.
 
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.  


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
Line 14: Line 17:
: mapping generators: ~2, ~243/200
: mapping generators: ~2, ~243/200


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~243/200 = 339.519
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~243/200 = 339.537
* [[POTE]]: ~2 = 1\1, ~243/200 = 339.519


{{Optimal ET sequence|legend=1| 7, 39, 46, 53, 152, 205, 463, 668, 873 }}
{{Optimal ET sequence|legend=1| 7, 32c, 39, 46, 53, 152, 205, 258, 1085, 1343, 1601, 1859b, 2117bc }}


[[Badness]]: 0.021960
[[Badness]]: 0.021960


=== Overview to extensions ===
=== Overview to extensions ===
The second comma to extend the 5-limit amity include [[4375/4374]] for septimal amity, [[225/224]] for houborizic, 65625/65536 for paramity, [[126/125]] for accord, [[245/243]] for bamity, [[2430/2401]] for hamity, [[1029/1024]] for gamity, [[10976/10935]] for chromat, [[703125/702464]] for trinity, [[2401/2400]] for amicable, [[2100875/2097152]] for calamity, [[420175/419904]] for witch, and [[16875/16807]] for familia.  
The second comma to extend the 5-limit amity include [[4375/4374]] for septimal amity, [[225/224]] for houborizic, 65625/65536 for paramity, [[126/125]] for accord, [[245/243]] for bamity, [[2430/2401]] for hamity, [[1029/1024]] for gamity, [[10976/10935]] for chromat, [[703125/702464]] for trinity, [[2401/2400]] for amicable, [[2100875/2097152]] for calamity, [[420175/419904]] for witcher, and [[16875/16807]] for familia.  


Temperaments discussed elsewhere include:  
Temperaments discussed elsewhere include:  
* ''[[Chromat]]'' → [[Hemimage temperaments #Chromat]] (+10976/10935)
* ''[[Chromat]]'' → [[Hemimage temperaments #Chromat]] (+10976/10935)
* ''[[Witch]]'' → [[Wizmic microtemperaments #Witch]] (+420175/419904)
* ''[[Witcher]]'' → [[Wizmic microtemperaments #Witcher]] (+420175/419904)


The rest are considered below.  
The rest are considered below.  
Line 40: Line 45:
{{Mapping|legend=1| 1 3 6 -2 | 0 -5 -13 17 }}
{{Mapping|legend=1| 1 3 6 -2 | 0 -5 -13 17 }}


{{Multival|legend=1| 5 13 -17 9 -41 -76 }}
Optimal tunings:
 
* CTE: ~2 = 1\1, ~128/105 = 339.446
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~128/105 = 339.432
* POTE: ~2 = 1\1, ~128/105 = 339.432


{{Optimal ET sequence|legend=1| 7, 32c, 39, 46, 53, 99, 251, 350, 601cd, 951bcdd }}
{{Optimal ET sequence|legend=1| 7, 32cd, 39, 46, 53, 99, 152, 251, 905bcdd }}


[[Badness]]: 0.023649
[[Badness]]: 0.023649
Line 55: Line 60:
Mapping: {{mapping| 1 3 6 -2 21 | 0 -5 -13 17 -62 }}
Mapping: {{mapping| 1 3 6 -2 21 | 0 -5 -13 17 -62 }}


Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.464
Optimal tunings:
* CTE: ~2 = 1\1, ~128/105 = 339.485
* POTE: ~2 = 1\1, ~128/105 = 339.464


{{Optimal ET sequence|legend=1| 46e, 53, 99e, 152, 555dee, 707ddee, 859bddee }}
Optimal ET sequence: {{Optimal ET sequence| 46e, 53, 99e, 152, 357d, 509dd, 661dd }}


Badness: 0.031506
Badness: 0.031506
Line 64: Line 71:
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 352/351, 540/539, 625/624, 847/845
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 3 6 -2 21 17 | 0 -5 -13 17 -62 -47 }}


Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.481
Optimal tunings:
* CTE: ~2 = 1\1, ~128/105 = 339.508
* POTE: ~2 = 1\1, ~128/105 = 339.481
 
Optimal ET sequence: {{Optimal ET sequence| 46ef, 53, 99ef, 152f, 205 }}
 
Badness: 0.028008
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
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 }}
 
Optimal tuning (CTE): ~2 = 1\1, ~17/14 = 339.496
 
Optimal ET sequence: {{Optimal ET sequence| 46ef, 53, 99ef, 152fg, 205gg }}
 
Badness: 0.026201
 
==== 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


{{Optimal ET sequence|legend=1| 46ef, 53, 99ef, 152f }} <nowiki>*</nowiki>
Mapping: {{mapping| 1 3 6 -2 21 17 -1 15 | 0 -5 -13 17 -62 -47 18 -38 }}


<nowiki>*</nowiki> optimal patent val: [[205edo|205]]
Optimal tuning (CTE): ~2 = 1\1, ~17/14 = 339.501


Badness: 0.028008
Optimal ET sequence: {{Optimal ET sequence| 46efh, 53, 99ef, 152fg, 205gg }}
 
Badness: 0.018782


=== Hitchcock ===
=== Hitchcock ===
Line 83: Line 116:
Mapping: {{mapping| 1 3 6 -2 6 | 0 -5 -13 17 -9 }}
Mapping: {{mapping| 1 3 6 -2 6 | 0 -5 -13 17 -9 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.390
Optimal tunings:
* CTE: ~2 = 1\1, ~11/9 = 339.390
* POTE: ~2 = 1\1, ~11/9 = 339.390


{{Optimal ET sequence|legend=1| 7, 39, 46, 53, 99 }}
Optimal ET sequence: {{Optimal ET sequence| 7, 25cdde, 32cd, 39, 46, 53, 99 }}


Badness: 0.035187
Badness: 0.035187
Line 96: Line 131:
Mapping: {{mapping| 1 3 6 -2 6 2 | 0 -5 -13 17 -9 6 }}
Mapping: {{mapping| 1 3 6 -2 6 2 | 0 -5 -13 17 -9 6 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.419
Optimal tunings:
* CTE: ~2 = 1\1, ~11/9 = 339.411
* POTE: ~2 = 1\1, ~11/9 = 339.419


{{Optimal ET sequence|legend=1| 7, 39, 46, 53, 99 }}
Optimal ET sequence: {{Optimal ET sequence| 7, 25cddef, 32cd, 39, 46, 53, 99 }}


Badness: 0.022448
Badness: 0.022448
Line 109: Line 146:
Mapping: {{mapping| 1 3 6 -2 6 2 -1 | 0 -5 -13 17 -9 6 18 }}
Mapping: {{mapping| 1 3 6 -2 6 2 -1 | 0 -5 -13 17 -9 6 18 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.366
Optimal tunings:
* CTE: ~2 = 1\1, ~11/9 = 339.366
* POTE: ~2 = 1\1, ~11/9 = 339.366


{{Optimal ET sequence|legend=1| 7, 39, 46, 53, 99 }}
Optimal ET sequence: {{Optimal ET sequence| 7, 25cddefgg, 32cdg, 39, 46, 99 }}


Badness: 0.019395
Badness: 0.019395
Line 122: Line 161:
Mapping: {{mapping| 1 3 6 -2 6 2 -1 0 | 0 -5 -13 17 -9 6 18 15 }}
Mapping: {{mapping| 1 3 6 -2 6 2 -1 0 | 0 -5 -13 17 -9 6 18 15 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.407
Optimal tunings:
* CTE: ~2 = 1\1, ~11/9 = 339.415
* POTE: ~2 = 1\1, ~11/9 = 339.407


{{Optimal ET sequence|legend=1| 7, 39h, 46, 53, 99h }}
Optimal ET sequence: {{Optimal ET sequence| 7, 25cddefgghh, 32cdgh, 39h, 46, 53, 99h }}


Badness: 0.017513
Badness: 0.017513
Line 137: Line 178:
Mapping: {{mapping| 1 3 6 -2 -7 | 0 -5 -13 17 37 }}
Mapping: {{mapping| 1 3 6 -2 -7 | 0 -5 -13 17 37 }}


Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.340
Optimal tunings:
* CTE: ~2 = 1\1, ~128/105 = 339.314
* POTE: ~2 = 1\1, ~128/105 = 339.340


{{Optimal ET sequence|legend=1| 46, 99e, 145, 244e }}
Optimal ET sequence: {{Optimal ET sequence| 46, 99e, 145 }}


Badness: 0.040976
Badness: 0.040976
Line 150: Line 193:
Mapping: {{mapping| 1 3 6 -2 -7 -11 | 0 -5 -13 17 37 52 }}
Mapping: {{mapping| 1 3 6 -2 -7 -11 | 0 -5 -13 17 37 52 }}


Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.313
Optimal tunings:
* CTE: ~2 = 1\1, ~128/105 = 339.277
* POTE: ~2 = 1\1, ~128/105 = 339.313


{{Optimal ET sequence|legend=1| 46, 99ef, 145 }}
Optimal ET sequence: {{Optimal ET sequence| 46, 99ef, 145, 191c, 336cef, 527bccef }}


Badness: 0.034215
Badness: 0.034215
Line 163: Line 208:
Mapping: {{mapping| 1 3 6 -2 -7 -11 -1 | 0 -5 -13 17 37 52 18 }}
Mapping: {{mapping| 1 3 6 -2 -7 -11 -1 | 0 -5 -13 17 37 52 18 }}


Optimal tuning (POTE): ~2 = 1\1, ~17/14 = 339.313
Optimal tunings:
* CTE: ~2 = 1\1, ~17/14 = 339.272
* POTE: ~2 = 1\1, ~17/14 = 339.313


{{Optimal ET sequence|legend=1| 46, 99ef, 145 }}
Optimal ET sequence: {{Optimal ET sequence| 46, 99ef, 145, 191c }}


Badness: 0.021193
Badness: 0.021193
Line 176: Line 223:
Mapping: {{mapping| 1 3 6 -2 -7 -11 -1 -13 | 0 -5 -13 17 37 52 18 61 }}
Mapping: {{mapping| 1 3 6 -2 -7 -11 -1 -13 | 0 -5 -13 17 37 52 18 61 }}


Optimal tuning (POTE): ~2 = 1\1, ~17/14 = 339.325
Optimal tunings:
* CTE: ~2 = 1\1, ~17/14 = 339.282
* POTE: ~2 = 1\1, ~17/14 = 339.325


{{Optimal ET sequence|legend=1| 46, 99ef, 145 }}
Optimal ET sequence: {{Optimal ET sequence| 46, 99ef, 145, 191c, 336cefg }}


Badness: 0.018864
Badness: 0.018864
Line 191: Line 240:
: mapping generators: ~99/70, ~64/55
: mapping generators: ~99/70, ~64/55


Optimal tuning (POTE): ~99/70 = 1\2, ~64/55 = 260.561
Optimal tunings:
* CTE: ~99/70 = 1\2, ~64/55 = 260.566
* POTE: ~99/70 = 1\2, ~64/55 = 260.561


{{Optimal ET sequence|legend=1| 14cde, 46, 106, 152, 350, 502d }}
Optimal ET sequence: {{Optimal ET sequence| 14cde, 32cde, 46, 106, 152, 350 }}


Badness: 0.031307
Badness: 0.031307
Line 204: Line 255:
Mapping: {{mapping| 2 1 -1 13 13 20 | 0 5 13 -17 -14 -29 }}
Mapping: {{mapping| 2 1 -1 13 13 20 | 0 5 13 -17 -14 -29 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~64/55 = 260.583
Optimal tunings:
* CTE: ~99/70 = 1\2, ~64/55 = 260.607
* POTE: ~99/70 = 1\2, ~64/55 = 260.583


{{Optimal ET sequence|legend=1| 46, 106f, 152f, 198, 350f, 548cdff }}
Optimal ET sequence: {{Optimal ET sequence| 46, 106f, 152f, 198 }}


Badness: 0.025784
Badness: 0.025784
Line 217: Line 270:
{{Mapping|legend=1| 1 3 6 11 | 0 -5 -13 -29 }}
{{Mapping|legend=1| 1 3 6 11 | 0 -5 -13 -29 }}


{{Multival|legend=1| 5 13 29 9 32 31 }}
Optimal tunings:
* CTE: ~2 = 1\1, ~243/200 = 339.154
* POTE: ~2 = 1\1, ~243/200 = 338.993


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~243/200 = 338.993
{{Optimal ET sequence|legend=1| 7d, 25cddd, 32cdd, 39d, 46 }}
 
{{Optimal ET sequence|legend=1| 7d, 39d, 46, 131c, 177c }}


[[Badness]]: 0.095612
[[Badness]]: 0.095612
Line 232: Line 285:
Mapping: {{mapping| 1 3 6 11 6 | 0 -5 -13 -29 -9 }}
Mapping: {{mapping| 1 3 6 11 6 | 0 -5 -13 -29 -9 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.047
Optimal tunings:
* CTE: ~2 = 1\1, ~11/9 = 339.136
* POTE: ~2 = 1\1, ~11/9 = 339.047


{{Optimal ET sequence|legend=1| 7d, 39d, 46, 177c, 223bc, 269bce }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 25cddde, 32cdd, 39d, 46 }}


Badness: 0.042468
Badness: 0.042468
Line 247: Line 302:
{{Mapping|legend=1| 1 3 6 13 | 0 -5 -13 -36 }}
{{Mapping|legend=1| 1 3 6 13 | 0 -5 -13 -36 }}


{{Multival|legend=1| 5 13 36 9 43 47 }}
Optimal tunings:
 
* CTE: ~2 = 1\1, ~243/200 = 339.711
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~243/200 = 339.763
* POTE: ~2 = 1\1, ~243/200 = 339.763


{{Optimal ET sequence|legend=1| 7d, 46d, 53, 113, 166 }}
{{Optimal ET sequence|legend=1| 7d, 32cdddd, 39ddd, 46d, 53, 166, 219c, 272c }}


[[Badness]]: 0.066638
[[Badness]]: 0.066638
Line 262: Line 317:
Mapping: {{mapping| 1 3 6 13 -9 | 0 -5 -13 -36 44 }}
Mapping: {{mapping| 1 3 6 13 -9 | 0 -5 -13 -36 44 }}


Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.763
Optimal tunings:
* CTE: ~2 = 1\1, ~243/200 = 339.751
* POTE: ~2 = 1\1, ~243/200 = 339.763


{{Optimal ET sequence|legend=1| 53, 113, 166 }}
Optimal ET sequence: {{Optimal ET sequence| 53, 113, 166, 551ccee }}


Badness: 0.067891
Badness: 0.067891
Line 275: Line 332:
Mapping: {{mapping| 1 3 6 13 -9 2 | 0 -5 -13 -36 44 6 }}
Mapping: {{mapping| 1 3 6 13 -9 2 | 0 -5 -13 -36 44 6 }}


Optimal tuning (POTE): ~2 = 1\1, ~39/32 = 339.764
Optimal tunings:
* CTE: ~2 = 1\1, ~39/32 = 339.754
* POTE: ~2 = 1\1, ~39/32 = 339.764


{{Optimal ET sequence|legend=1| 53, 113, 166 }}
Optimal ET sequence: {{Optimal ET sequence| 53, 113, 166 }}


Badness: 0.032996
Badness: 0.032996
Line 288: Line 347:
Mapping: [{{val| 1 3 6 13 6 }}, {{val| 0 -5 -13 -36 -9 }}]
Mapping: [{{val| 1 3 6 13 6 }}, {{val| 0 -5 -13 -36 -9 }}]


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.814
Optimal tunings:
* CTE: ~2 = 1\1, ~11/9 = 339.680
* POTE: ~2 = 1\1, ~11/9 = 339.814


{{Optimal ET sequence|legend=1| 7d, 46d, 53, 60e, 113e }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 32cdddd, 39ddd, 46d, 53 }}


Badness: 0.045232
Badness: 0.045232
Line 301: Line 362:
Mapping: [{{val| 1 3 6 13 6 2 }}, {{val| 0 -5 -13 -36 -9 6 }}]
Mapping: [{{val| 1 3 6 13 6 2 }}, {{val| 0 -5 -13 -36 -9 6 }}]


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.784
Optimal tunings:
* CTE: ~2 = 1\1, ~11/9 = 339.685
* POTE: ~2 = 1\1, ~11/9 = 339.784


{{Optimal ET sequence|legend=1| 7d, 46d, 53, 60e, 113e }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 32cdddd, 39ddd, 46d, 53 }}


Badness: 0.031331
Badness: 0.031331
Line 314: Line 377:
[[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 3 6 -17 | 0 -5 -13 70 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~243/200 = 339.553
Optimal tunings:
* CTE: ~2 = 1\1, ~243/200 = 339.554
* POTE: ~2 = 1\1, ~243/200 = 339.553


{{Optimal ET sequence|legend=1| 53, 205d, 258, 311, 675, 986, 1297c, 2283bc }}
{{Optimal ET sequence|legend=1| 53, 205d, 258, 311, 675, 986 }}


[[Badness]]: 0.113655
[[Badness]]: 0.113655
Line 329: Line 394:
Mapping: {{mapping| 1 3 6 -17 36 | 0 -5 -13 70 -115 }}
Mapping: {{mapping| 1 3 6 -17 36 | 0 -5 -13 70 -115 }}


Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.554
Optimal tunings:
* CTE: ~2 = 1\1, ~243/200 = 339.554
* POTE: ~2 = 1\1, ~243/200 = 339.554


{{Optimal ET sequence|legend=1| 53, 205de, 258, 311, 675, 986 }}
Optimal ET sequence: {{Optimal ET sequence| 53, 205de, 258, 311, 675, 986 }}


Badness: 0.064853
Badness: 0.064853
Line 342: Line 409:
Mapping: {{mapping| 1 3 6 -17 36 17 | 0 -5 -13 70 -115 -47 }}
Mapping: {{mapping| 1 3 6 -17 36 17 | 0 -5 -13 70 -115 -47 }}


Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.554
Optimal tunings:
* CTE: ~2 = 1\1, ~243/200 = 339.554
* POTE: ~2 = 1\1, ~243/200 = 339.554


{{Optimal ET sequence|legend=1| 53, 205de, 258, 311, 675, 986, 1661cf }}
Optimal ET sequence: {{Optimal ET sequence| 53, 205de, 258, 311, 675, 986, 1661cf }}


Badness: 0.030347
Badness: 0.030347
Line 355: Line 424:
Mapping: {{mapping| 1 3 6 -17 36 17 -31 | 0 -5 -13 70 -115 -47 124 }}
Mapping: {{mapping| 1 3 6 -17 36 17 -31 | 0 -5 -13 70 -115 -47 124 }}


Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.555
Optimal tunings:
* CTE: ~2 = 1\1, ~243/200 = 339.555
* POTE: ~2 = 1\1, ~243/200 = 339.555


{{Optimal ET sequence|legend=1| 53, 205deg, 258g, 311, 675, 1661cf, 2336bccf, 3011bccf }}
Optimal ET sequence: {{Optimal ET sequence| 53, 205deg, 258g, 311, 675, 1661cf, 2336bccf, 3011bccf }}


Badness: 0.024118
Badness: 0.024118
Line 368: Line 439:
Mapping: {{mapping| 1 3 6 -17 36 17 -31 15 | 0 -5 -13 70 -115 -47 124 -38 }}
Mapping: {{mapping| 1 3 6 -17 36 17 -31 15 | 0 -5 -13 70 -115 -47 124 -38 }}


Optimal tuning (POTE): ~2 = 1\1, ~208/171 = 339.555
Optimal tunings:
* CTE: ~2 = 1\1, ~208/171 = 339.555
* POTE: ~2 = 1\1, ~208/171 = 339.555


{{Optimal ET sequence|legend=1| 53, 205deg, 258g, 311, 675, 986, 1661cfh }}
Optimal ET sequence: {{Optimal ET sequence| 53, 205deg, 258g, 311, 675, 986, 1661cfh }}


Badness: 0.017420
Badness: 0.017420
Line 385: Line 458:
: mapping generators: ~343/240, ~7/6
: mapping generators: ~343/240, ~7/6


{{Multival|legend=1| 10 26 12 18 -9 -45 }}
Optimal tunings:
 
* CTE: ~343/240 = 1\2, ~7/6 = 260.563
[[Optimal tuning]] ([[POTE]]): ~343/240 = 1\2, ~7/6 = 260.402
* POTE: ~343/240 = 1\2, ~7/6 = 260.402


{{Optimal ET sequence|legend=1| 14c, 32c, 46, 60, 106d }}
{{Optimal ET sequence|legend=1| 14c, 32c, 46, 106d, 152d }}


[[Badness]]: 0.083601
[[Badness]]: 0.083601
Line 400: Line 473:
Mapping: {{mapping| 2 1 -1 3 3 | 0 5 13 6 9 }}
Mapping: {{mapping| 2 1 -1 3 3 | 0 5 13 6 9 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~7/6 = 260.393
Optimal tunings:
* CTE: ~99/70 = 1\2, ~7/6 = 260.653
* POTE: ~99/70 = 1\2, ~7/6 = 260.393


{{Optimal ET sequence|legend=1| 14c, 32c, 46, 60e, 106de }}
Optimal ET sequence: {{Optimal ET sequence| 14c, 32c, 46, 152de, 198, 244dee }}


Badness: 0.035504
Badness: 0.035504
Line 413: Line 488:
Mapping: {{mapping| 2 1 -1 3 3 0 | 0 5 13 6 9 17 }}
Mapping: {{mapping| 2 1 -1 3 3 0 | 0 5 13 6 9 17 }}


Optimal tuning (POTE): ~55/39 = 1\2, ~7/6 = 260.618
Optimal tunings:
* CTE: ~55/39 = 1\2, ~7/6 = 260.811
* POTE: ~55/39 = 1\2, ~7/6 = 260.618


{{Optimal ET sequence|legend=1| 14cf, 32cf, 46, 106def, 152def }}
Optimal ET sequence: {{Optimal ET sequence| 14cf, 32cf, 46 }}


Badness: 0.030885
Badness: 0.030885
Line 430: Line 507:
: mapping generators: ~2, ~14/9
: mapping generators: ~2, ~14/9


{{Multival|legend=1| 10 26 19 18 2 -29 }}
Optimal tunings:
 
* CTE: ~2 = 1\1, ~9/7 = 430.168
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 430.219
* POTE: ~2 = 1\1, ~9/7 = 430.219


{{Optimal ET sequence|legend=1| 14c, 39d, 53 }}
{{Optimal ET sequence|legend=1| 14c, 39d, 53 }}
Line 445: Line 522:
Mapping: {{mapping| 1 8 19 15 15 | 0 -10 -26 -19 -18 }}
Mapping: {{mapping| 1 8 19 15 15 | 0 -10 -26 -19 -18 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 430.192
Optimal tunings:
* CTE: ~2 = 1\1, ~9/7 = 430.220
* POTE: ~2 = 1\1, ~9/7 = 430.192


{{Optimal ET sequence|legend=1| 14c, 39d, 53 }}
Optimal ET sequence: {{Optimal ET sequence| 14c, 39d, 53 }}


Badness: 0.042947
Badness: 0.042947
Line 458: Line 537:
Mapping: {{mapping| 1 8 19 15 15 30 | 0 -10 -26 -19 -18 -41 }}
Mapping: {{mapping| 1 8 19 15 15 30 | 0 -10 -26 -19 -18 -41 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 430.216
Optimal tunings:
* CTE: ~2 = 1\1, ~9/7 = 430.233
* POTE: ~2 = 1\1, ~9/7 = 430.216


{{Optimal ET sequence|legend=1| 14cf, 39df, 53 }}
Optimal ET sequence: {{Optimal ET sequence| 14cf, 39df, 53 }}


Badness: 0.029753
Badness: 0.029753
Line 475: Line 556:
: mapping generators: ~2, ~320/189
: mapping generators: ~2, ~320/189


{{Multival|legend=1| 15 39 -5 27 -50 -121 }}
Optimal tunings:
* CTE: ~2 = 1\1, ~189/160 = 286.816
* POTE: ~2 = 1\1, ~189/160 = 286.787


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~189/160 = 286.787
{{Optimal ET sequence|legend=1| 46, 113, 159, 205d, 364d }}
 
{{Optimal ET sequence|legend=1| 46, 113, 159 }}


[[Badness]]: 0.125733
[[Badness]]: 0.125733
Line 490: Line 571:
Mapping: {{mapping| 1 13 32 -1 -11 | 0 -15 -39 5 19 }}
Mapping: {{mapping| 1 13 32 -1 -11 | 0 -15 -39 5 19 }}


Optimal tuning (POTE): ~2 = 1\1, ~33/28 = 286.797
Optimal tunings:
* CTE: ~2 = 1\1, ~33/28 = 286.813
* POTE: ~2 = 1\1, ~33/28 = 286.797


{{Optimal ET sequence|legend=1| 46, 113, 159 }}
Optimal ET sequence: {{Optimal ET sequence| 46, 113, 159, 205d, 364d }}


Badness: 0.051111
Badness: 0.051111
Line 503: Line 586:
Mapping: {{mapping| 1 13 32 -1 -11 -10 | 0 -15 -39 5 19 18 }}
Mapping: {{mapping| 1 13 32 -1 -11 -10 | 0 -15 -39 5 19 18 }}


Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 286.789
Optimal tunings:
* CTE: ~2 = 1\1, ~13/11 = 286.803
* POTE: ~2 = 1\1, ~13/11 = 286.789


{{Optimal ET sequence|legend=1| 46, 113, 159 }}
Optimal ET sequence: {{Optimal ET sequence| 46, 113, 159, 364df, 523ddff }}


Badness: 0.030297
Badness: 0.030297
Line 516: Line 601:
Mapping: {{mapping| 1 13 32 -1 -11 -10 -2 | 0 -15 -39 5 19 18 8 }}
Mapping: {{mapping| 1 13 32 -1 -11 -10 -2 | 0 -15 -39 5 19 18 8 }}


Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 286.795
Optimal tunings:
* CTE: ~2 = 1\1, ~13/11 = 286.804
* POTE: ~2 = 1\1, ~13/11 = 286.795


{{Optimal ET sequence|legend=1| 46, 113, 159 }}
Optimal ET sequence: {{Optimal ET sequence| 46, 113, 159, 364df, 523ddff }}


Badness: 0.022036
Badness: 0.022036
Line 531: Line 618:
{{Mapping|legend=1| 1 8 19 46 | 0 -15 -39 -101 }}
{{Mapping|legend=1| 1 8 19 46 | 0 -15 -39 -101 }}


{{Multival|legend=1| 15 39 101 27 118 125 }}
Optimal tunings:
* CTE: ~2 = 1\1, ~168/125 = 513.180
* POTE: ~2 = 1\1, ~168/125 = 513.178


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~168/125 = 513.178
{{Optimal ET sequence|legend=1| 7d, …, 145d, 152, 311, 774, 1085 }}
 
{{Optimal ET sequence|legend=1| 152, 311, 463, 774 }}


[[Badness]]: 0.119453
[[Badness]]: 0.119453
Line 546: Line 633:
Mapping: {{mapping| 1 8 19 46 18 | 0 -15 -39 -101 -34 }}
Mapping: {{mapping| 1 8 19 46 18 | 0 -15 -39 -101 -34 }}


Optimal tuning (POTE): ~2 = 1\1, ~121/90 = 513.177
Optimal tunings:
* CTE: ~2 = 1\1, ~121/90 = 513.181
* POTE: ~2 = 1\1, ~121/90 = 513.177


{{Optimal ET sequence|legend=1| 152, 311, 463, 774, 1237e }}
Optimal ET sequence: {{Optimal ET sequence| 7d, …, 145d, 152, 311, 774, 1085e, 1396e }}


Badness: 0.031296
Badness: 0.031296
Line 559: Line 648:
Mapping: {{mapping| 1 8 19 46 18 64 | 0 -15 -39 -101 -34 -141 }}
Mapping: {{mapping| 1 8 19 46 18 64 | 0 -15 -39 -101 -34 -141 }}


Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.182
Optimal tunings:
* CTE: ~2 = 1\1, ~35/26 = 513.184
* POTE: ~2 = 1\1, ~35/26 = 513.182


{{Optimal ET sequence|legend=1| 152f, 311 }}
Optimal ET sequence: {{Optimal ET sequence| 152f, 159, 311 }}


Badness: 0.026418
Badness: 0.026418
Line 572: Line 663:
Mapping: {{mapping| 1 8 19 46 18 64 -22 | 0 -15 -39 -101 -34 -141 61 }}
Mapping: {{mapping| 1 8 19 46 18 64 -22 | 0 -15 -39 -101 -34 -141 61 }}


Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.186
Optimal tunings:
* CTE: ~2 = 1\1, ~35/26 = 513.185
* POTE: ~2 = 1\1, ~35/26 = 513.186


{{Optimal ET sequence|legend=1| 152f, 159, 311, 1092cdg, 1403cdg, 1714cdeg }}
Optimal ET sequence: {{Optimal ET sequence| 152f, 159, 311, 1714cdeg, 2025cdefgg, 2336bccdefgg }}


Badness: 0.025588
Badness: 0.025588
Line 585: Line 678:
Mapping: {{mapping| 1 8 19 46 18 64 -22 53 | 0 -15 -39 -101 -34 -141 61 -114 }}
Mapping: {{mapping| 1 8 19 46 18 64 -22 53 | 0 -15 -39 -101 -34 -141 61 -114 }}


Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.185
Optimal tunings:
* CTE: ~2 = 1\1, ~35/26 = 513.184
* POTE: ~2 = 1\1, ~35/26 = 513.185


{{Optimal ET sequence|legend=1| 152f, 159, 311, 1403cdgh, 1714cdegh, 2025cdefgghh, 2336bccdefgghh }}
Optimal ET sequence: {{Optimal ET sequence| 152f, 159, 311 }}


Badness: 0.018412
Badness: 0.018412
Line 598: Line 693:
Mapping: {{mapping| 1 8 19 46 18 64 -22 53 49 | 0 -15 -39 -101 -34 -141 61 -114 -104 }}
Mapping: {{mapping| 1 8 19 46 18 64 -22 53 49 | 0 -15 -39 -101 -34 -141 61 -114 -104 }}


Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.185
Optimal tunings:
* CTE: ~2 = 1\1, ~35/26 = 513.184
* POTE: ~2 = 1\1, ~35/26 = 513.185


{{Optimal ET sequence|legend=1| 152f, 159, 311, 1092cdgh, 1403cdgh, 1714cdeghi }}
Optimal ET sequence: {{Optimal ET sequence| 152f, 159, 311, 1714cdeghi, 2025cdefgghhi, 2336bccdefgghhi }}


Badness: 0.014343
Badness: 0.014343
Line 611: Line 708:
Mapping: {{mapping| 1 8 19 46 18 64 -22 53 49 72 | 0 -15 -39 -101 -34 -141 61 -114 -104 -157 }}
Mapping: {{mapping| 1 8 19 46 18 64 -22 53 49 72 | 0 -15 -39 -101 -34 -141 61 -114 -104 -157 }}


Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.186
Optimal tunings:
* CTE: ~2 = 1\1, ~35/26 = 513.185
* POTE: ~2 = 1\1, ~35/26 = 513.186


{{Optimal ET sequence|legend=1| 152fj, 159, 311, 781dh, 1092cdgh, 1403cdgh }}
Optimal ET sequence: {{Optimal ET sequence| 152fj, 159, 311, 1403cdgh, 1714cdeghi, 2025cdefgghhij, 2336bccdefgghhij }}


Badness: 0.012038
Badness: 0.012038


== Amicable ==
== Amicable ==
The amicable temperament (99 & 311) tempers out the [[amity comma]] and the [[canousma]] in addition to the breedsma, and is closely associated with the canou temperament.  
The amicable temperament (99 &amp; 311) tempers out the [[amity comma]] and the [[canousma]] in addition to the breedsma, and is closely associated with the canou temperament.  


While it extends well into 2.3.5.7.13/11, there are multiple reasonable places for the prime 11 and 13 in the interval chain. Amical (311 & 410) does this with no compromise of accuracy, but is enormously complex. Amorous (212 & 311) has the new primes placed on the same side of the interval chain so blends smarter with the other harmonics. Pseudoamical (99 & 113) and pseudoamorous (14cf & 99ef) are the corresponding low-complexity interpretations. Floral (198 & 212) shares the semioctave 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.  
While it extends well into 2.3.5.7.13/11, there are multiple reasonable places for the prime 11 and 13 in the interval chain. Amical (311 &amp; 410) does this with no compromise of accuracy, but is enormously complex. Amorous (212 &amp; 311) has the new primes placed on the same side of the interval chain so blends smarter with the other harmonics. Pseudoamical (99 &amp; 113) and pseudoamorous (14cf &amp; 99ef) are the corresponding low-complexity interpretations. Floral (198 &amp; 212) shares the semioctave period and the ~21/20 generator with harry, but in a complementary style, including a characteristic flat 11. Finally, humorous (198 &amp; 311) is one of the best extensions out there and it splits the generator in two.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 628: Line 727:
{{Mapping|legend=1| 1 3 6 5 | 0 -20 -52 -31 }}
{{Mapping|legend=1| 1 3 6 5 | 0 -20 -52 -31 }}


{{Multival|legend=1| 20 52 31 36 -7 -74 }}
Optimal tunings:
* CTE: ~2 = 1\1, ~21/20 = 84.8831
* POTE: ~2 = 1\1, ~21/20 = 84.880


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~21/20 = 84.880
{{Optimal ET sequence|legend=1| 14c, …, 85c, 99, 212, 311, 721, 1032, 1753b }}
 
{{Optimal ET sequence|legend=1| 99, 212, 311, 410, 1131, 1541b }}


[[Badness]]: 0.045473
[[Badness]]: 0.045473
Line 643: Line 742:
Mapping: {{mapping| 1 3 6 5 -8 | 0 -20 -52 -31 162 }}
Mapping: {{mapping| 1 3 6 5 -8 | 0 -20 -52 -31 162 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8843
Optimal tunings:
* CTE: ~2 = 1\1, ~21/20 = 84.8843
* POTE: ~2 = 1\1, ~21/20 = 84.8843


{{Optimal ET sequence|legend=1| 99, 212e, 311, 410, 721, 1032, 1343 }}
Optimal ET sequence: {{Optimal ET sequence| 99, 212e, 311, 721, 1032, 1343, 2375bc }}


Badness: 0.100668
Badness: 0.100668
Line 656: Line 757:
Mapping: {{mapping| 1 3 6 5 -8 -5 | 0 -20 -52 -31 162 123 }}
Mapping: {{mapping| 1 3 6 5 -8 -5 | 0 -20 -52 -31 162 123 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8838
Optimal tunings:
* CTE: ~2 = 1\1, ~21/20 = 84.8837
* POTE: ~2 = 1\1, ~21/20 = 84.8838


{{Optimal ET sequence|legend=1| 99, 212ef, 311, 410, 721, 1032 }}
Optimal ET sequence: {{Optimal ET sequence| 99, 212ef, 311, 721, 1032 }}


Badness: 0.049893
Badness: 0.049893
Line 669: Line 772:
Mapping: {{mapping| 1 3 6 5 14 | 0 -20 -52 -31 -149 }}
Mapping: {{mapping| 1 3 6 5 14 | 0 -20 -52 -31 -149 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8896
Optimal tunings:
* CTE: ~2 = 1\1, ~21/20 = 84.8883
* POTE: ~2 = 1\1, ~21/20 = 84.8896


{{Optimal ET sequence|legend=1| 99e, 212, 311, 1145c, 1456cd }}
Optimal ET sequence: {{Optimal ET sequence| 99e, 212, 311, 2389bccd, 2700bccde, 3011bccde, 3322bccdde }}


Badness: 0.048924
Badness: 0.048924
Line 682: Line 787:
Mapping: {{mapping| 1 3 6 5 14 17 | 0 -20 -52 -31 -149 -188 }}
Mapping: {{mapping| 1 3 6 5 14 17 | 0 -20 -52 -31 -149 -188 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8910
Optimal tunings:
* CTE: ~2 = 1\1, ~21/20 = 84.8895
* POTE: ~2 = 1\1, ~21/20 = 84.8910


{{Optimal ET sequence|legend=1| 99ef, 212, 311, 834, 1145c }}
Optimal ET sequence: {{Optimal ET sequence| 99ef, 212, 311, 1145c, 1456cd, 1767cd }}


Badness: 0.034681
Badness: 0.034681
Line 695: Line 802:
Mapping: {{mapping| 1 3 6 5 -1 | 0 -20 -52 -31 63 }}
Mapping: {{mapping| 1 3 6 5 -1 | 0 -20 -52 -31 63 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.9091
Optimal tunings:
* CTE: ~2 = 1\1, ~21/20 = 84.9005
* POTE: ~2 = 1\1, ~21/20 = 84.9091


{{Optimal ET sequence|legend=1| 99, 113, 212, 961ccdeee }}
Optimal ET sequence: {{Optimal ET sequence| 14ce, …, 85cee, 99, 212 }}


Badness: 0.085837
Badness: 0.085837
Line 708: Line 817:
Mapping: {{mapping| 1 3 6 5 -1 2 | 0 -20 -52 -31 63 24 }}
Mapping: {{mapping| 1 3 6 5 -1 2 | 0 -20 -52 -31 63 24 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.9127
Optimal tunings:
* CTE: ~2 = 1\1, ~21/20 = 84.9049
* POTE: ~2 = 1\1, ~21/20 = 84.9127


{{Optimal ET sequence|legend=1| 99, 113, 212, 537cdeff, 749ccdeefff }}
Optimal ET sequence: {{Optimal ET sequence| 14ce, …, 85ceef, 99, 113, 212 }}


Badness: 0.047025
Badness: 0.047025
Line 721: Line 832:
Mapping: {{mapping| 1 3 6 5 7 | 0 -20 -52 -31 -50 }}
Mapping: {{mapping| 1 3 6 5 7 | 0 -20 -52 -31 -50 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8917
Optimal tunings:
* CTE: ~2 = 1\1, ~21/20 = 84.9022
* POTE: ~2 = 1\1, ~21/20 = 84.8917


{{Optimal ET sequence|legend=1| 99e, 212e }}
Optimal ET sequence: {{Optimal ET sequence| 14c, …, 85ce, 99e, 113, 212e }}


Badness: 0.056583
Badness: 0.056583
Line 734: Line 847:
Mapping: {{mapping| 1 3 6 5 7 10 | 0 -20 -52 -31 -50 -89 }}
Mapping: {{mapping| 1 3 6 5 7 10 | 0 -20 -52 -31 -50 -89 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.9164
Optimal tunings:
* CTE: ~2 = 1\1, ~21/20 = 84.9153
* POTE: ~2 = 1\1, ~21/20 = 84.9164


{{Optimal ET sequence|legend=1| 99ef, 113, 212ef }}
Optimal ET sequence: {{Optimal ET sequence| 14cf, …, 85ceff, 99ef, 113, 212ef, 325ce, 537cdeef }}


Badness: 0.042826
Badness: 0.042826
Line 747: Line 862:
Mapping: {{mapping| 2 6 12 10 13 | 0 -20 -52 -31 -43 }}
Mapping: {{mapping| 2 6 12 10 13 | 0 -20 -52 -31 -43 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~21/20 = 84.8788
Optimal tunings:
* CTE: ~99/70 = 1\2, ~21/20 = 84.8781
* POTE: ~99/70 = 1\2, ~21/20 = 84.8788


{{Optimal ET sequence|legend=1| 198, 212, 410 }}
Optimal ET sequence: {{Optimal ET sequence| 14c, …, 170bccde, 184c, 198, 212, 410 }}


Badness: 0.065110
Badness: 0.065110
Line 760: Line 877:
Mapping: {{mapping| 2 6 12 10 13 19 | 0 -20 -52 -31 -43 -82 }}
Mapping: {{mapping| 2 6 12 10 13 19 | 0 -20 -52 -31 -43 -82 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~21/20 = 84.8750
Optimal tunings:
* CTE: ~99/70 = 1\2, ~21/20 = 84.8759
* POTE: ~99/70 = 1\2, ~21/20 = 84.8750


{{Optimal ET sequence|legend=1| 198, 410 }}
Optimal ET sequence: {{Optimal ET sequence| 14c, …, 184cff, 198, 410 }}


Badness: 0.037013
Badness: 0.037013
Line 773: Line 892:
Mapping: {{mapping| 1 3 6 5 3 | 0 -40 -104 -62 13 }}
Mapping: {{mapping| 1 3 6 5 3 | 0 -40 -104 -62 13 }}


Optimal tuning (POTE): ~2 = 1\1, ~4096/3993 = 42.4391
Optimal tunings:
* CTE: ~2 = 1\1, ~4096/3993 = 42.4414
* POTE: ~2 = 1\1, ~4096/3993 = 42.4391


{{Optimal ET sequence|legend=1| 85c, 113, 198, 311, 509, 820 }}
Optimal ET sequence: {{Optimal ET sequence| 85c, 113, 198, 311, 1131, 1442, 1753be }}


Badness: 0.058249
Badness: 0.058249
Line 786: Line 907:
Mapping: {{mapping| 1 3 6 5 3 6 | 0 -40 -104 -62 13 -65 }}
Mapping: {{mapping| 1 3 6 5 3 6 | 0 -40 -104 -62 13 -65 }}


Optimal tuning (POTE): ~2 = 1\1, ~40/39 = 42.4391
Optimal tunings:
* CTE: ~2 = 1\1, ~40/39 = 42.4425
* POTE: ~2 = 1\1, ~40/39 = 42.4391


{{Optimal ET sequence|legend=1| 85c, 113, 198, 311, 509, 820f }}
Optimal ET sequence: {{Optimal ET sequence| 85c, 113, 198, 311, 1753beff, 2064beff, 2375bceff }}


Badness: 0.028267
Badness: 0.028267


== Calamity ==
== Calamity ==
The calamity temperament (46 & 311) tempers out the [[rainy comma]], 2100875/2097152, splitting the interval of two octaves plus an acute minor third into five.  
The calamity temperament (46 &amp; 311) tempers out the [[rainy comma]], 2100875/2097152, splitting the interval of two octaves plus an acute minor third into five.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 801: Line 924:
{{Mapping|legend=1| 1 13 32 -15 | 0 -25 -65 39 }}
{{Mapping|legend=1| 1 13 32 -15 | 0 -25 -65 39 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~48/35 = 547.9092
[[Optimal tuning]] (CTE): ~2 = 1\1, ~48/35 = 547.909


{{Optimal ET sequence|legend=1| 46, 219c, 265, 311 }}
{{Optimal ET sequence|legend=1| 46, 219c, 265, 311 }}


[[Badness]]: 0.198
[[Badness]]: 0.198130


=== 11-limit ===
=== 11-limit ===
Line 814: Line 937:
Mapping: {{mapping| 1 13 32 -15 -18 | 0 -25 -65 39 47 }}
Mapping: {{mapping| 1 13 32 -15 -18 | 0 -25 -65 39 47 }}


Optimal tuning (CTE): ~2 = 1\1, ~48/35 = 547.9080
Optimal tuning (CTE): ~2 = 1\1, ~48/35 = 547.908


{{Optimal ET sequence|legend=1| 46, 219c, 265, 311, 979, 1290 }}
Optimal ET sequence: {{Optimal ET sequence| 46, 219c, 265, 311, 979, 1290 }}


Badness: 0.0604
Badness: 0.060408


=== 13-limit ===
=== 13-limit ===
Line 827: Line 950:
Mapping: {{mapping| 1 13 32 -15 -18 -31 | 0 -25 -65 39 47 76 }}
Mapping: {{mapping| 1 13 32 -15 -18 -31 | 0 -25 -65 39 47 76 }}


Optimal tuning (CTE): ~2 = 1\1, ~48/35 = 547.9066
Optimal tuning (CTE): ~2 = 1\1, ~48/35 = 547.907


{{Optimal ET sequence|legend=1| 46, 265, 311, 668, 979, 1290 }}
Optimal ET sequence: {{Optimal ET sequence| 46, 265, 311, 668, 979, 1290 }}


Badness: 0.0336
Badness: 0.033617


== Familia ==
== Familia ==
Line 842: Line 965:
{{Mapping|legend=1| 1 8 19 20 | 0 -25 -65 -67 }}
{{Mapping|legend=1| 1 8 19 20 | 0 -25 -65 -67 }}


{{Multival|legend=1| 25 65 67 45 36 -27 }}
Optimal tunings:
 
* CTE: ~2 = 1\1, ~11907/10000 = 307.915
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11907/10000 = 307.941
* POTE: ~2 = 1\1, ~11907/10000 = 307.941


{{Optimal ET sequence|legend=1| 39d, 74cd, 113, 152, 265, 417, 986d }}
{{Optimal ET sequence|legend=1| 39d, 74cd, 113, 152, 265, 417, 1516ccdd, 1933ccdd }}


[[Badness]]: 0.144551
[[Badness]]: 0.144551
Line 857: Line 980:
Mapping: {{mapping| 1 8 19 20 5 | 0 -25 -65 -67 -6 }}
Mapping: {{mapping| 1 8 19 20 5 | 0 -25 -65 -67 -6 }}


Optimal tuning (POTE): ~2 = 1\1, ~3200/2673 = 307.906
Optimal tunings:
* CTE: ~2 = 1\1, ~3200/2673 = 307.915
* POTE: ~2 = 1\1, ~3200/2673 = 307.906


{{Optimal ET sequence|legend=1| 39d, 74cd, 113, 152, 417, 569de, 721de }}
Optimal ET sequence: {{Optimal ET sequence| 39d, 74cd, 113, 152, 265, 417, 1099cdee }}


Badness: 0.051740
Badness: 0.051740
Line 870: Line 995:
Mapping: {{mapping| 1 8 19 20 5 25 | 0 -25 -65 -67 -6 -83 }}
Mapping: {{mapping| 1 8 19 20 5 25 | 0 -25 -65 -67 -6 -83 }}


Optimal tuning (POTE): ~2 = 1\1, ~143/120 = 307.913
Optimal tunings:
* CTE: ~2 = 1\1, ~143/120 = 307.922
* POTE: ~2 = 1\1, ~143/120 = 307.913


{{Optimal ET sequence|legend=1| 39df, 74cdf, 113, 152f, 265, 417f }}
Optimal ET sequence: {{Optimal ET sequence| 39df, 74cdf, 113, 152f, 265 }}


Badness: 0.038473
Badness: 0.038473


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