Jubilismic clan: Difference between revisions

-5-limit lemba (moved to misc. 5-limit temps)
Review, +CTE tunings and error maps
Line 2: Line 2:


== Jubilic ==
== Jubilic ==
The head of this clan, jubilic, is generated by [[~]][[5/4]]. That and a semioctave gives ~[[7/4]].  
The head of this clan, jubilic, is generated by [[~]][[5/4]]. That and a semioctave give ~[[7/4]].  


[[Subgroup]]: 2.5.7
[[Subgroup]]: 2.5.7
Line 12: Line 12:
: sval mapping generators: ~7/5, ~5
: sval mapping generators: ~7/5, ~5


[[Gencom]] [[mapping]]: [{{val| 2 0 0 1 }}, {{val| 0 0 1 1 }}]
{{Mapping|legend=3| 2 0 0 1 | 0 0 1 1 }}


[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~5/4 = 380.840
[[Optimal tuning]]s:
* [[CTE]]: ~7/5 = 1\2, ~5/4 = 379.21
: [[error map]]: {{val| 0.000 -7.104 +10.384 }}
* [[POTE]]: ~7/5 = 1\2, ~5/4 = 380.840
: error map: {{val| 0.000 -5.474 +12.014 }}


{{Optimal ET sequence|legend=1| 2, 4, 6, 16, 22, 60d, 82d, 104dd }}
{{Optimal ET sequence|legend=1| 2, 4, 6, 16, 22, 60d }}
 
[[Badness]]: 0.00190


=== Overview to extensions ===
=== Overview to extensions ===
Line 54: Line 60:
{{Multival|legend=1| 6 -2 -2 -17 -20 1 }}
{{Multival|legend=1| 6 -2 -2 -17 -20 1 }}


[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~8/7 = 232.089
[[Optimal tuning]]s:
* [[CTE]]: ~7/5 = 1\2, ~8/7 = 232.927
: [[error map]]: {{val| 0.000 -3.175 -19.241 -1.753 }}
* [[POTE]]: ~7/5 = 1\2, ~8/7 = 232.089
: error map: {{val| 0.000 -5.689 -18.402 -0.915 }}


{{Optimal ET sequence|legend=1| 10, 16, 26, 62c }}
{{Optimal ET sequence|legend=1| 10, 16, 26, 62c }}
Line 67: Line 77:
Mapping: {{mapping| 2 2 5 6 5 | 0 3 -1 -1 5 }}
Mapping: {{mapping| 2 2 5 6 5 | 0 3 -1 -1 5 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~8/7 = 230.974
Optimal tunings:
* CTE: ~7/5 = 1\2, ~8/7 = 231.997
* POTE: ~7/5 = 1\2, ~8/7 = 230.974


{{Optimal ET sequence|legend=1| 10, 16, 26 }}
{{Optimal ET sequence|legend=0| 10, 16, 26 }}


Badness: 0.041563
Badness: 0.041563
Line 80: Line 92:
Mapping: {{mapping| 2 2 5 6 5 7 | 0 3 -1 -1 5 1 }}
Mapping: {{mapping| 2 2 5 6 5 7 | 0 3 -1 -1 5 1 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~8/7 = 230.966
Optimal tunings:
* CTE: ~7/5 = 1\2, ~8/7 = 232.100
* POTE: ~7/5 = 1\2, ~8/7 = 230.966


{{Optimal ET sequence|legend=1| 10, 16, 26 }}
{{Optimal ET sequence|legend=0| 10, 16, 26 }}


Badness: 0.025477
Badness: 0.025477
Line 99: Line 113:
{{Multival|legend=1| 10 2 2 -20 -25 -1 }}
{{Multival|legend=1| 10 2 2 -20 -25 -1 }}


[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~5/4 = 380.578
[[Optimal tuning]]s:
* [[CTE]]: ~7/5 = 1\2, ~8/7 = 380.355
: [[error map]]: {{val| 0.000 -0.180 -5.959 +11.529 }}
* [[POTE]]: ~7/5 = 1\2, ~5/4 = 380.578
: error map: {{val| 0.000 +0.937 -5.735 +11.752 }}


{{Optimal ET sequence|legend=1| 6, 16, 22, 60d, 82d }}
{{Optimal ET sequence|legend=1| 6, 16, 22, 60d }}


[[Badness]]: 0.082673
[[Badness]]: 0.082673
Line 112: Line 130:
Mapping: {{mapping| 2 0 4 5 5 | 0 5 1 1 3 }}
Mapping: {{mapping| 2 0 4 5 5 | 0 5 1 1 3 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 380.530
Optimal tunings:
* CTE: ~7/5 = 1\2, ~5/4 = 380.588
* POTE: ~7/5 = 1\2, ~5/4 = 380.530


{{Optimal ET sequence|legend=1| 6, 16, 22, 60de, 82de }}
{{Optimal ET sequence|legend=0| 6, 16, 22 }}


Badness: 0.039151
Badness: 0.039151
Line 125: Line 145:
Mapping: {{mapping| 2 0 4 5 5 8 | 0 5 1 1 3 -1 }}
Mapping: {{mapping| 2 0 4 5 5 8 | 0 5 1 1 3 -1 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 379.787
Optimal tunings:
* CTE: ~7/5 = 1\2, ~5/4 = 380.449
* POTE: ~7/5 = 1\2, ~5/4 = 379.787


{{Optimal ET sequence|legend=1| 6, 16, 22, 38f }}
{{Optimal ET sequence|legend=0| 6, 16, 22, 38f }}


Badness: 0.034376
Badness: 0.034376
Line 141: Line 163:
Mapping: {{mapping| 2 0 4 5 5 3 | 0 5 1 1 3 7 }}
Mapping: {{mapping| 2 0 4 5 5 3 | 0 5 1 1 3 7 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 379.837
Optimal tunings:
* CTE: ~7/5 = 1\2, ~5/4 = 379.762
* POTE: ~7/5 = 1\2, ~5/4 = 379.837


{{Optimal ET sequence|legend=1| 16, 22f, 38 }}
{{Optimal ET sequence|legend=0| 16, 22f, 38 }}


Badness: 0.035284
Badness: 0.035284
Line 158: Line 182:
{{Multival|legend=1| 2 -2 -2 -8 -9 1 }}
{{Multival|legend=1| 2 -2 -2 -8 -9 1 }}


[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~3/2 = 749.415
[[Optimal tuning]]s:
* [[CTE]]: ~7/5 = 1\2, ~3/2 = 754.204
: [[error map]]: {{val| 0.000 +52.249 +59.482 +76.970 }}
* [[POTE]]: ~7/5 = 1\2, ~3/2 = 749.415
: error map: {{val| 0.000 +47.460 +64.271 +81.759 }}


{{Optimal ET sequence|legend=1| 2, 6, 8d }}
{{Optimal ET sequence|legend=1| 2, 6, 8d }}
Line 171: Line 199:
Mapping: {{mapping| 2 0 8 9 7 | 0 1 -1 -1 0 }}
Mapping: {{mapping| 2 0 8 9 7 | 0 1 -1 -1 0 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 749.756
Optimal tunings:
* CTE: ~7/5 = 1\2, ~3/2 = 754.205
* POTE: ~7/5 = 1\2, ~3/2 = 749.756


{{Optimal ET sequence|legend=1| 2, 6, 8d }}
{{Optimal ET sequence|legend=0| 2, 6, 8d }}


Badness: 0.029193
Badness: 0.029193
Line 192: Line 222:
: [[gencom]]: [7/5 8/7; 50/49 64/63]
: [[gencom]]: [7/5 8/7; 50/49 64/63]


[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~8/7 = 214.095
[[Optimal tuning]]s:
* [[CTE]]: ~7/5 = 1\2, ~9/8 = 216.711
: [[error map]]: {{val| 0.000 +12.801 +3.025 +14.463 }}
* [[POTE]]: ~7/5 = 1\2, ~9/8 = 214.095
: error map: {{val| 0.000 +10.815 -0.409 +17.079 }}


{{Optimal ET sequence|legend=1| 4, 6, 16, 22, 28 }}
{{Optimal ET sequence|legend=1| 2, 4, 6, 16, 22, 28 }}


[[Tp tuning #T2 tuning|RMS error]]: 2.572 cents
[[Tp tuning #T2 tuning|RMS error]]: 2.572 cents
Line 210: Line 244:
{{Mapping|legend=1| 2 1 3 | 0 4 3 }}
{{Mapping|legend=1| 2 1 3 | 0 4 3 }}


[[Optimal tuning]] ([[CWE]]): ~625/432 = 1\2, ~6/5 = 325.815
: mapping generators: ~625/432, ~6/5
 
[[Optimal tuning]]s:
* [[CTE]]: ~625/432 = 1\2, ~6/5 = 326.170
: [[error map]]: {{val| 0.000 +2.727 -7.802 }}
* [[CWE]]: ~625/432 = 1\2, ~6/5 = 325.815
: error map: {{val| 0.000 +1.304 -8.869 }}


Supporting ETs: 22, 26, 18, 48, 14b, 30bc, 10bbc, 70c, 40b, 74c, 34bc, 92c, 56bcc, 62b
{{Optimal ET sequence|legend=1| 4, 14b, 18, 22, 48, 70c, 118c }}


[[Badness]] (Sintel): 5.319
[[Badness]]:
* Smith: 0.227
* Dirichlet: 5.32


=== 7-limit ===
=== 7-limit ===
Line 222: Line 264:


{{Mapping|legend=1| 2 1 3 4 | 0 4 3 3 }}
{{Mapping|legend=1| 2 1 3 4 | 0 4 3 3 }}
: mapping generators: ~7/5, ~6/5


{{Multival|legend=1| 8 6 6 -9 -13 -3 }}
{{Multival|legend=1| 8 6 6 -9 -13 -3 }}


[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~6/5 = 325.719
[[Optimal tuning]]s:
* [[CTE]]: ~7/5 = 1\2, ~6/5 = 325.769
: [[error map]]: {{val| 0.000 +1.120 -9.007 +8.481 }}
* [[POTE]]: ~7/5 = 1\2, ~6/5 = 325.719
: error map: {{val| 0.000 +0.921 -9.156 +8.331 }}


{{Optimal ET sequence|legend=1| 4, 14bd, 18, 22, 48, 70c }}
{{Optimal ET sequence|legend=1| 4, 14bd, 18, 22, 48 }}


[[Badness]]: 0.043462
[[Badness]]: 0.043462
Line 238: Line 286:
Mapping: {{mapping| 2 1 3 4 8 | 0 4 3 3 -2 }}
Mapping: {{mapping| 2 1 3 4 8 | 0 4 3 3 -2 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 325.545
Optimal tunings:
* CTE: ~7/5 = 1\2, ~6/5 = 325.719
* POTE: ~7/5 = 1\2, ~6/5 = 325.545


{{Optimal ET sequence|legend=1| 4, 14bd, 18, 22, 48, 70c, 118cd }}
{{Optimal ET sequence|legend=0| 4, 18, 22, 48 }}


Badness: 0.032058
Badness: 0.032058
Line 251: Line 301:
Mapping: {{mapping| 2 1 3 4 2 | 0 4 3 3 9 }}
Mapping: {{mapping| 2 1 3 4 2 | 0 4 3 3 9 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 327.038
Optimal tunings:
* CTE: ~7/5 = 1\2, ~6/5 = 326.684
* POTE: ~7/5 = 1\2, ~6/5 = 327.038


{{Optimal ET sequence|legend=1| 4e, 18e, 22 }}
{{Optimal ET sequence|legend=0| 4e, …, 18e, 22 }}


Badness: 0.035202
Badness: 0.035202
Line 264: Line 316:
Mapping: {{mapping| 2 1 3 4 2 3 | 0 4 3 3 9 8 }}
Mapping: {{mapping| 2 1 3 4 2 3 | 0 4 3 3 9 8 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 327.841
Optimal tunings:
* CTE: ~7/5 = 1\2, ~6/5 = 327.450
* POTE: ~7/5 = 1\2, ~6/5 = 327.841


{{Optimal ET sequence|legend=1| 4ef, 18e, 22, 84bddf }}
{{Optimal ET sequence|legend=0| 4ef, …, 18e, 22 }}


Badness: 0.031835
Badness: 0.031835
Line 277: Line 331:
Mapping: {{mapping| 2 1 3 4 1 | 0 4 3 3 11 }}
Mapping: {{mapping| 2 1 3 4 1 | 0 4 3 3 11 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 323.427
Optimal tunings:
* CTE: ~7/5 = 1\2, ~6/5 = 324.238
* POTE: ~7/5 = 1\2, ~6/5 = 323.427


{{Optimal ET sequence|legend=1| 22e, 26 }}
{{Optimal ET sequence|legend=0| 4e, 22e, 26 }}


Badness: 0.052899
Badness: 0.052899
Line 290: Line 346:
Mapping: {{mapping| 2 1 3 4 1 2 | 0 4 3 3 11 10 }}
Mapping: {{mapping| 2 1 3 4 1 2 | 0 4 3 3 11 10 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 323.396
Optimal tunings:
* CTE: ~7/5 = 1\2, ~6/5 = 324.187
* POTE: ~7/5 = 1\2, ~6/5 = 323.396


{{Optimal ET sequence|legend=1| 22ef, 26 }}
{{Optimal ET sequence|legend=0| 4ef, 22ef, 26 }}


Badness: 0.035040
Badness: 0.035040


== Elvis ==
== Elvis ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Elvis]].''
: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Elvis]].''


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 304: Line 362:


{{Mapping|legend=1| 2 1 10 11 | 0 2 -5 -5 }}
{{Mapping|legend=1| 2 1 10 11 | 0 2 -5 -5 }}
: mapping generators: ~7/5, ~64/45


{{Multival|legend=1| 4 -10 -10 -25 -27 5 }}
{{Multival|legend=1| 4 -10 -10 -25 -27 5 }}


[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~45/32 = 553.721
[[Optimal tuning]]s:
* [[CTE]]: ~7/5 = 1\2, ~64/45 = 645.313 (~64/63 = 45.313)
: [[error map]]: {{val| 0.000 -11.329 -12.879 +4.609 }}
* [[POTE]]: ~7/5 = 1\2, ~64/45 = 646.279 (~64/63 = 46.279)
: error map: {{val| 0.000 -9.397 -17.710 -0.222 }}


{{Optimal ET sequence|legend=1| 2, 24c, 26 }}
{{Optimal ET sequence|legend=1| 2, 24c, 26 }}
Line 320: Line 384:
Mapping: {{mapping| 2 1 10 11 8 | 0 2 -5 -5 -1 }}
Mapping: {{mapping| 2 1 10 11 8 | 0 2 -5 -5 -1 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 553.882
Optimal tunings:
* CTE: ~7/5 = 1\2, ~16/11 = 645.343 (~56/55 = 45.343)
* POTE: ~7/5 = 1\2, ~16/11 = 646.118 (~56/55 = 46.118)


{{Optimal ET sequence|legend=1| 2, 24c, 26 }}
{{Optimal ET sequence|legend=0| 2, 24c, 26 }}


Badness: 0.063212
Badness: 0.063212
Line 333: Line 399:
Mapping: {{mapping| 2 1 10 11 8 16 | 0 2 -5 -5 -1 -8 }}
Mapping: {{mapping| 2 1 10 11 8 16 | 0 2 -5 -5 -1 -8 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 553.892
Optimal tunings:
* CTE: ~7/5 = 1\2, ~16/11 = 645.208 (~56/55 = 45.208)
* POTE: ~7/5 = 1\2, ~16/11 = 646.108 (~56/55 = 46.108)


{{Optimal ET sequence|legend=1| 2f, 24cf, 26 }}
{{Optimal ET sequence|legend=0| 2f, 24cf, 26 }}


Badness: 0.043997
Badness: 0.043997


== Comic ==
== Comic ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Comic]].''
: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Comic]].''


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 347: Line 415:


{{Mapping|legend=1| 2 1 -3 -2 | 0 2 7 7 }}
{{Mapping|legend=1| 2 1 -3 -2 | 0 2 7 7 }}
: mapping generators: ~7/5, ~40/27


{{Multival|legend=1| 4 14 14 13 11 -7 }}
{{Multival|legend=1| 4 14 14 13 11 -7 }}


[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~81/80 = 54.699
[[Optimal tuning]]s:
* [[CTE]]: ~7/5 = 1\2, ~40/27 = 653.872 (~28/27 = 53.872)
: [[error map]]: {{val| 0.000 +5.789 -9.211 +8.277 }}
* [[POTE]]: ~7/5 = 1\2, ~40/27 = 654.699 (~28/27 = 54.699)
: error map: {{val| 0.000 +7.444 -3.417 +14.070 }}


{{Optimal ET sequence|legend=1| 20cd, 22 }}
{{Optimal ET sequence|legend=1| 2cd, …, 20cd, 22 }}


[[Badness]]: 0.084395
[[Badness]]: 0.084395
Line 363: Line 437:
Mapping: {{mapping| 2 1 -3 -2 -4 | 0 2 7 7 10 }}
Mapping: {{mapping| 2 1 -3 -2 -4 | 0 2 7 7 10 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~81/80 = 55.184
Optimal tunings:
* CTE: ~7/5 = 1\2, ~22/15 = 654.289 (~28/27 = 54.289)
* POTE: ~7/5 = 1\2, ~22/15 = 655.184 (~28/27 = 55.184)


{{Optimal ET sequence|legend=1| 20cde, 22 }}
{{Optimal ET sequence|legend=0| 2cde, …, 20cde, 22 }}


Badness: 0.045052
Badness: 0.045052
Line 376: Line 452:
Mapping: {{mapping| 2 1 -3 -2 -4 3 | 0 2 7 7 10 4 }}
Mapping: {{mapping| 2 1 -3 -2 -4 3 | 0 2 7 7 10 4 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~81/80 = 54.435
Optimal tunings:
* CTE: ~7/5 = 1\2, ~22/15 = 654.547 (~28/27 = 54.547)
* POTE: ~7/5 = 1\2, ~22/15 = 654.435 (~28/27 = 54.435)


{{Optimal ET sequence|legend=1| 22 }}
{{Optimal ET sequence|legend=0| 2cde, 20cde, 22 }}


Badness: 0.041470
Badness: 0.041470
Line 390: Line 468:


{{Mapping|legend=1| 2 0 -24 -23 | 0 1 9 9 }}
{{Mapping|legend=1| 2 0 -24 -23 | 0 1 9 9 }}
: mapping generators: ~7/5, ~3


{{Multival|legend=1| 2 18 18 24 23 -9 }}
{{Multival|legend=1| 2 18 18 24 23 -9 }}


[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~3/2 = 709.437
[[Optimal tuning]]s:
* [[CTE]]: ~7/5 = 1\2, ~3/2 = 708.695 (~15/14 = 108.695)
: [[error map]]: {{val| 0.000 +6.740 -8.058 +9.430 }}
* [[POTE]]: ~7/5 = 1\2, ~3/2 = 709.437 (~15/14 = 109.437)
: error map: {{val| 0.000 +7.482 -1.379 +16.109 }}


{{Optimal ET sequence|legend=1| 10cd, 12cd, 22 }}
{{Optimal ET sequence|legend=1| 10cd, 12cd, 22 }}
Line 406: Line 490:
Mapping: {{mapping| 2 0 -24 -23 -9 | 0 1 9 9 5 }}
Mapping: {{mapping| 2 0 -24 -23 -9 | 0 1 9 9 5 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 709.310
Optimal tunings:
* CTE: ~7/5 = 1\2, ~3/2 = 708.813 (~15/14 = 108.813)
* POTE: ~7/5 = 1\2, ~3/2 = 709.310 (~15/14 = 109.310)


{{Optimal ET sequence|legend=1| 10cd, 12cde, 22 }}
{{Optimal ET sequence|legend=0| 10cd, 12cde, 22 }}


Badness: 0.070910
Badness: 0.070910
Line 421: Line 507:
{{Multival|legend=1| 16 0 0 -37 -45 0 }}
{{Multival|legend=1| 16 0 0 -37 -45 0 }}


[[Optimal tuning]] ([[POTE]]): ~128/125 = 1\16, ~3/2 = 700.554
[[Optimal tuning]]s:
* [[CTE]]: ~128/125 = 1\16, ~3/2 = 701.955 (~525/512 = 26.955)
: [[error map]]: {{val| 0.000 0.000 -11.314 +6.174 }}
* [[POTE]]: ~128/125 = 1\16, ~3/2 = 700.554 (~525/512 = 25.554)
: error map: {{val| 0.000 -1.401 -11.314 +6.174 }}


{{Optimal ET sequence|legend=1| 16, 32, 48 }}
{{Optimal ET sequence|legend=1| 16, 32, 48 }}
Line 434: Line 524:
Mapping: {{mapping| 16 0 37 45 30 | 0 1 0 0 1 }}
Mapping: {{mapping| 16 0 37 45 30 | 0 1 0 0 1 }}


Optimal tuning (POTE): ~22/21 = 1\16, ~3/2 = 700.331
Optimal tunings:
* CTE: ~22/21 = 1\16, ~3/2 = 701.844 (~45/44 = 26.844)
* POTE: ~22/21 = 1\16, ~3/2 = 700.331 (~45/44 = 25.331)


{{Optimal ET sequence|legend=1| 16, 32, 48 }}
{{Optimal ET sequence|legend=0| 16, 32, 48 }}


Badness: 0.092774
Badness: 0.092774
Line 449: Line 541:
{{Mapping|legend=1| 12 19 28 34 0 | 0 0 0 0 1 }}
{{Mapping|legend=1| 12 19 28 34 0 | 0 0 0 0 1 }}


[[Optimal tuning]] ([[POTE]]): ~16/15 = 1\12, ~11/8 = 565.023
[[Optimal tuning]]s:
* [[CTE]]: ~16/15 = 1\12, ~11/8 = 551.318 (~33/32 = 48.682)
: [[error map]]: {{val| 0.000 -1.955 +13.686 +31.174 0.000 }}
* [[POTE]]: ~16/15 = 1\12, ~11/8 = 565.023 (~33/32 = 34.977)
: error map: {{val| 0.000 -1.955 +13.686 +31.174 +13.705 }}


{{Optimal ET sequence|legend=1| 12, 24d, 36d }}
{{Optimal ET sequence|legend=1| 12, 24d, 36d }}


[[Badness]]: 0.030536
[[Badness]]: 0.030536
== Notes ==


[[Category:Temperament clans]]
[[Category:Temperament clans]]