Jubilismic clan: Difference between revisions
-5-limit lemba (moved to misc. 5-limit temps) |
Review, +CTE tunings and error maps |
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== Jubilic == | == Jubilic == | ||
The head of this clan, jubilic, is generated by [[~]][[5/4]]. That and a semioctave | 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 | ||
{{Mapping|legend=3| 2 0 0 1 | 0 0 1 1 }} | |||
[[Optimal tuning]] | [[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 | {{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]] | [[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 | Optimal tunings: | ||
* CTE: ~7/5 = 1\2, ~8/7 = 231.997 | |||
* POTE: ~7/5 = 1\2, ~8/7 = 230.974 | |||
{{Optimal ET sequence|legend= | {{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 | Optimal tunings: | ||
* CTE: ~7/5 = 1\2, ~8/7 = 232.100 | |||
* POTE: ~7/5 = 1\2, ~8/7 = 230.966 | |||
{{Optimal ET sequence|legend= | {{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]] | [[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 | {{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 | Optimal tunings: | ||
* CTE: ~7/5 = 1\2, ~5/4 = 380.588 | |||
* POTE: ~7/5 = 1\2, ~5/4 = 380.530 | |||
{{Optimal ET sequence|legend= | {{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 | Optimal tunings: | ||
* CTE: ~7/5 = 1\2, ~5/4 = 380.449 | |||
* POTE: ~7/5 = 1\2, ~5/4 = 379.787 | |||
{{Optimal ET sequence|legend= | {{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 | Optimal tunings: | ||
* CTE: ~7/5 = 1\2, ~5/4 = 379.762 | |||
* POTE: ~7/5 = 1\2, ~5/4 = 379.837 | |||
{{Optimal ET sequence|legend= | {{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]] | [[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 | Optimal tunings: | ||
* CTE: ~7/5 = 1\2, ~3/2 = 754.205 | |||
* POTE: ~7/5 = 1\2, ~3/2 = 749.756 | |||
{{Optimal ET sequence|legend= | {{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]] | [[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]] | : 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 }} | |||
{{Optimal ET sequence|legend=1| 4, 14b, 18, 22, 48, 70c, 118c }} | |||
[[Badness]] | [[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]] | [[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 | {{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 | Optimal tunings: | ||
* CTE: ~7/5 = 1\2, ~6/5 = 325.719 | |||
* POTE: ~7/5 = 1\2, ~6/5 = 325.545 | |||
{{Optimal ET sequence|legend= | {{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 | Optimal tunings: | ||
* CTE: ~7/5 = 1\2, ~6/5 = 326.684 | |||
* POTE: ~7/5 = 1\2, ~6/5 = 327.038 | |||
{{Optimal ET sequence|legend= | {{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 | Optimal tunings: | ||
* CTE: ~7/5 = 1\2, ~6/5 = 327.450 | |||
* POTE: ~7/5 = 1\2, ~6/5 = 327.841 | |||
{{Optimal ET sequence|legend= | {{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 | Optimal tunings: | ||
* CTE: ~7/5 = 1\2, ~6/5 = 324.238 | |||
* POTE: ~7/5 = 1\2, ~6/5 = 323.427 | |||
{{Optimal ET sequence|legend= | {{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 | Optimal tunings: | ||
* CTE: ~7/5 = 1\2, ~6/5 = 324.187 | |||
* POTE: ~7/5 = 1\2, ~6/5 = 323.396 | |||
{{Optimal ET sequence|legend= | {{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 [[ | : ''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]] | [[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 | 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= | {{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 | 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= | {{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 [[ | : ''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]] | [[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 | 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= | {{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 | 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= | {{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]] | [[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 | 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= | {{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]] | [[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 | 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= | {{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]] | [[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]] | ||