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Gamelismic clan: Difference between revisions

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+CTE tunings and error maps (1/2)
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~8/7 = 233.889
* [[CTE]]: ~2 = 1200.000, ~8/7 = 233.889
: [[error map]]: {{val| 0.000 -0.288 -2.715 }}
* [[POTE]]: ~2 = 1200.000, ~8/7 = 233.688
* [[POTE]]: ~2 = 1200.000, ~8/7 = 233.688
: error map: {{val| 0.000 -0.892 -2.513 }}


{{Optimal ET sequence|legend=1| 36, 77, 113, 190 }}
{{Optimal ET sequence|legend=1| 36, 77, 113, 190 }}
Line 55: Line 57:
: [[gencom]]: [2 8/7; 896/891 1029/1024]
: [[gencom]]: [2 8/7; 896/891 1029/1024]


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~8/7 = 234.381
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~8/7 = 234.384
: [[error map]]: {{val| 0.000 +1.197 -3.210 +1.691 }}
* [[POTE]]: ~2 = 1200.000, ~8/7 = 234.381
: error map: {{val| 0.000 +1.187 -3.206 +1.735 }}


{{Optimal ET sequence|legend=1| 36, 41, 87, 128 }}
{{Optimal ET sequence|legend=1| 36, 41, 87, 128 }}
Line 70: Line 76:
: sval mapping generators: ~17/12, ~8/7
: sval mapping generators: ~17/12, ~8/7


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~8/7 = 233.616
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~8/7 = 234.138
* [[POTE]]: ~2 = 1200.000, ~8/7 = 233.616


{{Optimal ET sequence|legend=1| 10, 26, 36, 154f, 190ffg, 226ffg }}
{{Optimal ET sequence|legend=1| 10, 26, 36, 154f, 190ffg, 226ffg }}
Line 88: Line 96:
{{Multival|legend=1| 3 17 -1 20 -10 -50 }}
{{Multival|legend=1| 3 17 -1 20 -10 -50 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~8/7 = 234.417
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~8/7 = 234.450
: [[error map]]: {{val| 0.000 +1.396 -0.660 -3.276 }}
* [[POTE]]: ~2 = 1200.000, ~8/7 = 234.417
: error map: {{val| 0.000 +1.295 -1.229 -3.243 }}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 108: Line 120:
Mapping: {{mapping| 1 1 -1 3 6 | 0 3 17 -1 -13 }}
Mapping: {{mapping| 1 1 -1 3 6 | 0 3 17 -1 -13 }}


Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 234.459
Optimal tunings:
* CTE: ~2 = 1200.000, ~8/7 = 234.463
* POTE: ~2 = 1200.000, ~8/7 = 234.459


Minimax tuning:  
Minimax tuning:  
Line 117: Line 131:
Algebraic generator: positive root of ''x''<sup>2</sup> + 16''x'' - 31, or √95 - 8.
Algebraic generator: positive root of ''x''<sup>2</sup> + 16''x'' - 31, or √95 - 8.


{{Optimal ET sequence|legend=0| 41, 46, 87 }}
{{Optimal ET sequence|legend=0| 41, 87 }}


Badness (Smith): 0.023093
Badness (Smith): 0.023093
Line 128: Line 142:
Mapping: {{mapping| 1 1 -1 3 6 8 | 0 3 17 -1 -13 -22 }}
Mapping: {{mapping| 1 1 -1 3 6 8 | 0 3 17 -1 -13 -22 }}


Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 234.482
Optimal tunings:
* CTE: ~2 = 1200.000, ~8/7 = 234.482
* POTE: ~2 = 1200.000, ~8/7 = 234.482


Minimax tuning:  
Minimax tuning:  
Line 147: Line 163:
Mapping: {{mapping| 1 1 -1 3 6 8 8 | 0 3 17 -1 -13 -22 -20 }}
Mapping: {{mapping| 1 1 -1 3 6 8 8 | 0 3 17 -1 -13 -22 -20 }}


Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 234.524
Optimal tunings:
* CTE: ~2 = 1200.000, ~8/7 = 234.532
* POTE: ~2 = 1200.000, ~8/7 = 234.524


Minimax tuning:
Minimax tuning:
Line 153: Line 171:
: eigenmonzo (unchanged-interval) basis: 2.17/9
: eigenmonzo (unchanged-interval) basis: 2.17/9


{{Optimal ET sequence|legend=0| 41, 46, 87, 220dg, 307dgg }}
{{Optimal ET sequence|legend=0| 41, 46, 87 }}


Badness (Smith): 0.016743
Badness (Smith): 0.016743
Line 164: Line 182:
Mapping: {{mapping| 1 1 -1 3 6 -1 | 0 3 17 -1 -13 24 }}
Mapping: {{mapping| 1 1 -1 3 6 -1 | 0 3 17 -1 -13 24 }}


Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 234.639
Optimal tunings:
* CTE: ~2 = 1200.000, ~8/7 = 234.670
* POTE: ~2 = 1200.000, ~8/7 = 234.639


{{Optimal ET sequence|legend=0| 5, 41f, 46, 133ff }}
{{Optimal ET sequence|legend=0| 5, 41f, 46 }}


Badness (Smith): 0.033986
Badness (Smith): 0.033986
Line 177: Line 197:
Mapping: {{mapping| 1 1 -1 3 -3 | 0 3 17 -1 33 }}
Mapping: {{mapping| 1 1 -1 3 -3 | 0 3 17 -1 33 }}


Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 234.728
Optimal tunings:
* CTE: ~2 = 1200.000, ~8/7 = 234.719
* POTE: ~2 = 1200.000, ~8/7 = 234.728


{{Optimal ET sequence|legend=0| 41e, 46 }}
{{Optimal ET sequence|legend=0| 5e, 41e, 46 }}


Badness (Smith): 0.054294
Badness (Smith): 0.054294
Line 190: Line 212:
Mapping: {{mapping| 1 1 -1 3 -3 -1 | 0 3 17 -1 33 24 }}
Mapping: {{mapping| 1 1 -1 3 -3 -1 | 0 3 17 -1 33 24 }}


Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 234.782
Optimal tunings:
* CTE: ~2 = 1200.000, ~8/7 = 234.786
* POTE: ~2 = 1200.000, ~8/7 = 234.782


{{Optimal ET sequence|legend=0| 41ef, 46 }}
{{Optimal ET sequence|legend=0| 5e, 41ef, 46 }}


Badness (Smith): 0.035836
Badness (Smith): 0.035836
Line 203: Line 227:
Mapping: {{mapping| 1 1 -1 3 -2 | 0 3 17 -1 28 }}
Mapping: {{mapping| 1 1 -1 3 -2 | 0 3 17 -1 28 }}


Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 234.145
Optimal tunings:
* CTE: ~2 = 1200.000, ~8/7 = 234.197
* POTE: ~2 = 1200.000, ~8/7 = 234.145


{{Optimal ET sequence|legend=0| 36ce, 41 }}
{{Optimal ET sequence|legend=0| 5e, 36ce, 41 }}


Badness (Smith): 0.044937
Badness (Smith): 0.044937
Line 216: Line 242:
Mapping: {{mapping| 1 1 -1 3 -2 0 | 0 3 17 -1 28 19 }}
Mapping: {{mapping| 1 1 -1 3 -2 0 | 0 3 17 -1 28 19 }}


Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 234.089
Optimal tunings:
* CTE: ~2 = 1200.000, ~8/7 = 234.111
* POTE: ~2 = 1200.000, ~8/7 = 234.089


{{Optimal ET sequence|legend=0| 36ce, 41 }}
{{Optimal ET sequence|legend=0| 5e, 36ce, 41 }}


Badness (Smith): 0.032284
Badness (Smith): 0.032284
Line 235: Line 263:
{{Multival|legend=1| 3 -24 -1 -45 -10 65 }}
{{Multival|legend=1| 3 -24 -1 -45 -10 65 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~8/7 = 233.930
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~8/7 = 233.903
: [[error map]]: {{val| 0.000 -0.246 +0.012 -2.729 }}
* [[POTE]]: ~2 = 1200.000, ~8/7 = 233.930
: error map: {{val| 0.000 -0.165 -0.637 -2.756 }}


[[Minimax tuning]]:
[[Minimax tuning]]:
Line 255: Line 287:
: mapping generators: ~2, ~8/7
: mapping generators: ~2, ~8/7


Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 233.931
Optimal tunings:
* CTE: ~2 = 1200.000, ~8/7 = 233.930
* POTE: ~2 = 1200.000, ~8/7 = 233.931


Minimax tuning:
Minimax tuning:
Line 275: Line 309:
: mapping generators: ~2, ~8/7
: mapping generators: ~2, ~8/7


Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 233.890
Optimal tunings:
* CTE: ~2 = 1200.000, ~8/7 = 233.902
* POTE: ~2 = 1200.000, ~8/7 = 233.899


{{Optimal ET sequence|legend=0| 36e, 41, 77, 118 }}
{{Optimal ET sequence|legend=0| 36e, 41, 77, 118 }}
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== Mothra ==
== Mothra ==
Mothra tempers out [[81/80]] and finds the prime 5 at a stack of four fifths as does any temperament in the [[meantone family]]. It also tempers out [[1728/1715]], the orwellisma. It can be described as 26 & 31. Using [[31edo]] with a generator of 6/31 is an excellent tuning choice. However, a pure mos mothra scale is often described as directionless and has limited chord-building potential<ref>https://www.youtube.com/watch?v=uH3ahBzDSrs</ref>, so something other than a mos may be used as a scale to get the most out of mothra. There are examples of non-mos mothra scales in 31edo [[Strictly proper 7-tone 31edo scales|in the article on strictly proper 7-tone 31edo scales]].  
Mothra tempers out [[81/80]] and finds the prime 5 at a stack of four fifths as does any temperament in the [[meantone family]]. It also tempers out [[1728/1715]], the orwellisma. It can be described as 26 & 31. Using [[31edo]] with a generator of 6/31 is an excellent tuning choice. However, a pure mos mothra scale is often described as directionless and has limited chord-building potential<ref>[https://www.youtube.com/watch?v=uH3ahBzDSrs 31-EDO Music Theory: Supermajor Hexatonic Scale] by [[Zhea Erose]]</ref>, so something other than a mos may be used as a scale to get the most out of mothra. There are examples of non-mos mothra scales in 31edo [[Strictly proper 7-tone 31edo scales|in the article on strictly proper 7-tone 31edo scales]].  


Note that mothra is also called '''cynder''' in the 7-limit, which can be a little confusing sometimes.  
Note that mothra is also called '''cynder''' in the 7-limit, which can be a little confusing sometimes.  
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{{Multival|legend=1| 3 12 -1 12 -10 -36 }}
{{Multival|legend=1| 3 12 -1 12 -10 -36 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~8/7 = 232.193
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~8/7 = 232.400
: [[error map]]: {{val| 0.000 -4.756 +2.482 -1.226 }}
* [[POTE]]: ~2 = 1200.000, ~8/7 = 232.193
: error map: {{val| 0.000 -5.375 +0.005 -1.019 }}


[[Algebraic generator]]: Rabrindanath, largest real root of ''x''<sup>8</sup> - 3''x''<sup>2</sup> + 1, or 232.0774 cents.
[[Algebraic generator]]: Rabrindanath, largest real root of ''x''<sup>8</sup> - 3''x''<sup>2</sup> + 1, or 232.0774 cents.
Line 307: Line 347:
: [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5
: [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5


{{Optimal ET sequence|legend=1| 5, 26, 31 }}
{{Optimal ET sequence|legend=1| 5, 21c, 26, 31 }}


[[Badness]] (Smith): 0.037146
[[Badness]] (Smith): 0.037146
Line 320: Line 360:
{{Multival|legend=1| 3 12 -1 -8 12 -10 -23 -36 -60 -19 }}
{{Multival|legend=1| 3 12 -1 -8 12 -10 -23 -36 -60 -19 }}


Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 232.031
Optimal tunings:
* CTE: ~2 = 1200.000, ~8/7 = 232.203
* POTE: ~2 = 1200.000, ~8/7 = 232.031


{{Optimal ET sequence|legend=0| 5, 26, 31, 88, 150be, 181bee }}
{{Optimal ET sequence|legend=0| 5, 26, 31, 88, 119be, 150be }}


Badness (Smith): 0.025642
Badness (Smith): 0.025642
Line 333: Line 375:
Mapping: {{mapping| 1 1 0 3 5 1 | 0 3 12 -1 -8 14 }}
Mapping: {{mapping| 1 1 0 3 5 1 | 0 3 12 -1 -8 14 }}


Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 231.811
Optimal tunings:
* CTE: ~2 = 1200.000, ~8/7 = 231.993
* POTE: ~2 = 1200.000, ~8/7 = 231.811


{{Optimal ET sequence|legend=0| 5, 26, 31, 57, 88 }}
{{Optimal ET sequence|legend=0| 5, 26, 31, 57, 88 }}
Line 349: Line 393:
Mapping: {{mapping| 1 1 0 3 0 | 0 3 12 -1 18 }}
Mapping: {{mapping| 1 1 0 3 0 | 0 3 12 -1 18 }}


Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 231.317
Optimal tunings:
* CTE: ~2 = 1200.000, ~8/7 = 231.566
* POTE: ~2 = 1200.000, ~8/7 = 231.317


{{Optimal ET sequence|legend=0| 5e, 26, 57e, 83bce }}
{{Optimal ET sequence|legend=0| 5e, 21ce, 26 }}


Badness (Smith): 0.055706
Badness (Smith): 0.055706
Line 362: Line 408:
Mapping: {{mapping| 1 1 0 3 0 1 | 0 3 12 -1 18 14 }}
Mapping: {{mapping| 1 1 0 3 0 1 | 0 3 12 -1 18 14 }}


Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 231.293
Optimal tunings:
* CTE: ~2 = 1200.000, ~8/7 = 231.546
* POTE: ~2 = 1200.000, ~8/7 = 231.293


{{Optimal ET sequence|legend=0| 5e, 26, 57e, 83bce }}
{{Optimal ET sequence|legend=0| 5e, 21cef, 26 }}


Badness (Smith): 0.034124
Badness (Smith): 0.034124
Line 379: Line 427:
Wedgie: {{Multival| 3 12 -1 23 12 -10 26 -36 12 68 }}
Wedgie: {{Multival| 3 12 -1 23 12 -10 26 -36 12 68 }}


Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 232.419
Optimal tunings:
* CTE: ~2 = 1200.000, ~8/7 = 232.557
* POTE: ~2 = 1200.000, ~8/7 = 232.419


{{Optimal ET sequence|legend=0| 31, 129, 160be, 191bce, 222bce, 253bcee }}
{{Optimal ET sequence|legend=0| 5e, 26e, 31, 129 }}


Badness (Smith): 0.031334
Badness (Smith): 0.031334
Line 392: Line 442:
Mapping: {{mapping| 1 1 0 3 -1 7 | 0 3 12 -1 23 -17 }}
Mapping: {{mapping| 1 1 0 3 -1 7 | 0 3 12 -1 23 -17 }}


Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 232.640
Optimal tunings:
* CTE: ~2 = 1200.000, ~8/7 = 232.635
* POTE: ~2 = 1200.000, ~8/7 = 232.640


{{Optimal ET sequence|legend=0| 31, 36, 67, 98 }}
{{Optimal ET sequence|legend=0| 31, 67, 98 }}


Badness (Smith): 0.036857
Badness (Smith): 0.036857
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{{Multival|legend=1| 3 7 4 }}
{{Multival|legend=1| 3 7 4 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~10/9 = 227.426
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~8/7 = 228.700
: [[error map]]: {{val| 0.000 -15.856 +14.584 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 227.426
: error map: {{val| 0.000 -19.679 +5.664 }}


{{Optimal ET sequence|legend=1| 5, 16, 21, 37b }}
{{Optimal ET sequence|legend=1| 5, 11c, 16, 21, 37b }}


[[Badness]] (Smith): 0.161799
[[Badness]] (Smith): 0.161799
Line 425: Line 481:
{{Multival|legend=1| 3 7 -1 4 -10 -22 }}
{{Multival|legend=1| 3 7 -1 4 -10 -22 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~8/7 = 228.334
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~8/7 = 228.724
: [[error map]]: {{val| 0.000 -15.782 +14.756 +2.450 }}
* [[POTE]]: ~2 = 1200.000, ~8/7 = 228.334
: error map: {{val| 0.000 -16.954 +12.022 +2.840 }}


{{Optimal ET sequence|legend=1| 5, 11c, 16, 21 }}
{{Optimal ET sequence|legend=1| 5, 11c, 16, 21 }}
Line 438: Line 498:
Mapping: {{mapping| 1 1 1 3 1 | 0 3 7 -1 13 }}
Mapping: {{mapping| 1 1 1 3 1 | 0 3 7 -1 13 }}


Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 227.373
Optimal tunings:
* CTE: ~2 = 1200.000, ~8/7 = 227.833
* POTE: ~2 = 1200.000, ~8/7 = 227.373


{{Optimal ET sequence|legend=0| 16, 21, 37b }}
{{Optimal ET sequence|legend=0| 5e, 16, 21, 37b }}


Badness (Smith): 0.049500
Badness (Smith): 0.049500
Line 451: Line 513:
Mapping: {{mapping| 1 1 1 3 1 2 | 0 3 7 -1 13 9 }}
Mapping: {{mapping| 1 1 1 3 1 2 | 0 3 7 -1 13 9 }}


Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 227.230
Optimal tunings:
* CTE: ~2 = 1200.000, ~8/7 = 227.633
* POTE: ~2 = 1200.000, ~8/7 = 227.230


{{Optimal ET sequence|legend=0| 16, 21, 37b }}
{{Optimal ET sequence|legend=0| 5e, 16, 21, 37b }}


Badness (Smith): 0.032664
Badness (Smith): 0.032664
Line 464: Line 528:
Mapping: {{mapping| 1 1 1 3 5 | 0 3 7 -1 -8 }}
Mapping: {{mapping| 1 1 1 3 5 | 0 3 7 -1 -8 }}


Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 229.535
Optimal tunings:
* CTE: ~2 = 1200.000, ~8/7 = 229.420
* POTE: ~2 = 1200.000, ~8/7 = 229.535


{{Optimal ET sequence|legend=0| 5, 16e, 21, 47c, 68bcce }}
{{Optimal ET sequence|legend=0| 5, 16e, 21 }}


Badness (Smith): 0.062683
Badness (Smith): 0.062683
Line 477: Line 543:
Mapping: {{mapping| 1 1 1 3 5 2 | 0 3 7 -1 -8 9 }}
Mapping: {{mapping| 1 1 1 3 5 2 | 0 3 7 -1 -8 9 }}


Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 229.059
Optimal tunings:
* CTE: ~2 = 1200.000, ~8/7 = 228.758
* POTE: ~2 = 1200.000, ~8/7 = 229.059


{{Optimal ET sequence|legend=0| 5, 16e, 21, 68bccef }}
{{Optimal ET sequence|legend=0| 5, 16e, 21 }}


Badness (Smith): 0.047071
Badness (Smith): 0.047071
Line 488: Line 556:
== Gidorah ==
== Gidorah ==
: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #University]].''
: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #University]].''
16c-, 21cc-, and 26ccc-edo are among the possible tunings.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 497: Line 567:
{{Multival|legend=1| 3 2 -1 -4 -10 -8 }}
{{Multival|legend=1| 3 2 -1 -4 -10 -8 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~8/7 = 230.762
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~8/7 = 227.100
: [[error map]]: {{val| 0.000 -20.655 +67.886 +4.074 }}
* [[POTE]]: ~2 = 1200.000, ~8/7 = 230.762
: error map: {{val| 0.000 -9.668 +75.211 +0.412 }}


{{Optimal ET sequence|legend=1| 5, 16c, 21cc, 26ccc }}
{{Optimal ET sequence|legend=1| 1b, 5 }}


[[Badness]] (Smith): 0.062262
[[Badness]] (Smith): 0.062262
Line 512: Line 586:
{{Mapping|legend=1| 1 1 6 3 | 0 3 -19 -1 }}
{{Mapping|legend=1| 1 1 6 3 | 0 3 -19 -1 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~8/7 = 232.498
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~8/7 = 232.383
: [[error map]]: {{val| 0.000 -4.807 -1.585 -1.209 }}
* [[POTE]]: ~2 = 1200.000, ~8/7 = 232.498
: error map: {{val| 0.000 -4.461 -3.778 -1.324 }}


{{Optimal ET sequence|legend=1| 31, 98c, 129c, 160bc }}
{{Optimal ET sequence|legend=1| 31, 98c, 129c, 160bc }}
Line 527: Line 605:
{{Mapping|legend=1| 1 1 5 3 | 0 3 -14 -1 }}
{{Mapping|legend=1| 1 1 5 3 | 0 3 -14 -1 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~8/7 = 230.258
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~8/7 = 229.951
: [[error map]]: {{val| 0.000 -12.102 -5.626 +1.223 }}
* [[POTE]]: ~2 = 1200.000, ~8/7 = 230.258
: error map: {{val| 0.000 -11.180 -9.933 +0.916 }}


{{Optimal ET sequence|legend=1| 21, 26, 47, 73bc, 99bc }}
{{Optimal ET sequence|legend=1| 21, 26, 47, 73bc, 99bc }}
Line 544: Line 626:
{{Multival|legend=1| 3 -9 -1 -21 -10 23 }}
{{Multival|legend=1| 3 -9 -1 -21 -10 23 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~8/7 = 226.469
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~8/7 = 225.752
: [[error map]]: {{val| 0.000 -24.699 -18.081 +5.422 }}
* [[POTE]]: ~2 = 1200.000, ~8/7 = 226.469
: error map: {{val| 0.000 -22.548 -24.534 +4.705 }}


{{Optimal ET sequence|legend=1| 5c, 11, 16 }}
{{Optimal ET sequence|legend=1| 5c, 11, 16 }}
Line 557: Line 643:
Mapping: {{mapping| 1 1 4 3 4 | 0 3 -9 -1 -3 }}
Mapping: {{mapping| 1 1 4 3 4 | 0 3 -9 -1 -3 }}


Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 226.428
Optimal tunings:
* CTE: ~2 = 1200.000, ~8/7 = 225.384
* POTE: ~2 = 1200.000, ~8/7 = 226.428


{{Optimal ET sequence|legend=0| 5c, 11, 16 }}
{{Optimal ET sequence|legend=0| 5c, 11, 16 }}
Line 1,246: Line 1,334:


Badness (Smith): 0.021636
Badness (Smith): 0.021636
== Notes ==


[[Category:Temperament clans]]
[[Category:Temperament clans]]
Retrieved from "https://en.xen.wiki/w/Gamelismic_clan"