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Sensipent family: Difference between revisions

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TallKite (talk | contribs)
autopatrolled, Sysops
3,990 edits
added pergens. fixed some errors. added the color name. corrected the mappings to match the 1st paragraph's description of the generator as well as all the optimal tunings. deleted the warning about mappings not matching since now they match. changed "1\1" to "1200¢" because "one edostep of 1edo" is a very unnatural, obtuse description of an octave, and also inaccurate because 1edo can be stretched or compressed, but these tunings require exactly 1200¢. changed 1\2 and 1\3 for the same reasons.
Partial revert for "1\1" (Sorry, I don't buy those arguments. "1\1" is perfectly precise whereas "1200 cents" has a limited number of significant figures. I don't buy pergen hardcoding a form of mapping either, so don't call it pergen form! It's just the common form, not formally documented in the normal lists page yet)
Line 22: Line 22:
[[Comma list]]: 78732/78125
[[Comma list]]: 78732/78125


{{Mapping|legend=1| 1 -1 -1| 0 7 9 }}
{{Mapping|legend=1| 1 -1 -1 | 0 7 9 }}


: mapping generators: ~2, ~162/125
: mapping generators: ~2, ~162/125


[[Optimal tuning]] ([[POTE]]): 2 = 1200¢, ~162/125 = 443.058
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~162/125 = 443.058


{{Optimal ET sequence|legend=1| 8, 19, 46, 65, 539, 604c, 669c, 734c, 799c, 864c, 929c }}
{{Optimal ET sequence|legend=1| 8, 19, 46, 65, 539, 604c, 669c, 734c, 799c, 864c, 929c }}
Line 47: Line 47:
{{Optimal ET sequence|legend=1| 8, 11c, 19, 46, 65, 344, 409, 474, 539, 604c }}
{{Optimal ET sequence|legend=1| 8, 11c, 19, 46, 65, 344, 409, 474, 539, 604c }}


[[Optimal tuning]] ([[CTE]]): 2 = 1200¢, ~31/24 = 443.050
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~31/24 = 443.050


Badness (Dirichlet): 0.243
Badness (Dirichlet): 0.243
Line 63: Line 63:
{{Optimal ET sequence|legend=1| 19, 46j, 65, 149, 363j }}
{{Optimal ET sequence|legend=1| 19, 46j, 65, 149, 363j }}


[[Optimal tuning]] ([[CTE]]): 2 = 1200¢, ~31/24 = 442.989
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~31/24 = 442.989


Badness (Dirichlet): 0.283
Badness (Dirichlet): 0.283
Line 80: Line 80:
{{Optimal ET sequence|legend=1| 19, 46, 65, 176, 241, 306 }}
{{Optimal ET sequence|legend=1| 19, 46, 65, 176, 241, 306 }}


[[Optimal tuning]] ([[CTE]]): 2 = 1200¢, ~128/99 = 443.115
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~128/99 = 443.115


Badness (Dirichlet): 0.728
Badness (Dirichlet): 0.728
Line 97: Line 97:
{{Optimal ET sequence|legend=1| 19, 46, 65, 111, 176g }}
{{Optimal ET sequence|legend=1| 19, 46, 65, 111, 176g }}


[[Optimal tuning]] ([[CTE]]): 2 = 1200¢, ~22/17 = 443.188
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~22/17 = 443.188


Badness (Dirichlet): 0.639
Badness (Dirichlet): 0.639
Line 110: Line 110:
{{Optimal ET sequence|legend=1| 19, 46, 65, 111, 176g }}
{{Optimal ET sequence|legend=1| 19, 46, 65, 111, 176g }}


[[Optimal tuning]] ([[CTE]]): 2 = 1200¢, ~22/17 = 443.185
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~22/17 = 443.185


Badness (Dirichlet): 0.555
Badness (Dirichlet): 0.555
Line 125: Line 125:
{{Optimal ET sequence|legend=1| 19, 46, 65, 111, 176g }}
{{Optimal ET sequence|legend=1| 19, 46, 65, 111, 176g }}


[[Optimal tuning]] ([[CTE]]): 2 = 1200¢, ~22/17 = 443.183
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~22/17 = 443.183


Badness (Dirichlet): 0.490
Badness (Dirichlet): 0.490
Line 146: Line 146:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200¢, ~9/7 = 443.3166
* [[CTE]]: ~2 = 1\1, ~9/7 = 443.3166
* [[POTE]]: ~2 = 1200¢, ~9/7 = 443.383
* [[POTE]]: ~2 = 1\1, ~9/7 = 443.383


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 176: Line 176:
: mapping generators: ~2, ~9/7
: mapping generators: ~2, ~9/7


Optimal tuning (CTE): ~2 = 1200¢, ~9/7 = 443.4016
Optimal tuning (CTE): ~2 = 1\1, ~9/7 = 443.4016


{{Optimal ET sequence|legend=1| 19, 27, 46, 111df }}
{{Optimal ET sequence|legend=1| 19, 27, 46, 111df }}
Line 192: Line 192:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200¢, ~9/7 = 443.2987
* CTE: ~2 = 1\1, ~9/7 = 443.2987
* POTE: ~2 = 1200¢, ~9/7 = 443.294
* POTE: ~2 = 1\1, ~9/7 = 443.294


{{Optimal ET sequence|legend=1| 19, 27, 46, 111d }}
{{Optimal ET sequence|legend=1| 19, 27, 46, 111d }}
Line 209: Line 209:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200¢, ~9/7 = 443.3658
* CTE: ~2 = 1\1, ~9/7 = 443.3658
* POTE: ~2 = 1200¢, ~9/7 = 443.321
* POTE: ~2 = 1\1, ~9/7 = 443.321


{{Optimal ET sequence|legend=1| 19, 27, 46, 111df }}
{{Optimal ET sequence|legend=1| 19, 27, 46, 111df }}
Line 224: Line 224:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200¢, ~9/7 = 443.3775
* CTE: ~2 = 1\1, ~9/7 = 443.3775
* POTE: ~2 = 1200¢, ~9/7 = 443.365
* POTE: ~2 = 1\1, ~9/7 = 443.365


{{Optimal ET sequence|legend=1| 19, 27, 46 }}
{{Optimal ET sequence|legend=1| 19, 27, 46 }}
Line 243: Line 243:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200¢, ~9/7 = 443.4783
* CTE: ~2 = 1\1, ~9/7 = 443.4783
* POTE: ~2 = 1200¢, ~9/7 = 443.626
* POTE: ~2 = 1\1, ~9/7 = 443.626


{{Optimal ET sequence|legend=1| 19e, 27e, 46, 119c }}
{{Optimal ET sequence|legend=1| 19e, 27e, 46, 119c }}
Line 260: Line 260:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200¢, ~9/7 = 443.5075
* CTE: ~2 = 1\1, ~9/7 = 443.5075
* POTE: ~2 = 1200¢, ~9/7 = 443.559
* POTE: ~2 = 1\1, ~9/7 = 443.559


{{Optimal ET sequence|legend=1| 19e, 27e, 46 }}
{{Optimal ET sequence|legend=1| 19e, 27e, 46 }}
Line 275: Line 275:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200¢, ~9/7 = 443.5050
* CTE: ~2 = 1\1, ~9/7 = 443.5050
* POTE: ~2 = 1200¢, ~9/7 = 443.551
* POTE: ~2 = 1\1, ~9/7 = 443.551


{{Optimal ET sequence|legend=1| 19eg, 27eg, 46 }}
{{Optimal ET sequence|legend=1| 19eg, 27eg, 46 }}
Line 294: Line 294:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200¢, ~9/7 = 443.1886
* CTE: ~2 = 1\1, ~9/7 = 443.1886
* POTE: ~2 = 1200¢, ~9/7 = 443.962
* POTE: ~2 = 1\1, ~9/7 = 443.962


{{Optimal ET sequence|legend=1| 8d, 19, 27e }}
{{Optimal ET sequence|legend=1| 8d, 19, 27e }}
Line 311: Line 311:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200¢, ~9/7 = 443.2863
* CTE: ~2 = 1\1, ~9/7 = 443.2863
* POTE: ~2 = 1200¢, ~9/7 = 443.945
* POTE: ~2 = 1\1, ~9/7 = 443.945


{{Optimal ET sequence|legend=1| 8d, 19, 27e }}
{{Optimal ET sequence|legend=1| 8d, 19, 27e }}
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200¢, ~9/7 = 443.7814
* CTE: ~2 = 1\1, ~9/7 = 443.7814
* POTE: ~2 = 1200¢, ~9/7 = 443.518
* POTE: ~2 = 1\1, ~9/7 = 443.518


{{Optimal ET sequence|legend=1| 8d, 19e, 27 }}
{{Optimal ET sequence|legend=1| 8d, 19e, 27 }}
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200¢, ~9/7 = 443.7877
* CTE: ~2 = 1\1, ~9/7 = 443.7877
* POTE: ~2 = 1200¢, ~9/7 = 443.506
* POTE: ~2 = 1\1, ~9/7 = 443.506


{{Optimal ET sequence|legend=1| 8d, 19e, 27 }}
{{Optimal ET sequence|legend=1| 8d, 19e, 27 }}
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Badness: 0.023258
Badness: 0.023258


=== Bisensi (P8/2, ccP5/7) ===
=== Bisensi ===
Bisensi has pergen (P8/2, ccP5/7).
 
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 121/120, 126/125, 245/243
Comma list: 121/120, 126/125, 245/243


Pergen mapping: {{mapping| 2 -2 -2 -4 1 | 0 7 9 13 8}}
Mapping:
 
* common form: {{mapping| 2 -2 -2 -4 1 | 0 7 9 13 8 }}
: mapping generators: ~99/70, ~9/7
:: mapping generators: ~99/70, ~9/7
Mincents mapping: [⟨2 5 7 9 9], ⟨0 -7 -9 -13 -8]]
* mingen form: {{mapping| 2 5 7 9 9 | 0 -7 -9 -13 -8 }}
: mapping generators: ~99/70, ~11/10
:: mapping generators: ~99/70, ~11/10


Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 600¢, ~9/7 = 443.3688, ~11/10 = 156.6312
* CTE: ~99/70 = 1\2, ~9/7 = 443.3688 (~11/10 = 156.6312)
* POTE: ~99/70 = 600¢, ~9/7 = 443.308, ~11/10 = 156.692
* POTE: ~99/70 = 1\2, ~9/7 = 443.308 (~11/10 = 156.692)


{{Optimal ET sequence|legend=1| 8d, …, 38d, 46 }}
{{Optimal ET sequence|legend=1| 8d, …, 38d, 46 }}
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Comma list: 91/90, 121/120, 126/125, 169/168
Comma list: 91/90, 121/120, 126/125, 169/168


Pergen mapping: {{mapping| 2 -2 -2 -4 1 0| 0 7 9 13 8 10}}
Mapping:
: mapping generators: ~99/70, ~9/7
* common form: {{mapping| 2 -2 -2 -4 1 0 | 0 7 9 13 8 10}}
 
:: mapping generators: ~99/70, ~9/7
Mincents mapping: {{mapping| 2 5 7 9 9 10 | 0 -7 -9 -13 -8 -10 }}
* mingen form: {{mapping| 2 5 7 9 9 10 | 0 -7 -9 -13 -8 -10 }}
 
:: mapping generators: ~99/70, ~11/10
: mapping generators: ~99/70, ~11/10


Optimal tunings:  
Optimal tunings:  
* CTE: ~55/39 = 600¢, ~9/7 = 443.4416, ~11/10 = 156.5584
* CTE: ~55/39 = 1\2, ~9/7 = 443.4416, ~11/10 = 156.5584
* POTE: ~55/39 = 600¢, ~9/7 = 443.275, ~11/10 = 156.725
* POTE: ~55/39 = 1\2, ~9/7 = 443.275, ~11/10 = 156.725


{{Optimal ET sequence|legend=1| 8d, …, 38df, 46 }}
{{Optimal ET sequence|legend=1| 8d, …, 38df, 46 }}
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Comma list: 91/90, 121/120, 126/125, 154/153, 169/168
Comma list: 91/90, 121/120, 126/125, 154/153, 169/168


Pergen mapping: {{mapping| 2 -2 -2 -4 1 0 3 | 0 7 9 13 8 10 7}}
Mapping:
 
* common form: {{mapping| 2 -2 -2 -4 1 0 3 | 0 7 9 13 8 10 7}}
: mapping generators: ~99/70, ~9/7
:: mapping generators: ~99/70, ~9/7
 
* mingen form: {{mapping| 2 5 7 9 9 10 10 | 0 -7 -9 -13 -8 -10 -7 }}
Mincents mapping: {{mapping| 2 5 7 9 9 10 10 | 0 -7 -9 -13 -8 -10 -7 }}
:: mapping generators: ~99/70, ~11/10
 
: mapping generators: ~99/70, ~11/10


Optimal tunings:  
Optimal tunings:  
* CTE: ~17/12 = 600¢, ~9/7 = 443.4466, ~11/10 = 156.5534
* CTE: ~17/12 = 1\2, ~9/7 = 443.4466 (~11/10 = 156.5534)


{{Optimal ET sequence|legend=1| 8d, …, 38df, 46 }}
{{Optimal ET sequence|legend=1| 8d, …, 38df, 46 }}
Line 409: Line 408:
Badness: 0.0188
Badness: 0.0188


=== Hemisensi (P8, ccP5/14) ===
=== Hemisensi ===
Hemisensi has pergen (P8, ccP5/14).
 
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 419: Line 420:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200¢, ~25/22 = 221.5981
* CTE: ~2 = 1\1, ~25/22 = 221.5981
* POTE: ~2 = 1200¢, ~25/22 = 221.605
* POTE: ~2 = 1\1, ~25/22 = 221.605


{{Optimal ET sequence|legend=1| 27e, 38d, 65 }}
{{Optimal ET sequence|legend=1| 27e, 38d, 65 }}
Line 434: Line 435:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200¢, ~25/22 = 221.6333
* CTE: ~2 = 1\1, ~25/22 = 221.6333
* POTE: ~2 = 1200¢, ~25/22 = 221.556
* POTE: ~2 = 1\1, ~25/22 = 221.556


{{Optimal ET sequence|legend=1| 27e, 38df, 65f }}
{{Optimal ET sequence|legend=1| 27e, 38df, 65f }}
Line 452: Line 453:
{{Multival|legend=1| 7 9 32 -2 31 49 }}
{{Multival|legend=1| 7 9 32 -2 31 49 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200¢, ~162/125 = 442.755
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~162/125 = 442.755


{{Optimal ET sequence|legend=1| 19, 65d, 84, 103, 187, 290b }}
{{Optimal ET sequence|legend=1| 19, 65d, 84, 103, 187, 290b }}
Line 463: Line 464:
[[Comma list]]: 5120/5103, 78732/78125
[[Comma list]]: 5120/5103, 78732/78125


{{Mapping|legend=1| 1 -1 -1 15| 0 7 9 -33 }}
{{Mapping|legend=1| 1 -1 -1 15 | 0 7 9 -33 }}


: mapping generators: ~2, ~162/125
: mapping generators: ~2, ~162/125
Line 469: Line 470:
{{Multival|legend=1| 7 9 -33 -2 -72 -102 }}
{{Multival|legend=1| 7 9 -33 -2 -72 -102 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200¢, ~162/125 = 443.289
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~162/125 = 443.289


{{Optimal ET sequence|legend=1| 46, 111, 157, 268cd }}
{{Optimal ET sequence|legend=1| 46, 111, 157, 268cd }}
Line 484: Line 485:
: mapping generators: ~2, ~128/99
: mapping generators: ~2, ~128/99


Optimal tuning (POTE): ~2 = 1200¢, ~128/99 = 443.274
Optimal tuning (POTE): ~2 = 1\1, ~128/99 = 443.274


{{Optimal ET sequence|legend=1| 46, 65d, 111, 268cd, 379cdd}}
{{Optimal ET sequence|legend=1| 46, 65d, 111, 268cd, 379cdd}}
Line 496: Line 497:


Mapping: {{mapping| 1 -1 -1 15 9 17| 0 7 9 -33 -15 -36}}
Mapping: {{mapping| 1 -1 -1 15 9 17| 0 7 9 -33 -15 -36}}
: mapping generators: ~2, ~84/65
: mapping generators: ~2, ~84/65


Optimal tuning (POTE): ~2 = 1200¢, ~84/65 = 443.270
Optimal tuning (POTE): ~2 = 1\1, ~84/65 = 443.270


{{Optimal ET sequence|legend=1| 46, 65d, 111, 268cd, 379cddf}}
{{Optimal ET sequence|legend=1| 46, 65d, 111, 268cd, 379cddf}}
Line 510: Line 512:


Mapping: {{mapping| 1 -1 -1 15 9 17 10| 0 7 9 -33 -15 -36 -16}}
Mapping: {{mapping| 1 -1 -1 15 9 17 10| 0 7 9 -33 -15 -36 -16}}
: mapping generators: ~2, ~22/17
: mapping generators: ~2, ~22/17


Optimal tuning (POTE): ~2 = 1200¢, ~22/17 = 443.270
Optimal tuning (POTE): ~2 = 1\1, ~22/17 = 443.270


{{Optimal ET sequence|legend=1| 46, 65d, 111, 268cdg, 379cddfg }}
{{Optimal ET sequence|legend=1| 46, 65d, 111, 268cdg, 379cddfg }}
Line 518: Line 521:
Badness: 0.018105
Badness: 0.018105


== Bison (P8/2, ccP5/7) ==
== Bison ==
Bison has pergen (P8/2, ccP5/7). Related page: [[Bison/Eliora's Approach]].
 
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 6144/6125, 78732/78125
[[Comma list]]: 6144/6125, 78732/78125


Pergen {{Mapping|legend=1| 2 -2 -2 13 | 0 7 9 -10}}
Mapping:
 
* common form: {{mapping| 2 -2 -2 13 | 0 7 9 -10}}
: mapping generators: ~567/400, ~162/125
:: mapping generators: ~567/400, ~162/125
 
* mingen form: {{mapping| 2 5 7 3 | 0 -7 -9 10 }}
Mincents {{Mapping|legend=1| 2 5 7 3 | 0 -7 -9 10 }}
:: mapping generators: ~567/400, ~35/32
 
: mapping generators: ~567/400, ~35/32


{{Multival|legend=1| 14 18 -20 -4 -71 -97 }}
{{Multival|legend=1| 14 18 -20 -4 -71 -97 }}


[[Optimal tuning]] ([[POTE]]): ~567/400 = 600¢, ~162/125 = 443.075, ~35/32 = 156.925
[[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~162/125 = 443.075 (~35/32 = 156.925)


{{Optimal ET sequence|legend=1| 8, 38, 46, 84, 130 }}
{{Optimal ET sequence|legend=1| 8, 38, 46, 84, 130 }}


[[Badness]]: 0.070375
[[Badness]]: 0.070375
Related pages: [[Bison/Eliora's Approach]]


=== 11-limit ===
=== 11-limit ===
Line 546: Line 547:
Comma list: 441/440, 6144/6125, 8019/8000
Comma list: 441/440, 6144/6125, 8019/8000


Pergen {{Mapping|legend=1| 2 -2 -2 13 18| 0 7 9 -10 -15}}
Mapping:
: mapping generators: ~567/400, ~162/125
* common form: {{mapping| 2 -2 -2 13 18 | 0 7 9 -10 -15}}
 
:: mapping generators: ~567/400, ~162/125
Mincents mapping: {{mapping| 2 5 7 3 3 | 0 -7 -9 10 15 }}
* mingen form: {{mapping| 2 5 7 3 3 | 0 -7 -9 10 15 }}
 
:: mapping generators: ~567/400, ~35/32
: mapping generators: ~567/400, ~35/32


Optimal tuning (POTE): ~99/70 = 600¢, ~162/125 = 443.117, ~35/32 = 156.883
Optimal tuning (POTE): ~99/70 = 1\2, ~162/125 = 443.117 (~35/32 = 156.883)


{{Optimal ET sequence|legend=1| 46, 84, 130, 306, 436ce }}
{{Optimal ET sequence|legend=1| 46, 84, 130, 306, 436ce }}
Line 564: Line 564:
Comma list: 351/350, 364/363, 441/440, 10985/10976
Comma list: 351/350, 364/363, 441/440, 10985/10976


Pergen {{Mapping|legend=1| 2 -2 -2 13 18 17| 0 7 9 -10 -15 -13}}
Mapping:
: mapping generators: ~55/39, ~162/125
* common form: {{mapping| 2 -2 -2 13 18 17 | 0 7 9 -10 -15 -13 }}
:: mapping generators: ~55/39, ~162/125
* mingen form: {{mapping| 2 5 7 3 3 4 | 0 -7 -9 10 15 13 }}
:: mapping generators: ~55/39, ~35/32


Mincents mapping: {{mapping| 2 5 7 3 3 4 | 0 -7 -9 10 15 13 }}
Optimal tuning (POTE): ~55/39 = 1\2, ~162/125 = 443.096 (~35/32 = 156.904)
 
: mapping generators: ~55/39, ~35/32
 
Optimal tuning (POTE): ~55/39 = 600¢, ~162/125 = 443.096, ~35/32 = 156.904


{{Optimal ET sequence|legend=1| 46, 84, 130, 566ce, 596cef }}
{{Optimal ET sequence|legend=1| 46, 84, 130, 566ce, 596cef }}
Line 577: Line 576:
Badness: 0.023504
Badness: 0.023504


== Subpental (P8, c<sup>4</sup>P4/14) ==
== Subpental ==
Subpental has pergen (P8, c<sup>4</sup>P4/14).
 
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Line 588: Line 589:
{{Multival|legend=1| 14 18 45 -4 32 54 }}
{{Multival|legend=1| 14 18 45 -4 32 54 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200¢, ~56/45 = 378.467
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~56/45 = 378.467


{{Optimal ET sequence|legend=1| 19, 111, 130, 929c, 1059c, 1189bc, 1319bc }}
{{Optimal ET sequence|legend=1| 19, 111, 130, 929c, 1059c, 1189bc, 1319bc }}
Line 601: Line 602:
Mapping: {{mapping| 1 6 8 17 -6 | 0 -14 -18 -45 30 }}
Mapping: {{mapping| 1 6 8 17 -6 | 0 -14 -18 -45 30 }}


Optimal tuning (POTE): ~2 = 1200¢, ~56/45 = 378.440
Optimal tuning (POTE): ~2 = 1\1, ~56/45 = 378.440


{{Optimal ET sequence|legend=1| 19, 111, 130, 241, 371ce, 501cde, 872cde }}
{{Optimal ET sequence|legend=1| 19, 111, 130, 241, 371ce, 501cde, 872cde }}
Line 614: Line 615:
Mapping: {{mapping| 1 6 8 17 -6 16 | 0 -14 -18 -45 30 -39 }}
Mapping: {{mapping| 1 6 8 17 -6 16 | 0 -14 -18 -45 30 -39 }}


Optimal tuning (POTE): ~2 = 1200¢, ~56/45 = 378.437
Optimal tuning (POTE): ~2 = 1\1, ~56/45 = 378.437


{{Optimal ET sequence|legend=1| 19, 111, 130, 241, 371ce }}
{{Optimal ET sequence|legend=1| 19, 111, 130, 241, 371ce }}
Line 620: Line 621:
Badness: 0.023940
Badness: 0.023940


== Heinz (P8, c<sup>9</sup>P5/21) ==
== Heinz ==
A notable tuning of heinz not shown below for those who like [[19edo]]'s representation of the [[5-limit]] is [[57edo]] (= 103 - 46).
Heinz has pergen (P8, c<sup>9</sup>P5/21). A notable tuning of heinz not shown below for those who like [[19edo]]'s representation of the [[5-limit]] is [[57edo]] (57 = 103 - 46).


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 633: Line 634:
{{Multival|legend=1| 21 27 -7 -6 -70 -92 }}
{{Multival|legend=1| 21 27 -7 -6 -70 -92 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200¢, ~48/35 = 546.815
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~48/35 = 546.815


{{Optimal ET sequence|legend=1| 46, 103, 149, 699bdd }}
{{Optimal ET sequence|legend=1| 46, 103, 149, 699bdd }}
Line 648: Line 649:
: mapping generators: ~2, ~11/8
: mapping generators: ~2, ~11/8


Optimal tuning (POTE): ~2 = 1200¢, ~11/8 = 547.631
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 547.631


{{Optimal ET sequence|legend=1| 46, 103, 149, 252e, 401bdee }}
{{Optimal ET sequence|legend=1| 46, 103, 149, 252e, 401bdee }}
Line 661: Line 662:
{{Mapping|legend=1| 1 -8 -10 6 3 11| 0 21 27 -7 1 -16}}
{{Mapping|legend=1| 1 -8 -10 6 3 11| 0 21 27 -7 1 -16}}


Optimal tuning (POTE): ~2 = 1200¢, ~11/8 = 547.629
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 547.629


{{Optimal ET sequence|legend=1| 46, 103, 149, 252ef, 401bdeef }}
{{Optimal ET sequence|legend=1| 46, 103, 149, 252ef, 401bdeef }}
Line 674: Line 675:
{{Mapping|legend=1| 1 -8 -10 6 3 11 5| 0 21 27 -7 1 -16 -2}}
{{Mapping|legend=1| 1 -8 -10 6 3 11 5| 0 21 27 -7 1 -16 -2}}


Optimal tuning (POTE): ~2 = 1200¢, ~11/8 = 547.635
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 547.635


{{Optimal ET sequence|legend=1| 46, 103, 149, 252ef, 401bdeef }}
{{Optimal ET sequence|legend=1| 46, 103, 149, 252ef, 401bdeef }}
Line 687: Line 688:
{{Mapping|legend=1| 1 -8 -10 6 3 11 5 12| 0 21 27 -7 1 -16 -2 -17}}
{{Mapping|legend=1| 1 -8 -10 6 3 11 5 12| 0 21 27 -7 1 -16 -2 -17}}


Optimal tuning (POTE): ~2 = 1200¢, ~11/8 = 547.614
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 547.614


{{Optimal ET sequence|legend=1| 46, 103h, 149h, 252efhh }}
{{Optimal ET sequence|legend=1| 46, 103h, 149h, 252efhh }}
Line 693: Line 694:
Badness: 0.019005
Badness: 0.019005


== Trisensory (P8/3, M6/21) ==
== Trisensory ==
Trisensory has pergen (P8/3, M6/21).
 
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Line 704: Line 707:
{{Multival|legend=1| 21 27 12 -6 -40 -48 }}
{{Multival|legend=1| 21 27 12 -6 -40 -48 }}


[[Optimal tuning]] ([[POTE]]): ~63/50 = 400¢, ~36/35 = 43.147
[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~36/35 = 43.147


{{Optimal ET sequence|legend=1| 27, 57, 84, 111, 195d, 306d }}
{{Optimal ET sequence|legend=1| 27, 57, 84, 111, 195d, 306d }}
Line 717: Line 720:
Mapping: {{mapping| 3 4 6 8 8 | 0 7 9 4 22 }}
Mapping: {{mapping| 3 4 6 8 8 | 0 7 9 4 22 }}


Optimal tuning (POTE): ~63/50 = 400¢, ~36/35 = 43.292
Optimal tuning (POTE): ~63/50 = 1\3, ~36/35 = 43.292


{{Optimal ET sequence|legend=1| 27e, 84e, 111 }}
{{Optimal ET sequence|legend=1| 27e, 84e, 111 }}
Line 732: Line 735:
: mapping generators: ~49/39, ~36/35
: mapping generators: ~49/39, ~36/35


Optimal tuning (POTE): ~49/39 = 400¢, ~36/35 = 43.288
Optimal tuning (POTE): ~49/39 = 1\3, ~36/35 = 43.288


{{Optimal ET sequence|legend=1| 27e, 84e, 111 }}
{{Optimal ET sequence|legend=1| 27e, 84e, 111 }}
Line 745: Line 748:
Mapping: {{mapping| 3 4 6 8 8 11 10 | 0 7 9 4 22 1 21 }}
Mapping: {{mapping| 3 4 6 8 8 11 10 | 0 7 9 4 22 1 21 }}


Optimal tuning (POTE): ~49/39 = 400¢, ~36/35 = 43.276
Optimal tuning (POTE): ~49/39 = 1\3, ~36/35 = 43.276


{{Optimal ET sequence|legend=1| 27eg, 84e, 111 }}
{{Optimal ET sequence|legend=1| 27eg, 84e, 111 }}
Line 758: Line 761:
Mapping: {{mapping| 3 4 6 8 8 11 10 12 | 0 7 9 4 22 1 21 7 }}
Mapping: {{mapping| 3 4 6 8 8 11 10 12 | 0 7 9 4 22 1 21 7 }}


Optimal tuning (POTE): ~49/39 = 400¢, ~36/35 = 43.292
Optimal tuning (POTE): ~49/39 = 1\3, ~36/35 = 43.292


{{Optimal ET sequence|legend=1| 27eg, 84e, 111 }}
{{Optimal ET sequence|legend=1| 27eg, 84e, 111 }}
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