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Sensipent family: Difference between revisions

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→Sensi: removing for now because 1) it's definitely not a "play on words", though possibly it may be a contraction of those two words; 2) this could be covered better on the Temperament names page; 3) this fact is contentious and under discussion here: https://en.xen.wiki/w/Talk:Temperament_names
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Temperaments of the '''sensipent family''' temper out the [[sensipent comma]], 78732/78125, also known as medium semicomma. This temperament family includes sensi, sensei, bison, and heinz.
Temperaments of the '''sensipent family''' temper out the [[sensipent comma]], 78732/78125, also known as medium semicomma. This temperament family includes sensi, sensei, bison, and heinz.


Temperaments discussed elsewhere include:  
Temperaments discussed elsewhere include:  
* ''[[subpental]]'', {3136/3125, 19683/19600} → [[Hemimean clan #Subpental]]
* ''[[Subpental]]'' → [[Hemimean clan #Subpental]] (+3136/3125 or 19683/19600)
* ''[[catafourth]]'', {2401/2400, 78732/78125} → [[Breedsmic temperaments #Catafourth]]
* ''[[Catafourth]]'' → [[Breedsmic temperaments #Catafourth]] (+2401/2400)
* ''[[browser]]'', {16875/16807, 78732/78125} → [[Mirkwai clan #Browser]]
* ''[[Browser]]'' → [[Mirkwai clan #Browser]] (+16875/16807)


== Sensipent ==
== Sensipent ==
Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 78732/78125
[[Comma list]]: 78732/78125


[[Mapping]]: [{{val| 1 -1 -1 }}, {{val| 0 7 9 }}]
{{Mapping|legend=1| 1 6 8 | 0 -7 -9 }}


[[POTE generator]]: 162/125 = 443.058
: mapping generators: ~2, ~125/81
 
[[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 }}
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== Sensi ==
== Sensi ==
{{main| Sensi }}
{{Main| Sensi }}
{{see also| Sensamagic clan #Sensi }}
{{See also| Sensamagic clan #Sensi }}


Sensi tempers out [[686/675]], [[245/243]] and [[4375/4374]] in addition to [[126/125]], and can be described as the 19&27 temperament. It has as a generator half the size of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 2.3.5.7.13 sensi (sensation) tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available.  
Sensi tempers out [[686/675]], [[245/243]] and [[4375/4374]] in addition to [[126/125]], and can be described as the 19&27 temperament. It has as a generator half the size of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 2.3.5.7.13 sensi (sensation) tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available.  


=== Septimal sensi ===
=== Septimal sensi ===
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 126/125, 245/243
[[Comma list]]: 126/125, 245/243


[[Mapping]]: [{{val| 1 -1 -1 -2 }}, {{val| 0 7 9 13 }}]
{{Mapping|legend=1| 1 6 8 11 | 0 -7 -9 -13 }}


Mapping generators: ~2, ~9/7
: mapping generators: ~2, ~14/9


{{Multival|legend=1| 7 9 13 -2 1 5 }}
{{Multival|legend=1| 7 9 13 -2 1 5 }}


[[POTE generator]]: ~9/7 = 443.383
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 443.383


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit]]: ~9/7 = {{monzo| 2/13 0 0 1/13 }}  
* [[7-odd-limit]]: ~9/7 = {{monzo| 2/13 0 0 1/13 }}  
: [[Eigenmonzo]]s (unchanged-intervals): 2, 7
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.7
* [[9-odd-limit]]: ~9/7 = {{monzo| 1/5 2/5 -1/5 0 }}
* [[9-odd-limit]]: ~9/7 = {{monzo| 1/5 2/5 -1/5 0 }}
: [[Eigenmonzo]]s (unchanged-intervals): 2, 9/5
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.9/5


[[Tuning ranges of regular temperaments|Tuning ranges]]:  
[[Tuning ranges of regular temperaments|Tuning ranges]]:  
Line 65: Line 66:
[[Badness]]: 0.025622
[[Badness]]: 0.025622


==== Sensation ====
==== 2.3.5.7.13 subgroup (sensation) ====
Subgroup: 2.3.5.7.13
Subgroup: 2.3.5.7.13


Comma list: 91/90, 126/125, 169/168
Comma list: 91/90, 126/125, 169/168


Sval mapping: [{{val| 1 -1 -1 -2 0 }}, {{val| 0 7 9 13 10 }}]
Sval mapping: {{mapping| 1 6 8 11 10 | 0 -7 -9 -13 -10 }}


Gencom mapping: [{{val| 1 -1 -1 -2 0 0 }}, {{val| 0 7 9 13 0 10 }}]
Gencom mapping: {{mapping| 1 6 8 11 0 10 | 0 -7 -9 -13 0 -10 }}


Gencom: [2 9/7; 91/90 126/125 169/168]
Gencom: [2 14/9; 91/90 126/125 169/168]


POTE generator: ~9/7 = 443.322
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.322


{{Optimal ET sequence|legend=1| 19, 27, 46, 111de, 157de }}
{{Optimal ET sequence|legend=1| 19, 27, 46, 111de, 157de }}
Line 85: Line 86:
Comma list: 126/125, 245/243, 385/384
Comma list: 126/125, 245/243, 385/384


Mapping: [{{val| 1 -1 -1 -2 9 }}, {{val| 0 7 9 13 -15 }}]
Mapping: {{mapping| 1 6 8 11 -6 | 0 -7 -9 -13 15 }}


POTE generator: ~9/7 = 443.294
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.294


{{Optimal ET sequence|legend=1| 19, 27, 46, 111d, 157d, 268cdd }}
{{Optimal ET sequence|legend=1| 19, 27, 46, 111d, 157d, 268cdd }}
Line 98: Line 99:
Comma list: 91/90, 126/125, 169/168, 385/384
Comma list: 91/90, 126/125, 169/168, 385/384


Mapping: [{{val| 1 -1 -1 -2 9 0 }}, {{val| 0 7 9 13 -15 10 }}]
Mapping: {{mapping| 1 6 8 11 -6 10 | 0 -7 -9 -13 15 -10 }}


POTE generator: ~9/7 = 443.321
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.321


{{Optimal ET sequence|legend=1| 19, 27, 46, 111df, 157df }}
{{Optimal ET sequence|legend=1| 19, 27, 46, 111df, 157df }}
Line 111: Line 112:
Comma list: 91/90, 126/125, 154/153, 169/168, 256/255
Comma list: 91/90, 126/125, 154/153, 169/168, 256/255


Mapping: [{{val| 1 -1 -1 -2 9 0 10 }}, {{val| 0 7 9 13 -15 10 -16 }}]
Mapping: {{mapping| 1 6 8 11 -6 10 -6 | 0 -7 -9 -13 15 -10 16 }}


POTE generator: ~9/7 = 443.365
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.365


{{Optimal ET sequence|legend=1| 19, 27, 46, 157df, 203cdff, 249cddff }}
{{Optimal ET sequence|legend=1| 19, 27, 46, 157df, 203cdff, 249cddff }}
Line 124: Line 125:
Comma list: 56/55, 100/99, 245/243
Comma list: 56/55, 100/99, 245/243


Mapping: [{{val| 1 -1 -1 -2 2 }}, {{val| 0 7 9 13 4 }}]
Mapping: {{mapping| 1 6 8 11 6 | 0 -7 -9 -13 -4 }}


POTE generator: ~9/7 = 443.962
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.962


{{Optimal ET sequence|legend=1| 8d, 19, 27e, 73ee }}
{{Optimal ET sequence|legend=1| 8d, 19, 27e, 73ee }}
Line 137: Line 138:
Comma list: 56/55, 78/77, 91/90, 100/99
Comma list: 56/55, 78/77, 91/90, 100/99


Mapping: [{{val| 1 -1 -1 -2 2 0 }}, {{val| 0 7 9 13 4 10 }}]
Mapping: {{mapping| 1 6 8 11 6 10 | 0 -7 -9 -13 -4 -10 }}


POTE generator: ~9/7 = 443.945
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.945


{{Optimal ET sequence|legend=1| 19, 27e, 46e, 73ee }}
{{Optimal ET sequence|legend=1| 19, 27e, 46e, 73ee }}
Line 150: Line 151:
Comma list: 126/125, 176/175, 245/243
Comma list: 126/125, 176/175, 245/243


Mapping: [{{val| 1 -1 -1 -2 -8 }}, {{val| 0 7 9 13 31 }}]
Mapping: {{mapping| 1 6 8 11 23 | 0 -7 -9 -13 -31 }}


POTE generator: ~9/7 = 443.626
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.626


{{Optimal ET sequence|legend=1| 19e, 27e, 46, 119c, 165c }}
{{Optimal ET sequence|legend=1| 19e, 27e, 46, 119c, 165c }}
Line 163: Line 164:
Comma list: 91/90, 126/125, 169/168, 352/351
Comma list: 91/90, 126/125, 169/168, 352/351


Mapping: [{{val| 1 -1 -1 -2 -8 0 }}, {{val| 0 7 9 13 31 10 }}]
Mapping: {{mapping| 1 6 8 11 23 10 | 0 -7 -9 -13 -31 -10 }}


POTE generator: ~9/7 = 443.559
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.559


{{Optimal ET sequence|legend=1| 19e, 27e, 46, 165cf, 211bccf, 257bccff, 303bccdff }}
{{Optimal ET sequence|legend=1| 19e, 27e, 46, 165cf, 211bccf, 257bccff, 303bccdff }}
Line 176: Line 177:
Comma list: 91/90, 126/125, 136/135, 154/153, 169/168
Comma list: 91/90, 126/125, 136/135, 154/153, 169/168


Mapping: [{{val| 1 -1 -1 -2 -8 0 -7 }}, {{val| 0 7 9 13 31 10 30 }}]
Mapping: {{mapping| 1 6 8 11 23 10 23 | 0 -7 -9 -13 -31 -10 -30 }}


POTE generator: ~9/7 = 443.551
Optimal tuning (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 189: Line 190:
Comma list: 55/54, 77/75, 99/98
Comma list: 55/54, 77/75, 99/98


Mapping: [{{val| 1 -1 -1 -2 -1 }}, {{val| 0 7 9 13 12 }}]
Mapping: {{mapping| 1 6 8 11 11 | 0 -7 -9 -13 -12 }}


POTE generator: ~9/7 = 443.518
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.518


{{Optimal ET sequence|legend=1| 19e, 27, 46ee }}
{{Optimal ET sequence|legend=1| 19e, 27, 46ee }}
Line 202: Line 203:
Comma list: 55/54, 66/65, 77/75, 143/140
Comma list: 55/54, 66/65, 77/75, 143/140


Mapping: [{{val| 1 -1 -1 -2 -1 0 }}, {{val| 0 7 9 13 12 11 }}]
Mapping: {{mapping| 1 6 8 11 11 11 | 0 -7 -9 -13 -12 -11 }}


POTE generator: ~9/7 = 443.506
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.506


{{Optimal ET sequence|legend=1| 19e, 27, 46ee }}
{{Optimal ET sequence|legend=1| 19e, 27, 46ee }}
Line 215: Line 216:
Comma list: 126/125, 243/242, 245/242
Comma list: 126/125, 243/242, 245/242


Mapping: [{{val| 1 -1 -1 -2 -3 }}, {{val| 0 14 18 26 35 }}]
Mapping: {{mapping| 1 13 17 24 32 | 0 -14 -18 -26 -35 }}
 
: mapping generators: ~2, ~44/25


POTE generator: ~25/22 = 221.605
Optimal tuning (POTE): ~2 = 1\1, ~25/22 = 221.605


{{Optimal ET sequence|legend=1| 27e, 38d, 65, 157de, 222cde }}
{{Optimal ET sequence|legend=1| 27e, 38d, 65, 157de, 222cde }}
Line 228: Line 231:
Comma list: 91/90, 126/125, 169/168, 243/242
Comma list: 91/90, 126/125, 169/168, 243/242


Mapping: [{{val| 1 -1 -1 -2 -3 0 }}, {{val| 0 14 18 26 35 30 }}]
Mapping: {{mapping| 1 13 17 24 32 30 | 0 -14 -18 -26 -35 -30 }}


POTE generator: ~25/22 = 221.556
Optimal tuning (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 241: Line 244:
Comma list: 121/120, 126/125, 245/243
Comma list: 121/120, 126/125, 245/243


Mapping: [{{val| 2 5 7 9 9 }}, {{val| 0 -7 -9 -13 -8 }}]
Mapping: {{mapping| 2 5 7 9 9 | 0 -7 -9 -13 -8 }}
 
: mapping generators: ~99/70, ~11/10


POTE generator: ~11/10 = 156.692
Optimal tuning (POTE): ~99/70 = 1\2, ~11/10 = 156.692


{{Optimal ET sequence|legend=1| 8d, …, 38d, 46, 176dde, 222cdde, 268cddee }}
{{Optimal ET sequence|legend=1| 8d, …, 38d, 46, 176dde, 222cdde, 268cddee }}
Line 254: Line 259:
Comma list: 91/90, 121/120, 126/125, 169/168
Comma list: 91/90, 121/120, 126/125, 169/168


Mapping: [{{val| 2 5 7 9 9 10 }}, {{val| 0 -7 -9 -13 -8 -10 }}]
Mapping: {{mapping| 2 5 7 9 9 10 | 0 -7 -9 -13 -8 -10 }}


POTE generator: ~11/10 = 156.725
Optimal tuning (POTE): ~55/39 = 1\2, ~11/10 = 156.725


{{Optimal ET sequence|legend=1| 8d, …, 38df, 46 }}
{{Optimal ET sequence|legend=1| 8d, …, 38df, 46 }}
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== Sensei ==
== Sensei ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 78732/78125
[[Comma list]]: 225/224, 78732/78125


[[Mapping]]: [{{val| 1 -1 -1 -9 }}, {{val| 0 7 9 32 }}]
{{Mapping|legend=1| 1 6 8 23 | 0 -7 -9 -32 }}


{{Multival|legend=1| 7 9 32 -2 31 49 }}
{{Multival|legend=1| 7 9 32 -2 31 49 }}


[[POTE generator]]: ~125/81 = 757.245
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~162/125 = 442.755


{{Optimal ET sequence|legend=1| 19, 84, 103, 187, 290b }}
{{Optimal ET sequence|legend=1| 19, 84, 103, 187, 290b }}
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== Warrior ==
== Warrior ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 5120/5103, 78732/78125
[[Comma list]]: 5120/5103, 78732/78125


[[Mapping]]: [{{val|1 -1 -1 15}}, {{val|0 7 9 -33}}]
{{Mapping|legend=1| 1 6 8 -18 | 0 -7 -9 33 }}


{{Multival|legend=1| 7 9 -33 -2 -72 -102 }}
{{Multival|legend=1| 7 9 -33 -2 -72 -102 }}


[[POTE generator]]: ~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 297: Line 302:
Comma list: 176/175, 1331/1323, 5120/5103
Comma list: 176/175, 1331/1323, 5120/5103


Mapping: [{{val|1 -1 -1 15 9}}, {{val|0 7 9 -33 -15}}]
Mapping: {{mapping| 1 6 8 -18 -6 | 0 -7 -9 33 15 }}


POTE generator: ~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 310: Line 315:
Comma list: 176/175, 351/350, 847/845, 1331/1323
Comma list: 176/175, 351/350, 847/845, 1331/1323


Mapping: [{{val|1 -1 -1 15 9 17}}, {{val|0 7 9 -33 -15 -36}}]
Mapping: {{mapping| 1 6 8 -18 -6 -19 | 0 -7 -9 33 15 36 }}


POTE generator: ~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 323: Line 328:
Comma list: 176/175, 256/255, 351/350, 442/441, 715/714
Comma list: 176/175, 256/255, 351/350, 442/441, 715/714


Mapping: [{{val|1 -1 -1 15 9 17 10}}, {{val|0 7 9 -33 -15 -36 -16}}]
Mapping: {{mapping| 1 6 8 -18 -6 -19 -6 | 0 -7 -9 33 15 36 16 }}


POTE generator: ~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 332: Line 337:


== Bison ==
== Bison ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


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


[[Mapping]]: [{{val| 2 5 7 3 }}, {{val| 0 -7 -9 10 }}]
{{Mapping|legend=1| 2 5 7 3 | 0 -7 -9 10 }}
 
: mapping generators: ~567/400, ~35/32


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


[[POTE generator]]: ~35/32 = 156.925
[[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~35/32 = 156.925


{{Optimal ET sequence|legend=1| 8, 38, 46, 84, 130 }}
{{Optimal ET sequence|legend=1| 8, 38, 46, 84, 130 }}
Line 351: Line 358:
Comma list: 441/440, 6144/6125, 8019/8000
Comma list: 441/440, 6144/6125, 8019/8000


Mapping: [{{val| 2 5 7 3 3 }}, {{val| 0 -7 -9 10 15 }}]
Mapping: {{mapping| 2 5 7 3 3 | 0 -7 -9 10 15 }}


POTE generator: ~35/32 = 156.883
Optimal tuning (POTE): ~99/70 = 1\2, ~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 364: Line 371:
Comma list: 351/350, 364/363, 441/440, 10985/10976
Comma list: 351/350, 364/363, 441/440, 10985/10976


Mapping: [{{val| 2 5 7 3 3 4 }}, {{val| 0 -7 -9 10 15 13 }}]
Mapping: {{mapping| 2 5 7 3 3 4 | 0 -7 -9 10 15 13 }}


POTE generator: ~35/32 = 156.904
Optimal tuning (POTE): ~55/39 = 1\2, ~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 373: Line 380:


== Heinz ==
== Heinz ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 1029/1024, 78732/78125
[[Comma list]]: 1029/1024, 78732/78125


[[Mapping]]: [{{val| 1 -8 -10 6 }}, {{val| 0 21 27 -7 }}]
{{Mapping|legend=1| 1 13 17 -1 | 0 -21 -27 7 }}
 
: mapping generators: ~2, ~35/24


{{Multival|legend=1|21 27 -7 -6 -70 -92}}
{{Multival|legend=1| 21 27 -7 -6 -70 -92 }}


[[POTE generator]]: ~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 392: Line 401:
Comma list: 385/384, 441/440, 78732/78125
Comma list: 385/384, 441/440, 78732/78125


Mapping: [{{val| 1 -8 -10 6 3 }}, {{val| 0 21 27 -7 1 }}]
Mapping: {{mapping| 1 13 17 -1 4 | 0 -21 -27 7 -1 }}


POTE generator: ~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 405: Line 414:
Comma list: 351/350, 385/384, 441/440, 847/845
Comma list: 351/350, 385/384, 441/440, 847/845


Mapping: [{{val| 1 -8 -10 6 3 11 }}, {{val| 0 21 27 -7 1 -16 }}]
Mapping: {{mapping| 1 13 17 -1 4 -5 | 0 -21 -27 7 -1 16 }}


POTE generator: ~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 418: Line 427:
Comma list: 273/272, 351/350, 385/384, 441/440, 847/845
Comma list: 273/272, 351/350, 385/384, 441/440, 847/845


Mapping: [{{val| 1 -8 -10 6 3 11 5 }}, {{val| 0 21 27 -7 1 -16 -2 }}]
Mapping: {{mapping| 1 13 17 -1 4 -5 3 | 0 -21 -27 7 -1 16 2 }}


POTE generator: ~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 431: Line 440:
Comma list: 171/170, 209/208, 351/350, 385/384, 441/440, 969/968
Comma list: 171/170, 209/208, 351/350, 385/384, 441/440, 969/968


Mapping: [{{val| 1 -8 -10 6 3 11 5 12 }}, {{val| 0 21 27 -7 1 -16 -2 -17 }}]
Mapping: {{mapping| 1 13 17 -1 4 -5 3 -5 | 0 -21 -27 7 -1 16 2 17 }}


POTE generator: ~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 440: Line 449:


== Trisensory ==
== Trisensory ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 1728/1715, 78732/78125
[[Comma list]]: 1728/1715, 78732/78125


[[Mapping]]: [{{val|3 4 6 8}}, {{val|0 7 9 4}}]
{{Mapping|legend=1| 3 4 6 8 | 0 7 9 4 }}


{{Multival|legend=1|21 27 12 -6 -40 -48}}
{{Multival|legend=1| 21 27 12 -6 -40 -48 }}


[[POTE generator]]: ~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 459: Line 468:
Comma list: 176/175, 540/539, 78732/78125
Comma list: 176/175, 540/539, 78732/78125


Mapping: [{{val|3 4 6 8 8}}, {{val|0 7 9 4 22}}]
Mapping: {{mapping| 3 4 6 8 8 | 0 7 9 4 22 }}


POTE generator: ~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 472: Line 481:
Comma list: 176/175, 351/350, 540/539, 9295/9261
Comma list: 176/175, 351/350, 540/539, 9295/9261


Mapping: [{{val|3 4 6 8 8 11}}, {{val|0 7 9 4 22 1}}]
Mapping: {{mapping| 3 4 6 8 8 11 | 0 7 9 4 22 1 }}


POTE generator: ~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 485: Line 494:
Comma list: 176/175, 351/350, 442/441, 540/539, 715/714
Comma list: 176/175, 351/350, 442/441, 540/539, 715/714


Mapping: [{{val|3 4 6 8 8 11 10}}, {{val|0 7 9 4 22 1 21}}]
Mapping: {{mapping| 3 4 6 8 8 11 10 | 0 7 9 4 22 1 21 }}


POTE generator: ~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 498: Line 507:
Comma list: 176/175, 286/285, 324/323, 351/350, 400/399, 476/475
Comma list: 176/175, 286/285, 324/323, 351/350, 400/399, 476/475


Mapping: [{{val|3 4 6 8 8 11 10 12}}, {{val|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 }}


POTE generator: ~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 }}
Line 508: Line 517:
[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Sensipent family| ]] <!-- main article -->
[[Category:Sensipent family| ]] <!-- main article -->
[[Category:Sensipent]]
[[Category:Sensipent| ]] <!-- key article -->
[[Category:Sensi]]
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Sensipent_family"