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[[POTE generator]]: ~9/7 = 440.4881
[[POTE generator]]: ~9/7 = 440.4881


[[Val]]s: [[4edt|b4]], [[9edt|b9]], [[13edt|b13]], [[56edt|b56]], [[69edt|b69]], [[82edt|b82]], [[95edt|b95]]
[[Optimal GPV sequence]]: [[4edt|b4]], [[9edt|b9]], [[13edt|b13]], [[56edt|b56]], [[69edt|b69]], [[82edt|b82]], [[95edt|b95]]


== Sensi ==
== Sensi ==
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{{see also| Sensipent family #Sensi }}
{{see also| Sensipent family #Sensi }}


Sensi tempers out [[126/125]], [[686/675]] and [[4375/4374]] in addition to [[245/243]], 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|46EDO]] is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available. The name "sensi" is a play on the words "semi-" and "sixth."
Sensi tempers out [[126/125]], [[686/675]] and [[4375/4374]] in addition to [[245/243]], 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. The name "sensi" is a play on the words "semi-" and "sixth."


=== Septimal sensi ===
=== Septimal sensi ===
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[[POTE generator]]: ~9/7 = 443.383
[[POTE generator]]: ~9/7 = 443.383
[[Minimax tuning]]:
* [[7-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 1/13 0 0 7/13 }}, {{monzo| 5/13 0 0 9/13 }}, {{monzo| 0 0 0 1 }}]
: [[Eigenmonzo]]s (unchanged intervals): 2, 7
* [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 2/5 14/5 -7/5 0 }}, {{monzo| 4/5 18/5 -9/5 0 }}, {{monzo| 3/5 26/5 -13/5 0 }}]
: [[Eigenmonzo]]s (unchanged intervals): 2, 9/5
[[Algebraic generator]]: The real root of ''x''<sup>5</sup> + ''x''<sup>4</sup> - 4''x''<sup>2</sup> + ''x'' - 1, at 443.3783 cents.


{{Val list|legend=1| 19, 27, 46, 157d, 203cd, 249cdd, 295ccdd }}
{{Val list|legend=1| 19, 27, 46, 157d, 203cd, 249cdd, 295ccdd }}
Line 80: Line 70:
POTE generator: ~9/7 = 443.322
POTE generator: ~9/7 = 443.322


Vals: {{Val list| 19, 27, 46, 111de, 157de }}
Optimal GPV sequence: {{Val list| 19, 27, 46, 111de, 157de }}


=== Sensor ===
=== Sensor ===
Line 91: Line 81:
POTE generator: ~9/7 = 443.294
POTE generator: ~9/7 = 443.294


Vals: {{Val list| 19, 27, 46, 111d, 157d, 268cdd }}
Optimal GPV sequence: {{Val list| 19, 27, 46, 111d, 157d, 268cdd }}


Badness: 0.037942
Badness: 0.037942
Line 104: Line 94:
POTE generator: ~9/7 = 443.321
POTE generator: ~9/7 = 443.321


Vals: {{Val list| 19, 27, 46, 111df, 157df }}
Optimal GPV sequence: {{Val list| 19, 27, 46, 111df, 157df }}


Badness: 0.025575
Badness: 0.025575
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
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 }}]
POTE generator: ~9/7 = 443.365
Optimal GPV sequence: {{Val list| 19, 27, 46, 157df, 203cdff, 249cddff }}
Badness: 0.022908


=== Sensis ===
=== Sensis ===
Line 117: Line 120:
POTE generator: ~9/7 = 443.962
POTE generator: ~9/7 = 443.962


Vals: {{Val list| 8d, 19, 27e, 73ee }}
Optimal GPV sequence: {{Val list| 8d, 19, 27e, 73ee }}


Badness: 0.028680
Badness: 0.028680
Line 130: Line 133:
POTE generator: ~9/7 = 443.945
POTE generator: ~9/7 = 443.945


Vals: {{Val list| 19, 27e, 46e, 73ee }}
Optimal GPV sequence: {{Val list| 19, 27e, 46e, 73ee }}


Badness: 0.020017
Badness: 0.020017
Line 143: Line 146:
POTE generator: ~9/7 = 443.626
POTE generator: ~9/7 = 443.626


Vals: {{Val list| 19e, 27e, 46, 119c, 165c }}
Optimal GPV sequence: {{Val list| 19e, 27e, 46, 119c, 165c }}


Badness: 0.029486
Badness: 0.029486
Line 156: Line 159:
POTE generator: ~9/7 = 443.559
POTE generator: ~9/7 = 443.559


Vals: {{Val list| 19e, 27e, 46, 165cf, 211bccf, 257bccff, 303bccdff }}
Optimal GPV sequence: {{Val list| 19e, 27e, 46, 165cf, 211bccf, 257bccff, 303bccdff }}


Badness: 0.020789
Badness: 0.020789
Line 169: Line 172:
POTE generator: ~9/7 = 443.518
POTE generator: ~9/7 = 443.518


Vals: {{Val list| 19e, 27, 46ee }}
Optimal GPV sequence: {{Val list| 19e, 27, 46ee }}


Badness: 0.036835
Badness: 0.036835
Line 182: Line 185:
POTE generator: ~9/7 = 443.506
POTE generator: ~9/7 = 443.506


Vals: {{Val list| 19e, 27, 46ee }}
Optimal GPV sequence: {{Val list| 19e, 27, 46ee }}


Badness: 0.023258
Badness: 0.023258
Line 195: Line 198:
POTE generator: ~25/22 = 221.605
POTE generator: ~25/22 = 221.605


Vals: {{Val list| 27e, 65, 157de, 222cde }}
Optimal GPV sequence: {{Val list| 27e, 65, 157de, 222cde }}


Badness: 0.048714
Badness: 0.048714
Line 204: Line 207:
'''[[Bohpier]]''' is named after its [[Relationship between Bohlen-Pierce and octave-ful temperaments|interesting relationship with the non-octave Bohlen-Pierce equal temperament]].
'''[[Bohpier]]''' is named after its [[Relationship between Bohlen-Pierce and octave-ful temperaments|interesting relationship with the non-octave Bohlen-Pierce equal temperament]].


=== 5-limit (satheyo) ===
Subgroup: 2.3.5
Subgroup: 2.3.5


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* 11-odd-limit diamond monotone and tradeoff: ~12/11 = [145.455, 146.939]
* 11-odd-limit diamond monotone and tradeoff: ~12/11 = [145.455, 146.939]


Vals: {{Val list| 41, 90e, 131e }}
Optimal GPV sequence: {{Val list| 41, 90e, 131e }}


Badness: 0.033949
Badness: 0.033949
Line 296: Line 300:
* 15-odd-limit diamond monotone and tradeoff: ~12/11 = [146.341, 146.939]
* 15-odd-limit diamond monotone and tradeoff: ~12/11 = [146.341, 146.939]


Vals: {{Val list| 41, 90ef, 131ef, 221bdeff }}
Optimal GPV sequence: {{Val list| 41, 90ef, 131ef, 221bdeff }}


Badness: 0.024864
Badness: 0.024864
Line 316: Line 320:
POTE generator: ~77/75 = 48.828
POTE generator: ~77/75 = 48.828


Vals: {{Val list| 49, 123ce, 172 }}
Optimal GPV sequence: {{Val list| 49, 123ce, 172 }}


Badness: 0.162592
Badness: 0.162592
Line 329: Line 333:
POTE generator: ~77/75 = 48.822
POTE generator: ~77/75 = 48.822


Vals: {{Val list| 49f, 123ce, 172f, 295ce, 467bccef }}
Optimal GPV sequence: {{Val list| 49f, 123ce, 172f, 295ce, 467bccef }}


Badness: 0.082158
Badness: 0.082158
Line 361: Line 365:
POTE generator: ~28/27 = 55.126
POTE generator: ~28/27 = 55.126


Vals: {{Val list| 22, 65, 87, 196, 283 }}
Optimal GPV sequence: {{Val list| 22, 65, 87, 196, 283 }}


Badness: 0.035844
Badness: 0.035844
Line 374: Line 378:
POTE generator: ~28/27 = 55.138
POTE generator: ~28/27 = 55.138


Vals: {{Val list| 22, 65, 87, 283 }}
Optimal GPV sequence: {{Val list| 22, 65, 87, 283 }}


Badness: 0.031366
Badness: 0.031366
Line 404: Line 408:
POTE generator: ~11/9 = 351.014
POTE generator: ~11/9 = 351.014


Vals: {{Val list| 17, 24, 41, 106d, 147d }}
Optimal GPV sequence: {{Val list| 17, 24, 41, 106d, 147d }}


Badness: 0.039444
Badness: 0.039444
Line 417: Line 421:
POTE generator: ~11/9 = 351.025
POTE generator: ~11/9 = 351.025


Vals: {{Val list| 17, 24, 41, 106df, 147df }}
Optimal GPV sequence: {{Val list| 17, 24, 41, 106df, 147df }}


Badness: 0.030793
Badness: 0.030793
Line 466: Line 470:
POTE generator: ~7/5 = 549.945
POTE generator: ~7/5 = 549.945


Vals: {{Val list| 11cdee, 13cdee, 24 }}
Optimal GPV sequence: {{Val list| 11cdee, 13cdee, 24 }}


Badness: 0.082716
Badness: 0.082716
Line 479: Line 483:
POTE generator: ~7/5 = 549.958
POTE generator: ~7/5 = 549.958


Vals: {{Val list| 11cdeef, 13cdeef, 24 }}
Optimal GPV sequence: {{Val list| 11cdeef, 13cdeef, 24 }}


Badness: 0.049933
Badness: 0.049933
Line 509: Line 513:
POTE generator: ~9/7 = 439.152
POTE generator: ~9/7 = 439.152


Vals: {{Val list| 11cd, 30d, 41, 153be, 194be, 235bcee }}
Optimal GPV sequence: {{Val list| 11cd, 30d, 41, 153be, 194be, 235bcee }}


Badness: 0.070917
Badness: 0.070917
Line 522: Line 526:
POTE generator: ~9/7 = 439.119
POTE generator: ~9/7 = 439.119


Vals: {{Val list| 11cdf, 30df, 41 }}
Optimal GPV sequence: {{Val list| 11cdf, 30df, 41 }}


Badness: 0.052835
Badness: 0.052835
Line 554: Line 558:
POTE generator: ~5/4 = 391.503
POTE generator: ~5/4 = 391.503


Vals: {{Val list| 46, 95, 141bc }}
Optimal GPV sequence: {{Val list| 46, 95, 141bc }}


Badness: 0.045108
Badness: 0.045108
Line 567: Line 571:
POTE generator: ~5/4 = 391.366
POTE generator: ~5/4 = 391.366


Vals: {{Val list| 46, 233bcff, 279bccff }}
Optimal GPV sequence: {{Val list| 46, 233bcff, 279bccff }}


Badness: 0.043024
Badness: 0.043024
Line 593: Line 597:
POTE generator: ~3/2 = 704.554
POTE generator: ~3/2 = 704.554


Vals: {{Val list| 17, 29c, 46, 109, 264b, 373b, 637bbe }}
Optimal GPV sequence: {{Val list| 17, 29c, 46, 109, 264b, 373b, 637bbe }}


Badness: 0.050679
Badness: 0.050679
Line 606: Line 610:
POTE generator: ~3/2 = 704.571
POTE generator: ~3/2 = 704.571


Vals: {{Val list| 17, 29c, 46, 63, 109 }}
Optimal GPV sequence: {{Val list| 17, 29c, 46, 63, 109 }}


Badness: 0.032727
Badness: 0.032727
Line 619: Line 623:
[[POL2]] generator: ~7/6 = 262.1728
[[POL2]] generator: ~7/6 = 262.1728


[[Vals]]: [[3edf]], [[5edf]], [[8edf]]
[[Optimal GPV sequence]]: [[3edf]], [[5edf]], [[8edf]]


=== Semilupine ===
=== Semilupine ===
Line 630: Line 634:
[[POL2]] generator: ~7/6 = 264.3771
[[POL2]] generator: ~7/6 = 264.3771


[[Vals]]: [[8edf]], [[13edf]]
[[Optimal GPV sequence]]: [[8edf]], [[13edf]]


=== Hemilycan ===
=== Hemilycan ===
Line 641: Line 645:
[[POL2]] generator: ~7/6 = 261.5939
[[POL2]] generator: ~7/6 = 261.5939


[[Vals]]: [[8edf]], [[11edf]]
[[Optimal GPV sequence]]: [[8edf]], [[11edf]]
 


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]
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