Sensipent family: Difference between revisions

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__FORCETOC__
__FORCETOC__
<span style="display: block; text-align: right;">[[de:Sensi]]</span>
<span style="display: block; text-align: right;">[[de:Sensi]]</span>


Line 25: Line 26:


[|1 0 0 0&gt;, |2/5 14/5 -7/5 0&gt;,
[|1 0 0 0&gt;, |2/5 14/5 -7/5 0&gt;,
|4/5 18/5 -9/5 0&gt;, |3/5 26/5 -13/5 0&gt;]
|4/5 18/5 -9/5 0&gt;, |3/5 26/5 -13/5 0&gt;<nowiki>]</nowiki>


[[Eigenmonzo|Eigenmonzos]]: 2, 9/5
[[Eigenmonzo|Eigenmonzos]]: 2, 9/5
Line 39: Line 40:
[[generator|Generators]]: 2, 14/9
[[generator|Generators]]: 2, 14/9


[[EDO|EDO]]s: [[19edo|19]], [[27edo|27]], [[46edo|46]], [[157edo|157d]], [[203edo|203cd]], [[249edo|249cd]], [[295edo|295cd]]
[[EDO|EDO]]s: [[19edo|19]], [[27edo|27]], [[46edo|46]], [[157edo|157d]], [[203edo|203cd]], [[249edo|249cdd]], [[295edo|295ccdd]]


[[Badness|Badness]]: 0.0256
[[Badness|Badness]]: 0.0256
Line 50: Line 51:
[[Map|Map]]: [&lt;1 6 8 11 -6|, &lt;0 -7 -9 -13 15|]
[[Map|Map]]: [&lt;1 6 8 11 -6|, &lt;0 -7 -9 -13 15|]


[[EDO|EDO]]s: 19, 27, 46, 111d, 157d, 268cd
[[EDO|EDO]]s: 19, 27, 46, 111d, 157d, 268cdd


[[Badness|Badness]]: 0.0379
[[Badness|Badness]]: 0.0379
Line 72: Line 73:
[[Map|Map]]: [&lt;1 6 8 11 6|, &lt;0 -7 -9 -13 -4|]
[[Map|Map]]: [&lt;1 6 8 11 6|, &lt;0 -7 -9 -13 -4|]


[[EDO|EDO]]s: [[19edo|19]], [[27edo|27e]], [[73edo|73e]]
[[EDO|EDO]]s: [[19edo|19]], [[27edo|27e]], [[73edo|73ee]]


[[Badness|Badness]]: 0.0287
[[Badness|Badness]]: 0.0287
Line 83: Line 84:
[[Map|Map]]: [&lt;1 6 8 11 6 10|, &lt;0 -7 -9 -13 -4 -10|]
[[Map|Map]]: [&lt;1 6 8 11 6 10|, &lt;0 -7 -9 -13 -4 -10|]


[[EDO|EDO]]s: 19, 27e, 46e, 73e
[[EDO|EDO]]s: 19, 27e, 46e, 73ee


[[Badness|Badness]]: 0.0200
[[Badness|Badness]]: 0.0200
Line 94: Line 95:
[[Map|Map]]: [&lt;1 6 8 11 23|, &lt;0 -7 -9 -13 -31|]
[[Map|Map]]: [&lt;1 6 8 11 23|, &lt;0 -7 -9 -13 -31|]


[[EDO|EDO]]s: 46, 119c, 165c
[[EDO|EDO]]s: 19e, 27e, 46, 119c, 165c


[[Badness|Badness]]: 0.0295
[[Badness|Badness]]: 0.0295
Line 105: Line 106:
[[Map|Map]]: [&lt;1 6 8 11 23 10|, &lt;0 -7 -9 -13 -31 -10|]
[[Map|Map]]: [&lt;1 6 8 11 23 10|, &lt;0 -7 -9 -13 -31 -10|]


[[EDO|EDO]]s: 46, 165cf, 211bcf, 257bcf, [[303edo|303bcdf]]
[[EDO|EDO]]s: 19e, 27e, 46, 165cf, 211bccf, 257bccff, [[303edo|303bccdff]]


[[Badness|Badness]]: 0.0208
[[Badness|Badness]]: 0.0208
Line 118: Line 119:
Map: [&lt;1 6 8 11 11|, &lt;0 -7 -9 -13 -12|]
Map: [&lt;1 6 8 11 11|, &lt;0 -7 -9 -13 -12|]


EDOs: 19e, 27, 46e
EDOs: 19e, 27, 46ee


Badness: 0.0368
Badness: 0.0368
Line 129: Line 130:
Map: [&lt;1 6 8 11 11 10|, &lt;0 -7 -9 -13 -12 -11|]
Map: [&lt;1 6 8 11 11 10|, &lt;0 -7 -9 -13 -12 -11|]


EDOs: 19e, 27, 46e
EDOs: 19e, 27, 46ee


Badness: 0.0233
Badness: 0.0233

Revision as of 09:38, 18 August 2020


Sensipent

Comma: 78732/78125 = |2 9 -7>

POTE generator: 162/125 = 443.058 cents

Map: [<1 6 8|, <0 -7 -9|]

EDOs: 8, 19, 46, 65, 539, 604c, 669c, 734c, 799c, 864c, 929c

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 13-limit sensi 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."

Commas: 126/125, 245/243

7-limit minimax

[|1 0 0 0>, |1/13 0 0 7/13>, |5/13 0 0 9/13>, |0 0 0 1>]

Eigenmonzos: 2, 7

9-limit minimax

[|1 0 0 0>, |2/5 14/5 -7/5 0>, |4/5 18/5 -9/5 0>, |3/5 26/5 -13/5 0>]

Eigenmonzos: 2, 9/5

POTE generator: ~9/7 = 443.383

Algebraic generator: The real root of x^5+x^4-4x^2+x-1, at 443.3783 cents.

Map: [<1 6 8 11|, <0 -7 -9 -13|]

Wedgie: <<7 9 13 -2 1 5||

Generators: 2, 14/9

EDOs: 19, 27, 46, 157d, 203cd, 249cdd, 295ccdd

Badness: 0.0256

Sensor

Commas: 126/125, 245/243, 385/384

POTE generator: ~9/7 = 443.294

Map: [<1 6 8 11 -6|, <0 -7 -9 -13 15|]

EDOs: 19, 27, 46, 111d, 157d, 268cdd

Badness: 0.0379

13-limit

Commas: 91/90, 126/125, 169/168, 385/384

POTE generator: ~9/7 = 443.321

Map: [<1 6 8 11 -6 10|, <0 -7 -9 -13 15 -10|]

EDOs: 19, 27, 46, 111df, 157df

Badness: 0.0256

Sensis

Commas: 56/55, 100/99, 245/243

POTE generator: 443.962

Map: [<1 6 8 11 6|, <0 -7 -9 -13 -4|]

EDOs: 19, 27e, 73ee

Badness: 0.0287

13-limit

Commas: 56/55, 78/77, 91/90, 100/99

POTE generator: 443.945

Map: [<1 6 8 11 6 10|, <0 -7 -9 -13 -4 -10|]

EDOs: 19, 27e, 46e, 73ee

Badness: 0.0200

Sensus

Commas: 126/125, 176/175, 245/243

POTE generator: ~9/7 = 443.626

Map: [<1 6 8 11 23|, <0 -7 -9 -13 -31|]

EDOs: 19e, 27e, 46, 119c, 165c

Badness: 0.0295

13-limit

Commas: 91/90, 126/125, 169/168, 352/351

POTE generator: ~9/7 = 443.559

Map: [<1 6 8 11 23 10|, <0 -7 -9 -13 -31 -10|]

EDOs: 19e, 27e, 46, 165cf, 211bccf, 257bccff, 303bccdff

Badness: 0.0208

See Chords of sensus for a listing of chords.

Sensa

Commas: 55/54, 77/75, 99/98

POTE generator: ~9/7 = 443.518

Map: [<1 6 8 11 11|, <0 -7 -9 -13 -12|]

EDOs: 19e, 27, 46ee

Badness: 0.0368

13-limit

Commas: 55/54, 66/65, 77/75, 143/140

POTE generator: ~9/7 = 443.506

Map: [<1 6 8 11 11 10|, <0 -7 -9 -13 -12 -11|]

EDOs: 19e, 27, 46ee

Badness: 0.0233

Hemisensi

Commas: 126/125, 243/242, 245/242

POTE generator: ~25/22 = 221.605

Map: [<1 13 17 24 32|, <0 -14 -18 -26 -35|]

EDOs: 27e, 65, 157de, 222cde

Badness: 0.0487

Sensei

Commas: 225/224, 78732/78125

POTE generator: ~125/81 = 757.245

Map: [<1 6 8 23|, <0 -7 -9 -32|]

Wedgie: <<7 9 32 -2 31 49||

EDOs: 19, 84, 103, 187, 290b

Badness: 0.0592

Bison

Commas: 6144/6125, 78732/78125

POTE generator: ~35/32 = 156.925

Map: [<2 5 7 3|, <0 -7 -9 10|]

Wedgie: <<14 18 -20 -4 -71 -97||

EDOs: 8, 38, 46, 84, 130

Badness: 0.0704

11-limit

Commas: 441/440, 6144/6125, 8019/8000

POTE generator: ~35/32 = 156.883

Map: [<2 5 7 3 3|, <0 -7 -9 10 15|]

EDOs: 46, 84, 130, 306, 436ce

Badness: 0.0371

13-limit

Commas: 351/350, 364/363, 441/440, 10985/10976

POTE generator: ~35/32 = 156.904

Map: [<2 5 7 3 3 4|, <0 -7 -9 10 15 13|]

EDOs: 46, 84, 130, 566ce, 596cef

Badness: 0.0235

Heinz

Commas: 78732/78125, 1029/1024

POTE generator: ~48/35 = 546.815

Map: [<1 13 17 -1|, <0 -21 -27 7|]

EDOs: 46, 103, 149, 699bd

Badness: 0.1154

11-limit

Commas: 385/384, 441/440, 88208/87500

POTE generator: ~11/8 = 547.631

Map: [<1 13 17 -1 4|, <0 -21 -27 7 -1|]

EDOs: 46, 103, 149

Badness: 0.0424

13-limit

Commas: 351/350, 385/384, 441/440, 847/845

POTE generator: ~11/8 = 547.629

Map: [<1 13 17 -1 4 -5|, <0 -21 -27 7 -1 16|]

EDOs: 46, 57, 103, 149, 252e, 401bde

Badness: 0.0258

17-limit

Commas: 273/272, 351/350, 385/384, 441/440, 847/845

POTE generator: ~11/8 = 547.635

Map: [<1 13 17 -1 4 -5 3|, <0 -21 -27 7 -1 16 2|]

EDOs: 46, 103, 149, 252ef, 401bdef

Badness: 0.0185

19-limit

Commas: 171/170, 209/208, 351/350, 385/384, 441/440, 969/968

POTE generator: ~11/8 = 547.614

Map: [<1 13 17 -1 4 -5 3 -5|, <0 -21 -27 7 -1 16 2 17|]

EDOs: 46, 103h, 149h, 252efh

Badness: 0.0190

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