Sensi extensions: Difference between revisions

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→Tuning Spectra: improve and standardize tuning spectra tables
Line 240: Line 240:
: <sup>*</sup> in 2.3.5.7.13.17/11 POTE tuning
: <sup>*</sup> in 2.3.5.7.13.17/11 POTE tuning


== Tuning Spectra ==
== Tuning spectra ==
=== Spectrum of sensor tunings by eigenmonzos ===
=== Sensor ===
Gencom: [2 9/7; 91/90 126/125 169/168 385/384]
Gencom: [2 9/7; 91/90 126/125 169/168 385/384]


Gencom map: [{{val| 1 -1 -1 -2 9 0 }}, {{val| 0 7 9 13 -15 10 }}]
Gencom map: [{{val| 1 -1 -1 -2 9 0 }}, {{val| 0 7 9 13 -15 10 }}]


{| class="wikitable center-1 center-2"
{| class="wikitable center-all"
|-
|-
! Eigenmonzo
! [[eigenmonzo|eigenmonzo<br>(unchanged interval]])
! Supermajor <br>Third
! supermajor<br>third (¢)
! Comments
! comments
|-
|-
| 9/7
| 9/7
| 435.084
| 435.084
|  
|
|-
|-
| 15/14
| 15/14
| 439.814
| 439.814
|  
|
|-
|-
| 18/13
| 18/13
| 440.846
| 440.846
|  
|
|-
|-
| 15/13
| 15/13
| 441.290
| 441.290
|  
|
|-
|-
| 6/5
| 6/5
| 442.179
| 442.179
|  
|
|-
|-
| 14/13
| 14/13
| 442.766
| 442.766
|  
|
|-
|-
| 5/4
| 5/4
Line 282: Line 282:
| 16/15
| 16/15
| 443.017
| 443.017
|  
|
|-
|-
| 11/10
| 11/10
| 443.125
| 443.125
|  
|
|-
|-
| 15/11
| 15/11
| 443.127
| 443.127
|  
|
|-
|-
| 4/3
| 4/3
Line 298: Line 298:
| 11/9
| 11/9
| 443.193
| 443.193
|  
|
|-
|-
| 12/11
| 12/11
| 443.211
| 443.211
|  
|
|-
|-
| 11/8
| 11/8
| 443.245
| 443.245
|  
|
|-
|-
| 14/11
| 14/11
Line 325: Line 325:
| 16/13
| 16/13
| 444.053
| 444.053
|  
|
|-
|-
| 7/6
| 7/6
| 444.478
| 444.478
|  
|
|-
|-
| 7/5
| 7/5
| 445.628
| 445.628
|  
|
|-
|-
| 13/12
| 13/12
| 446.191
| 446.191
|  
|
|-
|-
| 13/10
| 13/10
| 454.214
| 454.214
|  
|
|}
|}


=== Spectrum of sensis tunings by eigenmonzos ===
=== Sensis ===
Gencom: [2 9/7; 56/55 78/77 91/90 100/99]
Gencom: [2 9/7; 56/55 78/77 91/90 100/99]


Gencom map: [{{val| 1 -1 -1 -2 2 0 }}, {{val| 0 7 9 13 4 10 }}]
Gencom map: [{{val| 1 -1 -1 -2 2 0 }}, {{val| 0 7 9 13 4 10 }}]


{| class="wikitable center-1 center-2"
{| class="wikitable center-all"
|-
|-
! Eigenmonzo
! eigenmonzo<br>(unchanged interval)
! Supermajor <br>Third
! supermajor<br>third (¢)
! Comments
! comments
|-
|-
| 9/7
| 9/7
| 435.084
| 435.084
|  
|
|-
|-
| 11/8
| 11/8
| 437.829
| 437.829
|  
|
|-
|-
| 15/14
| 15/14
| 439.814
| 439.814
|  
|
|-
|-
| 18/13
| 18/13
| 440.846
| 440.846
|  
|
|-
|-
| 15/13
| 15/13
| 441.290
| 441.290
|  
|
|-
|-
| 6/5
| 6/5
| 442.179
| 442.179
|  
|
|-
|-
| 14/13
| 14/13
| 442.766
| 442.766
|  
|
|-
|-
| 5/4
| 5/4
Line 389: Line 389:
| 16/15
| 16/15
| 443.017
| 443.017
|  
|
|-
|-
| 4/3
| 4/3
| 443.136
| 443.136
|  
|
|-
|-
| 10/9
| 10/9
Line 409: Line 409:
| 7/6
| 7/6
| 444.478
| 444.478
|  
|
|-
|-
| 15/11
| 15/11
| 444.746
| 444.746
|  
|
|-
|-
| 11/9
| 11/9
| 445.259
| 445.259
|  
|
|-
|-
| 7/5
| 7/5
| 445.628
| 445.628
|  
|
|-
|-
| 13/12
| 13/12
| 446.191
| 446.191
|  
|
|-
|-
| 14/11
| 14/11
| 446.390
| 446.390
|  
|
|-
|-
| 11/10
| 11/10
| 446.999
| 446.999
|  
|
|-
|-
| 13/11
| 13/11
| 448.202
| 448.202
|  
|
|-
|-
| 12/11
| 12/11
| 450.212
| 450.212
|  
|
|-
|-
| 13/10
| 13/10
| 454.214
| 454.214
|  
|
|}
|}


=== Spectrum of sensus tunings by eigenmonzos ===
=== Sensus ===
Gencom: [2 9/7; 91/90 126/125 169/168 352/351]
Gencom: [2 9/7; 91/90 126/125 169/168 352/351]


Gencom map: [{{val| 1 -1 -1 -2 -8 0 }}, {{val| 0 7 9 13 31 10 }}]
Gencom map: [{{val| 1 -1 -1 -2 -8 0 }}, {{val| 0 7 9 13 31 10 }}]


{| class="wikitable center-1 center-2"
{| class="wikitable center-all"
|-
|-
! Eigenmonzo
! eigenmonzo<br>(unchanged interval)
! Supermajor <br>Third
! supermajor<br>third (¢)
! Comments
! comments
|-
|-
| 9/7
| 9/7
| 435.084
| 435.084
|  
|
|-
|-
| 15/14
| 15/14
| 439.814
| 439.814
|  
|
|-
|-
| 18/13
| 18/13
| 440.846
| 440.846
|  
|
|-
|-
| 15/13
| 15/13
| 441.290
| 441.290
|  
|
|-
|-
| 6/5
| 6/5
| 442.179
| 442.179
|  
|
|-
|-
| 14/13
| 14/13
| 442.766
| 442.766
|  
|
|-
|-
| 5/4
| 5/4
Line 489: Line 489:
| 16/15
| 16/15
| 443.017
| 443.017
|  
|
|-
|-
| 4/3
| 4/3
| 443.136
| 443.136
|  
|
|-
|-
| 13/11
| 13/11
| 443.371
| 443.371
|  
|
|-
|-
| 14/11
| 14/11
| 443.472
| 443.472
|  
|
|-
|-
| 10/9
| 10/9
Line 509: Line 509:
| 11/8
| 11/8
| 443.591
| 443.591
|  
|
|-
|-
| 12/11
| 12/11
| 443.723
| 443.723
|  
|
|-
|-
| 8/7
| 8/7
Line 521: Line 521:
| 11/10
| 11/10
| 443.864
| 443.864
|  
|
|-
|-
| 11/9
| 11/9
| 443.965
| 443.965
|  
|
|-
|-
| 16/13
| 16/13
Line 533: Line 533:
| 15/11
| 15/11
| 444.203
| 444.203
|  
|
|-
|-
| 7/6
| 7/6
| 444.478
| 444.478
|  
|
|-
|-
| 7/5
| 7/5
| 445.628
| 445.628
|  
|
|-
|-
| 13/12
| 13/12
| 446.191
| 446.191
|  
|
|-
|-
| 13/10
| 13/10
| 454.214
| 454.214
|  
|
|}
|}


=== Spectrum of sensa tunings by eigenmonzos ===
=== Sensa ===
Gencom: [2 9/7; 55/54 66/65 77/75 143/140]
Gencom: [2 9/7; 55/54 66/65 77/75 143/140]


Gencom map: [{{val| 1 -1 -1 -2 -1 0 }}, {{val| 0 7 9 13 12 10 }}]
Gencom map: [{{val| 1 -1 -1 -2 -1 0 }}, {{val| 0 7 9 13 12 10 }}]


{| class="wikitable center-1 center-2"
{| class="wikitable center-all"
|-
|-
! Eigenmonzo
! eigenmonzo<br>(unchanged interval)
! Supermajor <br>Third
! supermajor<br>third (¢)
! Comments
! comments
|-
|-
| 14/11
| 14/11
| 417.508
| 417.508
|  
|
|-
|-
| 11/9
| 11/9
| 426.296
| 426.296
|  
|
|-
|-
| 15/11
| 15/11
| 434.238
| 434.238
|  
|
|-
|-
| 9/7
| 9/7
| 435.084
| 435.084
|  
|
|-
|-
| 15/14
| 15/14
| 439.814
| 439.814
|  
|
|-
|-
| 18/13
| 18/13
| 440.846
| 440.846
|  
|
|-
|-
| 15/13
| 15/13
| 441.290
| 441.290
|  
|
|-
|-
| 6/5
| 6/5
| 442.179
| 442.179
|  
|
|-
|-
| 14/13
| 14/13
| 442.766
| 442.766
|  
|
|-
|-
| 5/4
| 5/4
Line 605: Line 605:
| 16/15
| 16/15
| 443.017
| 443.017
|  
|
|-
|-
| 4/3
| 4/3
| 443.136
| 443.136
|  
|
|-
|-
| 10/9
| 10/9
Line 625: Line 625:
| 7/6
| 7/6
| 444.478
| 444.478
|  
|
|-
|-
| 7/5
| 7/5
| 445.628
| 445.628
|  
|
|-
|-
| 11/8
| 11/8
| 445.943
| 445.943
|  
|
|-
|-
| 13/12
| 13/12
| 446.191
| 446.191
|  
|
|-
|-
| 12/11
| 12/11
| 449.873
| 449.873
|  
|
|-
|-
| 13/10
| 13/10
| 454.214
| 454.214
|  
|
|-
|-
| 11/10
| 11/10
| 455.001
| 455.001
|  
|
|-
|-
| 13/11
| 13/11
| 455.395
| 455.395
|  
|
|}
|}


[[Category:Sensipent]]
[[Category:Sensipent]]
[[Category:Sensi]]
[[Category:Sensi]]

Revision as of 00:31, 30 September 2021

Sensi temperament has various extensions to the 11-limit. These are all members of the sensipent family, but in addition they are linear temperaments:

  • Sensor (19 & 27) - tempering out 126/125, 245/243, 385/384
  • Sensis (19 & 27e) - tempering out 56/55, 100/99, 245/243
  • Sensus (19e & 27e) - tempering out 126/125, 176/175, 245/243
  • Sensa (19e & 27) - tempering out 55/54, 77/75, 99/98

These can be extended 13 and 17 prime limits naturally by adding 91/90 and 154/153 to the comma list in this order. Then the generator represents 9/7, 13/10, and 22/17.

Interval chain

Generators Cents* Approximate ratios
Sensor Sensis Sensus Sensa
0 0.000 1/1
1 443.34 9/7, 13/10, 22/17 9/7, 13/10,
14/11, 17/13,
22/17
2 886.69 5/3 5/3, 17/10,
18/11, 22/13,
28/17
3 130.03 13/12, 14/13,
15/14 		12/11, 13/12,
14/13, 15/14,
17/16 		13/12, 14/13,
15/14 		11/10, 13/12,
14/13, 15/14,
18/17
4 573.38 7/5, 18/13 7/5, 11/8,
18/13, 24/17 		7/5, 18/13 7/5, 15/11,
17/12, 18/13
5 1016.72 9/5 9/5, 20/11 9/5 9/5, 11/6,
30/17
6 260.07 7/6, 15/13 7/6, 13/11,
15/13, 20/17 		7/6, 15/13
7 703.41 3/2 3/2, 26/17 3/2
8 1146.76
9 390.10 5/4 5/4, 14/11 5/4
10 833.45 13/8 13/8, 18/11,
28/17 		13/8
11 76.79 18/17 17/16
12 520.14 15/11 11/8
13 963.48 7/4 7/4, 30/17 7/4
14 206.83 9/8 9/8, 17/15 9/8
15 650.17 16/11 22/15
16 1093.51 15/8, 32/17 15/8 15/8, 17/9 15/8
17 336.86 11/9, 17/14
18 780.20 11/7
19 23.55
20 466.89 17/13
21 910.24 17/10, 22/13
22 153.58 12/11 11/10
23 596.93 24/17 17/12
24 1040.27 20/11 11/6
25 283.62 13/11, 20/17
26 726.96 26/17
27 1170.31
28 413.65 14/11
29 857.00 18/11, 28/17
30 100.34 18/17 17/16
31 543.68 15/11 11/8
32 987.03 30/17
* in 2.3.5.7.13.17/11 POTE tuning

Tuning spectra

Sensor

Gencom: [2 9/7; 91/90 126/125 169/168 385/384]

Gencom map: [⟨1 -1 -1 -2 9 0], ⟨0 7 9 13 -15 10]]

eigenmonzo
(unchanged interval) 		supermajor
third (¢) 		comments
9/7 435.084
15/14 439.814
18/13 440.846
15/13 441.290
6/5 442.179
14/13 442.766
5/4 442.924 5-odd-limit minimax
16/15 443.017
11/10 443.125
15/11 443.127
4/3 443.136 15-odd-limit minimax
11/9 443.193
12/11 443.211
11/8 443.245
14/11 443.482 11-odd-limit minimax
10/9 443.519 9- and 13-odd-limit minimax
13/11 443.568
8/7 443.756 7-odd-limit minimax
16/13 444.053
7/6 444.478
7/5 445.628
13/12 446.191
13/10 454.214

Sensis

Gencom: [2 9/7; 56/55 78/77 91/90 100/99]

Gencom map: [⟨1 -1 -1 -2 2 0], ⟨0 7 9 13 4 10]]

eigenmonzo
(unchanged interval) 		supermajor
third (¢) 		comments
9/7 435.084
11/8 437.829
15/14 439.814
18/13 440.846
15/13 441.290
6/5 442.179
14/13 442.766
5/4 442.924 5-odd-limit minimax
16/15 443.017
4/3 443.136
10/9 443.519 9-odd-limit minimax
8/7 443.756 7- and 11-odd-limit minimax
16/13 444.053 13- and 15-odd-limit minimax
7/6 444.478
15/11 444.746
11/9 445.259
7/5 445.628
13/12 446.191
14/11 446.390
11/10 446.999
13/11 448.202
12/11 450.212
13/10 454.214

Sensus

Gencom: [2 9/7; 91/90 126/125 169/168 352/351]

Gencom map: [⟨1 -1 -1 -2 -8 0], ⟨0 7 9 13 31 10]]

eigenmonzo
(unchanged interval) 		supermajor
third (¢) 		comments
9/7 435.084
15/14 439.814
18/13 440.846
15/13 441.290
6/5 442.179
14/13 442.766
5/4 442.924 5-odd-limit minimax
16/15 443.017
4/3 443.136
13/11 443.371
14/11 443.472
10/9 443.519 9-odd-limit minimax
11/8 443.591
12/11 443.723
8/7 443.756 7- and 11-odd-limit minimax
11/10 443.864
11/9 443.965
16/13 444.053 13- and 15-odd-limit minimax
15/11 444.203
7/6 444.478
7/5 445.628
13/12 446.191
13/10 454.214

Sensa

Gencom: [2 9/7; 55/54 66/65 77/75 143/140]

Gencom map: [⟨1 -1 -1 -2 -1 0], ⟨0 7 9 13 12 10]]

eigenmonzo
(unchanged interval) 		supermajor
third (¢) 		comments
14/11 417.508
11/9 426.296
15/11 434.238
9/7 435.084
15/14 439.814
18/13 440.846
15/13 441.290
6/5 442.179
14/13 442.766
5/4 442.924 5-odd-limit minimax
16/15 443.017
4/3 443.136
10/9 443.519 9-odd-limit minimax
8/7 443.756 7- and 11-odd-limit minimax
16/13 444.053 13- and 15-odd-limit minimax
7/6 444.478
7/5 445.628
11/8 445.943
13/12 446.191
12/11 449.873
13/10 454.214
11/10 455.001
13/11 455.395
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