Sensi extensions: Difference between revisions

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


=Tuning Spectra=
== Tuning Spectra ==
 
=== Spectrum of sensor tunings by eigenmonzos ===
==Spectrum of Sensor Tunings by Eigenmonzos==


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


{| class="wikitable"
{| class="wikitable center-1 center-2"
|-
|-
! | Eigenmonzo
! Eigenmonzo
! | Supermajor Third
! Supermajor Third
! 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
| | 442.924 (5 limit minimax)
| 442.924
| 5-odd-limit minimax
|-
|-
| | 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
| | 443.136 (15 limit minimax)
| 443.136
| 15-odd-limit minimax
|-
|-
| | 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
| | 443.482 (11 limit minimax)
| 443.482
| 11-odd-limit minimax
|-
|-
| | 10/9
| 10/9
| | 443.519 (9 and 13 limit minimax)
| 443.519
| 9- and 13-odd-limit minimax
|-
|-
| | 13/11
| 13/11
| | 443.568
| 443.568
|-
|-
| | 8/7
| 8/7
| | 443.756 (7 limit minimax)
| 443.756
| 7-odd-limit minimax
|-
|-
| | 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==
=== Spectrum of sensis tunings by eigenmonzos ===


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


{| class="wikitable"
{| class="wikitable center-1 center-2"
|-
|-
! | Eigenmonzo
! Eigenmonzo
! | Supermajor Third
! Supermajor Third
! 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
| | 442.924 (5 limit minimax)
| 442.924
| 5-odd-limit minimax
|-
|-
| | 16/15
| 16/15
| | 443.017
| 443.017
|
|-
|-
| | 4/3
| 4/3
| | 443.136
| 443.136
|
|-
|-
| | 10/9
| 10/9
| | 443.519 (9 limit minimax)
| 443.519
| 9-odd-limit minimax
|-
|-
| | 8/7
| 8/7
| | 443.756 (7 and 11 limit minimax)
| 443.756
| 7- and 11-odd-limit minimax
|-
|-
| | 16/13
| 16/13
| | 444.053 (13 and 15 limit minimax)
| 444.053
| 13- and 15-odd-limit minimax
|-
|-
| | 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==
=== Spectrum of sensus tunings by eigenmonzos ===


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


{| class="wikitable"
{| class="wikitable center-1 center-2"
|-
|-
! | Eigenmonzo
! Eigenmonzo
! | Supermajor Third
! Supermajor Third
! 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
| | 442.924 (5 limit minimax)
| 442.924
| 5-odd-limit minimax
|-
|-
| | 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
| | 443.519 (9 limit minimax)
| 443.519
| 9-odd-limit minimax
|-
|-
| | 11/8
| 11/8
| | 443.591
| 443.591
|
|-
|-
| | 12/11
| 12/11
| | 443.723
| 443.723
|
|-
|-
| | 8/7
| 8/7
| | 443.756 (7 and 11 limit minimax)
| 443.756
| 7- and 11-odd-limit minimax
|-
|-
| | 11/10
| 11/10
| | 443.864
| 443.864
|
|-
|-
| | 11/9
| 11/9
| | 443.965
| 443.965
|
|-
|-
| | 16/13
| 16/13
| | 444.053 (13 and 15 limit minimax)
| 444.053
| 13- and 15-odd-limit minimax
|-
|-
| | 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==
=== Spectrum of sensa tunings by eigenmonzos ===


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


{| class="wikitable"
{| class="wikitable center-1 center-2"
|-
|-
! | Eigenmonzo
! Eigenmonzo
! | Supermajor Third
! Supermajor Third
! 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
| | 442.924 (5 limit minimax)
| 442.924
| 5-odd-limit minimax
|-
|-
| | 16/15
| 16/15
| | 443.017
| 443.017
|
|-
|-
| | 4/3
| 4/3
| | 443.136
| 443.136
|
|-
|-
| | 10/9
| 10/9
| | 443.519 (9 limit minimax)
| 443.519
| 9-odd-limit minimax
|-
|-
| | 8/7
| 8/7
| | 443.756 (7 and 11 limit minimax)
| 443.756
| 7- and 11-odd-limit minimax
|-
|-
| | 16/13
| 16/13
| | 444.053 (13 and 15 limit minimax)
| 444.053
| 13- and 15-odd-limit minimax
|-
|-
| | 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:eigenmonzo]]
 
[[Category:sensa]]
[[Category:Sensipent]]
[[Category:sensi]]
[[Category:Sensi]]
[[Category:sensipent]]
[[Category:Sensor]]
[[Category:sensis]]
[[Category:Sensis]]
[[Category:sensor]]
[[Category:Sensus]]
[[Category:sensus]]
[[Category:Sensa]]
[[Category:spectrum]]

Revision as of 07:31, 6 April 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.

Tuning Spectra

Spectrum of sensor tunings by eigenmonzos

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 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

Spectrum of sensis tunings by eigenmonzos

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 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

Spectrum of sensus tunings by eigenmonzos

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 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

Spectrum of sensa tunings by eigenmonzos

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 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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