Sensi extensions: Difference between revisions

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[[Sensi]] temperament has various extensions to the 11-limit. These are all members of the [[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:  
* Sensor (19 & 27)
* Sensor (19 & 27) - tempering out 126/125, 245/243, 385/384
* Sensis (19 & 27e)
* Sensis (19 & 27e) - tempering out 56/55, 100/99, 245/243
* Sensus (19e & 27e)
* Sensus (19e & 27e) - tempering out 126/125, 176/175, 245/243
* Sensa (19e & 27)
* 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 ==
{| class="wikitable right-1 right-2"
|-
! rowspan=2 | Generators
! rowspan=2 | Cents<sup>*</sup>
! colspan=4 | Approximate ratios
|-
! Sensor
! Sensis
! Sensus
! Sensa
|-
| 0
| 0.000
| colspan=4 | 1/1
|-
| 1
| 443.34
| colspan=3 | 9/7, 13/10, 22/17
| 9/7, 13/10, <br>14/11, 17/13, <br>22/17
|-
| 2
| 886.69
| colspan=3 | 5/3
| 5/3, 17/10, <br>18/11, 22/13, <br>28/17
|-
| 3
| 130.03
| 13/12, 14/13, <br>15/14
| 12/11, 13/12, <br>14/13, 15/14, <br>17/16
| 13/12, 14/13, <br>15/14
| 11/10, 13/12, <br>14/13, 15/14, <br>18/17
|-
| 4
| 573.38
| 7/5, 18/13
| 7/5, 11/8, <br>18/13, 24/17
| 7/5, 18/13
| 7/5, 15/11, <br>17/12, 18/13
|-
| 5
| 1016.72
| 9/5
| 9/5, 20/11
| 9/5
| 9/5, 11/6, <br>30/17
|-
| 6
| 260.07
| 7/6, 15/13
| 7/6, 13/11, <br>15/13, 20/17
| colspan=2 | 7/6, 15/13
|-
| 7
| 703.41
| 3/2
| 3/2, 26/17
| colspan=2 | 3/2
|-
| 8
| 1146.76
|
|
|
|
|-
| 9
| 390.10
| 5/4
| 5/4, 14/11
| colspan=2 | 5/4
|-
| 10
| 833.45
| 13/8
| 13/8, 18/11, <br>28/17
| colspan=2 | 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
| colspan=2 | 7/4
|-
| 14
| 206.83
| colspan=2 | 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
|
|
|
|}
 
: <sup>*</sup> in 2.3.5.7.13.17/11 POTE tuning


== 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]


Line 15: Line 249:
|-
|-
! Eigenmonzo
! Eigenmonzo
! Supermajor Third
! Supermajor <br>Third
! Comments
! Comments
|-
|-
Line 111: Line 345:


=== 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]


Line 119: Line 352:
|-
|-
! Eigenmonzo
! Eigenmonzo
! Supermajor Third
! Supermajor <br>Third
! Comments
! Comments
|-
|-
Line 216: Line 449:


=== 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]


Line 224: Line 456:
|-
|-
! Eigenmonzo
! Eigenmonzo
! Supermajor Third
! Supermajor <br>Third
! Comments
! Comments
|-
|-
Line 321: Line 553:


=== 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]


Line 329: Line 560:
|-
|-
! Eigenmonzo
! Eigenmonzo
! Supermajor Third
! Supermajor <br>Third
! Comments
! Comments
|-
|-
Line 427: Line 658:
[[Category:Sensipent]]
[[Category:Sensipent]]
[[Category:Sensi]]
[[Category:Sensi]]
[[Category:Sensor]]
[[Category:Sensis]]
[[Category:Sensus]]
[[Category:Sensa]]