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]] | ||