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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.
{{Breadcrumb|Sensi}}


=Tuning Spectra=
[[Sensi]] has multiple competing [[extension]]s to the [[11-limit]]. The simplest [[7-limit]] [[comma]]s of sensi are [[126/125|starling (126/125)]] and [[245/243|sensamagic (245/243)]], and it can be viewed as the merge of the two corresponding [[rank-3 temperament]]s. These rank-3 temperaments are associated with distinct paths to the 11-limit. On one hand, [[starling]] strongly suggests tempering out [[176/175]], leading to thrush ({{nowrap|{126/125, 176/175}}}), since {{nowrap|126/125 {{=}} (176/175)(441/440)}}. On the other, [[sensamagic]] strongly suggests tempering out [[385/384]], leading to undecimal sensamagic ({{nowrap|{245/243, 385/384}}}), since {{nowrap|245/243 {{=}} (385/384)(896/891)}}. Taking either path for sensi leads us to one of the following entries:
* '''Sensor''' ({{nowrap| 19 & 27 }}) – tempering out 126/125, 245/243, and 385/384
* '''Sensus''' ({{nowrap| 19e & 27e }}) – tempering out 126/125, 176/175, and 245/243


==Spectrum of Sensor Tunings by Eigenmonzos==
The two unite in [[46edo|46et]], where both 176/175 and 385/384, as well as their sum, [[121/120]], are tempered out. They can be extended to the 13- and 17-limit 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]].


Gencom: [2 9/7; 91/90 126/125 169/168 385/384]
In addition, there are some low-complexity low-accuracy entries:  
* '''Sensis''' ({{nowrap| 19 & 27e }}) – tempering out 56/55, 100/99, and 245/243
* '''Sensa''' ({{nowrap| 19e & 27 }}) – tempering out 55/54, 77/75, and 99/98


Gencom map: [<1 -1 -1 -2 9 0|, <0 7 9 13 -15 10|]
Another possible path which relates a sense of compromise is to temper out [[121/120]], leading to bisensi. This has the effect of slicing the octave in two, and is supported by [[38edo|38df]], 46, and [[54edo|54c]].


{| class="wikitable"
See [[Sensipent family #Sensor]], [[Sensipent family #Sensus|#Sensus]], [[Sensipent family #Sensis|#Sensis]], and [[Sensipent family #Sensa|#Sensa]] for technical data.
 
== Interval chain ==
In the following table, odd harmonics and subharmonics 1–21 are in '''bold'''.
 
{| class="wikitable right-1 right-2"
|-
! rowspan="2" | #
! rowspan="2" | Cents*
! colspan="5" | Approximate ratios
|-
! Sensi
! Sensor
! Sensis
! Sensus
! Sensa
|-
| 0
| 0.0
| '''1/1'''
|
|
|
|
|-
| 1
| 443.4
| 9/7, 13/10, 22/17
|
|
|
| 14/11, 17/13
|-
| 2
| 886.8
| 5/3
|
|
|
| 17/10, 18/11, 22/13, 28/17
|-
| 3
| 130.2
| 13/12, 14/13, 15/14
|
| 12/11, '''17/16'''
|
| 11/10, 18/17
|-
| 4
| 573.6
| 7/5, 18/13
|
| '''11/8''', 24/17
|
| 15/11, 17/12
|-
| 5
| 1017.0
| 9/5
|
| 20/11
|
| 11/6, 30/17
|-
|-
! | Eigenmonzo
| 6
! | Supermajor Third
| 260.4
| 7/6, 15/13
|
| 13/11, 20/17
|
|  
|-
|-
| | 9/7
| 7
| | 435.084
| 703.8
| '''3/2'''
|
| 26/17
|  
|  
|-
|-
| | 15/14
| 8
| | 439.814
| 1147.2
| 27/14, 35/18
|  
|
|
|  
|-
|-
| | 18/13
| 9
| | 440.846
| 390.6
| '''5/4'''
|  
| 14/11
|
|  
|-
|-
| | 15/13
| 10
| | 441.290
| 834.0
| '''13/8''', 21/13
|  
| 18/11, 28/17
|
|  
|-
|-
| | 6/5
| 11
| | 442.179
| 77.4
| 21/20, 25/24
|  
| 18/17
|
| '''17/16'''
|-
|-
| | 14/13
| 12
| | 442.766
| 520.8
| 27/20
|
| 15/11
|  
| '''11/8'''
|-
|-
| | 5/4
| 13
| | 442.924 (5 limit minimax)
| 964.2
| '''7/4'''
|  
| 30/17
|
|  
|-
|-
| | 16/15
| 14
| | 443.017
| 207.6
| '''9/8'''
|
|
| 17/15
|  
|-
|-
| | 11/10
| 15
| | 443.125
| 651.0
| 35/24
| '''16/11'''
|
| 22/15
|  
|-
|-
| | 15/11
| 16
| | 443.127
| 1094.5
| '''15/8'''
| '''32/17'''
|
| 17/9
|  
|-
|-
| | 4/3
| 17
| | 443.136 (15 limit minimax)
| 337.9
| 39/32
|
|
| 11/9, 17/14
|  
|-
|-
| | 11/9
| 18
| | 443.193
| 781.3
| 25/16
|
|
| 11/7
|  
|-
|-
| | 12/11
| 19
| | 443.211
| 24.7
| 49/48, 65/64, 81/80
|
|
|  
|  
|-
|-
| | 11/8
| 20
| | 443.245
| 468.1
| '''21/16'''
|  
|
| 17/13
|  
|-
|-
| | 14/11
| 21
| | 443.482 (11 limit minimax)
| 911.5
| 27/16
|
|
| 17/10, 22/13
|  
|-
|-
| | 10/9
| 22
| | 443.519 (9 and 13 limit minimax)
| 154.9
| 35/32
| 12/11
|
| 11/10
|  
|-
|-
| | 13/11
| 23
| | 443.568
| 598.3
| 45/32
| 24/17
|
| 17/12
|  
|-
|-
| | 8/7
| 24
| | 443.756 (7 limit minimax)
| 1041.7
| 117/64
| 20/11
|  
| 11/6
|  
|-
|-
| | 16/13
| 25
| | 444.053
| 285.1
| 75/64
| 13/11, 20/17
|
|  
|  
|-
|-
| | 7/6
| 26
| | 444.478
| 728.5
| 49/32
| 26/17
|
|
|  
|-
|-
| | 7/5
| 27
| | 445.628
| 1171.9
| 63/32
|
|  
|
|  
|-
|-
| | 13/12
| 28
| | 446.191
| 415.3
| 81/64
| 14/11
|
|
|  
|-
|-
| | 13/10
| 29
| | 454.214
| 858.7
| 105/64
| 18/11, 28/17
|
|  
|  
|-
| 30
| 102.1
| 135/128
| 18/17
|
| '''17/16'''
|
|-
| 31
| 545.5
| 175/128
| 15/11
|
| '''11/8'''
|
|-
| 32
| 988.9
| 225/128
| 30/17
|
|
|
|}
|}
<nowiki/>* In 2.3.5.7.13.17/11 subgroup CTE tuning


==Spectrum of Sensis Tunings by Eigenmonzos==
== Tuning spectra ==
=== Sensor ===
{| class="wikitable center-all left-4"
|-
! Edo<br>generators
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]*
! Generator (¢)
! Comments
|-
|
| 9/7
| 435.084
|
|-
| 4\11
|
| 436.364
| 11cdefgg val
|-
|
| 15/14
| 439.814
|
|-
|
| 13/9
| 440.846
|
|-
|
| 15/13
| 441.290
|
|-
| 7\19
|
| 442.105
|
|-
|
| 5/3
| 442.179
|
|-
|
| 13/7
| 442.766
|
|-
|
| 5/4
| 442.924
| 5-odd-limit minimax
|-
|
| 15/8
| 443.017
|
|-
|
| 11/10
| 443.125
|
|-
|
| 15/11
| 443.127
|
|-
|
| 3/2
| 443.136
| 15-odd-limit minimax
|-
|
| 11/9
| 443.193
|
|-
|
| 11/6
| 443.211
|
|-
|
| 11/8
| 443.245
|
|-
| 17\46
|
| 443.478
|
|-
|
| 11/7
| 443.482
| 11-odd-limit minimax
|-
|
| 9/5
| 443.519
| 9- and 13-odd-limit minimax
|-
|
| 13/11
| 443.568
|
|-
|
| 7/4
| 443.756
| 7-odd-limit minimax
|-
|
| 13/8
| 444.053
|
|-
| 10\27
|
| 444.444
|
|-
|
| 7/6
| 444.478
|
|-
|
| 117/70
| 444.649
|
|-
|
| 7/5
| 445.628
|
|-
|
| 13/12
| 446.191
|
|-
| 3\8
|
| 450.000
| 8deg val
|-
|
| 13/10
| 454.214
|
|}
<nowiki/>* Besides the octave


Gencom: [2 9/7; 56/55 78/77 91/90 100/99]
=== Sensis ===
 
{| class="wikitable center-all left-4"
Gencom map: [&lt;1 -1 -1 -2 2 0|, &lt;0 7 9 13 4 10|]
|-
 
! Edo<br>generators
{| class="wikitable"
! Unchanged interval<br>(eigenmonzo)*
! Generator (¢)
! Comments
|-
|
| 9/7
| 435.084
|
|-
| 4\11
|
| 436.364
| 11cdf val
|-
|
| 11/8
| 437.829
|
|-
|
| 15/14
| 439.814
|
|-
|
| 13/9
| 440.846
|  
|-
|-
! | Eigenmonzo
|  
! | Supermajor Third
| 15/13
| 441.290
|
|-
|-
| | 9/7
| 7\19
| | 435.084
|  
| 442.105
|
|-
|-
| | 11/8
|  
| | 437.829
| 5/3
| 442.179
|  
|-
|-
| | 15/14
|  
| | 439.814
| 13/7
| 442.766
|  
|-
|-
| | 18/13
|  
| | 440.846
| 5/4
| 442.924
| 5-odd-limit minimax
|-
|-
| | 15/13
|  
| | 441.290
| 15/8
| 443.017
|  
|-
|-
| | 6/5
|  
| | 442.179
| 3/2
| 443.136
|  
|-
|-
| | 14/13
| 17\46
| | 442.766
|  
| 443.478
| 46e val
|-
|-
| | 5/4
|  
| | 442.924 (5 limit minimax)
| 9/5
| 443.519
| 9-odd-limit minimax
|-
|-
| | 16/15
|  
| | 443.017
| 7/4
| 443.756
| 7- and 11-odd-limit minimax
|-
|-
| | 4/3
|  
| | 443.136
| 13/8
| 444.053
| 13- and 15-odd-limit minimax
|-
|-
| | 10/9
| 10\27
| | 443.519 (9 limit minimax)
|  
| 444.444
| 27e val
|-
|-
| | 8/7
|  
| | 443.756 (7 and 11 limit minimax)
| 7/6
| 444.478
|  
|-
|-
| | 16/13
|  
| | 444.053 (13 and 15 limit minimax)
| 117/70
| 444.649
|
|-
|-
| | 7/6
|  
| | 444.478
| 15/11
| 444.746
|
|-
|-
| | 15/11
|  
| | 444.746
| 11/9
| 445.259
|  
|-
|-
| | 11/9
|  
| | 445.259
| 7/5
| 445.628
|
|-
|-
| | 7/5
|  
| | 445.628
| 13/12
| 446.191
|  
|-
|-
| | 13/12
|  
| | 446.191
| 11/7
| 446.390
|
|-
|-
| | 14/11
|  
| | 446.390
| 11/10
| 446.999
|
|-
|-
| | 11/10
|  
| | 446.999
| 13/11
| 448.202
|  
|-
|-
| | 13/11
| 3\8
| | 448.202
|  
| 450.000
| 8d val
|-
|-
| | 12/11
|  
| | 450.212
| 11/6
| 450.212
|
|-
|-
| | 13/10
|  
| | 454.214
| 13/10
| 454.214
|
|}
|}
<nowiki/>* Besides the octave


==Spectrum of Sensus Tunings by Eigenmonzos==
=== Sensus ===
 
{| class="wikitable center-all left-4"
Gencom: [2 9/7; 91/90 126/125 169/168 352/351]
|-
 
! Edo<br>generators
Gencom map: [&lt;1 -1 -1 -2 -8 0|, &lt;0 7 9 13 31 10|]
! Unchanged interval<br>(eigenmonzo)*
 
! Generator (¢)
{| class="wikitable"
! Comments
|-
|
| 9/7
| 435.084
|
|-
| 4\11
|
| 436.364
| 11cdeeeefggg val
|-
|
| 15/14
| 439.814
|
|-
|
| 13/9
| 440.846
|
|-
|  
| 15/13
| 441.290
|  
|-
|-
! | Eigenmonzo
| 7\19
! | Supermajor Third
|  
| 442.105
| 19eg val
|-
|-
| | 9/7
|  
| | 435.084
| 5/3
| 442.179
|  
|-
|-
| | 15/14
|  
| | 439.814
| 13/7
| 442.766
|  
|-
|-
| | 18/13
|  
| | 440.846
| 5/4
| 442.924
| 5-odd-limit minimax
|-
|-
| | 15/13
|  
| | 441.290
| 15/8
| 443.017
|  
|-
|-
| | 6/5
|  
| | 442.179
| 3/2
| 443.136
|  
|-
|-
| | 14/13
|  
| | 442.766
| 13/11
| 443.371
|  
|-
|-
| | 5/4
|  
| | 442.924 (5 limit minimax)
| 11/7
| 443.472
|  
|-
|-
| | 16/15
| 17\46
| | 443.017
|  
| 443.478
|
|-
|-
| | 4/3
|  
| | 443.136
| 9/5
| 443.519
| 9-odd-limit minimax
|-
|-
| | 13/11
|  
| | 443.371
| 11/8
| 443.591
|
|-
|-
| | 14/11
|  
| | 443.472
| 11/6
| 443.723
|
|-
|-
| | 10/9
|  
| | 443.519 (9 limit minimax)
| 7/4
| 443.756
| 7- and 11-odd-limit minimax
|-
|-
| | 11/8
|  
| | 443.591
| 11/10
| 443.864
|
|-
|-
| | 12/11
|  
| | 443.723
| 11/9
| 443.965
|
|-
|-
| | 8/7
|  
| | 443.756 (7 and 11 limit minimax)
| 13/8
| 444.053
| 13- and 15-odd-limit minimax
|-
|-
| | 11/10
|  
| | 443.864
| 15/11
| 444.203
|  
|-
|-
| | 11/9
| 10\27
| | 443.965
|  
| 444.444
| 27eg val
|-
|-
| | 16/13
|  
| | 444.053 (13 and 15 limit minimax)
| 7/6
| 444.478
|
|-
|-
| | 15/11
|  
| | 444.203
| 117/70
| 444.649
|
|-
|-
| | 7/6
|  
| | 444.478
| 7/5
| 445.628
|  
|-
|-
| | 7/5
|  
| | 445.628
| 13/12
| 446.191
|  
|-
|-
| | 13/12
| 3\8
| | 446.191
|  
| 450.000
| 8deegg val
|-
|-
| | 13/10
|  
| | 454.214
| 13/10
| 454.214
|
|}
|}
<nowiki/>* Besides the octave


==Spectrum of Sensa Tunings by Eigenmonzos==
=== Sensa ===
 
{| class="wikitable center-all left-4"
Gencom: [2 9/7; 55/54 66/65 77/75 143/140]
|-
 
! Edo<br>generators
Gencom map: [&lt;1 -1 -1 -2 -1 0|, &lt;0 7 9 13 12 10|]
! Unchanged interval<br>(eigenmonzo)*
 
! Generator (¢)
{| class="wikitable"
! Comments
|-
|
| 11/7
| 417.508
|
|-
|
| 11/9
| 426.296
|
|-
|
| 15/11
| 434.238
|
|-
|
| 9/7
| 435.084
|
|-
| 4\11
|  
| 436.364
| 11cdeef val
|-
|-
! | Eigenmonzo
|  
! | Supermajor Third
| 15/14
| 439.814
|
|-
|-
| | 14/11
|  
| | 417.508
| 13/9
| 440.846
|  
|-
|-
| | 11/9
|  
| | 426.296
| 15/13
| 441.290
|  
|-
|-
| | 15/11
| 7\19
| | 434.238
|  
| 442.105
| 19e val
|-
|-
| | 9/7
|  
| | 435.084
| 5/3
| 442.179
|  
|-
|-
| | 15/14
|  
| | 439.814
| 13/7
| 442.766
|  
|-
|-
| | 18/13
|  
| | 440.846
| 5/4
| 442.924
| 5-odd-limit minimax
|-
|-
| | 15/13
|  
| | 441.290
| 15/8
| 443.017
|  
|-
|-
| | 6/5
|  
| | 442.179
| 3/2
| 443.136
|  
|-
|-
| | 14/13
| 17\46
| | 442.766
|  
| 443.478
| 46ee val
|-
|-
| | 5/4
|  
| | 442.924 (5 limit minimax)
| 9/5
| 443.519
| 9-odd-limit minimax
|-
|-
| | 16/15
|  
| | 443.017
| 7/4
| 443.756
| 7- and 11-odd-limit minimax
|-
|-
| | 4/3
|  
| | 443.136
| 13/8
| 444.053
| 13- and 15-odd-limit minimax
|-
|-
| | 10/9
| 10\27
| | 443.519 (9 limit minimax)
|  
| 444.444
|
|-
|-
| | 8/7
|  
| | 443.756 (7 and 11 limit minimax)
| 7/6
| 444.478
|  
|-
|-
| | 16/13
|  
| | 444.053 (13 and 15 limit minimax)
| 117/70
| 444.649
|
|-
|-
| | 7/6
|  
| | 444.478
| 7/5
| 445.628
|  
|-
|-
| | 7/5
|  
| | 445.628
| 11/8
| 445.943
|
|-
|-
| | 11/8
|  
| | 445.943
| 13/12
| 446.191
|  
|-
|-
| | 13/12
|  
| | 446.191
| 11/6
| 449.873
|  
|-
|-
| | 12/11
| 3\8
| | 449.873
|  
| 450.000
| 8d val
|-
|-
| | 13/10
|  
| | 454.214
| 13/10
| 454.214
|
|-
|-
| | 11/10
|  
| | 455.001
| 11/10
| 455.001
|
|-
|-
| | 13/11
|  
| | 455.395
| 13/11
| 455.395
|
|}
|}
[[Category:eigenmonzo]]
<nowiki/>* Besides the octave
[[Category:sensa]]
 
[[Category:sensi]]
[[Category:Sensi]]
[[Category:sensipent]]
[[Category:Temperament extensions]]
[[Category:sensis]]
[[Category:Rank-2 temperaments]]
[[Category:sensor]]
[[Category:sensus]]
[[Category:spectrum]]
Retrieved from "https://en.xen.wiki/w/Sensi_extensions"