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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.
{{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:
=== Spectrum of sensor tunings by eigenmonzos ===
* '''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


Gencom: [2 9/7; 91/90 126/125 169/168 385/384]
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 map: [{{val| 1 -1 -1 -2 9 0 }}, {{val| 0 7 9 13 -15 10 }}]
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


{| class="wikitable center-1 center-2"
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]].
 
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
|-
|-
! Eigenmonzo
| 3
! Supermajor Third
| 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
|-
| 6
| 260.4
| 7/6, 15/13
|
| 13/11, 20/17
|
|
|-
| 7
| 703.8
| '''3/2'''
|
| 26/17
|
|
|-
| 8
| 1147.2
| 27/14, 35/18
|
|
|
|
|-
| 9
| 390.6
| '''5/4'''
|
| 14/11
|
|
|-
| 10
| 834.0
| '''13/8''', 21/13
|
| 18/11, 28/17
|
|
|-
| 11
| 77.4
| 21/20, 25/24
|
| 18/17
|
| '''17/16'''
|-
| 12
| 520.8
| 27/20
|
| 15/11
|
| '''11/8'''
|-
| 13
| 964.2
| '''7/4'''
|
| 30/17
|
|
|-
| 14
| 207.6
| '''9/8'''
|
|
| 17/15
|
|-
| 15
| 651.0
| 35/24
| '''16/11'''
|
| 22/15
|
|-
| 16
| 1094.5
| '''15/8'''
| '''32/17'''
|
| 17/9
|
|-
| 17
| 337.9
| 39/32
|
|
| 11/9, 17/14
|
|-
| 18
| 781.3
| 25/16
|
|
| 11/7
|
|-
| 19
| 24.7
| 49/48, 65/64, 81/80
|
|
|
|
|-
| 20
| 468.1
| '''21/16'''
|
|
| 17/13
|
|-
| 21
| 911.5
| 27/16
|
|
| 17/10, 22/13
|
|-
| 22
| 154.9
| 35/32
| 12/11
|
| 11/10
|
|-
| 23
| 598.3
| 45/32
| 24/17
|
| 17/12
|
|-
| 24
| 1041.7
| 117/64
| 20/11
|
| 11/6
|
|-
| 25
| 285.1
| 75/64
| 13/11, 20/17
|
|
|
|-
| 26
| 728.5
| 49/32
| 26/17
|
|
|
|-
| 27
| 1171.9
| 63/32
|
|
|
|
|-
| 28
| 415.3
| 81/64
| 14/11
|
|
|
|-
| 29
| 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
 
== Tuning spectra ==
=== Sensor ===
{| class="wikitable center-all left-4"
|-
! Edo<br>generators
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]*
! Generator (¢)
! Comments
! Comments
|-
|-
|
| 9/7
| 9/7
| 435.084
| 435.084
|  
|  
|-
|-
| 4\11
|
| 436.364
| 11cdefgg val
|-
|
| 15/14
| 15/14
| 439.814
| 439.814
|  
|  
|-
|-
| 18/13
|  
| 13/9
| 440.846
| 440.846
|  
|  
|-
|-
|
| 15/13
| 15/13
| 441.290
| 441.290
|  
|  
|-
|-
| 6/5
| 7\19
|
| 442.105
|
|-
|
| 5/3
| 442.179
| 442.179
|  
|  
|-
|-
| 14/13
|  
| 13/7
| 442.766
| 442.766
|  
|  
|-
|-
|
| 5/4
| 5/4
| 442.924
| 442.924
| 5-odd-limit minimax
| 5-odd-limit minimax
|-
|-
| 16/15
|  
| 15/8
| 443.017
| 443.017
|  
|  
|-
|-
|
| 11/10
| 11/10
| 443.125
| 443.125
|  
|  
|-
|-
|
| 15/11
| 15/11
| 443.127
| 443.127
|  
|  
|-
|-
| 4/3
|  
| 3/2
| 443.136
| 443.136
| 15-odd-limit minimax
| 15-odd-limit minimax
|-
|-
|
| 11/9
| 11/9
| 443.193
| 443.193
|  
|  
|-
|-
| 12/11
|  
| 11/6
| 443.211
| 443.211
|  
|  
|-
|-
|
| 11/8
| 11/8
| 443.245
| 443.245
|  
|  
|-
|-
| 14/11
| 17\46
|
| 443.478
|
|-
|
| 11/7
| 443.482
| 443.482
| 11-odd-limit minimax
| 11-odd-limit minimax
|-
|-
| 10/9
|  
| 9/5
| 443.519
| 443.519
| 9- and 13-odd-limit minimax
| 9- and 13-odd-limit minimax
|-
|-
|
| 13/11
| 13/11
| 443.568
| 443.568
|
|-
|-
| 8/7
|  
| 7/4
| 443.756
| 443.756
| 7-odd-limit minimax
| 7-odd-limit minimax
|-
|-
| 16/13
|  
| 13/8
| 444.053
| 444.053
|  
|  
|-
|-
| 10\27
|
| 444.444
|
|-
|
| 7/6
| 7/6
| 444.478
| 444.478
|  
|  
|-
|-
|
| 117/70
| 444.649
|
|-
|
| 7/5
| 7/5
| 445.628
| 445.628
|  
|  
|-
|-
|
| 13/12
| 13/12
| 446.191
| 446.191
|  
|  
|-
|-
| 3\8
|
| 450.000
| 8deg val
|-
|
| 13/10
| 13/10
| 454.214
| 454.214
|  
|  
|}
|}
<nowiki/>* Besides the octave


=== Spectrum of sensis tunings by eigenmonzos ===
=== Sensis ===
 
{| class="wikitable center-all left-4"
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 }}]
 
{| class="wikitable center-1 center-2"
|-
|-
! Eigenmonzo
! Edo<br>generators
! Supermajor Third
! Unchanged interval<br>(eigenmonzo)*
! Generator (¢)
! Comments
! Comments
|-
|-
|
| 9/7
| 9/7
| 435.084
| 435.084
|  
|  
|-
|-
| 4\11
|
| 436.364
| 11cdf val
|-
|
| 11/8
| 11/8
| 437.829
| 437.829
|  
|  
|-
|-
|
| 15/14
| 15/14
| 439.814
| 439.814
|  
|  
|-
|-
| 18/13
|  
| 13/9
| 440.846
| 440.846
|  
|  
|-
|-
|
| 15/13
| 15/13
| 441.290
| 441.290
|  
|  
|-
|-
| 6/5
| 7\19
|
| 442.105
|
|-
|
| 5/3
| 442.179
| 442.179
|  
|  
|-
|-
| 14/13
|  
| 13/7
| 442.766
| 442.766
|  
|  
|-
|-
|
| 5/4
| 5/4
| 442.924
| 442.924
| 5-odd-limit minimax
| 5-odd-limit minimax
|-
|-
| 16/15
|  
| 15/8
| 443.017
| 443.017
|  
|  
|-
|-
| 4/3
|  
| 3/2
| 443.136
| 443.136
|  
|  
|-
|-
| 10/9
| 17\46
|
| 443.478
| 46e val
|-
|
| 9/5
| 443.519
| 443.519
| 9-odd-limit minimax
| 9-odd-limit minimax
|-
|-
| 8/7
|  
| 7/4
| 443.756
| 443.756
| 7- and 11-odd-limit minimax
| 7- and 11-odd-limit minimax
|-
|-
| 16/13
|  
| 13/8
| 444.053
| 444.053
| 13- and 15-odd-limit minimax
| 13- and 15-odd-limit minimax
|-
|-
| 10\27
|
| 444.444
| 27e val
|-
|
| 7/6
| 7/6
| 444.478
| 444.478
|  
|  
|-
|-
|
| 117/70
| 444.649
|
|-
|
| 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
|  
| 11/7
| 446.390
| 446.390
|  
|  
|-
|-
|
| 11/10
| 11/10
| 446.999
| 446.999
|  
|  
|-
|-
|
| 13/11
| 13/11
| 448.202
| 448.202
|  
|  
|-
|-
| 12/11
| 3\8
|
| 450.000
| 8d val
|-
|
| 11/6
| 450.212
| 450.212
|  
|  
|-
|-
|
| 13/10
| 13/10
| 454.214
| 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]
 
Gencom map: [{{val| 1 -1 -1 -2 -8 0 }}, {{val| 0 7 9 13 31 10 }}]
 
{| class="wikitable center-1 center-2"
|-
|-
! Eigenmonzo
! Edo<br>generators
! Supermajor Third
! Unchanged interval<br>(eigenmonzo)*
! Generator (¢)
! Comments
! Comments
|-
|-
|
| 9/7
| 9/7
| 435.084
| 435.084
|  
|  
|-
|-
| 4\11
|
| 436.364
| 11cdeeeefggg val
|-
|
| 15/14
| 15/14
| 439.814
| 439.814
|  
|  
|-
|-
| 18/13
|  
| 13/9
| 440.846
| 440.846
|  
|  
|-
|-
|
| 15/13
| 15/13
| 441.290
| 441.290
|  
|  
|-
|-
| 6/5
| 7\19
|
| 442.105
| 19eg val
|-
|
| 5/3
| 442.179
| 442.179
|  
|  
|-
|-
| 14/13
|  
| 13/7
| 442.766
| 442.766
|  
|  
|-
|-
|
| 5/4
| 5/4
| 442.924
| 442.924
| 5-odd-limit minimax
| 5-odd-limit minimax
|-
|-
| 16/15
|  
| 15/8
| 443.017
| 443.017
|  
|  
|-
|-
| 4/3
|  
| 3/2
| 443.136
| 443.136
|  
|  
|-
|-
|
| 13/11
| 13/11
| 443.371
| 443.371
|  
|  
|-
|-
| 14/11
|  
| 11/7
| 443.472
| 443.472
|  
|  
|-
|-
| 10/9
| 17\46
|
| 443.478
|
|-
|
| 9/5
| 443.519
| 443.519
| 9-odd-limit minimax
| 9-odd-limit minimax
|-
|-
|
| 11/8
| 11/8
| 443.591
| 443.591
|  
|  
|-
|-
| 12/11
|  
| 11/6
| 443.723
| 443.723
|  
|  
|-
|-
| 8/7
|  
| 7/4
| 443.756
| 443.756
| 7- and 11-odd-limit minimax
| 7- and 11-odd-limit minimax
|-
|-
|
| 11/10
| 11/10
| 443.864
| 443.864
|  
|  
|-
|-
|
| 11/9
| 11/9
| 443.965
| 443.965
|  
|  
|-
|-
| 16/13
|  
| 13/8
| 444.053
| 444.053
| 13- and 15-odd-limit minimax
| 13- and 15-odd-limit minimax
|-
|-
|
| 15/11
| 15/11
| 444.203
| 444.203
|  
|  
|-
|-
| 10\27
|
| 444.444
| 27eg val
|-
|
| 7/6
| 7/6
| 444.478
| 444.478
|  
|  
|-
|-
|
| 117/70
| 444.649
|
|-
|
| 7/5
| 7/5
| 445.628
| 445.628
|  
|  
|-
|-
|
| 13/12
| 13/12
| 446.191
| 446.191
|  
|  
|-
|-
| 3\8
|
| 450.000
| 8deegg val
|-
|
| 13/10
| 13/10
| 454.214
| 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]
 
Gencom map: [{{val| 1 -1 -1 -2 -1 0 }}, {{val| 0 7 9 13 12 10 }}]
 
{| class="wikitable center-1 center-2"
|-
|-
! Eigenmonzo
! Edo<br>generators
! Supermajor Third
! Unchanged interval<br>(eigenmonzo)*
! Generator (¢)
! Comments
! Comments
|-
|-
| 14/11
|  
| 11/7
| 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
|  
|  
|-
|-
| 4\11
|
| 436.364
| 11cdeef val
|-
|
| 15/14
| 15/14
| 439.814
| 439.814
|  
|  
|-
|-
| 18/13
|  
| 13/9
| 440.846
| 440.846
|  
|  
|-
|-
|
| 15/13
| 15/13
| 441.290
| 441.290
|  
|  
|-
|-
| 6/5
| 7\19
|
| 442.105
| 19e val
|-
|
| 5/3
| 442.179
| 442.179
|  
|  
|-
|-
| 14/13
|  
| 13/7
| 442.766
| 442.766
|  
|  
|-
|-
|
| 5/4
| 5/4
| 442.924
| 442.924
| 5-odd-limit minimax
| 5-odd-limit minimax
|-
|-
| 16/15
|  
| 15/8
| 443.017
| 443.017
|  
|  
|-
|-
| 4/3
|  
| 3/2
| 443.136
| 443.136
|  
|  
|-
|-
| 10/9
| 17\46
|
| 443.478
| 46ee val
|-
|
| 9/5
| 443.519
| 443.519
| 9-odd-limit minimax
| 9-odd-limit minimax
|-
|-
| 8/7
|  
| 7/4
| 443.756
| 443.756
| 7- and 11-odd-limit minimax
| 7- and 11-odd-limit minimax
|-
|-
| 16/13
|  
| 13/8
| 444.053
| 444.053
| 13- and 15-odd-limit minimax
| 13- and 15-odd-limit minimax
|-
|-
| 10\27
|
| 444.444
|
|-
|
| 7/6
| 7/6
| 444.478
| 444.478
|  
|  
|-
|-
|
| 117/70
| 444.649
|
|-
|
| 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
|  
| 11/6
| 449.873
| 449.873
|  
|  
|-
|-
| 3\8
|
| 450.000
| 8d val
|-
|
| 13/10
| 13/10
| 454.214
| 454.214
|  
|  
|-
|-
|
| 11/10
| 11/10
| 455.001
| 455.001
|  
|  
|-
|-
|
| 13/11
| 13/11
| 455.395
| 455.395
|  
|  
|}
|}
<nowiki/>* Besides the octave


[[Category:Sensipent]]
[[Category:Sensi]]
[[Category:Sensi]]
[[Category:Sensor]]
[[Category:Temperament extensions]]
[[Category:Sensis]]
[[Category:Rank-2 temperaments]]
[[Category:Sensus]]
[[Category:Sensa]]
Retrieved from "https://en.xen.wiki/w/Sensi_extensions"