Sensi extensions: Difference between revisions

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[[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 ({126/125, 176/175}). Note: 126/125 = (176/175)(441/440). On the other, [[sensamagic]] strongly suggests tempering out [[385/384]], leading to undecimal sensamagic ({245/243, 385/384}). Note: 245/243 = (385/384)(896/891). Taking either path for sensi leads us to the following entries:  
{{Breadcrumb|Sensi}}
* '''Sensor''' (19 & 27) – tempering out 126/125, 245/243, 385/384
 
* '''Sensus''' (19e & 27e) – tempering out 126/125, 176/175, 245/243
[[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


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]].
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]].


In addition, here are some low-complexity low-accuracy entries:  
In addition, there are some low-complexity low-accuracy entries:  
* '''Sensis''' (19 & 27e) – tempering out 56/55, 100/99, 245/243
* '''Sensis''' ({{nowrap| 19 & 27e }}) – tempering out 56/55, 100/99, and 245/243
* '''Sensa''' (19e & 27) – tempering out 55/54, 77/75, 99/98
* '''Sensa''' ({{nowrap| 19e & 27 }}) – tempering out 55/54, 77/75, and 99/98


Another possible path which relates a sense of compromise is to temper out [[121/120]], leading to bisensi. This temperament is supported by [[38edo|38df]], 46, and [[54edo|54c]].  
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 ==
== Interval chain ==
In the following table, odd harmonics and subharmonics 1–21 are in '''bold'''.
{| class="wikitable right-1 right-2"
{| class="wikitable right-1 right-2"
|-
|-
! rowspan=2 | #
! rowspan="2" | #
! rowspan=2 | Cents<sup>*</sup>
! rowspan="2" | Cents*
! colspan=4 | Approximate ratios
! colspan="5" | Approximate ratios
|-
|-
! Sensi
! Sensor
! Sensor
! Sensis
! Sensis
Line 24: Line 31:
|-
|-
| 0
| 0
| 0.000
| 0.0
| colspan=4 | 1/1
| '''1/1'''
|
|
|
|
|-
|-
| 1
| 1
| 443.34
| 443.4
| colspan=3 | 9/7, 13/10, 22/17
| 9/7, 13/10, 22/17
| 9/7, 13/10, <br>14/11, 17/13, <br>22/17
|  
|
|
| 14/11, 17/13
|-
|-
| 2
| 2
| 886.69
| 886.8
| colspan=3 | 5/3
| 5/3
| 5/3, 17/10, <br>18/11, 22/13, <br>28/17
|  
|
|
| 17/10, 18/11, 22/13, 28/17
|-
|-
| 3
| 3
| 130.03
| 130.2
| 13/12, 14/13, <br>15/14
| 13/12, 14/13, 15/14
| 12/11, 13/12, <br>14/13, 15/14, <br>17/16
|
| 13/12, 14/13, <br>15/14
| 12/11, '''17/16'''
| 11/10, 13/12, <br>14/13, 15/14, <br>18/17
|  
| 11/10, 18/17
|-
|-
| 4
| 4
| 573.38
| 573.6
| 7/5, 18/13
| 7/5, 18/13
| 7/5, 11/8, <br>18/13, 24/17
|  
| 7/5, 18/13
| '''11/8''', 24/17
| 7/5, 15/11, <br>17/12, 18/13
|  
| 15/11, 17/12
|-
|-
| 5
| 5
| 1016.72
| 1017.0
| 9/5
| 9/5
| 9/5, 20/11
|  
| 9/5
| 20/11
| 9/5, 11/6, <br>30/17
|  
| 11/6, 30/17
|-
|-
| 6
| 6
| 260.07
| 260.4
| 7/6, 15/13
| 7/6, 15/13
| 7/6, 13/11, <br>15/13, 20/17
|  
| colspan=2 | 7/6, 15/13
| 13/11, 20/17
|  
|  
|-
|-
| 7
| 7
| 703.41
| 703.8
| 3/2
| '''3/2'''
| 3/2, 26/17
|
| colspan=2 | 3/2
| 26/17
|  
|  
|-
|-
| 8
| 8
| 1146.76
| 1147.2
| 27/14, 35/18
|  
|  
|  
|  
Line 78: Line 103:
|-
|-
| 9
| 9
| 390.10
| 390.6
| 5/4
| '''5/4'''
| 5/4, 14/11
|
| colspan=2 | 5/4
| 14/11
|  
|  
|-
|-
| 10
| 10
| 833.45
| 834.0
| 13/8
| '''13/8''', 21/13
| 13/8, 18/11, <br>28/17
|
| colspan=2 | 13/8
| 18/11, 28/17
|  
|  
|-
|-
| 11
| 11
| 76.79
| 77.4
| 21/20, 25/24
|  
|  
| 18/17
| 18/17
|  
|  
| 17/16
| '''17/16'''
|-
|-
| 12
| 12
| 520.14
| 520.8
| 27/20
|  
|  
| 15/11
| 15/11
|  
|  
| 11/8
| '''11/8'''
|-
|-
| 13
| 13
| 963.48
| 964.2
| 7/4
| '''7/4'''
| 7/4, 30/17
|
| colspan=2 | 7/4
| 30/17
|  
|  
|-
|-
| 14
| 14
| 206.83
| 207.6
| colspan=2 | 9/8
| '''9/8'''
| 9/8, 17/15
|
| 9/8
|
| 17/15
|  
|-
|-
| 15
| 15
| 650.17
| 651.0
| 16/11
| 35/24
| '''16/11'''
|  
|  
| 22/15
| 22/15
Line 123: Line 159:
|-
|-
| 16
| 16
| 1093.51
| 1094.5
| 15/8, 32/17
| '''15/8'''
| 15/8
| '''32/17'''
| 15/8, 17/9
|  
| 15/8
| 17/9
|  
|-
|-
| 17
| 17
| 336.86
| 337.9
| 39/32
|  
|  
|  
|  
Line 137: Line 175:
|-
|-
| 18
| 18
| 780.20
| 781.3
| 25/16
|  
|  
|  
|  
Line 144: Line 183:
|-
|-
| 19
| 19
| 23.55
| 24.7
| 49/48, 65/64, 81/80
|  
|  
|  
|  
Line 151: Line 191:
|-
|-
| 20
| 20
| 466.89
| 468.1
| '''21/16'''
|  
|  
|  
|  
Line 158: Line 199:
|-
|-
| 21
| 21
| 910.24
| 911.5
| 27/16
|  
|  
|  
|  
Line 165: Line 207:
|-
|-
| 22
| 22
| 153.58
| 154.9
| 35/32
| 12/11
| 12/11
|  
|  
Line 172: Line 215:
|-
|-
| 23
| 23
| 596.93
| 598.3
| 45/32
| 24/17
| 24/17
|  
|  
Line 179: Line 223:
|-
|-
| 24
| 24
| 1040.27
| 1041.7
| 117/64
| 20/11
| 20/11
|  
|  
Line 186: Line 231:
|-
|-
| 25
| 25
| 283.62
| 285.1
| 75/64
| 13/11, 20/17
| 13/11, 20/17
|  
|  
Line 193: Line 239:
|-
|-
| 26
| 26
| 726.96
| 728.5
| 49/32
| 26/17
| 26/17
|  
|  
Line 200: Line 247:
|-
|-
| 27
| 27
| 1170.31
| 1171.9
| 63/32
|  
|  
|  
|  
Line 207: Line 255:
|-
|-
| 28
| 28
| 413.65
| 415.3
| 81/64
| 14/11
| 14/11
|  
|  
Line 214: Line 263:
|-
|-
| 29
| 29
| 857.00
| 858.7
| 105/64
| 18/11, 28/17
| 18/11, 28/17
|  
|  
Line 221: Line 271:
|-
|-
| 30
| 30
| 100.34
| 102.1
| 135/128
| 18/17
| 18/17
|  
|  
| 17/16
| '''17/16'''
|  
|  
|-
|-
| 31
| 31
| 543.68
| 545.5
| 175/128
| 15/11
| 15/11
|  
|  
| 11/8
| '''11/8'''
|  
|  
|-
|-
| 32
| 32
| 987.03
| 988.9
| 225/128
| 30/17
| 30/17
|  
|  
Line 241: Line 294:
|  
|  
|}
|}
 
<nowiki/>* In 2.3.5.7.13.17/11 subgroup CTE tuning
: <sup>*</sup> in 2.3.5.7.13.17/11 POTE tuning


== Tuning spectra ==
== Tuning spectra ==
=== Sensor ===
=== Sensor ===
Gencom: [2 9/7; 91/90 126/125 169/168 385/384]
{| class="wikitable center-all left-4"
 
Gencom mapping: {{mapping| 1 -1 -1 -2 9 0 | 0 7 9 13 -15 10 }}
 
{| class="wikitable center-1 center-2"
|-
|-
! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval]])
! Edo<br>generators
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]*
! Generator (¢)
! 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


=== Sensis ===
=== Sensis ===
Gencom: [2 9/7; 56/55 78/77 91/90 100/99]
{| class="wikitable center-all left-4"
 
Gencom mapping: {{mapping| 1 -1 -1 -2 2 0 | 0 7 9 13 4 10 }}
 
{| class="wikitable center-1 center-2"
|-
|-
! Eigenmonzo<br>(Unchanged-interval)
! Edo<br>generators
! Unchanged interval<br>(eigenmonzo)*
! Generator (¢)
! 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
|
|  
|-
| 17\46
|
| 443.478
| 46e val
|-
|-
| 10/9
|  
| 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


=== Sensus ===
=== Sensus ===
Gencom: [2 9/7; 91/90 126/125 169/168 352/351]
{| class="wikitable center-all left-4"
 
Gencom mapping: {{mapping| 1 -1 -1 -2 -8 0 | 0 7 9 13 31 10 }}
 
{| class="wikitable center-1 center-2"
|-
|-
! Eigenmonzo<br>(Unchanged-interval)
! Edo<br>generators
! Unchanged interval<br>(eigenmonzo)*
! Generator (¢)
! 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
|
|
|-
| 17\46
|
| 443.478
|  
|-
|-
| 10/9
|  
| 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


=== Sensa ===
=== Sensa ===
Gencom: [2 9/7; 55/54 66/65 77/75 143/140]
{| class="wikitable center-all left-4"
 
Gencom mapping: {{mapping| 1 -1 -1 -2 -1 0 | 0 7 9 13 12 10 }}
 
{| class="wikitable center-1 center-2"
|-
|-
! Eigenmonzo<br>(Unchanged-interval)
! Edo<br>generators
! Unchanged interval<br>(eigenmonzo)*
! Generator (¢)
! 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
|
|  
|-
| 7\19
|
| 442.105
| 19e val
|-
|-
| 6/5
|  
| 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:Sensi]]
[[Category:Sensi]]
[[Category:Temperament extensions]]
[[Category:Rank-2 temperaments]]

Latest revision as of 12:04, 6 August 2025

< Sensi

Sensi has multiple competing extensions to the 11-limit. The simplest 7-limit commas of sensi are starling (126/125) and sensamagic (245/243), and it can be viewed as the merge of the two corresponding rank-3 temperaments. 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 ({126/125, 176/175}), since 126/125 = (176/175)(441/440). On the other, sensamagic strongly suggests tempering out 385/384, leading to undecimal sensamagic ({245/243, 385/384}), since 245/243 = (385/384)(896/891). Taking either path for sensi leads us to one of the following entries:

  • Sensor (19 & 27) – tempering out 126/125, 245/243, and 385/384
  • Sensus (19e & 27e) – tempering out 126/125, 176/175, and 245/243

The two unite in 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.

In addition, there are some low-complexity low-accuracy entries:

  • Sensis (19 & 27e) – tempering out 56/55, 100/99, and 245/243
  • Sensa (19e & 27) – tempering out 55/54, 77/75, and 99/98

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 38df, 46, and 54c.

See Sensipent family #Sensor, #Sensus, #Sensis, and #Sensa for technical data.

Interval chain

In the following table, odd harmonics and subharmonics 1–21 are in bold.

# Cents* 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
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

* In 2.3.5.7.13.17/11 subgroup CTE tuning

Tuning spectra

Sensor

Edo
generators 		Unchanged interval
(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

* Besides the octave

Sensis

Edo
generators 		Unchanged interval
(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
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
3/2 443.136
17\46 443.478 46e val
9/5 443.519 9-odd-limit minimax
7/4 443.756 7- and 11-odd-limit minimax
13/8 444.053 13- and 15-odd-limit minimax
10\27 444.444 27e val
7/6 444.478
117/70 444.649
15/11 444.746
11/9 445.259
7/5 445.628
13/12 446.191
11/7 446.390
11/10 446.999
13/11 448.202
3\8 450.000 8d val
11/6 450.212
13/10 454.214

* Besides the octave

Sensus

Edo
generators 		Unchanged interval
(eigenmonzo)* 		Generator (¢) Comments
9/7 435.084
4\11 436.364 11cdeeeefggg val
15/14 439.814
13/9 440.846
15/13 441.290
7\19 442.105 19eg val
5/3 442.179
13/7 442.766
5/4 442.924 5-odd-limit minimax
15/8 443.017
3/2 443.136
13/11 443.371
11/7 443.472
17\46 443.478
9/5 443.519 9-odd-limit minimax
11/8 443.591
11/6 443.723
7/4 443.756 7- and 11-odd-limit minimax
11/10 443.864
11/9 443.965
13/8 444.053 13- and 15-odd-limit minimax
15/11 444.203
10\27 444.444 27eg val
7/6 444.478
117/70 444.649
7/5 445.628
13/12 446.191
3\8 450.000 8deegg val
13/10 454.214

* Besides the octave

Sensa

Edo
generators 		Unchanged interval
(eigenmonzo)* 		Generator (¢) Comments
11/7 417.508
11/9 426.296
15/11 434.238
9/7 435.084
4\11 436.364 11cdeef val
15/14 439.814
13/9 440.846
15/13 441.290
7\19 442.105 19e val
5/3 442.179
13/7 442.766
5/4 442.924 5-odd-limit minimax
15/8 443.017
3/2 443.136
17\46 443.478 46ee val
9/5 443.519 9-odd-limit minimax
7/4 443.756 7- and 11-odd-limit minimax
13/8 444.053 13- and 15-odd-limit minimax
10\27 444.444
7/6 444.478
117/70 444.649
7/5 445.628
11/8 445.943
13/12 446.191
11/6 449.873
3\8 450.000 8d val
13/10 454.214
11/10 455.001
13/11 455.395

* Besides the octave

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