Sensi extensions
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}). 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:
- Sensor (19 & 27) – tempering out 126/125, 245/243, 385/384
- Sensus (19e & 27e) – tempering out 126/125, 176/175, 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, here are some low-complexity low-accuracy entries:
- Sensis (19 & 27e) – tempering out 56/55, 100/99, 245/243
- Sensa (19e & 27) – tempering out 55/54, 77/75, 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 38df, 46, and 54c.
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
Gencom: [2 9/7; 91/90 126/125 169/168 385/384]
Gencom mapping: [⟨1 -1 -1 -2 9 0], ⟨0 7 9 13 -15 10]]
| Eigenmonzo (Unchanged-interval) |
Generator (¢) | Comments |
|---|---|---|
| 9/7 | 435.084 | |
| 15/14 | 439.814 | |
| 18/13 | 440.846 | |
| 15/13 | 441.290 | |
| 6/5 | 442.179 | |
| 14/13 | 442.766 | |
| 5/4 | 442.924 | 5-odd-limit minimax |
| 16/15 | 443.017 | |
| 11/10 | 443.125 | |
| 15/11 | 443.127 | |
| 4/3 | 443.136 | 15-odd-limit minimax |
| 11/9 | 443.193 | |
| 12/11 | 443.211 | |
| 11/8 | 443.245 | |
| 14/11 | 443.482 | 11-odd-limit minimax |
| 10/9 | 443.519 | 9- and 13-odd-limit minimax |
| 13/11 | 443.568 | |
| 8/7 | 443.756 | 7-odd-limit minimax |
| 16/13 | 444.053 | |
| 7/6 | 444.478 | |
| 7/5 | 445.628 | |
| 13/12 | 446.191 | |
| 13/10 | 454.214 |
Sensis
Gencom: [2 9/7; 56/55 78/77 91/90 100/99]
Gencom mapping: [⟨1 -1 -1 -2 2 0], ⟨0 7 9 13 4 10]]
| Eigenmonzo (Unchanged-interval) |
Generator (¢) | Comments |
|---|---|---|
| 9/7 | 435.084 | |
| 11/8 | 437.829 | |
| 15/14 | 439.814 | |
| 18/13 | 440.846 | |
| 15/13 | 441.290 | |
| 6/5 | 442.179 | |
| 14/13 | 442.766 | |
| 5/4 | 442.924 | 5-odd-limit minimax |
| 16/15 | 443.017 | |
| 4/3 | 443.136 | |
| 10/9 | 443.519 | 9-odd-limit minimax |
| 8/7 | 443.756 | 7- and 11-odd-limit minimax |
| 16/13 | 444.053 | 13- and 15-odd-limit minimax |
| 7/6 | 444.478 | |
| 15/11 | 444.746 | |
| 11/9 | 445.259 | |
| 7/5 | 445.628 | |
| 13/12 | 446.191 | |
| 14/11 | 446.390 | |
| 11/10 | 446.999 | |
| 13/11 | 448.202 | |
| 12/11 | 450.212 | |
| 13/10 | 454.214 |
Sensus
Gencom: [2 9/7; 91/90 126/125 169/168 352/351]
Gencom mapping: [⟨1 -1 -1 -2 -8 0], ⟨0 7 9 13 31 10]]
| Eigenmonzo (Unchanged-interval) |
Generator (¢) | Comments |
|---|---|---|
| 9/7 | 435.084 | |
| 15/14 | 439.814 | |
| 18/13 | 440.846 | |
| 15/13 | 441.290 | |
| 6/5 | 442.179 | |
| 14/13 | 442.766 | |
| 5/4 | 442.924 | 5-odd-limit minimax |
| 16/15 | 443.017 | |
| 4/3 | 443.136 | |
| 13/11 | 443.371 | |
| 14/11 | 443.472 | |
| 10/9 | 443.519 | 9-odd-limit minimax |
| 11/8 | 443.591 | |
| 12/11 | 443.723 | |
| 8/7 | 443.756 | 7- and 11-odd-limit minimax |
| 11/10 | 443.864 | |
| 11/9 | 443.965 | |
| 16/13 | 444.053 | 13- and 15-odd-limit minimax |
| 15/11 | 444.203 | |
| 7/6 | 444.478 | |
| 7/5 | 445.628 | |
| 13/12 | 446.191 | |
| 13/10 | 454.214 |
Sensa
Gencom: [2 9/7; 55/54 66/65 77/75 143/140]
Gencom mapping: [⟨1 -1 -1 -2 -1 0], ⟨0 7 9 13 12 10]]
| Eigenmonzo (Unchanged-interval) |
Generator (¢) | Comments |
|---|---|---|
| 14/11 | 417.508 | |
| 11/9 | 426.296 | |
| 15/11 | 434.238 | |
| 9/7 | 435.084 | |
| 15/14 | 439.814 | |
| 18/13 | 440.846 | |
| 15/13 | 441.290 | |
| 6/5 | 442.179 | |
| 14/13 | 442.766 | |
| 5/4 | 442.924 | 5-odd-limit minimax |
| 16/15 | 443.017 | |
| 4/3 | 443.136 | |
| 10/9 | 443.519 | 9-odd-limit minimax |
| 8/7 | 443.756 | 7- and 11-odd-limit minimax |
| 16/13 | 444.053 | 13- and 15-odd-limit minimax |
| 7/6 | 444.478 | |
| 7/5 | 445.628 | |
| 11/8 | 445.943 | |
| 13/12 | 446.191 | |
| 12/11 | 449.873 | |
| 13/10 | 454.214 | |
| 11/10 | 455.001 | |
| 13/11 | 455.395 |