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}), 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.
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 |
Eigenmonzo (unchanged-interval)* |
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 | ||
7/5 | 445.628 | ||
13/12 | 446.191 | ||
3\8 | 450.000 | 8deg val | |
13/10 | 454.214 |
* Besides the octave
Sensis
Edo generators |
Eigenmonzo (unchanged-interval)* |
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 | ||
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 |
Eigenmonzo (unchanged-interval)* |
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 | ||
7/5 | 445.628 | ||
13/12 | 446.191 | ||
3\8 | 450.000 | 8deegg val | |
13/10 | 454.214 |
* Besides the octave
Sensa
Edo generators |
Eigenmonzo (unchanged-interval)* |
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 | ||
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