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