Sensi/Extensions

< 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