Sensi extensions

Sensi temperament has various extensions to the 11-limit. These are all members of the sensipent family, but in addition they are linear temperaments:

• Sensor (19 & 27) - tempering out 126/125, 245/243, 385/384
• Sensis (19 & 27e) - tempering out 56/55, 100/99, 245/243
• Sensus (19e & 27e) - tempering out 126/125, 176/175, 245/243
• Sensa (19e & 27) - tempering out 55/54, 77/75, 99/98

These can be extended 13 and 17 prime limits 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.

Interval chain

Generators	Cents*	Approximate ratios
		Sensor	Sensis	Sensus	Sensa
0	0.000	1/1
1	443.34	9/7, 13/10, 22/17			9/7, 13/10, 14/11, 17/13, 22/17
2	886.69	5/3			5/3, 17/10, 18/11, 22/13, 28/17
3	130.03	13/12, 14/13, 15/14	12/11, 13/12, 14/13, 15/14, 17/16	13/12, 14/13, 15/14	11/10, 13/12, 14/13, 15/14, 18/17
4	573.38	7/5, 18/13	7/5, 11/8, 18/13, 24/17	7/5, 18/13	7/5, 15/11, 17/12, 18/13
5	1016.72	9/5	9/5, 20/11	9/5	9/5, 11/6, 30/17
6	260.07	7/6, 15/13	7/6, 13/11, 15/13, 20/17	7/6, 15/13
7	703.41	3/2	3/2, 26/17	3/2
8	1146.76
9	390.10	5/4	5/4, 14/11	5/4
10	833.45	13/8	13/8, 18/11, 28/17	13/8
11	76.79		18/17		17/16
12	520.14		15/11		11/8
13	963.48	7/4	7/4, 30/17	7/4
14	206.83	9/8		9/8, 17/15	9/8
15	650.17	16/11		22/15
16	1093.51	15/8, 32/17	15/8	15/8, 17/9	15/8
17	336.86			11/9, 17/14
18	780.20			11/7
19	23.55
20	466.89			17/13
21	910.24			17/10, 22/13
22	153.58	12/11		11/10
23	596.93	24/17		17/12
24	1040.27	20/11		11/6
25	283.62	13/11, 20/17
26	726.96	26/17
27	1170.31
28	413.65	14/11
29	857.00	18/11, 28/17
30	100.34	18/17		17/16
31	543.68	15/11		11/8
32	987.03	30/17

^* in 2.3.5.7.13.17/11 POTE tuning

Tuning Spectra

Spectrum of sensor tunings by eigenmonzos

Gencom: [2 9/7; 91/90 126/125 169/168 385/384]

Gencom map: [⟨1 -1 -1 -2 9 0], ⟨0 7 9 13 -15 10]]

Eigenmonzo	Supermajor Third	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

Spectrum of sensis tunings by eigenmonzos

Gencom: [2 9/7; 56/55 78/77 91/90 100/99]

Gencom map: [⟨1 -1 -1 -2 2 0], ⟨0 7 9 13 4 10]]

Eigenmonzo	Supermajor Third	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

Spectrum of sensus tunings by eigenmonzos

Gencom: [2 9/7; 91/90 126/125 169/168 352/351]

Gencom map: [⟨1 -1 -1 -2 -8 0], ⟨0 7 9 13 31 10]]

Eigenmonzo	Supermajor Third	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

Spectrum of sensa tunings by eigenmonzos

Gencom: [2 9/7; 55/54 66/65 77/75 143/140]

Gencom map: [⟨1 -1 -1 -2 -1 0], ⟨0 7 9 13 12 10]]

Eigenmonzo	Supermajor Third	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