Sensipent

If we take a look at the 5-limit version of sensi called sensipent, we find a high-accuracy extension that specifically only requires prime 31, interpreting the generator accurately as ~40/31~31/24 (by splitting 16/15 into ~32/31~31/30). This can be left as is, or one can extend to other slightly less accurate primes; the main two strategies for doing so are called sendai, focusing on accuracy and adding primes 23 and 29, and sensible, which adds primes 11, 17 and 23 and focuses on adding more primes, in both cases doing so while avoiding the less accurate ~9/7 and ~13/10 interpretations of the sensi generator. They merge meaningfully (though not uniquely) in 65edo, which can be seen by that 65edo is an amazing no-7's no-13's 31-limit temperament, where we've gained prime 19 through a possible extension of either sendai or sensible. Furthermore, 65edo can also be used as a tuning of 7-limit sensi through the 65d val (which corresponds to 65edo roughly supporting garibaldi), though note that if one tries to use its patent but very sharp ~13 (which makes the most sense if one accepts the 65d val) then 13/10 is mapped distinctly and sharp of the ~9/7 sensi generator.

For technical data, see:

• Sensipent family#Sensipent for the 2.3.5.31-subgroup version,
• Sensipent family#Sendai for the 2.3.5.23.29.31-subgroup version, and
• Sensipent family#Sensible for the 2.3.5.11.17.23.31-subgroup version.

Sendai interval table

The following is the table of the 31-odd-limited 2.3.5.23.29.31 equivalents of the intervals of the 19-note MOS (8L 11s) in the CTE tuning of sendai, the sensipent extension 19 & 65 = {465/464 576/575 621/620 900/899}, made by VIxen.

Gens	Cents	Ratios
1	442.989338	31/24, 40/31
2	885.978677	5/3
3	128.968015	27/25, 29/27
4	571.957354	32/23, 25/18
5	1014.946692	9/5
6	257.936031	36/31, 29/25
7	700.925369	3/2
8	1143.914707	31/16, 29/15, 60/31
9	386.904046	5/4
10	829.893384	29/18, 50/31
11	72.882723	24/23, 25/24
12	515.872061	27/20, 31/23
13	958.8614	40/23, 54/31
14	201.850738	9/8
15	644.840076	29/20
16	1087.829415	15/8, 58/31
17	330.818753	29/24
18	773.808092	25/16, 36/23

Sensible interval table

The following is the table of the 115-odd-limited 2.3.5.11.17.23.31 equivalents of the intervals of the 27-note MOS (19L 8s) in the CTE tuning of sensible, the sensipent extension 46 & 65 = {(S16, S9/S10,) S23, S24, S31, S32, S33}, made by Godtone.

Gens	Cents	Ratios
1	443.254	85/66, 40/31, 31/24, 128/99, 22/17
2	886.208	5/3, 192/115, 92/55
3	129.312	100/93, 99/92, 69/64, 124/115, 55/51, 27/25, 92/85
4	572.416	25/18, 32/23, 46/33
5	1015.52	115/64, 124/69, 9/5, 92/51
6	258.624	51/44, 80/69, 36/31, 115/99, 93/80, 64/55, 99/85
7	701.728	3/2, 128/85
8	1144.832	85/44, 60/31, 31/16, 64/33, 33/17
9	387.936	5/4, 144/115, 124/99, 69/55, 64/51
10	831.04	50/31, 160/99, 186/115, 55/34, 81/50, 138/85
11	74.144	25/24, 24/23, 23/22
12	517.248	31/23, 27/20, 23/17
13	960.352	40/23, 54/31, 115/66, 96/55
14	203.456	9/8, 62/55, 115/102, 96/85
15	646.56	100/69, 45/31, 93/64, 16/11, 99/68, 124/85
16	1089.664	15/8, 216/115, 62/33, 32/17
17	332.768	75/62, 40/33, 62/51
18	775.872	25/16, 36/23, 69/44, 80/51
19	18.976	100/99, 93/92, 81/80, 69/68
20	462.08	30/23, 81/62, 115/88, 72/55
21	905.184	27/16, 93/55, 115/68, 144/85
22	148.288	25/23, 12/11, 93/85
23	591.392	45/32, 162/115, 31/22, 24/17
24	1034.496	20/11, 31/17
25	277.6	75/64, 27/23, 20/17
26	720.704	50/33

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