User:Overthink/41edo well temperament

A highly notable tuning system is 41edo, which is distinctly consistent and consistent to distance 2 in the 9-odd-limit, consistent to the 15-odd-limit, and is overall great for its size in all prime limits up to 13. However, the accuracy of some intervals is debateable, so we will construct a well temperament in order to fix this issue.

The chain of fifths

Our well temperament will be mainly based on a chain of fifths, and we will target harmonics 5, 7, 11, and 13. In 41edo, these prime harmonics are mapped as follows:

Prime	Fifths down	Fifths up
5	-8	+33
7	-14	+27
11	-18	+23
13	-21	+20

Prime 5 is closest to the root on the circle of fifths; being only 8 fifth down due to 41edo tempering out the schisma. We build our well temperament down the chain of fifths to reach a more accurate prime 5, using slightly flat fifths of 701.738 ¢, or 1/9 schisma flat of just. We continue this chain of schismic fifths until we reach -10 fifths, or 10/9.

41edo well temperament (Table incomplete)

Degree	Fifths	Cents	Fifth below (¢)	Fifth above (¢)
0	+0	0	701.738	?
1	+12	?	?	?
2	-17/+24	?	?	?
3	-5	?	?	?
4	+7	?	?	?
5	-22/+19	?	?	?
6	-10	?	?	?
7	+2	?	?	?
8	+14	?	?	?
9	-15	?	?	?
10	-3	?	?	?
11	+9	?	?	?
12	-20/+21	?	?	?
13	-8	?	?	?
14	+4	?	?	?
15	+16	?	?	?
16	-13	?	?	?
17	-1	498.262	701.738	701.738
18	?	?	?	?
19	?	?	?	?
20	?	?	?	?
21	?	?	?	?
22	?	?	?	?
23	?	?	?	?
24	+1	?	?	?
25	+13	?	?	?
26	?	?	?	?
27	?	?	?	?
28	?	?	?	?
29	?	?	?	?
30	?	?	?	?
31	?	?	?	?
32	?	?	?	?
33	-14	?	?	?
34	-2	?	?	?
35	+10	?	?	?
36	?	?	?	?
37	?	?	?	?
38	?	?	?	?
39	?	?	?	?
40	?	?	?	?
41	+0	1200	?	?