55edo

55 tone equal temperament

55edo divides the octave into 55 parts of 21.818 cents. It can be used for a meantone tuning, and is close to 1/6 comma meantone (and is almost exactly 10/57 comma meantone.) Telemann suggested it as a theoretical basis for analyzing the intervals of meantone, in which he was followed by Leopold and Wolfgang Mozart. It can also be used for mohajira and liese temperaments.

5-limit commas: 81/80, <31 1 -14|

7-limit commas: 81/80, 686/675, 6144/6125

11-limit commas: 81/80, 121/120, 176/175, 686/675

Intervals

Degrees of 55-EDO	Cents value	Ratios it approximates
0	0	1/1
1	21.818	128/125
2	43.636
3	65.455
4	87.273	25/24
5	109.091	16/15
6	130.909
7	152.727
8	174.545
9	196.364	9/8, 10/9
10	218.182
11	240.000
12	261.818
13	283.636
14	305.455
15	327.273
16	349.091
17	370.909
18	392.727
19	414.545
20	436.364
21	458.182
22	480.000
23	501.818
24	523.636
25	545.455
26	567.273
27	589.091
28	610.909
29	632.727
30	654.545
31	676.364
32	698.182
33	720.000
34	741.818
35	763.636
36	785.455
37	807.273
38	829.091
39	850.909
40	872.727
41	894.545
42	916.364
43	938.182
44	960.000
45	981.818
46	1003.636
47	1025.455
48	1047.273
49	1069.091
50	1090.909
51	1112.727
52	1134.545
53	1156.364
54	1178.182
55	1200.000

Selected just intervals by error

The following table shows how some prominent just intervals are represented in 43edo (ordered by absolute error).

Interval, complement	Error (abs., in cents)
5/4, 8/5
11/9, 18/11
8/7, 7/4
7/5, 10/7
15/14, 28/15
7/6, 12/7
12/11, 11/6
16/15, 15/8
15/11, 22/15
4/3, 3/2
6/5, 5/3
14/11, 11/7
9/7, 14/9
11/8, 16/11
11/10, 20/11
13/10, 20/13
9/8, 16/9
16/13, 13/8
10/9, 9/5
14/13, 13/7
15/13, 26/15
13/12, 24/13
18/13, 13/9
13/11, 22/13

Mozart - Adagio in B minor KV 540 by Carlo Serafini (blog entry)

"Mozart's tuning: 55edo" (containing another listening example) in the tonalsoft encyclopedia