56edo

56edo divides the octave into 56 parts of 21.429 cents each. It shares it's near perfect major third with 28edo, which it doubles, while also adding a superpythagorean 5th that is a convergent towards the bronze metallic mean, following 17edo and preceding 185edo.

56edo can be used to tune hemithirds, superkleismic, sycamore and keen temperaments, and using ⟨56 89 130 158] (56d) as the equal temperament val, for pajara. It provides the optimal patent val for 7-, 11- and 13-limit sycamore, and the 11-limit 56d val is close to the POTE tuning for 11-limit pajara.

Intervals

#	Cents	Approximate Ratios
0	0.000	1/1
1	21.429	49/48, 64/63, 81/80
2	42.857	28/27, 50/49
3	64.286	25/24, 36/35, 33/32
4	85.714	21/20, 22/21
5	107.143	16/15
6	128.571	15/14, 13/12, 14/13
7	150.000	12/11
8	171.429	10/9, 11/10
9	192.857	28/25
10	214.286	9/8
11	235.714	8/7
12	257.143	7/6, 15/13
13	278.571	75/64, 13/11
14	300.000	25/21
15	321.429	6/5
16	342.857	11/9, 39/32
17	364.286	27/22, 16/13, 26/21
18	385.714	5/4
19	407.143	14/11
20	428.571	32/25, 33/26
21	450.000	9/7, 13/10
22	471.429	21/16
23	492.857	4/3
24	514.286
25	535.714	27/20, 15/11
26	557.143	11/8
27	578.571	7/5
28	600.000	45/32, 64/45
…	…	…

Commas

• 5-limit commas: 2048/2025, |-5 -10 9>
• 7-limit commas: 686/675, 875/864, 1029/1024
• 11-limit commas: 100/99, 245/242, 385/384, 686/675

Scales

• supra7
• supra12