80edo

The 80 equal temperament, often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step represents a frequency ratio of exactly 15 cents. 80et is the first equal temperament that represents the 19-limit tonality diamond consistently (it barely manages to do so).

80 et tempers out 136/135, 169/168, 176/175, 190/189, 221/220, 256/255, 286/285, 289/288, 325/324, 351/350, 352/351, 361/360, 364/363, 400/399, 456/455, 476/475, 540/539, 561/560, 595/594, 715/714, 936/935, 969/968, 1001/1000, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539 and 1729/1728, not to mention such important non-superparticular commas as 2048/2025, 4000/3969, 1728/1715 and 3136/3125.

80 supports a profusion of 19-limit (and lower) rank two temperaments which have mostly not been explored. We might mention:

31&80 <<7 6 15 27 -24 -23 -20 ... ||

72&80 <<24 30 40 24 32 24 0 ... ||

34&80 <<2 -4 -50 22 16 2 -40 ... ||

46&80 <<2 -4 30 22 16 2 40 ... ||

29&80 <<3 34 45 33 24 -37 20 ... ||

12&80 <<4 -8 -20 -36 32 4 0 ... ||

22&80 <<6 -10 12 -14 -32 6 -40 ... ||

58&80 <<6 -10 12 -14 -32 6 40 ... ||

41&80 <<7 26 25 -3 -24 -33 20 ... ||

In each case, the numbers joined by an ampersand represent 19-limit patent vals (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.

Intervals of 80edo

degrees	cents	ratios*
0	0	1/1
1	15	64/63
2	30	81/80
3	45	34/33, 36/35
4	60	26/25, 28/27, 33/32, 35/34
5	75	22/21, 25/24, 27/26
6	90	19/18, 20/19, 21/20
7	105	16/15, 17/16, 18/17
8	120	14/13, 15/14
9	135	13/12
10	150	12/11
11	165	11/10
12	180	10/9, 21/19
13	195	19/17
14	210	9/8, 17/15
15	225	8/7
16	240
17	255	15/13, 22/19
18	270	7/6
19	285	13/11, 20/17
20	300	19/16, 25/21
21	315	6/5
22	330	17/14
23	345	11/9
24	360	16/13, 21/17
25	375
26	390	5/4
27	405	19/15, 24/19
28	420	14/11
29	435	9/7
30	450	13/10, 22/17
31	465	17/13
32	480	21/16, 25/19
33	495	4/3
34	510
35	525	19/14
36	540	26/19
37	555	11/8
38	570	18/13
39	585	7/5
40	600	17/12, 24/17

• based on treating 80edo as a 19-limit temperament; other approaches are possible.