86edo

g_

86 is an edo whose use is generally confined to my approach, and is up there with 74edo as one of my default large edos. It's a straddle edo good for Interarch and my quartertone theory. Alongside being double the already respectable 43edo, this makes it my favorite edo at the time of writing.

SS

86edo may be seen as a system introducing neutral intervals to 43edo

Intervals in selected erac subroups in 86edo (x3 for <3.>3)

Step	Cents	2.x3.x5.x7.x11 81-odd-limit, max 3 eracs	2.x3.x5.x7.x11.13.x17.x19.23.29.31.37 37-odd-limit, max 1 erac
86	1200.000	2/1	2/1
85	1186.047	>>>96/49 >>>160/81 >>49/25 >63/32
84	1172.093	>96/49 >160/81 49/25 <63/32
83	1158.140	>>>48/25 <96/49 <160/81 >>27/14 >>35/18 <<49/25 <<<63/32	72/37 >68/35 >33/17 >37/19
82	1144.186	>48/25 <<<96/49 <<<160/81 27/14 35/18	64/33 >48/25 >56/29 60/31 <68/35 27/14 29/15 31/16 <33/17 35/18 <37/19
81	1130.233	<48/25 >>>40/21 <<27/14 <<35/18	<48/25 <56/29 >44/23 >52/27 >21/11 >23/12 25/13
80	1116.279	<<<48/25 >40/21	>40/21 >36/19 <44/23 <52/27 19/10 <21/11 <23/12
79	1102.326	<40/21 >>>28/15 >>15/8	>32/17 <40/21 <36/19 >17/9 66/35 70/37
78	1088.372	<<<40/21 >28/15 15/8	<32/17 >28/15 15/8 <17/9 >54/29 58/31 62/33
77	1074.419	<28/15 <<15/8 >>>50/27 >>>90/49	>24/13 <28/15 >13/7 <54/29 >37/20
76	1060.465	>>64/35 <<<28/15 >50/27 >90/49	<24/13 <13/7 >68/37 46/25 >50/27 >35/19 <37/20
75	1046.512	64/35 >>>9/5 <50/27 <90/49 >>>49/27	64/35 11/6 <68/37 42/23 <50/27 >31/17 <35/19
74	1032.558	<<64/35 >9/5 <<<50/27 <<<90/49 >49/27	20/11 >56/31 >9/5 >38/21 29/16 <31/17
73	1018.605	<9/5 >>>25/14 <49/27	<56/31 <9/5 <38/21
72	1004.651	>>16/9 <<<9/5 >25/14 <<<49/27	52/29 34/19 >25/14 66/37
71	990.698	16/9 <25/14	16/9 >44/25 >30/17 23/13 <25/14 62/35
70	976.744	<<16/9 >7/4 <<<25/14	>7/4 <44/25 <30/17 >54/31 58/33 37/21
69	962.791	<7/4	>40/23 <7/4 <54/31 >33/19
68	948.837	>>>128/75 >>12/7 >>140/81	64/37 <40/23 26/15 19/11 <33/19
67	934.884	>128/75 12/7 >>>27/16 140/81	12/7 50/29 >29/17 31/18
66	920.930	<128/75 <<12/7 >>42/25 >27/16 <<140/81	>56/33 >22/13 17/10 >46/27 >27/16 <29/17
65	906.977	<<<128/75 42/25 <27/16	>32/19 <56/33 <22/13 42/25 <46/27 <27/16 >37/22
64	893.023	>>5/3 <<42/25 <<<27/16 >>81/49	<32/19 52/31 62/37 <37/22
63	879.070	5/3 81/49	>48/29 5/3 >38/23 58/35 >33/20
62	865.116	<<5/3 >>>80/49 >>49/30 >>81/50 <<81/49	<48/29 28/17 >18/11 <38/23 >23/14 <33/20
61	851.163	>80/49 49/30 81/50	<18/11 <23/14 >31/19
60	837.209	<80/49 >>45/28 <<49/30 <<81/50	44/27 13/8 60/37 >34/21 21/13 <31/19
59	823.256	>8/5 <<<80/49 45/28	>8/5 <34/21 50/31 29/18 37/23
58	809.302	<8/5 >>>100/63 <<45/28 >>63/40	<8/5 27/17 >35/22
57	795.349	>>128/81 >100/63 63/40	>30/19 19/12 46/29 <35/22
56	781.395	128/81 >>>14/9 >>25/16 <100/63 >>>54/35 <<63/40	36/23 11/7 52/33 <30/19 58/37
55	767.442	<<128/81 >14/9 25/16 <<<100/63 >54/35	>48/31 >14/9 25/16 >54/35 >31/20
54	753.488	<14/9 <<25/16 <54/35 >>49/32 >>>75/49	<48/31 >20/13 <14/9 17/11 <54/35 <31/20 >37/24
53	739.535	>>32/21 <<<14/9 <<<54/35 49/32 >75/49	<20/13 >26/17 >38/25 23/15 >29/19 <37/24
52	725.581	32/21 <<49/32 <75/49	32/21 >56/37 >44/29 <26/17 <38/25 <29/19 35/23
51	711.628	<<32/21 >3/2 >>112/75 <<<75/49	>3/2 <56/37 <44/29 50/33
50	697.674	<3/2 112/75	<3/2
49	683.721	>>40/27 <<112/75 >>72/49	52/35 >34/23 46/31 37/25
48	669.767	40/27 72/49 >>>35/24 >>>81/56	40/27 28/19 >22/15 <34/23 >19/13 >25/17 >54/37 31/21
47	655.814	<<40/27 >>36/25 <<72/49 >35/24 >81/56	>16/11 <22/15 <19/13 <25/17 <54/37 >29/20 >35/24
46	641.860	36/25 <35/24 <81/56	<16/11 36/25 42/29 <29/20 <35/24
45	627.907	>>>64/45 >>10/7 <<36/25 <<<35/24 <<<81/56	13/9 23/16 33/23
44	613.953	>64/45 10/7 >>>45/32	10/7 >44/31 27/19 37/26
43	600.000	<64/45 <<10/7 >>7/5 >45/32	24/17 <44/31 17/12 >31/22
42	586.047	<<<64/45 7/5 <45/32	7/5 52/37 38/27 <31/22
41	572.093	>>>48/35 <<7/5 >>>112/81 >>25/18 <<<45/32	32/23 18/13 46/33
40	558.140	>48/35 >112/81 25/18	>48/35 >40/29 >11/8 25/18 29/21
39	544.186	<48/35 <112/81 <<25/18 >>27/20 >>49/36	<48/35 <40/29 <11/8 >26/19 >15/11 >34/25 >37/27
38	530.233	<<<48/35 <<<112/81 27/20 49/36	<26/19 <15/11 <34/25 19/14 42/31 >23/17 27/20 <37/27
37	516.279	<<27/20 <<49/36 >>75/56	<23/17 50/37 31/23 35/26
36	502.326	>4/3 75/56	>4/3
35	488.372	<4/3 >>21/16 >>>98/75 <<75/56	<4/3 >29/22 33/25 >37/28
34	474.419	>>64/49 21/16 >98/75	>17/13 >38/29 21/16 46/35 >25/19 <29/22 <37/28
33	460.465	64/49 >>>9/7 <<21/16 >>>35/27 <98/75	>48/37 >13/10 30/23 <17/13 <38/29 <25/19
32	446.512	>>32/25 <<64/49 >9/7 >35/27 <<<98/75	<48/37 >40/31 >9/7 22/17 <13/10 >31/24 >35/27
31	432.558	32/25 <9/7 <35/27 >>>63/50 >>81/64	32/25 <40/31 <9/7 <31/24 <35/27
30	418.605	<<32/25 >>80/63 <<<9/7 <<<35/27 >63/50 81/64	14/11 >19/15 23/18 33/26 37/29
29	404.651	80/63 <63/50 <<81/64	24/19 >44/35 <19/15 29/23
28	390.698	>5/4 <<80/63 >>56/45 <<<63/50	>5/4 <44/35 34/27
27	376.744	<5/4 56/45 >>>49/40	<5/4 36/29 >21/17 46/37 31/25
26	362.791	<<56/45 >>60/49 >>100/81 >49/40	16/13 26/21 >38/31 <21/17 27/22 37/30
25	348.837	60/49 100/81 <49/40	>28/23 >11/9 <38/31
24	334.884	>>6/5 <<60/49 <<100/81 <<<49/40 >>98/81	>40/33 <28/23 <11/9 17/14 >23/19 >29/24
23	320.930	6/5 98/81	6/5 <40/33 <23/19 <29/24 35/29
22	306.977	>>>32/27 <<6/5 >>25/21 <<98/81	>44/37 >19/16 31/26 37/31
21	293.023	>32/27 25/21 >>>75/64	>32/27 <44/37 >13/11 <19/16 25/21 >27/23 >33/28
20	279.070	<32/27 >>7/6 <<25/21 >75/64 >>81/70	<32/27 20/17 <13/11 >34/29 <27/23 <33/28
19	265.116	<<<32/27 7/6 <75/64 81/70	7/6 36/31 <34/29 29/25
18	251.163	<<7/6 <<<75/64 <<81/70	22/19 15/13 >38/33 >23/20 37/32
17	237.209	>8/7	>8/7 <38/33 <23/20 >31/27
16	223.256	<8/7 >>>28/25 >>9/8	<8/7 >17/15 42/37 >25/22 <31/27 33/29
15	209.302	>28/25 9/8	>28/25 9/8 26/23 <17/15 <25/22 35/31
14	195.349	>>>10/9 <28/25 <<9/8 >>>54/49	<28/25 19/17 29/26 37/33
13	181.395	>10/9 <<<28/25 >54/49	>10/9 >21/19 >31/28
12	167.442	<10/9 >>>27/25 <54/49 >>35/32 >>>49/45	32/29 <10/9 11/10 >34/31 <21/19 <31/28
11	153.488	<<<10/9 >27/25 <<<54/49 35/32 >49/45	12/11 <34/31 >38/35 23/21 >27/25 35/32 >37/34
10	139.535	>>>15/14 <27/25 <<35/32 <49/45	>40/37 >14/13 >13/12 <38/35 25/23 <27/25 <37/34
9	125.581	>>16/15 >15/14 <<<27/25 <<<49/45	<40/37 <14/13 <13/12 >15/14 >29/27
8	111.628	16/15 <15/14 >>>21/20	16/15 >18/17 <15/14 >17/16 <29/27 31/29 33/31
7	97.674	<<16/15 <<<15/14 >21/20	<18/17 <17/16 >19/18 >21/20 35/33 37/35
6	83.721	<21/20 >>>25/24	>24/23 20/19 >22/21 <19/18 <21/20 >23/22 >27/26
5	69.767	>>28/27 >>36/35 <<<21/20 >25/24	<24/23 <22/21 26/25 <23/22 >25/24 <27/26 >29/28
4	55.814	28/27 36/35 <25/24 >>>49/48 >>>81/80	32/31 28/27 36/35 30/29 >34/33 >38/37 <25/24 <29/28 31/30 33/32 >35/34
3	41.860	>>>64/63 <<28/27 <<36/35 <<<25/24 >>50/49 >49/48 >81/80	<34/33 <38/37 <35/34 37/36
2	27.907	>64/63 50/49 <49/48 <81/80
1	13.953	<64/63 <<50/49 <<<49/48 <<<81/80
0	0.000	1/1 <<<64/63 >>>63/64	1/1

22&86bde is very good at generating 86edo Archy pental blackdye and its related quasi-Porcupine. It's similar to Comic temperament. See Straddle cluster temperaments#Quartertone.

11-limit 22&86bde, 81-odd-limit

Gens	Pd. 1	Pd. 2	Interpretations
24	139.5	739.5	75/49
23	83.7	683.7
22	27.9	627.9	50/49
21	572.1	1172.1	150/77
20	516.3	1116.3	75/56
19	460.5	1060.5	100/77 90/49
18	404.7	1004.7	25/14
17	348.8	948.8	60/49 75/44
16	293.0	893.0	25/21 90/77 75/64 81/49
15	237.2	837.2	80/49 25/22 45/28
14	181.4	781.4	120/77 25/16 100/63 54/49 55/49
13	125.6	725.6	15/14 50/33 81/77
12	69.8	669.8	80/77 72/49 25/24 45/44 81/56
11	14.0	614.0	10/7 108/77 45/32
10	558.1	1158.1	96/49 15/11 25/18 27/14 55/28
9	502.3	1102.3	40/21 144/77 15/8 66/49 81/44
8	446.5	1046.5	64/49 20/11 9/7 50/27 55/42 81/64
7	390.7	990.7	96/77 5/4 80/63 88/49 27/22
6	334.9	934.9	12/7 40/33 100/81 27/16 55/32 110/63
5	279.1	879.1	128/77 5/3 18/11 33/28 81/70
4	223.3	823.3	8/7 9/8 35/22 55/48
3	167.4	767.4	12/11 10/9 11/7 54/35 35/32
2	111.6	711.6	32/21 3/2 35/33 55/36 81/55
1	55.8	655.8	16/11 40/27 36/35 22/21 33/32 35/24 63/44 81/80
0	0.0	600.0	1/1 64/63 108/55 55/54 63/32
-1	544.2	1144.2	64/33 48/35 160/81 11/8 88/63 21/11 27/20 35/18
-2	488.4	1088.4	4/3 72/55 21/16 66/35 110/81
-3	432.6	1032.6	64/35 14/11 9/5 11/6 35/27
-4	376.7	976.7	16/9 96/55 7/4 44/35
-5	320.9	920.9	6/5 56/33 11/9 140/81 77/64
-6	265.1	865.1	32/27 64/55 7/6 33/20 63/55 81/50
-7	209.3	809.3	8/5 44/27 49/44 63/40 77/48
-8	153.5	753.5	128/81 14/9 11/10 84/55 27/25 49/32
-9	97.7	697.7	16/15 88/81 21/20 49/33 77/72
-10	41.9	641.9	28/27 56/55 36/25 22/15 49/48
-11	586.0	1186.0	64/45 7/5 77/54
-12	530.2	1130.2	48/25 112/81 88/45 49/36 77/40
-13	474.4	1074.4	28/15 33/25 154/81
-14	418.6	1018.6	32/25 49/27 98/55 63/50 77/60
-15	362.8	962.8	56/45 44/25 49/40
-16	307.0	907.0	128/75 42/25 98/81 77/45
-17	251.2	851.2	88/75 49/30
-18	195.3	795.3	28/25
-19	139.5	739.5	49/45 77/50
-20	83.7	683.7	112/75
-21	27.9	627.9	77/75
-22	572.1	1172.1	49/25
-23	516.3	1116.3
-24	460.5	1060.5	98/75