Equable heptatonic

In the theory of Margo Schulter, equable heptatonic is a category of intervals which occupy regions intermediate between 11/10 and 10/9, or 9/5 and 20/11. There are two heartland regions given below, with approximate cents ranges from Schulter's article Regions of the Interval Spectrum:

• Neut2–Maj2 – intermediate between 11/10 and 10/9 – 160¢–182¢ (submajor second)
• min7–Neut7 – intermediate between 9/5 and 20/11 – 1018¢–1040¢ (supraminor seventh)

Equable heptatonic intervals are well-represented in 7edo at 171.429¢ (1＼7) and 1028.571¢ (6＼7). They also appear in 27edo, 34edo and 41edo. As they fall in ambiguous zones between simpler categories, they are inevitably xenharmonic.

Examples

Some equable heptatonic intervals in all two ranges, both just and tempered, are listed below.

Neut2–Maj2 (submajor second)

Interval	Cents Value	Prime Limit (if applicable)
34/31	159.920	31
2＼15	160.000	-
79/72	160.627	79
45/41	161.161	41
7＼52	161.538	-
101/92	161.579	101
56/51	161.915	17
5＼37	162.162	-
67/61	162.422	67
78/71	162.786	71
89/81	163.060	89
100/91	163.274	13
3＼22	163.636	-
7＼51	164.706	-
11/10	165.004	11
4＼29	165.517	-
5＼36	166.667	-
98/89	166.772	89
87/79	166.995	79
76/69	167.284	23
6＼43	167.442	-
65/59	167.670	59
7＼50	168.000	-
54/49	168.213	7
97/88	168.577	97
43/39	169.035	43
75/68	169.627	17
32/29	170.423	29
85/77	171.125	17
1＼7	171.429	-
53/48	171.550	53
74/67	172.037	67
95/86	172.309	43
21/19	173.268	19
94/85	174.237	47
73/66	174.517	77
7＼48	175.000	-
52/47	175.021	47
83/75	175.465	83
6＼41	175.610	-
31/28	176.210	31
5＼34	176.471	-
72/65	177.069	13
41/37	177.718	41
4＼27	177.778	-
92/83	178.227	83
51/46	178.636	23
7＼47	178.723	-
61/55	179.253	61
71/64	179.697	71
3＼20	180.000	-
81/73	180.031	73
91/82	180.291	41
5＼33	181.818	-
10/9	182.404	5
7＼46	182.609	-
2＼13	184.615	-

min7–Neut7 (supraminor seventh)

Interval	Cents Value	Prime Limit (if applicable)
11＼13	1015.385	-
39＼46	1017.391	-
9/5	1017.596	5
28＼33	1018.182	-
17＼20	1020.000	-
40＼47	1021.277	-
92/51	1021.364	23
83/46	1021.773	83
23＼27	1022.222	-
74/41	1022.282	41
65/36	1022.931	13
29＼34	1023.529	-
56/31	1023.790	31
35＼41	1024.390	-
47/26	1024.979	47
41＼48	1025.000	-
85/47	1025.763	47
38/21	1026.732	19
67/37	1027.963	67
6＼7	1028.571	-
29/16	1029.577	29
78/43	1030.965	43
49/27	1031.787	7
43＼50	1032.000	-
69/38	1032.716	23
37＼43	1032.558	-
89/49	1033.228	89
31＼36	1033.333	-
25＼29	1034.483	-
20/11	1034.996	11
44＼51	1035.294	-
19＼22	1036.364	-
91/50	1036.726	13
71/39	1037.214	71
32＼37	1037.838	-
51/28	1038.085	17
45＼52	1038.462	-
82/45	1038.839	41
13＼15	1040.000	-
31/17	1040.080	31

See also

• Interseptimal regions
• Gentle region
• Gallery of just intervals