# 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