Equable heptatonic
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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 | Size (cents) |
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 | Size (cents) |
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 |