Superfourth
A "superfourth" is an interval too wide to sound like a perfect fourth and too narrow to sound like a tritone. Margo Schulter, in her article Regions of the Interval Spectrum, proposes an approximate range for a superfourth to be from 528¢ to 560¢. Some of the simplest superfourths in Just Intonation are 11/8 (about 551.3¢) and 15/11 (about 537¢), both undecimal (11-based) superfourths; and 48/35 (about 546.8¢) and 49/36 (about 533.7¢), both septimal (7-based) superfourths.
The inversion of a superfourth is a subfifth.
Of course, it should never be taken for granted that these categories are subjective and culturally influenced, and the borders are "fuzzy". Other description are possible and legitimate.
Examples[edit]
Below is a list of some intervals in the superfourth range, both just and tempered.
| Interval | Cents Value | Prime Limit (if applicable) |
|---|---|---|
| 6\88cET or 11\25edo | 528.000 | - |
| 19/14 | 528.687 | 19 |
| 87/64 | 531.532 | 29 |
| 34/25 | 532.328 | 17 |
| 4\9edo | 533.333 | - |
| 49/36 | 533.742 | 7 |
| 64/47 | 534.493 | 47 |
| 15/11 | 536.951 | 11 |
| 13\29edo | 537.931 | - |
| 56/41 | 539.764 | 41 |
| 9\20edo | 540.000 | - |
| 41/30 | 540.794 | 41 |
| 175/128 | 541.453 | 7 |
| 14\31edo | 541.935 | - |
| 26/19 | 543.015 | 19 |
| 5\11edo | 545.455 | - |
| 37/27 | 545.479 | 37 |
| 48/35 | 546.815 | 7 |
| 11\24edo | 550.000 | - |
| 11/8 | 551.318 | 11 |
| 6\13edo | 553.846 | - |
| 62/45 | 554.812 | 31 |
| 40/29 | 556.737 | 29 |
| 13\28edo | 557.143 | - |
| 243/176 | 558.457 | 11 |
| 29/21 | 558.796 | 29 |
| 47/34 | 560.551 | 47 |
| 7\15edo | 560.000 | - |