Superfourth
A superfourth, ultrafourth or semi-augmented fourth is an interval that spans three steps of the diatonic scale with a quality between augmented and perfect. It exists in neutralized diatonic scales as exactly one half of a major seventh.
In just intonation, an interval may be classified as a superfourth if it is reasonably mapped to 3\7 and 11\24 (precisely three steps of the diatonic scale and five and a half steps of the chromatic scale).
As a concrete interval region, it is typically near 550 ¢ in size. It is 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 ¢. Of course, this categorization should not be taken for granted. Since music is subjective and culturally influenced, the borders of what is a superfourth are "fuzzy". Other descriptions are possible and legitimate.
Some of the simplest superfourths in just intonation are 11/8 (about 551 ¢) and 15/11 (about 537 ¢), both undecimal (11-based) superfourths; and 48/35 (about 547 ¢) and 49/36 (about 534 ¢), both septimal (7-based) superfourths.
The inversion of a superfourth is a subfifth.
Information about superfourths in the conventional interval-region format may be found at Tritone.
Examples
Below is a list of some intervals in the superfourth range, both just and tempered.
| Interval | Cents | Prime limit (if applicable) |
|---|---|---|
| 6\88cET or 11\25 |
528.000 | — |
| 19/14 | 528.687 | 19 |
| 87/64 | 531.532 | 29 |
| 34/25 | 532.328 | 17 |
| 4\9 | 533.333 | — |
| 49/36 | 533.742 | 7 |
| 64/47 | 534.493 | 47 |
| 15/11 | 536.951 | 11 |
| 13\29 | 537.931 | — |
| 56/41 | 539.764 | 41 |
| 9\20 | 540.000 | — |
| 41/30 | 540.794 | 41 |
| 175/128 | 541.453 | 7 |
| 14\31 | 541.935 | — |
| 26/19 | 543.015 | 19 |
| 5\11 | 545.455 | — |
| 37/27 | 545.479 | 37 |
| 48/35 | 546.815 | 7 |
| 11\24 | 550.000 | — |
| 11/8 | 551.318 | 11 |
| 6\13 | 553.846 | — |
| 62/45 | 554.812 | 31 |
| 40/29 | 556.737 | 29 |
| 13\28 | 557.143 | — |
| 243/176 | 558.457 | 11 |
| 29/21 | 558.796 | 29 |
| 47/34 | 560.551 | 47 |
| 7\15 | 560.000 | — |
See also
- 43/31 – a tritone with a "superfourth-ish" taste
- Gallery of just intervals
- Subfifth – the octave complement region
| V • T • EInterval regions | |
|---|---|
| Seconds and thirds | Comma and diesis • Semitone • Neutral second • Major second • (Interseptimal second-third) • Minor third • Neutral third • Major third |
| Fourths and fifths | (Interseptimal third-fourth) • Perfect fourth • Superfourth • Tritone • Subfifth • Perfect fifth • (Interseptimal fifth-sixth) |
| Sixths and sevenths | Minor sixth • Neutral sixth • Major sixth • (Interseptimal sixth-seventh) • Minor seventh • Neutral seventh • Major seventh • Octave |