Superfourth: Difference between revisions
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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 [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum], proposes an approximate range for a superfourth to be from 528{{cent}} to 560{{cent}}. Some of the simplest superfourths in [[just intonation]] are [[11/8]] (about 551 | A '''superfourth''', '''ultrafourth''' or '''semi-augmented fourth''' is an [[interval]] that spans three steps of the [[5L 2s|diatonic]] scale with a quality between augmented and perfect. It exists in [[neutralization|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 [[7edo|3\7]] and [[24edo|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{{cent}} 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 [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum], proposes an approximate range for a superfourth to be from 528{{cent}} to 560{{cent}}. 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{{c}}) and [[15/11]] (about 537{{c}}), both undecimal (11-based) superfourths; and [[48/35]] (about 547{{c}}) and [[49/36]] (about 534{{c}}), both septimal (7-based) superfourths. | |||
The inversion of a superfourth is a [[subfifth]]. | The inversion of a superfourth is a [[subfifth]]. | ||
Information about superfourths in the conventional interval-region format may be found at [[Tritone]]. | |||
== Examples == | == Examples == | ||
| Line 12: | Line 18: | ||
! Interval | ! Interval | ||
! Cents | ! Cents | ||
! Prime limit<br | ! Prime limit<br>(if applicable) | ||
|- | |- | ||
| 6\ | | [[88cET|6\88cET]]<br>or [[25edo|11\25]] | ||
| 528.000 | | 528.000 | ||
| — | | — | ||
| Line 30: | Line 36: | ||
| 17 | | 17 | ||
|- | |- | ||
| | | [[9edo|4\9]] | ||
| 533.333 | | 533.333 | ||
| — | | — | ||
| Line 46: | Line 52: | ||
| 11 | | 11 | ||
|- | |- | ||
| | | [[29edo|13\29]] | ||
| 537.931 | | 537.931 | ||
| — | | — | ||
| Line 54: | Line 60: | ||
| 41 | | 41 | ||
|- | |- | ||
| | | [[20edo|9\20]] | ||
| 540.000 | | 540.000 | ||
| — | | — | ||
| Line 66: | Line 72: | ||
| 7 | | 7 | ||
|- | |- | ||
| | | [[31edo|14\31]] | ||
| 541.935 | | 541.935 | ||
| — | | — | ||
| Line 74: | Line 80: | ||
| 19 | | 19 | ||
|- | |- | ||
| | | [[11edo|5\11]] | ||
| 545.455 | | 545.455 | ||
| — | | — | ||
| Line 86: | Line 92: | ||
| 7 | | 7 | ||
|- | |- | ||
| | | [[24edo|11\24]] | ||
| 550.000 | | 550.000 | ||
| — | | — | ||
| Line 94: | Line 100: | ||
| 11 | | 11 | ||
|- | |- | ||
| | | [[13edo|6\13]] | ||
| 553.846 | | 553.846 | ||
| — | | — | ||
| Line 106: | Line 112: | ||
| 29 | | 29 | ||
|- | |- | ||
| | | [[28edo|13\28]] | ||
| 557.143 | | 557.143 | ||
| — | | — | ||
| Line 122: | Line 128: | ||
| 47 | | 47 | ||
|- | |- | ||
| | | [[15edo|7\15]] | ||
| 560.000 | | 560.000 | ||
| — | | — | ||
| Line 129: | Line 135: | ||
== See also == | == See also == | ||
* [[43/31]] – a tritone with a "superfourth-ish" taste | * [[43/31]] – a tritone with a "superfourth-ish" taste | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[Subfifth]] – the [[octave complement]] region | * [[Subfifth]] – the [[octave complement]] region | ||
Latest revision as of 08:57, 6 March 2025
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
| View • Talk • EditInterval classification | |
|---|---|
| Interval regions | |
| Unison and octave | Unison • Comma and diesis • Octave |
| Seconds | Minor second • Neutral second • Major second |
| Thirds | Minor third • Neutral third • Major third |
| Fourths and fifths | Perfect fourth • Superfourth • Tritone • Subfifth • Perfect fifth |
| Sixths | Minor sixth • Neutral sixth • Major sixth |
| Sevenths | Minor seventh • Neutral seventh • Major seventh |
| Interseptimal intervals | Interseptimal 2nd-3rd • Interseptimal 3rd-4th • Interseptimal 5th-6th • Interseptimal 6th-7th |
| Interval qualities | |
| Diatonic qualities | Diminished • Minor • Perfect • Major • Augmented |
| Tuning ranges | Neutral (interval quality) • Submajor and supraminor • Pental major and minor • Novamajor and novaminor • Neogothic major and minor • Supermajor and subminor • Ultramajor and inframinor |