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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 551.3{{c}}) and [[15/11]] (about 537{{c}}), both undecimal (11-based) superfourths; and [[48/35]] (about 546.8{{c}}) and [[49/36]] (about 533.7{{c}}), both septimal (7-based) superfourths.
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]].


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.
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 />(if applicable)
! Prime limit<br>(if applicable)
|-
|-
| 6\[[88cET]]<br />or 11\[[25edo|25]]
| [[88cET|6\88cET]]<br>or [[25edo|11\25]]
| 528.000
| 528.000
| -
| —
|-
|-
| [[19/14]]
| [[19/14]]
Line 30: Line 36:
| 17
| 17
|-
|-
| 4\[[9edo|9]]
| [[9edo|4\9]]
| 533.333
| 533.333
| -
| —
|-
|-
| [[49/36]]
| [[49/36]]
Line 46: Line 52:
| 11
| 11
|-
|-
| 13\[[29edo|29]]
| [[29edo|13\29]]
| 537.931
| 537.931
| -
| —
|-
|-
| 56/41
| 56/41
Line 54: Line 60:
| 41
| 41
|-
|-
| 9\[[20edo|20]]
| [[20edo|9\20]]
| 540.000
| 540.000
| -
| —
|-
|-
| 41/30
| 41/30
Line 66: Line 72:
| 7
| 7
|-
|-
| 14\[[31edo|31]]
| [[31edo|14\31]]
| 541.935
| 541.935
| -
| —
|-
|-
| [[26/19]]
| [[26/19]]
Line 74: Line 80:
| 19
| 19
|-
|-
| 5\[[11edo|11]]
| [[11edo|5\11]]
| 545.455
| 545.455
| -
| —
|-
|-
| 37/27
| 37/27
Line 86: Line 92:
| 7
| 7
|-
|-
| 11\[[24edo|24]]
| [[24edo|11\24]]
| 550.000
| 550.000
| -
| —
|-
|-
| [[11/8]]
| [[11/8]]
Line 94: Line 100:
| 11
| 11
|-
|-
| 6\[[13edo|13]]
| [[13edo|6\13]]
| 553.846
| 553.846
| -
| —
|-
|-
| 62/45
| 62/45
Line 106: Line 112:
| 29
| 29
|-
|-
| 13\[[28edo|28]]
| [[28edo|13\28]]
| 557.143
| 557.143
| -
| —
|-
|-
| 243/176
| 243/176
Line 122: Line 128:
| 47
| 47
|-
|-
| 7\[[15edo|15]]
| [[15edo|7\15]]
| 560.000
| 560.000
| -
| —
|}
|}


== See also ==
== See also ==
* [[43/31]] – a tritone with a "superfourth-ish" taste
* [[43/31]] – a tritone with a "superfourth-ish" taste
* [[Interval category]]
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]
* [[Subfifth]] – the [[octave complement]] region
* [[Subfifth]] – the [[octave complement]] region
{{Navbox intervals}}


[[Category:Superfourth| ]] <!-- main article -->
[[Category:Superfourth| ]] <!-- main article -->

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


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
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