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A "superfourth" is an interval too wide to sound like a [[Perfect_fourth|perfect fourth]] and too narrow to sound like a [[tritone|tritone]]. [[Margo_Schulter|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¢ to 560¢. Some of the simplest superfourths in [[Just_intonation|Just Intonation]] are [[11/8|11/8]] (about 551.3¢) and [[15/11|15/11]] (about 537¢), both undecimal (11-based) superfourths; and [[48/35|48/35]] (about 546.8¢) and [[49/36|49/36]] (about 533.7¢), 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]].  


The inversion of a superfourth is a [[Subfifth|subfifth]].
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).


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 description are possible and legitimate.
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.


==Examples==
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]].
 
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.
Below is a list of some intervals in the superfourth range, both just and tempered.


{| class="wikitable"
{| class="wikitable center-1 right-2"
|-
|-
! | Interval
! Interval
! | Cents Value
! Cents
! | Prime Limit (if applicable)
! Prime limit<br>(if applicable)
|-
|-
| | 6\[[88cET|88cET]] or 11\[[25edo|25edo]]
| [[88cET|6\88cET]]<br>or [[25edo|11\25]]
| | 528.000
| 528.000
| | -
| —
|-
|-
| | [[19/14|19/14]]
| [[19/14]]
| | 528.687
| 528.687
| | 19
| 19
|-
|-
| | 87/64
| 87/64
| | 531.532
| 531.532
| | 29
| 29
|-
|-
| | 34/25
| 34/25
| | 532.328
| 532.328
| | 17
| 17
|-
|-
| | 4\[[9edo|9edo]]
| [[9edo|4\9]]
| | 533.333
| 533.333
| | -
| —
|-
|-
| | [[49/36|49/36]]
| [[49/36]]
| | 533.742
| 533.742
| | 7
| 7
|-
|-
| | 64/47
| 64/47
| | 534.493
| 534.493
| | 47
| 47
|-
|-
| | [[15/11|15/11]]
| [[15/11]]
| | 536.951
| 536.951
| | 11
| 11
|-
|-
| | 13\[[29edo|29edo]]
| [[29edo|13\29]]
| | 537.931
| 537.931
| | -
| —
|-
|-
| | 56/41
| 56/41
| | 539.764
| 539.764
| | 41
| 41
|-
|-
| | 9\[[20edo|20edo]]
| [[20edo|9\20]]
| | 540.000
| 540.000
| | -
| —
|-
|-
| | 41/30
| 41/30
| | 540.794
| 540.794
| | 41
| 41
|-
|-
| | 175/128
| 175/128
| | 541.453
| 541.453
| | 7
| 7
|-
|-
| | 14\[[31edo|31edo]]
| [[31edo|14\31]]
| | 541.935
| 541.935
| | -
| —
|-
|-
| | [[26/19|26/19]]
| [[26/19]]
| | 543.015
| 543.015
| | 19
| 19
|-
|-
| | 5\[[11edo|11edo]]
| [[11edo|5\11]]
| | 545.455
| 545.455
| | -
| —
|-
|-
| | 37/27
| 37/27
| | 545.479
| 545.479
| | 37
| 37
|-
|-
| | [[48/35|48/35]]
| [[48/35]]
| | 546.815
| 546.815
| | 7
| 7
|-
|-
| | 11\[[24edo|24edo]]
| [[24edo|11\24]]
| | 550.000
| 550.000
| | -
| —
|-
|-
| | [[11/8|11/8]]
| [[11/8]]
| | 551.318
| 551.318
| | 11
| 11
|-
|-
| | 6\[[13edo|13edo]]
| [[13edo|6\13]]
| | 553.846
| 553.846
| | -
| —
|-
|-
| | 62/45
| 62/45
| | 554.812
| 554.812
| | 31
| 31
|-
|-
| | 40/29
| 40/29
| | 556.737
| 556.737
| | 29
| 29
|-
|-
| | 13\[[28edo|28edo]]
| [[28edo|13\28]]
| | 557.143
| 557.143
| | -
| —
|-
|-
| | 243/176
| 243/176
| | 558.457
| 558.457
| | 11
| 11
|-
|-
| | 29/21
| 29/21
| | 558.796
| 558.796
| | 29
| 29
|-
|-
| | 47/34
| 47/34
| | 560.551
| 560.551
| | 47
| 47
|-
|-
| | 7\[[15edo|15edo]]
| [[15edo|7\15]]
| | 560.000
| 560.000
| | -
| —
|}
|}


See: [[interval_category|Interval Category]], [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]    
== See also ==
[[Category:superfourth]]
* [[43/31]] – a tritone with a "superfourth-ish" taste
* [[Gallery of just intervals]]
* [[Subfifth]] – the [[octave complement]] region
 
{{Navbox intervals}}
 
[[Category:Superfourth| ]] <!-- main article -->
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