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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, 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.
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]]     [[Category:superfourth]]
== See also ==
* [[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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