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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''' 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¢ to 560¢. Some of the simplest superfourths in [[Just intonation]] are [[11/8]] (about 551.3¢) and [[15/11]] (about 537¢), both undecimal (11-based) superfourths; and [[48/35]] (about 546.8¢) and [[49/36]] (about 533.7¢), both septimal (7-based) superfourths.


The inversion of a superfourth is a [[Subfifth|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 description are possible and legitimate.
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.
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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 Value
! | Prime Limit (if applicable)
! Prime Limit <br> (if applicable)
|-
|-
| | 6\[[88cET|88cET]] or 11\[[25edo|25edo]]
| 6\[[88cET]] <br> or 11\[[25edo|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]]
| 4\[[9edo|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]]
| 13\[[29edo|29]]
| | 537.931
| 537.931
| | -
| -
|-
|-
| | 56/41
| 56/41
| | 539.764
| 539.764
| | 41
| 41
|-
|-
| | 9\[[20edo|20edo]]
| 9\[[20edo|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]]
| 14\[[31edo|31]]
| | 541.935
| 541.935
| | -
| -
|-
|-
| | [[26/19|26/19]]
| [[26/19]]
| | 543.015
| 543.015
| | 19
| 19
|-
|-
| | 5\[[11edo|11edo]]
| 5\[[11edo|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]]
| 11\[[24edo|24]]
| | 550.000
| 550.000
| | -
| -
|-
|-
| | [[11/8|11/8]]
| [[11/8]]
| | 551.318
| 551.318
| | 11
| 11
|-
|-
| | 6\[[13edo|13edo]]
| 6\[[13edo|31]]
| | 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]]
| 13\[[28edo|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]]
| 7\[[15edo|15]]
| | 560.000
| 560.000
| | -
| -
|}
|}


See: [[interval_category|Interval Category]], [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]    
== See also ==
[[Category:superfourth]]
 
* [[Interval category]]
* [[Gallery of just intervals]]
* [[Subfifth]]
 
[[Category:Superfourth]]
[[Category:Interval]]
Retrieved from "https://en.xen.wiki/w/Superfourth"