Superfourth: Difference between revisions

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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.
Line 8: Line 8:
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]]

Revision as of 12:57, 13 June 2020

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 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.

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.

Examples

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

Interval Cents Value 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\31 553.846 -
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

Retrieved from "https://en.xen.wiki/index.php?title=Superfourth&oldid=46702"