Superfourth

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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 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