Superfourth: Difference between revisions
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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 [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}}. Some of the simplest superfourths in [[just intonation]] are [[11/8]] (about 551.3{{c}}) and [[15/11]] (about 537{{c}}), both undecimal (11-based) superfourths; and [[48/35]] (about 546.8{{c}}) and [[49/36]] (about 533.7{{c}}), both septimal (7-based) superfourths. | A '''superfourth''' 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]]. | ||
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). | |||
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. | |||
Some of the simplest superfourths in [[just intonation]] are [[11/8]] (about 551.3{{c}}) and [[15/11]] (about 537{{c}}), both undecimal (11-based) superfourths; and [[48/35]] (about 546.8{{c}}) and [[49/36]] (about 533.7{{c}}), both septimal (7-based) superfourths. | |||
The inversion of a superfourth is a [[subfifth]]. | The inversion of a superfourth is a [[subfifth]]. | ||
== Examples == | == Examples == | ||
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! Interval | ! Interval | ||
! Cents | ! Cents | ||
! Prime limit<br | ! Prime limit<br>(if applicable) | ||
|- | |- | ||
| 6\ | | [[88cET|6\88cET]]<br>or [[25edo|11\25]] | ||
| 528.000 | | 528.000 | ||
| — | | — | ||
| Line 30: | Line 34: | ||
| 17 | | 17 | ||
|- | |- | ||
| | | [[9edo|4\9]] | ||
| 533.333 | | 533.333 | ||
| — | | — | ||
| Line 46: | Line 50: | ||
| 11 | | 11 | ||
|- | |- | ||
| | | [[29edo|13\29]] | ||
| 537.931 | | 537.931 | ||
| — | | — | ||
| Line 54: | Line 58: | ||
| 41 | | 41 | ||
|- | |- | ||
| | | [[20edo|9\20]] | ||
| 540.000 | | 540.000 | ||
| — | | — | ||
| Line 66: | Line 70: | ||
| 7 | | 7 | ||
|- | |- | ||
| | | [[31edo|14\31]] | ||
| 541.935 | | 541.935 | ||
| — | | — | ||
| Line 74: | Line 78: | ||
| 19 | | 19 | ||
|- | |- | ||
| | | [[11edo|5\11]] | ||
| 545.455 | | 545.455 | ||
| — | | — | ||
| Line 86: | Line 90: | ||
| 7 | | 7 | ||
|- | |- | ||
| | | [[24edo|11\24]] | ||
| 550.000 | | 550.000 | ||
| — | | — | ||
| Line 94: | Line 98: | ||
| 11 | | 11 | ||
|- | |- | ||
| | | [[13edo|6\13]] | ||
| 553.846 | | 553.846 | ||
| — | | — | ||
| Line 106: | Line 110: | ||
| 29 | | 29 | ||
|- | |- | ||
| | | [[28edo|13\28]] | ||
| 557.143 | | 557.143 | ||
| — | | — | ||
| Line 122: | Line 126: | ||
| 47 | | 47 | ||
|- | |- | ||
| | | [[15edo|7\15]] | ||
| 560.000 | | 560.000 | ||
| — | | — | ||