Perfect fourth: Difference between revisions
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The concept started as an interval in the diatonic scale, and is still used this way. The interval region is a later association. You can't just make it the main definition Tag: Undo |
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{{About|the [[interval region]]|the just perfect fourth|4/3}} | {{About|the [[interval region]]|the just perfect fourth|4/3}} | ||
{{Wikipedia}} | {{Wikipedia}} | ||
A '''perfect fourth (P4)''' | A '''perfect fourth (P4)''' is an interval that spans three steps of the [[5L 2s|diatonic]] scale with a perfect quality, i.e. the quality that exists in all but one modes. Depending on the specific tuning, it ranges from 480 to 514{{cent}} ([[5edo|2\5]] to [[7edo|3\7]]). | ||
In [[just intonation]], the just perfect fourth is [[4/3]]. Other intervals are also classified as perfect fourths, sometimes called '''wolf fourths''' or '''imperfect fourths''', if they are reasonably mapped to three steps of the diatonic scale and five steps of the chromatic scale. | In [[just intonation]], the just perfect fourth is [[4/3]]. Other intervals are also classified as perfect fourths, sometimes called '''wolf fourths''' or '''imperfect fourths''', if they are reasonably mapped to 3\7 and [[24edo|10\24]] (precisely three steps of the diatonic scale and five steps of the chromatic scale). The use of 24edo's 10\24 as the mapping criteria here rather than [[12edo]]'s 5\12 better captures the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]]. | ||
As a concrete [[interval region]], it is typically near 500{{c}} in size, distinct from the [[semiaugmented fourth]] of roughly 550{{c}}. A rough tuning range for the perfect fourth is about 470 to 530{{c}} according to [[Margo Schulter]]'s theory of interval regions. Another common range is the stricter range from 480 to 514{{c}}, which generates a diatonic scale. | |||
This article covers intervals from 450 to 540{{c}}, but intervals between 540 and 550 cents have been "grandfathered in" due to the fact that superfourths and subfifths were not originally given their own articles. | This article covers intervals from 450 to 540{{c}}, but intervals between 540 and 550 cents have been "grandfathered in" due to the fact that superfourths and subfifths were not originally given their own articles. | ||
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== In | == In edos == | ||
The following table lists the best tuning of 4/3, as well as other fourths if present, in various significant [[edo | The following table lists the best tuning of 4/3, as well as other fourths if present, in various significant [[edo]]s. | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | ! Edo | ||
! 4/3 | ! 4/3 | ||
! Other fourths | ! Other fourths | ||
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== In moment-of-symmetry scales == | == In moment-of-symmetry scales == | ||
Intervals between 450 and 545 cents generate the following [[mos | Intervals between 450 and 545 cents generate the following [[mos]] scales: | ||
These tables start from the last monolarge | These tables start from the last monolarge mos generated by the interval range. | ||
Scales with more than 12 notes are not included. | Scales with more than 12 notes are not included. | ||
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|- | |- | ||
! Range | ! Range | ||
! colspan="6" | | ! colspan="6" | Mos | ||
|- | |- | ||
| 450–480{{c}} | | 450–480{{c}} | ||