Perfect fifth: 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 fifth|3/2}} | {{About|the [[interval region]]|the just perfect fifth|3/2}} | ||
{{Wikipedia}} | {{Wikipedia}} | ||
A '''perfect fifth (P5)''' | A '''perfect fifth (P5)''' is an interval that spans four 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 686 to 720{{cent}} ([[7edo|4\7]] to [[5edo|3\5]]). | ||
In [[just intonation]], the just perfect fifth is [[3/2]]. Other intervals are also classified as perfect fifths, sometimes called '''wolf fifths''' or '''imperfect fifths''', if they are reasonably mapped to four steps of the diatonic scale and seven steps of the chromatic scale. | In [[just intonation]], the just perfect fifth is [[3/2]]. Other intervals are also classified as perfect fifths, sometimes called '''wolf fifths''' or '''imperfect fifths''', if they are reasonably mapped to 4\7 and [[24edo|14\24]] (precisely four steps of the diatonic scale and seven steps of the chromatic scale). The use of 24edo's 14\24 as the mapping criteria here rather than [[12edo]]'s 7\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 700{{c}} in size, distinct from semidiminished fifths of rougly 650{{c}}. A rough tuning range for the perfect fifth is about 670 to 730 [[cents]] according to [[Margo Schulter]]'s theory of interval regions. Another common range is the stricter range from 686 to 720{{c}}, which generates a diatonic scale. | |||
This article covers intervals from 660 to 750{{c}}, but intervals between 650 and 660 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 660 to 750{{c}}, but intervals between 650 and 660 cents have been "grandfathered in" due to the fact that superfourths and subfifths were not originally given their own articles. | ||
== In just intonation == | == In just intonation == | ||
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* The 13-limit '''ultrafifth''' is a ratio of 20/13, and is about 746{{c}}, but it might be better analyzed as an [[minor sixth|inframinor sixth]]. Despite that, it is also here for completeness. | * The 13-limit '''ultrafifth''' is a ratio of 20/13, and is about 746{{c}}, but it might be better analyzed as an [[minor sixth|inframinor sixth]]. Despite that, it is also here for completeness. | ||
== In | == In edos == | ||
The following table lists the best tuning of 3/2, as well as other fifths if present, in various significant [[edo | The following table lists the best tuning of 3/2, as well as other fifths if present, in various significant [[edo]]s. | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | ! Edo | ||
! 3/2 | ! 3/2 | ||
! Other fifths | ! Other fifths | ||
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* Various historical [[well temperament]]s generated by tempered 4/3s or 3/2s, equivalent to 12edo as compton and meantone | * Various historical [[well temperament]]s generated by tempered 4/3s or 3/2s, equivalent to 12edo as compton and meantone | ||
== In | == In mos scales == | ||
Intervals between 654 and 750{{c}} generate the following [[mos | Intervals between 654 and 750{{c}} 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 | ||
|- | |- | ||
| 720–750{{c}} | | 720–750{{c}} | ||