Perfect fifth: Difference between revisions
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{{About|the [[interval region]]|the just perfect fifth|3/2}} | |||
{{Wikipedia}} | |||
A '''perfect fifth''' ('''P5'''), is the large and most common of the two fifths – intervals spanning 5 degrees or 4 scale steps in the diatonic scale. It is found between the 1st and 5th degrees of all diatonic modes except Locrian. Another diatonic interval around the same size is the '''diminished sixth''' ('''d6'''). More generally, an interval close to 700 cents can be called a perfect fifth. | |||
== As an interval region == | |||
{{Infobox interval region | {{Infobox interval region | ||
| Name = Perfect fifth | | Name = Perfect fifth | ||
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| Higher region = [[Minor sixth]] | | Higher region = [[Minor sixth]] | ||
}} | }} | ||
As a concrete [[interval region]], a perfect fifth 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 mos scales === | |||
Intervals between 654 and 750{{c}} generate the following [[mos]] scales: | |||
These tables start from the last monolarge mos generated by the interval range. | |||
Scales with more than 12 notes are not included. | |||
{| class="wikitable" | |||
|- | |||
! Range | |||
! colspan="6" | Mos | |||
|- | |||
| 720–750{{c}} | |||
| rowspan="5" | [[1L 1s]] | |||
| rowspan="5" | [[2L 1s]] | |||
| [[3L 2s]] | |||
| colspan="3" | [[5L 3s]] | |||
|- | |||
| 700–720{{c}} | |||
| rowspan="4" | [[2L 3s]] | |||
| rowspan="2" | [[5L 2s]] | |||
| colspan="2" | [[5L 7s]] | |||
|- | |||
| 686–700{{c}} | |||
| colspan="2" | [[7L 5s]] | |||
|- | |||
| 667–686{{c}} | |||
| rowspan="2" | [[2L 5s]] | |||
| colspan="2" | [[7L 2s]] | |||
|- | |||
| 654–667{{c}} | |||
| [[2L 7s]] | |||
| [[9L 2s]] | |||
|} | |||
== As a diatonic interval category == | |||
{{Infobox | |||
| Title = Diatonic perfect fifth | |||
| Header 1 = MOS | Data 1 = [[5L 2s]] | |||
| Header 2 = Other names | Data 2 = Perfect 4-diastep | |||
| Header 3 = Generator span | Data 3 = +1 generator | |||
| Header 4 = Tuning range | Data 4 = 686–720{{c}} | |||
| Header 5 = Basic tuning | Data 5 = 700{{c}} | |||
| Header 6 = Function on root | Data 6 = Dominant | |||
| Header 7 = Interval regions | Data 7 = Perfect fifth | |||
| Header 8 = Associated just intervals | Data 8 = [[3/2]] | |||
| Header 9 = Octave complement | Data 9 = [[Perfect fourth]] | |||
}} | |||
A perfect fourth 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. It is a [[generator]] of the diatonic scale. 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, or formally 4\7 and [[24edo|14\24]]. 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]]. | |||
In [[TAMNAMS]], this interval is called the '''perfect 4-diastep'''. | |||
== In just intonation == | == In just intonation == | ||
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* [[Mavila]], the temperament flattening 3/2 such that four 3/2s stack to [[6/5]] | * [[Mavila]], the temperament flattening 3/2 such that four 3/2s stack to [[6/5]] | ||
* 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 | ||
{{Navbox intervals}} | {{Navbox intervals}} | ||