Perfect fifth: Difference between revisions
No edit summary |
Use about template, better integration of the diatonic range, markup |
||
| Line 1: | Line 1: | ||
'' | {{About|the [[interval region]]|the just perfect fifth|3/2}} | ||
A '''perfect fifth (P5)''' is an interval that is near 700 [[cent]]s in size, distinct from diminished fifths (a type of [[tritone]], about 600 cents). A rough tuning range for the perfect fifth is about 650 to 750 [[cents]], though this is extremely wide; some might prefer to restrict it to around 670-730 cents. Another common range is the even stricter [[diatonic range]], from ~686 to 720 cents, which corresponds to [[diatonic perfect fifth]]s that can be used to generate a [[5L 2s|diatonic scale]]. | |||
== In just intonation == | |||
==In just intonation== | |||
The only "perfect" fourth in JI is the '''Pythagorean perfect fifth''' of [[3/2]], about 702 cents in size, which corresponds to the MOS-based interval category of the diatonic perfect fifth, and is the generator for Pythagorean tuning and the diatonic scale. However, various "out of tune" fifths exist, such as the '''Pythagorean wolf fifth [[262144/177147]]''', which is flat of 3/2 by one [[Pythagorean comma]], and is about 678 cents in size. | The only "perfect" fourth in JI is the '''Pythagorean perfect fifth''' of [[3/2]], about 702 cents in size, which corresponds to the MOS-based interval category of the diatonic perfect fifth, and is the generator for Pythagorean tuning and the diatonic scale. However, various "out of tune" fifths exist, such as the '''Pythagorean wolf fifth [[262144/177147]]''', which is flat of 3/2 by one [[Pythagorean comma]], and is about 678 cents in size. | ||
| Line 15: | Line 11: | ||
**There is also an 11-limit '''acute fifth,''' which is a ratio of 50/33, and is about 720 cents. | **There is also an 11-limit '''acute fifth,''' which is a ratio of 50/33, and is about 720 cents. | ||
*The 13-limit '''ultrafifth''' is a ratio of 20/13, and is about 746 cents, 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 cents, but it might be better analyzed as an [[Minor sixth|inframinor sixth]]. Despite that, it is also here for completeness. | ||
==In EDOs== | |||
== In EDOs == | |||
The following table lists the best tuning of 3/2, as well as other fifths if present, in various significant [[EDOs]]. | The following table lists the best tuning of 3/2, as well as other fifths if present, in various significant [[EDOs]]. | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 91: | Line 88: | ||
|748c ≈ 20/13, 724c ≈ 32/21, 679c ≈ 40/27, 657c ≈ 22/15 | |748c ≈ 20/13, 724c ≈ 32/21, 679c ≈ 40/27, 657c ≈ 22/15 | ||
|} | |} | ||
==In temperaments== | |||
== In temperaments == | |||
The simplest perfect 5th ratio is 3/2. The following notable temperaments are generated by it: | The simplest perfect 5th ratio is 3/2. The following notable temperaments are generated by it: | ||
===Temperaments that use 3/2 as a generator=== | ===Temperaments that use 3/2 as a generator=== | ||
*[[Compton]], the temperament of the Pythagorean comma, equivalent to 12edo | *[[Compton]], the temperament of the Pythagorean comma, equivalent to 12edo | ||
| Line 100: | Line 99: | ||
*[[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|well temperaments]] generated by tempered 4/3s or 3/2s, equivalent to 12edo as compton and meantone | *Various historical [[Well temperament|well temperaments]] generated by tempered 4/3s or 3/2s, equivalent to 12edo as compton and meantone | ||
{{Navbox intervals}} | {{Navbox intervals}} | ||