Perfect fifth
The perfect fifth (P5), represented by the frequency ratio 3/2, is a generator of the MOS diatonic scale and of Pythagorean tuning. It is also the most consonant octave-reduced interval after the octave itself. The note a perfect fifth above the root serves as an important structural anchor for scales, similarly to the perfect fourth. Nearly all musical cultures use the perfect fifth. The perfect fifth contrasts with the diatonic diminished fifth, a dissonant "tritone" interval. In purely tuned just intonation, it is approximately 702 cents in size, but as an interval in the abstract diatonic scale it may range from 685.7 to 720 cents, depending on the tuning.
Due to the fifth's role in diatonic, Pythagorean intervals are usually conceptualized in terms of a chain of fifths. Many temperaments, called monocot temperaments, use the perfect fifth as a generator. Additionally, it is the bounding interval of most common triads.
Edos that approximate the perfect fifth well, in order of increasing accuracy, include 5, 12, 29, 41, and 53edo.
Scale info
The diatonic scale contains six perfect fifths. In the Ionian mode, perfect fifths are found on all but the 7th degree of the scale, which instead has a diminished fifth.
Just intonation
The perfect fifth is a superparticular interval.
Tuning range
| Range (in cents) | Description | Notable edos |
|---|---|---|
| 685.7-720 | Range of fifths capable of generating a diatonic scale. | 4\7 = 685.7c, 7\12 = 700c, 3\5 = 720c |
| 666.7-685.7 | Range of intervals that generate a soft antidiatonic scale and may be considered fifths. | 9\16 = 675c |
| ~678-693 | Range of intervals that generate an equiheptatonic diatonic or antidiatonic scale. | 13\23 = 678.3c, 4\7 = 685.7c, 15\26 = 692.3c |
| 691.5-694.7 | Range of viable generators of Flattone temperament. | 26\45 = 693.3c, 15\26 = 692.3c |
| 694.7-700 | Range of viable generators of Septimal Meantone temperament. | 11\19 = 694.7c, 18\31 = 696.8c, 29\50 = 696c, 7\12 = 700c |
| 698.5-705.5 | Pythagorean tuning; fifths within a just noticeable difference of just intonation. Contains schismic tunings. | 7\12 = 700c; 24\41 = 702.4c; 31\53 = 701.9c |
| 703.4-705.9 | Range of "gentle" fifths, which generate neogothic intervals. | 17\29 = 703.4c; 10\17 = 705.9c |
| ~709-711 | Range of viable generators of Superpyth temperament. | 13\22 = 709.1c; 16\27 = 711.1c |
| ~711-715 | Range of viable generators of other Archy temperaments. | 22\37 = 713.5c |
| ~709-730 | Range of intervals that generate an equipentatonic pentic or antipentic scale. | 22\37 = 713.5c, 3\5 = 720c, 23\38 = 726.3c |
