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. 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

TODO: Insert info about different tuning ranges of the perfect fifth here. Discussion of the gentle region should go here and be mirrored in Neogothic interval. Also discuss edo tunings of the perfect fifth, and the 685.7-720 cent diatonic range.