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The term perfect has also been used as a synonym of just, to distinguish intervals tuned to ratios of small integers from those that are "tempered" or "imperfect" in various other tuning systems, such as equal temperament. [6] [7] The perfect unison has a pitch ratio 1:1, the perfect octave 2:1, the perfect fourth 4:3, and the perfect fifth 3:2.
All-fifths tuning. All-fifths tuning refers to the set of tunings for string instruments in which each interval between consecutive open strings is a perfect fifth. All-fifths tuning is the standard tuning for mandolin and violin and it is an alternative tuning for guitars. All-fifths tuning is also called fifths, perfect fifths, or mandoguitar ...
In terms of frequency ratios, in order to close the circle of fifths, the product of the fifths' ratios must be 128 (since the twelve fifths, if closed in a circle, span seven octaves exactly; an octave is 2:1, and 2 7 = 128), and if f is the size of a fifth, 128 : f 11, or f 11 : 128, will be the size of the wolf.
Comparison of notes derived from, or near, twelve perfect fifths (B ♯). In musical tuning, a temperament is a tuning system that slightly compromises the pure intervals of just intonation to meet other requirements. Most modern Western musical instruments are tuned in the equal temperament system.
A Pythagorean comma is the difference between twelve justly tuned perfect fifths and seven octaves. It is expressed by the frequency ratio 531441:524288 (23.5 cents). A syntonic comma is the difference between four justly tuned perfect fifths and two octaves plus a major third. It is expressed by the ratio 81:80 (21.5 cents).
To build chords, Fripp uses "perfect intervals in fourths, fifths and octaves", so avoiding minor thirds and especially major thirds, [26] which are sharp in equal temperament tuning (in comparison to thirds in just intonation). It is a challenge to adapt conventional guitar-chords to new standard tuning, which is based on all-fifths tuning. [27]
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By definition, in quarter-comma meantone 1 so-called "perfect" fifth (P5 in the table) has a size of approximately 696.6 cents ( 700 − ε cents, where ε ≈ 3.422 cents); since the average size of the 12 fifths must equal exactly 700 cents (as in equal temperament), the other one must have a size of 700 + 11 ε cents, which is about 737.6 ...