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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.
Pythagorean perfect fifth on C Play ⓘ: C-G (3/2 ÷ 1/1 = 3/2).. In musical tuning theory, a Pythagorean interval is a musical interval with a frequency ratio equal to a power of two divided by a power of three, or vice versa. [1]
The Pythagorean scale is any scale which can be constructed from only pure perfect fifths (3:2) and octaves (2:1). [5] In Greek music it was used to tune tetrachords, which were composed into scales spanning an octave. [6] A distinction can be made between extended Pythagorean tuning and a 12-tone Pythagorean temperament.
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 ...
(A schismic major third is a schisma different from a just major third, eight fifths down and five octaves up, F ♭ in C.) A kleisma is the difference between six minor thirds and one tritave or perfect twelfth (an octave plus a perfect fifth), with a frequency ratio of 15625:15552 (8.1 cents) (Play ⓘ).
Pythagoras construed the intervals arithmetically, allowing for 1:1 = Unison, 2:1 = Octave, 3:2 = Fifth, 4:3 = Fourth. Pythagoras's scale consists of a stack of perfect fifths, the ratio 3:2 (see also Pythagorean Interval and Pythagorean Tuning). The earliest such description of a scale is found in Philolaus fr. B6.
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Difference between 12 just perfect fifths and seven octaves. Difference between three Pythagorean ditones (major thirds) and one octave. A just perfect fifth has a frequency ratio of 3:2. It is used in Pythagorean tuning, together with the octave, as a yardstick to define, with respect to a given initial note, the frequency of any other note.