3-limit tuning and intervals

Pythagorean interval

In musical tuning theory, a Pythagorean interval is a musical interval with frequency ratio equal to a power of two divided by a power of three, or vice versa. For instance, the perfect fifth with ratio 3/2 (equivalent to 31/ 21) and the perfect fourth with ratio 4/3 (equivalent to 22/ 31) are Pythagorean intervals. All the intervals between the notes of a scale are Pythagorean if they are tuned using the Pythagorean tuning system. However, some Pythagorean intervals are also used in other tuning systems. For instance, the above-mentioned Pythagorean perfect fifth and fourth are also used in just intonation. (Wikipedia).

Pythagorean interval
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Related pages

Ditone | Exponentiation | Cent (music) | Unison | Størmer's theorem | Generated collection | Syntonic comma | Perfect fifth | Pythagorean comma | Equal temperament | Interval ratio | Pythagorean tuning | List of intervals in 5-limit just intonation | Shí-èr-lǜ | Perfect fourth