What are the ratios of Just Intonation?

"Just" Intonation refers to simple low-integer-ratio frequency ratios developed by the Ancient Greeks:

• 1:1 unison.
• 2:1 octave.
• 3:2 perfect fifth.
• 4:3 perfect fourth.
• 5:3 major sixth.
• 5:4 major third.
• 8:5 minor sixth.
• 6:5 minor third.

1. How many notes are in just intonation?
2. Is just intonation Pythagorean?
3. What is 5 limit just intonation?

How many notes are in just intonation?

This twelve-tone scale is fairly close to equal temperament, but it does not offer much advantage for tonal harmony because only the perfect intervals (fourth, fifth, and octave) are simple enough to sound pure.

Is just intonation Pythagorean?

Applying the first part of this concept, some scholars refer to Pythagorean tuning as "3-limit just intonation," since all intervals are derived either from fifths (3:2) or octaves (2:1), ratios involving 3 as the largest prime.

What is 5 limit just intonation?

The 5-limit consists of all just intonation intervals whose numerators and denominators are both products of the primes 2, 3, and 5; these are sometimes called regular numbers. Some examples of 5-limit intervals are 5/4, 6/5, 10/9 and 81/80.