List of intervals in 5-limit just intonation

The intervals of 5-limit just intonation (prime limit, not odd limit) are ratios involving only the powers of 2, 3, and 5. The fundamental intervals are the superparticular ratios 2/1 (the octave), 3/2 (the perfect fifth) and 5/4 (the major third). That is, the notes of the major triad are in the ratio 1:5/4:3/2 or 4:5:6.

In all tunings, the major third is equivalent to two major seconds. However, because just intonation does not allow the irrational ratio of $\sqrt{5}$/2, two different frequency ratios are used: the major tone (9/8) and the minor tone (10/9).

The intervals within the diatonic scale are shown in the table below.

(The Pythagorean minor second is found by adding 5 perfect fourths.)

The table below shows how these steps map to the first 31 scientific harmonics, transposed into a single octave.

§ These intervals also appear in the upper table, although with different ratios.