5-odd-limit

Odd limit

---

1-odd-limit  3-odd-limit →

The 5-odd-limit is the set of all rational intervals which can be written as 2^k(a/b) where a, b ≤ 5 and k is an integer. To the 3-odd-limit, it adds 2 pairs of octave-reduced intervals involving 5.

Below is a list of all octave-reduced intervals in the 5-odd-limit.

• 1/1
• 6/5, 5/3
• 5/4, 8/5
• 4/3, 3/2

Ratio	Size (¢)	Color name		Name
6/5	315.641	g3	gu 3rd	minor third
5/4	386.314	y3	yo 3rd	major third
8/5	813.686	g6	gu 6th	minor sixth
5/3	884.359	y6	yo 6th	major sixth

The smallest equal division of the octave which is consistent through to the 5-odd-limit is 3edo; that which is distinctly consistent through to the same is 9edo.

See also

• 5-limit (prime limit)
• Diamond5 – as a scale