5-odd-limit

Odd limits:

---

• 1-odd-limit
• 3-odd-limit
• 5-odd-limit
• 7-odd-limit
• 9-odd-limit
• 11-odd-limit
• 13-odd-limit
• 15-odd-limit
• 17-odd-limit
• 19-odd-limit
• 21-odd-limit
• 23-odd-limit
• 25-odd-limit
• 27-odd-limit
• 29-odd-limit
• 31-odd-limit

The 5-odd-limit is the set of all rational intervals for which neither the numerator nor the denominator of the frequency ratio exceeds 5, once all powers of 2 are removed. To the 3-odd-limit, it adds 2 interval pairs 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 in the 5-odd-limit is 3edo; that which is distinctly consistent in the same is 9edo.

See also

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