9-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 9-odd-limit is the set of all rational intervals which can be written as 2^k(a/b) where a, b ≤ 9 and k is an integer. To the 7-odd-limit, it adds 3 pairs of octave-reduced intervals involving 9.

Below is a list of all octave-reduced intervals in the 9-odd-limit.

• 1/1
• 10/9, 9/5
• 9/8, 16/9
• 8/7, 7/4
• 7/6, 12/7
• 6/5, 5/3
• 5/4, 8/5
• 9/7, 14/9
• 4/3, 3/2
• 7/5, 10/7

Ratio	Size (¢)	Color name		Name(s)
10/9	182.404	y2	yo 2nd	classic whole tone minor whole tone
9/8	203.910	w2	wa 2nd	Pythagorean whole tone major whole tone
9/7	435.084	r3	ru 3rd	septimal supermajor third
14/9	764.916	z6	zo 6th	septimal subminor sixth
16/9	996.090	w7	wa 7th	Pythagorean minor seventh
9/5	1017.596	g7	gu 7th	classic minor seventh

The smallest equal division of the octave which is consistent in the 9-odd-limit is 5edo; that which is distinctly consistent in the same is 41edo. The density of edos consistent in the 9-odd-limit is 1/4.

See also

• Diamond9 – as a scale