7-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 7-odd-limit is the set of all rational intervals which can be written as 2^k(a/b) where a, b ≤ 7 and k is an integer. To the 5-odd-limit, it adds 3 pairs of octave-reduced intervals involving 7.

Below is a list of all octave-reduced intervals in the 7-odd-limit.

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

Ratio	Size (¢)	Color name		Name(s)
8/7	231.174	r2	ru 2nd	septimal supermajor second
7/6	266.871	z3	zo 3rd	septimal minor third
7/5	582.512	zg5	zogu 5th	narrow tritone / Huygens tritone
10/7	617.488	ry4	ruyo 4th	high tritone / Euler's tritone
12/7	933.129	r6	ru 6th	septimal supermajor sixth
7/4	968.826	z7	zo 7th	harmonic seventh

The smallest equal division of the octave which is consistent in the 7-odd-limit is 4edo; that which is distinctly consistent in the same is 27edo. The density of edos consistent in the 7-odd-limit is 1/2.

See also

• 7-limit (prime limit)
• Diamond7 – as a scale