7/11 comma

Interval information

Ratio	45927/45056
Factorization	2-12 × 38 × 7 × 11-1
Monzo	[-12 8 0 1 -1⟩
Size in cents	33.14797¢
Name	7/11 comma
Color name	L1uz1, Laluzo comma
FJS name	[math]\text{A1}^{7}_{11}[/math]
Special properties	reduced
Tenney height (log2 nd)	30.9465
Weil height (log2 max(n, d))	30.9741
Wilson height (sopfr(nd))	66
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.5015 bits
Comma size	medium
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The Sagittal 7/11 comma is a comma with a ratio of 45927/45056 and a value of approximately 33.15 cents. It is the apotome complement of 22/21, and the difference between the Pythagorean comma and the pentacircle comma (896/891). It is the comma that separates 11/7 and the Pythagorean augmented fifth, and separates 14/11 and the Pythagorean diminished fourth.

In the Sagittal system, the downward version of this comma (possibly tempered) is represented by the sagittal ⁠ ⁠ and is called the 11/7 comma, or 11/7C for short, because the simplest interval it notates is 11/7, as for example in E⁠ ⁠⁠ ⁠-B⁠ ⁠⁠ ⁠. The upward version is called 7/11C or 11/7C up and is represented by ⁠ ⁠.