736/729

Interval information

Ratio	736/729
Subgroup monzo	2.3.23 [5 -6 1⟩
Size in cents	16.54434¢
Name	23-limit Tenney/Cage comma (HEJI)
Color name	s23o2, satwetho 2nd
FJS name	[math]\displaystyle{ \text{P1}^{23} }[/math]
Special properties	reduced
Tenney height (log2 nd)	19.0333
Weil height (log2 max(n, d))	19.0471
Wilson height (sopfr(nd))	51
Comma size	small
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736/729, the 23-limit Tenney/Cage comma, is a 2.3.23 subgroup comma. It is the amount by which the octave-reduced 23rd harmonic 23/16 exceeds the Pythagorean augemented fourth (729/512).

Notation

This interval is significant in the Functional Just System and Helmholtz-Ellis notation as the formal comma to translate a Pythagorean interval to a nearby 23-limit (vicesimotertial) interval.

Sagittal notation

In the Sagittal system, this comma (possibly tempered) is represented by the sagittal ⁠ ⁠ and is called the 23 comma, or 23C for short, because the simplest interval it notates is 23/1 (equiv. 23/16), as for example in F-B⁠ ⁠⁠ ⁠. The downward version is called 1/23C or 23C down and is represented by ⁠ ⁠.