Sesdecal comma

Interval information

Ratio	234375/234256
Factorization	2-4 × 3 × 57 × 11-4
Monzo	[-4 1 7 0 -4⟩
Size in cents	0.8792285¢
Name	sesdecal comma
FJS name	[math]\displaystyle{ \text{dddd}{-2}^{5,5,5,5,5,5,5}_{11,11,11,11} }[/math]
Special properties	reduced
Tenney height (log2 nd)	35.6762
Weil height (log2 max(n, d))	35.6769
Wilson height (sopfr(nd))	90
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.20545 bits
Comma size	unnoticeable
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The sesdecal comma (monzo: [-4 1 7 0 -4⟩, ratio: 234375/234256) is an unnoticeable 11-limit (also 2.3.5.11 subgroup) comma measuring about 0.879 cents. It is the difference between four intervals of 25/22 and 5/3. This comma also functions as a way to introduce prime 41 into the 2.3.5.11 subgroup, by noting this to be the difference between 1025/1024 and 600281/600000, and also connects to harmonies of 31 through tempering out 961/960 and 3751/3750 implying that 234375/234256 is also tempered out.

Etymology

The sesdecal was named before 2023, though its etymology seems lost. The "decal" part presumably refers to the decal temperament, which tempers it out.