217/216

Interval information

Ratio	217/216
Subgroup monzo	2.3.7.31 [-3 -3 1 1⟩
Size in cents	7.996476¢
Name	tricesimoprimal kleisma
FJS name	[math]\displaystyle{ \text{P1}^{7,31} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	15.5164
Weil height (log2 max(n, d))	15.5231
Wilson height (sopfr(nd))	53
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.77468 bits
Comma size	small
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217/216, the tricesimoprimal kleisma, is a small 31-limit (also 2.3.7.31-subgroup) comma measuring almost exactly 8 cents. It is the difference between 9/7 and 31/24, two intervals that commonly represent sharp supermajor/flat ultramajor thirds; as well as the difference of 8/7 from 31/27 (a good approximation of 1\5), and the difference of 28/27 from 32/31.

Etymology

This comma is known as the tricesimoprimal kleisma due to its proximity (differing only by 15625/15624) to the classical kleisma, 15625/15552 and to other commas sometimes referred to as "kleismas", such as 1029/1024 (differing by 3969/3968) and 225/224 (differing by 6076/6075).