217/216
Jump to navigation
Jump to search
Ratio
217/216
Subgroup monzo
2.3.7.31 [-3 -3 1 1⟩
Size in cents
7.996476¢
Name
tricesimoprimal kleisma
FJS name
[math]\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]\sqrt{nd}[/math])
~1.77468 bits
Comma size
small
Open this interval in xen-calc
| Interval information |
reduced
(Shannon, [math]\sqrt{nd}[/math])
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 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).