Septendecima

From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Ratio 582 076 609 134 674 072 265 625 /
581 595 589 965 365 114 830 848
Factorization 2-52 × 3-17 × 534
Monzo [-52 -17 34
Size in cents 1.4312567¢
Name septendecima
Color name LLy34-8, lala-sebiyo negative octave
FJS name [math]\text{17d}{-8}^{5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}[/math]
Special properties reduced
Tenney height (log2 nd) 157.89
Weil height (log2 max(n, d)) 157.891
Wilson height (sopfr (nd)) 325
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.45098 bits
Comma size unnoticeable
open this interval in xen-calc

The septendecima (monzo: [-52 -17 34) is a 5-limit unnoticeable comma. It represents the difference between a stack of seventeen 25/24 intervals and one octave, and tempering it out means that 25/24 equal-step tuning is equated with 17edo. Therefore, a temperament must be divisible by 17 in order to temper out this comma, any edo such as 311edo, which isn't a multiple of 17 cannot be tempering out the 25/24 kleisma.

See also