Septendecima

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	1.431257¢
Name	septendecima
Color name	LLy34-8, lala-sebiyo negative octave
FJS name	[math]\displaystyle{ \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]\displaystyle{ \sqrt{nd} }[/math])	~1.21895 bits
Comma size	unnoticeable
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The septendecima (monzo: [-52 -17 34⟩) is an unnoticeable 5-limit comma. It is the difference between a stack of seventeen 25/24's and one octave.

Temperaments

The temperament which tempers out only this comma is 5-limit chlorine. The octave must be divisible by 17 in order to temper out this comma. Any edo such as 311edo, which is not a multiple of 17 cannot be tempering out this comma.

Etymology

This comma was once named by Gene Ward Smith in 2001 in terms of the corresponding temperament, heptadecal, for the temperament has 17 periods per octave. The logical name for the comma would be heptadeca, following enneadeca. It was unclear how and why it was changed to septendecima, the Latin equivalent.