Septendecima: Difference between revisions

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The '''septendecima''' ([[monzo]]: {{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. The temperament which tempers out only this comma is 5-limit [[Ragismic microtemperaments#Chlorine|chlorine]].
The '''septendecima''' ([[monzo]]: {{monzo| -52 -17 34 }}) is an [[unnoticeable comma|unnoticeable]] [[5-limit]] [[comma]]. It is the difference between a stack of seventeen [[25/24]]'s and one [[octave]].  


== See also ==
The [[regular temperament|temperament]] which [[tempering out|tempers out]] only this comma is 5-limit [[Ragismic microtemperaments #Chlorine|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.
* [[Unnoticeable comma]]


[[Category:Chlorine]]
[[Category:Chlorine]]

Revision as of 07:35, 23 July 2024

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 norm (log2 nd) 157.89
Weil norm (log2 max(n, d)) 157.891
Wilson norm (sopfr(nd)) 325
Comma size unnoticeable
Open this interval in xen-calc

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.

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.