Septendecima: Difference between revisions

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| Monzo = -52 -17 34
| Monzo = -52 -17 34
| Name = septendecima
| Name = septendecima
| FJS name = -
| Color name = LLy<sup>34</sup>-8, lala-sebiyo negative octave
| Color name = LLy<sup>34</sup>-8, lala-sebiyo negative octave
| Comma = yes
| Comma = yes
}}
}}
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 [[2/1|octave]].


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]].  
== Temperaments ==
The [[regular temperament|temperament]] which [[tempering out|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.  


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.  
== 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<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2121.html Yahoo! Tuning Group | ''Shismic & co'']</ref>. The logical name for the comma would be ''heptadeca'', following ''[[enneadeca]]''. By 2012, it had been changed to ''septendecima'', the Latin equivalent<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104268.html#104413 Yahoo! Tuning Group | ''2D temperament names, part I -- reclassified temperaments from message #101780'']</ref>. It was unclear how and why the change was made.  
 
== References ==


[[Category:Chlorine]]
[[Category:Chlorine]]
[[Category:Commas named for their periods per equave]]

Latest revision as of 09:03, 5 March 2026

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{ - }[/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.

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[1]. The logical name for the comma would be heptadeca, following enneadeca. By 2012, it had been changed to septendecima, the Latin equivalent[2]. It was unclear how and why the change was made.

References