Chalmersia: Difference between revisions

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The '''chalmersia'''<ref>As in [http://www.huygens-fokker.org/docs/intervals.html Huygens-Fokker Foundation's interval list]. There are other similar names that this comma sometimes goes by, including ''chalmersma'', ''chalmersima'', ''chalmerisma'' and ''chalmersisma'', though at least some of these are mistakes.</ref> is an [[unnoticeable comma|unnoticeable]] [[13-limit]] comma with a ratio of '''123201/123200''' and a size of approximately 0.014{{cent}}. Named in honor of [[John H. Chalmers]], it is the smallest 13-limit [[superparticular]] comma. Tempering it out equates [[351/350]] and [[352/351]], thus splitting [[176/175]] into two, and equates 385/351 and 351/320, thus splitting [[77/64]] into two – these are features highly characteristic of '''chalmers temperaments'''. In addition, it equates a stack consisting of a [[729/512]] tritone plus a [[169/128]] grave fourth with a stack consisting of a [[25/16]] augmented fifth plus a [[77/64]] minor third.  
The '''chalmersia''' is an [[unnoticeable comma|unnoticeable]] [[13-limit]] comma with a ratio of '''123201/123200''' and a size of approximately 0.014{{cent}}. Named in honor of [[John H. Chalmers]], it is the smallest 13-limit [[superparticular]] comma. Tempering it out equates [[351/350]] and [[352/351]], thus splitting [[176/175]] into two, and equates 385/351 and 351/320, thus splitting [[77/64]] into two – these are features highly characteristic of '''chalmers temperaments'''. In addition, it equates a stack consisting of a [[729/512]] tritone plus a [[169/128]] grave fourth with a stack consisting of a [[25/16]] augmented fifth plus a [[77/64]] minor third.
 
== Etymology ==
The chalmersia was named by [[Gene Ward Smith]] in 2003 after [[John Chalmers]].
 
:''The remarkable 123201/123200 might be named the chalmersia, since John Chalmers is presumably the first to see it.''
— Gene Ward Smith, [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_7316.html ''Nameable 13-limit''].  


== See also ==
== See also ==
* [[Unnoticeable comma]]
* [[Unnoticeable comma]]
* [[List of superparticular intervals]]
* [[List of superparticular intervals]]
== References ==
<references/>


[[Category:Chalmers]]
[[Category:Chalmers]]

Revision as of 09:39, 11 January 2023

Interval information
Ratio 123201/123200
Factorization 2-6 × 36 × 5-2 × 7-1 × 11-1 × 132
Monzo [-6 6 -2 -1 -1 2⟩
Size in cents 0.01405217¢
Name chalmersia
Color name Lathotholurugugu comma
FJS name [math]\displaystyle{ \text{d1}^{13,13}_{5,5,7,11} }[/math]
Special properties square superparticular,
reduced
Tenney height (log2 nd) 33.8213
Weil height (log2 max(n, d)) 33.8213
Wilson height (sopfr(nd)) 84
Comma size unnoticeable
S-expressions S351,
S78 / S80
Open this interval in xen-calc

The chalmersia is an unnoticeable 13-limit comma with a ratio of 123201/123200 and a size of approximately 0.014 ¢. Named in honor of John H. Chalmers, it is the smallest 13-limit superparticular comma. Tempering it out equates 351/350 and 352/351, thus splitting 176/175 into two, and equates 385/351 and 351/320, thus splitting 77/64 into two – these are features highly characteristic of chalmers temperaments. In addition, it equates a stack consisting of a 729/512 tritone plus a 169/128 grave fourth with a stack consisting of a 25/16 augmented fifth plus a 77/64 minor third.

Etymology

The chalmersia was named by Gene Ward Smith in 2003 after John Chalmers.

The remarkable 123201/123200 might be named the chalmersia, since John Chalmers is presumably the first to see it.

— Gene Ward Smith, Nameable 13-limit.

See also

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