Chalmersia: Difference between revisions

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Created page with "{{Infobox Interval | Icon = | Ratio = 123201/123200 | Monzo = -6 6 -2 -1 -1 2 | Cents = 0.01405 | Name = chalmersia | Color name = Lathotholurugugu comma | FJS name = | Soun..."
 
Simpler approaches to this comma
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The '''chalmersia''' is an [[unnoticeable comma|unnoticeable]] [[13-limit]] comma with a ratio of '''123201/123200''' and a value of approximately 0.01 [[cent|cents]]. Tempering this comma out 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- a feature highly characteristic of '''[[chalmers temperaments]]'''.
The '''chalmersia''' is an [[unnoticeable comma|unnoticeable]] [[13-limit]] comma with a ratio of '''123201/123200''' and a value of approximately 0.014 [[cent]]s. 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.  


== See also ==
== See also ==
* [[Chalmers temperaments]]
* [[Unnoticeable comma]]
* [[Unnoticeable comma]]
* [[List of superparticular intervals]]
* [[List of superparticular intervals]]
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[[Category:Ratio]]
[[Category:Ratio]]
[[Category:Superparticular]]
[[Category:Superparticular]]
[[Category:Chalmers]]

Revision as of 14:35, 26 December 2020

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
Open this interval in xen-calc

The chalmersia is an unnoticeable 13-limit comma with a ratio of 123201/123200 and a value of approximately 0.014 cents. 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.

See also