Chalmersia: Difference between revisions
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The '''chalmersia''' is an [[unnoticeable comma|unnoticeable]] [[13-limit]] comma with a ratio of '''123201/123200''' and a size of approximately 0.014{{cent}}. 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 '''chalmersic 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}}. 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 '''chalmersic 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. | ||
It factors into the two smallest 17-limit superparticular ratios: 123201/123200 = (194481/194480)(336141/336140). | |||
== Etymology == | == Etymology == | ||
The chalmersia was named by [[Gene Ward Smith]] in 2003 after [[John Chalmers]]. | The chalmersia was named by [[Gene Ward Smith]] in 2003 after [[John Chalmers]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_7316.html Yahoo! Tuning Group | ''Nameable 13-limit'']</ref>. | ||
:''The remarkable 123201/123200 might be named the chalmersia, since John Chalmers is presumably the first to see it.'' | :''The remarkable 123201/123200 might be named the chalmersia, since John Chalmers is presumably the first to see it.'' | ||
—Gene Ward Smith | —Gene Ward Smith | ||
== See also == | == See also == | ||
* [[Unnoticeable comma]] | * [[Unnoticeable comma]] | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
== Notes == | |||
[[Category:Chalmersic]] | [[Category:Chalmersic]] | ||
Revision as of 11:58, 10 February 2023
| Interval information |
reduced
S78 / S80
The chalmersia is an unnoticeable 13-limit comma with a ratio of 123201/123200 and a size of approximately 0.014 ¢. 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 chalmersic 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.
It factors into the two smallest 17-limit superparticular ratios: 123201/123200 = (194481/194480)(336141/336140).
Etymology
The chalmersia was named by Gene Ward Smith in 2003 after John Chalmers[1].
- The remarkable 123201/123200 might be named the chalmersia, since John Chalmers is presumably the first to see it.
—Gene Ward Smith