Chalmersia: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Aura (talk | contribs)
No edit summary
Spelling variants need not be listed in infobox, especially if they are mistakes
Line 4: Line 4:
| Monzo = -6 6 -2 -1 -1 2
| Monzo = -6 6 -2 -1 -1 2
| Cents = 0.01405
| Cents = 0.01405
| Name = chalmersia, <br> chalmersma, <br> chalmersima, <br> chalmerisma, <br> chalmersisma
| Name = chalmersia
| Color name = Lathotholurugugu comma
| Color name = Lathotholurugugu comma
| FJS name =  
| FJS name =  
Line 10: Line 10:
}}
}}


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.  
The '''chalmersia'''<ref>as in [http://www.huygens-fokker.org/docs/intervals.html Huygens-Fokker Foundation's interval list]. There are other spelling variants that this comma sometimes goes by, including ''chalmersma'', ''chalmersima'', ''chalmerisma'' and ''chalmersisma'', but these are probably mistakes. </ref> is an [[unnoticeable comma|unnoticeable]] [[13-limit]] comma with a ratio of '''123201/123200''' and a value of approximately 0.014 [[cent]]s. 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.  


Although "chalmersia" is the name that is primarily used for this article as it is the name for this comma on the [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'''.  Regardless of the exact name used for this comma, it seems that the temperament itself was named in honor of [[John H. Chalmers]], and that all the various names for this comma are etymologically derived from the temperament name.
<references/>


== See also ==
== See also ==

Revision as of 07:25, 27 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[1] is an unnoticeable 13-limit comma with a ratio of 123201/123200 and a value of approximately 0.014 cents. 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.

  1. as in Huygens-Fokker Foundation's interval list. There are other spelling variants that this comma sometimes goes by, including chalmersma, chalmersima, chalmerisma and chalmersisma, but these are probably mistakes.

See also