6144/6125: Difference between revisions

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'''6144/6125''', the '''porwell comma''', is a [[7-limit]] [[small comma]] measuring about 5.4 cents. It is the amount by which a stack of two [[35/32]]'s falls short of [[6/5]], and the amount by which a stack of two [[48/35]]'s exceeds [[15/8]].  
'''6144/6125''', the '''porwell comma''', is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 5.4 [[cent]]s. It is the amount by which a stack of two [[35/32]]'s falls short of [[6/5]], and the amount by which a stack of two [[48/35]]'s exceeds [[15/8]].  


== Temperaments ==
== Temperaments ==
Tempering out this comma leads to the [[porwell family]] of temperaments.  
Tempering out this comma alone in the 7-limit leads to the [[porwell]] temperament. See [[Porwell family]] for the family of rank-3 temperaments where it is tempered out. See [[Porwell temperaments]] for a collection of rank-2 temperaments where it is tempered out.  


== Etymology ==
== Etymology ==
The porwell comma was named by [[Gene Ward Smith]] in 2010. It is the concatenation of [[porcupine]] and [[orwell]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_88759.html ''Some unnamed 7-limit temperaments'']</ref>.
This comma was first named as ''hewuermity'' by [[Gene Ward Smith]] in 2005 as a contraction of ''[[hemiwürschmidt]]'' and ''[[amity]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group | ''Seven limit comma names from pairs of temperament names'']</ref>, and was renamed to ''porwell'' in 2010 as a contraction of ''[[porcupine]]'' and ''[[orwell]]'' per [[Petr Pařízek]]'s suggestion<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_88759.html Yahoo! Tuning Group | ''Some unnamed 7-limit temperaments'']</ref>.
 
== See also ==
* [[Porwell family]], the rank-3 family where it is tempered out
* [[Porwell temperaments]], a collection of rank-2 temperaments where it is tempered out
* [[Small comma]]


== Notes ==
== Notes ==


[[Category:Porwell]]
[[Category:Porwell]]
[[Category:Commas named by combining multiple temperament names]]
[[Category:Commas named after other creatives]]
[[Category:Commas named after compositions]]

Latest revision as of 02:14, 4 November 2024

Interval information
Ratio 6144/6125
Factorization 211 × 3 × 5-3 × 7-2
Monzo [11 1 -3 -2
Size in cents 5.362046¢
Name porwell comma
Color name srrg31, sarurutrigu 1sn,
Sarurutrigu comma
FJS name [math]\displaystyle{ \text{d1}_{5,5,5,7,7} }[/math]
Special properties reduced
Tenney height (log2 nd) 25.1655
Weil height (log2 max(n, d)) 25.1699
Wilson height (sopfr(nd)) 54
Comma size small
Open this interval in xen-calc

6144/6125, the porwell comma, is a small 7-limit comma measuring about 5.4 cents. It is the amount by which a stack of two 35/32's falls short of 6/5, and the amount by which a stack of two 48/35's exceeds 15/8.

Temperaments

Tempering out this comma alone in the 7-limit leads to the porwell temperament. See Porwell family for the family of rank-3 temperaments where it is tempered out. See Porwell temperaments for a collection of rank-2 temperaments where it is tempered out.

Etymology

This comma was first named as hewuermity by Gene Ward Smith in 2005 as a contraction of hemiwürschmidt and amity[1], and was renamed to porwell in 2010 as a contraction of porcupine and orwell per Petr Pařízek's suggestion[2].

Notes