1716/1715: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Name = lummic comma
| Name = lummic comma
| Color name = 3o1or<sup>3</sup>g-2
| Color name = 3o1or<sup>3</sup>g-2, tholotriru-agu negative 2nd
| Comma = yes
| Comma = yes
}}
}}
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Tempering it out leads to the rank-5 '''lummic temperament'''. It is tempered out by several notable edos including [[72edo]], [[270edo]] and [[400edo]] among others.  
Tempering it out leads to the rank-5 '''lummic temperament'''. It is tempered out by several notable edos including [[72edo]], [[270edo]] and [[400edo]] among others.  
== Etymology ==
This comma was named after [[Carl Lumma]]. Perhaps interestingly, a ''lummisma'' was first proposed by [[Gene Ward Smith]] in 2011 as a name for 1001/1000, but Carl Lumma pointed out that 1716/1715 was "better"<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_97947.html Yahoo! Tuning Group | ''Short commas'']</ref>, which might ultimately led to this comma being named so.
== Notes ==


[[Category:Lummic]]
[[Category:Lummic]]
[[Category:Commas named after composers]]
[[Category:Commas named after music theorists]]

Latest revision as of 15:22, 14 June 2025

Interval information
Ratio 1716/1715
Factorization 22 × 3 × 5-1 × 7-3 × 11 × 13
Monzo [2 1 -1 -3 1 1
Size in cents 1.009172¢
Name lummic comma
Color name 3o1or3g-2, tholotriru-agu negative 2nd
FJS name [math]\displaystyle{ \text{M}{-2}^{11,13}_{5,7,7,7} }[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 21.4888
Weil height (log2 max(n, d)) 21.4897
Wilson height (sopfr(nd)) 57
Comma size unnoticeable
Open this interval in xen-calc

The lummic comma, 1716/1715, is a 13-limit superparticular comma measuring about 1.0 ¢. It often arises as the difference between simpler commas: (176/175)/(196/195), (351/350)/(441/440), (1573/1568)/(385/384), (540/539)/(1575/1573), and (1001/1000)/(2401/2400). It factors into (2080/2079)(9801/9800).

Tempering it out leads to the rank-5 lummic temperament. It is tempered out by several notable edos including 72edo, 270edo and 400edo among others.

Etymology

This comma was named after Carl Lumma. Perhaps interestingly, a lummisma was first proposed by Gene Ward Smith in 2011 as a name for 1001/1000, but Carl Lumma pointed out that 1716/1715 was "better"[1], which might ultimately led to this comma being named so.

Notes