1701/1690: Difference between revisions

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Created page with "{{Infobox interval | Name = Kuhnausma | Comma = yes }} The '''Kuhnausma''' is a small 13-limit comma. It is tempered out in 41edo among others. It tempers out the difference between 189/169 and 10/9. == Etymology == This comma was named by phlub in 2026 after {{w|Johann Kuhnau}}. He published the first part of his Neue Clavier-Übung in 1690, and was appointed {{w|Thomaskantor}} of Leipzig in 1701, a post which h..."
 
Decompose the intervals more. + factorization. Style
 
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{{Infobox interval
{{Infobox interval
| Name = Kuhnausma
| Name = kuhnausma
| Comma = yes
| Comma = yes
}}
}}
The '''Kuhnausma''' is a [[small comma|small]] [[13-limit]] [[comma]]. It is [[tempering out|tempered out]] in [[41edo]] among others. It tempers out the difference between [[189/169]] and [[10/9]].
The '''kuhnausma''' is a [[small comma|small]] [[13-limit]] [[comma]]. It is [[tempering out|tempered out]] in [[41edo]] among others. It is the amount by which a stack of two [[13/9]]'s exceeds [[21/10]]. Alternatively, it is the difference between [[21/13]] and a stack consisting of [[10/9]] and [[13/9]].
 
It factors into simpler commas as ([[196/195]])⋅([[729/728]]) or ([[441/440]])⋅([[1188/1183]]).  


== Etymology ==
== Etymology ==

Latest revision as of 06:53, 28 February 2026

Interval information
Ratio 1701/1690
Factorization 2-1 × 35 × 5-1 × 7 × 13-2
Monzo [-1 5 -1 1 0 -2
Size in cents 11.23187¢
Name kuhnausma
FJS name [math]\displaystyle{ \text{A1}^{7}_{5,13,13} }[/math]
Special properties reduced
Tenney norm (log2 nd) 21.455
Weil norm (log2 max(n, d)) 21.4643
Wilson norm (sopfr(nd)) 55
Comma size small
Open this interval in xen-calc

The kuhnausma is a small 13-limit comma. It is tempered out in 41edo among others. It is the amount by which a stack of two 13/9's exceeds 21/10. Alternatively, it is the difference between 21/13 and a stack consisting of 10/9 and 13/9.

It factors into simpler commas as (196/195)⋅(729/728) or (441/440)⋅(1188/1183).

Etymology

This comma was named by phlub in 2026 after Johann Kuhnau. He published the first part of his Neue Clavier-Übung in 1690, and was appointed Thomaskantor of Leipzig in 1701, a post which he held 21 years until his death, when he was succeeded by Johann Sebastian Bach.