15/13: Difference between revisions

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In [[13-limit]] [[Just Intonation]], 15/13 is an interval measuring about 247.7¢. In the language of [[Margo Schulter]], 15/13 is an instance of an [[interseptimal]] interval, as it falls in an ambiguous zone between two septimal extremes -- namely the large major second [[8/7]] and the small minor third [[7/6]]. (15/13)*([[13/10]])=[[3/2]], which implies that 15/13 and 13/10 make a 3/2 perfect fifth. Thus you can make a [[List_of_root-3rd-P5_triads_in_JI|root-3rd-P5]] triad that goes 26:30:39, with a 15/13 "inframinor third" up from the root. When being used as type of second, it is given the name "ultra second" as it is even sharper than 8/7 which is often called a "super major second".  
In [[13-limit]] [[Just Intonation]], '''15/13''' is an interval measuring about 247.7¢. In the language of [[Margo Schulter]], 15/13 is an instance of an [[interseptimal]] interval, as it falls in an ambiguous zone between two septimal extremes -- namely the large major second [[8/7]] and the small minor third [[7/6]]. (15/13)*([[13/10]])=[[3/2]], which implies that 15/13 and 13/10 make a 3/2 perfect fifth. Thus you can make a [[List_of_root-3rd-P5_triads_in_JI|root-3rd-P5]] triad that goes 26:30:39, with a 15/13 "inframinor third" up from the root. When being used as type of second, it is given the name "ultra second" as it is even sharper than 8/7 which is often called a "super major second".  


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

Revision as of 21:23, 18 October 2018

Interval information
Ratio 15/13
Factorization 3 × 5 × 13-1
Monzo [0 1 1 0 0 -1
Size in cents 247.7411¢
Names tredecimal super second,
or ~ sub third
FJS name [math]\displaystyle{ \text{A2}^{5}_{13} }[/math]
Special properties reduced
Tenney norm (log2 nd) 7.60733
Weil norm (log2 max(n, d)) 7.81378
Wilson norm (sopfr(nd)) 21

[sound info]
Open this interval in xen-calc

In 13-limit Just Intonation, 15/13 is an interval measuring about 247.7¢. In the language of Margo Schulter, 15/13 is an instance of an interseptimal interval, as it falls in an ambiguous zone between two septimal extremes -- namely the large major second 8/7 and the small minor third 7/6. (15/13)*(13/10)=3/2, which implies that 15/13 and 13/10 make a 3/2 perfect fifth. Thus you can make a root-3rd-P5 triad that goes 26:30:39, with a 15/13 "inframinor third" up from the root. When being used as type of second, it is given the name "ultra second" as it is even sharper than 8/7 which is often called a "super major second".

See also