15/13: Difference between revisions

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Go for "semifourth" for this interval
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| Monzo = 0 1 1 0 0 -1
| Monzo = 0 1 1 0 0 -1
| Cents = 247.74105
| Cents = 247.74105
| Name = tridecimal ultramajor second, <br>tridecimal inframinor third
| Name = tridecimal semifourth
| Color name = 3uy2, thuyo 2nd
| Color name = 3uy2, thuyo 2nd
| FJS name = A2<sup>5</sup><sub>13</sub>
| FJS name = A2<sup>5</sup><sub>13</sub>
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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 "supermajor second".  
In [[13-limit]] [[just intonation]], '''15/13''', the '''tridecimal semifourth''' 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 ''ultramajor second'' as it is even sharper than 8/7 which is often called a "supermajor second".  


== See also ==
== See also ==
* [[26/15]] – its [[octave complement]]
* [[26/15]] – its [[octave complement]]
* [[13/10]] – its [[fifth complement]]
* [[13/10]] – its [[fifth complement]]
* [[Gallery of Just Intervals]]
* [[Gallery of just intervals]]
* [[The Archipelago]]
* [[The Archipelago]]


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[[Category:Interval]]
[[Category:Interval]]
[[Category:Interseptimal]]
[[Category:Interseptimal]]
[[Category:Semifourth]]
[[Category:Third]]
[[Category:Third]]
[[Category:Subminor third]]
[[Category:Inframinor third]]
[[Category:Second]]
[[Category:Second]]
[[Category:Supermajor second]]
[[Category:Ultramajor second]]
[[Category:Taxicab-2]]
[[Category:Taxicab-2]]
[[Category:Whole tone]]
[[Category:Godzilla third]]
[[Category:Pages with internal sound examples]]
[[Category:Pages with internal sound examples]]

Revision as of 14:36, 10 April 2021

Interval information
Ratio 15/13
Factorization 3 × 5 × 13-1
Monzo [0 1 1 0 0 -1
Size in cents 247.7411¢
Name tridecimal semifourth
Color name 3uy2, thuyo 2nd
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, the tridecimal semifourth 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 ultramajor second as it is even sharper than 8/7 which is often called a "supermajor second".

See also