15/13: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Inthar (talk | contribs)
mNo edit summary
m +FJS name; cleanup
Line 4: Line 4:
| Monzo = 0 1 1 0 0 -1
| Monzo = 0 1 1 0 0 -1
| Cents = 247.74105
| Cents = 247.74105
| Name = tredecimal super second, or ~ sub third
| Name = tridecimal ultramajor second, <br>tridecimal ultraminor third
| Color name = 3uy2, thuyo 2nd
| FJS name = A2<sup>5</sup><sub>13</sub>
| Sound = jid_15_13_pluck_adu_dr220.mp3
| Sound = jid_15_13_pluck_adu_dr220.mp3
| Color name = 3uy2, thuyo 2nd
}}
}}


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 "supermajor second".  


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


[[Category:13-limit]]
[[Category:13-limit]]
Line 20: Line 22:
[[Category:Interseptimal]]
[[Category:Interseptimal]]
[[Category:Third]]
[[Category:Third]]
[[Category:Subminor third]]
[[Category:Second]]
[[Category:Second]]
[[Category:Supermajor second]]
[[Category:Supermajor second]]

Revision as of 11:43, 20 September 2020

Interval information
Ratio 15/13
Factorization 3 × 5 × 13-1
Monzo [0 1 1 0 0 -1
Size in cents 247.7411¢
Names tridecimal ultramajor second,
tridecimal ultraminor third
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 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 "supermajor second".

See also