15/13

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
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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 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

• Gallery of Just Intervals,
• The Archipelago
• 26/15 its octave complement