13/10

Interval information

Ratio	13/10
Factorization	2-1 × 5-1 × 13
Monzo	[-1 0 -1 0 0 1⟩
Size in cents	454.2139¢
Names	Barbados third, tridecimal semisixth
Color name	3og4, thogu 4th
FJS name	[math]\text{d4}^{13}_{5}[/math]
Special properties	reduced
Tenney height (log2 nd)	7.02237
Weil height (log2 max(n, d))	7.40088
Wilson height (sopfr(nd))	20
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.2437 bits
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In 13-limit just intonation, 13/10, the tridecimal semisixth is an interseptimal interval measuring about 454.2¢. It falls in an ambiguous zone between a wide major third such as 9/7 and a flat perfect fourth such as 21/16. The descriptor "interseptimal" comes from Margo Schulter, and indicates its position between those two septimal (7-based) extremes. 13/10 appears between the 10th and 13th overtones of the harmonic series and appears in such chords as 8:10:13, a quasi-augmented triad. 13/10 also appears in the relatively-simple 10:13:15 triad, which consists of an interseptimal ultramajor third (13/10) and an interseptimal inframinor third (15/13) which stack to make a 3/2 perfect fifth. It is well-approximated in 16edo, 21edo, 24edo, 29edo, 37edo, and of course, infinitely many other EDO systems.

See also

• 20/13 – its octave complement
• 15/13 – its fifth complement
• Gallery of just intervals
• List of root-3rd-P5 triads in JI
• The Archipelago