5120/5103

Interval information

Ratio

5120/5103

Factorization

2¹⁰ × 3^-6 × 5 × 7^-1

Monzo

[10 -6 1 -1⟩

Size in cents

5.757802¢

Names

hemifamity,
7/5-kleisma

FJS name

[math]\displaystyle{ \text{P1}^{5}_{7} }[/math]

Special properties

reduced

Tenney height (log₂ nd)

24.6391

Weil height (log₂ max(n, d))

24.6439

Wilson height (sopfr(nd))

50

Open this interval in xen-calc

The hemifamity or 7/5-kleisma, 5120/5103, is a 7-limit comma measuring about 5.8 cents. It is the difference between the small septimal tritone of 7/5 and the Pythagorean diminished fifth of 1024/729. It is also the difference between 15/14 and 2187/2048, between 21/20 and 256/243, between 80/63 and 81/64, etc., hence, between the septimal comma of 64/63 and the syntonic comma of 81/80.

Tempering it out leads to the rank-3 hemifamity family, which splits the septimal quartertone 36/35 into two equal parts, each representing 81/80~64/63. Rank-2 temperaments that temper it out include hemififths and amity, to name two. Edos that temper it out include 29, 34, 41, 46, 53, 58, 87, 94, 99, 111, 140, 239, 292, 391, etc.

5120/5103

See also