625/624

Interval information

Ratio

625/624

Factorization

2^-4 × 3^-1 × 5⁴ × 13^-1

Monzo

[-4 -1 4 0 0 -1⟩

Size in cents

2.772193¢

Names

vinctrias comma,
vinctriasma

FJS name

[math]\displaystyle{ \text{dd}{-2}^{5,5,5,5}_{13} }[/math]

Special properties

square superparticular,
reduced

Tenney height (log₂ nd)

18.5731

Weil height (log₂ max(n, d))

18.5754

Wilson height (sopfr(nd))

44

Open this interval in xen-calc

625/624, currently dubbed the vinctrias comma or vinctriasma, is an unnoticable 13-limit comma with a value of roughly 2.77 cents. Tempering out this comma not only equates 25/24 with 26/25- splitting 13/12 in half and going part of the way towards splitting the 9/8 whole tone into three (the other comma that needs to be tempered in order to finish this job is 676/675)- but also equates 39/32 with the interval that results from stacking four 5/4 major thirds then octave-reducing.

The term "vinctrias", from which both of this comma's names are derived, is a portmanteau of Latin vincire (to bind, to tie up) and Latin trias (referring to the the number three or to a triad) that was coined in reference to the fact that 625/624 is tempered out in such well-known temperaments as Catakleismic, Tritikleismic, Quadritikleismic, Octoid, Benediction, Sqrtphi, Ekadash, Countercata, Widefourth, Portentious, Yajna, Enlil, Hanuman, Marvel and Agni, and to how tempering it out simulataneously equates different kinds of neutral third and goes part of the way towards dividing the whole tone into thirds.