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
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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.