225/224

Interval information

Ratio

225/224

Factorization

2^-5 × 3² × 5² × 7^-1

Monzo

[-5 2 2 -1⟩

Size in cents

7.711523¢

Names

septimal kleisma,
marvel comma

Color name

ryy-2, ruyoyo negative 2nd,
Ruyoyo comma

FJS name

[math]\displaystyle{ \text{d}{-2}^{25}_{7} }[/math]

Special properties

square superparticular,
reduced

Tenney height (log₂ nd)

15.6211

Weil height (log₂ max(n, d))

15.6276

Wilson height (sopfr(nd))

33

Open this interval in xen-calc

The interval of 225/224, the septimal kleisma or marvel comma is a 7-limit superparticular ratio. It pops up as the difference between pairs of 7-limit ratios, for example as (15/14)/(16/15) or (45/32)/(7/5). It is also the difference between 81/80 and 126/125 and is tempered out alongside these two commas in Septimal meantone. If we don't temper out this interval and instead repeatedly stack (and octave-reduce) it, we get 311edo, where it is equal to 2 steps, meaning 311edo is a circle of 225/224's. Note that this is not true for 226/225 or 224/223, the adjacent superparticulars, as they accumulate too much error to close into a circle in 311edo.

English Wikipedia has an article on:

Septimal kleisma

Temperaments

Tempering out this comma leads to the marvel family of temperaments, which enables marvel chords.

225/224

Temperaments

See also