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}^{5,5}_{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
Comma size	small
S-expressions	S15, S25 × S26 × S27
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Septimal kleisma

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. In the 11-limit, it factors neatly into (385/384)(540/539).

Temperaments

Tempering out this comma alone in the 7-limit leads to the marvel temperament, which enables marvel chords. See marvel family for the family of rank-3 temperaments where it is tempered out. See marvel temperaments for a collection of rank-2 temperaments where it is tempered out.

Approximation

If we do not 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.

See also

• Small comma
• Gallery of just intervals
• List of superparticular intervals