# Meter

 Ratio 703125/702464 Factorization 2-11 × 32 × 57 × 7-3 Monzo [-11 2 7 -3⟩ Size in cents 1.6282794¢ Names meter,metric comma Color name Lr3y7-4, latriru-asepyo negative 4th FJS name $\text{5d}{-4}^{5,5,5,5,5,5,5}_{7,7,7}$ Special properties reduced Tenney height (log2 nd) 38.8455 Weil height (log2 max(n, d)) 38.8468 Wilson height (sopfr (nd)) 84 Harmonic entropy(Shannon, $\sqrt{nd}$) ~1.223 bits Comma size unnoticeable open this interval in xen-calc

The meter, also known as the metric comma (monzo[-11 2 7 -3, ratio: 703125/702464), is an unnoticeable 7-limit comma with a value of approximately 1.6 cents. It is the difference between a stack of three septimal kleismas and a syntonic comma.

## Temperaments

Tempering it out leads to the metric temperament, which splits the syntonic comma into three equal parts, one for the septimal kleisma, and two for the septimal semicomma. It is also tempered out in septimal meantone, but this is a trivial case since 81/80 and 225/224 are both tempered out.

See metric microtemperaments for a collection of rank-2 temperaments where it is tempered out.

### Metric (31 & 171 & 323)

Subgroup: 2.3.5.7

Comma list: 703125/702464

Mapping[1 0 2 1], 0 1 1 3], 0 0 -3 -7]]

Optimal tuning (POTE): ~3/2 = 701.8766, ~75/56 = 505.2613