Meter

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Interval information
Ratio 703125/702464
Factorization 2-11 × 32 × 57 × 7-3
Monzo [-11 2 7 -3
Size in cents 1.6282794¢
Names meter,
metric comma,
meter comma
FJS name [math]\text{5d}{-4}^{5,5,5,5,5,5,5}_{7,7,7}[/math]
Special properties reduced
Tenney height (log2 n⋅d) 38.8455
Weil height (max(n, d)) 703125
Benedetti height (n⋅d) 493920000000
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.40945 bits
Comma size unnoticeable
open this interval in xen-calc

The meter, also known as the metric comma or the meter comma, is an unnoticeable 7-limit comma with a ratio of 703125/702464 and 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.

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

Optimal GPV sequence12, 19, 31, 81, 90, 102d, 109, 121, 140, 152, 171, 665, 836, 1007, 2185, 3192c

Badness: 0.1498 × 10-3

See also