Meter

Interval information

Ratio	703125/702464
Factorization	2-11 × 32 × 57 × 7-3
Monzo	[-11 2 7 -3⟩
Size in cents	1.628279¢
Names	meter, metric comma, meter comma
FJS name	[math]\displaystyle{ \text{5d}{-4}^{5,5,5,5,5,5,5}_{7,7,7} }[/math]
Special properties	reduced
Tenney height (log2 nd)	38.8455
Weil height (log2 max(n, d))	38.8468
Wilson height (sopfr(nd))	84
Comma size	unnoticeable
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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 ET sequence: 12, 19, 31, 81, 90, 102d, 109, 121, 140, 152, 171, 665, 836, 1007, 2185, 3192c

Badness: 0.1498 × 10^-3

See also

• Unnoticeable comma