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
Color name	Lr3y7-4, latriru-asepyo negative 4th
FJS name	[math]\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
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.223 bits
Comma size	unnoticeable
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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

Optimal ET sequence: 12, 19, 31, 81, 90, 102d, 109, 121, 140, 152, 171, 665, 836, 1007, 2185, 3192c

Badness: 0.1498 × 10^-3

Etymology

This comma was first named as tertiaendec by Gene Ward Smith in 2005 as a contraction of tertiaseptal and enneadecal. It is not clear how it later became meter in 2010.