Meter
Ratio | 703125/702464 |
Factorization | 2^{-11} × 3^{2} × 5^{7} × 7^{-3} |
Monzo | [-11 2 7 -3⟩ |
Size in cents | 1.6282794¢ |
Names | meter, metric comma |
Color name | Lr^{3}y^{7}-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 (log_{2} nd) | 38.8455 |
Weil height (log_{2} max(n, d)) | 38.8468 |
Wilson height (sopfr (nd)) | 84 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~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
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^{[1]}. It is not clear how it later became meter.