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, 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 sequence: 12, 19, 31, 81, 90, 102d, 109, 121, 140, 152, 171, 665, 836, 1007, 2185, 3192c
Badness: 0.1498 × 10-3