Laser comma
(Redirected from 57375/57344)
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| Ratio | 57375/57344 |
| Factorization | 2-13 × 33 × 53 × 7-1 × 17 |
| Monzo | [-13 3 3 -1 0 0 1⟩ |
| Size in cents | 0.93564722¢ |
| Name | laser comma |
| Color name | L17ory3-2, lasorutriyo negative 2nd |
| FJS name | [math]\text{d}{-2}^{5,5,5,17}_{7}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 31.6155 |
| Weil height (log2 max(n, d)) | 31.6163 |
| Wilson height (sopfr(nd)) | 74 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.20641 bits |
| Comma size | unnoticeable |
| S-expression | S15 / S16 |
| open this interval in xen-calc | |
The laser comma, 57375/57344 is an unnoticeable 17-limit (and 2.3.5.7.17) comma that separates a stack of three 16/15 diatonic semitones from a 17/14 supraminor third. It also equates the 17/16 semitone with 3584/3375, which, while far more complex than the more typical approximation of 16/15, is also far more accurate.
As an ultraparticular, it is also the difference between 225/224 and 256/255, two commonly tempered commas in the 7- and 17-limits, respectively.
Interestingly, this happens to be the difference between a 32805/32768 schisma and the 1701/1700 palingenesis.