57375/57344
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Ratio | 57375/57344 |
Factorization | 2^{-13} × 3^{3} × 5^{3} × 7^{-1} × 17 |
Monzo | [-13 3 3 -1 0 0 1⟩ |
Size in cents | 0.93564722¢ |
Name | laser comma |
Color name | L17ory^{3}-2, lasorutriyo negative 2nd |
FJS name | [math]\text{d}{-2}^{5,5,5,17}_{7}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 31.6155 |
Weil height (log_{2} max(n, d)) | 31.6163 |
Wilson height (sopfr (nd)) | 74 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.40123 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.