Laser comma
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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
0.9356472¢
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
| Interval information |
(Shannon, [math]\sqrt{nd}[/math])
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.