Laser comma

Interval information

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
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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.