Rarity comma

Interval information

Factorization	2-57 × 317 × 513
Monzo	[-57 17 13⟩
Size in cents	155.3133¢
Name	rarity comma
Color name	L4y13-5, quadla-theyo negative 5th
FJS name	[math]\text{10d}{-5}^{5,5,5,5,5,5,5,5,5,5,5,5,5}[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	114.129
Weil height (log2 max(n, d))	114.259
Wilson height (sopfr(nd))	230
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.23584 bits
Comma size	large
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Rarity comma is a 5-limit interval, which when tempered out produces the rarity temperament.

Temperaments

Tempering it out produces rarity temperament in the 5-limit. On it's own it is quite a large interval, being the size of a neutral second, however each individual generator step of the temperament is flattened by a small amount which is evenly spread out in the scale.

Etymology

Rarity comma was named by Eliora as a pronounceable shortening of "radian-thirteen", taken from comma's monzo. A radian is 57 degrees and 17 arcminutes, and the final number is 13, and thus "radian-thirteen" was collapsed to "rarity".