Yggdrasil comma

Interval information

Factorization	210 × 3-2 × 53 × 7-5 × 11-1 × 13
Monzo	[10 -2 3 -5 -1 1⟩
Size in cents	0.1113269 ¢
Names	Yggdrasil comma, yggdrasilsma
Color name	satholuquinru-atriyoma, s3o1ur^5g^3M
FJS name	[math]\displaystyle{ \text{dd}{-3}^{5,5,5,13}_{7,7,7,7,7,11} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	41.3324
Weil norm (log2 max(n, d))	41.3324
Wilson norm (sopfr(nd))	100
Comma size	unnoticeable
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The yggdrasil comma or yggdrasilsma is an unnoticeable comma in the 13-limit, measuring about 0.111 cents. It is the difference between 13/11 and a stack consisting of three instances of 21/20's and one instance of 49/48.

In terms of other commas, it is the difference between 2080/2079 and 2401/2400. It factors into the harmonisma and the ragnaroksma.

Temperaments

Tempering out this comma alone in the 13-limit leads to the rank-5 yggdrasil temperament.

It can be tempered out alongside the harmonisma, leading to the rank-4 alfheim temperament, which is notable for being a high-efficiency detemperament of freyr. It is also tempered out in any temperament where both 2080/2079 and 2401/2400 vanish, such as lif, eir, and greenland.

Etymology

The comma was named by Flora Canou in 2026, after the world tree in Norse mythology, Yggdrasil.