Ragnaroksma

Interval information

Ratio	35153041/35152000
Factorization	2-7 × 5-3 × 74 × 114 × 13-3
Monzo	[-7 0 -3 4 4 -3⟩
Size in cents	0.05126843 ¢
Name	Ragnaroksma
Color name	trithu-aquadlozo-atriguma, 3u^31o^4z^4g^3M
FJS name	[math]\displaystyle{ \text{d2}^{7,7,7,7,11,11,11,11}_{5,5,5,13,13,13} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	50.1342
Weil norm (log2 max(n, d))	50.1343
Wilson norm (sopfr(nd))	140
Comma size	unnoticeable
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The ragnaroksma is an unnoticeable comma in the no-3's 13-limit, measuring about 0.0513 cents. It is found as the difference between a stack of four 77/64's and a stack of three 65/64's up an octave.

In terms of other commas, it equals the difference between a symbiotic comma and a stack of three ibnsinmas, (19712/19683)/(2080/2079)³, or between a wilschisma and a stack of four ibnsinmas, (532480/531441)/(2080/2079)⁴. Alternatively, it manifests as the three-comma relation: (10648/10647)/((2080/2079)/(2401/2400)), in other words, as the difference between a harmonisma and an yggdrasilsma.

Temperaments

Tempering out this comma alone in the 13-limit leads to the rank-5 ragnaroksmic temperament, or in the 2.5.7.11.13 subgroup, the rank-4 ragnarok temperament. It is tempered out in alfheim, or more simply symbiotic, as well as lower-rank temperaments such as freyr and cassaschismic.

Etymology

The comma was named by Flora Canou in 2026 after the great battle of Ragnarök in Norse mythology, which leads to the end of the world and the death of almost all gods, thereby portraying the temperament's immense accuracy and being an absolute end to the detemperament sequence (after alfheim).