Amaranthine comma

Interval information

Ratio	5767168/5764801
Factorization	219 × 7-8 × 11
Monzo	[19 0 0 -8 1⟩
Size in cents	0.7106906¢
Name	amaranthinisma
Color name	Loquadbiru comma
FJS name	[math]\displaystyle{ \text{dd}{-4}^{11}_{7,7,7,7,7,7,7,7} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	44.9183
Weil norm (log2 max(n, d))	44.9189
Wilson norm (sopfr(nd))	105
Comma size	unnoticeable
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5767168/5764801, the amaranthinisma, is an unnoticeable 11-limit comma between a stack of eight 8/7's and 32/11, measuring 0.711 cents; it can also be expressed as the difference between 99/98 and two gamelismas (1029/1024). Since both 99/98 and 1029/1024 are tempered out in undecimal mothra, this comma is also tempered out.

Etymology

The word "amaranthine" means "unfading", and so this comma was named by Lériendil in 2025, as it is the one portion of the structure of the undecimal slendric extensions that refuses to fade even at the high precision of a near justly tuned 8/7.

Temperaments

Tempering out this comma in the full 11-limit results in the rank-4 amaranthinismic temperament, and tempering it out in the 2.7.11 subgroup results in the rank-2 amaranthine temperament.

As its order of 11 is one, any 7-limit temperament can be immediately extended to the 11-limit in theory by tempering out this comma. To make practical sense, however, it requires low complexity and high accuracy of 8/7.