Amaranthinisma

Interval information

Ratio	5767168/5764801
Factorization	219 × 7-8 × 11
Monzo	[19 0 0 -8 1⟩
Size in cents	0.7106906¢
Names	amaranthinisma, convenience comma
Color name	Loquadbiru comma
FJS name	[math]\text{dd}{-4}^{11}_{7,7,7,7,7,7,7,7}[/math]
Special properties	reduced
Tenney height (log2 nd)	44.9183
Weil height (log2 max(n, d))	44.9189
Wilson height (sopfr(nd))	105
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.20454 bits
Comma size	unnoticeable
Open this interval in xen-calc

5767168/5764801, the amaranthinisma, is an unnoticeable 11-limit comma between a stack of eight 8/7's and 32/11 (one octave above 16/11), 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. It had previously been named the "convenience comma" by Scott Dakota in 2024, in a reference both to its "convenience" in easily extending septimal harmony and to the 7-11 convenience store (both due to bridging prime 7 to prime 11 and being 0.711 cents), though this name was deemed ambiguous by virtue of coming to refer to several other commas as well.

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.