Amaranthine comma: Difference between revisions
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'''5767168/5764801''', the '''amaranthinisma''', is an [[unnoticeable comma|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 [[1029/1024|gamelismas (1029/1024)]]. Since both 99/98 and 1029/1024 are tempered out in undecimal [[mothra]], this comma is also tempered out. | '''5767168/5764801''', the '''amaranthinisma''', is an [[unnoticeable comma|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 [[1029/1024|gamelismas (1029/1024)]]. Since both 99/98 and 1029/1024 are tempered out in undecimal [[mothra]], this comma is also tempered out. | ||
== Etymology == | == Etymology == | ||
Revision as of 06:11, 7 February 2025
| Interval information |
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.
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.