User talk:FloraC: Difference between revisions

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: [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:18, 11 September 2025 (UTC)

== On temperament degeneracy ==

Hello Flora, regarding the changes in concept I submitted to Bixby and Archon, why aren't they not degenerate?

For Bixby, if you temper out 4/3, it results in ~3/2 being mapped to an octave. If you temper 3/2 instead, 4/3 is 1 octave. If you temper 3/1 instead, then all 3's become unisons. In all of these cases, you are effectively destroying prime 3 and forcing it to be equal to some number of octaves, however as many as you like, so it matters little what you temper. Same with Archon destroying prime 5.

It would be the same thing as tempering out 17/16, tempering an octave-reduced harmonic to the nearest octave would be effectively removing it from the system assuming pure octaves. It should follow that the simplest subgroup of this temperament, 2.17, it is equivalent to the 2-limit, and can only be represented by 1edo; you get no real sonic benefit from just using octaves.

Running tuning optimizations on those is possible, but the data you get is wild because the optimizer is trying to make up for the fact that a prime would be mapped to pure octaves.

Antitonic wouldn't be a degenerate temperament because while 9/8 is a wild thing to be called a comma, it can be represented ''at least'' in 2edo and 4edo, and you get the tiniest semblance of 3/2... truly a troll temperament.

I would call degenerate any temperament that can only represented by patent val by 1edN, or worse by 0edo (which of course is trivial). --[[User:Eufalesio|Eufalesio]] ([[User talk:Eufalesio|talk]]) 12:30, 31 December 2025 (UTC)

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 : [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:18, 11 September 2025 (UTC)
+== On temperament degeneracy ==
+Hello Flora, regarding the changes in concept I submitted to Bixby and Archon, why aren't they not degenerate?
+For Bixby, if you temper out 4/3, it results in ~3/2 being mapped to an octave. If you temper 3/2 instead, 4/3 is 1 octave. If you temper 3/1 instead, then all 3's become unisons. In all of these cases, you are effectively destroying prime 3 and forcing it to be equal to some number of octaves, however as many as you like, so it matters little what you temper. Same with Archon destroying prime 5.
+It would be the same thing as tempering out 17/16, tempering an octave-reduced harmonic to the nearest octave would be effectively removing it from the system assuming pure octaves. It should follow that the simplest subgroup of this temperament, 2.17, it is equivalent to the 2-limit, and can only be represented by 1edo; you get no real sonic benefit from just using octaves.
+Running tuning optimizations on those is possible, but the data you get is wild because the optimizer is trying to make up for the fact that a prime would be mapped to pure octaves.
+Antitonic wouldn't be a degenerate temperament because while 9/8 is a wild thing to be called a comma, it can be represented ''at least'' in 2edo and 4edo, and you get the tiniest semblance of 3/2... truly a troll temperament.
+I would call degenerate any temperament that can only represented by patent val by 1edN, or worse by 0edo (which of course is trivial). --[[User:Eufalesio|Eufalesio]] ([[User talk:Eufalesio|talk]]) 12:30, 31 December 2025 (UTC)