User talk:FloraC: Difference between revisions

Line 69:

:: --[[User:Eufalesio|Eufalesio]] ([[User talk:Eufalesio|talk]]) 16:55, 31 December 2025 (UTC)

::: ''Degeneracy'' from wiktionary:

::: > (''mathematics'') A limiting case of a class of objects which appears to be qualitatively different from (and usually simpler than) the rest of the class.

::: I believe this is the broader mathematical definition you're talking about.

::: As I said, the only way to reduce a 3-limit structure to 2-limit to make it appear qualitatively different is to temper out 2/1 or 3/1. Tempering out 4/3 isn't the same as tempering out 3/1 since 3/2 can be "rounded" to 2/1 to result in 1edo just as 2/1 can be "rounded" to 3/2 to result in 1edf. While the former is the same as the 2-limit, the latter is not, nor is anything in between. This is the behavior of an ordinary temperament and not a degenerate one.

::: Furthermore, bixby is the rank-2 temp that uses the 1et for the 3-limit part but gives an independent generator for prime 5. The way it uses 1et for the 3-limit isn't different from how blackwood uses 5et for the 3-limit, and is perfectly functional. In fact bixby is supported by the following GPVs: {{val| 1 2 2 }} (1), {{val| 1 2 3 }} (1c), {{val| 2 4 5 }} (2b), and {{val| 3 6 8 }} (3bbcc). Note that 1c is equivalent to b2, the patent val of 2edt. 2b is the patent val of a slightly stretched 4edt, and 3bbcc is the patent val of a carefully stretched 3edo. So it's not like it's only supported by a single equal temperament. Even if it was, it would only qualify for degeneracy in a very peculiar sense.

::: Therefore, it follows that calling bixby ''degenerate'' is not only conceptually unfounded, but takes away the verbal distinction of truly degenerate temps. Now I don't mind giving them a new category inside or alongside exotemps for their extreme inaccuracy (that would possibly include any temps less accurate than father) but I urge you to be careful with your choice of terms.

::: —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 18:11, 31 December 2025 (UTC)

@@ Line 69: / Line 69: @@
 :: --[[User:Eufalesio|Eufalesio]] ([[User talk:Eufalesio|talk]]) 16:55, 31 December 2025 (UTC)
+::: ''Degeneracy'' from wiktionary:
+::: > (''mathematics'') A limiting case of a class of objects which appears to be qualitatively different from (and usually simpler than) the rest of the class.
+::: I believe this is the broader mathematical definition you're talking about.
+::: As I said, the only way to reduce a 3-limit structure to 2-limit to make it appear qualitatively different is to temper out 2/1 or 3/1. Tempering out 4/3 isn't the same as tempering out 3/1 since 3/2 can be "rounded" to 2/1 to result in 1edo just as 2/1 can be "rounded" to 3/2 to result in 1edf. While the former is the same as the 2-limit, the latter is not, nor is anything in between. This is the behavior of an ordinary temperament and not a degenerate one.
+::: Furthermore, bixby is the rank-2 temp that uses the 1et for the 3-limit part but gives an independent generator for prime 5. The way it uses 1et for the 3-limit isn't different from how blackwood uses 5et for the 3-limit, and is perfectly functional. In fact bixby is supported by the following GPVs: {{val| 1 2 2 }} (1), {{val| 1 2 3 }} (1c), {{val| 2 4 5 }} (2b), and {{val| 3 6 8 }} (3bbcc). Note that 1c is equivalent to b2, the patent val of 2edt. 2b is the patent val of a slightly stretched 4edt, and 3bbcc is the patent val of a carefully stretched 3edo. So it's not like it's only supported by a single equal temperament. Even if it was, it would only qualify for degeneracy in a very peculiar sense.
+::: Therefore, it follows that calling bixby ''degenerate'' is not only conceptually unfounded, but takes away the verbal distinction of truly degenerate temps. Now I don't mind giving them a new category inside or alongside exotemps for their extreme inaccuracy (that would possibly include any temps less accurate than father) but I urge you to be careful with your choice of terms.
+::: —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 18:11, 31 December 2025 (UTC)