Talk:Porcupine family: Difference between revisions

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:::::::: * Porcupine naturally extends to 2.3.5.11, while meantone naturally extends to 2.3.5.7

:::::::: * Porcupine's three odd primes are found adjacent to each other and near +0 gens, while meantone's require significant stacking to reach (especially 7) -- [[User:VectorGraphics|VectorGraphics]] ([[User talk:VectorGraphics|talk]]) 02:34, 17 May 2025 (UTC)

::::::::: The similarities and differences you listed are from properties of 5-limit porcupine and 5-limit meantone. "Porcupine is generated by 11/10, while meantone is diatonic" is pointless, cuz of course two temps are ''in general'' generated by different gens, and you can write 11/10 as 10/9.

::::::::: "Both porcupine and meantone have a badness of around 0.01" makes absolutely no sense. It's a mistake to use Smith's badness metric across subgroups. Sintel's Dirichlet badness is the first true attempt of inter-subgroup badness comparison, but even that isn't perfect. 7 and 11 are inherently different primes, so they have different utilities and tendencies. That's why I said to meaningful compare temps they need to be tempering of the same subgroup.

::::::::: [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 09:50, 17 May 2025 (UTC)

@@ Line 47: / Line 47: @@
 :::::::: * Porcupine naturally extends to 2.3.5.11, while meantone naturally extends to 2.3.5.7
 :::::::: * Porcupine's three odd primes are found adjacent to each other and near +0 gens, while meantone's require significant stacking to reach (especially 7) -- [[User:VectorGraphics|VectorGraphics]] ([[User talk:VectorGraphics|talk]]) 02:34, 17 May 2025 (UTC)
+::::::::: The similarities and differences you listed are from properties of 5-limit porcupine and 5-limit meantone. "Porcupine is generated by 11/10, while meantone is diatonic" is pointless, cuz of course two temps are ''in general'' generated by different gens, and you can write 11/10 as 10/9.
+::::::::: "Both porcupine and meantone have a badness of around 0.01" makes absolutely no sense. It's a mistake to use Smith's badness metric across subgroups. Sintel's Dirichlet badness is the first true attempt of inter-subgroup badness comparison, but even that isn't perfect. 7 and 11 are inherently different primes, so they have different utilities and tendencies. That's why I said to meaningful compare temps they need to be tempering of the same subgroup.
+::::::::: [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 09:50, 17 May 2025 (UTC)