User talk:Sintel: Difference between revisions

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:: So could the term be repurposed for something more useful (like scales with negative or blown-out steps)? [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 10:04, 16 April 2025 (UTC)

::: Common examples like collapsed and equalized scales are more accurately described as {{w|Degeneracy (mathematics)|degenerate}} than {{w|Pathological (mathematics)|pathological}}. If you look at examples of pathological objects in mathematics from the Wikipedia article, you'll notice that they're not just "exaggerated" versions of common stuff, they really behave strangely and unintuitively. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 15:10, 16 April 2025 (UTC)

:::: I thought about collapsed and equalized, but decided those don't really belong to "pathological" — but I am still willing to propose that something like a diatonic scale with a negative value for ''s'' is pathological, since you end up with with D sharper than E in the same octave, and B of one octave sharper than C of the next octave. An example on the other end of the Meantone spectrum would be 5L 2s with a fifth flatter than 7edo, but continuing down the Meantone spectrum instead of switching to Mavila   here the sharp of one note is flatter than the flat of the same note, ~~unless~~ you redefine how the circle of fifths works. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 22:15, 16 April 2025 (UTC)

:::: I thought about collapsed and equalized, but decided those don't really belong to "pathological" — but I am still willing to propose that something like a diatonic scale with a negative value for ''s'' is pathological, since you end up with with D sharper than E in the same octave, and B of one octave sharper than C of the next octave. An example on the other end of the Meantone spectrum would be 5L 2s with a fifth flatter than 7edo, but continuing down the Meantone spectrum instead of switching to Mavila   here the sharp of one note is flatter than the flat of the same note, and thirds which sound major are actually minor and vice versa, and you have to redefine how the circle of fifths works or redefine major and minor. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 22:17, 16 April 2025 (UTC)

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 :: So could the term be repurposed for something more useful (like scales with negative or blown-out steps)?  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 10:04, 16 April 2025 (UTC)
 ::: Common examples like collapsed and equalized scales are more accurately described as {{w|Degeneracy (mathematics)|degenerate}} than {{w|Pathological (mathematics)|pathological}}. If you look at examples of pathological objects in mathematics from the Wikipedia article, you'll notice that they're not just "exaggerated" versions of common stuff, they really behave strangely and unintuitively. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 15:10, 16 April 2025 (UTC)
-:::: I thought about collapsed and equalized, but decided those don't really belong to "pathological" &mdash; but I am still willing to propose that something like a diatonic scale with a negative value for ''s'' is pathological, since you end up with with D sharper than E in the same octave, and B of one octave sharper than C of the next octave.  An example on the other end of the Meantone spectrum would be 5L&nbsp;2s with a fifth flatter than 7edo, but continuing down the Meantone spectrum instead of switching to Mavila &nbsp; here the sharp of one note is flatter than the flat of the same note, unless you redefine how the circle of fifths works.  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 22:15, 16 April 2025 (UTC)
+:::: I thought about collapsed and equalized, but decided those don't really belong to "pathological" &mdash; but I am still willing to propose that something like a diatonic scale with a negative value for ''s'' is pathological, since you end up with with D sharper than E in the same octave, and B of one octave sharper than C of the next octave.  An example on the other end of the Meantone spectrum would be 5L&nbsp;2s with a fifth flatter than 7edo, but continuing down the Meantone spectrum instead of switching to Mavila &nbsp; here the sharp of one note is flatter than the flat of the same note, and thirds which sound major are actually minor and vice versa, and you have to redefine how the circle of fifths works or redefine major and minor.  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 22:17, 16 April 2025 (UTC)