Talk:126/125: Difference between revisions

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:: Interestingly, if you go back in history, the sentence dates back to genewardsmith, see https://en.xen.wiki/index.php?title=126/125&diff=prev&oldid=4553 BTW: it started with consonances (instead of ratios) which might be less wrong... --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 10:33, 13 June 2021 (UTC)

Ah, "consonances" rather than "superparticular ratios" make much more sense, however it wasn't true nonetheless, since 2401/2400 and 4375/4374 are also not the difference between any two 7-limit consonances, unless you count the septimal neutral thirds (49/40 and 60/49) or the subminor third resulting from stacking two 27/25 as "consonances", which is a bit of a stretch. I suppose we could stack 7/6 and 27/25 a bit, but it still wouldn't help getting two notably different consonances with these exact differences.

The neutral third consonance is rather 11/9, for which 49/40 is merely an approximation (16/13 isn't as distinctly consonant although its inverse 13/8 actually is, since octave equivalence is only approximately correct in our direct perception). And 27/25 is rather an approximation for the two semiconsonances 13/12 and 14/13, which when stacked yields the true consonance 7/6 rather than a mere approximation (like (27/25)²). [[User:Henrik Ljungstrand|Henrik Ljungstrand]] ([[User talk:Henrik Ljungstrand|talk]]) 10:59, 13 June 2021 (UTC)

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 :: Interestingly, if you go back in history, the sentence dates back to genewardsmith, see https://en.xen.wiki/index.php?title=126/125&diff=prev&oldid=4553 BTW: it started with consonances (instead of ratios) which might be less wrong... --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 10:33, 13 June 2021 (UTC)
+Ah, "consonances" rather than "superparticular ratios" make much more sense, however it wasn't true nonetheless, since 2401/2400 and 4375/4374 are also not the difference between any two 7-limit consonances, unless you count the septimal neutral thirds (49/40 and 60/49) or the subminor third resulting from stacking two 27/25 as "consonances", which is a bit of a stretch. I suppose we could stack 7/6 and 27/25 a bit, but it still wouldn't help getting two notably different consonances with these exact differences.
+The neutral third consonance is rather 11/9, for which 49/40 is merely an approximation (16/13 isn't as distinctly consonant although its inverse 13/8 actually is, since octave equivalence is only approximately correct in our direct perception). And 27/25 is rather an approximation for the two semiconsonances 13/12 and 14/13, which when stacked yields the true consonance 7/6 rather than a mere approximation (like (27/25)²). [[User:Henrik Ljungstrand|Henrik Ljungstrand]] ([[User talk:Henrik Ljungstrand|talk]]) 10:59, 13 June 2021 (UTC)