Just to clean up a bit...Jerry Freeman wrote:In our just intonation scale, C-G# is 8/5. It's not two stacked major thirds, as you have correctly pointed out.BoneQuint wrote:But Jerry, you do agree about the counter-example I gave, C-E-G# (two major thirds)? The distance from E to G# in your table is larger than 5/4 (it's 32/25, or 5.12/4, or 1.28).
Another one that doesn't work is the "stacked minor thirds", C-Eb-F#. Neither does C-G#-B, or C-F#-A.
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There's nothing wrong with this. The relationships between the major third and the root, and between the augmented fifth and the root are strongly consonant. There's more tension between the augmented fifth and the major third, but why should that be problematic?
I wasn't saying there was anything wrong with it -- on the contrary, I said it was more consonant than the equal-tempered version. But as I said in my post a few before the one you responded to, Lorenzo was using "pure" to mean something like "all intervals are uniform and at the simplest possible ratio to each other." As I pointed out, quite a few chords fit that definition in just intonation. But some don't -- those are the ones I said didn't "work" as "perfect purity" in Lorenzo's sense.
We seem to be agreeing on all the points you mention, but I do appreciate the recap and your comments on tension and dissonance. I hope my blatherings have been one tenth as useful to somebody as this thread has been to me.
