Re: [tuning] Re: The Golden Mediant: Complex ratios and metastable intervals

Margo, Dave (and Keenan),

Bravo! It's really great to see this type of a meaty multiple list
member collaboration.

One quick point or question on a first read through... I don't think
it's always clear that Golden Mediant algorithm and the mediant method
are essentially asking opposite questions; in other words, I'm seeing
the Golden Mediant as a wonderful little closed-form shortcut to a
sort of "eventuality of mediant iterations." But isn't the mediant
method in its usual application generally being asked to give the
*least* complex (or most stable) point between two others, with only
successive iterations eventually closing in on maximally complex zone?
It seemed as though all these points are nicely delineated at one
point or another but perhaps not consistently clear -- maybe I should
just read through it a few more times!

So, what do the significantly larger discrepancies between these two
mediant methods mean (the 5/4 6/5 example for instance)? That the
traditional mediant is a non trivial distance from the actual point of
maximum complexity (i.e., the Golden Mediant)... that would be my
take.

Anyway, looking forward to reading it a few more times, and once
again -- my compliments to the chefs!

d