Re: Wilson's footprints on plateau!

Dave,

you wrote:

>At first glance I thought it was possible, but now it seems to me that the
>greatest distinction between interval classes occurs when all the scale
>steps are the same size. So what is it we are really trying to optimise here?

Doesn't it depend on which intervals we want to distinguish? ET will
equate intervals which have distinct expressions in terms of reiterations
of the generator. For instance, in 12-tET a minor third and aug. 2nd are
equivalent, but in Kornerup tuning they are well distinguished, but not so
much that they threaten the distinction between, say, min and maj thirds.
Whether Kornerup tuning is a maximum distinction across the board I suppose
depends on how you define maximum distinction, but intuitively I think it
would, with a reasonable definition requiring distinctions of every
interval formed by a different number of generator reiterations, prove a
maximum distinction. Is that accurate?

Jason wrote,

>Whether Kornerup tuning is a maximum distinction across the board I suppose
>depends on how you define maximum distinction, but intuitively I think it
>would, with a reasonable definition requiring distinctions of every
>interval formed by a different number of generator reiterations, prove a
>maximum distinction. Is that accurate?

If you continue the process to infinity, I think that's accurate, but is
shared by all the other noble generators (though if you look at the very
first steps I think we agree that the phi-octave generator of 741.64 cents
beats even the Kornerup generator).