--- In tuning-math@y..., genewardsmith@j... wrote:
> --- In tuning-math@y..., genewardsmith@j... wrote:
>
> > I'll get back to you if I can find this conjecture you speak of.
>
> I think you either need to find a better keyboard

Done. The thinking goes as follows. The "length" of a unison vector
n/d, n~=d, in the Tenney lattice with taxicab metric, or van Prooijen
lattice with triangular-taxicab metric, is proportional to log(n) +
log(d) (hence approx. proportional to log(d)), and also to
the "number" (in some weighted sense) of consonant intervals making
up that unison vector. Thus, in order to temper this unison vector
out (assuming that other UVs being tempered out, if any, are
orthogonal to this one), one must temper each consonant interval
involved by an "average" amount proportional to w/log(d), where w is
the musical width of the unison vector.

w=log(n/d)
w~=n/d-1
w~=(n-d)/d

Hence the amount of tempering implied by the unison vector is approx.
proportional to

(n-d)/(d*log(d))

Yes?