>13-limiit JI?

Dave Keenan wrote...

> Thanks for a good laugh David. It does rather point up the ridiculousness
> of claiming that some piece is >15 limit JI. Who could tell? Even 13 is
> pushing things.

I believe this statement is at best ambiguous. Dave, if you mean to say
what limit we begin to encounter significant tolerance effects, I would
say 7.

At what limit does increasing the limit add no new 'independent' ratios?
For practical purposes, in a tonal setting, I would say 19 (in certain
settings, like using complete series segments in an almost timbre-like way,
maybe much higher).

I'll grant you that 19 adds only one 'independent' ratio as far as I can
tell -- 19:16. But then, how do we define "independent"? In theory,
every ratio falls under a part of every other ratio's distribution...

I can live without 19, but I can't live without 17 -- it's part of some
gorgeous chords, including my favorite "diminished 7th". As for 13, I
can tune it by ear very quickly and to a great degree of accuracy, if
I am allowed reference pitches at 12 and 14, and I can tune each of those
from a single reference pitch -- any one you'd like from about G2 to G5.

-Carl

Dave Keenan wrote,

>> Thanks for a good laugh David. It does rather point up the ridiculousness
>> of claiming that some piece is >15 limit JI. Who could tell? Even 13 is
>> pushing things.

Carl wrote,

>As for 13, I
>can tune it by ear very quickly and to a great degree of accuracy,

So could Dave, when we were discussing my harmonic entropy charts. So I
suspect what really happened here was that Dave failed to express his
meaning clearly. Perhaps what he really meant was, it's pushing things to
say that a piece, performed on non-electronic instruments, is in such
accurate 13-limit JI that it could be said that it's _not_ in 270-tET -- the
two are so very close. I don't know . . . Dave Keenan needs to clarify here
. . .

Anyway, the linear/non-linear distinction Dave brought up is pretty
important . . . I can say that in the performance of the Scelsi solo violin
piece at the Microthon, the sustained intervals were in such accurate
11-limit JI (at least) that it was _not_ 72-tET, but that's only because of
the non-linearities associated with intervals played on a single violin.
(David Beardsley clearly misunderstood this non-linearity bit -- you could
sustain an interval for years and this would have no bearing on the
linearity or non-linearity with which the interval is heard.)