A simple trick - update

A while back, I posted a 5- and a 7-limit retuning of the first movement
of Schubert's piano sonata, D894, with only half the tuning correction
from 12-tET as would be needed for strict JI. This was TD 463.14.

Now, for comparison, using the new spring method, I'm following up with
some tunings that I think are improvements over that simple trick. It
is my hope that one or more of these will not irritate even the most
sensitive ear, yet still offer at least some improvement over 12-tET.

http://www.idcomm.com/personal/jadl/

Contained in d894-1s.zip are:

Five-limit files:

d894-1r5.mid: what I would consider my new 5-limit standard of
reference. Some relaxation of strict JI, but not
much.
d894-1s5.mid: Softer springs in vertical tuning by a factor of
1/4 of the original.
d894-1ss5.mid: Even softer springs in vertical tuning by a factor
of 1/16 of the original.
d894-1sss5.mid: Even softer springs in vertical tuning by a factor
of 1/64 of the original.

Seven-limit files:

d894-1r7.mid: what I would consider my new 7-limit standard of
reference. Some relaxation of strict JI, but not
much.
d894-1s7.mid: Softer springs in vertical tuning by a factor of
1/4 of the original.
d894-1ss7.mid: Even softer springs in vertical tuning by a factor
of 1/16 of the original.
d894-1sss7.mid: Even softer springs in vertical tuning by a factor
of 1/64 of the original.

Original file:

d894-1.mid: Original and still champion 12-tET.

Because every note is sprung to ground, i.e., resists to some extent
ANY deviation from 12-tET, the softer vertical tuning springs result in
files only slightly modified from 12-tET.

What can I say about five vs. seven? Make your own pick. But if you
want to get into seven gradually, work from sss7 up, stopping as
necessary.

JdL

John A. deLaubenfels wrote,

" . . . as would be needed for strict JI"

and

"Some relaxation of strict JI, but not much."

John, I think you should replace "strict" with "vertical" here. "Strict JI"
is something that we've lately been using to describe JI of the California
school, where all horizontal intervals, as well as vertical ones, are simple
ratios. Clearly that is not what you are suggesting.