Reply to Paul E on adaptive tuning

[Paul, TD 495.25:]
>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.

Oops! Consider it done.

[Paul:]
>Is there any way to get rid of the springs to "ground"? Isn't it true
>that all you really need is to "ground" one note, say C, and let the
>rest fall as they may? At least in a piece of music where every note in
>the scale is harmonically connected (directly or indirectly) to the
>overall tonic, which I would think would take care of all pieces of
>interest.

Now that's a clever idea; why didn't I think of that? (Hey! Not
funny!). Maybe start by scanning the entire sequence to establish which
note is most represented, and ground it, either exclusively or at least
more heavily than other notes.

There would be danger when a piece goes through an extended passage very
distantly modulated from tonic (or whatever note is grounded), that
tuning would drift aimlessly and irritatingly. In general, though, I
really like the idea of nailing down one pitch and letting the others
find themselves according to the harmonic needs of the sequence. I'll
play with adding that capability to the program, and should have some
trial results by Monday, if not sooner.

[Paul:]
>What I would think is that, in a pre-19th century piece of music,
>occurences of G# and Ab, though named identically in the MIDI file,
>would occur far enough apart in the music so that they wouldn't be
>attached with a spring, or at least not a very strong one. As a result,
>the two pitches would come out quite different, as they would in a
>meantone tuning. In fact, I would expect most pre-19th century music to
>_naturally_ approach something close to meantone tuning (if 5-limit is
>the overall paradigm expressed in your tuning files) if this method is
>used.

I wouldn't be surprised if you're right! And in any case, the results
should be verrrry interesting!!

JdL