Re: Digest Adaptive JI

John A. deLaubenfels wrote:

> I do see that your approach does a good job of cutting down on retune
> motion. I am curious: how do you handle rampant modulations? A circle
> of fifths, for example

A progression that essentially involves a circle of 12 fifths would not work well with my approach. Such a
progression would have to be notated using enharmonic equivalents, which are not identical pitches in meantone.
But such progressions were very rare before the Romantic period, when the hegemony of 12 began in full force.
Before that, since the start of the Renaissance, music essentially obeyed a meantone logic. And modern pop music
does in the vast majority of cases.

> or a progression from C major to E major to G#
> major?

Such a progression would work great in my approach. No retune motion would be required, as the intervals c-e and
e-g# are already purely tuned in 1/4-comma meantone. However, if you wish to get back to C major be
reinterpreting B# as C, you are assuming a closed circle of 12 fifths and you run into the same problem as
above.

>> So, are we starting to make sense to each other?

>Yes, I think so. By the way, do you have a web site? Please forgive
>me if I've missed a posting where you have referenced it.

The closest thing there is to a website for me right now is http://www-math.cudenver.edu/~jstarret/Erlich.html.
I'm still waiting for John Starrett to add some more links to my ideas to this page. Nothing on adaptive JI,
though the idea of adaptive JI could prove very important to me in my proposed 22-tone 7-limit system. The
mistuning of the 7:5 by 17 cents in 22-tET is bad enough to warrant very serious investigation into adaptive
retuning. Also, as a guitarist I often adjust intervals towards JI by bending one or more notes; typically this
represents a form of adaptive JI with the constraint that notes can only be bent upwards, not downwards.

-Paul E.