Re: TD 642: Adaptive JI and diesis distinctions

> Message: 1
> Date: Thu, 18 May 2000 07:33:34 -0600
> From: "John A. deLaubenfels" <jadl@idcomm.com>
> Subject: Re: Web site update

> For the older-style pieces, which CAN successfully be played in extended
> meantone without experiencing a "diesis pump", it would make sense to
> begin the analysis by mapping the piece onto extended meantone, thus
> differentiating as many notes as needed to be, perform a COFT (constant
> optimized fixed tuning) on all those notes (>12), then do an adaptive JI
> calc grounded to those tunings.

Hello, there, and I'd like strongly to agree that the need to avoid a
"diesis pump" (that is, the need to have notes such as G#/Ab be
interchangeable) is a specific feature of certain styles of music, as
opposed to some kind of "general" or "universal" standard.

From a 16th-century perspective, the diesis can be a feature rather than a
bug, and I would regard a "general" method which assumes that B# and C,
for example, should be interchangeable rather than about a 128:125 diesis
or a fifthtone or 1/31 octave or what have you, apart, to be an artificial
limitation on the expressiveness of the music -- quite apart from the
Erlichan criterion of minimizing tuning adjustments (where 1/4-comma
meantone is an attractive basis).

> Such a method doesn't appeal to me, however, simply because its scope is
> so limited: it falls to pieces when challenged with later works that DO
> have built-in diesis pumps. I'm still groping for the perfect answer,
> ideally one which satisfies all of the following:

This may raise a basic philosophical issue: is a "universal" method for
styles of music which may have radically different expectations really so
universal? I'm tempted to remark that assuming an equivalence between G#
and Ab, for example, seems a very "limiting" assumption -- although I
recognize that certain specific styles indeed make such an assumption the
basis for some artful structures and effects.

> . One approach applies to pieces old and new, constrained and bold.

As an interesting problem of the same kind as "tune a 12-note keyboard so
that it can be used at least tolerably to play European compositions from
both the medieval and Renaissance eras," this search for a single tuning
algorithm is the kind of question that can engage our mathematical skills
and reveal something about our musical tastes and priorities.

However, speaking for myself, I would far prefer to use algorithms adapted
to the assumptions and artistic potentials of a specific style. Thus
1/4-comma meantone or something close to it seems a logical basis to me
for some kind of adaptive just intonation applied to Gesualdo, for
example; for music based on the radically different assumptions of 12-tet
or something not too far from it, that temperament might serve as the best
basis.

Most respectfully,

Margo Schulter
mschulter@value.net

Margo Schulter, TD 643.13, makes a good point, and upon further
reflection my desire for a tuning method universal across the centuries
seems misguided.

My own tastes tend toward the 19th century and beyond, where mapping
12-tET onto no more than 12 retuned notes seems to make a lot more
sense.

But, for the 18th century and earlier, it does seem overly harsh to
squeeze everything into 12 notes.

I am now thinking of trying to map any piece of music onto 31-tET, with
the goal of deciding whether or not it makes sense; if it does, then
the world of more than 12 notes is open; if it does not, then a 12 note
universe (howbeit with the possibility of adaptive tuning) seems to be
more fitting.

JdL