Re: TD 873: Keenan Pepper's "chromatic modes"

Hello, there, Keenan Pepper, and upon a bit of consideration, maybe
I've come up with a name which might fit with your very interesting
analogy in Tuning Digest 877:

> Why not just call them "keys"? :)

On reflection, I realize that in fact "modal colors" or "key colors"
might nicely express the effect of these different sets of 12 notes in
styles such as early 15th-century music in Pythagorean tuning, or
18th-century music in unequal well-temperaments.

Usually, when these qualities are discussed, the effect is ascribed to
different modes or keys in a single tuning (or "color") rather than to
these different tuning "colors" for the same piece. However, as in
Newtonian or Einsteinian relativity, we can associate the change or
"motion" with either the choice of mode or transposition in the music,
or with the choice of tuning set or "modal/key color."

For example, in an early 15th-century Pythagorean tuning of Gb-B,
cadences on F will have regular Pythagorean major thirds and sixths
expanding to fifths and octaves, while cadences on D or G will have
"smoothed" diminished fourths and sevenths. The former cadences will
have the usual compact diatonic semitones or limmas, the latter the
large chromatic semitones or apotomes.

SImilarly, in an 18th-century well-temperament, the key of C major
will have meantone-like thirds not too far from pure, somewhat narrow
fifths, and large diatonic semitones; something like G# minor will
have Pythagorean or near-Pythagorean thirds, pure or near-pure fifths,
and narrow diatonic semitones.

However, rather than changing the location of a cadence or key, we can
also change the tuning "color" itself. Thus in the early 15th century
Pythagorean setting, we might take a piece in D Dorian -- or maybe
just a cadence on D (which can happen in various modes) -- and change
from a Gb-B color to an Eb-G# color. This makes the cadential major
thirds and sixths the usual Pythagorean flavor rather than the
smoother (and less dynamic) diminished fourths and sevenths.

Likewise, in an 18th-century setting, we could take the same piece in
C major and change the permutations of the pure and tempered fifths in
the well-temperament to get different "colors."

Here there's one possible complication: we have been assuming that
changing the "color" will produce different but musically "acceptable"
results in a given style. For example, either a regular Pythagorean
major third or a diminished fourth seems "acceptable" for early
15th-century music; and likewise the various flavors of intervals in
an 18th-century well-temperament.

One distinction between these two examples is that with 15th-century
Pythagorean tuning, we have the matter of the Wolf fifth or fourth
(actually diminished sixth or augmented third, e.g. Eb-G# or Gb-B) to
consider. If a piece calls for a prominent fifth B-F#, and our "change
of color" substitutes B-Gb, this may not be good news. However,
15th-century theorists themselves provide a solution: we don't have to
limit ourselves to the 12 notes of a single "color." A 13-note set
with both Gb and F# solves this kind of problem.

In this early 15th-century setting, _many_ changes of "color" remain
musically acceptable, just as in your example of changing the mode of a
piece, where substituting a tritone or diminished fifth for a regular
fourth or fifth can likewise be a complication -- solvable by the use
of an accidental alteration (e.g. Bb-F, B-F#).

With Renaissance mantone, however, there is an important caution:
substituting a diminished fourth like E-Ab for a major third like E-G#
is rarely likely to be musically "acceptable" in this kind of style.
It's less of a "nuance of color" -- the early 15th-century situation
-- than a "wrong note."

Note that this is a matter of style: changes of color are much more
restricted in a 16th-century meantone context than in an early
15th-century Pythagorean or 18th-century well-tempered one. We might
say that most changes of color which alter intervals alter them into
"Wolves" -- as defined by conventional 16th-century standards.

However, if we came up with a timbre and style where either meantone
major thirds or diminished fourths could be freely interchanged while
remaining "stylistically apt," then we could have free changes of
"modal/key color" just as in the historical 15th-century and
18th-century styles I've discussed.

One such style might be a kind of far-out neo-early-15th-century
neo-Gothic based on 1/4-comma meantone or 31-tET, for example, where
diminished fourths (32:25, ~427 cents) are the favored major thirds
for cadences involving sharps, while the 5:4 major thirds can be used
in certain cadential and noncadential settings also (like Pythagorean
diminished fourths).

A 12-note color of Gb-B in 1/4-comma meantone provides the basis for
this "far-out" style.

Anyway, getting back to 15th-century or 18th-century practice, I
wonder whether you might find "modal/key color" a useful term for a
"chromatic mode" -- or maybe an encouragement to come up with
something better? As to the names of these colors or whatever, I guess
Paul Erlich has provided a solution there.

Most appreciatively,

Margo Schulter
mschulter@value.net