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

Hello, there, Keenan Pepper and everyone.

If I read your examples of "chromatic modes" correctly, then I might
call them "12-note tuning sets" or maybe "12-note gamuts."

This concept is in fact very important in approaching Pythagorean and
meantone tunings of the 14th-17th centuries, where changing the
12-note gamut or combining two or more gamuts in a larger tuning
(e.g. 15, 17, 19, 24, or 31 notes) opens new musical possibilities.

[In a latter post, Keenan, you specified the region from 7-tET to 12-tET,
but since some of what follows might be relevant to meantone, also, I'll
share my original response.]

Generally I would identify these "12-note sets" by specifying the
extreme notes in the chain of fifths, e.g.:

Eb-G# = Eb-Bb-F-C-G-D-A-E-B-F#-C#-G# (C-C#-D-Eb-E-F-F#-G-G#-A-Bb-B-C)
Gb-B = Gb-Db-Ab-Eb-Bb-F-C-G-D-A-E-B (C-Db-D-Eb-E-F-Gb-G-Ab-A-Bb-B-C)

Note that the outer notes of such a 12-note chain, Eb-G# or Gb-B in
these two example, will form an interval of 11 fifths up, an augmented
third not generally synonymous with a regular fourth (12-tone equal
temperament or 12-tET is a notable exception).

In Pythagorean tuning, for example, it's the "Wolf fourth" of
177147:131072 (~522 cents). In a meantone, it's a different flavor of
"Wolf" _narrower_ than a useful fourth, for example ~462 cents in a
1/4-comma tuning with pure major thirds. In a neo-Gothic tuning such
as your wonderful "Noble" temperament, it's quite close to an 11:8 --
for example, ~545 cents in your tuning.

Maybe one reason for calling these sets something other than "modes"
is that we might sometimes perform the same late 14th-century or early
15th-century European piece in different sets without changing the
basic "scale" pattern (often defined by whole-tones and semitones),
but with some changes in the color or "aura" (to borrow Mark Lindley's
term) of the music.

In our Eb-G# set, for example, cadential or other major thirds
involving sharps (specifically E-G#, D-F#, A-C#) are regular thirds
(as the spelling suggests) and will have a "bright" and active flavor.

In our Gb-B set, however, these same intervals will be diminished
fourths or "schisma thirds" (E-Ab, D-Gb, A-Db) very close to a pure
5:4, with a flavor which might be described either as "smooth" or as
"less than fully perfected" from a traditional 14th-century viewpoint
-- they are not as active and cadentially efficient as the regular
versions.

It's quite possible that the same piece by a composer such as
Francesco Landini (1325-1397) might have been performed around 1370 in
the Eb-G# set, but around 1400 or 1420 in the Gb-B set.

One interesting solution I enjoy for some early 15th-century pieces is
to combine both these sets, the "traditional" 14th-century Eb-G# and
the "modern" early 15th-century Gb-B, into a 15-note tuning with one
keyboard in each 12-note set. This offers such choices as using E-G#
for a directed cadential progression where this interval expands to
the fifth D-A, but E-Ab for some prolonged noncadential sonority.

(With a 14th-century composer such as Machaut, I'd generally use E-G#
in both contexts.)

Anyway, the situation around 1400-1450 may illustrate how using or
combining different "12-note sets" can indeed make a musical
difference.

Note, by the way, that naming a set such as "Eb-G#" doesn't depend on
the specifics of a regular tuning as long as that tuning stays within
a certain range of parameters: it can apply to 14th-century
Pythagorean, 16th-century meantone, and turn-of-the-20th/21st-century
29-tET or Pepperian Phi-based tuning.

Incidentally, theorists of the early to middle 15th century give these
distinctions some attention, and one way of expressing the difference
is to say whether the Pythagorean minor (i.e. diatonic) semitone is
played "below" or "to the left" (e.g. G-Ab-A), or "above" or "to the
right" (e.g. G-G#-A).

Both Prosdocimus de Beldemandis (1413) and Ugolino of Orvieto (c. 1435
or 1440?) compare these two divisions, and conclude that a 17-note
tuning including both five flats (Gb-B) and five sharps (F-A#) is
needed for a "perfect" system, which Ugolino recommends for use on a
17-note keyboard by "the intelligent organist."

Most respectfully,

Margo Schulter
mschulter@value.net

>If I read your examples of "chromatic modes" correctly, then I might
>call them "12-note tuning sets" or maybe "12-note gamuts."

Why not just call them "keys"? :)
But they're still "modes" in the sense of "a scale played in such a way that
one pitch is considered central," which is really a hazy definition because
sometimes it's not clear when the "central" pitch changes or even if there
is one at all. They have a definite feel, though, and I think they should
have proper names.

>Maybe one reason for calling these sets something other than "modes"
>is that we might sometimes perform the same late 14th-century or early
>15th-century European piece in different sets without changing the
>basic "scale" pattern (often defined by whole-tones and semitones),
>but with some changes in the color or "aura" (to borrow Mark Lindley's
>term) of the music.

Well, don't pentatonic or diatonic modes work the same way? When you play
something in, say, Aeolian instead of Ionian ("minor" instead of "major"),
it's still very recognizable and has the same melodic contour and basic
harmony, but it has a different "aura" that (in this case) most people would
say was "sad" or "scary"; a very powerful musical effect. To do this
microtonally (and make it sound good) would be a great achievement.

Since I didn't get any replies answering my original question ("What are
their names?"), I take it to mean they haven't got any, so I get to name
them myself. Any suggestions? All proposed names should end in "-ian".

-Keenan P.

>Since I didn't get any replies answering my original question ("What are
>their names?"), I take it to mean they haven't got any, so I get to name
>them myself. Any suggestions? All proposed names should end in "-ian".

Did you check Yasser, as I suggested?

OK, since you're giving me the opportunity to be creative:
We have to use something that there are 12 of -- how about the
constellations in the zodiac?

C-C#-D-D#-E-E#-F#-G-G#-A-A#-B-C
C Arian

C-C#-D-D#-E-F-F#-G-G#-A-A#-B-C
C Taurian

C-C#-D-D#-E-F-F#-G-G#-A-Bb-B-C
C Geminian

C-C#-D-Eb-E-F-F#-G-G#-A-Bb-B-C
C Cancerian

C-C#-D-Eb-E-F-F#-G-Ab-A-Bb-B-C
C Leonian

C-Db-D-Eb-E-F-F#-G-Ab-A-Bb-B-C
C Virgonian

C-Db-D-Eb-E-F-Gb-G-Ab-A-Bb-B-C
C Libran

C-Db-D-Eb-E-F-Gb-G-Ab-A-Bb-Cb-C
C Scorpian

C-Db-D-Eb-Fb-F-Gb-G-Ab-A-Bb-Cb-C
C Sagittarian

C-Db-D-Eb-Fb-F-Gb-G-Ab-Bbb-Bb-Cb-C
C Capricornian

C-Db-Ebb-Eb-Fb-F-Gb-G-Ab-Bbb-Bb-Cb-C
C Aquarian

C-Db-Ebb-Eb-Fb-F-Gb-Abb-Ab-Bbb-Bb-Cb-C
C Piscian

Of course, the next mode in this sequence would be

Dbb-Db-Ebb-Eb-Fb-F-Gb-Abb-Ab-Bbb-Bb-Cb-Dbb

which is simply Dbb Arian -- you've gone all the way around the zodiac!