Yahoo Tuning Groups Ultimate Backup makemicromusic Composing: mp3 snippets for Carl

Hello, everyone, and recently George Secor asked about
sources of creativity for composition. Here I'd like to
document with a couple of mp3 snippets -- modest but not
unproductive -- how Carl Lumma lent me a friendly goad in
this direction.

Carl, we were having a discussion about my modified meantone
or temperament extraordinaire, and related schemes, when you
offered a comment that made me both reflect on musical
limitations I tend to take for granted that others
(including you) might not; and take to a bit of
improvisation and composition to tell my side of the story.

Here's the creative goad, referring to temperaments like
mine with eight fifths tempered as in Zarlino's 2/7-comma
meantone, and the others equally wide -- first the Scala
file, and then the goad:

! zarte84a.scl
!
Temperament extraordinaire, F-C# in Zarlino's 2/7-comma, other 5ths equally wide
12
!
25/24
191.62069
287.43104
383.24139
504.18965
574.86208
695.81035
779.05173
887.43104
995.81035
1079.05173
2/1

> It's a shame the approximate 9/7 doesn't occur in a mode with
> the good 7/4 in these tunings... with a 7 present, I much less
> trouble using the 9/7.

Carl, certainly I agree that 9:7 is most effective as a
usual major third when used in an environment with other
congenial interval sizes, including 7:4 as well as 7:6 and
12:7, etc. The interesting question is what "occur in a
mode" means here, and I suspect that we may each have our
own meanings, semantic and musical.

Why don't I document how the near-9:7 and near-7:4 can from
my perspective routinely occur in the same mode -- the spur
to creativity here -- and then offer a friendly guess as to
your meaning, Carl, inviting your feedback.

First, from my point of view, "septimal harmony" means
mostly full or partial tetrads of 12:14:18:21 or 14:18:21:24.
The near-12:14:18:21 sonority Bb-Db-F-Ab or A#-C#-E#-G#,
with my spelling varying with the mode or context, combines
the best approximations of 7:6 (using both 275-cent minor
thirds), 9:7 (using the one 434-cent major third), and 7:4
(using one of three 983-cent minor sevenths).

Enough precompositional theory -- what to do musically? My
creative strategy was to pick a mode which would have this
fine tetrad -- and interesting subsets -- adjacent to the
final or resting note of the mode. This led to a choice of
C Phrygian or B Lydian, for reasons we'll hear and see
shortly.

Having already composed a fauxbourdon piece in C Phrygian,
I was certainly familiar with using the near-9:7 (Db-F) in
an approximate 7:9:12 sonority (Db-F-Bb) expanding to a
stable 2:3:4 on the final:

Bb C
F G
Db C

This is the first cadence in the following example, but
devising the final cadence you'll hear was fun because it
required innovating a bit on historical fauxbourdon, which
tends to favor mildly unstable thirds and sixths but treat
minor sevenths more demurely:

<http://www.bestII.com/~mschulter/CPhrygian97-74ex.mp3>

What I realized is that it would be easy, and to my ears
felicitous, to have a descending approach to a final cadence
where we have a mildly unstable sonority of a third plus
fifth above the lowest voice (C-Eb-G), expanding out to a
tempered 12:14:18:21 (Bb-Db-F-Ab) that would then contract
to a stable fifth on the final of the mode (C-G). Here C4 is
middle C, and one might note free keyboard voicing expanding
from three parts to four:

Ab4 G4
C5 Bb Ab4 G4 F4 G4
G4 F4 Eb4 Db4 C4
C4 Eb4 Db4 C4 Bb3 C4

Let me just add that, as we might expect in an unequal
temperament, the near-septimal intervals mix congenially
with others in a general Pythagorean-to-septimal range in
this part of the circle. Thus Eb4-G4-C5 is 0-408-913 cents,
not too far from Pythagorean, and C4-Eb4-Ab4 is 0-287-779
cents, with the third between 13:11 and 33:28 and the sixth
a bit narrow of 11:7. Mixing these kinds of colors is
routine for me.

By the way, here's the earlier C Phrygian piece that also
illustrates this type of mixture:

<http://www.bestII.com/~mschulter/InHoraObservationis.mp3>

Now for B Lydian: I went for a three-voice discant style
maybe typical of a classical conductus, or often mostly
note-against-note setting. Here's the music:

<http://www.bestII.com/~mschulter/BLydian97-74ex.mp3>

My theme was to highlight 9:7 in 14:18:21 and 7:9:12, as
well as 7:4 in 4:6:7, with each featured in a cadence:

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6
1 2 | 1 2 | 1 2 | 1 2 | 1 2 ||
B4 A#4 G#4 F#4 G#4 G#4 F#4 G#4 A#4 B4
F#4 D#4 E#4 F#4 E#4 E#4 F#4 F#4 E#4 F#4
B3 D#4 C#4 B3 , A#3 A#3 B C#4 B3

Moving from the opening ~2:3:4 (~ meaning "near" or "tempered"), we
come to a stable fifth D#-A#4 and then the ~14:18:21 at C#-E#-G#,
resolving to the fifth B3-F#4 on the final with the ~9:7 nicely
expanding to this fifth. Then we have the prominent ~4:6:7 at
A#-E#-G#, with the outer seventh contracting to another fifth on the
final and the upper ~7:6 third to a unison on the upper note of this
resolving fifth. Then comes a kind of coda, one of my favorite
cadences: from a mildly unstable ~6:8:9 (here with F#-G# at around 204
cents virtually just, although one can hardly say this for the fifth
or fourth!), the upper voices expand to the fourth of a sonority with
an outer sixth and lower third -- here our ~7:9:12 at C#-E#-A#, then
expanding to a ~2:3:4 on the final.

Of course, music is more than intonation: there are other things going
on, such as the "fifthing" that often occurs between the outer voices
moving together at this concordant interval while the middle voice
proceeds in contrary motion, often alternating stable and unstable
sonorities (as in the first two measures).

Also, while the ~9:7 third has its special charms, I would say that
similar passages can be very effective also with the 408-cent or
421-cent major thirds.

Now that I've told my story, Carl, let me venture my first guess as to
your point. Were you saying -- quite correctly, of course -- that we
can't have both a ~9/7 and a ~7/4 _above the same note_, for example a
drone on the final of a mode?

From one viewpoint, this is a logical limitation of a 12-note
circulating temperament. Having both a 9/7 and a 7/4 above the same
note means an interval of 64/49 or about 534 cents -- but in a
circulating scheme of this kind, all fourths are within about seven
cents of pure.

What might be more curious is that in many of my favorite just tunings
as well as temperaments for 12:14:18:21 or 14:18:21:24 tetrads, I take
it for granted that a note will often have one of these types
available -- but not both for the same note.

Aaron Johnson encouraged me to explore a 2-3-7 JI system like a couple
he has used designed by Gene Ward Smith, and there I was fascinated by
intervals like 49:32 and 49:36. It's curious, however, how I take
12:14:18:21 or 14:18:21:24 as "usual" septimal harmony, with 4:6:7:9
or the exquisite 16:21:24:28 (about which I learned from Keenan
Pepper, and later from Kyle Gann that LaMonte Young was using in it
the 1960's) as stimulating variations. The latter is a nice guarantee
that I'll regard a 12-note circulating temperament, however
attractive, as only _one_ solution, rather than _the one_ solution.

Nevertheless, Carl, my guess at your meaning (however accurate or
otherwise) raises a more general question. Have I simply been taking
for granted what you, as a versatile musician, can quickly recognize
as a notable musical limitation?

Here I might reflect that I've been playing and composing for not
quite 40 years -- and for about the first 32 of those years, hardly
even considered that there were things called "neutral thirds." Now I
recognize their absence as one of the serious limitations of any
circulating 12-note tuning -- and also of almost any conventional
historical 12-note European tuning scheme.

Each system indeed has its own patterns and resources -- but if I
interpreted your remark about 9:7 and 7:4 correctly, it's curious how
another person can reveal angles one hadn't fully considered, as well
as in the process foster a bit of musical creativity.

Peace and love,

Margo

Composing: mp3 snippets for Carl

🔗Margo Schulter <mschulter@...>

🔗Gene Ward Smith <genewardsmith@...>

🔗Carl Lumma <ekin@...>

🔗Gene Ward Smith <genewardsmith@...>

🔗Carl Lumma <ekin@...>