TUNING digest 641 - Mode & Mood

Dear Matthew et al.,

Two audible effects which may relate mode to mood, one local, the other
global:

Proportionally beating triads. These have a characteristic "ringing" sound.

The key coloration that results from irregular interval sizes. In the
so-called "well-temperaments", the C major triad is closest to just,
and travel around the circle of fifths, either toward the dominant or the
subdominant, yields triads which are progressively farther from just.

-+-+-+-+

Since we are no longer limited to the keyboard's 12 pitches/octave, we
don't get to hear the sound of the wolf diminished sixth in 1/4 syntonic
comma meantone. It's been disected into 31 equal parts in 31-ET. The
same can be said for the wolf diminished fourth (7:9) or augmented
fifth.

One question that the musicologists haven't answered to my satisfaction:

Did composers avoid these sounds, i.e. did performers tune their keyboards
to the pieces they were performing, or did they simply regard them as
somewhat different-sounding intervals to be utilized/exploited/dealt with?

Laurence W. Key

(flute001@peabody.jhu.edu)

1 East Mount Vernon Place
Baltimore, Maryland 21202
Phone: (410) 659-4009



Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Sat, 24 Feb 1996 20:15 +0100
Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id LAA14049; Sat, 24 Feb 1996 11:14:42 -0800
Date: Sat, 24 Feb 1996 11:14:42 -0800
Message-Id: <960224191236_71670.2576_HHB67-8@CompuServe.COM>
Errors-To: madole@ella.mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu

First of all, let me put in another plug for Paul's 88CET music. Neat stuff!




> if the links between this musical
> world and one's traditional world are few, the whole experience becomes
> "abstract". It becomes more on par with "noise as sound"

I think that Paul is right on with reality here. I'm also very interested in
any comments any of you might have on the topic.



> ... slightly "off" consonances, like the "major octave".

This isn't really all that important, but that terminology may be a little
risky. To those with classical training, it might sound like the ol'
fingernails on the chalkboard, since octaves are perfect consonances. But it's
certainly true that my terminology of "sharp off-octave" and "flat off-octave",
pretty much stereotypes them as unusable intervals. As far as I'm concerned,
I'm all for people finding ways to use them. But anyway, perhaps something like
"quarter-augmented octave" might be appropriate?



> Played alone,
> they both sound awful. They are very dissonant and produce ugly beatings.
> But within the context of a loud triumphant chord (especially in a
> "blaring" timbre), perhaps at the end of a major key cadence, a chord with
> a major octave sounds very consonant, even thought the off octave is
> clearly audible.

The same seems to be true, but to a lesser degree, of the off-fourth
interval, six 88-cent steps. It can, however, be approached as a very
approximate rendition of 15:11 ratio (9 cents off). Also, a side note: I'm
amazed by how flagrantly these off-octaves "stick out" even from large chords in
moderately fast counterpoint.)




> This "struggle" between "everything going as expected" and
> "everything going dreadfully wrong" is *the* main feature of my interest in
> alternate tunings.

Perhaps it's worth pointing out that I have found this sort of momentary
diversion into very strange harmony, a little more tricky to achieve in 88CET,
than in perhaps 31 for example. The reason probably stems from the fact that,
by virtue of its nonoctave orientation, traditional and nontraditional thirds
cluster within octave spans. You can't, for example, move a voice from a major
third above some root, through a neutral third, down to a minor third. Why?
Because the neutral is only available in the close octave, whereas the major and
minor are available only in the second octave as tenths.

But as long as your chord spans well over an octave, that's no problem, since
you can move the placement of the traditional vs. nontraditional intervals from
outer to inner voices. That "buries" the nontraditional interval, by the way,
which may be desirable in this sort of usage. It would be the opposite in Alpha
tuning for example, where the traditional intervals are in the close octave and
nontraditionals are in the second octave. This approach presumably (I haven't
tried it personally) would have a very different sound in Alpha.



> Because of
the asymmetrical octave nature of 88CET, chord progression tend to sound
relatively normal, but might end up someplace unexpected -- either too high
or too low.

This sort of wandering tonic effect is, I'm told, a favorite area of
exploration in 53TET, by the way. It also has especially powerful effects in
5-limit JI, 22TET, and 34TET as well. It's a really wild musical feeling!


Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Mon, 26 Feb 1996 03:31 +0100
Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id SAA23231; Sun, 25 Feb 1996 18:30:24 -0800
Date: Sun, 25 Feb 1996 18:30:24 -0800
Message-Id: <199602260229.SAA03417@hopf.dnai.com>
Errors-To: madole@ella.mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu