88CET #21: Melodies and Voice-Leading

Continuing with considerations for playing traditional harmony in 88CET...

The most important constraint to producing traditional harmony in 88CET is
that the properties generally regarded as producing interesting melodies in any
tuning, don't lend themselves to traditional harmonization. In particular,
arpeggios, or step-wise runs spanning more than a third, almost always require
nontraditional chords or nontraditional progressions of traditional chords in
their harmonizations. These pose problems because they call out pitch
relationships, notably thirds, other than the traditional diatonic ones.
Obviously that makes convincing diatonic harmony very challenging.

For example, let's suppose that you've established a certain C as the tonic,
and built what I guess could be called a C-major chord around it:
How do you harmonize the E a neutral third above it appearing right after it?
Do you call it scale-degree traditional diatonic scale degree 3 or flat 3?
Obviously this is not a problem for nontraditional harmony, but traditional
harmony requires that it masquerade as some diatonic function.

Audiences can be "tricked" into accepting this E as diatonic more easily than
you might think, because of a phenomenon I jokingly call "relativistic
voice-leading". This is the perfect embodiment of the idea of functional
harmony - the idea that how a pitch is perceived is based on how it moves within
the counterpoint, more than its absolute pitch. In another sense, it
illustrates why modulation works: You can convince people that some new pitch
is now the tonic, if you make the step below it sound like a leading tone, and
resolve that pitch up to the new tonic in a well-understood way.

But in 88CET's relativistic voice-leading requirement, a given pitch is ONLY
understandable as a particular traditional diatonic role in terms how it relates
to the previous chord. Since that E falls between two diatonic roles, your
audience will only be able to extrapolate a diatonic role for it by hearing that
E's usage (or adjacent pitches) in the previous chord.

This has a huge effect on the melodic harmonization process. In traditional
harmonization of a melody, you automatically know what function a given melodic
pitch will have just by knowing its pitch. In the key of C, a B has to be
perceived as a leading tone (provided of course that it truly is B rather than a
C-flat or an A-double-sharp). In 88CET traditional harmony on the other hand,
there is no way to know without filling in the intervening harmony what function
a given pitch will perform.

Arpeggiation in a melody, also good for making melodies sound interesting,
causes problems because they usually outline close-triadic harmony. Since
88CET's close-triadic harmonies are inherently nontraditional, you can't
harmonize those fragments traditionally.

With rapid step-wise motion and arpeggiation unavailable, it seems like only
uninteresting melodies that gravitate around a single pitch - can be harmonized
traditionally. Luckily that isn't true after all. Here are some melodic
formulas that get around these constraints:
1. Leap upward by either sixth, followed by slow step-wise motion downward to
return to the tonic. Leaps of a sixth, as Tamino's first aria in Die
Zauberflote illustrates so marvelously, have a debonair, poignant
demeanor.
2. Leap upward by a perfect fifth, followed by slow step-wise resolution to
the tonic. This has a much less poignant quality, but often works.
3. Either of these in retrograde; the latter in reverse seems more effective
to my ears, probably because it outlines the tonic triad.
4. Leap upward by tritone, followed by slow step-wise resolution to the
tonic. This has a more mysterious effect.
5. Any of the above in inversion.
6. Hover around the tonic for a while, leap upward by a fifth or sixth and
hover there for a while, leap back down to the tonic vicinity.


Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Wed, 18 Oct 1995 12:52 +0100
Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id DAA01710; Wed, 18 Oct 1995 03:51:38 -0700
Date: Wed, 18 Oct 1995 03:51:38 -0700
Message-Id: <009980E0B8F59336.5ABA@ezh.nl>
Errors-To: madole@ella.mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu