source file: mills2.txt
Date: Tue, 18 Mar 1997 08:11:30 -0800

Subject: Re: Milne/Wolf 4-5-6-7-8 and Gr Aug6th/Fr Aug6th chords

From: Daniel Wolf <DJWOLF_MATERIAL@compuserve.com>

>From recent postings:

<''>These "chords" are the by-product of very nice chromatic voice-leading.
<>I.E., they are linear structures, not vertical sonorities.  Our
<>traditional "music theory" courses (I prefer to call them "music systems"
<>courses, for they examine past, well-established practices, and really
<>do not address 'theory' at all) get too carried away with Harmony as the
<>primary structure, while linear melodic connections are actually the most
<>important area of construction.

<That's interesting. I think our traditional "counterpoint" courses get too
<carried away with linear melodic connections as the primary structure,
<ignoring harmony. Seriously, I think that one of traditional music
theory's
<biggest mistakes is to teach that, for European music from at least the
<16th to 19th centuries, it is possible to separate the "linear" from the
<"vertical" and judge their relative "importance" separately.''

I think that this is a critical example of how the paper trail of theory
has diverged from practice - and how the theory can feed back upon music
making in a creative misreading (not unlike the literary hermeneutics of
Bloom). From Monteverdi's largely textural division into two practices, and
the solid tradition of counterpoint taught before figured bass, developed
the notion that counterpoint and harmony are independent domains - two
separate courses of study fitting tightly into semester schedules at large
Universities. To be fair, the best teachers and theorists (from Schenker
and Schoenberg to Boulanger) never made things out to be so black and
white, but their attempts to integrate vertical and horizontal viewpoints
rarely survived the journey to the heartlands, and by the mid-1950s, modal
counterpoint was seldom taught at all. A Schenker-inspired countermovement
would move again in the counter-direction, but like the set-theory-based
''new math'' of the 1960's, my impression is that it has been largely
taught in a mechanical way (with the goal of producing identical
'schenkergrams') by teachers not completely comfortable with the
theoretical rationale. I have heard that some schools are now moving in an
algorithmic direction. (Actually, the MacHose text that my Junior High band
director gave me used a statistical approach that could be considered a
prototype of certain trends in this direction). 

The most interesting thing is that all of these swings in theoretical
orientation have made real marks on the way that people do make music, both
composing and performing. Ivor Darreg, to take just one curious example
from the microtonal community, learned from his teacher to assemble a
thematic catalog and to outline as many potential harmonizations as
possible. Had his teacher worked from a more contrapuntal basis, I imagine
that Ivor's music would have had a very different character.  Partch's
impulse to harmonize on the basis of chords built on ''stacked thirds'' -
as well as the systemic use of inversion - can be heard as a token of a
particular theoretical orientation.

To bring the thread back, Milne criticized my position on the 4-5-6-7
tuning of the dominant by arguing that harmonies with ninths and elevenths
voided my argument. However, I think that the repertoires in which such
extended harmonies are present are already well beyond the tonic-dominant
dynamic, and I am extremely hesitant to speculate about the intonational
content of such repertoires (M. Vogel's book on the ''Tristan'' chord
should be cited in this context). The question is, is 4-5-6-7 an
_acceptable_ (note that I have not said ''authentic'') tuning for the
dominant  in a repertoire - say Viennese classical music - where this
dynamic is well established?  While practically out of the question for
keyboard instruments, for strings, I find it acceptable - and in some
cases, desirable.

The augmented sixth chord's approximation of 4-5-6-7 in meantone deserves
further comment. As someone has pointed out, this chord was heard in
passing in choral music (which may or may not have been accompanied) and
only with frequency as a sustained chord in repertoire where ET was
established (at least as an ideal). So the question remains, why was this
wonderful chord not used more often in meantone keyboard music? I think
this is an excellent example of how our prejudice towards ''harmony'' - our
bias via training to hearing the vertical consonance - makes us relatively
deaf to the contextual, melodic ''dissonance'' caused by the proximate use
of tones from relatively distant scalar collections. This is, for me, a
wonderful example of how context can make an in-tune chord sound
''dissonant''.     

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