Please let me comment that while you are addressing 20th-century music, your
post to rec.music.early seems to me not inapposite, because many of the same
issues arise when the theory of late 17th-19th century major/minor tonality
is applied to medieval, Renaissance, and Manneristic music.

When 13th-14th century music is analyzed in this fashion, the predictable
consequence is major misunderstanding. Unfamiliarity with medieval theory
and practice can produce what I might term highly curious conclusions from
even the most elect. Thus Hindemith, analyzing a secular composition of
Machaut, concludes that there is little contrast in the levels of vertical
or harmonic tension -- taking the later "triad" as the lowest level of
tension. From either a 14th-century or 21st-century perspective, of course,
what Hindemith takes as the lowest level of tension is actually a mildly
unstable _quinta fissa_ or "split fifth" sonority with an outer fifth plus
two thirds, with the latter intervals calling for eventual resolution.
The standard of rich stability, analogous to the later triad, is what might
be termed the complete _trine_ with outer octave, lower fifth, and upper
fourth. Similarly, a sonority with a major sixth above the lowest note,
often combined with the major third and/or tenth above this note, plays a
role in directed cadences which Margaret Hasselman has compared to V-I or
V7-I in major/minor tonalty.

Similarly, one later 20th-century book on the history of tonality rather
surrealistically includes an analysis of a motet by Petrus de Cruce which
describes how the composer "avoids the third" at stable cadence points --
a bit like describing how Bach, similarly, "avoids the seventh" in his
closing sonorities. While this passage may have been written as something
of a humorous demonstration of how well -- or poorly -- 18th-century
tonality fits the analysis of an outstanding 13th-century composer,
as I recall the author did not, at least in this portion of his
discussion, attempt a more period-appropriate analysis.

However, recent authors such as Hasselman, Richard Crocker, and Sarah
Fuller have done precisely this, articulating the short-range and
long-range events that shape forms and expectations in these centuries.

With Renaissance and Manneristic styles, the consequence of an
18th-century analysis may be a more subtle distortion, but also a
consequential one, of the actual organizing principles and nuances
of the style. In all these styles, the role of thirds and sixths as
the richest stable intervals, and common rules and assumptions such
as the exclusion from serious counterpoint of parallel fifths or
octaves, produce some notable resembles: but the differences are also
quite significant. The fluidity of 16th-century and indeed early
17th-century music, informed by a continued use of medieval two-voice
progressions such a major third expanding to a fifth in the new
context of a smooth concourse of tertian sonorities, makes possible
effects which would be uncharacteristic in a typical 18th-century
tonal style.

One development with medieval affinities which was so recognized in the
early 20th century might be termed quartal or quintal harmony: the
revival of styles where fifths and/or fourths are the preferred stable
concords. Thus one early 20th-century handbook on "modern harmony"
actually described medieval organum as an "impressionistic" technique!
Debussy, Bartok, and Hindemith are among composers exploring in this
direction -- as well as some styles of jazz, for example. One might see
this quartal/quintal trend both as a deliberate allusion to medieval
technique, and more generally as a movement to go in some direction
other than that of the conventional tertian harmony prevalent in the
19th century.

A related development, in two-voice counterpoint as well as multi-voice
settings, is the use of a variety of intervals and vertical sonorities,
rather like the pluralistic interval structures or "partitions" favored
in the 13th century, although 20th-century pluralism has its own
techniques and does not necessarily sound "neo-medieval." Bartok, for
example, often typifies this line of development.

Yet another tendency is a move toward "layered" styles where, although
vertical sonorities are important, the free development of melodic
lines has greater weight than in many tertian 19th-century styles.

Still another related aspect is the use of "probabilistic" techniques
in both 13th-century and 20th-century polyphony, where some events
are more probable than others, but few seem "wrong" or excluded.
As Ludmila Ulehla has written, such styles involve "the control of
dissonance" in fashions other than that of major/minor tonality.

Neomodality has often been noted as an important trend in 20th-century
music, ranging from the Renaissance-flavored settings of Ralph Vaughan
Williams to the folk-related styles of Bartok, Stravinsky's
arrangements of Gesualdo, and jazz performances of Miles Davis. Such
styles might involve a quartal/quintal technique or a tertian one --
or possibly, as in Debussy and some progressive jazz settings, the
use of more complex sonorities built out of stacked thirds or other
intervals.

An interesting essay might be written about the uses of medieval style
in contemporary composition and criticism. Thus one commentator writing
in 1938 or so drew a parallel between the styles of Perotin and
Schoenberg as likewise "indifferent" to aural beauty; while Steve Reich
has cited Perotin as one germinal source for modern "minimalist"
styles. While I might ask whether a monumental composition by Perotin
such as _Viderunt omnes_ can really be called "minimalist" in any
usual sense, nevertheless it is clear that Reich's appreciation
focuses on such traits as an admirable economy in making simple
melodic themes and ideas the basis for an extended piece of music.

To conclude this curious note, I would add that as one recent
journal article pointed out, those of us who urge that medieval
theory is invaluable in understanding medieval music should not
argue that such theoretical knowledge makes analysis simple or
uncontroversial: there is still a need to interpret and flesh
out, whether one is reading a treatise or describing the style
of a 13th-century conductus or motet. Similarly, a thorough
familiarity with 20th-century theory does not solve the problem
of analyzing the subtle techniques of Debussy or Bartok, for
example -- but it can afford a more auspicious starting point
for such an endeavor.

Also, a better understanding of medieval or 20th-century
technique need not exclude comparisons to 18th-19th century
harmony, but can actually facilitate more meaningful and
satisfying comparisons, as in the writings of Crocker,
Hasselman, and Fuller on 14th-century vertical forms of
organization and listener expectations which reveal
phenomena distinct from but analogous to those of
major/minor tonality.

Margo Schulter
mschul...@calweb.com