1. Tradtional - Major/minor tonality (Aaron Copland)
2. Aleatoric - "Chance" music (John Cage, Ives, Stockhausen)
3. Neo-classicism - Stravinsky (traditional forms with non-traditional harmonies and orchestration
4. Electronic - this is not just pop music with electronic instruments but "Musique concrète," works composed with traditional instruments with the addition of taped sounds. [Look at the Notable Composers link: everyone from Frank Zappa and the Beatles to Edward Varèse and Xenakis]
5. Serialism - compositions based on the 12 1/2 steps of the octave (versus the eight tones in a major or minor scale). Arnold Schoenberg, Anton Webern, Alban Berg, Karlheinz Stockhausen, Pierre Boulez, Luigi Nono.
6. Jazz (Bernstein)

I don't remember Thomson's categories, either, but I do have a few
observations about your other points:

: Major/minor tonality began to break down with the invention of
: chromaticism, started by Richard Wagner in the late Romantic
: era

I suppose that, when simplifying things for a beginner, you can
attribute the breakdown of tonality to the *increase* in chromaticism
in the middle of the 19th century, but it was not "invented" at that
time (Your student's next question is liable to be "What about Bach's
Chromatic Fantasy and Fugue, then?"), and Wagner didn't start the
trend, either. To be more accurate, the use of chromaticism didn't
just "happen" and thereby cause the dissolution of the functional
harmonic system. Rather, the increase in chromaticism was itself a
product of composers' increasing exploitation of linear harmonies, a
process which can be seen prominently already in the music of J. S.
Bach.

I would be very surprised if Thomson pointed to Aaron Copland as an
exemplar of major/minor tonality without making a caveat. Your student
will have nearly as much difficulty trying to use this framework to
analyze Vitebsk, the Piano Variations, the Piano Quartet, or Inscape
as he would in attempting to apply it to Cage's 4'33". You had better
qualify this statement by specifying pieces like the Danz�n Cubano, El
Sal�n M�xico, or Billy the Kid.

Similarly with category no. 3. The Rite of Spring is scarcely a
neoclassical work, nor is Petrushka,  Les Noces, the Movements for
Piano and Orchestra, or Threni.

The description of category 4, "electronic music", is confused.
"Musique concr�te" is a particular technique, and is sometimes found
in in pop music as well (e.g., Beatles' songs like "A Day in the
Life"). You should also be aware that the Wikipedia articles around
this subject are particularly contentious at the moment, and you are
linking only to the "Musique concr�te" article, where even the "see
also" links do not include "Electronic art music" or "Electronic
music", which are probably where your student should start (though
these two articles are particularly subject to editorial debate at the
present time).

Your student will get a much better idea of category 5, "serialism",
from the Wikipedia, but he is bound to come back with questions about
this "based on the 12 1/2 steps of the octave (versus the eight tones
in a major or minor scale)" business (and I'll bet he's already
questioned the number of notes in a major or minor scale being set at
eight instead of seven). Stockhausen's Stimmung, for example, is a
serial composition, but its pitches do not comprise the chromatic
scale--in fact, there are only six, and they are from the overtone
series. Henri Pousseur's electronic composition Scambi is also a
serial composition, but has no pitches at all, being composed from
filtered white noise. Your definition better fits twelve-tone
technique:

than the broader category of serialism and, though the serialism
article has a link to it, I think it would be better for your student
to begin there. Also, as with the other categories, when naming
Schoenberg, Berg, and Webern, it is necessary to stipulate that even
twelve-tone serialism will not be found in any of their works from
before 1920 (e.g., Verkl�rte Nacht, Wozzeck, the Passacaglia for
orchestr op. 1, respectively), and there are later exceptions in
Schoenberg's output, as well.

As for Penderecki, much of his music from after about 1975 (e.g., the
Polish Requiem, Cello Concerto No. 2) can in fact be "evaluated and
analyzed in terms of major/minor tonality", though naturally of the
extended sort found in late-nineteenth-century composers. Once again,
it is necessary to specify which pieces you are speaking of.

I hope you find these comments helpful.

-- 
Jerry Kohl
"L�gp�rn�s haj�m tele van angoln�kkal." 

Margo Schulter:

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.

Being quite ignorant as to Thomson's scheme, what I might comment on
is the influence of medieval and Renaissance/Manneristic music on
20th-century developments.

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, Bartók, 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." Bartók, 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 Bartók, 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 Bartók, 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.

Most appreciatively,

Margo Schulter
mschul...@calweb.com 

Ear Training Texts:

Conducting Elgar

Michael Dickreiter, Reinhard G. Pauly. Score Reading: A Key to the Music Experience

Knud Jeppesen. Counterpoint: The Polyphonic Vocal Styles of the Sixteenth Century

Norman Lebrecht. The Maestro Myth: Great Conductors in Pursuit of Power

Alfred Mann. The Study of Fugue

Brock McElheran. Conducting Technique for Beginners and Professionals

Reginald O. Morris, Howard Ferguson. Preparatory Exercises in Score Reading

Walter Piston. Orchestration

Jean Rameau. Treatise on Harmony

Nikolay Rimsky-Korsakov. Principles of Orchestration

Jeff Rona. The Reel World: Scoring for Pictures

Max Rudolf. The Grammar of Conducting: A Comprehensive Guide to Baton Technique and Interpretation

Felix Salzer. Structural Hearing Tonal Coherence in Music (Two Volumes Bound As One) [Schenkerian analysis: read Piston and Fux first.]

Hermann Scherchen. Handbook of Conducting

Arnold Schoenberg. Structural Functions of Harmony

Gunther Schuller. The Compleat Conductor

Ernst Toch. The Shaping Forces in Music: An Inquiry into the Nature of Harmony, Melody, Counterpoint, Form (The Dover Series of Study Editions, Chamber Music, Orchestral Works, Operas in Full Score)

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