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       M U S I C          T H E O R Y         O N L I N E
                     A Publication of the
                   Society for Music Theory
          Copyright (c) 1995 Society for Music Theory
| Volume 1, Number 2      March, 1995      ISSN:  1067-3040   |
  All queries to: mto-editor@boethius.music.ucsb.edu or to
AUTHOR: Forte, Allen
TITLE: Tristan Redux: Comments on John Rothgeb's article on the 
       Tristan Chord in MTO 1.1
KEYWORDS: chromaticism, enharmonic equivalence, graphic analysis, harmony, 
       opera, Tristan und Isolde
REFERENCE: mto.95.1.1.rothgeb.art
Allen Forte
Yale University
Department of Music
P.O. Box 208310
New Haven, CT 06520-8310
ABSTRACT: A discussion of the 1907 Louis and Thuille reading of the TC
precedes a critical analysis of Rothgeb's interpretation of it, making
a case for the validity of its identity as a half-diminished seventh
harmony, not only by citing supporting passages in the opera and
multiple allusions to and quotations of that sonority by 20th-century
composers but also by comparing a linear reading of the opening
section of the Prelude based upon the half-diminished seventh
interpretation with Rothgeb's graphic analysis, which follows from his
"slide" explanation of the contextual origin of the TC.
ACCOMPANYING FILES:  mto.95.1.2.forte1.gif
[1] To obtain a certain historical perspective and as a point of
departure for my comments on John Rothgeb's remarkable and provocative
theory of the "Tristan Chord" (hereafter TC), I begin with a brief
discussion of two excerpts from one of the best known and most widely
used harmony textbooks of the very early 20th century, the
Harmonielehre of Rudolf Louis and Ludwig Thuille, hereafter L&T.
Under the general heading "Secondary Harmonies in Minor" (Die
Nebenharmonien in Moll), L&T address the situation in which a harmony
on scale degree II is to be placed under the aegis of one of the
primary harmonic functions, I, IV, or V.  They write:
     It can happen also in minor that the
     harmony on the second degree must be
     understood in the sense of a dominant,
     namely, when the dominant (V or VII)
     follows it.  Compare, for example, the
     Tristan Prelude [bar 83] where the
     seventh chord F-Ab-Cb-Eb upon which
     the ascent terminates is to be
     regarded as a modification of the
     dominant of Eb minor.(1)
See Example 1, supplied by the author. (2)
1. Auch in Moll kann es vorkommen, dass die II.
Stufe im Sinne der Dominant verstanden werden
muss, dann naemlich, wenn sie dieser nachfolgt
(V--VII).  Man vergl. z. B. im Tristan-Vorspiel
. . . wo der Septaccord f-as-ces-es, auf dem die
Steigerung abbricht, durchweg als eine
Modification der Dominant von es moll anzusehen
ist. Rudolph Louis and Ludwig Thuille,
*Harmonielehre* (Stuttgart, 1907), p. 129.
2. In his analysis, Paul Hindemith also
interprets the TC, along with the harmonies on
either side, as expressing a dominant function,
describing the interval between bass and upper
voice as "the interval of a minor third (written
as an augmented second)"  It is one of his Class
IIb2 chords, in which the root lies above the
bass tone.  Paul Hindemith, *The Craft of
Musical Composition* (New York, 1942), p. 210
[2] What is remarkable here is that L&T do not attempt to equate this
locally diatonic half- diminished seventh chord (hd7) with the TC,
even though the latter follows almost immediately.  This certainly
seems to support Rothgeb's view that the TC is not an hd7, and,
indeed, L&T say nothing to contradict that interpretation.  But it
also suggests that there is an important historical-chronological
aspect to their interpretation, that adherents to a classical
19th-century tonal view would always have drawn that distinction,
whereas others, especially those of an avant-garde 20th-century
persuasion, such as Debussy, Schoenberg, or Berg, would not, and, in
fact, did not, as I will point out in the sequel.
[3] In interesting ways the TC hovers over several of L&T's
presentations of chromatic harmonies, but under the general heading
"The Altered Chords" (Die alterierten Accorde), and as shown in
Example 2, they refer to it specifically, in the following terms:
          By comparison [with the previous
     example, where a chord in the Scherzo of
     Bruckner's Ninth symphony resolves into a
     tonic sonority], in the case of the famous
     chord at the beginning of the Tristan
     Prelude, which is constructed in the same
     way, it is more correct to understand the
     G# as it is actually heard: namely, as a
     suspension (that enters freely and leads
     upward), so that the chord itself does not
     belong to the harmony on scale degree VII
     (and thus to the dominant), but to scale
     degree II (and therefore to the
     subdominant). (3)
3. Dagegen ist es bei dem in gleicher Weise
zusammengesetzten beruehmten Accord zu Anfang
des Tristan-Vorspiels richtiger, das gis der
Oberstimme so aufzufassen, wie es tatsaechlich
gehoert wird: naemlich als (frei eintretenden
und aufwaertsfuehrenden) Vorhalt, so dass also
der Accord selbst nicht zur VII. Stufe (und
damit zur Dominante), sondern zur II. Stufe (und
damit zur Unterdominante) gehoert. Louis and
Thuille, p. 232.
[4] Leaving out of account for the moment L&T's compulsion always to
locate harmonies with respect to the Riemannian functions, their
observations here resemble some of those that Rothgeb makes in his
initial remarks--notably, with respect to the contrapuntal origin and
destination of the errant g#.  Remarkably, however, L&T's "Schema"
(Example 2) shows a final reduction of the TC to the second inversion
of a seventh chord on II in A minor, which thus brings it under the
control of the subdominant function.  In the process, the TC's G#
vanishes into A and its D# is squashed down to D, to become the
seventh of the following dominant seventh; the TC is now but a shadow
of its former self.  More important, L&T do not inform us as to the
significance of the transformed TC in the music of the opera--
although it is a sonority of the same type as the TC.  But on the
musical example, they do take the precaution of showing the reader
that the TC is not a chord based upon scale degree VII (i.e., not V of
F#/Gb major), which would require a considerable tonal reorientation
were it so!
[5] Although we might argue several aspects of these interpretations
of the TC, nonetheless they are interesting insofar as they represent
a serious effort by intelligent and experienced musicians to
comprehend the unusual sonority, and to locate it within Riemann's
theory of functions.  And, in a specific sense, their analysis may be
taken to represent the best of late 19th-century thought on
chromaticism at a time when chromaticism was being radically reshaped,
most strikingly in the atonal music of Schoenberg and Webern.
[6] Invoking notational, contextual, and contrapuntal criteria, as
well as an elaborate mechanism of derivation--the "slide" theory--
Rothgeb develops a powerful explanation to show that the TC is not an
hd7.  I propose, however, that the hd7 label is not quite as untenable
as he claims.  I have already cited some evidence in support of this
counter-argument, namely, the music shown in Example 1.  Consider,
now, the music near the end of Act I, at the beginning of the love
scene, following Isolde's "ich trink' sie dir" (Example 3).  There we
see the hd7 F-Cb-Eb-Ab linked by ties to the corresponding enharmonic
notes of the TC, which introduces the second phase of its original
musical context.  I hasten to add that this correspondence in no way
affects Rothgeb's account of the origin of the TC, but it should
influence any consideration of its identity, the other aspect of the
TC he addressed in his article.  At the end of my response I shall
offer a compromise solution to this apparent dilemma.
[7] Leaving theorists and their elaborate exegetical mechanisms aside
I turn now to the interpretation of the TC that can be inferred from
quotations and allusions to it by composers, among them Bartok, Berg,
Brahms, Britten, Bruckner, Debussy, Kern, Porter, Schoenberg,
Schwartz, Scriabin, Strauss, and Weill. This is a diverse list, to say
the least, and the most general statement that can be made is that in
all cases the TC clearly seems to be regarded as an independent,
symbolic sonority lifted from its original context for expressive
purposes that vary with the composer and the composition.  In
connection with the recitation of this list, I wish to make three
statements.  First, I do not ignore John Rothgeb's negative opinion of
these as authentic TCs, but at the end of this response I will return
to the second of the two central issues that his analytical
interpretation engages, the identity of the TC.  Second, some of the
quotations and allusions in my list are "near-Tristan chords," and not
literal in every respect.  Third, and most important, some of the
quotations go far beyond the trivial and arbitrary in respect of their
influence upon the music.(4) But even in "cameo appearances" the TC is
intended to convey its symbolic meanings, ingrained by long-
established tradition, most often connoting the erotic, but in a
purely musical sense often serving as a token of a large-scale
harmonic domain.(5) A famous example of quotation is bars 26 and 27 of
movement VI (Largo desolato) of Berg's *Lyrische Suite*, in which the
lower dyad F-B of the TC is now understood as a musically encrypted
reference to the initials of Berg's friend, Hanna Fuchs.  The first
violin plays the upper dyad of the TC as a double stop, but uses the
enharmonic notation Eb-Ab instead of D#-G#.  For Berg, in this atonal
(partly serial) work, the original notation, with its tonal-melodic
implications so eloquently described by Rothgeb, is meaningless.
4. Schoenberg's epic song cycle, *Das Buch der
Haengenden Gaerten*, Opus 15, provides many
instances.  See my article, "Concepts of
Linearity in Schoenberg's Atonal Music: A Study
of the Opus 15 Song Cycle," Journal of Music
Theory 36/2 (1992): 285-382.
5. This is the case, for example, in Debussy's
music, where the TC is a token of a large-scale
octatonic presence.  In his music we sometimes
hear the inversional image of the TC, a "G7"
harmony, which, together with the TC forms
an octatonic hexachord whose prototype is
familiar from its appearance as the primary
sonority in the Coronation Scene of Musorgsky's
*Boris Godunov*.
[8] To press my argument, surely these many quotations of the TC in
its hd7 form cannot be disregarded.  I do not wish to make a case for
composers as analysts or as theorists (God forbid), but it seems to me
that no extensive rhetoric is required to establish their status as
particularly sensitive auditors and as intuitively gifted students of
musical art works.
[9] Finally, I wish to make a few comments on Rothgeb's analytical
graph of the first seventeen bars of the Tristan Prelude (his Example
4).  He has offered a critique of this graph himself, stating that
". . . the structure shown in Ex. 4 might be viewed as a prototype for
the music of the Prelude's first seventeen bars, but it cannot be
claimed to represent the structure of the finished product."  Yet,
considering it as a graphic analysis of the "finished product"
nevertheless yields some interesting food for thought.  Most striking
of these is the representation of the assumed A minor tonic triad by
implication alone--the parenthesized notes on Ex. 4.  It is important
to recognize that this and every feature of Rothgeb's graph derive
directly from his reading of the origin of the TC, more precisely by
his reinterpretation of the TC as a *non-chord*, of which he has given
us a detailed and precise account.  One would hardly expect a less
rigorous procedure from an analyst of Rothgeb's depth and range of
[10] Indeed, it is Rothgeb's scrupulous concern for analytical method
that provides a context for discussing an alternative view.  I refer
to the parenthesized gaps in his graphic analysis, which suggest that
another kind of large-scale configuration might be considered to
explain structural continuity over the span of the first seventeen
bars of the Tristan Prelude.  And, in fact, my published graph of this
section (Example 4) reads the large-scale upper voice as a projection
of a transposition (T3) of the hd7 version of the TC. (6) (7)
6. Allen Forte, "New Approaches to the Linear
Analysis of Music," Journal of the American
Musicological Society 41/2 (1988), p. 327 ff.
It is not inconsequential that the two
tetrachords, the vertical TC and its T3 related
image projected over the "middleground" descant,
together comprise one of the octatonic
hexachords, for the Tristan Prelude was an
innovative musical statement in a number of
ways, of which its inclusion of octatonic
material stands as a remarkable instance.
7. The graphic reading in Ex. 4 was anticipated
by Milton Babbitt's original analytical
observations in "Responses: A First
approximation," Perspectives of New Music 14/2
and 15/1 (1976): 21, motivated by Edward Cone's
dim view of his idea that a remarkable canonic
structure unfolds at the very opening of the
Prelude.  See Cone's "'Yet Once More, O Ye
Laurels'," in the same issue of Perspectives of
New Music.  In his response Babbitt attacks what
he calls "counterfactual tonal explanations" of
the opening of the Prelude.
[11] To return now to the TC, my analytical interpretation (Example 4)
supports my claim to the validity of the hd7 version of the TC, since
it demonstrates that that version is not simply a local sonority, but
that its transpositionally derived sonorous image penetrates the
"middleground" design of the music--not only the first seventeen bars
but the Prelude as a whole.  Having made this assertion, I am obliged
to admit that, once again, as John Rothgeb would remind me, I
disregard the notational and aurally experienced voice-leading
implications of the fateful G# in the original context of the TC.
[12] To compensate, however, I offer a compromise solution, one that I
trust will reconcile the conflicting readings.  The TC first occurs in
an ambiguous way, portraying an atmosphere of mystery and foreboding
at the beginning of the opera.  As the Prelude develops, however, the
TC assumes its other identity, the "half-diminished seventh" form.
And this becomes manifest both at the end of the Prelude, where
F-Ab-B-Eb serves as II7 to the referential key of Eb minor, and also
elsewhere in the opera--for instance, in the crucial connective
passage shown in Example 3.
[13] The dual interpretation of the TC is itself symbolic,
representing passionate love controlled by destiny (the initial TC)
and death, which ultimately resolves the drama.  The musical
correlates are the tonalities to which the two versions of the TC
refer.  The "G# TC" refers to A minor, although that tonality is never
explicitly stated in the Prelude, while the hd7 version F-Cb-Eb-Ab
refers to Eb minor.  In this way the tritone-related tonalities A
minor and Eb minor express one of the many dualities that pervade
Tristan und Isolde.  This compromise solution resolves a basic issue.
It permits a clear distinction to be drawn between the localized TC in
the context of the opening music and the "global" forms derived from
it by enharmonic transformation and reinterpretation of harmonic
function.  The one event is dynamic because of its
contrapuntal/voice-leading origin and context; the other is stable and
fixed.  Indeed, the "G# version," in Rothgeb's view, is elusively
dynamic because of the role of its soprano note, for as a consequence
of his theoretical genesis of the constellation that occurs on the
downbeat of bar 2, that G# is not a member of an independent 4-note
chord.  Thus, his use of the term TC for that simultaneity carries
with it an implicit and even radical disclaimer. (8)
8. An even more radical interpretation is to be
found in Jean-Jacques Nattiez, *Wagner
Androgyne* (Christian Bourgois Editeur, 1990),
p. 333, where the author poses the question "Is
the Tristan Chord an androgynous chord?"
("L'accord de Tristan est-il un accord
androgyne?") and discusses the sometimes
ambiguous relation between the personae of
Tristan and Isolde throughout the opera.
[14] The Tristan Chord may ultimately resist a definitive analysis, 
however, in the context of the entire opera.  For instance, no one, 
as far as I know, has offered an explanation of its final disposition, 
beginning with its appearance five bars before the end of the opera.  
Perhaps that is the subject of yet another mini-article for MTO.
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