Volume 1, Number 1, January 1995
Copyright © 1995 Society for Music Theory
The Tristan Chord: Identity and Origin
KEYWORDS: harmony, enharmonic equivalence, diminution, Wagner, slide, elision, enlargement, contextuality
ABSTRACT: Theorists have struggled many decades to explain the first simultaneity of the Prelude to Wagner’s Tristan und Isolde. An interpretation that seems to be widely credited today equates the TC with the enharmonically related half-diminished seventh chord. The difficulty with this notion is that the outer-voice interval of the TC is specifically an augmented ninth, not a minor tenth, and these two intervals differ radically in tonal music, not only in function but in sheer sonority. The TC is explained here as resulting from an enlarged slide formation together with a daring application of elision.
 One might conclude from the sheer quantity of literature on Wagner’s Prelude to Tristan und Isolde and in particular on the Tristan Chord (TC hereafter) that every conceivable approach to the explanation of that famous sonority had by now been proposed. A sampling of that literature, however, suggests that the identity and origin of the TC is far from settled. Most historical accounts of the chord have been preoccupied by the often irrelevant a- priori assumptions of one or another “system of harmony” and have failed to address the issue from the perspective of composing technique. I will argue that a particular technique of diminution—one well precedented in musical tradition—has been applied by Wagner in a highly original way with results uniquely suited to depict the psychological milieu of the beginning of the opera. To understand the TC fully, however, we must first be clear about its identity—that is, the inventory of intervals it comprises.
The intervals of the TC
 Several recent contributions to the critical and theoretical literature not devoted primarily to Tristan or its chord refer to one or another half-diminished seventh chord as a “Tristan-chord,”(1) while the actual TC as it is presented at the beginning of the opera’s Prelude has on the other hand been called a “half-diminished seventh chord.” Such nomenclature presupposes either that Wagner misspelled the chord on the downbeat of bar 2 of his Prelude or that the language of the music under discussion in the particular case—whether Tristan or another work—makes no distinction between enharmonically equivalent but differently spelled intervals.
 The second of these assumptions seems to me obviously
untenable, and I shall not deal further with it here. The
first assumption—that the TC is actually an enharmonic
spelling of a different chord—can, according to Martin
Vogel, be traced back at least to an 1899 account by Salomon
Jadassohn, who represented the bass f as an alternate
 How can such an assertion of enharmonic spelling be
evaluated? The answer is that it can be evaluated only with
respect to the musical context, and only in the light of a
principle that I will take as axiomatic: the ear will in
general seek simpler explanations over more complex ones,
and, in particular, will posit an enharmonic change only if
compelled to do so by context. For example, the interval 0–4 (in “atonal” notation) is automatically interpreted by the
ear as a major third. An appropriate context can oblige the
ear to hear it as a diminished fourth (in which case it
sounds radically different), but the conditions under which
this will occur are very special ones indeed. Now if we
assume, in the first bar plus upbeat of the Tristan
Prelude, a normal spelling of the first note (A instead of
g-double-sharp), then it is inescapable that the second and
third notes are G and E respectively, since the first
melodic interval will scarcely be heard as an augmented
fifth. (The arguments in support of this contention may,
after the discussion to follow, be supplied by the reader.)
The bass note that enters in bar 2 is at least
enharmonically equivalent, if not identical, to the first
melodic note of bar 1, F. Is it possible that this pitch
has become enharmonically revalued as
 Here the ascending continuation of the notated F
strongly suggests its possible interpretation as
 Jadassohn’s account of the TC probably does not need to
be refuted for very many modern readers. But the currently
fashionable assimilation of the TC into the category of
“half-diminished seventh” (or vice versa) is really no more
plausible. Since it is established that the bass of this
chord is F, a major third lower than the first note of the
Prelude, the TC can be a half-diminished seventh only if the
 The intervals of the TC as measured from the bass up, then, are: A4, A6, A9 (=A2), exactly as notated. Not one of these intervals is present in a half-diminished seventh chord constructed above its root as bass. Only one of them—the A4—is present in any inversion of such a chord.
“Precursors” of the TC
 Vogel reports that
In the course of the treatments [described above, by Schoenberg, Hindemith, and Fortner] it was variously noted that the chords could already be found in earlier style-periods. In the quest for precursors it is possible to go back as far as Guillaume de Machaut and Gesualdo da Venosa.
 If the TC does in fact “appear” in Beethoven’s sonata,
then in what sense is it a “precursor” in that context?
Shouldn’t its name be changed, perhaps to something like
“the Op. 31 No. 3 chord”? The obvious answer is that
Beethoven’s chord—leaving aside the fact that its
 The difference, in tonal music, between a minor third and an augmented second is profound. The two intervals fall on opposite sides of the most fundamental dividing line in its language: that between consonance and dissonance. It is hardly surprising, therefore, that they sound very different from one another, as do the TC and the half-diminished-seventh chords.
 Among the many accounts of the
TC that have been proposed in the past, those most nearly
plausible explain the
Note that the phrasing slur for the oboe in bars 2–3 begins on the
 It is true that Mitchell’s reference to a “chordal
interchange” begs the question by presupposing that the
 Example 2 shows, in four stages, what I propose as the
origin and evolution that led to the TC. (The augmented-sixth chord in the progression at a has, of course, a still
simpler diatonic origin.) The treble in Example 2a takes the
line of least resistance, which is to follow the bass in
parallel tenths and thus to descend a step. If, in a given
application of this basic voice-leading pattern, the
compositional aim is instead to have the treble ascend, then
the tenor may take over the completion of the underlying
descent as in Example 2b. The ascending step in the treble,
however, is “difficult” and requires an expenditure of
effort. It is a deeply rooted musical impulse to provide
some assistance to the treble in negotiating such an
ascending step. One possibility, for example, would be to
apply the technique of “reaching over” (Schenker’s
Uebergreifen), perhaps by letting the upper voice first
leap to C and reach the B thence by descending a step; this
might result in a cadential
 Let us digress for a moment and consider bars 100–108
from Scarlatti’s Sonata K. 461 shown in Example 3a and the
graphic interpretation in Example 3b. The dominant of C
(locally inflected to the minor mode) is reached in bar 102
and extends through bar 107. The extension first repeats
the treble C – B with bass set in parallel tenths; bar 105
appears to initiate a second repetition, but in bar 106 the
treble not only follows the descent of the bass but also
breaks free and ascends to D. (The resulting third-space, B
– D, answers the descending third
 Wagner, too, was capable of composing such a slide, and
he did so in bars 2–3 of his Prelude to Tristan. The
 The elision, or suppression, of the A1 of bar 2 is
but the first of several such acts that lend the music a
portentously laconic quality. The dominant-seventh chord of
bar 3 “should” continue to an A-minor tonic chord, almost
certainly with C2 in the treble; the bass A would provide
the point of departure for the chromatic passing
 This chord requires a contextual explanation different
from that of the two TCs. The bass must enter on C in order
to descend by half-step to its destination, B (the root of V
of V, which now, finally, falls a fifth as expected). The
ascending slide figure in the treble, to be consistent with
the procedure followed thus far, must enter on the same note
as that with which the preceding slide ended—that is, on
d natural rather than the
 These observations alone are sufficient to account for the first simultaneity of bar 10. It is certainly possible that the enharmonic equivalence of this chord to the TC and to the half-diminished seventh chord was also a factor in Wagner’s choice of the perfect rather than the augmented fourth at the downbeat of bar 10. After all, it is well known that this enharmonicism is exploited extensively as the opera unfolds. It is possible that authoritative documents (unknown to me) exist which permit inferences about Wagner’s compositional chronology in this matter, but in the absence of such documents I would maintain that considerations such as those I have mentioned in  may well have come first and have served as the cradle for the particular enharmonicisms that come to play such an important role later.
 These enharmonicisms are of a very special and novel
character. It is well known that the enharmonic equivalence
of different spellings of the diminished-seventh had long
provided an important musical resource. The same is true of
the enharmonic relationship between the dominant-seventh and
 A voice-leading graph incorporating the elements
described above as elided might appear as in Example 4a (a
simplification of which is given in 4b), where elided
elements are enclosed in parentheses. The relationship of
this graph to the music, however, is perhaps somewhat
different from the normal one of a well-made foreground
sketch to the music it represents: such a sketch should and
does vividly portray the general outline of the finished
composition in such a way as to be immediately recognizable
to anyone who knows the music well. Example 4a as it stands
does not satisfy this criterion. The passage depicted
incorporates modifications so profound that the overall
effect is quite different. Most striking among these is the
suppression of the tonic bass note that “should” appear in
bars 4–5. The result is that the bass arpeggiation of the
tonic triad shown in Example 4 is obliterated in favor of a
prolongation, through bar 16, of the dominant of bar 3.(10) The connection of bar 16 to bar 3 is confirmed by the
reappearance in bars 16–17 of the third-space
 The advantages I see in the above explanation of the TC
are that it releases me from the apparent dilemma of having
to interpret the
1. For example, Joseph Kerman “Close Readings of the Heard
Kind,” 19th Century Music XVII:3 (1994), 214; Allen
Forte, “Secrets of Melody: Line and Design in the Songs of
Cole Porter,” The Musical Quarterly 77:4 (1993), 623–24.
2. Martin Vogel, Der Tristan Akkord und die Krise der
modernen Harmonielehre (Duesseldorf: Gesellschaft zur
Foerderung der systematischen Musikwissenschaft, 1962), 24. Exactly how Jadassohn accounts for the inclusion of
4. “Im Verlauf der Auseinandersetzung wurde verschiedentlich
darauf hingewiesen, dass sich die Akkorde schon im frueheren
Stilepochen finden lassen. Auf der Suche nach Vorlaeufern
kann bis zu Guillaume de Machaut und Gesualdo da Venosa
5. “. . . den vom Meister R. Wagner selbst so werth
geschaetzten Theoretiker unserer Kunst.” Hans v. Wolzogen,
Foreword to Carl Mayrberger, Die Harmonik Richard Wagner’s
an den Leitmotiven des Preludes zu “Tristan und Isolde”
erlaeutert (Chemnitz, 1882), 4. Mayrberger’s text was
originally published in Bayreuther Blaetter 4 (1881).
Although Mayrberger’s instinct about the
7. A formation related to the composed slide is the
appoggiatura from below, when such an appoggiatura is
prepared and the note of preparation is embellished by its
own lower neighbor. These idioms are particularly favored
by Scarlatti. For only two examples, see the Sonata K. 426,
bars 32–33, and the Sonata K. 460, bars 12–13.
8. Here I should emphasize that I have cited an example from
Scarlatti not to suggest any historical connection between
the two composers, but merely to illustrate a figure of
diminution—applied, to be sure, in a drastically
different and otherwise unrelated musical context.
9. Nevertheless, this chord is much more similar in sonority
to a half-diminished seventh than is the TC. I attribute
this to the initially uncertain identity of the ‘cellos’
For example, Joseph Kerman “Close Readings of the Heard Kind,” 19th Century Music XVII:3 (1994), 214; Allen Forte, “Secrets of Melody: Line and Design in the Songs of Cole Porter,” The Musical Quarterly 77:4 (1993), 623–24.
Martin Vogel, Der Tristan Akkord und die Krise der modernen Harmonielehre (Duesseldorf: Gesellschaft zur Foerderung der systematischen Musikwissenschaft, 1962), 24. Exactly how Jadassohn accounts for the inclusion of
“Im Verlauf der Auseinandersetzung wurde verschiedentlich darauf hingewiesen, dass sich die Akkorde schon im frueheren Stilepochen finden lassen. Auf der Suche nach Vorlaeufern kann bis zu Guillaume de Machaut und Gesualdo da Venosa zurueckgegangen werden.
“. . . den vom Meister R. Wagner selbst so werth geschaetzten Theoretiker unserer Kunst.” Hans v. Wolzogen, Foreword to Carl Mayrberger, Die Harmonik Richard Wagner’s an den Leitmotiven des Preludes zu “Tristan und Isolde” erlaeutert (Chemnitz, 1882), 4. Mayrberger’s text was originally published in Bayreuther Blaetter 4 (1881). Although Mayrberger’s instinct about the
William J. Mitchell, “The Tristan Prelude. Techniques and Structure,” The Music Forum I (1967), 174.
A formation related to the composed slide is the appoggiatura from below, when such an appoggiatura is prepared and the note of preparation is embellished by its own lower neighbor. These idioms are particularly favored by Scarlatti. For only two examples, see the Sonata K. 426, bars 32–33, and the Sonata K. 460, bars 12–13.
Here I should emphasize that I have cited an example from Scarlatti not to suggest any historical connection between the two composers, but merely to illustrate a figure of diminution—applied, to be sure, in a drastically different and otherwise unrelated musical context.
Nevertheless, this chord is much more similar in sonority to a half-diminished seventh than is the TC. I attribute this to the initially uncertain identity of the ‘cellos’
In this respect I concur with Mitchell’s reading; see Mitchell, 170–171 (his Example 4).
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