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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 1     January, 1995     ISSN:  1067-3040   |
  All queries to: mto-editor@husc.harvard.edu
AUTHOR: Rothgeb, John
TITLE: The Tristan Chord: Identity and Origin
KEYWORDS: harmony, enharmonic equivalence, diminution, Wagner,
slide, elision, enlargement, contextuality
John Rothgeb
Binghamton University
Department of Music
Binghamton, NY 13902-6000
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.
[1] 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.
[2] *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.
1. For example, Joseph Kerman "Close Readings of the Heard
Kind," *19th Century Music* XVII:3 (1994), p. 214; Allen
Forte, "Secrets of Melody: Line and Design in the Songs of
Cole Porter," *The Musical Quarterly* 77:4 (1993), pp. 623-
[3] 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
spelling of e-sharp, and the TC itself as a leading-tone
seventh of the key of F-sharp minor.(2)
2. Martin Vogel, *Der Tristan Akkord und die Krise der
modernen Harmonielehre* (Duesseldorf: Gesellschaft zur
Foerderung der systematischen Musikwissenschaft, 1962), p.
24.  Exactly how Jadassohn accounts for the inclusion of d-
sharp instead of d in this chord is not explained by Vogel.
[4] 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 f 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 e-sharp?  Only the
continuation can answer this question.  One can imagine
continuations that would make the assumption of enharmonic
change at least plausible, and perhaps even necessary; one
such continuation is shown in Ex. 1.
[5] Here the ascending continuation of the notated f
strongly suggests its possible interpretation as e-sharp.
Wagner's descending continuation, however, dispels any
reasonable doubt about the identity of this pitch as f, not
e-sharp: the descending half-step of bars 2-3, like the
identical (and intimately associated) succession in bar 1,
certainly involves two distinct letter names, or, to say the
same thing in another way, two different scale degrees.
[6] 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
oboe's g-sharp of bar 2 is really an a-flat.  In that case
we must definitely posit an enharmonic change from a-flat of
bar 2 to g-sharp of bar 3, for the chordal interval of bar 3
is unquestionably a major third, not a diminished fourth.
But why should we assume an enharmonic change?  The written
g-sharp of bar 2 does, after all, ascend to an a (without
prejudice to the question of whether this a is the
"resolution" of the g-sharp), and the melodic interval in
bar 2 surely is heard as an inversion of that of bar 1 (thus
as a minor second) rather than as two different inflections
of the same scale degree.  The assumption of enharmonic
change here would be no less bizarre than Jadassohn's
assignment of the four simultaneities of bars 2- 3 to as
many different keys.(3) The oboe's g-sharp is indeed a g-
sharp, and Wagner's spelling of the remainder of the TC as
well reflects aural necessity.
3. Vogel, p. 24.
[7] 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.
[8] *"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. . . . In Beethoven's
        Piano Sonata in E-flat, Op. 31 No. 3, the Tristan-
        Chord appears in the same register and at the same
        pitch.  [An example comprising bars 33-36 of the
        named sonata follow, with an arrow singling out the
        downbeat chord of bar 36.](4)
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
zurueckgegangen werden. . . .  In Beethovens Klaviersonate
in Es-dur, op. 31, Nr. 3, tritt der Tristan-Akkord in
gleicher Lagerung und Tonhoehe auf."  Vogel, p. 12.
[9] 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
correctly notated e-flat is the seventh of a 7-6 suspension
-- is not a "Tristan Chord" but rather a half-diminished
seventh.  Its treble pitch is an a-flat, which forms an
outer-voice interval of a minor 10th (3d), not an augmented
9th.  As such it would be free to proceed by leap -- perhaps
to f over a bass b-flat (in the sense of II7 - V of E-flat);
any such continuation of Wagner's g-sharp would at the very
least create an unbridgeable detachment from the Prelude's
first bar.  Wagner's g-sharp, as an A9, must in some way
ascend by step.
[10] 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.
[11] *Compositional origin.*  Among the many accounts of the
TC that have been proposed in the past, those most nearly
plausible explain the g-sharp of bar 2 as an accented long
appoggiatura to the a that follows.  This was the view of
Carl Mayrberger, who was represented by the editor of the
Bayreuther Blaetter as "the theorist of our art so highly
esteemed by Master R. Wagner himself";(5) it is a view that
seems to me greatly preferable to the neutralization of this
pungent g-sharp that necessarily attends its assimilation as
a chord tone.  The two notes g-sharp - a form a 9-10
succession above the bass -- a very credible "resolution"
formation, especially when the 9 is augmented, as in this
case.  Yet this account is not completely satisfactory.  The
following remarks by William J. Mitchell, for example,
cannot be summarily dismissed:
     Note that the phrasing slur for the oboe in bars 2-3
     begins on the g-sharp^1^ under examination and carries
     through to b^1^ . . . .  But this is not characteristic
     of the usual two-tone slur (g-sharp^1^ to a^1^) for the
     indication and execution of an appoggiatura.  It should
     also be observed that the oboe's g-sharp^1^ to b^1^ is
     accompanied by a very frequent kind of chordal
     interchange as the bassoon leaps from b to g-
     sharp . . . .(6)
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), p. 4.  Mayrberger's text was
originally published in Bayreuther Blaetter 4 (1881).
Although Mayrberger's instinct about the g-sharp was
correct, he was otherwise forced into absurdity by his
allegiance to Simon Sechter's prescriptions about how
fundamental basses might be allowed to move.
6. William J. Mitchell, "The Tristan Prelude.  Techniques
and Structure," *The Music Forum* I (1967), p. 174.
[12] It is true that Mitchell's reference to a "chordal
interchange" begs the question by presupposing that the g-
sharp is chordal.  The account offered here will address
Mitchell's concerns without reaching his conclusion that the
g-sharp is a member of an independent four-note chord.
[13] 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 Ex. 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 Ex. 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 6/4 above the bass e.  Another
possibility, however, is to apply a *slide* (Schleifer) as
in Ex. 2c.  This ornament makes it possible for the treble
to express the stepwise motion in both ascending and
descending directions, and to compose out the third-space
between the two goal-tones.
[14] Let us digress for a moment and consider bars 100-108
from Scarlatti's Sonata K. 461 shown in Ex. 3a and the
graphic interpretation in Ex. 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 e-flat - c of bars 100-
101; the two thirds constitute an instance of "unfolding"
(*Ausfaltung*) as indicated by the brackets in Ex. 3b.)  It
accomplishes this with precisely such a slide as that shown
in Ex. 2c, except that instead of being written as an
ornament, the slide is composed and expressed in large
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.
[15] Wagner, too, was capable of composing such a slide, and
he did so in bars 2-3 of his Prelude to *Tristan*.  The
tones g-sharp-a-a-sharp-b of those bars should be understood
as an indivisible entity, and indeed one that properly
belongs above the bass note E of bar 3.  The a that should
precede this succession -- indeed, that should appear as the
tenth of the bass f of bar 2 -- is, quite simply, missing:
it is suppressed, or elided.  In its place, the tones of the
ascending slide enter prematurely, above the bass note
preceding the one to which they really belong (Ex. 2d); the
collision of the first of them, g-sharp, with the remaining
notes of an otherwise well-precedented augmented-sixth
chord, produce the poignant formation that has come to be
known as the TC.  Although absent, the missing a is to be
"understood," as it quite easily can be from the admittedly
sparse context provided by bar 1.  Its absence, together
with the unaccompanied opening and other omissions to be
described presently, seems to me a fitting musical depiction
of the mysterious psychological state to be established by
the beginning of the Prelude.(8)
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.
[16] The elision, or suppression, of the a^1^ 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 c^2^ in the treble; the bass A would provide
the point of departure for the chromatic passing A-flat on
which the second TC is based.  That continuation, however,
is suppressed in favor of a direct connection to the second
slide formation and the second TC.  This establishes the
precedent that after the opening melodic statement, each
subsequent entrance will begin with a chordal arpeggiation
within the preceding statement's final chord.  The
consequence of this precedent for the third entrance, that
of bar 9 plus upbeat, is that it must begin with the broken
interval d^2^ - b^2^.  The first simultaneity of this
entrance (bar 10) is placed analogously to the two TCs but
differs from them in intervallic structure.  Like the TC, it
is enharmonically equivalent to a half-diminished seventh
chord (this time in the "third inversion"), but, also like
the TC, its specific intervals (in particular the augmented
fifth) do not correspond to those of any position of such a
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' g-
sharp in bar 10; especially as we have just heard a
chromatic passing b-flat, the g-sharp can very plausibly be
interpreted at the outset as a-flat, in which case the
intervals of the chord in question are exactly those of the
half-diminished-seventh chord in the 4/2 position.
[17] 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 d-sharp that would be required by
strict parallelism to the two preceding slide figures.  The
'cello motive that precedes this unique chord likewise
requires adjustment in comparison to its two predecessors.
As mentioned above, it must begin by arpeggiating the
chordal interval d^2^ - b^2^; a descent from the b^2^ of
only two half-steps (as in the preceding entrances),
however, would leave the 'cellos' voice on the note a, a
major rather than an augmented sixth above the bass.  This
note, rather than moving by half-step into the seventh of
the coming dominant-seventh chord as its predecessors did,
would in fact anticipate that seventh -- clearly an
unacceptable result. The incorporation of one additional
half-step, resulting in an arrival on g-sharp, was
undoubtedly the best way to approximate a parallelism with
the two preceding entrances.  As an expansion, it had the
additional advantage of agreeing with the necessary
expansion (also by one half-step) of the slide motive.  The
tenor voice (first bassoon in the score) now takes a perfect
fourth above the bass (f-natural) in contrast to the
analogous augmented fourths of the two TCs. The use of f-
sharp here would have anticipated the fifth of the coming
harmony (in this case B) just as the previous augmented
fourths did; but the f-natural has the distinct advantage of
being a diatonic note in the key, so that the two
chromatically altered elements (d-sharp and f-sharp) are
reserved for the arrival of the chord for which they are
[18] 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 [17] may well have come first and have served as the
cradle for the particular enharmonicisms that come to play
such an important role later.
[19] 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
the augmented 6/3 and 6/5 chords (the "Italian" and "German"
sixths, respectively).  These relationships differ
fundamentally from that between the TC and the half-
diminished seventh, however.  The diminished-seventh chord
has the property that any normal respelling yields exactly
the same collection of intervals to within inversion (A2 =
D7, etc.).  True, this does not hold of the dominant-
seventh, where an appropriate respelling yields an augmented
6/5; but the two enharmonically equivalent intervals (minor
seventh and augmented sixth) nonetheless both belong on the
same side of tonal music's fundamental dichotomy --
specifically, on the side of dissonance.  None of the above
properties holds for the relationship between the TC as it
appears in bar 2 of the Prelude and a half-diminished
seventh constructed above the same bass: here a dissonant
interval in the one chord corresponds enharmonically to a
consonant interval in the other.  This, I submit, is what
makes the enharmonic equivalence of the two chords all but
unrecognizable to the ear except by a deliberate act of
intellect.  My speculation is that the exploitation of
enharmonic equivalence of exactly this kind is a Wagnerian
[20] A voice-leading graph incorporating the elements
described above as elided might appear as in Ex. 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.  Ex. 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 Ex. 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 g-sharp - b,
as represented by the brackets in Ex. 5.  Thus 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.
10. In this respect I concur with Mitchell's reading; see
Mitchell, pp. 170-171 (his Ex. 4).
[21] 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 g-sharp as either a chord tone or a long
appoggiatura that resolves specifically and completely to a
at the last eighth-note of bar 2.  Neither of these
alternatives appeared to me to correspond to the sound of
the passage.  Moreover, it provides a way to acknowledge
Mitchell's voice exchange (g-sharp above b moving to b above
g-sharp), again without assuming chordal status for the g-
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