Volume 1, Number 2, March 1995
Copyright © 1995 Society for Music Theory

Tristan Redux: Comments on John Rothgeb’s article on the Tristan Chord in MTO 1.1

Allen Forte


REFERENCE: http://www.mtosmt.org/issues/mto.95.1.1/mto.95.1.1.rothgeb.html

KEYWORDS: chromaticism, enharmonic equivalence, graphic analysis, harmony, opera, Tristan und Isolde

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.

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[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–AflatCflatEflat upon which the ascent terminates is to be regarded as a modification of the dominant of Eflat minor.(1)

See Example 1, supplied by the author.(2)

[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 Gsharp 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)

[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 Gsharp. 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 Dsharp 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 Fsharp/Gflat 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–CflatEflatAflat 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 EflatAflat instead of DsharpGsharp. For Berg, in this atonal (partly serial) work, the original notation, with its tonal-melodic implications so eloquently described by Rothgeb, is meaningless.

[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 Example 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 Example 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 experience.

[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)

[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 Gsharp 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–Aflat–B–Eflat 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 “Gsharp TC” refers to A minor, although that tonality is never explicitly stated in the Prelude, while the hd7 version F–CflatEflatAflat refers to Eflat minor. In this way the tritone-related tonalities A minor and Eflat 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 “Gsharp 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 Gsharp 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)

[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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Allen Forte
Yale University
Department of Music
P.O. Box 208310
New Haven, CT 06520-8310
allenf@minerva.cis.yale.edu

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Footnotes

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), page 129.
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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 IIflat2 chords, in which the root lies above the bass tone. Paul Hindemith, The Craft of Musical Composition (New York, 1942), page 210.
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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, page 232.
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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.
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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.
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6. Allen Forte, “New Approaches to the Linear Analysis of Music,” Journal of the American Musicological Society 41/2 (1988), page 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.
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7. The graphic reading in Example 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.
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8. Aneven more radical interpretation is to be found in Jean-Jacques Nattiez, Wagner Androgyne (Christian Bourgois Editeur, 1990), page 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.
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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), page 129.
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 IIflat2 chords, in which the root lies above the bass tone. Paul Hindemith, The Craft of Musical Composition (New York, 1942), page 210.
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, page 232.
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.
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.
Allen Forte, “New Approaches to the Linear Analysis of Music,” Journal of the American Musicological Society 41/2 (1988), page 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.
The graphic reading in Example 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.
Aneven more radical interpretation is to be found in Jean-Jacques Nattiez, Wagner Androgyne (Christian Bourgois Editeur, 1990), page 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.
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