Tristan chord

Template:Short description Template:Template other The original Tristan chord is heard in the opening phrase of Richard Wagner's opera Tristan und Isolde as part of the leitmotif relating to Tristan. It is made up of the notes F, B, D♯, and G♯:

<score sound="1"> {

\override Score.TimeSignature #'stencil = ##f

  \new PianoStaff <<
     \new Staff <<
        \relative c' {
            \clef treble \key c \major \time 4/4
            <dis gis>1
            }
           >>
    \new Staff <<
        \relative c {
            \clef bass \key c \major \time 4/4
            <f b>1
            }
        >>
   >>

} </score> More generally, the term refers to any chord that consists of the same intervals: augmented fourth, augmented sixth, and augmented ninth above a bass note.

Background

The notes of the Tristan chord are not unusual; they could be respelled enharmonically to form a common half-diminished seventh chord. What distinguishes the Tristan chord is its unusual relationship to the implied key of its surroundings.

<score lang="lilypond">

   {
     \new PianoStaff <<
       \new Staff <<
           \new Voice \relative c {
               \clef treble \key a \minor \time 6/8
               \voiceOne \partial8 r8 R2. \once \override NoteHead.color = #red gis4.->(~ gis4 a8 ais8-> b4~ b8) r r
               }
           \new Voice \relative c' {
               \override DynamicLineSpanner.staff-padding = #4.5
               \once \override DynamicText.X-offset = #-5
               \voiceTwo \partial8 a\pp( f'4.~\< f4 e8 \once \override NoteHead.color = #red dis2.)(\> d!4.)~\p d8 r r
               }
           >>
       \new Staff <<
           \relative c {
               \clef bass \key a \minor \time 6/8
               \partial8 r8 R2. \once \override NoteHead.color = #red <f b>2.( <e gis>4.)~ <e gis>8 r r
               }
           >>
   >> }

</score>

File:Wagner Tristan opening (orchestral).ogg

This motif also appears in measures 6, 10, and 12, several times later in the work,Template:Clarification needed and at the end of the last act.

Template:Ill points out the chord in earlier works by Guillaume de Machaut, Carlo Gesualdo, J. S. Bach, Mozart, Beethoven, or Louis Spohr as in the following example from the first movement of Beethoven's Piano Sonata No. 18:

<score lang="lilypond">

   {
     \new PianoStaff <<
       \new Staff <<
           \new Voice \relative c {
               \clef treble \key es \major \time 3/4
               \override DynamicLineSpanner.staff-padding = #4
               \stemUp ces8.^( f,16) f4 r4 ces'8.^( f,16) f4 r4 <es f>^.^(\< <es f>^. <es ges>^.)\! \once \override NoteHead.color = #red aes2.
               }
           \new Voice \relative c' {
               \stemDown <ces es>2 s4 <ces es>2 s4 s2. \once \override NoteHead.color = #red es2_(\> d4)\!
               }
           >>
       \new Staff <<
           \relative c {
               \clef bass \key es \major \time 3/4
               <aes es' f aes>2 r4 <aes es' f aes>2 r4 <aes' ces>4_._( <aes ces>_. <ges ces>_.) \once \override NoteHead.color = #red <f ces'>2.
               }
           >>
   >> }

</score>

File:Beethoven op 31 No 3 (audio only).wav

The chord is found in several works by Chopin, from as early as 1828, in the Sonata in C minor, Op. 4 and his Scherzo No. 1, composed in 1830.Template:Sfn It is only in late works where tonal ambiguities similar to Wagner's arise, as in the Prelude in A minor, Op. 28, No. 2, and the posthumously published Mazurka in F minor, Op. 68, No. 4.Template:Sfn

The Tristan chord's significance is in its move away from traditional tonal harmony, and even toward atonality. With this chord, Wagner actually provoked the sound or structure of musical harmony to become more predominant than its function, a notion that was soon explored by Debussy and others. In the words of Robert Erickson, "The Tristan chord is, among other things, an identifiable sound, an entity beyond its functional qualities in a tonal organization".Template:Sfn

Analysis

Much has been written about the Tristan chord's possible harmonic functions or voice leading and the motif has been interpreted in various ways. Though enharmonically equivalent to the half-diminished seventh chord F^ø7 (F–A♭–C♭–E♭), the Tristan chord can also be interpreted in many ways. Nattiez distinguishes between functional and nonfunctional analyses of the chord.Template:Sfn

Functional analyses

Functional analyses have interpreted the chord in the key of A minor in many ways:

<score sound="1"">

   {
     \new PianoStaff <<
       \new Staff <<
           \new Voice \relative c {
               \clef treble \key a \minor \time 6/8
               \voiceOne \partial8 r8 R2. gis4.(~ gis4 \once \override NoteHead.color = #red a8 ais8 b4~ b8) r r
               }
           \new Voice \relative c' {
               \voiceTwo \partial8 a( f'4.~ f4 e8 \once \override NoteHead.color = #red dis2.)( d!4.)~ d8 r r
               }
           >>
       \new Staff <<
           \relative c {
               \clef bass \key a \minor \time 6/8
               \partial8 r8 R2. \once \override NoteHead.color = #red <f b>2.(_\markup { \concat { "Fr" \raise #1 \small "+6" \hspace #8 "V" \raise #1 \small "7" } } <e gis>4.)~ <e gis>8 r r
               }
           >>
   >> }

</score>

The Tristan chord analyzed as a French sixth (in red) with appoggiatura and dominant seventh with passing tone in A minorTemplate:Sfn

• The chord is an augmented sixth chord, specifically a French sixth chord, F–B–D♯-A, with the note G♯ heard as an appoggiatura resolving to A. (Theorists debate the root of French sixth chords.) The harmonic function as a predominant is intact, with the chord moving to V⁷. Note that, in this view, the G♯ resolving upward to A is the 2nd of 3 consecutive accented dissonances resolving by half step. Alfred Lorenz and others interpret it more broadly as an augmented sixth chord F–A–D♯,Template:SfnTemplate:SfnTemplate:SfnTemplate:Sfn based after Hugo Riemann on the principle that there are only three chord functions: tonic, predominant, and dominant.
• The root is the second scale degree, B.Template:SfnTemplate:SfnTemplate:SfnTemplate:Sfn
• The root is the fourth scale degree, D. Arend interprets it as "a modified minor seventh chord"Template:Sfn

F–B–D♯–G♯ → F–C♭–E♭–A♭ → F–B–D–A = D–F–A

• The chord is a secondary dominant, V/V, and thus also with a root on B.Template:SfnTemplate:SfnTemplate:Sfn This favors the fifth motion from B to E, seeing the chord as a seventh chord with lowered fifth (B–D♯(D♮)–F♯–A).

Vincent d'Indy analyses the chord as a IV chord after Riemann's transcendent principle (as phrased by Serge Gut:Template:Sfn "the most classic succession in the world: Tonic, Predominant, Dominant" ) and rejects the idea of an added "lowered seventh", eliminates "all artificial, dissonant notes, arising solely from the melodic motion of the voices, and therefore foreign to the chord," finding that the Tristan chord is "no more than a predominant in the key of A, collapsed in upon itself melodically, the harmonic progression represented thus:

<score sound="1">

{

  \new PianoStaff <<
     \new Staff <<
        \relative c' {
            \clef treble \key c \major \time 3/4
            <d a'>2. <e b'>
            }
           >>
    \new Staff <<
        \relative c {
            \clef bass \key c \major \time 3/4
            <f a>2._\markup { \concat { "IV" \raise #1 \small "6" \hspace #3.5 "V" } } <e gis>
            }
        >>
   >>

} </score>

Template:Interlanguage link, independently, sees the G♯ as an appoggiatura to A, describing that

<score sound="1">

   {
     \new PianoStaff <<
       \new Staff <<
           \new Voice \relative c {
               \clef treble \key a \minor \time 6/8
               \partial8 s8 s2. \stemUp \slashedGrace { dis'8 } gis4.^~ gis4 \parenthesize a8 \slashedGrace { ais8 } \stemUp b2.
               }
           \new Voice \relative c' {
               \partial8 a8 \slashedGrace { f'8 } \parenthesize <a, c e>2. \stemDown dis2._( d)
               }
           >>
       \new Staff <<
           \relative c {
               \clef bass \key a \minor \time 6/8
               \partial8 r8 R2. <e~ b'>2. <e gis>2.
               }
           >>
   >> }

</score>

The Tristan chord as appoggiaturas resolving to a dominant

According to Jacques,Template:Sfn discussing Dommel-DiényTemplate:Sfn and Gut, "it is rooted in a simple dominant chord of A minor [E major], which includes two appoggiaturas resolved in the normal way". Thus, in this view it is not a chord but an anticipation of the dominant chord in measure three. Chailley did once write:

Fred Lerdahl presents alternate interpretations of the Tristan motive, as either i ii♯643 [French sixth: F–B–D♯–A] V7 or as VI (iv) (vii♯64♯2) [ altered pre-dominant: F–B–D♯–G♯] V7, both in A minor, concluding that while both interpretations have strong expectation or attraction, that the version with G♯ is the stronger progression.Template:Sfn

Nonfunctional analyses

Nonfunctional analyses are based on structure (rather than function), and are characterized as vertical characterizations or linear analyses.

Vertical characterizations include interpreting the chord's root as on the seventh degree (VII),Template:SfnTemplate:Sfn of F♯ minor.Template:SfnTemplate:Sfn

Linear analyses include that of NoskeTemplate:Sfn and Schenker was the first to analyze the motif entirely through melodic concerns. Schenker and later Mitchell compare the Tristan chord to a dissonant contrapuntal gesture from the E minor fugue of The Well-Tempered Clavier, Book I.

William Mitchell, viewing the Tristan chord from a Schenkerian perspective, does not see the G♯ as an appoggiatura because the melodic line (G♯–A–A♯–B) ascends to B, making the A a passing note. This ascent by minor third is mirrored by the descending line (F–E–D♯–D), a descent by minor third, making the D♯, like A♯, an appoggiatura. This makes the chord a diminished seventh chord (G♯–B–D–F).

Serge Gut argues that, "if one focuses essentially on melodic motion, one sees how its dynamic force creates a sense of an appoggiatura each time, that is, at the beginning of each measure, creating a mood both feverish and tense ... thus in the soprano motif, the G♯ and the A♯ are heard as appoggiaturas, as the F and D♯ in the initial motif."Template:Sfn The chord is thus a minor chord with an added sixth (D–F–A–B) on the fourth degree (IV), though it is engendered by melodic waves.

Allen Forte first identifies the chord as an atonal set, 4–27 (half-diminished seventh chord), then "elect[s] to place that consideration in a secondary, even tertiary position compared to the most dynamic aspect of the opening music, which is clearly the large-scale ascending motion that develops in the upper voice, in its entirety a linear projection of the Tristan Chord transposed to level three, g♯′–b′–d″–f♯″.Template:Sfn

Schoenberg describes it as a "wandering chord [vagierender Akkord]... it can come from anywhere".Template:Sfn

Mayrberger's opinion

After summarizing the above analyses Nattiez asserts that the context of the Tristan chord is A minor, and that analyses which say the key is E major or E♭ minor are "wrong".Template:Sfn He privileges analyses of the chord as on the second degree (II). He then supplies a Wagner-approved analysis, that of Czech professor Carl MayrbergerTemplate:Sfn who "places the chord on the second degree, and interprets the G♯ as an appoggiatura. But above all, Mayrberger considers the attraction between the E and the real bass F to be paramount, and calls the Tristan chord a Zwitterakkord (an ambiguous, hybrid, or possibly bisexual or androgynous, chord), whose F is controlled by the key of A minor, and D♯ by the key of E minor".Template:Sfn

Responses and influences

<score sound="1"> {

 #(set-global-staff-size 17)
  \new PianoStaff <<
     \new Staff <<
       \key ges \major \time 2/4
       \partial 4.
       \new Voice \relative c' {
           \once \hide Score.MetronomeMark \once \hide Score.MetronomeMark\tempo 4 = 80 r8 \voiceOne a4( \tempo "Cédez" f'4.^\markup { \dynamic p \italic "avec une grande émotion" } e8)
           \tempo "a Tempo" r8 \once \hide Score.MetronomeMark \tempo 4 = 105 \acciaccatura{\slurUp d'} \once \stemDown <ces es>8-.[ \acciaccatura{\slurUp c} \once \stemDown <ces des>-. \acciaccatura{\slurUp d} \once \stemDown <ces es>-.]
           r8 \acciaccatura{\slurUp d} \once \stemDown <ces es>8-.[ \acciaccatura{\slurUp c} \once \stemDown <ces des>-. \acciaccatura{\slurUp d} \once \stemDown <ces es>-.]
       }
       \new Voice \relative c' { 
           \voiceTwo s8 a4(~ a4. bes8 <ces es!>2)
       }
    >>
    \new Staff <<
       \clef bass
       \key ges \major \time 2/4
       \partial 4.
       \new Voice \relative c, {
         << {
         \voiceOne r8 r4 r2
         r8 \stemDown <as ces f>-.[ <as ces f>8-. <as ces f>8-.]
      }
      \new Voice \relative c { 
         \voiceTwo es,8([ f ges]
         a[ bes ces c]
         <as des>2)} >>
         r8 <as ces f>8-.[ <as ces f>8-. <as ces f>8-.]
       }
        >>
   >>

}

</score>

Four measures of "Golliwogg's Cakewalk" from Claude Debussy's Children's Corner that quote the opening of the opera

The chord and the figure surrounding it is well enough known to have been parodied and quoted by a number of later musicians. Debussy includes the chord in a setting of the phrase je suis triste in his opera Pelléas et Mélisande.Template:Sfn Debussy also jokingly quotes the opening bars of Wagner's opera several times in "Golliwogg's Cakewalk" from his piano suite Children's Corner.Template:Sfn Benjamin Britten slyly invokes it at the moment in Albert Herring when Sid and Nancy spike Albert's lemonade and then, when he drinks it, the chord "runs riot through the orchestra and recurs irreverently to accompany his hiccups".Template:Sfn Paul Lansky based the harmonic content of his first electronic piece, mild und leise (1973), on the Tristan chord.Template:Sfn This piece is best known from being sampled in the Radiohead song "Idioteque".

Bernard Herrmann incorporated the chord in his scores for Vertigo (1958) and Tender is the Night (1962).

Christian Thielemann, the music director of the Bayreuth Festival from 2015–20, discussed the Tristan chord in his book, My Life with Wagner: the chord "is the password, the cipher for all modern music. It is a chord that does not conform to any key, a chord on the verge of dissonance", and "The Tristan chord does not seek to be resolved in the closest consonance, as the classic theory of harmony requires; [it] is sufficient unto itself, just as Tristan and Isolde are sufficient unto themselves and know only their love."Template:Sfn

More recently, American composer and humorist Peter Schickele crafted a tango around the Tristan prelude, a chamber work for four bassoons entitled Last Tango in Bayreuth.Template:Sfn The Brazilian conductor and composer Flavio Chamis wrote Tristan Blues, a composition based on the Tristan chord. The work, for harmonica and piano, was recorded on the CD Especiaria, released in Brazil by the Biscoito Fino label.Template:Sfn New York-based composer Dalit Warshaw's narrative concerto for piano and orchestra, Conjuring Tristan, employs the Tristan chord in exploring the themes of Thomas Mann's novella Tristan through Wagner's music.Template:Sfn

The prelude of Wagner's opera is prominently used in the film Melancholia by Lars von Trier.Template:Sfn

See also

• Elektra chord
• Mystic chord
• Petrushka chord
• Psalms chord
• Synthetic chord

References

Sources

• Anon. 2006. "Especiaria CD: Flávio Chamis". Biscoito Fino website (archive from 24 August 2011, accessed 16 May 2014).
• Arend, M. (1901). "Harmonische Analyse des Tristan-Vorspiels", Bayreuther Blätter. No. 24: 160–169. Cited in .
• Benward, Bruce, and Marilyn Nadine Saker (2008). Music in Theory and Practice, vol. 2. Boston: McGraw-Hill. Template:ISBN.
• Chailley, Jacques (1963). Tristan et Isolde de Richard Wagner. 2 vols. Les Cours de Sorbonne. Paris: Centre de Documentation Universitaire.
• Deliège, Célestin (1979)
• D'Indy, Vincent (1903). Cours de composition musicale, vol. 1. Paris: Durand.
• Dommel-Diény, Amy. 1965. Douze dialogues d'initiation à l'harmonie classique; suivis de quelques notions de solfège, preface by Louis Martin. Paris: Les Editions Ouvrières.
• Ergo, E. (1912). "Über Wagners Harmonik und Melodik". Bayreuther Blätter, no. 35:34–41.
• Forte, Allen (1988). New Approaches to the Linear Analysis of Music. Journal of the American Musicological Society 41, no. 2 (Summer): 315–348.
• Gołąb, Maciej. 1987. "O 'akordzie tristanowskim' u Chopina". Rocznik Chopinowski 19:189–98. German version, as "Über den Tristan-Akkord bei Chopin". Chopin Studies 3 (1990): 246–256. English version, as "On the Tristan Chord", in: M. Gołąb, Twelve Studies in Chopin, Frankfurt am Main 2014: 81-92
• Gut, Serge (1981). "Encore et toujours: 'L'accord de Tristan'", L'avant-scène Opéra, nos. 34–35 ("Tristan et Isole"): 148–151.
• Jadassohn, Josef. 1899. L'organisation actuelle de la surveillance médicale de la prostitution est-elle susceptible d'amélioration? Brussels: [s.n.].
• .
• Kurth, Ernst. 1920. Romantische Harmonik und ihre Krise in Wagners "Tristan". Bern: Paul Haupt; Berlin: Max Hesses Verlag.
• Lorenz, Alfred Ottokar. 1924–33. Das Geheimnis der Form bei Richard Wagner, in 4 volumes. Berlin: M. Hesse. Reprinted, Tutzing: H. Schneider, 1966.
• Mayrberger, Carl. 1878. Lehrbuch der musikalischen Harmonik in gemeinfasslicher Darstellung, für höhere Musikschulen und Lehrerseminarien, sowie zum Selbstunterrichte. Part 1: "Die diatonische Harmonik in Dur". Pressburg: Gustav Heckenast.
• Noske, Frits R. (1981). "Melodic Determinants in Tonal Structures". Muzikoloski zbornik Ljubljana / Ljubljana Musicological Annual 17, no. 1:111–121.
• Page, Tim (23 December 2011). "Filmmaker's Audacious Teaming of His 'Melancholia' with Wagner's Music". The Washington Post.
• Sadai, Yizhak (1980). Harmony in Its Systemic and Phenomenological Aspects, translated by J. Davis and M. Shlesinger. Jerusalem: Yanetz.
• Schenker, Heinrich (1925–30). Das Meisterwerk in der Musik, 3 vols. Munich: Drei Masken Verlag. English translation, as The Masterwork in Music: A Yearbook, edited by William Drabkin, translated by Ian Bent, Alfred Clayton, William Drabkin, Richard Kramer, Derrick Puffett, John Rothgeb, and Hedi Siegel. Cambridge Studies in Music Theory and Analysis 4. Cambridge and New York: Cambridge University Press, 1994–1997.
• Schoenberg, Arnold (1954). Die formbildenden Tendenzen der Harmonie, translated by Erwin Stein. Mainz: B. Schott's Sohne.
• Schoenberg, Arnold (1969). "Structural Functions of Harmony", revised edition. New York: W. W. Norton. Library of Congress – 74-81181.
• Vogel, Martin (1962). Der Tristan-Akkord und die Krise der modernen Harmonielehre. Orpheus-Schriftenreihe zu Grundfragen der Musik 2. Düsseldorf: Gesellschaft zur Förderung der systematischen Musikwissenschaft. Titled in response to Kurth (1920).

Further reading

• Contains complete orchestral score, together with extensive discussion of the Prelude (especially the chord), Wagner's sketches, and leading essays by various analysts.
• Contains discussion of the Tristan chord as "androgynous".
• Supplement by F. Stieger.
• Reprint (3 vols. in 1), Hildesheim: G. Olms, 1967. Reprint (3 vols. in 2), Nendeln/Liechtenstein: Kraus Reprint, 1976.
• Reprinted in Musikhören, edited by B. Dopheide, 14–47. Darmstadt: [s.n.?], 1975.
• Reprinted, Hildesheim: G. Olms, 1990. Template:ISBN.
• Formerly titled Katechismus der Harmonie- und Modulationslehre and Skizze einer neuen Methode der Harmonielehre.
• Introduction by Hans von Wolzogen.