Tristan chord

The Tristan chord is a chord made up of the notes F, B, D♯, and G♯:

Tristan chord
Component intervals from root
augmented second
augmented sixth
augmented fourth (tritone)
root [F]
Forte no. / Complement
4–27 / 8–27

More generally, it can be any chord that consists of these same intervals: augmented fourth, augmented sixth, and augmented ninth above a bass note. It is so named as it is heard in the opening phrase of Richard Wagner's opera Tristan und Isolde as part of the leitmotif relating to Tristan.

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 chord is its unusual relationship to the implied key of its surroundings.

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

Martin Vogel points out the "chord" in earlier works by Guillaume de Machaut, Carlo Gesualdo, J.S. Bach, Mozart, Beethoven, or Louis Spohr (Vogel 1962, p. 12, cited in Nattiez 1990, p. 219) as in the following example from the first movement of Beethoven's Piano Sonata No. 18:

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[1]. 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 (Gołąb 1987, ).

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" (Erickson 1975, p. 18).

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 Fø7 (F–A♭–C♭–E♭), the Tristan chord can also be interpreted in many ways. Nattiez (1990, pp. 219–29), distinguishes between functional and nonfunctional analyses of the chord.

Functional analyses

Functional analyses have interpreted the chord's root on different scale degrees, in A minor:

F–B–D♯–G♯ → F–C♭–E♭–A♭ → F–B–D–A = D–F–A
while Alfred Lorenz and others, interpret it as an augmented sixth chord F–A–D♯ (D'Indy 1903, , Lorenz 1924–33, , Deliège 1979, , Gut 1981, ) based after Riemann on the transcendent principle that there are only three functions: tonic, predominant, and dominant.
The Tristan chord analyzed as a French sixth (in red) with appoggiatura and dominant seventh with passing tone in A minor (Benward and Saker 2008, p. 233).

Vincent D'Indy (1903, p. 117, cited in Nattiez 1990, p. 224) analyses the chord as a IV chord after Riemann's transcendent principle (as phrased by Serge Gut (Gut 1981, p. 150): "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:

Célestin Deliège, independently, sees the G♯ as an appoggiatura to A, describing that

in the end only one resolution is acceptable, one that takes the subdominant degree as the root of the chord, which gives us, as far as tonal logic is concerned, the most plausible interpretation ... this interpretation of the chord is confirmed by its subsequent appearances in the Prelude's first period: the IV6 chord remains constant; notes foreign to that chord vary. (Deliège 1979, p. 23)

The Tristan chord as appoggiaturas resolving to a dominant

According to Jacques Chailley (1963, p. 40), discussing Dommel-Diény 1965 and Gut 1981, p. 149, cited in Nattiez (1990, p. 220), "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:

Tristan's chromaticism, grounded in appoggiaturas and passing notes, technically and spiritually represents an apogee of tension. I have never been able to understand how the preposterous idea that Tristan could be made the prototype of an atonality grounded in destruction of all tension could possibly have gained credence. This was an idea that was disseminated under the (hardly disinterested) authority of Schoenberg, to the point where Alban Berg could cite the Tristan Chord in the Lyric Suite, as a kind of homage to a precursor of atonality. This curious conception could not have been made except as the consequence of a destruction of normal analytical reflexes leading to an artificial isolation of an aggregate in part made up of foreign notes, and to consider it—an abstraction out of context—as an organic whole. After this, it becomes easy to convince naive readers that such an aggregation escapes classification in terms of harmony textbooks. (Chailley 1963, p. 8)

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) (Ward 1970, Sadai 1980), of F♯ minor (Kistler 1879, , Jadassohn 1899, ).

Linear analyses include that of Noske (1981, pp. 116–17) 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 (cf. Schenker 1925–30, 2: p. 29).

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 (1981, p. 150), 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." 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 (1988, p. 328) 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♯″."

Schoenberg describes it as a "wandering chord [vagierender Akkord]... it can come from anywhere" (Schoenberg 1911, p. 284).

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 or E♭ are "wrong". He privileges analyses of the chord as on the second degree (II). He then supplies a Wagner-approved analysis, that of Czech professor Carl Mayrberger (1878), 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 major" (Nattiez 1990, ).

Responses and influences
Four measures of "Golliwog'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 (Huebner 1999, p. 477). Debussy also jokingly quotes the opening bars of Wagner's opera several times in "Golliwogg's Cakewalk" from his piano suite Children's Corner (Groos 2011, p. 163). 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" (Howard 1969, pp. 57–58). Paul Lansky based the harmonic content of his first electronic piece, mild und leise (1973), on the Tristan chord (Grimshaw). This piece is best known from being sampled in the Radiohead song "Idioteque".

More recently, American composer and humorist Peter Schickele crafted a tango around this same figure, a chamber work for four bassoons entitled Last Tango in Bayreuth. 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 (Anon. 2006).

In 1993, the opening theme was used in the film Thirty Two Short Films About Glenn Gould in the scene on Lake Simcoe as performed by the NBC Symphony Orchestra, conducted by Arturo Toscanini (recorded 1952). Gould had been a fan of Wagner and adapted some of his music to piano, some of Gould's rare recordings from the Romantic Period. The prelude of Wagner's opera is also prominently used in the film Melancholia by Lars von Trier (Page 2011).

gollark: Yes. I know since you have test.
gollark: Ah. You do NOT have April Folly.
gollark: Meh, rounding errors.
gollark: Well in that case you would have more than 104.7 points.
gollark: The one for an attempted XSS attack?

See also

References
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Further reading
  • Bailey, Robert (1986). Prelude and Transfiguration from Tristan and Isolde (Norton Critical Scores). New York: W. W. Norton & Co., Inc. ISBN 0-393-95405-6. Contains complete orchestral score, together with extensive discussion of the Prelude (especially the chord), Wagner's sketches, and leading essays by various analysts.
  • Magee, Bryan (2002), The Tristan Chord: Wagner and Philosophy, ISBN 0-8050-7189-X
  • Nattiez, Jean-Jacques (1990), Wagner androgyne, ISBN 2-267-00707-X Contains discussion of the Tristan chord as "androgynous". 1997 English edition (translated by Stewart Spencer) ISBN 0-691-04832-0.
  • Stegemann, Benedikt (2013). Theory of Tonality. Theoretical Studies. Wilhelmshaven: Noetzel. ISBN 978-3-7959-0963-5.

References
  1. Walker, A. (2018, p.187-8), Chopin, a Life and Times. London, Faber.
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