Tristan chord
The Tristan chord is a chord made up of the notes F, B, D, and G: \override Score.TimeSignature #'stencil = ##f </score> 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. </score> 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 as in the following example from the first movement of Beethoven's Piano Sonata No. 18: </score> 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. 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. 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". 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 (F–A–C–E), the Tristan chord can also be interpreted in many ways. Nattiez 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: Vincent d'Indy analyses the chord as a IV chord after Riemann's transcendent principle (as phrased by Serge Gut: "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> , independently, sees the G as an appoggiatura to A, describing  that According to Jacques, discussing Dommel-Diény 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: 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), of F minor. Linear analyses include that of Noske 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." 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  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". 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 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". Responses and influences. 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". Debussy also jokingly quotes the opening bars of Wagner's opera several times in "Golliwogg's Cakewalk" from his piano suite "Children's Corner". 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". Paul Lansky based the harmonic content of his first electronic piece, "mild und leise" (1973), on the Tristan chord. 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). 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. 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. References. Sources