View source for Tristan chord

{{Short description|Musical chord}}
{{Infobox chord|
chord_name=Tristan chord|
first_interval=[[Root (chord)|root]] [F]|
second_interval=augmented fourth ([[tritone]])|
third_interval=[[augmented sixth]]|
fourth_interval=[[augmented second]]|
forte_number=4–27|
complement=8–27
}}
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{{music|sharp}}, and G{{music|sharp}}:

:<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 (music)|chord]] that consists of the same [[Interval (music)|interval]]s: [[augmented fourth]], [[augmented sixth]], and [[augmented second|augmented ninth]] above a [[bass note]].

==Background==
The notes of the Tristan chord are not unusual; they could be [[Enharmonic spelling|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 (music)|motif]] also appears in measures 6, 10, and 12, several times later in the work,{{Clarification needed|reason=which work?|date=January 2023}} and at the end of the last act.

{{ill|Martin Vogel|de|Martin Vogel (Musikwissenschaftler)}} points out the chord in earlier works by [[Guillaume de Machaut]], [[Carlo Gesualdo]], [[Johann Sebastian Bach|J. S. Bach]], [[Wolfgang Amadeus Mozart|Mozart]], [[Ludwig van Beethoven|Beethoven]], or [[Louis Spohr]]<ref>{{harvnb|Vogel|1962|p=12}}, cited in {{harvnb|Nattiez|1990|p=219}}</ref> as in the following example from the first movement of Beethoven's [[Piano Sonata No. 18 (Beethoven)|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 [[Fryderyk Chopin|Chopin]], from as early as 1828, in the [[Piano Sonata No. 1 (Chopin)|Sonata in C minor, Op. 4]] and his [[Scherzo No. 1 (Chopin)|Scherzo No. 1]], composed in 1830.{{sfn|Walker|2018|pp=187–188}} It is only in late works where tonal ambiguities similar to Wagner's arise, as in the [[Preludes (Chopin)#24 Preludes, Op. 28|Prelude in A minor, Op. 28, No. 2]], and the posthumously published [[Mazurkas, Op. 68 (Chopin)|Mazurka in F minor, Op. 68, No. 4]].{{sfn|Gołąb|1987|loc={{Page needed|date=October 2014}}}}

The Tristan chord's significance is in its move away from traditional [[tonality|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 (music)|function]], a notion that was soon explored by [[Claude Debussy|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".{{sfn|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 F{{music|halfdim}}<sup>7</sup> (F–A{{music|flat}}–C{{music|flat}}–E{{music|flat}}), the Tristan chord can also be interpreted in many ways. Nattiez distinguishes between [[Function (music)|functional]] and nonfunctional analyses of the chord.{{sfn|Nattiez|1990|pp=219–229}}

===Functional analyses===
Functional analyses have interpreted the chord in the key of A minor in many ways:
{{Image frame|content=<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>|width=390|caption=The Tristan chord analyzed as a [[French sixth]] (in red) with [[Nonchord tone#Appoggiatura|appoggiatura]] and [[dominant seventh]] with [[passing tone]] in A minor{{sfn|Benward and Saker|2008|p=233}}}}

*The chord is an augmented sixth chord, specifically a [[Augmented sixth chord#French sixth|French sixth chord]], F–B–D{{music|sharp}}-A, with the note G{{music|sharp}} heard as an [[Nonchord tone#Appoggiatura|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 V{{sup|7}}. Note that, in this view, the G{{music|sharp}} 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{{music|sharp}},{{sfn|D'Indy|1903|loc={{page needed|date=October 2014}}}}{{sfn|Lorenz|1924–33|loc={{Page needed|date=October 2014}}}}{{sfn|Deliège|1979|loc={{Page needed|date=October 2014}}}}{{sfn|Gut|1981|loc={{Page needed|date=May 2014}}}} 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.{{sfn|Piston|1987|loc=|p=426}}{{sfn|Goldman|1965|loc={{Page needed|date=May 2014}}}}{{sfn|Schoenberg|1954|loc={{Page needed|date=May 2014}}}}{{sfn|Schoenberg|1969|p=77}} 
*The root is the fourth scale degree, D. Arend interprets it as "a modified [[minor seventh chord]]"{{sfn|Arend|1901|loc={{Page needed|date=March 2015}}}}
:: F–B–D{{music|sharp}}–G{{music|sharp}} → F–C{{music|flat}}–E{{music|flat}}–A{{music|flat}} → F–B–D–A = D–F–A
*The chord is a [[secondary dominant]], V/V, and thus also with a root on B.{{sfn|Ergo|1912|loc={{Page needed|date=May 2014}}}}{{sfn|Kurth|1920|loc={{Page needed|date=May 2014}}}}{{sfn|Distler|1940|loc={{Page needed|date=May 2014}}}} This favors the fifth motion from B to E, seeing the chord as a [[Dominant seventh flat five chord|seventh chord with lowered fifth]] (B–D{{music|sharp}}(D{{music|natural}})–F{{music|sharp}}–A).

[[Vincent d'Indy]]<ref>{{harvnb|D'Indy|1903|p=117}}, cited in {{harvnb|Nattiez|1990|p=224}}</ref> analyses the chord as a IV chord after Riemann's transcendent principle (as phrased by [[Serge Gut]]:{{sfn|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:

:<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>

{{Interlanguage link|Célestin Deliège|fr}}, independently, sees the G{{music|sharp}} as an appoggiatura to A, describing that

{{quote|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 IV<sup>6</sup> chord remains constant; notes foreign to that chord vary.{{sfn|Deliège|1979|p=23}}}}
{{Image frame|content=<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>|width=320|caption=The Tristan chord as appoggiaturas resolving to a dominant}}According to [[Jacques Chailley|Jacques]],{{sfn|Chailley|1963|p=40}} discussing Dommel-Diény{{sfn|Dommel-Diény|1965}} and Gut,<ref>{{harvnb|Gut|1981|p=149}}, cited in {{harvtxt|Nattiez|1990|p=220}}</ref> "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 (music)|anticipation]] of the [[dominant chord]] in measure three. Chailley did once write:

{{quote|''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 [[Arnold Schoenberg|Schoenberg]], to the point where [[Alban Berg]] could cite the Tristan Chord in the ''[[Lyric Suite (Berg)|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.{{sfn|Chailley|1963|p=8}}|sign=|source=}}

[[Fred Lerdahl]] presents alternate interpretations of the Tristan motive, as either i ii{{music|#}}643 [French sixth: F–B–D{{music|#}}–A] V7 or as VI (iv) (vii{{music|#}}64{{music|#}}2) [ [[altered chord|altered]] [[predominant chord|pre-dominant]]: F–B–D{{music|#}}–G{{music|#}}] V7, both in A minor, concluding that while both interpretations have strong expectation or attraction, that the version with G{{music|#}} is the stronger progression.{{sfn|Lerdahl|2001|p=184}}

===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),{{sfn|Ward|1970}}{{sfn|Sadai|1980}} of F{{music|sharp}} minor.{{sfn|Kistler|1879|loc={{Page needed|date=October 2014}}}}{{sfn|Jadassohn|1899|loc={{Page needed|date=October 2014}}}}

Linear analyses include that of Noske{{sfn|Noske|1981|pp=116–117}} and [[Heinrich Schenker|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.<ref>cf. {{harvnb|Schenker|1925–30|loc=2: p.&nbsp;29}}</ref>

William Mitchell, viewing the Tristan chord from a Schenkerian perspective, does not see the G{{music|sharp}} as an [[appoggiatura]] because the melodic line (G{{music|sharp}}–A–A{{music|sharp}}–B) ascends to B, making the A a [[passing note]]. This ''ascent'' by [[minor third]] is mirrored by the descending line (F–E–D{{music|sharp}}–D), a ''descent'' by minor third, making the D{{music|sharp}}, like A{{music|sharp}}, an appoggiatura. This makes the chord a [[diminished seventh chord]] (G{{music|sharp}}–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{{music|sharp}} and the A{{music|sharp}} are heard as appoggiaturas, as the F and D{{music|sharp}} in the initial motif."{{sfn|Gut|1981|p=150}} The chord is thus a [[minor chord]] with an [[Sixth chord|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, [[Forte number|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{{music|sharp}}′–b′–d″–f{{music|sharp}}″.{{sfn|Forte|1988|p=328}}

[[Arnold Schoenberg|Schoenberg]] describes it as a "wandering chord [vagierender Akkord]... it can come from anywhere".{{sfn|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 major or E{{music|flat}} minor are "''wrong''".{{Sfn|Nattiez|1990|p=233}} 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{{sfn|Mayrberger|1878|loc={{Page needed|date=May 2014|reason=A skim through the whole book fails to turn up any mention of either Wagner or of Tristan, but the 'composer-approved' analysis seems to be the one published three years later.}}}} who "places the chord on the second degree, and interprets the G{{music|sharp}} as an [[Ornament (music)#Appoggiatura|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{{music|sharp}} by the key of E minor".{{sfn|Nattiez|1990|loc=|p=235-236}}

==Responses and influences==
{{Image frame|content=<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>|width=550|caption=Four measures of "Golliwogg's Cakewalk" from [[Claude Debussy]]'s ''[[Children's Corner]]'' that [[Musical quotation|quote]] the opening of the opera}}
The chord and the figure surrounding it is well enough known to have been parodied and [[Musical quotation|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 (opera)|Pelléas et Mélisande]]''.{{sfn|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]]''.{{sfn|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".{{sfn|Howard|1969|pp=57–58}} [[Paul Lansky]] based the harmonic content of his first electronic piece, ''mild und leise'' (1973), on the Tristan chord.{{sfn|Grimshaw}} This piece is best known from being sampled in the [[Radiohead]] song "[[Idioteque]]".

[[Bernard Herrmann]] incorporated the chord in his scores for ''[[Vertigo (film)|Vertigo]]'' (1958) and ''[[Tender Is the Night (film)|Tender is the Night]]'' (1962).{{citation needed|date=September 2021}}

[[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."{{sfn|Thielemann|2016|pp=194-195}}

More recently, American composer and humorist [[Peter Schickele]] crafted a [[tango music|tango]] around the Tristan prelude, a chamber work for four [[bassoon]]s entitled ''Last Tango in Bayreuth''.{{sfn|Ross|2013}} 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.{{sfn|Anon.|2006}} 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 (novella)|Tristan]]'' through Wagner's music.{{sfn|Kaczmarczyk|2015}}

The prelude of Wagner's opera is prominently used in the film [[Melancholia (2011 film)|''Melancholia'']] by [[Lars von Trier]].{{sfn|Page|2011}}

==See also==
{{Portal|Classical music}}
*[[Elektra chord]]
*[[Mystic chord]]
*[[Petrushka chord]]
*[[Psalms chord]]
*[[Synthetic chord]]

==References==
{{reflist|18em}}

===Sources===
{{div col|colwidth=45em}}
* {{wikicite|ref={{harvid|Anon.|2006}}|reference=Anon. 2006. "[https://web.archive.org/web/20110824185322/http://www.biscoitofino.com.br/en/cat_produto_cada.php?id=246 Especiaria CD: Flávio Chamis]". Biscoito Fino website (archive from 24 August 2011, accessed 16 May 2014).}}
* {{wikicite|ref={{harvid|Arend|1901}}|reference=Arend, M. (1901). "Harmonische Analyse des Tristan-Vorspiels"<!--Harmonic analysis of the Tristan prelude-->, ''Bayreuther Blätter''. No. 24: 160–169. Cited in {{harvnb|Nattiez|1990|p=223}}.}}
* {{wikicite|ref={{harvid|Benward and Saker|2008}}|reference=Benward, Bruce, and Marilyn Nadine Saker (2008). ''Music in Theory and Practice'', vol. 2. Boston: McGraw-Hill. {{ISBN|978-0-07-310188-0}}.}}
* {{wikicite|ref={{harvid|Chailley|1963}}|reference=Chailley, Jacques (1963). ''Tristan et Isolde de Richard Wagner''. 2 vols. Les Cours de Sorbonne. Paris: Centre de Documentation Universitaire.}}
* {{wikicite|ref={{harvid|Deliège|1979}}|reference=Deliège, Célestin (1979){{Full citation needed|date=May 2014}}<!--Cited as such in the text. Title, and details of publication (book, article, etc.) are all needed.-->}}
* {{wikicite|ref={{harvid|D'Indy|1903}}|reference=D'Indy, Vincent (1903). ''Cours de composition musicale'', vol. 1. Paris: Durand.}}
* {{cite book|last=Distler|first=Hugo|author-link=Hugo Distler|year=1940|title=Funktionelle Harmonielehre |location=Basel|publisher=Bärenreiter-Verlag}}
* {{wikicite|ref={{harvid|Dommel-Diény|1965}}|reference=[[Amy Dommel-Dieny|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.}}
* {{wikicite|ref={{harvid|Ergo|1912}}|reference=Ergo, E. (1912). "Über Wagners Harmonik und Melodik". ''Bayreuther Blätter'', no. 35:34–41.}}
*{{cite book|last=Erickson|first=Robert|year=1975|title=Sound Structure in Music|location=Oakland, California|publisher=University of California Press|isbn=0-520-02376-5}}
* {{wikicite|ref={{harvid|Forte|1988}}|reference=[[Allen Forte|Forte, Allen]] (1988). New Approaches to the Linear Analysis of Music. ''[[Journal of the American Musicological Society]]'' 41, no. 2 (Summer): 315–348.}}
*{{wikicite|ref={{harvid|Gołąb|1987}}|reference= 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}}
* {{cite book|last=Goldman|first=Richard Franko|author-link=Richard Franko Goldman|year=1965|title=Harmony in Western Music|url=https://archive.org/details/harmonyinwestern00gold|url-access=registration |location=New York |publisher=W. W. Norton}}
*{{Cite web|url=https://www.allmusic.com/composition/mild-und-leise-for-computer-synthesized-tape-mc0002504290|title=mild und leise, computer synthesized tape |last=Grimshaw|first=Jeremy |website=AllMusic |access-date=2019-02-19}}
*{{Cite book|title=Richard Wagner: Tristan und Isolde|publisher=Cambridge University Press|year=2011|isbn=9780521431385|editor1-link=Arthur Groos|editor-last=Groos|editor-first=Arthur|location=Cambridge |oclc=660804858}}
* {{wikicite|ref={{harvid|Gut|1981}}|reference=[[Serge Gut|Gut, Serge]] (1981). "Encore et toujours: 'L'accord de Tristan'", ''L'avant-scène Opéra'', nos. 34–35 ("Tristan et Isole"): 148–151.}}
* {{citation|last=Howard|first=Patricia|title=The Operas of Benjamin Britten: An Introduction|location=New York and Washington|publisher=Frederick A. Praeger, Publishers|year=1969}}
*{{Cite book|title=French Opera at the Fin de Siècle: Wagnerism, Nationalism, and Style|last=Huebner|first=Steven|location=Oxford|publisher=Oxford University Press|year=1999 |isbn=9780195189544 |oclc=40043694}}
* {{wikicite|ref={{harvid|Jadassohn|1899}}|reference=[[Josef Jadassohn|Jadassohn, Josef]]. 1899. ''L'organisation actuelle de la surveillance médicale de la prostitution est-elle susceptible d'amélioration?'' Brussels: [s.n.].<!--All that was found at the inline citation was "Jadassohn 1899". Is this the one meant?-->}}
* {{Cite web |last=Kaczmarczyk |first=Jeffrey |date=2015-01-31 |title=Many lovely moments in Grand Rapids Symphony's evening of music by Wagner |url=https://www.mlive.com/entertainment/grand-rapids/2015/01/many_lovely_moments_in_grand_r.html |access-date=2023-03-06 |website=mlive |language=en}}
* {{citation|last=Kistler|first=Cyrill|year=1879|title=Harmonielehre für Lehrer und Lernende, Opus 44 |location=Munich|publisher=W. Schmid}}.
* {{wikicite|ref={{harvid|Kurth|1920}}|reference=[[Ernst Kurth|Kurth, Ernst]]. 1920. ''[https://archive.org/details/romantischeharmo00kurt Romantische Harmonik und ihre Krise in Wagners "Tristan"]''. Bern: Paul Haupt; Berlin: Max Hesses Verlag.}}
* {{cite book|last=Lerdahl|first=Fred|author-link=Fred Lerdahl|year=2001|title=Tonal Pitch Space|publisher=Oxford University Press|location=Oxford|isbn=0-19-517829-7}}
* {{wikicite|ref={{harvid|Lorenz|1924–33}}|reference=Lorenz, Alfred Ottokar. 1924–33. ''Das Geheimnis der Form bei Richard Wagner'', in 4 volumes. Berlin: M. Hesse. Reprinted, Tutzing: H. Schneider, 1966.}}
* {{wikicite|ref={{harvid|Mayrberger|1878}}|reference=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.}}
*{{cite book|last=Nattiez|first=Jean-Jacques|author-link=Jean-Jacques Nattiez|translator=[[Carolyn Abbate]]|year=1990|orig-year=1987|title=Music and Discourse: Toward a Semiology of Music (Musicologie générale et sémiologue)|location=Princeton, New Jersey|publisher=Princeton University Press|isbn=0-691-02714-5}}
* {{wikicite|ref={{harvid|Noske|1981}}|reference=Noske, Frits R. (1981). "Melodic Determinants in Tonal Structures". ''Muzikoloski zbornik Ljubljana'' / ''Ljubljana Musicological Annual'' 17, no. 1:111–121.}}
* {{wikicite|ref={{harvid|Page|2011}}|reference=Page, Tim (23 December 2011). "[https://www.washingtonpost.com/lifestyle/style/filmmakers-audacious-teaming-of-his-melancholia-with-wagners-music/2011/12/15/gIQAWRpgDP_story.html Filmmaker's Audacious Teaming of His 'Melancholia' with Wagner's Music]". ''[[The Washington Post]]''.}}
* {{cite book|last=Piston|first=Walter|author-link=Walter Piston|others=Revised by Mark Devoto|year=1987 |isbn=978-0-393-95480-7|title=Harmony|edition=5th|location=New York|publisher=W. W. Norton}}
* {{Cite magazine |last=Ross |first=Alex |author-link=Alex Ross (music critic) |date=2013-05-19 |title=A Wagner Birthday Roast |url=https://www.newyorker.com/culture/culture-desk/a-wagner-birthday-roast |access-date=2022-07-16 |magazine=[[The New Yorker]] |language=en-US}}
* {{wikicite|ref={{harvid|Sadai|1980}}|reference=Sadai, Yizhak (1980). ''Harmony in Its Systemic and Phenomenological Aspects'', translated by J. Davis and M. Shlesinger. Jerusalem: Yanetz.}}
* {{wikicite|ref={{harvid|Schenker|1925–30}}|reference=[[Heinrich Schenker|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.}}
* {{cite book|last=Schoenberg|first=Arnold|author-link=Arnold Schoenberg|year=1911|title=Harmonielehre |location=Leipzig and Vienna|publisher=Verlagseigentum der Universal-Edition}}
* {{wikicite|ref={{harvid|Schoenberg|1954}}|reference=Schoenberg, Arnold (1954). ''Die formbildenden Tendenzen der Harmonie'', translated by Erwin Stein. Mainz: B. Schott's Sohne.}}
* {{wikicite|ref={{harvid|Schoenberg|1969}}|reference=Schoenberg, Arnold (1969). "Structural Functions of Harmony", revised edition. New York: W. W. Norton. Library of Congress – 74-81181.}}
* {{wikicite|ref={{harvid|Vogel|1962}}|reference=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.<!--Society for the Promotion of Systematic Musicology--> Titled in response to Kurth (1920).}}
*{{Cite book |last=Thielemann |first=Christian |title=My life with Wagner : fairies, rings, and redemption : exploring opera's most enigmatic composer |date=2016 |publisher=Pegasus Books |isbn=978-1-68177-125-0 |location=New York |oclc=923794429|pages=194–195}}
* {{cite book|last=Walker|first=Alan|author-link=Alan Walker (musicologist)|year=2018|title=Fryderyk Chopin: A Life and Times|publisher=Faber & Faber|isbn=9780571348572}}
* {{cite book|last=Ward|first=William R.|year=1970|title=Examples for the Study of Musical Style |location=Dubuque |publisher=W. C. Brown Co.|isbn=9780697035417|url-access=registration |url=https://archive.org/details/examplesforstudy0000ward}}
{{div col end}}

==Further reading==
{{div col|colwidth=45em}}
* {{cite book|last=Bailey|first=Robert|year=1986|title=Prelude and Transfiguration from Tristan and Isolde|series=Norton Critical Scores|location=New York|publisher=W. W. Norton|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.
* {{cite book|last=Ellis|first=Mark|year=2010|title=A Chord in Time: The Evolution of the Augmented Sixth from Monteverdi to Mahler|location=Farnham|publisher=Ashgate|isbn=978-0-7546-6385-0}}
* {{cite book|author-link=Salomon Jadassohn|last=Jadassohn|first=Salomon|year=1899a|title=Erläuterungen der in Joh. Seb. Bach's Kunst der Fuge enthaltenen Fugen und Kanons|location=Leipzig|publisher=Breitkopf & Härtel|trans-title=An Analysis of the Fugues and Canons Contained in Joh. Seb. Bach's "Art of fugue"}}
* {{cite book|last=Jadassohn|first=Salomon|year=1899b|title=A Manual of Harmony|location=New York|publisher=G. Schirmer}}
* {{cite book|last=Jadassohn|first=Salomon|year=1899c|title=Ratschläge und Hinweise für die Instrumentationsstudien der Anfänger|location=Leipzig|publisher=Breitkopf & Härtel}}
* {{cite book|last=Jadassohn|first=Salomon|year=1899d|title=Das Wesen der Melodie in der Tonkunst|location=Leipzig|publisher=Breitkopf & Härtel}} {{cite book|title=Das Tonbewusstsein: die Lehre vom musikalischen Hören|trans-title=A Practical Course in Ear Training; or, a Guide for Acquiring Relative and Absolute Pitch|translator-first=Le Roy B.|translator-last=Campbell|location=Leipzig|publisher=Breitkopf & Härtel|year=1899}}
* {{cite book|last=Jadassohn|first=Salomon|year=1899e|title=Zur Einführung in J.S. Bach's Passions-Musik nach dem Evangelisten Matthaeus|location=Berlin|publisher=Harmonie}}
* {{cite book|ref=none|last=Magee|first=Bryan|year=2002|title=The Tristan Chord: Wagner and Philosophy|publisher=Macmillan |isbn=0-8050-7189-X|url-access=registration|url=https://archive.org/details/tristanchordwagn0000mage}}
* {{cite book|last=Mayrberger|first=Carl|year=1994|orig-year=1881|chapter=Die Harmonik Richard Wagner’s a den Leitmotiven aus ''Tristan und Isolde'' (1881)|editor-link=Ian Bent|translator-last=Bent|translator-first=Ian|title=Music Analysis in the Nineteenth Century|volume=1: Fugue, Form and Style|editor-first=Ian|editor-last=Bent|pages=221–252|publisher=Cambridge University Press|isbn=978-0-521-25969-9}}
* {{citation|ref=none|last=Nattiez|first=Jean-Jacques|author-link=Jean-Jacques Nattiez|year=1990b|title=Wagner androgyne|publisher=C. Bourgois |isbn=2-267-00707-X}} Contains discussion of the Tristan chord as "androgynous". {{cite book|year=1997|edition=English|title= Wagner androgyne |translator-first=Stewart|translator-last=Spencer|isbn=0-691-04832-0}}
* {{cite journal|author-link=Hugo Riemann|last=Riemann|first=Hugo|date=1872|title=Über Tonalität"|journal=[[Neue Zeitschrift für Musik]]|volume=68|pages=443–445, 451–454}}
* {{cite book|last=Riemann|first=Hugo|year=1875|title=Die Hülfsmittel der Modulation: Studie von Dr. Hugo Riemann|location=Kassel|publisher=F. Luckhardt}}
* {{cite book|last=Riemann|first=Hugo|year=1877|title=Musikalische Syntaxis: Grundriss einer harmonischen Satzbildungslehre|edition=revised|location=Leipzig|publisher=Breitkopf & Härtel}}
* {{cite book|last=Riemann|first=Hugo|year=1882|chapter=Die Natur der Harmonik|title=Sammlung musikalischer Vorträge 40|edition=revised|editor-first=P. Graf|editor-last=Waldersee|volume=4|pages=157–190|location=Leipzig|publisher=Breitkopf & Härtel}} {{cite book|chapter=The Nature of Harmony|translator-first=John Comfort|translator-last=Fillmore|title=New Lessons in Harmony|pages=3–32|location=Philadelphia|publisher=Theodore Presser|year=1887}}
* {{cite book|last=Riemann|first=Hugo|year=1883a|title=Elementar-Musiklehre|location=Hamburg|publisher=K. Grädener & J. F. Richter}}
* {{cite book|last=Riemann|first=Hugo|year=1883b|title=Neue Schule der Melodik: Entwurf einer Lehre des Kontrapunkts nach einer neuen Methode|location=Hamburg|publisher=K. Grädener & J. F. Richter}}
* {{cite book|last=Riemann|first=Hugo|year=1887|title=Systematische Modulationslehre als Grundlage der musikalischen Formenlehre|location=Hamburg|publisher=J. F. Richter}}
* {{cite book|last=Riemann|first=Hugo|year=1893|title=Opern-Handbuch|edition=second|location=Leipzig|publisher=Koch}} Supplement by F. Stieger.
* {{cite book|last=Riemann|first=Hugo|year=1895|title=Präludien und Studien: gesammelte Aufsätze zur Ästhetik, Theorie und Geschichte der Musik|edition=revised|volume=1|location=Frankfurt|publisher=Bechhold}}
* {{cite book|last=Riemann|first=Hugo|year=1900|title=Präludien und Studien: gesammelte Aufsätze zur Ästhetik, Theorie und Geschichte der Musik|edition=revised|volume=2|location=Leipzig|publisher=Seemann}}
* {{cite book|last=Riemann|first=Hugo|year=1901a|title=Präludien und Studien: gesammelte Aufsätze zur Ästhetik, Theorie und Geschichte der Musik|volume=3|location=Leipzig|publisher=Seemann}} Reprint (3 vols. in 1), Hildesheim: G. Olms, 1967. Reprint (3 vols. in 2), Nendeln/Liechtenstein: Kraus Reprint, 1976.
* {{cite book|last=Riemann|first=Hugo|year=1901b|title=Geschichte der Musik seit Beethoven (1800–1900)|location=Berlin and Stuttgart|publisher=W. Spemann}}
* {{cite book|last=Riemann|first=Hugo|year=1903|title=Vereinfachte Harmonielehre oder die Lehre von den tonalen Funktionen der Akkorde|edition=second|location=London, New York|publisher=Augener, G. Schirmer}}
* {{cite journal|last=Riemann|first=Hugo|year=1905|title=Das Problem des harmonischen Dualismus|journal=[[Neue Zeitschrift für Musik]]|volume=101|pages=3–5, 23–26, 43–46, 67–70}}
* {{cite book|last=Riemann|first=Hugo|orig-year=1902|year=1913|title=Grosse Kompositionslehre|edition=revised|location=Berlin and Stuttgart|publisher=W. Spemann}}
* {{cite book|last=Riemann|first=Hugo|year=1915|chapter=Ideen zu einer 'Lehre von den Tonvorstellungen|title=Jahrbuch der Musikbibliothek Peters 1914–15|pages=1–26}} Reprinted in ''Musikhören'', edited by B. Dopheide, 14–47. Darmstadt: [s.n.?], 1975. {{cite journal|title=Riemann's "Ideen zu Einer 'Lehre von den Tonvorstellungen' ": An Annotated Translation|translator-last=Wason|translator-first=Robert W.|translator-last2=Marvin|translator-first2=Elizabeth West|journal=[[Journal of Music Theory]]|volume=36|year=1992|pages=69–117}}
* {{cite book|last=Riemann|first=Hugo|year=1916|chapter=Neue Beiträge zu einer Lehre von den Tonvorstellungen|title=Jahrbuch der Musikbibliothek Peters 1916|page=1–21}}
* {{cite book|last=Riemann|first=Hugo|year=1919|title=Elementar-Schulbuch der Harmonielehre|edition=third|location=Berlin|publisher=Max Hesse}}
* {{cite book|last=Riemann|first=Hugo|year=1921|title=Geschichte der Musiktheorie im 9.–19. Jahrhundert|edition=revised|location=Berlin|publisher=Max Hesse}} Reprinted, Hildesheim: G. Olms, 1990. {{ISBN|9783487002569}}.
* {{cite book|last=Riemann|first=Hugo|year=1922|chapter=Allgemeine Musiklehre: Handbuch der Musik|edition=ninth|title=Max Hesses Handbücher 5|location=Berlin|publisher=Max Hesse}}
* {{cite book|last=Riemann|first=Hugo|year=1929|title=Handbuch der Harmonielehre|edition=tenth|location=Leipzig|publisher=Breitkopf & Härtel}} Formerly titled ''Katechismus der Harmonie- und Modulationslehre'' and ''Skizze einer neuen Methode der Harmonielehre''.
* {{cite book|author-link=Arnold Schering|last=Schering|first=Arnold|year=1935|chapter=Musikalische Symbolkunde|title=Jahrbuch der Musikbibliothek|pages=15–36}}
* {{cite book|last=Stegemann|first=Benedikt|year=2013|title=Theory of Tonality|series=Theoretical Studies|location=Wilhelmshaven|publisher=Noetzel|isbn=978-3-7959-0963-5}}
* {{cite book|last=Wolzogen|first=Hans von|author-link=Hans von Wolzogen|year=1883|title=Erinnerungen an Richard Wagner: ein Vortrag, gehalten am 13 April 1883 im Wissenschaftlichen Club zu Wien |location=Vienna |publisher=C. Konegen|ref=none}}
* {{cite book|last=Wolzogen|first=Hans von|year=1888|title=Wagneriana. Gesammelte Aufsätze über R. Wagner's Werke, vom Ring bis zum Gral. Eine Gedenkgabe für alte und neue Festspielgäste zum Jahre 1888 |location=Leipzig |publisher=F. Freund|ref=none}}
* {{cite book|last=Wolzogen|first=Hans von|year=1891|title=Erinnerungen an Richard Wagner |url=https://archive.org/details/erinnerungenrich00wolz|edition=new|location=Leipzig|publisher=P. Reclam|ref=none}}
* {{cite book|editor-last=Wolzogen|editor-first=Hans von|year=1904|title=Wagner-Brevier|series=Die Musik, Sammlung illustrierter Einzeldarstellungen 3|location=Berlin|publisher=Bard und Marquardt|ref=none}}
* {{cite book|last=Wolzogen|first=Hans von|year=1906a|title=Musikalisch-dramatische Parallelen: Beiträge zur Erkenntnis von der Musik als Ausdruck |location=Leipzig|publisher=Breitkopf & Härtel |url=https://archive.org/details/musikalischdram00wolzgoog|ref=none}}
* {{cite book|last=Wolzogen|first=Hans von|year=1906b|chapter=Einführung|editor-first=Heinrich|editor-last=Porges|title=Tristan und Isolde|location=Leipzig|publisher=Breitkopf & Härtel}} Introduction by Hans von Wolzogen.
* {{cite book|last=Wolzogen|first=Hans von|year=1907|chapter=Einführung|editor-first=Richard|editor-last=Wagner|title=Entwürfe zu: Die Meistersinger von Nürnberg, Tristan und Isolde, Parsifal|editor-first2=Hans von|editor-last2=Wolzogen|location=Leipzig|publisher=C. F. W. Siegel}}
* {{cite book|last=Wolzogen|first=Hans von|year=1908|title=Aus Richard Wagners Geisteswelt: neue Wagneriana und Verwandtes|location=Berlin|publisher=Schuster & Loeffler|ref=none}}
* {{cite book|last=Wolzogen|first=Hans von|year=1924|title=Wagner und seine Werke, ausgewählte Aufsätze |series=Deutsche Musikbücherei |volume=32|location=Regensburg|publisher=Gustav Bosse Verlag|ref=none}}
* {{cite book|last=Wolzogen|first=Hans von|year=1929|title=Musik und Theater|series=Von deutscher Musik |volume=37 |location=Regensburg|publisher=Gustav Bosse|ref=none}}
{{div col end}}

{{chords}}
{{Tristan and Iseult}}
{{Richard Wagner}}

[[Category:Chords]]
[[Category:Opera terminology]]
[[Category:Richard Wagner]]
[[Category:Post-tonal music theory]]