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 F7 (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 in the key of A minor in many ways: {{Image frame|content= { \new PianoStaff > \new Staff 2.(_\markup { \concat { "Fr" \raise #1 \small "+6" \hspace #8 "V" \raise #1 \small "7" } } 4.)~ 8 r r } >> >> } |width=390|caption=The Tristan chord analyzed as a
French sixth (in red) with
appoggiatura and
dominant seventh with
passing tone in A minor}} • 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 V. 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, 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. • The root is the fourth scale degree, D. Arend interprets it as "a modified
minor seventh chord" :: 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. This favors the fifth motion from B to E, seeing the chord as a
seventh chord with lowered fifth (B–D(D)–F–A). It would therefore act as the
supertonic chord in a ii-V
imperfect cadence.
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: : { \new PianoStaff 2. } >> \new Staff 2._\markup { \concat { "IV" \raise #1 \small "6" \hspace #3.5 "V" } } } >> >> } , independently, sees the G as an appoggiatura to A, describing that {{Image frame|content= { \new PianoStaff 2. \stemDown dis2._( d) } >> \new Staff 2. 2. } >> >> } |width=320|caption=The Tristan chord as appoggiaturas resolving to a dominant}}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:
Fred Lerdahl presents alternate interpretations of the Tristan motive, as either i ii643 [French sixth: F–B–D–A] V7 or as VI (iv) (vii642) [
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.
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 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″.
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 major or E minor 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 minor". ==Responses and influences==