Functional analyses

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

• 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♯,^{[7][8][9][10]} 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.^{[11][12][13][14]}
• The root is the fourth scale degree, D. Arend interprets it as "a modified minor seventh chord"^[15]

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.^[16][17][18] 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^[19] analyses the chord as a IV chord after Riemann's transcendent principle (as phrased by Serge Gut:^[20] "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 [fr], 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.^[21]

According to Jacques,^[22] discussing Dommel-Diény^[23] and Gut,^[24] "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.^[25]

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.^[26]

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),^[27][28] of F♯ minor.^[29][30]

Linear analyses include that of Noske^[31] 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.^[32]

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."^[20] 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♯″.^[33]

Schoenberg describes it as a "wandering chord [vagierender Akkord]... it can come from anywhere".^[34]

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".^[35] 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^[36] 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".^[37]