A Curious Case of Convergent Evolution

William Carragan
Contributing Editor, Anton Bruckner Collected Edition, Vienna
Vice-President, Bruckner Society of America

Additional Information about the Paper


IIn 1895, at Steinbach on the Attersee, in view of the rugged and desperate cliffs of the Höllengebirge, Gustav Mahler developed five new nature-inspired symphonic movements which he thought of in Nietzschean terms as “The Joyful Wisdom”, and which would eventually appear after revision as the final five movements of his Third Symphony. The last of those movements is a tightly-constructed adagio in five-part song form, a design originating with Beethoven in his Ninth Symphony and A-minor string quartet, and used by Anton Bruckner in seven symphonies of his own. Although Beethoven and Bruckner, and Mahler himself in his fourth and sixth symphonies, used this structural paradigm for inner movements which end quietly, in the Third it has the task of providing a triumphant ending for a work on the grandest of scales.

Only one year before, late in 1894 in Vienna, Anton Bruckner brought to conclusion his last adagio movement, that of his Ninth Symphony, the finale of which he was not destined to complete. This adagio also has the outward appearance of a five-part song form, but expressed rather differently than in the other six symphonies in which that form is used. Indeed other schemes than the five-part rondo have been suggested for this movement by many people. But it turns out that the forms of these two movements, however they may be analyzed, have some striking individual similarities, in what must be a fortuitous evolutionary convergence. That convergence is the subject of this paper.

The last movement of Gustav Mahler’s Third Symphony is also unusual, in a number of ways. Unlike nearly all classical finales it is slow, it is basically peaceful with only four areas at an extended dynamic above forte, and it contains not one single sixteenth note. It is very tightly constructed, in contrast to all the other movements, and it spends a lot of time in the home tonality of D major. Nonetheless it has a complex emotional contour, with the particularly stressful areas laid out logically in the five-part structure. Thus in the first, third, and fifth parts the A theme in two distinct melodies reigns alone. The initial melody A1, at first quietly moving between the dominant and the tonic above, is made of nothing but quarter and half notes, while the ensuing melody A2 is the only theme in the movement that contains runs of eighth notes. In contrast, the B1 and B2 themes that populate the second and fourth parts are mostly built in half notes. In parts 4 and 5 there is introduced into A2, then into A1, a turn in quintole eighths recalling the prayer of Rienzi; these are the fastest notes in the movement. The simplicity of all of these ideas give this movement a stately declamation, in which even the Bk theme, recalling the epic struggles of the first movement in agonized climaxes near the ends of the second and fourth parts, still has self-possessed, hieratic grandeur.

The adagio movement of Anton Bruckner’s Ninth Symphony, coming third in sequence as in his Eighth, the first concept of his Second, and Beethoven’s own ninth symphony, has much greater
rhythmic contrast among its themes than the Mahler, is written in a substantially more progressive harmonic idiom, and has as its job the presentation of a further aspect of the eschatological tension of the first two movements. The adagio is conceived in a hermetic version of E major, which does not become clear to the listener until the cadence in measure 7. In the first three parts of the five-part structure, the themes are deployed much as the themes are in his other adagios in which the five-part song form is universally accepted to be used. In the first part, four distinct thematic ideas can be distinguished. A1 begins with the famous leap of the minor ninth and sweeps upward via the “Grail” motive from “Parsifal” to an E major chord in measure 7. A2 emerges from the bass in that same measure with the “Grail” motive and continues in further development of it. Then there comes the climactic A3 with the “Cross motive” in the trumpets, possibly recalling the first four notes of the passion hymn “Vexilla regis” (“The royal banners”) and a version of A1 in the trombones. Finally, A4 is played by the four Wagner tuben with partial reinforcement of the upper line by two horns. This chorale-like passage was named by Bruckner himself as the “Farewell to Life”. These four ideas follow each other rather closely, but in the later development of the movement, they have very different histories. In the second part, two themes are laid out. B1 is an extended lyric in A flat major with the first four notes quoting in inversion the melody of the word “miserere” (have mercy) in the Gloria of the D-Minor Mass of some thirty years before. By strong contrast, B2 in G flat major is a dense1y contrapuntal episode in 16th and occasional 32nd notes leading to an ecstatic melody recalling A1 high in the violins. The result, though deliberate, is more premonitory than stately; already a brooding menace hangs over everything.
Both movements are analyzed in Table 1, and the basic themes in their earliest manifestations are given in Tables 2 and 3. The themes are presented in much greater detail on the website accessible through the quick recognition code in the margin.

Intricacies of the Mahler Adagio

Part 1 of the Mahler finale is basically A1, A2, A1, and a closing passage, while part 2 begins with B1, and in ten measures B2 follows, eventually leading to a threatening climax and the Bk theme in the horns. Then part 3 begins with a developed version of A2, followed by the familiar version of A2 and A1 in due order. By contrast, Bruckner begins his third parts with a clear statement of his A1 in every one of the seven adagios he wrote in this form. One could say that Mahler is instead developing here a technique of continuous variation, which is apparent in many other places in his work, notably in the finale of his Seventh.

Mahler’s part 4 begins with two statements of B1 and B2 overlapping each other instead of being stated sequentially as in part 2. But as part of a crescendo, and most anomalously for this form, a disguised developed A2 and A1 enter where they do not normally belong, and lead to an anguished quotation of the first movement. When that subsides, a developed A2 enters by way of consolation. But this leads to another even more threatening climax with Bk newly combined with another idea from the first movement. Now this part 4 could be considered to be three shorter parts, with B, A, and B dominating the shorter parts in order. But it is more economical and logical to regard this whole area as one part, because it begins with the opening themes of the B group, and it concludes the way Part 2 concludes with the closing formula of B, which is
Bk. By adopting this scheme one asserts that the A section of part 4 is an interleaving of part 1 material into a structural element where it is otherwise alien.

The ensuing part 5 once more presents A1, A2, and A1 in order, with each theme given a very special orchestration. The A1 melody is given to the first trumpet and at the same time to the first trombone in inversion. The trumpet line is slightly adjusted for the sake of perfect and calm euphony, concealing the virtuosity of the concept. I have seen at least one video in which the trumpeter plays this entrance on the high G trumpet he had also used for the “posthorn” solo in the third movement, but it is indicated in the score to be played by the big, noble trombone-like trumpet in F over an octave lower, which was used so often in the time of Mahler and Bruckner but is almost never heard today. The A2 entrance is in the cellos, backed up by the horns which oscillate in pairs playing the melody, so that in the first measure the first and third horns play the melody, in the second measure the fifth and seventh play, in the third measure the first and third horns play again, in the fourth measure the fifth and seventh horns once again, and in the fifth measure the three trumpets take over the melody as it rises. The horns not playing the melody at any time make their contributions to the harmonic richness and emotional warmth of the final statement of that melody in the symphony. This kind of orchestrational trickery one inevitably associates with Richard Strauss and other Wagner epigones, but not at all with Bruckner who achieves his striking gestures with fluent but quite traditional means.

As mentioned above, there are three quotations from the first movement, two in part 4, and one in part 5. The part 4 quotations are from the transition from the exposition to the development in the first movement. The exposition is about to conclude the summer-morning march triumphantly in D major, but there is a sudden catastrophe and the sound returns to the cold world of the movement’s beginning. Thus the quotation at measure 181 of the finale, in the middle of part 4, is from measure 369 of the first movement, though it had been adumbrated as early as measure 7, and the quotation at measure 221, associated with the Bk motive nearer the end of part 4, is from measure 364 of the first movement. Bk itself has a similar rhetoric to the wintry music at the beginning of the first movement, but is not literally present there. The third quotation is at measure 269 of the finale, near the beginning of part 5, where in free extension of the A1 theme the bold and menacing opening theme of the symphony is made to be consoling and reassuring following the treatment in first movement m. 808.

The quintole eighths mentioned above are used in part 4, in the second variation of A2 in the “interleaved” A material, then in part 5 in A2, then finally in A1 only a few measures later. These groups of five suggest the turn ornament in the prayer theme quoted in the overture to Wagner’s opera “Rienzi”, and are very prominently used by Bruckner in his Eighth Symphony, third movement m. 16 and later. What is remarkable in the Mahler adagio is that they are used as decoration for both A2 and A1. Whatever theoretical objections one might have toward doing that are utterly wiped away in the drama created by them.

Anomalies of the Bruckner Adagio

The first three parts of the adagio of Bruckner’s Ninth Symphony present no unusual structural details, indeed nothing that departs from his practices in his other six adagios written in five-part
song form. As mentioned above, four basic ideas can be discerned in part 1, with the last one, the famous tuben chorale “Farewell to Life” concluding the theme group as it slowly subsides. Then in part 2 there are two contrasting themes stated in sequence with the second one, B2, developing into the opening phrase of B1 before B1 returns on its own, much as previously though abbreviated. Part 2 concludes with a flute solo over a French augmented-sixth chord in the tuben, C-E-F#-A#, which resolves mentally on the chord of E minor in second inversion, B-E-G-B, even though only the pitch B is heard. Thus part 3 begins with A1 as part 1 did, but with a greater sense of harmonic location than Bruckner affords at the beginning. Then instead of going ahead to A2, he treats the minor-ninth phrase of A1 further in an elaborate four-part canon in the winds, and then A2 and A1 together, until finally reaching A3, the “Cross motive”, 44 measures into the part instead of 17 as before. Again, this technique is completely typical for the composer. But then, the “Cross motive” is abbreviated and the “Farewell to Life” is omitted, and Part 4 begins directly with B2, not B1. That last is the first of several significant anomalies in this movement.

In part 4, the initial B2 is confined to only ten measures, breaking off abruptly just as the melody reaches its concluding development of B1. Then after a short transition, A1 enters where it does not belong, not with the minor ninth, but with a phrase which had appeared two measures after the minor ninth in both parts 1 and 3, beginning the upward sweep to the E major chord. In the musical examples this phrase is labeled A1b, and it is the source of very substantial development over the next 14 measures. Then there is a chorale, reminiscent of the chorale in the third theme group of the finale of the Eighth, which also looks forward to the great brass chord intact in the sketches for the finale of the Ninth. This chorale is stated twice over eight measures, and then the initial part of A1 and its inversion in canon, making a transition of sorts with insistent repeated eighth notes for the oboes and clarinets of almost unbearable psychological intensity.

The next thematic element of the adagio of Bruckner’s Ninth Symphony begins with an upper-first-violins melody in the home key of E major, with an ornate accompaniment consisting of a counter-melody in the lower-first violins, a moving eighth-note foundation line for the cellos and basses, syncopated afterbeats in the violas, and an ornate thirty-second-note filigree for the second violins. This kind of very elaborate treatment, customarily accorded by Bruckner to the A theme at the beginning of Part 5, was first used in the slow movement of his Second Symphony, and was employed again quite successfully in his Third, Fourth, Fifth, Seventh, and Eighth Symphonies, and even in the Sixth at what is usually described as the recapitulation of a sonata form in that unique movement. But here the ornate treatment is given to the B1 theme, not the A theme, and that is the second great anomaly of this movement. To the ear, alive to the texture and momentum, this treatment certainly sounds like the beginning of the last crescendo, which is a reliable design feature of these movements. Indeed in a survey of time allotments in the song-form adagios, it appears at that place in time where we expect to hear the A theme begin the climb to the climax of the movement all within Part 5. But in terms of its melody it seems still to belong to Part 4, in which the full B1 theme must still make an appearance. Indeed, in terms of thematic recurrence rather than texture, Part 5 cannot be said to begin until we hear once again from the A1 theme. The result of this delay brings a more and more intense anticipation of the opening theme when it makes its final entrance.

And differently from every other use of this form by Bruckner or anyone else, the final entrance of the A1 theme appears fortissimo in the bass in C sharp minor, with canonic trumpet entries and a furiously active accompaniment with swirling upper strings and repeated triplets in the whole wind choir. Only the very beginning of the theme appears, without the A1b motive which had been treated out of place in Part 4, and it concludes with a chord which has F sharp as its bass but contains nearly every note of the chromatic scale. After that, and a long pause, Part 5 continues with A2, an expression of the ‘Grail” motive, and A4, in which the harmonized four-note “Miserere” motive from the D-minor Mass and the Third Symphony replaces the “Farewell to Life” to which it is rhythmically similar. The trend of thought implicit in these relationships, where the consciousness of approaching death evokes a plea for mercy, hardly needs to be argued. These three elements of the A theme, without considering the introductory crescendo, constitute a rather brief Part 5 of 32 measures, only one third as long as the giant 96-measure Part 5 of the 1887 Eighth, but still full of drama and significance.

And differently from every other use of this form by Bruckner or anyone else, the final entrance of the A1 theme appears fortissimo in the bass in C sharp minor, with canonic trumpet entries and a furiously active accompaniment with swirling upper strings and repeated triplets in the whole wind choir. Only the very beginning of the theme appears, without the A1b motive which had been treated out of place in Part 4, and it concludes with a chord which has F sharp as its bass but contains nearly every note of the chromatic scale. After that, and a long pause, Part 5 continues with A2, an expression of the ‘Grail” motive, and A4, in which the harmonized four-note “Miserere” motive from the D-minor Mass and the Third Symphony replaces the “Farewell to Life” to which it is rhythmically similar. The trend of thought implicit in these relationships, where the consciousness of approaching death evokes a plea for mercy, hardly needs to be argued. These three elements of the A theme, without considering the introductory crescendo, constitute a rather brief Part 5 of 32 measures, only one third as long as the giant 96-measure Part 5 of the 1887 Eighth, but still full of drama and significance.

Indeed the climax of the A theme, coming after a crescendo based on B1 rather than A1, is Bruckner’s only clear adagio climax in a minor key. Table 4 shows the tonalities of the movements and of the climaxes, and also the proportion of the music from Part 5 to the end and the proportion from the climax to the end. For the Ninth I also calculate the proportion from the B1 crescendo to the end. Considering the percent of the movement devoted to part 5 through the end, the Ninth is the least of all the symphonies unless the B1 crescendo is counted in. But the percentage from the climax to the end is quite close to that of the Seventh and Eighth, while the Third, Fourth, and Fifth devote much less space to the climax and coda.

From Table 4 one also sees that in most Bruckner adagios the climax is not in the tonic key of the movement, but is a second or third displaced from the tonic. Thus the climax is not to be understood as an apotheosis of the material of the rest of the movement, but instead as a radical and ecstatic departure from it. This is especially clear in the Seventh and Eighth, but it is even true in the Second where the first Part 5 that Bruckner ever devised was something of an afterthought, being inserted in the already complete movement in the latest stages of composition of the early version of the symphony. But in the Ninth, the tonality of the climax is the relative minor of the home key, and for all its concomitant dissonance, it is very closely welded to it. There is thus the sense that the world painted so vividly and direly in the rest of the movement is not to be escaped through this movement. For this reason alone, the Ninth Symphony should not be regarded as “complete in its incompleteness”, but as an unfinished torso which the composer was desperate to bring to resolution through a regular allegro finale.

The claim in this paper that the “Miserere” motive serves in Part 5 as a substitute for the “Farewell to Life” motive of Part 1 is reinforced by the similarity of the distinctive string accompaniment, which in Part 1 is used for both A3 (“Cross”) and A4 (“Farewell”) and in Part 3 for A3 only before the theme breaks off suddenly. The antecedents of the “Miserere” motive in the mass and the symphony are shown in the complete thematic files accessible through the QR code above. Leopold Nowak, in the preface to his edition of the Mass in D minor, says; “How highly Bruckner thought of his Mass can best be deduced from the fact that he included the Miserere theme from the Gloria in the Adagio of his IX. Symphony. He said ‘Farewell to Life’
and knew no better melodies than the humble, imploring series of sixth chords from his Linz period.”
After the compact Part 5, with eight measures for A1 and twelve measures each for A2 and A4, the placid coda in pure E major brings rest to this tumultuous movement. There are near-quotes of the Eighth and Seventh symphonies, with a gentle but piercing final high note for all four horns in unison which is one of the terrors of the literature.

What does the interleaving accomplish?

Mahler explicitly said in public that the later-downplayed title of the last movement of his Third Symphony, “What love tells me”, referred to the love of God as manifested by the richness of the gift of nature. And in a letter he wrote about it to Anna von Mildenburg, the soprano he had just conducted at Hamburg in the role of Brünnhilde, he wrote: “Just imagine a work of such magnitude that it actually mirrors the whole world—one is, so to speak, only an instrument, played on by the universe.” But considering also the theme of human love would make much easier the parsing of the various crises that appear in this movement with short but explosive preparation.

In this movement in five-part song form, just as in the customary treatment established by Bruckner in 1872, there is a mood associated with parts 1, 3, and 5, and a contrasting mood for parts 2 and 4. Parts 1 and 3 are dominated by the warm and reassuring melodies of A1 and A2, where A1 is placid and A2 is more active. Parts 2 and 4 also have two distinctive ideas, the mysterious and unstable B1 and B2, that are stated in sequence in Part 2 and together in Part 4. But in Part 2 near its end there is a passionate outbreak of a threatening melody in the horns, reminiscent of the wintry music of the beginning of the symphony although the melody itself is not present there. Now according to the scheme, this same thing has to happen also in Part 4, but with appropriately far greater intensity. This is where the interleaving plays its role. After the presentation at the beginning of Part 4 of the two themes very nearly at the same time, the A2 theme in running notes enters by surprise and first seems to console, but then there is a sudden crescendo and a theme of three insistent rising notes that really is from the first movement provides another ominous interruption. In due course the interleaved A-group music becomes calmer again, but when the music returns to the B group, the closing theme Bk comes back in the same way as in Part 2, but even more catastrophically. That could hardly have been accomplished effectively in Part 4 without the help from the interleaved A and first-movement themes inserted into the middle of that area. In Bruckner’s use of this form, the A themes are typically the serious ones, representing natural beauty (Second), devout faith (Third), wandering and searching (Fourth), anxiety and dislocation (Fifth), elegiac sorrow (Seventh), intense love (Eighth), and approaching death (Ninth). In each of these movements, it was completely natural for Bruckner to place climaxes in both Parts 1 and 3, and allow Parts 2 and 4 to provide in the B themes diversion, relief, consolation, even ecstasy by way of essential contrast. But Mahler has turned this whole process inside out, and finds himself adjusting the form in order to achieve the emotional contour he wants. In the adagio of Mahler’s Fourth and the andante of his Sixth, no such device is needed, and the form proceeds much more simply. But in the Third, the contrast of reassurance and instability is just as palpable as with the Bruckner adagios, notwithstanding the
much greater similarity of Mahler’s themes and the essential rarity of rhythmic disturbance in the whole movement. Thus the double crisis in part 4 created by the interleaved A-theme material makes possible a Part 5 that is wholly calm and serene. The dramatic stresses having been worked out, Part 5 begins with simple-sounding but texturally imaginative presentations of A1, A2, and A1 again just as in Part 1, but here leading to a grand and magnificent celebratory outpouring of D major in the short coda at the end, finishing out the emotional inversion of the form already present in the rest of the movement.

In Bruckner’s previous six five-part adagios, Part 5 begins with a recurrence of the melody which begins the movement, accompanied by an elaborate orchestral texture, complex in detail and in rhythm. But the melody itself begins in the home key every time, and remains unaltered for a while before being developed. In the Second, his first use of the form, there are 10 basically unaltered notes (pitch classes) at the beginning of Part 5, in the Third, 15; in the Fourth, 10; in the Fifth, 21; in the Seventh, no fewer than 38, and in the Eighth, 41. But the opening theme of the Ninth is deeply unsuitable for such treatment. It begins with a five-note gesture in which the first interval is a leap of a minor ninth, and then, starting tentatively, it sweeps up to a cadence in D major, and then to a firmer cadence in E major, the home tonality. The two sweeping motions seem to be based on the “Grail” motive from Parsifal, but there is a similar motion in the prominent climaxes present in the adagio of the Eighth. It does not in any way possess he meditative, thoughtful, pensive quality in those other themes; it is a cry of anguish and a desperate, impassioned prayer. But there is another theme in this movement which is superbly apt for decorative accompaniment; it is the B1 theme that begins part 2. So Bruckner uses that for the adagio crescendo, and he is able to use it beginning with 22 unaltered notes. The listener barely notices that it is the wrong theme, because the crescendo builds in exactly the expected way, at the right location in the piece. Nothing seems anomalous until at the climax, the minor ninth of A1 thunders out in eight apocalyptic measures, with the famous, outrageous dissonant chord echoing in the silence, the hearer aghast.

Why was the ardent, lyrical B1 melody available for Bruckner to use in this way? In the other adagios the B theme group is fully developed in Part 4 just as it was presented in Part 2, and the B theme could hardly be used immediately afterward in an apparent Part 5. But here Part 4 begins out of order with B2, not B1, and after only 12 measures the music continues with a treatment of A1b, then the initial five notes of A1. This is the interleaving of the A theme into Part 4 where it would normally not belong. This is the formal anomaly which allows the Bruckner to use B1 for the crescendo leading to the final climax. And most significantly it permits the climax to be a catastrophe, instead of the transcendent vision present in the final outbursts of all of Bruckner’s other adagios in this form. The thematic role reversal continues with the transmogrification of “Farewell to Life” into “Miserere”. The story is not over, and Bruckner tried as hard as he could to resolve it in the finale.


Bruckner and Mahler were always trying to surpass their previous works in some way. This is true even with their mid-career retrenchments in scale, Bruckner with the Quintet and Mahler with his Fourth Symphony, in both of which the gigantic is made to give way to the refined.
Whether Mahler took Bruckner or Beethoven as his adagio model is hard to say, but he certainly was familiar with the five-part form, and he wanted to do something to it which would permit him to end his slow movement with triumph, not resignation. But Bruckner had to base the final loud music on a theme of pain and anguish, not contemplation and other-worldly vision. Both goals were strongly in contrast with the usual purposes of the five-part song form, and the temporary inversion of thematic content represented by the interleaving of A material into Part 4 which is in other cases reserved strictly to B material, is what enabled the two composers to achieve their distinct, individual goals. It is tempting to speculate on how this convergence took place. Steinbach am Attersee is not a continent apart from the Belvedere Kustodenstöckl, but these two greatest Austrian romantic composers almost certainly did not compare notes. Whatever it was, was in the air; opposites must be made to tell the story, and we are all richer for the cleverness and inspiration Mahler and Bruckner bequeathed to us in doing that.

A Curious Case of Convergent Evolution (Additional Tables)

Anton Bruckner

Symphony no. 9 in D Minor, Adagio

Thematic Synopsis

Gustav Mahler

Symphony no. 3, Adagio

Thematic Synopsis