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On the Subject of COGNITION VS. INFORMATION Strategic Method Strategic Method IN MUSIC

Beyond Bach: Beethoven’s Studies of Bach’s Works by Ortrun Cramer

ll great Classical composers When Beethoven started his stud- after Bach studied his works ies with in —the Aand learned from them, but hoped-for studies with Mozart had no one succeeded, as Mozart and been rendered impossible by the lat- Beethoven did, in grasping and fur- ter’s early death—he was welcomed ther developing Bach’s science of and received by the admirers of composition in such a way, that ’s music in something entirely new emerged, Vienna. There was the well-known again pointing into the future. Baron Gottfried van Swieten, in had been whose house the musical elite of familiar with Bach’s art of composi- Vienna would gather every Sunday, tion since his early youth. In 1783, an and where, according to Mozart, article appeared in Cramers Magazin “nothing was played but Handel and der Musik, which stated that young Bach,” and whose library Mozart Beethoven “could become a second described as “although in quality a Mozart.” The proof of his extraordi- very large store of good music, yet in Reproduced by permission of the Beethoven-Haus, Bonn nary talent was: “He plays most of Ludwig van Beethoven quantity a very small one.” And The Well-Tempered Clavier by Sebast- there were more admirers of Bach ian Bach, which Mr. Neefe has Leipzig-Vienna, Bonn, and Zurich. among the musicians, poets, publish- placed in his hands. Anyone who Beethoven’s teacher Christian Gott- ers, and personalities from the nobili- knows this collection of preludes and lob Neefe, who was in contact with ty and from economic life. (which one could almost call Bach’s son Carl Philipp Emanuel, In an essay recently published in the nec plus ultra) will know what served as a proofreader of the edition Fidelio magazine on “Moses that means . . ..” of the Simrock publishing house in Mendelssohn and the Bach Tradi- In 1783, The Well-Tempered Bonn. From the essay in Cramers tion,” Steven Meyer points to the Clavier existed only in private or Magazin der Musik, one can conclude special role of the family of the Jew- commercial manuscripts; the first that the copies must have been circu- ish banker Daniel Itzig from .1 printed editions were published, first lated rather widely among music Frequent cultural gatherings at his in 1799 in England, and in 1800-01 in lovers. house were attended by (among oth-

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© 2000 Schiller Institute, Inc. All Rights Reserved. Reproduction in whole or in part without permission strictly prohibited. tions on a theme by Beethoven, which he dedicated to his teacher. He had an impressive library, which Beethoven could use, which con- tained a large number of works by J.S. Bach in print, hand-written copies, or manuscripts, as well as many theoretical works on music with further Bach pieces. In Rudolph’s library were: The Art of the , The Well-Tempered Clavier, all four parts of the Clavierübung, the Two- and Three-Part Inventions, the French and English Suites, Motets, Masses, the Four-Part Choral Songs, The Granger Collection and much more. Bettmann/CORBIS C.P.E. Bach For Beethoven, this library was ers) Moses Mendelssohn and Got- of great value; it enabled him to ment as Archbishop of Olmuez. thold Ephraim Lessing, and by the pick out what was “most appropri- In his correspondence with his brothers Wilhelm Friedemann and ate” for his studies, as he declared in publishers, too, Beethoven showed Carl Philipp Emanuel Bach. Itzig’s a letter to the Archduke. It is his constant concern with the work daughter, Sara Levy, had studied remarkable, that Beethoven dedi- of J.S. Bach: On the one hand, he piano with Wilhelm Friedemann; cated to the Archduke a whole constantly requested copies of newly she became a key figure in the net- series of his greatest compositions, published editions, for example, a works defending Bach’s music. Her which are most clearly influenced copy of the B-minor Mass, from the sister, Babette Salomon, was Felix by his Bach studies, among them publishers Breitkopf and Härtel in Mendelssohn’s grandmother; she the Piano Sonatas Op. 106 and 111, Leipzig, and Nägeli in Zürich. He gave him a copy of the full score of and the Grosse Fuge Op. 133. What thanked Breitkopf and Härtel for Bach’s St. Matthew Passion. Two oth- Beethoven considered his greatest sending him Bach compositions, er daughters of Itzig, Fanny von work, the Missa Solemnis, was origi- writing, “For the beautiful things of Arnstein and Cäcilie Eskeles, were nally intended to be performed on Sebastian Bach, I thank you very married in Vienna. Fanny von Arn- the occasion of Rudolph’s enthrone- much indeed, I shall preserve them stein was a co-founder of the and study them.” Beethoven wel- Gesellschaft der Musikfreunde comed the planned project for a (Society of Friends of Music) in complete edition of Bach’s works, at Vienna; Beethoven wrote a small the beginning of the Nineteenth cen- composition into Cäcilie’s album: tury, as “what does my heart good, “Edel sei der Mensch, hilfreich und my heart which beats fully for the gut” (“Let man be noble, helpful and elevated, great art of this original good”). father of harmony.” Of special value for Beethoven In Beethoven’s sketchbooks, was the library of his student, friend, interspersed among work on his own sponsor, and protector, the Archduke compositions, there are numerous Rudolph, son of Emperor Leopold II, entries of short or long passages from half-brother of Franz I. Archduke Bach’s works, among them, the Rudolph, who later became Cardinal Chromatic Fantasy, and fugues from and Archbishop of Olmuez, was a The Well-Tempered Clavier and highly talented musician. He played The Art of the Fugue. the piano part in the first perfor- The method of noting down asso-

mance of Beethoven’s Violin Sonata Bettmann/CORBIS ciation of ideas right away, Bee- Op. 96, and composed forty varia- Archduke Rudolph thoven explained in 1823 in a letter

79 to Archbishop Rudolph, whom he advised the following:

Right at the piano, quickly, fleeting- ly write down your ideas. . . . Through this, not only will your imagination be strengthened, but one also learns how to fix the remotest ideas in an instant. . . . Gradually, the ability emerges to present precisely and only what we wish/feel, which is such an essential need of noble men.

If Beethoven copied out long pas- sages or special transitions from Bach’s compositions, for study and for later use, he was following a method which J.S. Bach had already applied, who only achieved his sci- ence of composition through the study of good fugue writers, and “only through my own reflections,” as Carl Philipp Emanuel Bach reported. Only through the conscious replication of the creative discoveries of great predecessors, does the stu- dent reach true knowledge—as opposed to obtuse, rote learning. (It would be useless, for example, to condemn composition students to copy The Well-Tempered Clavier ten times over!) The Art of Four-Voice Song In Beethoven, this enduring dia- logue with J.S. Bach—and with the works of Mozart, which took up Bach’s discoveries and developed them—leads to a fundamental fur- ther development in his late compo- sitions. FIGURE 1. Autograph score, “Wenn ich einmal soll scheiden,” from J.S. Bach “St. Matthew In an interview with Fidelio Passion.” magazine,2 Norbert Brainin, the Beethoven writes in his late quar- the voices need not be concerned primarius of the unforgettable tets, a kind of four-voice setting, in with how loudly or how softly they Quartet (whom we will which the four voices are played, sing, because everything is so perfect- see shortly in a film clip), explained that is, sung, together. All the voices ly composed. The most important where the decisive progress of sing something which is element here, is the Motivführung Beethoven over J.S. Bach’s composi- important—and, that is, all equally [thorough-composition], because the tion method, lies: important. The balance is perfect; motifs that Beethoven uses, all origi-

80 to discover the alto and tenor voices FIGURE 2. Passage from Beethoven’s String Quartet Op. 127. themselves.” Later, “he taught them

sotto voce to write the bass voice themselves.” Violin I b b 12 j œ. œ j j & b b 8 j j j œb œ ˙. œ œn œ œb œ œn œ. œ œb œ ˙. œ œ J Let us listen to an example of a œ œ four-voice chorale, perhaps the best pizz. Violin II b b 12 & b b 8 ‰Œ‰ ∑ ∑ Œ‰ ‰Œ‰ ‰ known four-voice Bach chorale com- œ œ position: “Wenn ich einmal soll schei- sotto voce j j ˙b . œ œ. œ . den” (“Should I at some time B bb b 12 ‰Œ‰ Œ j ˙ œ œn œœ œn œn œb b 8 œn œ œn . J J J depart”), from the St. Matthew Pas- sion [SEE autograph, Figure 1]. We pizz. Violoncello ? 12 will hear a performance by the bbbb 8 ‰Œ‰ ∑ ∑ Œ‰ ‰Œ‰ ‰ œ œb Wiener Singverein (Vienna Singing ˙. w. Group), conducted by Wilhelm b n # # œ‹ œ œ# œ. œ. œ b b j ‰ n n # # Œ J J œ œ œ 3 & b œ. œœ œ n J J Furtwängler, from 1954. After the . œ p cresc. - - - - -cresc. - “rediscovery” and performance of arco # œ bb b j œ# n n## # ˙. œ œ œ œ œ j j œ j œ #jœ œ the Passion under the direction of the & b Œ‰ ‰Œ œ‹ œ# n n J œ œ œœ œ j ‰Œ‰ œ J J J œ œ œ young Felix Mendelssohn in 1829 in cresc. - - - - p Berlin, it has become traditional b b œœ j n n# ## œ œ j œ j j œ œ j B b b œ. œ œ œ j n n # J œ œ œ œ œ œ j œ j#jœ J œn among conductors to perform this J œ ˙# . œ J œ œ œ œ œ cresc. - - - - p -cresc. - chorale a capella, that is, without ? b arco # # j œ j j j j j instrumental accompaniment, and b bb Œ‰ œ‰Œ‰Œ j nnnn # # œ œœ œ œ œ j œ œ œ# œ ˙# . œ J œ œ œ œ œ ˙. this is how it is performed in this cresc. - - - - p cresc. - example. . . # # œ j œ œ œ œ œ . œ. œ. œ œ The chorale comes immediately # # œ œ œ j œ œ œ# œ ‰Œ‰ œ. œ œ J J œ œ. œn J J & œ J œ œ J œ J œ J J J J after the presentation of Christ’s ----p cresc. - - - death, in the Passion, and signifies a # # j # # ∑ Ó. j j œ# ˙. œ j j j œ point of self-reflection for the listen- & . œ œ œ‹ œ J œ œn œ œ œ. . œ œ œ œ. . . . er, on one’s own death and on eternal p cresc. - - - # ## œ j j œ œ œ ˙. j j life. That this moves one’s feelings B # œ œ œ œ œ j œ j#jœ j J J œ œ œ œ j j J œ œ œ œ œ. œ œ œ . . œ. œ. œn œ most deeply, is obvious. ----p . . cresc. - - - Let us now investigate, how ? # ## j j Beethoven decisively further devel- # œ. œ jœ œ# w. œ. œ œ j j ˙. ˙. œ. œ‹ . œ. œ. œn œ oped the art of the four-voice song— - p . . ---- cresc. - - - which, as we heard in the earlier con- tribution, is shaped by Bach also in a very polyphonic manner. nate from the piece and are related Bach became accustomed, by his For Beethoven, the sense and to one another. father, he said, “not to see anything aim of the study of his predecessors, as a master work”; the works were to was indeed his own further devel- However, Brainin added, serve connoisseurs and those eager to opment, toward new idea-mani- learn the art of composition, to study folds. Beethoven described this very It must be sung correctly, with the the “very special arrangement of the clearly in a letter to the Archbishop right voice . . . I assume, that a bel harmony and the natural flowing of Rudolph, in which he explicitly canto-trained singer, would recog- the middle voices and the bass.” Johann names Bach and Handel as the only nize this immediately. Sebastian Bach did not treat his own true geniuses, among his predeces- In order to investigate this idea students with “dry ,” sors: “The aim of the world of art, further, we will use the following but rather—after having initially as indeed in the whole creation, is musical examples. worked through the pure four-voice freedom, progress; if we moderns The four-voice choral phrases by general bass—led them into the have not the same firmness as our Johann Sebastian Bach, appeared in chorales, such that he “first set the ancestors, yet the refinement of our print in 1784. Carl Philipp Emanuel bass to it,” and then his students “had manners has in many ways

81 enlarged our sphere of action.” What this expansion involved, can FIGURE 3. Opening of “Heiliger Dankgesang” of Beethoven’s Quartet Op. 132. be heard in two examples, taken Heiliger Dankgesang eines Genesenen an die Gottheit, in der lydischen Tonart. from Beethoven’s late string quartets. Molto adagio 1 œ œ œ œ In autumn 1995, Norbert Brainin c œ œ œ œ œ ˙ Violin I & œ œ œ œ œ ˙ ˙ ˙ ˙ ˙ œ ˙ ˙ demonstrated the thorough-compo- œ ˙ ˙ ˙ sotto voce cresc. - p sition method in Beethoven’s late c Ó sotto voce Ó Violin II & œ œ œ œ ˙ string quartets, during a master-class œ œ œ œ ˙ ˙ ˙ ˙ œ œ œ œ œ ˙ ˙ ˙ œ ˙ ˙ p˙ œ œ of the Schiller Institute in Dolna B c Ó Ó sotto voceœ ˙ cresc. - Ó Ó œ œ 4 Viola œ œ ˙ ˙ œ ˙ Krupa, Slovakia. I would like to œ œ ˙ ˙ ˙ ˙ œ œ ˙ œ œ œ ˙ ˙ show a film clip from this master p ? c Ó ∑ sotto voce ˙ cresc. - ˙ÓD Ó œ œ class. Let us first listen to a short pas- Violoncello œ ˙ ˙ ˙ ˙ œ œ œ œ ˙ œ ˙ p ˙ ˙ sage from the slow movement of the cresc. - quartet Op. 127; the piece should be 10 œ œ Ó Ó ˙ ˙ ˙ ˙ ˙ ˙ œ œ œ œ œ œ ˙ performed Adagio molto espressivo & ˙ ˙ ˙ ˙ œ œ ˙ ˙ ˙ p œ œ ˙ [SEE Figure 2]. We will hear it per- cresc. - - f p Ó Ó Ó formed by the Auer Quartet from & œ ˙ ˙ ˙ ˙ ˙ ˙ œ œ œ œ ˙ ˙ œ œ œ ˙ œ œ œ œ ˙ ˙ ˙ ˙ ˙ p œ œ ˙ Budapest. [During the demonstra- p cresc. - - ˙ f˙ œ tion, Brainin remarks: “This is per- B Ó ˙ Ó Œ œ œ ˙ ˙ œ œœ ˙ œ œ œ œ œ ˙ ˙ ˙ ˙ ˙ ˙ œ œ ˙ fect counterpoint. If you were told ˙ p œ ˙ f p ? œ œ œ œ cresc.˙ -˙ - œ œ that it was by Bach, you would ˙ œ œ œ œ œ ˙ ˙ ˙ ˙ ˙ Ó Ó œ œ ˙ ˙ ˙ œ ˙ ˙ p believe it.”] p cresc. - - f Now, to the third movement of . . 21 œ œ œ œ œ ˙ ˙ œ œ œ œ œ ˙ ˙ ˙ the string quartet in A-minor, Op. & ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ p p p 132, which was composed in 1825, cresc. - - cresc. - cresc. œ . . . and, like the quartets Op. 127, 130, & Ó œ cresc. œ ˙ ˙ . œ œ œ and 131, was written for Russian ˙ ˙ ˙ ˙ ˙ œ œ ˙ œ œ œ p ˙ ˙ ˙ ˙ ˙ œ# cresc. - - p cresc. - p cresc. œ œ ˙ ˙ ˙ . . . . Count Nikolai Galitzin. The move- B œ Ó Œ œ œ ˙ ˙ œ œ œ œ ment of the quartet is entitled, ˙ ˙ ˙ ˙ ˙ œ œ ˙ œ ˙ ˙ ˙ ˙ p cresc. p cresc. - p cresc. “Heiliger Dankgesang eines Gene- ? cresc. - - œ œ . . . . ˙ ˙ Ó Ó œ ˙ ˙ ˙ ˙ œ œ œ œ senden an die Gottheit” (“Holy song ˙ ˙ ˙ ˙ ˙ œ ˙ ˙ ˙ p p cresc. - p cresc. of thanks, from a convalescent, to the cresc. - - Godhead”). We have already heard about the importance of the “Lydian interval” for the decisive condensa- 1825, Beethoven was seriously ill, Kuhlau during an excursion: tion of the well-tempered system, of and was forced to interrupt work on “Kuehl, nicht lau,” (“Cool, not luke- the 24 major and minor keys. Quar- the quartets, for some time. The warm”), which is a pun on the name, tet Op. 132 begins in the first move- composition did not leave him alone, composed on the B-A-C-H (Bf AC ment (which we are not considering as one can see in his conversation Bn) motif. Beethoven often uses this here) with a dense series of Lydian notebooks, how involved with it he form of irony, when he is dealing and double-Lydian chords, as prepa- was. This reaches from short sketch- with the most serious, even funda- ration for the development of the lat- es for the quartet and sketches on the mental problems. er composition, and especially this title “Dank-Hymne eines Kranken Noteworthy is also the emphasis third movement.5 an Gott bey seiner Genesung” that Beethoven lays on the correct The “Heilige Dankgesang” is to (“Hymns of thanks to God, from an reproduction of the dynamic signs of be counted among the high points of invalid in his convalescence”); the voices in the proof copy. In the Beethoven’s compositional art. The “Gefühl neuer Kraft und wieder- first performance of Op. 132, he listener cannot escape the over- erwachtem Gefühl” (“The feeling of reportedly played a phrase of the sec- whelming effect of the self-fulfilling new strength and reawakened feel- ond violin himself, in order to development process. The composi- ing”); up to ironic jokes, such as the demonstrate the correct expression. tion bears autobiographical traits: In sketched canon for Danish composer After the performance, the violinist

82 a new element, a second subject, is FIGURE 4. “Neue Kraft fühlend” section of the “Heiliger Dankgesang.” introduced into the composition, a

Neue Kraft fühlend part in D-major: “Neue Kraft füh- . . Andante Ÿ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ œ œ œ. œ. œ. œ. œ lend” (“Feeling new strength”), c ## 3 œ & ˙ ˙ ˙ 8 which initially appears to be in the p f p f p cresc. most marked contrast to the chorale. cresc. ten. # ten.œ œ Then, the chorale returns, in an c œ œ œ # 3 œ ≈ ® œ œ œœ œ œœ œ. œ ≈ œ ® œ œ œ & . . . 8 . œ R œ R œ œ œ œ altered form, with accompanying ˙ ˙ œ# . f . S p f . p p cresc. . œ. voices after the Andante, thence fol- # œ œ œ œ B c œ œ œ œ # 83 œ . ‰ œ. ‰ œ. ‰ . ‰ lowed by the Andante part in altered ˙ ˙ . . . . œ. œ. œ p f f form. Finally, the chorale appears a cresc. p . . p . ? # 3 œ œ œ third time, but this time in a com- c ˙ œ œ œ œ # 8 œ ‰ œ. ‰ œ. ‰ . ‰ ˙ . . . . œ . œ pletely different form, in an incredi- . p p cresc. f f p ble intensification with altered, . . œ. œ. œ œ œ accompanying motifs which have ten. . . . . œ œ œ Ÿ # œ œ œ œ œ œ œ. œ œ. # ≈ R ® œ become fully independent voices, & . and a tightly led, repeated presenta- p œ S f . . cresc. - - - - tion of the chorale through all voices. # œ œ ten.œ # œ. ‰ œ. ‰ ≈ œ œ œ œ œ œ Let us consider a short film-clip & œ œ œ œ œ œ œ. œ p. f . from Norbert Brainin’s presentation .. œ. cresc. - - - # œ . œ. on the principle of composition. In B # œ.. œ ‰ œ j œ j J ‰ œ œ œ œ œ. œn œ. this part of the master-class in Dolna p œ. . cresc. - - - - Krupa, he demonstrated the works ? # œ.. ‰ œ j œ œ ‰ alone, without other players, and # œ œ œ œ œ# œ œ. .. œ marked the voices of all the instru- p cresc. - - - - f. ments involved [SEE Figures 4, 5, and 6]. (In the video, Brainin makes the following comments: FIGURE 5. Cantabile espressivo in the “Heiliger Dankgesang.” —“Now we are in the dominant œ œ # œ œ. œ œ œ œ œ œ œ œ of D-major.” & # 83 J J J —“Now comes ‘Neue Kraft füh- p cantabile espressivo lend.’ ” # # 3 œ ‰ ‰ ‰ œ —“Then there are trills again, the & 8 œ œ œ œ œ œ œ first violin trills so beautifully there.” p —“Now comes a real—such a # B # 3 j fervent song [measures 67-70]. Here 8 œ œ œ. œ. œ. p is written: Cantabile espressivo, but only in the first violin!” ? ## 3 œn œ œ œ œn œ# œ œ œ œ œ 8 œ# œ œ# œ œ œ œ# œ œ œ œ œn œ —“Now the others begin to play p along.” — “And so forth, it is all themat- ic.” Holz wrote, in Beethoven’s conversa- chorale (from F), with a short intro- —“Now, again the same, but in a tion notebook, “I am happy now to duction and short contrapuntal inter- completely different form. The con- be able to say, that I have received a ludes, which are redefined in the fur- trapuntal moment here is found in violin lesson from Beethoven.” Keep ther development. Let us first hear the second violin, viola, and ’. I in mind, that Beethoven was entirely the beginning of the “Heilige can not play it for you as beautifully deaf at this time! Dankgesang,” in a performance by as it actually should sound. I can The “Heiliger Dankgesang” the Amadeus Quartet [SEE Figure 3]. only play one voice at a time. But begins as a simple, four-voice, Lydian After the first strophe of the chorale, they are all very independent, and

83 nonetheless together.”) FIGURE 6. Second entry of “Heiliger Dankgesang” chorale. And, in conclusion, the last part of the “Heiliger Dankgesang,” where Molto Adagioœn . Beethoven has characterized four ˙ ˙ ˙ ˙ ˙ & c Œ ‰Œ ∑ Ó voices with the additional remark: π “Mit innigster Empfindung” (“with œ jœ. œ œ œ ˙ œ deepest, innermost feeling”) [SEE & c Œ œ . œ J œ œ œ œ œ œ œ œ π œ Figure 7]. œ œ œ œ œ This conclusion suggests that we B c Œ ‰Œ jœ œ œ œ œ. œ. œ œ œ œ œ think back once again, to Johann π œ Sebastian Bach. In 1738, Bach com- œ . œ. œ œ œ œ œ œ. j œ ? c Œ œ. ‰Œ Ó œ œ J œ . j œ œ œ posed a short study on the thorough- J œ bass, which only exists in a copy by π one of his students. In this, is written: ˙ ˙ ˙ & ∑ The original cause of finish and end cresc. p of all music, also of the thorough- œ . œ œ ˙ œ œ œ œ . œ œ J œ bass, should be nothing other than & J to be for the worship of God and p cresc. recreation of the spirit. Where this is œ œ œ. œ œ œ œ œ œ not taken into consideration, is not B œ œ œ J œ. J œ p music, but rather a diabolical bawl- cresc. œ œ œ. œ œ . œ œ ing and mindless singsong. ? œ œ œ œ J J œ œ œ œ œ cresc. p NOTES 1. Steven P. Meyer, “Moses Mendelssohn and the Bach Tradition,” Fidelio, Summer 1999 (Vol. VIII, No. 2). 2. “‘As free, as it is rigorous’—Beethoven’s Art of Four-Voice Composition,” inter- FIGURE 7. Final entry of the “Heiliger Dankgesang” chorale. view with Professor Norbert Brainin, Fidelio, Fall 1998 (Vol. VII, No. 3). Molto adagio 3. EMI 7243-5-65509-2-6. œ. Mit innigster Empfindung 168 4. A report on the master-class appears in & c Œ ‰ŒD ∑ ∑ ‰ jœœDœœ œœœ œ œ œ œ œ œ œ œ œ œ œ “The Principle of Motivführung: Reviving Mit innigster Empfindung the Classical Ideal in Slovakia,” Fidelio, c Œ œ. œ œœœ œ œ ˙ ˙ ˙ ˙ ˙ Winter 1995 (Vol. IV, No. 4). & jœ œœ œ œ œ œ œ œ p 5. On the significance of Op. 132, a number of articles by Bruce Director and Anno Mit innigster Empfindungœ œ œœDœ œ œ œ œ Hellenbroich have been published in Fide- B c Œ ‰ŒD ‰ œ œ œ œ œ ∑ Ó ˙ œ. J œ ˙ lio over the past years. See, for example: Bruce Director, “What Mathematics Can Mit innigster Empfindungœ . œ œ œ œ œ œ œ œ œ Learn from Classical Music,” Fidelio, ? c Œ œ ‰ŒD Ó ‰ œ œ œ œ œ œ œ Winter 1994 (Vol. III, No. 4); and Anno J p ˙ Hellenbroich and Bruce Director, “On Questions of Motivic Thorough-Composi- tion in Beethoven’s Late Works,” Fidelio, Winter 1998 (Vol. VII, No. 4). The latter appears in “The Case of Classical Motivic Thorough-Composition,” an appendix to “The Substance of Morality,” by Lyndon H. LaRouche, Jr.

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