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The idea of creative contributions bysovereign individuals of any histor-
ical era, which act upon all other contri-butions of the past, present, and future,can be wonderfully studied in a kind of“dialogue” among the three greatestmusical composers, Bach, Mozart, andBeethoven—a dialogue on one subject,which is discussed by all of them, andwhere new contributions and new solu-tions for a discovered problem are pro-vided by each of them, on each level.(There exist more contributions to thedialogue, both from the three composersdiscussed, and from other composers aswell, than the examples we will discusshere.)
This chapter will investigate threecompositions: Bach’s A Musical Offering(1747), Mozart’s C minor Fantasy forPiano K. 457 (1784) and C minorSonata K. 475 (1785), and Beethoven’sSonata for Piano Op. 111 (1821/22). Forreasons of clarity, Beethoven’s Sonatafor Piano Op. 13, the so-called “Pathé-tique” (1798/99), is briefly referenced.All these works are composed in (or, asthe earlier composers would have said,“out of”) the key of C minor.
‘Setting the Theme’: J.S. Bach’s A Musical Offering
After some hesitation, in 1747 Bachaccepted an invitation of the PrussianKing Frederick II (“The Great”) to visitPotsdam, where Bach’s son, CarlPhilipp Emanuel, had been serving asmusic master to the court since 1740.Bach’s older son, Wilhelm Friedemann,accompanied his father on the visit, andthe descriptions of the course of the visitare based on his eyewitness reports. Onthe first day of the visit, Frederick intro-
duced Bach to his collection of the newlydeveloped Silbermann fortepianos. Bachwas invited to try them, and to impro-vise new compositions. After a while, heasked the King to give him a subject,which he started to execute immediate-ly, without preparation.
Later, after Bach’s return to Leipzig,he elaborated the subject into a 13-sec-tion composition, which he titled AMusical Offering (BWV 1079) and dedi-cated to Frederick, with the followingwords: “In deepest humility I dedicateherewith to Your Majesty a musicaloffering, the noblest part of whichderives from Your Majesty’s OwnAugust Hand. . . .” With respect to thesubject and its elaboration, Bach wrote:“I noticed very soon, however, that, forlack of necessary preparation, the execu-tion of the task did not fare as well assuch an excellent theme demanded. Iresolved therefore and promptlypledged myself to work out this rightRoyal theme more fully and then makeit known to the world. . . .”
The work, which carries the inscrip-tion “Regis Iussu Cantio Et ReliquaCanonica Arte Resoluta” (“At theKing’s command, the song and theremainder resolved with canonic art”),whose first letters are an anagramspelling out the word “Ricercar,” ofwhich we find one in three parts, andlater one with six parts, composed in amuch freer manner. The work alsoincludes a number of “various canons onthe Royal Theme” (two of these areshown in Figure 4.1), which are indica-tive of Bach’s mastery in the art of inver-sion. Then, finally, there is an extensive,three-movement trio sonata for flute(the instrument played by the King),
violin, and bass continuo.A Musical Offering later became
known also as the “Prussian Fugue.” Aletter by J.S. Bach to his cousin EliasBach, written in 1748, indicates, howthe piece was later distributed: “I can-not oblige you at present with thedesired copy of the Prussian Fugue, theedition having been exhausted justtoday, since I had only 100 printed,most of which were distributed gratis togood friends.”
From a letter of the Austrianambassador to the Prussian court, Got-tfried van Swieten, from 1774—that is,more than 25 years after Bach’s visit atPotsdam—we learn that Frederick theGreat told him about Bach’s visit, and“sang, in a loud voice, a chromaticfugal subject, which he had given thisold Bach, who immediately made fromit a fugue in four, then five, and finallyin eight parts.” Thus, we know, thatvan Swieten, who hosted Haydn,Mozart, and, later, Beethoven in hisVienna salon, knew of the MusicalOffering.
For a better understanding of the keypart of the Musical Offering, the six-partRicercar, it is helpful to introduce somecomments from the first biography ofJ.S. Bach, published in 1802, which waswritten by Johann Nicolaus Forkel inclose cooperation and correspondencewith Bach’s sons Wilhelm Friedemannand Carl Philipp Emanuel. In this book,Forkel writes about Bach’s method ofcomposing: “Now, when Bach began tounite melody and harmony so that evenhis middle parts did not merely accom-pany, but had a melody of their own,when he extended the use of the keys,partly by deviating from the ancient
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The ‘Royal Theme’ from A Musical Offering 4 In Dialogue among Bach, Mozart,
And Beethovenby Ortrun Cramer
modes of church music, which werethen very common even in secularmusic, partly by mixing the diatonic andchromatic scales, and had learned totune the instrument so that it could beplayed in all the 24 keys, he was at thesame time obliged to contrive anothermode of fingering, better adapted to hisnew methods, and particularly to use thethumb in a manner different from thathitherto employed.”
Bach “considered music entirely as alanguage, and the composer as a poet,who, in whatever language he mightwrite, must never be without sufficientexpressions to represent his feelings.”
On Bach’s polyphonic setting,Forkel—who often literally quotes fromthe letters of C.P.E. or Wilhelm Friede-mann—writes: “Very different is thecase when two melodies are so interwo-ven with each other that they, as it were,
converse together, like two persons ofthe same rank and equally wellinformed. . . . [T]his kind of union oftwo melodies gives occasion to newcombinations of tones and consequentlyto an increase of the store of musicalexpressions. In proportion as more partsare added and interwoven with eachother in the same free and independentmanner, the store of musical expressionsincreases, and finally becomes inex-haustible when different time and theendless variety of rhythms are added.”And later, Forkel elaborates: “But toproduce such harmony, in which thesingle parts must be in the highestdegree flexible and yielding towardseach other if they are all to have a freeand fluent melody, Bach made use ofquite peculiar means, which were nottaught in the treatises of musical instruc-tion of those times, but with which his
great genius inspired him. These meansconsisted in the great liberty which hegave to the progress of the parts.”
A little further on: “Hence, in themodulation of his instrumental works,every advance is a new thought, a con-stantly progressive life and motion with-in the circle of the keys chosen and thosenearest related to them. Of the harmonywhich he already has, he retains thegreatest part; but at every advance, hemixes something related to it; and, inthis manner, he proceeds to the end of apiece so softly, so gently and gradually,that no leap or harsh transition is to befelt; and yet no bar is like another. Withhim, every transition is required to havea connection with the preceding idea,and to appear to be a necessary conse-quence of it.” And: “A single part neverneeds to force itself through, but severalmust, in their combination, occasionallyturn, bend, and yield in a very intricateand delicate manner. This of necessitycauses uncommon, strange, and entirelynew, hitherto unheard-of turns in themelodies.”
Concerning the composition offugues, we read: “It fulfills all the con-ditions which we are otherwise accus-tomed to demand only of freer speciesof composition. A highly characteristictheme; an uninterrupted principalmelody [Gesang], wholly derived from itand equally characteristic from thebeginning to the end; not mere accom-paniment in the other parts, but in eachof them an independent melody, inaccordance with the others, also fromthe beginning to the end; freedom,lightness, and fluency in the progress ofthe whole; inexhaustible variety ofmodulation combined with perfectpurity; the exclusion of every arbitrarynote not necessarily belonging to thewhole.”
Concerning this latter point, the“exclusion of every arbitrary note,”Forkel writes of Bach’s method of teach-ing composition: “Every note wasrequired to have a connection with thepreceding: if any one appeared concern-ing which it was not apparent whence itcame, nor whither it tended, it wasinstantly banished as suspicious. . . .The confused mixture of the parts, so
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Two canons from J.S. Bach’s A Musical Offering
that a note which belongs to the tenor isthrown into the alto and the reverse;further, the untimely dropping-in ofseveral notes in certain harmonies—notes which, as if dropped from the sky,suddenly increase the established num-ber of the parts in a single passage, tovanish in the next one following, and inno manner belong to the whole; in short,what Bach is said to have called‘mantschen’ [daubbing, or mixing notesand parts together in a disorderly man-ner]—is not to be found either in him-self or in any of his pupils. He consid-ered his parts as if they were personswho conversed together like a selectcompany. If there were three, each couldsometimes be silent and listen to the oth-ers until it again had something usefulto say. But, if in the midst of the mostinteresting part of the discourse, someuncalled for and importunate strangenotes suddenly rushed in and attemptedto say a word, or even a mere syllable,without sense of vocation, Bach lookedon this as a great irregularity, and madehis pupils comprehend that it was neverto be allowed.”
Forkel’s treatise represents an almostcontemporary document, and it givestoday’s readers beautiful insights intohow Bach’s music and composition gen-erally were thought about, in the time ofMozart, Haydn, and Beethoven.
Now, let us turn to a brief examina-tion of the six-part Ricercar from AMusical Offering. This is a six-partfugue, composed in a rather free man-ner, in which the parts (or voices) enterpairwise, and—as is typical for Bach’streatment of the middle voices—withthe third and second voices followed bythe fifth and fourth. Only after a briefinterlude, do the soprano and bass voicesenter, and here, we can already observea first change in the continuation of thesoprano voice after the opening state-ment. In the subsequent development,new subjects are introduced in the vari-ous parts, which are nonetheless allderived from the original theme; theyare all changed through inversion andmodulation. At the end, all are interwo-ven, until the bass voice finally, in con-clusion, re-presents the theme in its orig-
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The entrance of the second voice creates all the crucial intervals, which Mozart later picked up on in his K. 475 Fantasy: the diminished seventh from the “modulated” theme, the minor third, the Lydian, and the augmented second.
dim. 7th
minor 3rd Lydian aug. 2nd
FIGURE 4.2a
J.S. Bach, six-part Ricercar from A Musical Offering,open-score version
inal form. A wonderful example of apredecessor of Motivführung.
For the sake of later discussion, letus briefly look, close up, at the charac-teristic conflict, or paradox, that is cre-ated right at the beginning, when thesecond voice enters, and the first shiftsto sing an additional part. The secondvoice, which presents the theme in amodulated form, runs into a conflictwith its companion, when the modulat-ed falling interval from e˛ to fˇ is con-trasted to a longer c of the companionfirst voice. Here, we observe a pair oftwo intervals, which create a shift, fromthe e˛ -c minor third, to the c -fˇLydian interval, which indicates a wayout of the C minor key of the composi-tion. Also note, that at the beginning ofthe next measure, we find anothercharacteristic interval b˛ -cˇ , an aug-mented second, which we will meetagain later on.
This paradoxical result of juxtapos-ing two voices—of two compositionallevels, or “keys,” if you wish—is alsowhat we will meet again later, as we
move on to Mozart and Beethoven.Bach originally wrote the six-part
Ricercar, as shown in Figure 4.2a, on sixdifferent staves, without indicatingwhich instruments are to play them. Hehimself re-wrote it also, on two staves(Figure 4.2b), so that it could be playedon keyboard instruments. In the originalopen score, each staff has a different clef,indicating a different implied species ofhuman singing voice. With the excep-tion of a few notes in the extreme highand low registers, the fugue can be read-ily sung by a bel canto-trained six-partchoir.
In general, the distinguishing charac-teristic of the theme lies in the connec-tion of the minor-triad with the chro-matic line, which opens up a great num-ber of options for development—asBach proves in his Musical Offering. It isan outstanding theme, especially for amusical amateur like Frederick theGreat. However, C.P.E. Bach was in hisservice, and many researchers consider ita possibility, that he may have helpedthe King to formulate the theme. In
1774, C.P.E. Bach wrote in a letter toForkel, about his father: “When he lis-tened to a rich and many-voiced fugue,he could soon say, after the first entriesof the subjects, what contrapuntaldevices it would be possible to apply;and to which of them the composer byrights ought to apply, and on such occa-sions, when I was standing next to him,and he had voiced his surmises to me, hewould joyfully nudge me when hisexpectations were fulfilled.”
Mozart: ‘Nothing Is Played, But Handel and Bach’
We know for a fact, that Mozart studiedBach’s works in the house of Gottfriedvan Swieten, the already-mentionedAustrian diplomat, whose father, animmigrant from The Netherlands, hadbeen the personal physician of EmpressMaria Theresa. In 1782, Mozart wroteto his father in Salzburg: “Every Sundayat noon, I visit the Baron van Swieten—and there, nothing is played but Handeland Bach.—I am just now making acollection of the Bach fugues, of Sebast-ian and Emanuel and Friedemann Bach. . . .” A few days later, he writes to hissister Nannerl: “The cause of his fugue’scoming into the world is really my dearKonstanze. Baron van Swieten, towhom I go every Sunday, has let metake all the works of Handel and Sebast-ian Bach home, after I played themthrough for him. When Konstanzeheard the fugues, she fell quite in lovewith them. She will hear nothing butfugues, especially (in this field) nothingbut Handel and Bach. Now, since shehad heard me frequently improvisefugues, she asked me whether I hadnever written any down, and when Isaid ‘No,’ she gave me a proper scoldingfor not wanting to write the most intri-cate and beautiful kind of music, andshe did not give up begging me until Iwrote her a fugue, and that is how itcame about.” In the same letter, Mozartdescribed van Swieten’s musical libraryas “although in quality a very large storeof good music, yet in quantity a verysmall one.”
The proof that Mozart must haveknown the Musical Offering, or at the
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FIGURE 4.2b
J.S. Bach’s own keyboard reduction of the six-part Ricercarfrom A Musical Offering
very least its subject, is in his pianosonata in C minor, K. 457, to which helater added the C minor Fantasy K.475.1 The Fantasy was written in 1785,less than three weeks before the compo-sition of the Lied “Das Veilchen” (seeChapter 1), which also represents a mile-stone in the development of musicalcomposition.
In the opening section of the sonata’sfirst movement (Figure 4.3), we find allthe elements of the “Royal Theme,” butin a changed presentation and registra-tion. We also find, more elaborated, theconflict of the two parts of Bach’s com-position, which is now presented in thehorizontal development also: a juxtapo-sition of the opening arpeggio in Cminor, and the “repetition” a fourthlower, starting from G, and appearing asif in G major!
In the course of the exposition, onecan also study how a “second subject” ofthe sonata is derived—according to theMotivführung principle—from the first,but in such a way, that it can hardly berecognized at first. In this piece, weagain find the chromatic element, ininversion and rhythmically changed(Figure 4.4).
The opening motif of the thirdmovement (Figure 4.5) represents adirect quotation from the openingtheme of the first movement, but in adoubly-inverted way. In addition, weare led to our conflict of two keys andmodes, the C minor-“G major” con-frontation, leading into the presentationof our “old acquaintance” interval e˛ -fˇ , now presented as a melodic line(Figure 4.6).
In the sonata’s second movement,Mozart again presents the Motivführungelements of the entire sonata, which werecognize this time in inversion andmodulation of the intervals of the open-ing theme, and we find the chromaticelement, used as a means of expression(Figure 4.7, measures 21-22). The sec-ond theme introduced in the movement(Figure 4.7, measures 5-6)—againthrough inversion—is later picked up,almost verbatim, as the leading theme inthe second movement of Beethoven’s“Pathétique” sonata. It is indicative,both for understanding the movement
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A seemingly new element, in the exposition of the first movement, is generated by inverting the chromatic descending line from the “Royal Theme.”
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Ascending chromatic sequence in Mozart’s Sonata K. 457
The opening of the first movement shows the “Royal Theme,” in a different gestalt.
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W.A. Mozart, Sonata K. 457, opening of first movement
in respect to clear voice registration, andfor the conception of the expression, thatMozart added the indication “sotto voce”at the beginning of this movement, as ahint to the performer and listener.
Before undertaking a brief examina-tion of the opening of the Fantasy K.475, let us keep in mind C.P.E. Bach’sshort definition of the intervals, from hisfamous Essay on the True Art of PlayingKeyboard Instruments (New York: W.W.Norton, 1949): “The comparison of onetone with another, is called an interval”(“Die Vergleichung eines Tons mit demanderen heißt ein Intervall”). In otherwords, it is the relationship of the tones,and not their distance, which is heard bythe mind.
In the C minor Fantasy, Mozart addsqualitatively new steps, which put thispiece above the K. 457 sonata, whichwas already a milestone in Mozart’sworks, in respect to its density andcoherence. Here, we find him examin-ing a problem, which we have so far metonly in the interweaving of two voices:the importance of the F ,̌ not only as the“leading tone” to the dominant key of Gminor/G major (as seen from C major/Cminor), as it is usually taught, but in itsimportance for the C minor/C major mode, and the incredibly com-plex potentialities of development,which includes the entire sphere of the24-key well-tempered domain. [text con-tinues on page 62]
61
The second theme of the slow movement of this sonata was chosen by Beethoven as the theme for the second movement of his Sonata for Piano Op. 13, “Pathétique.”
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FIGURE 4.7Opening, and second theme, of second movement of Mozart’s Sonata K. 457
The opening motif of the third movement consists of an inversion of the first movement’s opening theme.
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E b -F # interval in third movement of Mozart’s Sonata K. 457
In hearing the opening (Figure 4.8),it is more difficult to recognize the“Royal Theme,” because it is changed,in a characteristic way, already at thebeginning, and the chromatic lineappears “only” in the harmonic progres-sion.
We find that Mozart has integratedthe F ,̌ which we know from Bach, andfrom the third movement of the sonata,into the theme itself—i.e., the paradox isnow in the theme. We find the E˛-Fˇinterval, now in its inversion an aug-mented second. The irony of the inte-gration is underlined by the short twofigures, which again repeat this interval,accompanied by half-steps in differentdirections, underlining the principle ofinversion.
We now recognize in this openingpart how this integrated Fˇ becomes thepivot-point of constant change, throughwhich the complexity of the 24-keywell-tempered domain is explored: Wefind the Fˇ, and its “well-temperedtwin” G ;̨ we find the Fˇ in the contextof C major/C minor, of B major, of Fˇmajor, and then, through a new, andsurprising turn, showing up briefly aspart of a clear D major (Figure 4.9)!Each time, the Fˇ is involved, and eachtime, its surrounding has changed. Keepin mind the fact, that there is a scalefrom C, which contains the Fˇ—namely,the famous “Lydian mode,” whichBeethoven so obviously picked up in allof his late works, not only in the“Heiliger Dankgesang” of his Op. 132string quartet.
In conclusion, there is a contempo-rary report, which is very important,concerning the relationship of Mozartand J.S. Bach: During Mozart’s last visitto Berlin, in 1789, he traveled throughLeipzig, where he immediately visitedthe cantor at St. Thomas Church,Johann Friedrich Doles, who had been astudent of Bach. A witness (most proba-bly J.F. Reichardt) later says of this visit:“On April 22, he was heard withoutprior announcement, and without finan-cial compensation, on the organ in theSt. Thomas Church. He played there,for one hour, beautifully and artistically,for many listeners. The organist Görnerand the late Cantor Doles were with
62
The opening of Mozart’s Fantasy K. 475 integrates the Lydian C-F# interval. It contains all key intervals generated by Bach in the interaction of the first two voices in the six-part Ricercar.
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FIGURE 4.8
Opening of Mozart’s Fantasy for Piano, K. 475
him, pulling the stops. I saw him myself,a young man, dressed according to thefashion, and middle-sized. Doles wasexcited about the playing of the artist,and thought that the old Seb. Bach, histeacher, had been resurrected.” At theend of his visit, Cantor Doles and the St.Thomas choir sang for Mozart Bach’smotet “Singet dem Herrn ein neuesLied.” According to the report, Mozartlistened with concentration, and thensaid: “This is something to learn from!”He asked for the parts—a full score didnot exist—spread them all out beforehimself, and studied them carefully.[text continues below]
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Pivot around F# in Mozart’s Fantasy K. 475
Beethoven chose the key interval from Bach and Mozart as the opening of his own last piano sonata.
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FIGURE 4.10
Beethoven Piano Sonata Op. 111, opening of first movement
Beethoven: ‘He Could Become A Second Mozart’
There is a well-known pun byBeethoven, on J.S. Bach: “Nicht Bach—Meer sollte er heissen” (“He shouldn’tbe called Brook [“Bach”]; his nameought to be Ocean”).
Already in his early education inBonn, Beethoven had been introducedto Bach’s works—at that time a ratherexceptional experience—through histeacher Christian Gottlob Neefe. Neefehad studied law in Leipzig, but had thenswitched to music, and became a studentof the later Cantor at the St. ThomasChurch, Johann Adam Hiller. Hillerhimself had been a student of Doles. In1783, Neefe wrote in an article inCramer’s Magazin der Musik: “Louis vanBetthoven, son of the above-mentioned
tenor, a boy of 11 years, who has a talentthat promises much. He plays very flu-ently and powerfully on the clavier,reads very well at sight, and, to sayeverything in a word, he plays most ofthe Well-Tempered Clavier by SebastianBach, which Mr. Neefe has placed in hishands. Anyone who knows this collec-tion of preludes and fugues in all thekeys (which one could almost call thenon plus ultra) will know what thatmeans. . . . This young genius woulddeserve support so that he might travel.He would certainly become a secondWolfgang Amadeus Mozart if he wereto continue as he had begun.”
Later, in Vienna, Beethoven wasamong the guests in van Swieten’s salon,and he dedicated his First Symphony tohim. Through his entire life, he consid-ered Bach to be one of the greatest com-posers. In his conversation books, thereis an exchange, where Beethoven ironi-cally asks a visitor: “Bach, is he dead?”He asked his publishers for copies ofBach’s works, and included also Bach’ssons in his high estimation. In a letter tohis publisher Breitkopf und Härtel inLeipzig, in 1809, he wrote: “Generally, Iwould appreciate, if you would gradual-ly send me most of the scores, which youhave, for example Mozart’s Requiemetc., Haydn’s masses, Bach, JohannSebastian Bach, Emanuel, etc. I haveonly a few of Emanuel’s piano works,but some of them must not only servethe artist for his pleasure, but also for hisstudies.”
But Beethoven speaks out most clear-ly in his compositions, which stand inthe context of the Bach-Mozart treat-ment of the “Royal Theme.” We findelements of the problem treated in manyworks, but most directly first in hisPiano Sonata Op. 13 in C minor, thefamous “Pathétique.” While the firstmovement, with its “Grave” introduc-tion, and then the jump into the “Allegromolto e con brio,” appears to be a sort ofsynthesis of Mozart’s Fantasy and thesonata’s first movement, the secondmovement quotes explicitly from thesecond theme of Mozart’s second move-ment.
Thus, Beethoven, already relativelyearly on, deals with the Bach-Mozart
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Beethoven Piano Sonata Op. 111, opening theme
material, and the sonata marks a keypoint in his own development.
The high point of the dialogueamong the three geniuses, however, isfound in Beethoven’s final piano sonata,No. 32, Op. 111 in C minor, composedin 1821/22. Already the opening (Figure4.10) attacks the core, the punctumsaliens of the dialogue. We meet againour familiar interval E -̨F ,̌ this time in afalling line, played in all voices, forte andin unison, in the “Maestoso” introductionof the first movement, before the themeis introduced in the “Allegro con brio edappassionato” section (Figure 4.11).Thus, this movement again, like thePathétique, appears to be a kind of syn-thesis of Mozart’s C minor Fantasy andSonata. One is obliged to understand theentire sonata from the standpoint ofBach’s and Mozart’s dealing with thegiven problem; and, at the same time, tore-examine them from the new, higherstandpoint of Beethoven, which addsnew value to their effort!
In conclusion, a brief examination ofthe second movement of Beethoven’sOp. 111 sonata provides some strikingelements, in the context of the “C minorissue.” The sonata has “only” two move-ments. The second one is a large-scaleintegrated variations movement, whichin the course of development becomemore and more complex, but also free.The movement is called “Arietta,” to beplayed “Adagio molto semplice ecantabile” (Figure 4.12). Thus, we againfind explicitly the demand, which weknow from Bach’s “playing in a singablefashion,” something strongly reiteratedby C.P.E. Bach in his book on playingkeyboard instruments.
At the end of the second movement’sfourth variation, which also marks thebeginning of an extremely free, coda-like end section, we have the incredibletriple trill, never heard before, and rightafterwards, with a brief shift in the keysignature to the “C minor coding,” wefind reference to an old acquaintance: amodified form of the opening of theMozart fantasy (Figure 4.13)! [text con-tinues on page 66]
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Immediately after the highest point of tension and condensation, in the triple trill, Beethoven introduces a remembrance of the opening of Mozart’s Fantasy K. 475.
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From there, Beethoven proceeds tothe final development of the movement(Figure 4.14), which ends in a uniqueway: We find variants of the movemen-t’s theme presented under and above along, pedal-point-like trill, which,although the same tones are alwaysplayed, is constantly changing its voiceand registral characteristic. Thus, an oldmeans of fugal polyphonic composition,the pedal-point, concludes the fugue, bygiving a clear bass orientation to theconclusion of the modulations. Here, wefind a “pedal-point,” which itselfbecomes a kind of pivot-point.
Much remains to be discovered in thedialogue among these works. And,many later composers have gotteninvolved: even Chopin, for example.
It was not an arbitrary choice byLyndon LaRouche, to repeatedly insistin the unique importance of the “Cminor series,” for understanding of thedevelopment of Classical composition.It was the process of “standing on eachother’s shoulders,” of looking a littlefurther or deeper, that made the succes-sive qualitative steps possible. It will bethe intense, in-depth re-living of theseexperiences, that will enable us, in thefuture, to bring forth new “partners inthe dialogue.”
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1. The original manuscript of the fantasyand sonata was re-discovered in 1990, inPhiladelphia. A facsimile of the manuscripthas been published by the InternationalStiftung Mozarteum Salzburg, and byBärenreiter-Verlag (ISBN 3-9500072-1-2[Internationale Stiftung Mozarteum] andISBN 3-7618-1041-5 [Bärenreiter]).
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continued on following page
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Conclusion of Beethoven Sonata Op. 111
Let us take as our point of departure,the following passage from Lyndon
LaRouche’s main article, a passage thathas specific bearing upon Mozart’s com-position of the Fantasy in C minor, K.475, in May 1785:
“A further refinement is required.The mind hears the inversion of anyinterval (e.g., C-E-G heard as G-E-C),to such effect that a simple Lydian scaleis derived as an inversion of a C-minor,Fˇ pivotted scale. The effort to bring theintervals represented by the scale indi-cated by the inversion, [into coherence]with the scale which has been inverted,introduces a further degree of refine-ment of the well-tempering. Add, theinversion heard across the polyphonicparts to the inversions generated withineach part, and a further refinement isintroduced.”
Mozart opens the K. 475 Fantasywith a bare statement of just such a “C-minor, Fˇ pivotted scale” (Figure 5.1).But before we plunge into the workitself, let us first see precisely whatkinds of inversions are required toderive a “simple Lydian scale” from it.Let us represent the leading features of
the original scale as C-E˛-(Fˇ)-G. Theintervals described are an ascendingminor third, followed by an ascendingaugmented second, and then anascending half-step. Now, using C asour pivot, invert the direction of theintervals from ascending, to descend-ing. The result is C-A-(G˛/Fˇ)-F, akind of F major with a G˛ hoveringjust above the tonic. Finally, taking Fas our point of departure, take the C-G˛/Fˇ interval and reverse the directionagain, projecting it upward (Figure5.2). The result: F-A-(B˝)-C, a simpleLydian scale. That the mind hears suchrelations implicitly, is proven beyond adoubt by the power of Mozart’s K. 475Fantasy.
Another unique property of Lydianintervals should also be touched uponbefore we begin to grapple withMozart’s compositions in detail. Disre-garding different spellings for themoment (in actual composition, they arecrucial for the shaping of tone), onequickly discovers that there exist six,and only six, unique Lydian intervals inthe well-tempered domain, namely: C-F ,̌ D -̨G, D-A ,̨ E -̨A˝, E˝-B ,̨ and F˝-B˝
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The trill forms a higher-order “pedal point,” which becomes a pivot-point of the conclusion.
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FIGURE 5.2
Derivation of Lydian scale
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W.A. Mozart’s Fantasy in C minor, K. 475, 5 And the Generalization of the Lydian Principle
Through Motivic Thorough-Compositionby John Sigerson
