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˝

67

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Opening of K. 475 Fantasy

W.A. Mozart’s Fantasy in C minor, K. 475, 5 And the Generalization of the Lydian Principle

Through Motivic Thorough-Compositionby John Sigerson

(Figure 5.3). These intervals are not “allalike,” but flow in a certain hierarchy aswe move away from C-F ,̌ upon whichthe entire well-tempered domain is piv-otted. After C-F ,̌ come the pair F-B˝ (aswe saw derived above), and close after it,E˛-A˝, by virtue of the close relation ofthe E˛ major scale to the C major/minormode. (Beethoven, in the opening of ActII of his opera Fidelio, goes so far as totune the two kettle-drums to preciselythose two tones, E˛ and A˝!) Next wehave another pair, each pivotted onother members of the C-major triad: E˝-B ,̨ and G-D .̨ And finally, there is D˝-A ,̨ the most “distant” Lydian.

Just as with the hierarchy of the reg-ister-shifts of the six species of bel canto-trained voices, so the mind hears thisimplicit hierarchy of Lydians. But therelationship between Lydians and regis-ter-shifts is far more profound than that:If one makes a list of the six Lydianintervals, and cross-grids this with thesix human voice species, one finds thatevery Lydian interval crosses at least onevocal register of each of the six voicespecies. Or, put another way: The intro-duction of any one Lydian interval,implies a register shift for every speciesof singing-voice. Other intervals largerthan the Lydian also share this property;but the next smaller interval, the fourth,does not have that property. E.g., for theascending fourth C-F, the soprano nevershifts registers across this interval.

The Lydian interval, therefore, rep-resents the minimum action required tomove into the domain of multiply-con-nected, polyphonic vocal registration.And conversely, the interval of a fourthrepresents the threshold of that domain,just as the soprano’s and tenor’s F˝ is thethreshold of the Fˇ register shift.

It was implicit principles such asthese—and not the mere form of fugal

writing—that struck Mozart like a boltof lightning when he was introduced toJ.S. Bach’s works by Gottfried van Swi-eten and his circles, beginning around1782. From this standpoint, let us takeyet another look at one of the workswhich Mozart studied intensively, thesix-part Ricercar from Bach’s A MusicalOffering. Focus on the end of the openingstatement (measures 9-11 in Figure 5.4):As the second voice enters, the first voicecontinues with a sequence of ascendingfourths. On the first beat of measure 11,the new voice creates a Lydian intervalC-Fˇ with the first voice; this is followedby a series of descending fourths. As Bachproceeds through each successive varia-tion, he uses inversion to increase thedensity of sequences of fourths; in mea-sure 89 (Figure 5.5), he also introduces arhythmic shift, such that the first note ofthe pair is shifted from the “strong” beatsof the measure (beats 1 and 2), to the off-beats (beats 1!/2 and 2!/2). The density ofrising and descending fourths reaches itsgreatest in measures 180ff., where thederived cross-voices all focus to form theLydian interval C-F .̌

The revolution in Mozart’s mind,consisted in making these discoveredprinciples into the explicit, primary sub-ject of the composition, using the newmethod of motivic thorough-composi-tion as pioneered by his friend JosefHaydn. The fruit of Mozart’s composi-tions of those years, quickly ripened into

a new modal method of composition, inwhich the Lydian-register shift plays thepivotal role. In his explorations, Mozartstuck close to the key of C minor inorder to maximize his focus on workingout the implications of his discovery.Examples of these efforts are the Fuguein C minor for Two Pianos, K. 426(which he reworked five years later forstring quartet), and his unfinished GreatMass in C minor, K. 427.

But greatest of them all, is his C minorFantasy K. 475, and its companion work,the Sonata in C minor for solo piano, K.457. Without additional commentary,Mozart had both works published togeth-er; to the educated audiences of his day,he did not need to explicitly state theobvious point, that the Fantasy was hisown investigation into the principlesemployed in his composition of the earliersontata. And, as we shall see below, theFantasy indeed picks up exactly wherethe Sonata leaves off. (Beethoven, inmany of his later works, took thisapproach one step further, interruptingthe composition in mid-stream if neces-sary, in order to force the audience to turntheir attention away from the rich exter-nalities of the composition, to the discov-eries of principles implied therein. One ofthe most accessible examples of this, is thebaritone’s recitative “O Freunde, nichtdiese Töne!” (“Not these tones, myfriends!”) in the fourth choral movementof his Ninth Symphony.)

In order to even reach the doorknob ofMozart’s Fantasy, therefore, we mustfirst, at very minimum, take a “guidedtour” of the companion sonata. For, justas it is impossible to grasp the significanceof Gauss’s discovery of the orbit of Cereswithout working through the problemstep-by-step, so it is with Mozart’s discov-eries here. The toil will be well worth it.[text continues on page 69]

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The K. 457 SonataThe K. 457 sonata consists of threemoments: the first a “Molto allegro” in Cminor; the second, an extended“Adagio” in E˛ major, and the third, an“Allegro assai”—to which Mozart lateradded the word “agitato”—once againin C minor.

The first movement opens with asimple ascending C minor arpeggio,played forte, followed by a contrastingpiano sequence consisting of a descend-ing fifth G-C (inversion of a fourth), anda descending diminished seventh A˛-B˝—the same interval which marks theopening motivic statement of Bach’s AMusical Offering (Figure 5.6). The firstLydian interval is formed with that B˝,but its significance does not go muchbeyond its cadential function. This isfollowed by a restatement of the samesequence, but beginning on G, with theB˛ changed to a B˝, in order to keep it inthe mode of C minor, once again endingin a cadentially-used F-B˝ Lydian. Theparadoxes only really begin with the fol-lowing, second poetic couplet of theopening (measures 9-12): against an osti-nato G-g in the bass, are descendingfourths in two voices. The first voicedescends in half-steps: G-Fˇ-F˝-E˝-E˛-D—again an explicit reference to thedescending line in the opening of Bach’sA Musical Offering. And, as with Bach’swork, it is introduced as a mezzosopra-no voice. The second descending fourthis E˛-D-C-B˝—a diminished fourth,introduced in the soprano voice but withstrong registral implications for the tenorvoice. (This is probably why Beethovenfocussed on this very interval in hisSonata Op. 5, No. 2 for Piano and Vio-loncello, since the predominant vocalreference for the ’cello is the tenorvoice.) Mozart repeats this double figurean octave higher, in such a way that themezzosoprano line is now sung by asoprano voice—once again in keepingwith Bach’s treatment. To conclude theopening idea, Mozart repeats thedescending half-step interval a˛ -gtwice, as an inversion of the implicitlystated G-A˛ of the opening measures 3and 4.

Let us now skip to the second part of

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the first movement, beginning at thedouble-bar on measure 75 (Figure 5.7).Here the opening arpeggio is re-intro-duced, but now in C major. Mozartalmost immediately moves us to theimplied inversion of C major, which is Fminor, with many mentions of the Lydi-an B˝. The passage ends on measure 98with the same a -̨g as in the first section,only shifted down two octaves to pre-cisely the location where the bass voiceshifts between the second and first regis-ters; the interval is suspended against theB˝ (Figure 5.8).

The original C-minor arpeggio isnow restated, but now it is enrichedwith a canon focussing on A˛ (measures118-120), and a sudden shift into D˛,with the implicit, rising figure C-D˛being heard as the inversion of thefalling C-B˝ (Figure 5.9). The density ofLydians and inversions reaches a high-point at measure 125, where C-Fˇ issuperimposed right on top of B ˝-F.(Beethoven clearly recognized the sig-nificance of this passage, and inMozart’s honor, made them into thehigh-point of the Kyrie section of hisMass in C major, Op. 86.)

The extended “Adagio” of thesonata’s second movement creates thenecessary attention span for workingthrough the paradoxes introduced in thefirst movement. As is the hallmark ofMozart’s motivic thorough-composition,no additional musical material is reallyadded. The opening (Figure 5.10) is adescending fourth, b˛ -f , ending with arising fourth b ˛ -e˛ , and then adescending combination of both, endingwith a very prominent dwelling on theLydian e˛ -a˝ . The introduction is thenrepeated, but with an added element: adescending diminished fourth e˛ -b˝ ,which was also briefly referenced in thefirst movement but not explored. In thismovement, it is explored exhaustively,through multiple inversions.

The implications of the first move-ment’s A˛-G are now also intensivelyworked through in a section in A˛ (Fig-ure 5.11). Against an ostinato A˛-a˛ (asopposed to G-g in the first movement),two other voices are at work: the firstdescends from e˛-d˛-c-B˛, while in the

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second, Mozart simply reverses theorder of the first and second pair ofnotes, thus: c -b˛-e˛ -d˛ . And—shouldwe be surprised by now?—Beethovencelebrates his great teacher here as well,by quoting this passage “verbatim” inthe second “Adagio cantabile” movementof his C minor sonata for Piano, Op. 13(Pathétique).

Mozart now introduces the most“distant” Lydian, A˛-D˝, into the musi-cal fabric (measure 27), and in shortorder (measure 32, Figure 5.12), leads usinto what can only be described as“ontological surprise”: the same A˛material is begun again, but in G .̨ Aha!F !̌ [text continues on page 72]

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A series of arpeggios (measures 38-40) leads us to g , a˛ , a˝ , and b˛ , andback “home” to the opening statement,but now highly ornamented (Figure5.13). The registral shifts implied byE˛-A˝ and A˛-D˝ are now brought outclearly, both in measure 49, with thesudden drop into the “chest” register(Figure 5.14), and in the two grandscales in measures 51 and 52, movingfrom the soprano’s high b ˛ to thebass’s low A ,̨ and then back up a higha˝ -a˛ , with each note suspended by afermata (Figure 5.15). [text continueson page 73]

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FIGURE 5.13

Return to opening theme of second movement of K. 457 sonata

The third and final movement of thesonata is organized as a kind of rondo,where the same theme repeatedlyreturns, unaltered. Each time, onemoves farther afield, only to be joltedback, as in Poe’s refrain “Nevermore.”In the opening (Figure 5.16), we areback to the same material as the firsttwo movements, but now the Fˇ is moreprominently ending the phrase on fˇ -g .A very rapid descending fourth f -c isfollowed by repeated g s, ending with aseries of double Lydian, arpeggiatedchords focusing on B˝; followed by apregnant silence. And quietly (measure26), we hear what everything seems tohave been driving at all along: e˛ -fˇ -g -a˛ —the beginnings of Mozart’s explicit-ly Fˇ-pivotted C minor. However, anuneasy paradox remains: by placing thee˛ above the fˇ , implicitly in the sopra-no voice, there is no register shift. Thisabsence of register-shift is what makesthe passage so haunting each time itrecurs in the rondo. Indeed, the paradoxis never really satisfactorily resolved inthe sonata itself—which is probably whyMozart added “agitato” to the descrip-tion, and which is decidedly part of hismotivation for composing the Fantasylater on.

We move into a passage in E˛ major,with its A˝ Lydian reference (Figure5.17), harkening back to the secondmovement, ending with a sequence ofrising fourths B -̨C-D-E˛ in three differ-ent voices, all harkening back to theopening of the second movement. [textcontinues on page 74]

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FIGURE 5.18

F minor section of K. 457 third movement

The rondo returns, and now wemove to the F minor of the first move-ment, with the added figure c -d˛ -cbringing to mind the first movement’sg-a˛ and a˛-g (Figure 5.18). The suspi-cion is confirmed when the same mater-ial is repeated in C minor (measures168-169), and g -a˛ -g is heard explicit-ly. Yet another shift, and this is invertedas F -̌G in five different voices (Figure5.19).

A new round of the rondo, and fur-ther aspects of the preceding movementare brought into focus. Then, with afinal reference to F minor, Mozart pro-ceeds to his remarkable coda, whichstarkly presents two sequences. The firstis a descending scale (measures 293-300)which seems oddly bent out of shape: c-b˛ -a˛ -f -e˛ -d˛ -c -(b˝ ) (Figure 5.20).But in the domain of the mind’s hearingof implicit inversions, it is not “bent” atall, for, if one inverts it, it is a simple Cmajor sequence: C-D-E-G-A-B-C. Butthere is a note missing: the fourthdegree, F. The final sequence (Figure5.21) solves that problem, not with F,but with F .̌ First c -e˛ is stated high inthe soprano’s fourth register, followedby a huge leap to an Fˇ at the very bot-tom of the piano’s range, below the reg-ular singing ranges; and ended with G -A˛ , then F˝ , and a final C. Which isprecisely where Mozart begins in theFantasy. [text continues on page 75]

The K. 475 FantasyIt is impossible to reduce the opening ofthe Fantasy to a “theme.” The openingrepresents a multiple dimensionality,whose implications only begin to unfoldas one ponders over the kaleidoscopicsequence of all sections of the Fantasy,taken as a whole; the which, obviously,can only be done if one has workedthrough it in a good deal of detail.

The most immediately evident fea-ture is Mozart’s inclusion of the Fˇ intothe very first measure (Figure 5.22).This Fˇ has a register shift “written allover it”: The shift from E˛ to Fˇ is a reg-ister shift for the four most common ofthe six voice species: soprano, mezzoso-prano, tenor, and baritone.

The Promethean challenge posed bythis included Fˇ is then underlined, qui-etly, in the second measure, with asequence of double Lydians, all revolv-ing around F -̌G. It is essential that thesetwo pairs be performed as true appog-giaturas, with the emphasis on the firstmember of each pair. If this is done cor-rectly, the second pair leads as a cross-voice into the silence of the measure’sfinal beat; if it is performed incorrectly,the pairs degenerate into perfunctory,meaningless cadences.

But we must also consider the fol-lowing dimensionality: The openingmeasure has three parts: (1) the open-ing C; (2) the four subsequent notesE˛-Fˇ-G-A˛, which describe a risingfourth which has been oddly “bent outof shape”; and (3) the leap back intothe “chest register” on C-B˝, with itsimplications for the simple F-basedLydian.

And, as yet another dimensionality,we should consider the downward, G-pivotted inversion of the openingsequence: G-E˝-D˛-C-G-A˛, with itsincluded prominent G-D˛ Lydian.Already in measure 4, this interval isbrought out explicitly as well, andbeginning with measure 6, the opening,descending C-B˝ is inverted into a risingC-D .̨ In measure 10, Mozart re-invertsthis relationship into B˝ again, this timereferencing the full B˝ mode. But weremain there only momentarily, as thebass descends by half-steps from theredown to G˛ (measure 15). And, surprise!

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Opening of Mozart Fantasy for Piano, K. 475

In measure 16, G˛ is transformed intoF ,̌ in a passage which is an unmistak-able reference to the surprising G˛ pas-sage in the second movement of thesonata. Only here in the Fantasy, it tookMozart only sixteen measures to bringus there!

Fˇ remains the focus of the followingmeasures, leading to measure 25 (Fig-ure 5.23), where repeated fˇ s move intothe key of D major—a key which wasentirely absent from the K. 457 sonata. Itis also striking that the Lydian Gˇ isentirely absent from opening bars of thisD major section; Mozart’s focus here,rather, is on the motivic thorough-com-position associated with C-B˝, but thistime transformed into descendingwhole-steps, such that the entire melodyis constructed from nothing but thesedescending and ascending whole steps.

The situation is entirely reversed,with a vengeance, in the following “alle-gro” passage (measures 36ff.), where arepeated E-F˝ is played against repeatedd -gˇ (Figure 5.24). The samesequence is then repeated one steplower, on D-E˛ and c -fˇ , in such a waythat we are led directly into an Fmajor/minor section with a stress on theB˝-F Lydian (Figure 5.25). But not forlong, as we are pressed back to a grandsequence of double-Lydian arpeggios,against a descending bass line from Fˇ tothe lowest Fˇ on the piano keyboard(Figure 5.26). We go a half-step lowerstill, to F˝ , and then swing with arpeg-gios and scales from the bottom to thetop of the vocal range, finally descend-ing slowly to two long, held notes, e˝and e˛ —a reference to the held a˝ anda˛ in the sonata’s second movement.[text continues on page 77]

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Focus on F # in K. 475 Fantasy

Quite an adventure! We havealready worked through the content ofthe entire sonata. But it is far from over.Mozart now focusses on an ascendingsequence of four descending fourths,such that the sequence itself describes afourth (measures 86-88, Figure 5.27),after which he repeats the sequencedown an octave, and then down anotheroctave. Of all the subsections of the Fan-tasy, Mozart tarries here the longest; thedescending fourths are filled out withhalf-steps, are complemented by parallelsixths, and are repeated in all registers.All of this occurs in B˛ major. [text con-tinues on page 78]

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Finally, Mozart shifts the same mate-rial to C minor (Figure 5.28). What adifference! Instead of the fourth, we geta diminished fourth e˛-d-c-b˝ which wehave encountered a number of timesbefore. And now Mozart launches into a“Più allegro” section that consists ofnothing but sequences and inversions,with successive rising fourths soon sup-planted by rising Lydians, of which everytype is referenced. To make sure the dis-covery is not lost, Mozart cycles througha series of summary cadences, eachpunctuated by double-Lydian arpeggios,which recapitulate every mode refer-enced in the work: C major/minor, Fminor, D major, G minor, finally end-ing, in measure 154 (Figure 5.29), on C,f ,̌ and e˛ played simultaneously (to callthis a “chord” would miss the pointentirely). Three successive repetitions ofthe descending figure A˛-G, again inthree different voices, then lead backinto the Fantasy’s opening statement(Figure 5.30); only this time, in measure162, we are likewise brought to the samefigure A˛-G. In the concluding mea-sures, Mozart celebrates the discovery ofthis new Fˇ-pivotted modal principle,first in the bass voice with the sequenceF-Fˇ-G-A˛-F-G-C (measures 165-168,Figure 5.31), and then, even morepoignantly, in the soprano voice, with gand fˇ played simultaneously, followedby g against f˝ . Two “false” cadenceson G-A˛ follow. A simple C minor scaleconcludes the composition.

The foregoing “guided tour” of the Cminor Fantasy is only the first, but nec-essary step in grasping the discoveredprinciples as a unity in the mind’s eye.Through multiple comparisons of thesuccessive transformations across sec-tions—and not necessarily in their tem-poral sequence!—we can finally graspthe actual course of Mozart’s discoveries.

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