Beginning in 1782-83, Mozart revolu-tionized the concept of modality,

and its relationship to motivic thorough-composition. As two of his most pro-found religious works demonstrate, themotet Ave verum corpus and hisRequiem, great musical compositions donot develop in a linear, mechanistic way,from an initial theme, but are conceivedfrom the beginning as a whole, in whichit is often the end of the composition, ora key part of it, which determines thebeginning. In the case of the motet Aveverum corpus, it is the final statementabout Christ dying on the cross to savehumanity (“in cruce pro homine”)which determines the opening statement“Ave.” In the Requiem, one of the mostpoetic parts is the soloists’ quartet“Recordare” (“Recall”), which againforces the listener to go back to thebeginning of the Requiem from a differ-ent standpoint, that of rememberingChrist’s sacrifice on the cross. How theprofound moral and religious content ofthese works of art and their musicalmotivic development coincide with theidea of “time reversal,” of the futuredetermining our present and past, is thesubject of this investigation.1

Mozart’s Ave verum corpus

Beginning in 1782, Mozart made a funda-mental creative leap: the treatment of themajor and minor modes as a “One,” andnot as separate major and minor modes.The “one-ness” of the major and minor,for Mozart, has the following signifi-cance. Take the case of the modality ofthe Ave verum corpus, D major/D minor.Think how D major generates G minor,by taking the same intervals of the Dmajor ascending scale, and changing theirdirection, playing the intervals downward,instead of upward, from D (Figure 6.1).

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‘Recordare,’ from Mozart’s RequiemSTROPHE 1Recordare, Jesu pie,Quod sum causa tuae viae:Ne me perdas illa die.

Quaerens me, sedisti lassus:Redemisti crucem passus:Tantus labor non sit cassus.

STROPHE 2Juste Judex ultionis,Donum fac remissionisAnte diem rationis.

Ingemisco tanquam reus:Culpa rubet vultus meus:Supplicanti parce, Deus.

Qui Mariam absolvisti,Et latronem exaudisti,Mihi quoque spem dedisti.

STROPHE 3Preces meae non sunt dignae:Sed tu bonus fac benigne,Ne perenni cremer ignae.

Inter oves locum praesta,Et ab haedis me sequestra,Statuens in parte dextra.

Recall, merciful JesusThat I was the reason for Thy journey;Do not destroy me on that day.

Seeking me, Thou didst sit down weary,Thou didst redeem me, having endured the cross;Let not such great pains have been vain.

Just Judge of vengeance,Give me the gift of redemptionBefore the day of reckoning.

I groan as one guilty,My face blushes with guilt;Spare the supplicant, O God.

Thou who didst absolve Mary,And hear the prayer of the thiefHast given me hope, too.

My prayers are not worthy,But Thou, O good one, show mercy,Lest I burn in everlasting fire.

Give me a place among the sheep,And separate me from the goats,Placing me on Thy right hand.

The Principle of ‘Time-Reversal’ 6 In Mozart’s Worksby Mindy Pechenuk

D major generates G minor, by taking the same intervals of the D major ascending scale, and changing their direction.

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Such explicit or implicit changes ofdirectionality are crucial, both for the dis-covery of the paradoxes of the “newmodality,” and for Mozart’s develop-ment of motivic thorough-composition.

Now, think about all the potentiali-ties that exist in the entire composi-tion—major and minor—as a One, andyou begin to grasp the higher hypothesiswhich governs the composition as awhole.

The question is, What governs the shiftwhich Mozart has made? To find theanswer, we must consider, in succession,each section of the Ave verum corpus, inthe same way as Plato treats the idea ofhypothesis, higher hypothesis, andhypothesizing the higher hypothesis.For example, to begin with, consider theopening interval pairs as a paradoxderived from this process. In order tofocus us upon the very first interval pair,Mozart departs from the standard Latintext of the poem, by repeating the firstword, “Ave” (“Hail”) a second time;instead of “Ave verum corpus,” Mozartcomposes “Ave, ave verum corpus.” Inthis way, Mozart sets up the openingparadox, which is crucial to the develop-ment of motivic thorough-composition.

There is only one other place in theentire composition, where Mozartrepeats the text: the concluding line, “inmortis examine”—“in the test of death.”The second “in mortis examine” is total-ly different than the first. What isMozart saying about how creativityworks, and about how the human mindworks? How do you reflect on your life,so that you live your life in order tocheat death, by being a creative person?That is why Mozart repeats this “inmortis examine” differently (Figure6.2).

Bach’s A Musical Offering

Let us take a brief look at what Mozartwas looking at in J.S. Bach’s A MusicalOffering. As Lyndon LaRouche states inthe main article: “J.S. Bach’s develop-ment of a form of polyphony situatedwith respect to the Florentine ‘bel canto’voice-training standard, led into a deter-mination of both pitch and of counter-point derived from a rigorous applica-tion of the principle of a multiply-con-

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nected manifold. The related treatmentof the principle of polyphonic (e.g.,‘cross voice’) inversions led into suchcrucial of Bach’s works as his A MusicalOffering and The Art of the Fugue.”

The entire six-part Ricercare of theMusical Offering is a series of hypotheses,which are progressing to higher ordersof changes. Bach unfolds the paradox ofthe Lydian interval, i.e., the soprano reg-ister shift c -fˇ (Figure 6.3). Comparethe rates of change throughout the pieceas Bach, unfolds each voice entrance,which itself changes the entire orderingof the composition and the different lev-els of hypothesis, which unfold through-out the entire composition.

Mozart takes his discovery of Bach’sdiscovery, with the insight he has dis-covered from Haydn’s work, in motivicthorough-composition, and creates a

revolution in music. Mozart discovers anew higher modality, the “Lydian ”modality, in which the new modalityredefines all the relationships of theintervals, including the major/minor,which Mozart now treats as a “One”—and, once again, it is based on inversion.So, intervals are not fixed distances, butare themselves undergoing a constantprocess of change; a change, which isgoverned by a valid axiomatic-revolu-tionary discovery of principle, whichalso represents elevation to a “highercardinality.”

As Lyndon LaRouche states in themain article, for Bach, Mozart, et al.:“We must never hear intervals merelywithin voice parts, or even merely acrossvoices, except that we also hear the total-ity of the implied, complementary inver-sion within and across the voices, asthese unfold in the course of thatmotivic development which is the unityof the composition as an indivisiblewhole.”

Mozart’s Requiem

Another such example of “time-rever-sal” is Mozart’s Requiem. Key to theunderstanding of the whole work is thesoloists’ quartet “Recordare” (the fourthitem within the “Sequence” section ofthe mass, coming after “Dies irae,”“Tuba mirum,” and “Rex tremendae”).Mozart, treats the entire Recordare as apoem [SEE Box, page 79].

As in the case of the Ave verumcorpus, so, too, in the “Recordare,”Mozart increases the density of singular-ities in the final strophe, subsuming allprevious hypotheses. Within the space ofonly five measures (Figure 6.4), Mozartdevelops through inversion, what he hasbeen playing across the entire “Recor-dare”; this time, it is C major and itsinversion F minor (note the playbetween the strings and the voices,where the voices are unfolding the Lydi-an pair of b˝-f and a˛ -d ). The Lydianpairs unfold, d˛ to g , across the bass’sd˛ and the tenor’s g , and it is thisunfolding which is primary and governsthe bass voice and part. The point beingthat the bass line, starting in measure110, is not a series of ascending anddescending half steps, but is generated

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from the Lydian modality and theinversion of the interval pairs.

Finally, look at the opening of the“Recordare” (Figure 6.5). Here we havethe unfolding of our paradoxical inter-val pair: in this case, the two bassethorns are an inversion of one another.Here, Mozart generates the paradox ofthe Lydian/fifth between the two voices,unfolding the possibility of the Fmajor/B˛ minor, C minor/F major, Gminor/C major, D minor/G major. Thisis a far cry from the evil textbookapproach, which claims this opening as asimple series of suspensions at the sec-ond, totally denying the question of theLydian modality and the generatingprinciple of hypothesis.

It is time to throw out the textbooksof counterpoint, harmony, andHelmholtz’s crazy ideas of chords, notesas vibrations per second, intervals asmeasurement of distance. Mozart hasrevolutionized the axioms of those whocame before him, i.e., Bach and Haydn,and for all those after, Beethoven,Brahms, Schubert, Schumann. As Lyn-don LaRouche says in the main article:“[I]f we continue polyphonic and relat-ed developments, there is no simplyalgebraic determination of a well-tem-pered scale, but rather a counterpoint-determined interval of non-constantcurvature.”

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In each measure, Mozart increases the density of singularities of our original, paradoxical interval pair.

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___________1. In an article on “The Essential Role

of ‘Time-Reversal’ in Mathematical Eco-nomics” (Fidelio, Winter 1996, Vol. V, No.4), Lyndon LaRouche referred to Mozart’sAve verum corpus, and “a presentation byMindy Pechenuk, with chorus directed byJohn Sigerson, during the Labor Day week-end conference of the Schiller Institute onAugust 31, 1996,” as follows: “This highlysophisticated, compact, and beautiful work,is among the most convenient illustrations ofthe same principle of ‘time-reversal’ other-wise underlying both experimental physicsin general, and physical-economic processesspecifically. Any master’s Classical composi-tion according to the principles of motivicthrough-composition, such as those of Wolf-gang Mozart, L. van Beethoven, F. Schubert,R. Schumann, Johannes Brahms, et al., mustbe performed by applying the developedconception reached at the close of the com-position, from the beginning of the perfor-mance of the composition. The modificationso imposed by the intent of such a composer,results in what the celebrated conductor Wil-helm Furtwängler identified as ‘playingbetween the notes.’ Video recordings of theAug. 31 pedagogical presentation of themotet are available through the SchillerInstitute.”