In his 1680 “Rules for the Promo-tion of the Sciences,” GottfriedWilhelm Leibniz wrote an idea,to which he attached a metaphorwhich would seem funny to us today,an idea which is now more impor-tant than ever: “Those who walkaround in the sun, take on a differentcolor, and so likewise will a musi-cian, having observed in the compo-sitions of capable people thousandsupon thousands of beautiful cadencesand, so to speak, phrases of music,will, thus equipped with this beauti-ful material, be himself enabled toinspire his own imagination.” And,as a good teacher, who does not wantto discourage those who are willingto learn, Leibniz adds: “There areeven such people who are musiciansby nature, and compose beautifulmelodies.”

To recognize something in theobservation of thousands of musicalphrases “which inspires one’s ownimagination.” This is the Classical-humanist method of teaching, which

challenges those who are willing tolearn to re-live, from the sources ofgreat compositions, the discovery forthemselves, whether these be discov-eries in the natural sciences, or newartistic creations.

Johann Sebastian Bach (1685-1750) did exactly that when he was achild, and he became a genius.Mozart and Beethoven wrote down

“new counterpoint phrases” from theworks of their predecessors, but espe-cially from those of Bach, in order tomake the new musical “idea,” or“thought-object,” their very own, asLaRouche described it in his ground-breaking essay, “Mozart’s 1782-1786Revolution in Music,” in 1992.1

As it seems, it is only today, 250years after Bach’s death, that we are

62

J.S. Bach’s Musical Revolution

by Anno Hellenbroich

__________

This speech opened the conference panelon May 28. Footnotes have been added.

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COGNITION VS. INFORMATIONIN MUSIC

On the Subject ofStrategic MethodOn the Subject ofStrategic Method

FIGURE 1. The six species of human singing voice.

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better able to understand the musicalrevolutions which Mozart andBeethoven recognized in Bach’s lateworks, especially in A Musical Offer-ing (1747), and in The Art of theFugue.

Many of the ideas which Leibniz,some forty years earlier, articulatedin his late work The Monadology andin Principles of Reason in Nature, andGrace, can help to make Bach’s wayof thinking, of composing, moreintelligible today. We can obtain adeeper insight into Bach’s intellectualprinciples of composition, which sofundamentally revolutionized Classi-cal thinking, from remarks whichLeibniz made with respect to music:his comparison to the principles ofconstruction in nature, the divineorder of creation, and the lawfulnessof musical harmony.

In his Principles of Reason, forexample, Leibniz speaks about thegrowing joy in the knowledge of theperfection of the universe God creat-ed, the same joy which arises fromthe beauty of a musical work of art,which sounds harmonic:

Since God is the most perfect andthe happiest, and consequently themost worthy of love of all sub-stances, and since truly pure loveconsists in an emotional conditionwhich allows of the perception ofdesire for the perfection and happi-ness of that which one loves, thislove gives us the greatest desire ofwhich one can be capable, as soon asGod is its object. Thus do we takejoy in music, although its beautyseemingly only consist in the con-cord of numbers and in counting—of which we are not conscious—ofthe waves and vibrations of sound-ing bodies, which take on certainintervals.

In order to avoid misunderstand-ing: Leibniz sees—as did Kepler andNicolaus of Cusa before him—innumbers and counting, a characteris-tic of the cosmos ordered by God, a

measuring, an aspect of a fundamen-tal lawfulness which characterizes usand our universe. In particular, Leib-niz makes the important remark that“music pleases us by means of theconcord of numbers and counting, ofwhich we are not conscious.” Is Leib-niz speaking about our souls, per-haps as the midwife of Reason, inwhich beauty is unconsciously per-ceived? An idea which FriedrichSchiller develops in his essay on theaesthetic education of the beautifulsoul.

In another passage of the Princi-ples of Reason, Leibniz formulates theprinciple of “the best of all possibleworlds” in the following way:

It follows from the highest perfec-tion of God that, when he createdthe universe, He selected the bestpossible plan, in which there wasthe greatest multiplicity in theframework of the greatest order, in

which space, position, and time arebest employed, so that He achievedthe greatest effect with the simplestof means, endowing the creatureswith the greatest power, the highestknowledge, the greatest happinessand the greatest good, of which theuniverse was capable.

“Greatest multiplicity in theframework of the greatest order”: Isnot the immense work of JohannSebastian Bach’s life permeated bythis principle?

Bach wrote all of his works “toGod alone the glory,” soli Deo gloria,hundreds of spiritual and secularLieder, cantatas, motets, the powerfulPassions and the large fugal works,and, not least, the later work withthe royal theme, A Musical Offering,as a “painful and tedious work.”Each of his works attests to theattempt to generate the largest multi-plicity in a unity, a perfection, to cre-

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FIGURE 2. Concluding refrain in “Ach Golgatha” from J.S. Bach’s “St. MatthewPassion.”

FIGURE 3. Opening of “Ach Golgatha” from J.S. Bach’s “St. Matthew Passion.”

karencockshuttNew Stamp

ate the greatest effect by employmentof the simplest means. Bach’s devel-opment of polyphony, the fugue, hisuse of the organ point, are noticeableelements of this principle of thegreatest effect with the simplestmeans.

That is why we concern ourselveswith Classical music, from theAugustinian tradition to Leonardoda Vinci’s researches on the bel cantohuman voice, to Bach’s revolutionaryinvention of the well-tempered sys-tem—because we are convinced ofthe fundamental intelligibility of cre-ative thinking. For, both in research-es in the physical-natural sciences, aswell as in investigating our powers ofthinking, our creative thinkingprocesses in the forming of works ofart, we run up against the paradoxtoday more than ever: lawful devel-opment versus discontinuity—whichwe have to solve.

Bach: Master of SongIt took a long time for Bach’s actuallymagnificent discovery of the charac-teristics of the six species of thehuman voice [SEE Figure 1]—forexample, in choral singing and in thechoral passages of the Passions—tobe adequately appreciated.

Today, we have to rediscover thecharacteristics of hearing and singingof Bach’s time, the heritage of theBach family extending over six gen-erations, about which Bach’s greatson, Carl Philipp Emanuel, reports.

I want to provide one example toillustrate this, in the brief form ofthis introduction to our panel.

In the second part of the great St.Matthew Passion, which was probablyfirst performed in 1727 (rediscoveredand performed anew 100 years laterby the young Felix MendelssohnBartholdy in Berlin), Bach composesa recitativo for the alto voice and twoalto oboes (Oboe da Caccia in F),“Ach Golgatha,” which represents a

prelude to a magnificent alto aria.These two alto solos are situated fol-lowing the scene of the Crucifixionof Jesus, before Jesus dies on theCross. “Ach Golgatha” reflects thegreat paradox for all Christians, asexpressed in the text of the aria,which says: “ ’Twas there the Lord ofglory was vilely rejected,” and itpeaks in the cry of agony, “ . . . theinnocent must die, as do the guilty.Ah! how this grief afflicts my soul!”The aria that follows, placed at thisprominently dramatic passage of thePassion, takes up the idea of salva-tion (“See ye, see the Savior’s out-stretched Hands!”/ He would drawus to Himself. Come.”). Composi-tionally, the aria echoes the interject-ed calls, which one can hear in the

introductory double chorus of the St. Matthew Passion.

Compositionally, Bach employedthe special characteristics of the alto(or mezzosoprano) voice, to repre-sent this painful paradox. Thisbecomes clear, for example in theconcluding refrain of “Ach Gol-gatha” [SEE Figure 2], which dropsfrom a Df in the middle register tothe Ef in the chest register, beforeBach ends the alto voice in the mid-dle register on the shallow-soundingG, polyphonically set against theoboe voices. With the oboes and theaccompanying pizzicato bass, whichare polyphonically singing with thehuman voice, Bach created one of themost gripping of vocal compositions.This is also true with respect to its

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FIGURE 5. Lydian intervals in “Ach Golgatha” from J.S. Bach’s “St. MatthewPassion.”

harmonic boldness, which anticipatesthe paradoxes of the later theme ofhis A Musical Offering.

The opening interval “Ach Gol-gatha” [SEE Figure 3], which consistsof a diminished seventh Ef to Gf=Fs,was later “used” by Mozart andBeethoven, for example inBeethoven’s Piano Sonata Opus 111[SEE Figure 4]. The paradoxes of thepoetic text are characterized by a suc-cession of Lydian interval-leaps andcombinations. Each Lydian intervalsung by the soloist also introduces anew degree of poetic tension in thetext. For example, as shown in Figure5, in the lines “der Segen und das Heilder Welt / wird als ein Fluch an’s Kreuzgestellt” (“The blessing and the salva-tion of the world / is being, as if acurse, put up on the cross”), the con-traries “Der Segen” and “an’s Kreuz”are both sung on Lydian intervals.This is a peculiarity which Mozartdiscovered in 1782-83, based on AMusical Offering, as a new tool ofcomposition. In earlier times, thisLydian interval was outright “cursed”as Tritonus, the “devil” (Diabolus) inmusic.

One of the special characteristicsof the Lydian interval is connectedwith the matrix of the six species ofvoices. The natural shift in the regis-ter upwards or downwards occurseither at distances of the octave orLydian interval. So one can say: TheLydian interval is the smallest inter-val-unit which effects a register shiftin all of the voice species. There areonly six Lydian intervals, and theyremain the same upwards or down-wards, i.e., also in the inversion [SEEFigure 6].

The particularly impressiverecording of “Ach Golgotha” which Iwill play, is from the year 1954,under the direction of WilhelmFurtwängler with the Vienna Phil-harmonic orchestra, one of the veryfew performances of the Passionunder Furtwängler.2 Furtwängler

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FIGURE 7. Autograph score, “Ach Golgatha” from J.S. Bach’s “St. Matthew Passion.”

FIGURE 6. The six Lydian intervals.

died that year. The alto is MargaHoeffgen. In this performance, theyoung Dietrich Fischer-Dieskausang the words of Christ [SEE auto-graph, Figure 7].

One characteristic of all Classicalmusic, as you can perceive it in theinterpretation of this segment of theSt. Mathhew Passion, is carried by thefundamental idea of the Passion,love—agapē—in the Christian sense.In other words, the essential musicalemotion is not sensuousness, butagapē, as Plato and the Apostle Pauldefine that emotion. In true contra-puntal polyphony, the essential ideasof the composition are chieflydefined in two ways. First, as physi-cal principles are defined in science,by ontological paradoxes. In music,the relevant paradoxes are posed bythe metaphorical forms of transitions,lawfully generated dissonances, gen-erated within the composition. Sec-ond, by explicit or implied quotationfrom ideas stated in other composi-tions, either by the same, or othercomposers. For this reason, the twolate works, A Musical Offering andThe Art of the Fugue, about which weshall learn more from ProfessorVyaskova, have their prominentimportance for succeeding musicalrevolutions.

Bach’s A Musical OfferingI shall play three short examplesfrom A Musical Offering to illustratethis. What is striking in the basictheme of A Musical Offering, is theseemingly paradoxical Fs in the C-minor key area, that Fs in the sec-ond part of the royal theme, alongwith the already-mentioned dimin-ished seventh Af to Bn, which Bachput on the first accentuated beat ofthe bar. With the entrance of thesecond voice, this allows for thedevelopment of lawful dissonances,which were so inspiring for suc-ceeding generations of composers.

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Then, we shall hear two furthercanons, the very compressed shortform of A Musical Offering by Bach,with the characteristics of thesimultaneous upward and down-ward movements of the same con-trapuntal voice, thus the ambiguityof the intervals, which Bach formu-lated as the simple movement [SEEFigure 8], and then the inversion of the movement [SEE Figures 9and 10].

In a letter written to NicolausHartsöcker around 1711, Leibnizwrote the following on the subject ofdissonances:

The imperfections which exist inthe universe are like the dissonancesin an excellent composition, which,in the opinion of those who wellunderstand the connection, con-tribute to make this [the composi-tion] more perfect.

And to Goldbach (a correspon-dent mathematician from St. Peters-

burg), he wrote about the sparing useof dissonances:

Dissonances are pleasing as an occa-sional accompanying element andare employed to great effect: theyare inserted between the harmo-nious sounds [Wohlklänge] likeshadows in the order and in thelight, so that we all take great joy inthe great order.

[Text continues on page 69]

FIGURE 8. J.S. Bach’s own keyboard reduction of the Six-part Ricercar from “A Musical Offering.”

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FIGURE 9. “Canon Perpetuus Super Thema Regium” from J.S. Bach’s “A Musical Offering.”

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FIGURE 10. Contrary Motion Canon from J.S. Bach’s “A Musical Offering.”

Mozart’s ‘Great Mass’ in C-minor

Mozart understood this revolutionwhich Bach had introduced, and he,in turn, revolutionized his method ofcomposition with the principle of“Motivführung.” One fruit of thiseffort to extend the C-minor/Fsparadox he recognized in Bach, isrepresented by Mozart’s incompleteMass in C-minor, where the use ofthe four-voice chorus, especially thefugal part, is built on a variation ofthe second part of the royal theme,the towering polyphonies of the“Kyrie” introductory chorus [SEEFigure 11].

This work, which was composedsome 35 years after Bach’s A MusicalOffering and The Art of the Fugue,opened the way to a new freedom ofmusical expression. Another 50 yearswould pass, until, with the immenseMissa Solemnis of Beethoven, writtenin 1824 and performed for the firsttime in St. Petersburg, Bach’s revolu-tionary discovery would be broughtto a new culmination point in the artof composition. If we can follow andrelive the progressions of such mag-nificent “musical thought-objects”today, in the year 2000, which com-memorates the anniversary of Bach’sdeath; and if we can make this musi-cal revolution really intelligible; thenwe can take the branches of humanknowledge—the natural sciencesand the science of art, which, thanksto the immoral Immanuel Kant,were artificially divided—once againback to their single source: the cre-ative Reason of man.

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1. Lyndon H. LaRouche, Jr., “Mozart’s 1782-1786 Revolution in Music,” Fidelio, Win-ter 1992 (Vol. I, No. 4).

2. Wilhelm Furtwängler’s 1954 recording ofthe St. Matthew Passion is available onEMI 7243-5-65509-2-6, performed by theVienna Philharmonic, Wiener Sing-akademie, Wiener Sängerknaben.

FIGURE 11. Choral opening of “Kyrie” from Mozart’s “Mass in C,” K. 427.