Harmony inglés

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ByHEINRICH SCHENKERE d it ed a n d a nt /o ta te d b yOSWALD JONAS

TraHs /ateJ byELISABETH MANN BORGESE

THE UNIVERSITY Of CHICAGO PRESS


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Library of Congress Catalog Card Number: 54-II:!z3THE UNIVERSITY OF CHICAGO PRESS, CHICAGO 60637The University of Chicago Press, Ltd., London W.c. I

The book presented here in its first English edition was publishedinitsoriginal almost half a century ago.Why, one might wonder, didit take all this time to bring it before the public again? It should bepointed out, first of all , that a similar fate, if not worse, has befallenother books as well. C. P. E. Bach's Essay , for example, which is,beyond doubt, one of the most important books ever written onmusic theory, was grossly neglected for almost two hundred years,to be reissued, in a complete edition, only quite recently. This newedition isin English translation (by W. J. Mitchell), and it isdeplor-able that the work is stil l unavailable in its German original!This fact, which reflects fairly well the whole situation in which

our musical culture finds itselftoday, may offer a general explanation,not an excuse. The particular circumstances at the root of the casepresented here will appear more clearly aswe go on with this Intro-duction.Heinrich Schenker published his Harmony anonymously in 1906,under the most unusual title, "New Musical Theories and Fanta-

sies-by an Artist." The tit le itself was to indicate the author's inten-tion of finding artistic solutions to artistic problems rather than anyconcern for commonplace theoretical discussions. This volume wasthe first in a long series and marks the beginning of a lifelong de-velopment, which was concluded only with the last volume, FreeCompos i t ion, published thirty years later-a few months after theauthor's death. In this sequence of works, interspersed with a goodnumber of other publications, Schenker revealed his theories as theydeveloped. Each volume represents a step forward, based on an evergrowing artistic experience. This process, however, entailed certaindifficulties. Some concepts were still immature when first publishedand found their final and clear expression only in a subsequent vol-ume. Furthermore, certain parts of the work, though each one ofthem constituted an essential basis for subsequent constructions,would, in certain aspects, be obsolete when the later work appeared.


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Schenker's doctrine thus was ina continuous process of growth anddevelopment; and the author, always occupied with the completionof new work, was never in a position of even considering the re-vision of older works. This provides a partia l answer to our originalquery. One need only consider, in addition, the unquestionablediff iculty of the subject matter as such, aggravated by the author 'srecalci trance toward any form of belletr ist ic presentat ion, and hisattitude, on the other hand, of ruthlessly standing his ground, nomatter whether this put him into shrill contrast with all his con-temporaries; and it becomes obvious that he soon was to find himselfin a state of total isolat ion. What else could be in store for an authorwho dedicated, in the face of his contemporaries, his monograph onBeethoven's N in th S ym ph on y "to the memory of the last master ofGerman music-Johannes Brahms"? Owing to its undoubtedlyoriginal and comprehensive manner of presentation, the book itselfwas well received and widely perused. This fact, however, did notmodify in the least the negative attitude widely held toward theauthor personally-paradoxical as this may seem. Indeed, it can besaid that Schenker's works were read and studied more than somecare to admit and more than one would expect, in view of the per-sonal attacks on the author and, on the other hand, the conspiracy ofsilence that greeted his work.In the long run, however, neither hosti le attacks nor silence could

subdue the need for a more object ive grappling with the problems.This was true with regard to Schenker's work, as it is true with re-gard to any important intellectual movement. And at no time hasthere been a more urgent need for a basic reorientation than just now.We are passing through a period admittedly submerged inexperi-ments, with all basic concepts thrown into a state of hopeless con-fusion. There are many who, consciously or unconsciously, have setout to f ind a solut ion; who arc groping for a clar if ication of the basicproblems of art, a clarification which is essential for an understandingof the fundamentals of music as art. Of course, there are also thosewho still try to escape reality and to circumvent the answers. Thereare also those who know Schenker's theories only from secondhandsources, which are responsible for a number of misunderstandings.

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INTRODUCTION

Both categories of musicians may be skeptical with regard toSchenker's work, and they will ask whether and why Schenkershould be considered the man to bring the needed clar ification. I t isup to the writer of this Introduction to give a convincing affirmativeanswer to these questions in the following pages. It is legitimate,however, to quote here an opinion whose complete impartialitymust be beyond any suspicion. In December, I936, when Schenker'sname and work were blacklisted for polit ical reasons, an art ic le ap-peared in the Allgemeine Musik Zeitung under the title, "Can WeStill Listen to Music?" Whether the author, HansJenkner, proceeded~om defiance or unawareness of the circumstances is beyond myJudgment. Whatever his motives, he deserves to be rescued fromoblivion.

laymen as well as experts will raise th e question as to whether it isprobable Schenker, of all men, is the one who was destined to wrest frommusic her secr~ts . To. this one might answer: Th e l evel of Schenker' s thinking onthe art of musIC is higher than that of most other people. He has l is tened moremten sely and has perceived her law. Creativ e composers have f ulfilled the lawwithout ever grasping it rat iona lly (wi th the one exception of Brahms , the GreatReti cent ): The ~ev~la tion of the wonder fu l narcral Ia w regulating the flow ofmusic In Its totalIty IS t an tamount to an acous ti c percept ion of the moral law. Thustheory comes to be more than the teaching of forms ; i t becomes percept ion of f ir stcauses. . T his work, created by a man who is faithful to art, indicates to us theway to regeneration.Roger Sessions once described Schenker's Harmony as "certainly

unsurpassed and perhaps unequalled in its sphere." The book is ofthe,g~eates~ imp~rtance, if only because it contains many of Schen-ker s ideas tn their embryonic stage. It isnatural, on the other hand,that the author at that time was still largely under the influence ofconventional concepts, from which he broke away during laterstages of his development. For these reasons i t seemed advisable toprovide the work with a running commentary which should fore-stall the danger of possible misunderstandings and misinterpretations.It.alsoshould forestall attacks against Schenker on the ground of cer-ram more or less speculative and chal lengeable ideas which the au-thor himself repudiated in his subsequent work. Such ideas are ex-pressed, for example, in the chapter on the "mystic number five."

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This chapter, its content often misunderstood and distorted, has beena target of much unfavorable criticism ( II, 15, 17, II3). Thechapters on seventh-chords ( 52, 99 fE ) and on modulation ( 17IfE ) were completely remodeled in Schenker's later work. All this isnoted at the proper places in the running commentary.We have left the illustrations used by Schenker throughout thework asnearly as possible in their original form; even in those cases

where Schenker himself, in a later stage of his development, probablywould have read fewer scale-steps and more voice-leading for aproper analysis. We have added, however, an Appendix to this In-troduction in which a number of illustrations are presented in theform which, according to all probability, Schenker would havegiven them in a later stage; and we have added the necessary explana-tions for this hypothetical development.If Schenker's Harmony isto serve asa practical introduction to hi s

whole work, this Introduction has to fulfi l two tasks. First, it shouldgive a brief account of the general situation in which musical theoryfound itself at the time when Schenker began his work and shouldexpose any widespread errors which h e had to face. Second, itshould give a synopsis of the development of Schenker 's theories inhis later works.Before embarking on this twofold enterprise, we should like toanticipate one of the main objections to Schenker's work. It has beensaid time and again that his theory is too "narrow," too "lopsided,"since it docs not offer any key to the understanding of modern musicor music written after, say, the time of Brahms. This objection shouldbe rejected on the ground that Schenker 's theory isdeeply rooted inthe principles of tonality as he found them elaborated in the worksof the great masters from Bach to Brahms, fulfi ll ing an almost mil-lennial development of music as art! One may even say that, forSchenker, tonality isthe c on ditio sin e q ua n on of music as art; and theproof of this hypothesis constitutes the content of hi s teachings. IfSchenker has succeeded in proving that tonality isthe foundation of2_Rccendy anatt ompt w" ,-' rnadet o offs et tbi ,object ion by applying S chcnker'sidlo:l-Sto

modem music and it, interpretation: SI""luT~1 Hearhlg by Fel ix Salzer {New York: Char lesBani , (952 ). Such an a ttempt was pOSSible, only through misinterpretat ion of Sch=kcr 'sbasi ctheori cs , fi rst of all his concept of t onalit y, and theref or elj doomed to fad

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the musical masterworks-though his concept is essentially differ-ent from the ordinary one-the burden of proof is now on thosewho claim that there are other foundations, as strongly rooted inthe laws of nature, for music as an art to rest upon .aThe chief merit of Schenker's early work consists in having disen-

tangled the concept of scale-step (which is part of the theory ofhar-mony) from the concept of voice-leading (which belongs in thesphere of counterpoint). The two had been confused for decades.Schenker's operation wrought a complete change even in the externalaspect of the teaching of harmony, in that he banned from his hand-book all exercises in voice-leading and relegated them to the studyof counterpoint.The significance of this undertaking cannot be fully grasped except

in the context of its historical setting. We have to consider herebriefly the development of musical theory since the end of theeighteenth century. This survey will also help to clarify the meaningof Schenker 's two basic concepts, "prolongation," and "composi-tional unfolding," or Auskomponierung.According to the theory of prolongation, free composition, too, is

subject to the laws of strict composition, albeit in "prolonged form."The theory of Auskomponierul1g shows voice-leading as the meansby which the chord, as a harmonic concept, is made to unfold andextend in time, This, indeed, isthe essence of music. Ausleomponierunothus insures the unity and continuity of the musical workThe core of music theory asithad developed and was taught inthe

eighteenth century was voice-leading, The study of theory wasdivided into two parts: the study of strict counterpoint and the studyof figured bass ("thorough bass" or "continuo"). The rules guidingthe former were derived from the epoch of vocal music. They werecodified byJoseph Fux in G ra d us a d P ar na ss um (recently reprinted inpart in an English translation). In this work Fu x undertook ananalysis of the nature of intervals, a distinction between consonantand dissonant notes, and a study of the use ofthe latter. I t was a studyof voice-leading in its purest form, totally free of any considerationsof harmony. More than anything else, it was a body of rules for the

3.Cf. Appendix II. below.

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training of the ear. In this sense counterpoint has attained universalvalidity. But it never could lay claim to the teaching of advancedcomposition, although this may have been the original intention ofC ra du s a d P ar na ss um ; in this respect Fux was still too deeply underthe influence of the vocal epoch.The development of figured basswas somewhat different. Follo",,:-ing the development of instrumental music, i t s~0-:ve~more fl~XI-biliry and freedom. It remained, however, a dlsclphne of vorce-leading and never degenerated to a mere juxtaposition. of chor~s. Inthis sense, the study of figured bass served asa preparation and mtro-duction to the study of composition. Bach, indeed, went so far as tocall it "the school of composition." Since the composers of that t imenever executed the details of their compositions but left it to theirinterpreters to fill in the upper voices in accordance with the nu-merals, figured bass became a most efficient conveyer of generalmusical education; for anyone who wanted to play music had tohave an adequate theoretical preparation. The study of figured .basswas the obligatory gateway to any musical performance. Planoplaying "for its own sake" and without general musicianship wasutterly unthinkable at that t ime. The dependence of performance ontheory isindicated by the very tit le ofC. P. E. Bac~'s t~eatise, ~ssayo n the T rue A rt of P la yi ng K e yb oa rd I ns tr um e nt s, which IS a codifica-tion of the rules' of fIgured bass at the acme of their development(r762). .If the theories of counterpoint and figured bass had remained thebasis of teaching during the following generations, musical historymight have taken a different course. This, however, ishistory of themight-have-been. In 1722 Ramcau discovered the princi~les of har-mony and developed them in his T ra it ! d ' ha rmGn ie . In rhis work herevealed the function of harmonic steps and inversions. He demon-strated that the harmony of a triad does not change when the root istransferred from the bass to another voice. The concept of theharmonic step as such may have enriched musical theory, though itshould be remembered that the inversion of intervals had alreadybeen well known to the school of strict counterpoint. But the use towhich Rameau put this concept certainly created confusion and was

baneful to the further development of music theory. Ramcau's con-cept was much too narrow. This may be due to the fact that he wastotally unaware of the new trends in German music. Perhaps histheory was adequate for an understanding of his own music, whichassumed almost identical meaning of chord and scale-step; it mostcertainly was inadequate if applied to the finesses of voice-leading inthe works of Bach as understood in the theories of C. P. E. Bach'sEssay. Rameau did not even suspect the possibility that voice-leadingcould be the means for the "compositional unfolding" of widerharmonic areas. For him "chord" and "scale-step" were identical.He reduced any simultaneity of tones to its supposed root posit ionand rent the artful texture of voice-leading into strips of marc or lessclosely related chords. The chord, endowed by voice-leading withits full meaning and contextual logic, now was to stand in isolation,generally without reference to what preceded and what followed.The bass line, meaningful as the Auskomponierung of a chord-ablessing that had accrued to composition from instrumental musicand figured bass-was weighted down, note for note, by the burdenof the "ground bass," which inhibited and finally arrested its mo-tion. All the life of music congealed. Thus the same year, 1722,which brought forth the first volume of Bach's Well- temperedClavier, with its miracles of voice-leading, also heralded the decayof musical theory and practice.In broadest terms, Rameau's great error was to interpret har-

monically, or vertically, a bass that was composed horizontally, ac-cording to contrapuntal principles. The possibili ty of Aushomponie -rung was totally overlooked. The bass line of a thorough-bass com-position represented a happy attempt at horizontal construction. Theupper voices, whose movement was directed by the continuo nu-merals, moved along similar horizontal l ines. To reduce this livingbassline to the so-called "ground bass" was the fundamental error ofRameau's doctrine.To illustrate further: the continuo numerals indicated the move-

ment and progression of the upper voices, not a chordal structure ofharmonic steps. Thus we read in Bach's C bomi eM e lo di es w ith FiguredBass:

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The indication 8-7 leaves no doubt that Bach wanted the seventhto descend in passing from the octave. The indication 8 cannot b.eexplained otherwise; for any other interpretation would render t!usindication superfluous. The numerals indicate a moveme:~t, a.spec~ficmovement-not, indeed, a "dominant seventh-chord. Likewise,the numerals (b ) indicate a slow turn; a chordal interpretation wouldbe equally meaningless. Kimberger writes in hi~ A r: o j Pure CO Ill-

(1774), I, 30: "The genesis [of the essential dissonances] canreconstructed as follows:

Rameau's theory was introduced into Germany by Marpurg, whotranslated D'Alambert's brief Introduction to the works of Rarneau.The reception was cool. I t was, indeed, so skeptical that i t is~ard ~osee how Rameau's prestige and influence could have survived It.Bachand his circle offriends remained completely negative. EmanuelBach wrote to Kirnberger, who was a faithful pupil of SebastianBach and, at that time, engaged in a controversy with Marpurg:"You may announce it publicly that my father's principles and myown are anti-Rameau." Kirnberger himself, in The True Princip les o fH armo nic P ra cti ce (1773) has the following passage: "Rameau hasstuffed his theory with so many inconsistencies that I am just won-dering how it could have come to pass that there are Germans whofall for it and even fight for it. We always have had among us thegreatest harmoniscs, and their treatment of harmony certainly couldnot be explained by Rameau's proposit ions. Some have gone so far

INTRODUCTION

as to throw doubt even on Bach's treatment of chords and theirprogressions rather than admit that the Frenchman could be inerror." And in his P ur e C om po sit io n (I , 248) Kirnberger writes:"Rameau himself has not grasped the simplicity of harmony in itstrue purity; for he occasionally mistakes passing notes for funda-mental ones. "This latter observation already reveals a distinction be-tween voice-leading and a merely "harmonic conception."Art precludes any approach by short cuts or oversimplifications;

and the danger of oversimplif icat ion inherent in Rameau's theorywas recognized even in France. No lesser critic than Rousseauexpressed his alarm asearly as I752, and his comment anticipates theconditions in which the teaching of harmony finds i tself in our day:"The study of composition, which used to require about twentyyears, now can be completed in a couple of months; musicians aredevouring the theories of Rameau, and the number of students hasmultiplied .... France has been inundated by bad music and badmusicians; everybody thinks he has understood the finesses of artbefore having learned as much as the rudiments; and everybodytries to invent new harmonies before having trained his ear to dis-t inguish between right and wrong ones." This passage could havebeen written today.In Germany, however, strict composition was still the basis of

teaching. Our masters still applied themselves to the study ofc. P. E. Bach's Essay, not to that of Rameau. Haydn said of C. P. E.Bach that he owed him everything. The Essay and Pux's Gradus werethe foundations of his own teaching and later also of Beethoven's .The fate of music was sealed when figured bass, once fal len into

disuse practically, became obsolete also in theory as a method of in-struction. Owing to the lack of alternatives, it was still adhered toformally; but its essence was completely falsified by Rameau's theoryof the ground bass. From this amalgamation of voice-leading andharmonic steps there arose our own "harmony" as a rigid theory of"chords." For a while, tradition survived. There is no doubt thatMendelssohn, for example, was instructed in the old style. C. P. E.Bach and Quanta had kft some traces of their work in Berlin. ButBrahms had already complained that , before being able to do any-

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thing constructive himself, he had first " to unlearn everything" hehad learned; and his dictmn-"even Schumann did not learn any-thing any more. . nor did Wagner"-gives cause for alarm."You would not believe," he wrote to Riemann, "what I had tosuffer from incompetent textbooks." Riemann, on the other hand,was naive enough to propose to dedicate to Brahms his own Har-mony, which, indeed, he did, much against the latter 's desire.It is small wonder that, in the long run, the consequences of an

instruct ion restricted to the teaching of chords began to show in thestyle of composit ion. Composers began to think only "vertical ly"and to write accordingly. The great ones among them were fullyaware ofthis danger. In his cri tique of the "Waverley Ouverture" byBerl ioz (1839), Schumann wrote: "Often it isonly a series of emptysound effects , oflumps of chords thrown together , that seems to de-termine the character of the piece." And Delacroix noted in hisdiary a conversation with Chopin, during which the lat ter told him:"It has become customary now to learn chords ahead of counter-point, which means, ahead of the sequences of notes by which thechords are formed. Berlioz simply sets down the chords and fills theinterstices as best he can."By also reducing merely passing chords to "fundamental chords,"

Rameau destroyed all continuity. The bassline had itself been a resultof Auskomponierung, and this had been achieved by means which be-longed in the sphere of counterpoint, such as passing notes orneighboring notes. It now lost its meaning and continuity. Thetheory of the ground bass was tantamount to the destruction ofcontrapuntal thinking, which it replaced by the so-called "harmonic"way of thinking. It rested on false premises. The reduction of apassing chord to a fundamental one divested i t of i ts logic and dis-torted the perspective of the value it possessed asa passing chord andderived only from that posi tion. In response to the need fOra moremeaningful standard of evaluat ing notes, there arose the so-cal led"theory of functions," which reduced all chords simply to tonic,dominant, or subdominant. This attempt was to no avail either.It was bound to fail because it overlooked the possibility thatidentical chords have different meanings according to the context in

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which they move. The concept of the "secondary dominant"(Hiljsdominante), likewise, could not lead very far because it appliedonly to the relations between two neighboring chords. It could neverbring about a synthesis of the whole. In what concerns the apprecia-t ion of the great masterpieces of music, al l that could be learned bythese methods was to drag one's ear from the perception of one chordto that of the next. As a consequence, the energy necessary for abroader understanding was lost.The overemphasis on the vertical was bound to arouse a reaction.

The pendulum, however, had swung too far in one direct ion for thecountermotion to stop at the center of reason and moderat ion. Theopposite extreme was to be reached in the theory of "linear counter-point" and the school of "linear composition" it engendered. All thethinking and writing now was "horizontal ," without any regard tothe natural laws of harmony, to whose unfolding any sequence orsimultanei ty of notes must be subordinated. Only where the hori-zontal serves the unfolding of harmony can vertical relations beintegrated into a whole. Justice can be done to the bassline only whenit is understood in i ts double function: within the large structureof tonality, it must be the bearer ofharmony; at the same time, how-ever , i t must be so led as to express, through and beside the pillars ofharmony, a continuity of melodic unfolding.Heinrich Schenker has shown the correct relationship between the

horizontal and the vertical. His theory is drawn from a profoundunderstanding of the masterpieces of music which his genius notonly interpreted but, so to speak, created anew. Thus he indicates tous the way: to sat isfy the demands of harmony while master ing thetask of voice-leading.

"In contrast to the theory of counterpoint, the theory of Har-mony presents i tself to me as a purely spiritual universe, a system ofideally moving forces, born of Nature or of art ." With these words,on the very first page of his Introduction to Harmony, Schenker em-barks on his long journey. He immediately arrives at a considerablybroader concept of the scale-step, at least ideally . For i ts practicalapplicat ion to the understanding of the masterpieces, a host of ex-


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periences was still needed. A glance at the wealth of examples of-fered in Harmony should be sufficient, however, to make it clear howfar even his early concept of the scale-step deviates from the usualone (examples 120, 121, 124, 130, and 201 should be noted in par-ticular). Here his concept of "step" is already no longer identicalwith the concept of a mere chord. It has rather become the artisticexpression of an ideal chord, a chord given nature. The task ofthe artist, then, is to fashion this raw and to endow it withform, according to the laws of art.'The chord isa simultaneity. To use a metaphor, i t has a dimension

in space; and the nature of music, which flows in time, demands itstranslation into a temporal sequence. This process, called by Schenker"compositional unfolding" or is dearly under-stood in Harmony, Schenker's first ( lIS ff. shouldbe noted in particular in this It could find its final ex-pression, however, only after an incursion into the field of counter-point, since the goal of creation in time, can bereached only via voice-leading. Basically, the of ouroccidental music begins from an understanding of nature and aninterpretation of its relations to man-made art . I t ismarked, stage bystage, by the conquest of the necessary means of expression, i.e.,voice-leading. Metaphorically, one could say that this philogeneticdevelopment was recapitulated ontogenetically in Schenker's pro-gressive stages of interpreting the masterpieces. The final aim was toreach a balance between the two components of any musical struc-ture: the "vertical" of the chord and the "horizontal" of voice-leading.Before proceeding with this exposition, however, we should con-sider Schenker's use of one more artistic means. It embodies the

law of repetition, and its primary expression in musical compositionis the motif. The opening paragraphs of this book, with the com-mentary notes, will provide the reader with an adequate interpreta-

(see abovevp-vi).

INTl,ODUCTION

tion of this phenomenon. We may therefore restrict our observa-tions here to those of its aspects which must be considered as asignificant advance in the development of Schenker's theory.Again, a detour over the theory of counterpoint was obligatory, asvoice-leading was a decisive factor also in this respect.In 7 of Harmony Schenker says that the "cancellation of par-

allelisms" constitutes an "exception." The motif for him is some-thing more or less unalterable, which can be identified only if itsnotes are maintained in their original form. He does not yet suspectthe existence, in the background, of forces strong enough to fixwhat is essential , even where the externals of a motif arc subjectedto change. Only as he developed his theories on counterpoint andstrove to reconcile them with the principles of free compositioncould he discover those basic laws which apply, with equal validity,both to strict and to free composition. He took up the concept of"prolongation" (seeAppendix I). He proved that whatever notes orchords are to be understood as passing in strict composition retainthis function also in free composition, albeit in a prolonged or ex-tended context. Thus Schenker came to understand that any melodicdevelopment, in the external aspect of a work of art , can be reducedto some simple principle of counterpoint, such as passing notes,neighboring notes, etc.It isobvious that those notes or chords which are passing between

diatonic intervals and, so to speak, constitute the lifeblood of thewhole composition also penetrate the motif, whose recurrence orrepetition may now be established even where its notes are not re-produced faithfully and its content and meaning are presented in anexternally altered form. It was these recurrences which led Schenkerto the concept of the "primordial line," or Urlinie . This concept wasprobably the one which provoked the most violent objections on thepart of Schenker' s critics, mainly for the reason that he could not finda {mal and unequivocal formulation for it until a later stage in hisdevelopment. We shall soon see why this must have been so. TheUrlinie concept was, nevertheless, of decisive importance for thedevelopment of hi s theory. It was significant in two ways.First of all, certain external phenomena of composition now could

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be reduced to simple contrapuntal passing notes (as pointed outabove, in connection with the concept of "prolongation"). The lawsof strict composition thus acquired effectiveness and validity also infree composition, although in expanded and veiled form. Counter-point thereby came into its own and was freed from the commonprejudice according to which it was nothing but a traditional matterof instruction without practical value, except, perhaps, for the com-position of fugues or other "academic" exercises.Second, the Urlinie led, in turn, to a clearer, though more specific,

understanding of the concept of AU.lkomponierung. For it demon-strated the unfolding of a harmonic idea or interval into a melodic.horizontal line. This unfolding was achieved by a contrapuntaldevice, the passing note.It is true, as we said above, that the Urlinie concept had not yet

found its ultimate and precise formulation. Inparticular, its applica-tion was still restricted to the upper voice and had not yet been ad-justed to the bass. Nevertheless, even at that early stage of Schenker'sdevelopment, the concept was by no means as vague as claimed byhis critics.~ I : : : : : : : j f l i r 1 1 : 1 1 . ' 1 2 k + 1

m " VI I~a IV ilvnlv) u r v V 1In one of his earliest presentations of the Urltnie, with reference to

the E-fut minor prelude of the W e ll -t em p er ed C la vi er . Book I (Ton-wille [1922]) . Schenker is quite precise in point ing to the AU.lkom-ponierung of the interval of a third, which he recognizes to be farmore significant than an "arbitrary" linear concept. (In subsequentwritings, this kind of Auskomponierung is called span . The span variesaccording to inrerval lic differences. Thus there are third-spans,sixth-spans, etc).In broad terms, Schenker's concept of the Urlinie signifies his de-

parture from simple "foreground" hearing to a perception of thexviii

INTRODUCTIONforces operating in the "background" of a piece ofart . The mere factthat his theory begins from the observation of the simplest fore-ground phenomenon, the "motif," should be sufficient to ward offthe accusation of "construccionalism" which has been so frequentlyleveled at him. The discovery of the "background" and its hiddenconnections was essential to the perception of the continuity of awork of art: points separated in t ime could be heard and understoodas belonging together, because they constituted the initial and con-cluding points of an interval, rooted in nature and grasped as aunity. Such points were l inked by the passing notes, familiar fromthe study of counterpoint , and were severed, at the same time, by themanifold and expansive al terations of the foreground. It is obviousthat Schenker did not stop at the perception of slight ly altered mo-tivic repetition. Further penetration revealed to him the existence ofstil l greater complexes of repet it ion in the background. The readermay be referred here to the first four examples in Appendix I (A1-A4) which attempt a reconstruction, in the light of Schenker'sla ter theories , of Examples 2, 11,12, and 14of the Harmony, A com-parison between his early definition of the motif as "an association ofideas intrinsic in music" (Harmony, 2) and his later presentation ofthose background repetit ions in which our masterpieces abound( F re e Compo si ti on , 254) will i llustrate most dramatically the dis-tance covered by Schenker's intellectual journey. (Note also thearpeggios in bars 1-4 and 9-10 in Fig. 8,aspresented by this editor inAppendix II . The arpeggios in question are marked by beams.)The discovery of the Urlinie signified the introduction of the

"horizontal" into Schenker's theory. This horizontal, however,moves within definite intervals and is therefore to be distinguishedsharply from that other "horizontal, " which, derived from the so-cal led "linear principle," has recently invaded musical theory andprac.tice. Owing to its origin in the contrapuntal concept of thep~ssmg not~: i~ further .signif ied a clarification of the concept ofdissonance. DISSonanceIS always in passing, never a harmonic aim."This quotat ion isthe ti tle of Schenker 's essay in the second Yearbookq 1926], p. 24) , a classic, which defines most precisely the nature ofdissonance and its origin. It is true that in Harmony Schenker still

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clings to the "chordal" concept of the seventh-chord; but even heresome anticipations of his later concept can be traced, as indicated inthe commentary notes. This later concept, however, could find itsfinal formulation only in counterpoint (see 10,52, and, particular-ly, 55 and 99). Incidentally, it may be pointed out that even theexamples quoted earlier from Bach and Kirnberger should give anapproximate idea of the derivation of the dominant seventh-chord.In so far as the Urlinie was a horizontal concept, it presented itself

as a "sequence." This sequence, however, was composed of rathershort units, at least initially. The units were short for the simplereason that the passing dissonances were pressing toward their respec-tive goals and, as "motor forces," resisted any slowing-down. Inspite of the various transformations to which the foreground motifsmay be subjected, those brief recurrent units in the background aresufficiently strong to uni fy the "idiom" of the whole composition(see Bach's Prelude in E-fl.at minor, as quoted above). The basicproblem, however, still remained unsolved. How was it possibleto integrate these units into one unity comprehending the whole?How was it possible to create a truly organic whole, to transform amere addition of sequences or juxtapositions into a hierarchy ofcompositional values?To anticipate the answer: the relation of the Urlinie to the wholewas modified by a new concept grasping the Urlinie as a part of a"primordial composition," or Ursotz. This concept created thenecessary balance between the vertical and the horizontal (seeabove,p. xiv; also 19, n. 21). Again, a long stretch of road had to becovered by Schenker to reach this final goal. The bass line in itsdouble function (seep. xiv) assustainer of the harmonies aswell asoftheir connecting melodic progressions (arpeggios or passing notes)had to be brought into agreement with the upper voice. It becameclear in this process that passing notes which were dissonant withinthe context of the bass line and passing notes which were dissonantwithin the context of the upper voice could be consonant in theirrelationship to each other. The dissonance thus appeared, passingly,asa consonance. Temporarily the urge toward its tonal goal could berelaxed, and a new chordal region was thus procured for Aus kom-

INTRODlJCTION

ponieruno, The dissonance was, so to speak, arrested and transmutedinto a region of consonant sounds. As such, it was hierarchically sub-o~dinated to the original setting, where it appeared as a passingdissonance. The units thus were integrated into a hierarchy, i.e., astratification of primary and subordinated parts.A passing dissonance in the upper voice could be arrested and

transmuted, furthermore, by having the bass skip to an intervalwhi~ would be consonant with the passing note. We shall brieflyexamine here the most common instance of this phenomenon, withthe bass skipping to the fifth:~:?f iR: I I

(V)The passing note d in the upper voice, within the t hi rd - sp a n c - d- c ofthe c major diatonic scale, is accompanied by a G, obtained by a skipin the bass voice from C. The two voices meet in a fifth-intervalwhich now may be expanded into a dominant-chord and inter-preted as such. This probably constitutes the most common exampleof the expansion of musical content. A dominant-chord obtained bythis process is called a "divider" (Tei ler ) in Schenker's terminology.The divider chord, in turn, may be extended by passing notes of it sown; and thus there ispractically no limit to the possibili ties of fur-ther transmutations, except by the aim of intelligibility. What appliesto this "divider chord" obviously applies to any other consonantchord obtained by this process. The note which is to be transmutedmay be passing within a third (see example), i.e., a third-span, orwithin any other interval: fifth-span, sixth-span, etc. The particularspall in question will present, hierarchically, the next higher stratumor order, which, in turn, may be subordinated to the next higherspan, until we reach the ultimate one, which spans the unity of thewhole composition. This ultimate and supreme unity, which sus-tains the unity of the whole, represents, in its Ursatz form, the Aus -komponierung of one single chord, the bearer of tonality. It isobviousthat Schenker's concept of tonality differs widely from the customaryone. For Schenker, tonality is the fashioning and expression in time

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INTRODUCTIONof one single chord as given by Nature and extending inspace. Thisconcept is not changed by the fact that the subordinate strata mayacquire, by the use of chromatic devices, some autonomy: Schenkercalls this process "ronicalization" and describes it asearly asHarmony( 136 ff.) . On the contrary, "ronicalization" restores to thework of art the needed contrast and color, which music was boundto lose in the process of systematization (cf 18). "Tonicaliza-tion," however, affects only the subordinate stra ta -the m id dleground, in Schenker's terminology-or the surface phenomena of acomposition-its foreground, It never takes place in the background,the ultimate stratum expressing the whole. Accordingly, Schenkerlater on rejected the concept of modula t ion in its strict sense, al-though in Harmony this concept isstill retained. However, this workalready contains some amazing premonitions, hinting at the laterconcept of stratification (see 82, 86, 88, and 155, 157, with theircorresponding notes). One almost feels tempted to draw a compari-son between this theory of the strata and its effects, on the one hand,and the concept of perspective and its effects, on the other. In bothcases "spatial depth" has been reduced to a surface or line.The fragmentary example below and the entire "Little Prelude

in F Major" by Bach, as reproduced in Appendix II, may furtherillustrate this concept. The former, the second theme of Mozart'sSonata in F,is presented asExample 7 in Harmony . In this connection,one more of Schenker's terms-interruption-needs to be clarified;furthermore, a few words ought to be said about the graphicmethod of its interpretation, to the elaboration of which Schenkerdedicated much time and effort. This graphic presentation oftenattains such a degree of precision that it could dispense with anyexplanatory text.j~~':I:llti~'l~l;

I (IV v .. I)-JtI- vxxii

ll~ I I I I ! I r I i t I i I I1 (TV - - V - I) rfv ISchenker offers this example in 5 in order to show how repe-

tition takes place not only on a small scale within the motif butwithin a somewhat larger complex; in other words, how repetitionengenders the form of antecedent and consequent. It is true thatSchenker here deals merely with repetit ion as such, without goinginto its musical foundation. But the principle of repetit ion rests pri-marily on psychological premises, and it isup to the composer's forceof conviction to demonstrate its cause and shape its musical effect.A most powerful urge to repeat is created by initiating a certainmovement whose starting and concluding points may be unequiv-ocally presumed by the listener, then to interrupt this movement atthe crucial moment-say, just before the concluding step. A tensionis thereby created which can be relaxed only by a repetition, thistime without interruption, running its full course to a satisfactoryconclusion. Before Schenker, such a phenomenon of tension (bar 8)would have been called a "half-cadence," i.e., onlv the bass voicewould have been considered in the explanation of ;he interruption.Schenker's theory has added the melodic, horizontal, factor. The"melody"-the fifth-span-demands its full course. The note d, atwhich the movement is interrupted, is a passing note. Just at themoment when this d is pressing toward its goal, supported by a Gin the bass voice, which transmutes it into a consonant fifth, thefifth of the dominant-chord, i t isarrested. The span isinterrupted. Ina wider sense, the melody, too, has been led to a half-cadence.Bars 9-16 show the completed fifth-span, supported in the bass b y

the arpeggiated chords of a C-cadence. This isthe Ursatz form of thispart of the composition. Schenker, in analogous cases,would use theterm "figurative Ursatr" form, because the part in question consti-tutes only one s tratum of the whole sonata. The Ursatz is graphicallyindicated by those half-notes which are connected by beams, aswell

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INTR.ODUCTION

as by numerals: the Arabic numerals with carets indicating the dia-tonic notes, the Roman numerals indicating the notes sustaining theharmony in its Auskomponierung in the basic steps: I-V-1.The graphic presentation of the antecedent (bars 1-8) shows some

detail . In the first four bars, the third-span g-e isindicated by quar-ter-notes connected by beams, in contrast to the half-notes, which be-long to a higher stratum. Every note of the third-span, in turn, isprovided with a newly unfolding third-interval (seethe slurs in thegraphic presentation). The third and last unfolding introduces a d,passing within the lowest stratum. The whole process is accompaniedby bass arpeggios of a lower stratum. In bar 2, the g leads the uppervoice into a passing dominant; the d in the upper voice (bar 3, thirdbeat) is transmuted by the bass G (divider) into a consonance. Thef in the upper voice first appears as consonant in bar 5 but returns inthe next bar as dissonant, as in a prepared suspension in syncopatedcounterpoint.Example Al (Appendix II) demonstrates the effects ofUrsatz andstrat!ficatron on a whole piece of composition. It would have beentempting to present here a larger work, say, a sonata or a fugue.This, however, would exceed the scope of this Introduction, whichrepresents merely an attempt to facili tate the understanding of thisbook and to present a summary outline of Schenker's later develop-ment.A masterpiece of music is, in Schenker's conception, the fulfilment

of a primary musical event which is discernible in the background.The process of composition means the foreground realization of thisevent. This explains the boundless wealth and power of the mastersand the improvisational effects in which their works abound. Thecomposer, his balance centered unconsciously or instinctively in theUrsatz, can wander unerringly, l ike a somnambulist, and span anydistance and bridge any gap, no matter what the dimension of hiswork.With the Ursatz concept, the circle of Schenker's system isclosed:

it opened, in Harmony , with the quest for a pattern in Nature formusic as art. It closed with the discovery of the primordial chordand its artistic re-creation through the process of Auskomponierung .

CmCAGO 19S4 OSWALD JONASxxiv

In contrast to other books on music theory, conceived, one mightsay, for their own sake and apart from art, the aim of this book is tobuild a real and practicable bridge from composition to theory. Ifthisaim is good and worth while and if the way we chose to reach it iswell chosen, this book should be self-explanatory, and the ad-vantages of its approach should result clearly even without a preludeof diffuse preannouncements. There are some points, however,which need preliminary clarification.The critique of current methods of teaching as offered in 90 ff

implies two consequences. First, all exercises in voice-leading,which so far have constituted the main material of textbooks, had tobe banned from the teaching of harmony and relegated to that ofcounterpoint. Second, it became impossible, accordingly, to followthe standard practice of dividing the book into a theoretical and apractical part. In contrast to the theory of counterpoint, the theory ofharmony presents itself to me asa purely spiri tual universe, a systemof ideally moving forces, born of Nature or of art. If in a sphere soabstract any division in the usual sense could be imposed at all, ithad to be drawn along somewhat different lines. The theoretical partnow presents, so to speak, all matters of topographical orientation,such as tonal systems, intervals, triads and other chords, etc. Thepractical part, on the other hand, describes their functioning, themoving forces of the primordial ideas of music, such asprogressionof harmonic steps, chromatic alteration and modulation, etc.I should like to stress in particular the biological factor in the life

of tones.We should get used to the idea that tones have lives of theirown, more independent of the artist's pen in their vitality than onewould dare to believe.This whole work is guided by this exalted concept of the vitality

of tones in the reality of the work of art. Every verbally abstractedexperience or proposition is therefore illustrated, without exception


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throughout the work, by a living example from the great mastersthemselves.I will refer several t imes ( 84and passrm) to a work on counter-

point which is in preparation. There are three factors which mighthave induced me to present, first ofall. a theory of voice-leading andonly subsequently the more abstract theory of harmony. A logicaland natural disposition of the whole material mediated in favor ofsuch an order. supported, second, by the historical priority ofcounterpoint over harmony and, third, by my own concept of therelation between the two as it will result from these pages. Never-theless, I thought it preferable to begin with the harmony. Any de-lay, however small, in initiating the needed reforms seemed to meto be counterindicated by the very factors just enumerated. For thatsame reason I shall also hasten the publication of a supplement, underthe title, "On the Decadence of the Art of Composing Music: ATechnical-critical Analysis," which should reinforce the ideas hereexpressed and facilitate their practical utilization. And only thenshall I proceed with the publication of my Psy c ho lo g y o j C o ume rp o ir u.

In closing, a few words ought to be said to clarify the meaning of 9, which rejects the derivation of the minor triad from the seriesof undertones. From this theory Riemann quite legitimately drewthe conclusion that, in reality, the root of the minor triad is to beassumed to lie above, whereas the bass voice represents the fifth.This very conclusion leads the whole theory a d a b su r dum . For if art,in its becoming and being, is to be explained by theory and notvice versa, theory has to accept the fact that composers at all timeshave followed the principle of basing harmonic progression on theroots in the bass voice and that they have proceeded to do so withequal verve in both major and minor modes and without any regardfor the occurrence of minor triads. This argument, taken from apurely artistic angle, would stand, even if the acoustic phenomenonof the undertone series were proved more scientifically than is thecase today. The problem, ill essence, is the following: Consideringthat at least two components of the minor triad-the root and thefifth-are in no way contrary to the series of overtones; consideringalso that. from an artistic and psychological angle, the treatment of

xxvi

the minor triad isquite analogous to that of the major triad, would itseem advisable, in view of such determining factors, to remove theminor triad from so firm a concept as the overtone series, merelyon account of its minor third, and to force it into the much moredubious concept of the undertone series? In this caseall three com-ponents of the minor triad would have to stand on the shaky groundof a hypothesis, and, furthermore, the assumption of the root in theupper voice would violate the artist's instinct and practice of har-monic-step progression.

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PART ITHEORETICAL APPLICATION

D I VI S ION IT on al S yste ms: T he ir O rig in a nd D iff ere ntia tio n w ith

R eg ar d t o P osi ti on a nd P ur it y

T h e O r ig in oj T on al S y st em s

4555

S E eTION IITheD!fJerent iat iot l T o na l S ys te m w it h R e g ar d

and Pu r i tyI TRAN,P05ITIOKSII COMBINATIONS

778,

D I V I S ION I I

T he or y o f I nte rv al s a nd H ar mo ni es

Theory o f Imervo lsI THE CONSTRUCTION OF INTERVALS( 53--D3) 117II nmMEANING O


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TABLE Of CONTBNTS

D IV I S ION I I

T he or y o f th e P ro gr es sio n ~fKeysSECTION I

Theory oj Modula t ionI MODULATION BY CHANGING THE MEANING OF A SCALE-STJJ P ( [71,6) 321I I MODULATION BY CHROMATIC CHANGE ( 177/8) 330III MODULATION BY ENHARMONIC CHANGE ( 179-80) 332

S ECTIO N I I

T he T he or y o f M o du /a tit lg a nd P re lu d iz itl g ( 181-82)

I APPENDIX TO "HARMONY"

I I APPENDIX TO INTRODUCfION

xxxii

34 3

34935 3Jj

THEORETICALAPPLICATION


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HARMONY

Man repeats himself in man; tree in tree. In other words, anycreature repeats itself in its 0\V11 kind, and only in its own kind; andby this repetition the concept "man" or the concept "tree" isforme~.Thus a series of tones becomes an individual in the world of mUSIConly by repeating itself in its own kind; and, as in nature in general,so music manifests a procreative urge, which initiates this process ofrepetition.We should get accustomed to seeing tones as creatures. Weshould learn to assume in them biological urges" as they characterizeliving beings. We are faced, then, with the following equation:In Nature: procreative urge -+ repetition ___,.ndividual kind;

THE NATURAL TONAL SYSTEM (MAJOR)In music, analogously: procreative urge ___,.epetition ___,.ndivid-

ual motif.The musical image created by repetit ion need not be, in all cases,a painstakingly exact reproduction of the original series of tones.Even freer forms of repetition and imitation, including manifoldlittle contrasts, will not cancel the magical effects of association.It should be added, furthermore, that not only the melody but

the other elements of music as well (e.g., rhythm, harmony, etc.)may contribute to the associative effect of more or lessexact repeti-tion and thus to delimiting the individualities of various patterns.Exampl e 3. Beethoven, Piano Sonata, op. 90, First Movement:

! ~ : f f f f : ~ : ' I T : IThe upbeat to the first bar (marked by the first bracket) consistsof an eighth-note followed by an eighth-rest. Under the secondbracket this upbeat is repeated without change; under the thirdand fourth brackets, however, the upbeat certain contrastingchanges: the eighth-note is transformed into a full quarter-note,emphasized, in its fourth recurrence, even b y a por tamento .Exampl e 4. Beethoven, Piano Sonata, op. 90, Last Movement:

!!~~Ift.1~ h ,t~ ,


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Example 8. Haydn, Piano Sonata, GMinor, No. 44:

1~~i:'::I~::~! : : : ; : ~ , : = :The next problem was to discover the conditions under which a

deviation from the strict rule of immediate repetition could be riskedwithout jeopardizing the effects of association.If there are, for ex-ample, two members, ar and az, associativelylinked, it is possibletoinsert all extraneous member b, which, so to speak, increases thetension and thereby emphasizes the effect of the repetition. Thus,apparently, there arisesa three-part form. It should be stressed: "ap-parently." for a true three-part form should consist of three mem-bers, viz., arbic-r-a form whose application to music is simplyunthinkable and isprobably ruled out forever.The form ar :braa, onthe other hand, which seems to be the only three-part form ap-

THE NATURAL TONAL SYSTEM (MAJOR)

plicablc to music, can be reduced ideally to the two-part form,ar :ba, on which it is originally founded. The inserted member b,however, whose function it is to delay the repetition, must be socharacterized that it should not require, in its turn, a repetition for itsclarification. For, in that case,we would obtain the form ar : br :az :ba, in other words, a four-part form with an underlying two-partbasis.This isthe real meaning of the three-part or so-called l i e d form. If

we now rise from the consideration of such structural details to thatof larger formal units, we find that this same three-part structurear :b: az constitutes the foundation alsoof the fugue, with its articu-lation into exposition, modulation, and fmal development; or of thesonata, with its exposition, development, and recapitulation.'Even where an artist succeedsin associatinghis ideasor images in a

still more complicated way, still the principle of repetition can berecognized asunderlying even the most daring feats.Thus music hasrisen to the ranks of art. By its own means and without direct aidfrom nature," it has reached a degree of sublimity on which it cancompete with the other arts, supported by direct associationsof ideasfrom Nature.


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the concurrence of several quite heterogeneous elements in bringingabout a certain result.16To return to our problem of acoustics: it should be clear now

what ismeant by my observation that it may be a wonderful, strange,and inexplicably mysterious fact, but a fact, nevertheless, that the earcan penetrate only up to the fifth division."?

12. T he P re vale nc e of th e Perfect FifthThe first consequence to be drawn from our new approach is thatthe fifth, g, ismore powerful than the third, e' , asthe former, result-ing from the third division, precedes the latter, which results fromthe fifth division. It isnot due to chance, therefore, but in accordancewith Nature's prescription, if the artist always has felt, and still feels,the perfect fifth to be more potent than the third. The fifth enjoysamong the overtones, the right of primogeniture, so to speak. Itconstitutes for the artist a unit by which to measure what he hears.The fifth is, to use another metaphor, the yardstick of the composer.

13. The Major Triad in Nature and in Our SystemOur major triad is founded on these two tones, the fifth and thethird. It should be noted, however, that Nature's version of themajor triad ismore ample than the one usually applied in music. Thenatural version of the major triad is shown in Example 16.Example 16 (20): _ _ _ _ _ _ _ h t _ THIRD~FIFTH

1.:& FUN DAM KNTALIt is perhaps not without interest to note that the opening of the

first movement of Beethoven's Ninth Symphony reveals this piece ofNature, albeit with a concealed third, C-sharp. Another illustrationisoffered, in the same symphony, at the beginning of the Alla marciain the lastmovement. Here the third, to beperformed by the clarinet,

,6. Thesclf-stylcd"reformers"ofotlrsystemofmtl,iCl.lnotationprobabIyncvcrthoughtof that.


is assigned the high place destined for it by Nature; the fifth is im-plicit.In the concluding passage of Chopin's Prelude No. 23, on the other

hand, almost at the end, a seventh-chord is built on the tonic by theaddition of the seventh c - H a r . Instead of hearing in this chord a trueseventh-chord, I feel inclined to interpret i t as a poetic-visionary at-tempt to offer the association of the seventh overtone+the only at-tempt, to the best of my knowledge."Example 17(21). Chopin, Prelude, op. 28, No.23:

Modsrato!::::r;j~::.ri\ 1 ~ : i : : J ~ : : I : : I ;. . . . .)It is, however, one of the obvious consequences of human limi-

tation that, in so far aspractical art is concerned, we have no furtheruse for this ample version of the major third. Having bumped againstour first l imitation and having receded from the foreclosed sphere ofthe seventh overtone, we now recede, for the same reason, from that

might rather in Chopin's esCl.pc. the concludingsi tt lat ionmnchl ike the one fo und i n measu re f z, Rather than run fora second time thronghthe consequence , o f thi s s imat ion. Chopin . through thi ,d if ft lsea lte rna tive , com", to an,b ruptend . Schenker's pos thumom work. inc idcn taUy. con ta ins an ear ly . tnst s tl cci nct no te t o t his

r=es= ~ "Condmion:-Aho considering the earlier I/V-!a,t attempt'"

("SchIll": allchwegender fruherenI/V-letzterVcr'tlch'"j.1


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17. The Discovery as a Consequenceof Inversion: Adoption into System

This inversion of the fdihs, leading in a fivefold descent down tothe tonic, entailed a new consequence: The artist, face to face withthe tonic, felt an urge to apply inversion once more, searching, so tospeak, for the ancestor of this tonic with its stately retinue of tones.Thus he discovered the subdominant fifth F, which represents,metaphorically speaking, a piece of the past history of the tonic C.As compositional practice confirmed the good artistic effect of

inversion in general, the inversion from the tonic to the subdominantfifth in particular became well-established. There thus arose theneed of assigning to this tone a place in the tonal system.To illustrate further the effect of this particular inversion, wc

shall quote here some passages from J . S. Bach. He had a particularpredilection for this method. It was almost a rule for him to anchorhis tonic, right at the outset, by quoting, first of all , the subdominantand then the dominant fifth, and only then to proceed with hisexposition."Example 31 (35).J. S. Bach, W e ll -t em p er ed C la vi er , I, Prelude, E-FlatMinor:

~ I

VII I(V)

Example 32 (37). J . S. Bach, Organ Prelude, E Minor:

l l ! : C : g l f 1 ! ~ 1l l ~ : t ~ n c r = 1 1 !Example 33 (38).23J. S. Bach, Parti ta, D Major, NO.4 , Sarabande:l ~ : : ' l l l ! = b jM ; : 1

IV VThe slstem of the tone C, then, represents a community consisting

of that root tone and five other root tones whose locations are deter-mined by the rising fifth-relationship. One more root tone, the sub-dominant fifth, was added to this community and represents, so tospeak, its link with the past. The whole system, accordingly, takesthe following form:Emmpl e 3 4 ( J9 )'

2, < , I I. U PPER F IFTH, - .,II IIt IITONICS UB D O M IN A NT

39


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THE ARTIFICIAL TONAL SYSTEM (MINOR)


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This analysis has three corollaries. First, it proves the inner necessityand inevitabili ty of the principles summarized in the opening para-graph of this section; second, it proves that the principle of stepprogression in the minor mode is not at all original but has beentransferred artificially, nay, forcibly, from the major mode, out ofthis necessity. And it proves, third. that for this very reason thenatural major mode is no doubt superior to the minor mode.

22. C on tra sts b etw ee n M ajo r a nd M in or M od esIf we now compare the relations of the tones in the minor with

those of the major mode, even a superficial glance will discover adiscrepancy with regard to the third, sixth, and seventh intervals,

48

which are major in the major (Ionian) and minor in the minor(Aeolian) mode.Exampl e 39 (44):

This difference gives rise to a further one, in that, contrary to themajor mode, the minor mode shows minor triads on the dominantand subdominant as well as on the tonic.Example 4' (45):

It isthese differences which oppose the major and minor modes asveritable antitheses. 23 T he M e lo dic a nd M otiv ic R ea so ns fo r T his A rtific ia l C on tra stAny attempt to derive even as much as the first foundation of this

system, i.c., the minor triad itself, from Nature, i .e., from the over-tone series,would be more than futile. But even ifwe were to assumethat the minor triad really rests on the proportions 10: 12: 15 of theovertone series, which, it must be granted, produces these partials inthis sequence, yet the system asa whole could not be explained with-out the help of artificial elements-disregarding, for argument'ssake, the fact that those overtones, owing to their remoteness, havelittle effect on our ear, even though the number of divisions by whichthey are created is, in each case, the multiple of a prime number(I, 3, 5). We still would have to explain why the artists chose asystem which. not only on the tonic, but also on the dominant andsubdominant, offers minor triads with minor thirds.

49

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The explanation becomes much easier if artistic intention ratherthan Nature herself is credited with the origin of the minor mode.Only melodic, i .e., motivic, reasons could have induced the artist

to create, artificially, the minor triad as the foundation of the system;and in my opinion it was merely the contrast to the major triad thatincited him to fashion his melos accordingly.The following example may elucidate how these same motivic

considerations, which, first of all, led to the creation of the minortriad itself and subsequently encouraged the formation of minortriads also on the dominant and the subdominant, thus completingthe minor mode in its present shape.Exampl e 41 (46). J . S. Bach, We l l -t emp e re d C i a vi e r, I, Fugue, DMinor:' b , J ] J J ] I J a J ~ . 1 I JThe subject, thus put down, ispossessed of an inherent urge toward

the dominant to complete its nearest and strongest stage of develop-ment. It is true that such a development would leave the composerfree to conceive quite naturally a major triad on the dominant, A,and to answer the subject, accordingly, in the D major key.Exampl e 42 (47):

@ & , r ~ ~ " , r r I " F j . J P m I ,Bach's instinct, however, urging him to preserve, at least for the

time being, the minor character of his subject, rejects all other con-siderations. During the epoch of polyphonic composition it seemednatural to the artist to contrast his subject, at least during the firstpart of the fugue, merely by transposing it by a fifth, i.e., to answerit in the key of the dominant while maintaining its identity in allother respects. To complicate this contrast further by subjecting histheme to essential changes with regard to intervals and harmonieswould have seemed to him much less natural. At any rate, he sensedthat both processes had different effects; he recognized dearly whichof the two was more natural, and he preferred to conform to Nature

50

by keeping the exposition of his fugue clear of elements which wouldfind their place more appropriately in a later phase. Thus the exposi-t ion remained exposition, the development was what it should havebeen: each part was in its right place and carried its right meaning.Thus the fugue attained its functional structure and its own style.Exigencies of motivic development and exposition have brought a

remedy not only in the case of the fugue but also in other forms,including those of free composition. Such a remedy was found inconceiving the dominant of the Aeolian system as a minor triad,just like its tonic."For motivic purposes it was enticing for the artist to have at his

disposal three analogous minor triads on the tonic, the dominant,and the subdominant. As already indicated, the collective artisticinstinct could not, and cannot, be deterred from this concept in prac-tice. How it could have come to pass, on the other hand, that thetheoreticians are still so helpless vis-a-vis the minor mode-recogniz-ing it at one time in this guise:

p ' e 10at another, in that:

10and, at still another, in a mixture of both:Exampl e 45 (50):

-we shall have occasion to examine later on. We shall also have tocome back to the secondary question: Why arc the theoreticians so

f,. Cf.n.l.]5

THE ARTli'ICIAL TONAL SYSTEM (MINOR)


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confused when they try to derive from Nature this system whichthey themselves so arbitrarily creatcdi"

24. The A rtific ia l Syste m as the Claim of the A rtistIn this sense, the minor mode springs from the originality of the

artist, whereas the sources, at least, of the major mode flow, so tospeak, spontaneously from Nature. 25. T he O cc urre nc e of the M ina r M ad e am ang P rim itiv e Pe ople s

D oe s N ot D isp ro ve Its A rt if ic ia l C ha ra cte rOne may ask whether the above characterization of the minor

mode isnot bel ied by the well-known fact that many primitive peo-ples seem to take to the minor much more easily than to the majormode.' If the minor mode occurs among primitive peoples andseems even better developed among them than the major and pre-ferred to the latter, this fact alone-so one might argue-should suf-fice to prove that the minor mode, too-that is, its perfect fifth andminor third-must be somehow rooted in Nature, and perhaps evenmore solidly so than the I:3 :5 of the major mode.It is often assumed that savage primitive peoples are closer to

Nature and have firsthand, and therefore more reliable, informationregarding her intent ions than do the more cultivated peoples. This

[4. C 42 and 45.][5 . It might be adde d here that the minor mode undoubtedly isto bec re di te dto~ea rtist

anddenvedfromhisexpenence--apointsufficientiystre"cdbySchenkerhim


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Example 48 (55). Beethoven, Piano Sonata, op. 7, Andante:THE OTHER SYSTEMS (CHURCH MODES)

should be noted that, accordingly, i t is not the two B's by themselves


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t H I 1 r - - r - p u1h v 2 ~ IApplied to our case, this example dearly indicates that, in progress-ing from the II step to the v, we, too, may use a chrol11ati~ B onthe II step of F major. This will have the result of disguising, if onlytemporarily, the V step asa tonic, and it issubsequently all the moreeffective to fall to the real tonic of F major via that alleged I in Cmajor, which, in reality, was merely the V step in F major.In this respect there isthus no difference at all between the above-

quoted, allegedly Lydian, composition by Beethoven and the generaltreatment of the major or minor modes-in this particular case,ofF major. The only difference isthat we usually have the chromaticB followed by a diatonic B-flat-the root of the subdominant chord-which emphasizes the character of our key {cf I]). In otherwords, if we considered the piece asa regular F major composition,we would still use the chromatic B, there being no reason for scorn-ing a chromatic step progression; but we would follow it up with adiatonic B-flat. Thus, for example:Example 49 (56):

!~~n~3 vb7 VIBut for the sake of maintaining the fiction of the Lydian mode,

Beethoven stubbornly abstained from using this B-flat in either ofthe two places where it would have been so gratifying to our ear. It

64

which give the composition its allegedly Lydian character-as wehave seen, these B' s are of a trivial chromatic nature, and it is notnecessary to trace them back to a Lydian origin-but it is rather theomission of B-flat in the following harmonics which distinguishesthis piece from other classic compositions. Most listeners are par-ticularly sensitive to this lack of B-flat, because the opportunities forintroducing it are sovery scarce; the second and third part, and evenfour measures of the fourth part, are already plainly inC major, thusoffering no possibili ty atall ofusing any B-flat. But even if! grant, inaccordance with most listeners, that their demand for a B-flat, asanelement of the subdominant chord, isjustified, i t does not follow inany way that the composition must be considered as Lydian ratherthan as in F major, just because there happen to be B's on the II stepon two occasions. If it is erroneous to exclude F major on accountof a chromatic B on the II step, the lack of the B-flat by itself cannotcancel the F major character of the composition either, consideringthat this lack is preconceived and forcibly maintained in a com-position where so many other factors indicate F major as the basickey. Besides, is not the gap opened by the lacking B-flat-the sub-dominant-at least partially filled by this very II step, only with achromatic B (cf II9 ff.)? Apart from the modulation and theinterrupted cadence of the first part, one should also consider the keyof the second subject: D major! Does not this key prove the concep-tion of P major in the preceding section?It is true that several other factors contribute to arousing in the

listener the impression of an old church mode. Consider, for ex-ample, the chorale-like progression of the half-notes, the consistentpreference given to triads, which, in most cases,even appear in theirroot posit ions (there are only very few harmonic inversions), and,especially, the strict avoidance of any chromatic progression, forwhich our ear has developed such an urgent demand. If the listenerremembers that the old church modes, l ikewise, lacked the B-flat, hewill immediately rally to the composer's desire in attributing to thecomposition a true Lydian mode. All this iseasily understood, as italso can be understood that Beethoven himself believed in his

65


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HARMONY

insist: None of the B 's occurring in this beautiful chorale is to beTHE OTHER SYSTEMS (CHURCH MODES)

ten in the church modes, spontaneously came out asmajor or minor


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derived, asBrahms believed, from the Dorian scale assuch; we mustsubstitute, rather, the following explanations.The first bars constitute, basically, the A minor scale; hence the B

isjustified merely in consideration of that key. It istrue that, with theC-sharp of measure 2, the composition changes to D minor. If in thisD minor the IV step ispresented with the third B-natural rather thanwith the diatonic third B-fiat, the idea of D minor remains neverthe-less alive in the listener. More than that, we recognize here the veryB-natural which we employ in our daily practice in D~ {cf 38 ff.) and, to boot, in this same sequence, IV'LV~3, withoutsacrificing in any way the identity of the D minor! That Brahmsabstains from using the H-flat in the subsequent development (meas-ures 10-I3) issimply explained by the turn the composition istakingtoward C major.It should be noted, on the other hand-s-if we now pay some atten-tion to the seventh of the Dorian system-crhat Brahms, without anyqualms, uses the Cvsharp asthe third of his V [measures 2,3,4, etc.)whenever he aims at the conclusion V-Ion D. Could anyone claimthe C-sharp to be a legitimate part of the Dorian system, strictlyspeaking? The answer must be No. In defense ofBrahm~, one mightrecall that, even at the time of the strictest orthodoxy WIth regard tothe church modes, such a C-sharp often was imposed on the Doriansystem. This, however, merely proves, in my opinion, that theDorian system never led an independent and wholly natural exist-ence, any more than did the Phrygian, Lydian, and Mixolydia~lsystems, and that our ancestors were already forced to remedy thisunnaturalness by sharping and flatt ing certain individual diatonictones. It proves, in other words, that events took the course they hadto take.Thus this example, too, demonstrates how music itself holds onto the minor mode even where the artist's intention aims at theDorian system.I have quoted these two rather recent examples merely t.o provea much older truth: Even in olden times, when the faith 111 thosetheories held strong, many works, consciously or intentionally writ-

68

(Ionian or Aeolian system), This happened whenever the genius ofthe artist was so strong that Music could use him as a medium, so tospeak, without his knowledge and quite spontaneously, while otherworks, perhaps the vast majority, were born crippled from crippledtheories, for the lack of that power which, standing behind the artist,might have saved him, despite his rheoretico-practical error.'

3 o. R ea so ns f or th e L on g P er se ve ra nc e a nd F in al D is in te gr atio nof the C hu rc h M od es

One may ask why those unnatural systems were not thrown over-board much sooner. The answer is not hard to find.First of all, they were backed up by the authority of the church,

which had created them. This authority alone was sufficient, duringthat age, to hold its own.Second, developments had not yet begun to emerge from the fog

of experimentation, and the instinct of the artist was too becloudedas yet even to suspect the all-comprehensive significance of theIonian and Aeolian modes.To these factors should be added a third one-not to be under-


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THE OTHER SYSTEMS (CHURCH MODES)

How are these examples to be explained?


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Shall we try here to muddle through with the notion of modula-tion (measures 5 and 6)? But what is to be done about the unques-tionable fact that the basic key, D major, turns up again in measure7? If it is thus impossible to get through on the assumption of amodulation, what explanation could be offered for a C major triad(measure 5 ) and an E-flat major triad (measure 6) ina composition inDmajor?To quote one more example: How is the emergence of the V

chord ofE-flat major to be explained in A minor?Example 56 (63). Schubert , "Deutsche Tanze," op. 33, No.

74

Alas! we do not explain them at all. We do not even hear them.And if, occasionally, a sensitive listener turns up, whom such passagesstrike as odd and who asks for explanations, he will be fed a com-fortable answer: All those instances represent unaccountable excep-tions; l icenses which men of genius take occasionally, etc. "Excep-tions?!" "Exceptions from what?" I should like to ask. Isit true thatthe alleged "norm" of genius is established in manuals and lectures?Or is it not true, on the contrary, that our theory does not reach tothe level of even the most primitive problem raised by a piece ofart?If theory could reach but there, it would immediately understandthat those examples, far from constituting exceptions, derive fromthe normal, most normal, process of thought of any composer. Thereis something humorous in the assertion of some scholars, as, for ex-ample, Spitta, that it was only Brahms, or some very few talents ofmore or less his caliber, who succeeded in maintaining a spiritualaffinity with the old modes and were able to make practical use ofthem, by which they manifested their greatness. Fa r from it! It wasnot Brahms alone who thought and wrote this way, and it certainlywas not this abili ty that accounts for his greatness. For we all writethis way, and our ancestors would recognize with great pleasuretheir Dorian, Phrygian, Mixolydian, etc., systems in our composi-tions.Faced with the examples quoted above, they would exclaim: "Is

not this, basically, the very phenomenon we cultivated in the Phryg-ian mode?6 The half-tone above the tonic as we find it herc-whether asa passing note in the melody, asin Wagner (Example 51),Brahms (Example 52), Chopin (Example 53), or asharmonic step,asin the excerpts from Schumann, Lisee, or Schubert-is it not pro-vided for by our Phrygian system? erc.>"They could not understand at all how it could be claimed that we

dropped their systems, since, in their opinion, we obviously are sti llusing them in our practice.Now what would be our answer to such questioning? Most of us

would be so baffled by being told, all of a sudden, that we are still16. Cf. n.H,rega rdi ng th ei nt npretat iono[th ePh ry g;onIli nt hemi normode (50l- 1

75

writing in the Dorian, Phrygian, or Mixolydian mode that, in our


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surprise, we would not find a prompt answer.I myself find it not difficult to answer, and I shall not hesitate to

speak up. When we shall discuss, later on, the combination of themajor and minor modes, to which discussion we shall dedicate aseparate chapter, we shall discover two of the old systems asproductsof this combination. Note well: merely asproducts of this combina-tion. In the meantime I wish to restrict my observations to the follow-ing: The artists' intuition in dropping all the old modes with theexception of our major and minor was perfectly justified. Nature'ssecret hints, reinforced by experiences, ever growing in scope andmeaning, pleaded with the artist in favor of major and minor to theexclusion of the other modes. And even ifhe occasionally did thingswhich he could not explain with the major or minor modes alone,his basic instinct for these two modes remained unswerving, never-theless. Indeed, who would be tempted to erect new systems merelyfor the sake of some particular tnrn and despite the fact that his in-stinct isperfectly at peace? Isit not true that a system must be strongenough to explain, without exception, all phenomena within itsrange? And is not that system always to be considered the betterone which covers more individual cases?The artist's instinct can beinterpreted accordingly: "If the major and minor modes alone (un-derstood correctly, of course) are adequate to evoke the charm ofthe so-called Dorian and Mixolydian modes, why should we burdenourselves with still more independent systems?" It was quite logical,hence, that matters went as they did, even though the reduction ofthose many systems took place, for the time being, in the instinct ofthe artist only, without being reflected in the theoretical l iterature.

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SECTION II

T he D iffe re ntia tio n o f th e T on al S yste m w ithR eg ar d t o P osi ti on a nd P u ri ty

CHAPTER [TRANSPOSITIONS

3 I. T he P rin cip le o f F if th -R el atio ns hip s A pp lie d to Transposit ionsEvery system can be transposed, without any trouble, from its

root .tone ~oany other tone. All we have to do is imitate exactly therelatl?nshlp between the tones as observed in the respective systems.Keeping in mind the principle of development or evolution in the~rection of the rising fifths and the principle of inversion in the~Irecti?n of descending fifths, we will notice at once that transposi-~~~t~s~lllfollow most naturally the directions of the rising or falling

32. S ha rp in g a nd F l at ti ngIf the Ionian system is to be transposed to the first fifth in rising

or.der, C : al1~ i f the imitation of the model is to be complete andfaithful, I t will be necessary to raise the seventh, F, to F-sharp.Example 57 (64):$ . 1 i F rLike,",:isewe are faced with the necessity of again sharping the

~eve.n~hIfwe want to transpose the major system to the second fifth:n nstng order, i.e., D. This sharp hits the tone C, transforming itInto C-sharp.Example 58 (65):, J ~ t

77

In the inverse direction of descending fifths, the transposition ofrRANSPoSITIONS

Example 61 (68):


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the system results in the flatting of whatever happens to be thefourth tone.Example 59 (66):- $ J A' r

r 5 ' 33. T he A na log y be tw ee n the O rd er o f F ifths a nd th e

Orde r ~fSha rp s a nd F la tsAs these examples demonstrate, the F-sharp isintroduced prior to

the Ccsharp, the Ii-flat prior to the Eflat , etc. This order inevitablyfollows from the faithful imitation of the intervals of the major sys-tem. Hence the axiom, the importance of which cannot be over-emphasized: We may encounter an F-sharp without a C-sharp, aH-flat without an E-flat; but never the other way round: there isno C-sharp without an F-sharp, no E-flat without a B-flat. Thus thefirst fif th in rising order has introduced one sharp; the second fifth,two sharps; the first fif th in descending order, one flat; the second,two. The transposition to the third fifth in rising order will intro-duce a third sharp; the fourth, a fourth the fifth, a fifth one;etc. In other words, the re is an be twe en the o rd iHalnumber or de scend illg fifthsharp it.E xam ple 60 (67 ):, - . .4

78

,It will be seen, for example, that A-sharp is the fifth sharp to ap-

pear and points to the fifth fifth in rising order, i.e., B major. It fol-lows, furthermore, that, whenever the tone A-sharp occurs, the fourpreceding sharps are at once to be taken for granted; likewise, that theordinal number 5 can never belong to any sharp but A-sharp.

34. Do ub le -S ha rp s a ll d D o ub le -F l at sIf we continue our climb from fifth to fifth, we will soon be faced

with the necessity of raising the single-sharps, which have continuedto accrue on whatever note happened to occupy the seventh place, toooubre-snarps. We see that, accordingly, this will give rise to a se-

with double-sharps which will correspond to the se-an the rising fifth 1-7, with single-sharps.

J:xample 62 (69):,I" I"To summarize, we obtain the following correspondences:

Example 63 (70):, 7I I, i I ' " '10 II 12 13 "79

The same phenomenon is to be observed with regard to the flatsaccruing beyond the seventh fifth in descending order.

TR.ANSPOSITIONS

tribute to a truly artist ic insight into the functioning ofeven the mostminute passing or auxiliary notes (cf. 144).


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Example 64 (71):

, 2~e &0 i.. b e. . . ., !I. ii..& 1 f . b I i . > . . . . . . .~ 18 12 II 10J ii " ~&It will be seen that, beginning with C-sharp major [Ccsharpbeing the seventh fifth in rising order), the whole diatonic system ofC major has been raised by half a tone. Likewise, G-sharp major re-sults from raising the G major system by half a tone, and the samecorrespondence obtains between D-sharp major and D major, A-sharp major and A major, etc. The ordinal numbers 8~14can be re-placed, accordingly, if so desired, by the ordinal numbers II' pro-vided that key No. 8 is assumed to be half a tone higher than keyNo. 1. In fact, G-sharp major is the first key in the series of keyswith double sharps, which series begins with C-sharp major, i.e., theC major system raised by half a tone.This conception facil itates the process of taking one's bearings

with regard to transpositions. For example, whenever a G-double-sharp occurs, all one has to do is to think of G-sharp with its ordinalnumber 3 in the series of single-sharps. By way of A major, as thekey corresponding to the ordinal number 3, this thought will leadstraight to A-sharp major, which, in the series of keys with double-sharps, l ikewise bears the number 3 (or 10).The understanding of this straight correspondence between sharps

and double-sharps, on the one hand, and the respective keys, on theother, isinvaluable to the musician, not only when he istrying to findhis way quickly through the most complicated passages, but also fora far more important consideration. Such understanding will con-

go

The following excerpt from Chopin's Etude op. 25 No. 10, isquoted here as a paragon of overcomplicated notation (Example65a). Since all that is involved is a half-dose in B minor, it wouldhave been simpler, and probably more correct, to write this passageas shown in Example 65, b.Example 65 (72). Chopin, Etude, op. 25, No.a) b)

If Chopin, at the beginning of this same etude, writes F-double-sharp, Ccdouble-sharp , and A-double-sharp,Example 66 (73). Chopin, Etude, op. 25 No. 10:

i t isobvious, nevertheless, that we are not dealing here either with atrue G-sharp major or A-sharp major or B-sharp major.Jr isequallytrue, however, that the F-double-sharp, followed by G-sharp, mustbe understood to belong to Ocsharp major, strictly speaking. Thesetwo apparent contradictions are reconciled by the fact that the toneG-sharp itself, preceded by its own diatonic VII step, F-double-sharp, plays only a secondary rolc in this context, viz., that of a

8,

HARMONY

passing note between the tone F-sharp in measure I and the firstnote, B, in measure 5 of the etude.

TRANSPOSITIONS

adoption of this artifice. The tuning-down of the twelve fifths. andespecially the downward adjustment of each individual fifth by one-


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In the field of music it isparticularly important to pay attention toevery phenomenon, even the least significant, and to hear every de-tail, even the smallest, in its cause and effect. In so doing, we will dojustice not only to the artists but to music itself It is a peculiarity ofthe musical art that it gives effect to several laws simultaneously andthat, while one law may be stronger than the others and imposeitself more powerfully on our consciousness, such a law does notsilence the orher laws, which govern the smaller and more restrictedunits of tones. He who learns to hear wirh the ear of a true artist,grasping the coincidences in time and space of various musical eventsand their manifold separate causes,' will save himself the trouble ofhaving to hunt for new harmonics and to damar for new theories,as so many do today whenever they are faced with a more complexphenomenon which defies any single explanation.

35. T ra ns po si ti on i n t he Chunh ModesIt goes without saying that the method of transposition, aswe havejust studied it, applies equally to the old modes.

36. E q u al T em pe r am e n t'If we want to follow Nature, in her purity and infinity, and con-

tinue in our rise from fifth to fift

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