© 1979 James Lamb

A GRAPHIC ANALYSIS OF BRAHMS, OPUS 118, WITH AN

INTRODUCTION TO SCHENKERIAN THEORY

AND THE REDUCTION PROCESS

by

JAMES BOYD LAMB, B.M., M.A.

A DISSERTATION

IN

FINE ARTS

Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for

the Degree of

DOCTOR OF PHILOSOPHY

Approved

Accepted

December 197 9

ACKNOWLEDGNENT

The author wishes to ackno-'ledge the con t r ibu

t i ons of both time and thought from the members of

the committee, p a r t i c u l a r l y Cr. Harold Luce, who took

time from h i s administrat ivi^ du t ies to cha i r the

committee and to Dr. Lee Rigsby, who came out of

r e t i r emen t to a id in the completion of t h i s p r o j e c t -

Their va luable comments and support are deeply

apprec ia t ed . I t i s a d i f f i c u l t task to acknowledge

a l l those who have made t h i s p r o j e c t a r e a l i t y . I

must, however, c i t e the con t r ibu t ions of my o the r

p ro fe s so r s and e s p e c i a l l y my s tudents at Kansas

S t a t e Un ive r s i t y . I a l so express g r a t i t u d e to Gary

Cobb, who often served as a sounding board for the

refinement of many i d e a s . To Pat Stewart for her

t imely c l e r i c a l a s s i s t a n c e , I extend my thanks .

An.d, of course , I o f fer a very s p e c i a l , warm thanks

to ra>' wi fe , Lynn and daughter , Kathlyn, for t h e i r

c ea se l e s s unders tanding and p a t i e n c e , and many words

of encouragement during a time of frequent n e g l e c t .

i i

CONTENTS

ACKNOWLEDGMENT ii

I. INTRODUCTION 1

II. AN INTRODUCTION TO SCHENKERIAN THEORY 10

III. THE REDUCTION PROCESS 33

IV. A GRAPHIC ANALYSIS OF BRAHMS, OPUS 118 66

Glossary of Graphic Symbols 66

The Work as a Whole 68

No. 1, Intermezzo 69


No. 3, Ballade 94


No. 5, Romance 114


V. CONCLUSION 146

BIBLIOGRAPHY 151

1 1 1

CHAPTER I

INTRODUCTION

Analysis, in the words of Allen Forte in his Contemporary Tone

Structures, is "neither composition nor a method of teaching compo

sition; nor is it perception, or a way of learning to hear. It is

a systematic attempt to obtain significant information about a tonal

structure." Forte continues by stating that analysis is the work of

the theorist and that it "claims to deal more directly and rigorously

with music than does any other type of discursive treatment because

it is closer to music. [It] is part of music theory and has its roots

in the works of the medieval theorists, while music criticism and

many phases of musicology stem from literary criticism." What is to

be gained from analysis is increased understanding. Through this

increased understanding, more artistic interpretations in perfor

mances, more perceptive listening, and perhaps more inspired

creations will result.

Edward T. Cone exhibits a somewhat different:, but similar point

of view when he states in his article, "Analysis Today," that the

best analysis is the one that "recognizes various levels functioning

simultaneously, as when a tone resolves once in the immediate context

Allen Forte, Contemporary Tone Structures (New York: Columbia University Press, 1955), p. 2.

but tu rns out to have a d i f f e r e n t goal in the long run . " Cone,

recogniz ing more of a dependence on the e a r , con t inues .

The g r e a t e s t ana lys t s ( l i ke Schenker a t h is bes t ) are those with the keenest e a r s : t h e i r i n s i g h t s r evea l how a p iece of music should be heard, which in turn impl ies how i t should be p layed .^

An ana lys i s of any work of the n ine teen th century must be able

to deal with one aspect which i s of paramount impor tance- - tha t of

t o n a l i t y , which was perhaps the prime organizing fac to r of musical

uni ty in the music of t ha t century. The tonal events of a musical

work must be i n v e s t i g a t e d in r e l a t i o n to what precedes them and what

succeeds them and in r e l a t i o n to the whole.

A tona l musical work unfolds on various l e v e l s - - f o r m a l l y , the

whole, the movement, the s e c t i o n , the phrase , the motive. The

musician has always u t i l i z e d the concept of musical h i e r a r c h i c a l

s t r u c t u r e s , as depic ted in the diagram of Figure 1.

Tonal r e l a t i o n s h i p s e x i s t in h i e r a r c h i c order as well as formal

r e l a t i o n s h i p s . This concept of h i e r a r c h i c s t r u c t u r e or leve led

s t r u c t u r e , der ives preeminent ly from the a n a l y t i c a l approaches of

Heinrich Schenker (1868-1955). Over a per iod of more than t h i r t y

years he formulated an approach whicn has r evo lu t ion i zed the f i e l d of

musical a n a l y s i s . He i s perhaps the most s i g n i f i c a n t t h e o r i s t of the

1

"Edward T. Cone, "Analysis Today," Musical Qua r t e r l y , 4b, No. 2 (Apri l 1960), p . 178.

Edward T. Cone, " A n a l y s i s , " p . 174.

entire composition r

movement

section r

phrase groups r

phrase

motive 1 1

notes

Figure 1. Formal hierarchic structure.

twentieth century. Some evidence of his stature and influence lies in

the following statements (some quite lengthy, but pertinent) by many

of the leaders in the field.

He has been the first modern theorist to find out how the imagination of a composer works, and to differentiate between the raw material itself and the consummate art that turns this raw material into a great masterpiece. For some of us at least, Schenker's work has revolutionized the whole conception of music as art.^

In the past thirty years or so, we have witnessed the beginning of a revolution in the theory and analysis of tonal music . . . there seems to be a recognition that many of the concepcs and methods commonly employed are seriously inadequate. Dissatisfaction with the misleading results of the old descriptive procedures—the naive associations inherent in the Roman-numeral analysis of harmonic function, the lifelessness of symbolizing form by letters or numbers (ABA, 4-1-4), the trivial results

4 Adelle Katz, "Heinrich Schenker's Method of Analysis,"

Musical Quarterly, 21 (1935), p. 328.

of analyzing melodic "climax" according to curvilinear graphs (symmetrical vs. skewed shapes, etc.)—has resulted in a growing appreciation of the work of Heinrich Schenker. . . . His recognition of the importance of harmonic process in tonal music, his symbolization of it through the formulation of the Ursatz and the Urlinie, and particularly his concept of harmonic transformations on various levels all clearly remain among the most consequential achievements of music theory in this century. . . . In our time only Schenker can claim to have created an entirely new system of analysis. . . . The importance allotted Schenker's theory and the enthusiasm surrounding his work seem justified.^

Some writers go so far as to designate his approach as the mainstream;

"Of the numerous analytical systems now applied to music, none has

gained more universal recognition than the Schenkerian approach."

Heinrich Schenker's theoretical work was completed as long ago as 1935, with the posthumous publication of Per freie Satz, but only in the last decade or so has its influence grown to the extent that it must be considered the mainstream of musical analysis. . . the hegemony of Schenkerian analysis is virtually total in the current world of the music theorist, certainly for tonal music and often for other repertories as well; it seems to be an idea whose time has finally come.

Cogan and Escot also recognize Schenker as one of the most influential

of twentieth-century theorists.

Eugene Narmour, Beyond Schenkerism: the Need for Alternatives in Music Analysis (Chicago: University of Chicago Press, 1977), p. 1,

c Charles M. Joseph, rev. of Layer Analysis by Gerald Warfield,

The American Music Teacher, Feb.-March 1979, p. 47.

Ruth A. Solie, rev. of Beyond Schenkerism by Eugene Narmour, Notes, 34 (1977), p. 857.

The Austrian theor i s t Heinrich Schenker and his followers revolutionized musician's [sic] views by i l l u s t r a t i n g in many elegant analyses the l inear motion in eighteenth and nineteenth century music (and i t s relevance for that music's ent i re s t r u c t u r e ) , . . . For almost two hundred years . . . musical analysis followed Rameau almost exclusively, whereas compositional t ra ining and prac t ice were deeply influenced by Fux, Not un t i l the early twentieth century did theor i s t s . . . p r inc ipa l ly the Austrian, Schenker--openly consider and resolve the contradict ions . In the process the two theories emerged as con^lementary, and the nature of spa t ia l motion in tonal music began to be il luminated by analysis .8

The technique of graphic analysis through reduction, i s a

process developed by Schenker and one which reveals tonal r e la t ion

ships on more remote leve ls . Schenkerian analysis i s , as aptly

described by Maury Yeston.

far more than an arhythmic portrayal of long-range voice-leading. I t i s , pr imari ly , a means of uncovering organic unity within masterwcrks of tonal music, with "organic unity" understood not as an abs t rac t aes thet ic norm but ra ther as a demonstrably concrete re la t ionship of par t to whole.^

Of p a r t i c u l a r i n t e r e s t i s his description of the graphic notation

system, as he continues.

g Robert Cogan and Pozzi Escot, Sonic Design: the Nature and

Sound of Music (Englewood C l i f f s , New Jersey: Prent ice-Hal l , I n c . , 1977), pp. 153 and 77.

9 Maury Yeston, ed . , Readings in Schenker Analysis and Other

Approaches (New Haven and London: Yale University Press , 1977), p . 6.

What makes the uncovering possible is the spa t i a l mode of presentat ion that Schenker integrated into his system, since the very medium of discourse about the object under considerat ion--the work of music—is also music. In th is respect an analysis can aspire to the musical elegance of i t s object much in the same way that l i t e r a ry cr i t ic i sm aspires to the condition of l i t e r a t u r e . ^ ^

Diverse analyt ica l approaches offer new, fresh insights into a

work. No one approach i s necessari ly the best approach, as each may

be a b e t t e r tool than another to i l luminate one aspect of the work,

a view held by most ana lys ts , and cer tainly evident in the following

quotat ion. In discussing the nature of a piece of music and of

musical analys is , Charles J . Smith, in his a r t i c l e "The Notations of

Analysis" claims.

The purpose of an analysis of a piece of music i s to communicate something about that p iece , while idea l ly re f lec t ing in i t s own form something of that which i t i s about. . . . A piece of music is^ in as many ways as i t can be described, experienced, e t c . There is no such thing as "the way a piece i s , " - - eve ry approach yields a new viewpoint and hence a new "piece ," whether that "approach" resu l t s from a complex of innate aural prejudices or from the most "sophis t icated" analyt ical theory.

An analysis of a piece i s an exp l i c i t project ion of a s t ruc ture of re la t ions "heard" in a piece.^^

The aspect of music which Schenkerian analysis i s perhaps the

best tool with which to gain understanding, as evidenced by Yeston's

Maury Yes ton. Readings, p . 6.

Cliarles J . Smith, '^Tae Notations of Analysis: An Approach to a Theory of Musical Relat ions," In Theory Only, 1 (Dec.-Jan. 19^*5-76), p . 15.

d e s c r i p t i o n , i s t o n a l i t y and tona l coherence. However, even staunch

Schenkerians c e r t a i n l y w i l l admit t h a t much i s to be gained from other

approaches. Yeston, in the preface to h is c o l l e c t i o n of a r t i c l e s

c l e a r l y r e f l e c t s t h i s a t t i t u d e as he s t a t e s .

I t i s c l e a r t h a t a l l of the authors of t h i s volume are un i t ed by a common passion for musical unders tanding and t h a t no s ing le approach, no mat te r how a l l -encompass ing , can exhaust a musical masterp iece of i t s meaning.-^2

That one Schenkerian ana lys i s may d i f f e r from another i s also

13 a p o s s i b i l i t y , as evidenced by an occasional " ana ly s i s forum" in

recen t i s sues of In Theory Only and o ther j o u r n a l s . The c r i t i c i s m

t h a t Schenkerian ana lys i s i s dogmatic with no room for a l t e r n a t i v e s

has been leve led aga ins t i t . However, d i f fe rences in readings do

occur as in the Rothgeb and Schachter analyses of the Schubert

Impromptu, Opus 94, No. 1, analyses which Yeston descr ibes as "a

f o r t u i t o u s demonstration of d i f ferences t h a t can a r i s e in the context

of two Schenkerian approaches to the same p i e c e .

One must remain aware a t a l l t imes , t h a t the v i s u a l , the graphs,

are a r e s u l t of an aura l p e r c e p t i o n , as evidenced in Milton B a b b i t t ' s

s ta tement regarding the method.

^ Maury Yeston, Readings, p . 6,

^"^See "Analysis Symposium: Brahms, Der Tod, das i s t die kiihle Nacht, Op. 9 6 / 1 , " In Theory Only, 2 , No. 6 (Sept. 1979).

1 A

Maury Yeston, Readings, p . 5 .

[Schenker's] procedures are essen t ia l ly a description of his own hearing of musical works, and the orderly formulation of the pr inciples derived from such hearing. . . . Within the framework of Schenker's analyt ica l p r inc ip le s , one can arrive at an analysis of a specif ic work at variance with Schenker's own. There is no authority of ultimate va l id i ty beyond the formed, informed, and i n t e l l i gently experienced musical perception.15

The aural sense i s , of course, basic to a l l musical a c t i v i t y , since

music i s an a r t of sound, and as Katz s t a tes "The art of hearing in

motion—that i s the sum to ta l of the Schenker method."

Schenker's musical concepts in general are not simple. Until

the forthcoming release in the iiranediate future of Oster 's t r ans la

t ion , Der freie Satz, his final and most s ignif icant work is available

17 commercially only in the or ig ina l German. I t s complexity and

general unava i lab i l i ty i s evidenced in John D. White's statement:

" I t i s a val id method, though a b i t con^lex for general use . . .

and the beginning analyst should be aware of th is method for l a t e r

s tudy."

Quoted in Sonia S l a t in , "The Theories of Heinrich Schenker in Perspect ive ," Ph.D. d i s s . Columbia University 1967, p . 555.

"^^Adelle Katz, "Heinrich Schenker's Method," p . 528.

17 A t rans la t ion by Theodore H. Krueger was completed as a

doctoral d i s se r t a t ion at University of Iowa in 1960, but was never published commercially. I t i s avai lable , however, through University Microfilms, Ann Arbor.

18 John D. White, The Analysis of Music (Englewood C l i f f s , New Jersey: Prent ice-Hal l , 1976), p . 10.

The present work atteii5)ts, in the ensuing chapters, to (1) present

the theories on which his analyt ical method is based, (2) to present

the tool of ana lys i s , the reduction technique, and (3) through the

applicat ions of (1) and (2) an analysis of Brahms' Opus 118.

CHAPTER II

AN INTRODUCTION TO SCHENKERIAN THEORY

The t h e o r i e s of Heinrich Schenker (1868-1935), often obscured

by h i s own obscure language and the d i f f i c u l t i e s of t r a n s l a t i o n ,

s t i l l remain awesome to more than a few musicians today. P r e s e n t l y ,

an a t t e n p t w i l l be made to descr ibe h is t heo r i e s in not the t echn ica l

jargon of the t h e o r i s t , bu t , as near ly as p o s s i b l e , in the musical

language of the t r a d i t i o n a l l y t r a i n e d , and p r a c t i c i n g , musician.

The core of the study of music theory in Germany as i t had

developed in the e igh teen th century was vo ice - l ead ing , involving the

study of counterpoin t as codi f ied by Johann Joseph Fux in h i s Gradus

ad Pamassum (1725) and the study of thorough bass as codi f ied by Carl

Ph i l i pp Emanuel Bach in h i s Versuch uber die wahre Art das Clavier zu

sp i e l en (1762). Jean-Ph i l ippe Rameau's d i scover ies of the p r i n c i p l e s

of harmony were developed in h i s T r a i t e de I 'harmonie of 1722, and

were in t roduced in Germany by F r i ed r i ch Marpurg in h i s Handbuch bey

2 dem Generalbasse und der KomiDOsition." As Rameau's inf luence became

A few such passages a re given in Theodore H. Krueger, " ' P e r f r e i e S a t z ' by Heinrich Schenker: A Complete T rans l a t i on and Re-e d i t i n g . Vol. I : The Complete Text. Vol. I I : Supplement of Musical Examples," Diss . Univers i ty of Iowa 1960, p . Ix ix .

"For a thorough d i scuss ion of Schenker 's p r e d e c e s s o r s , r e f e r to Sonia S l a t i n , "The Theories of Heinrich Schenker in P e r s p e c t i v e , " Diss . Columbia Univers i ty 1967, and Robert P. Morgan, "Schenker and the Theo re t i c a l T r a d i t i o n : The Concept of Musical Reduct ion ," College Music Symposium, 18, No. 1 (Spring 1978), pp. 72-96.

10

11

widespread, the amalgamation of voice-leading, harmonic center , and

sca le -s tep led to a theory of chords. According to Rameau, a t r i ad

and a l l of i t s inversions generated one and the same fundamental root ,

a theory whose basis i s in the natural harmonic s e r i e s . Consequently,

underlying music was a fundamental, or ground, bass , derived from the

roots of a l l the t r i a d s . Since each note of th is ground bass was

derived from the sounding chord, a mere passing chord could produce

the same root as the cadence chord, suggesting equali ty of the two

chords as pa r t of the fundamental bass. The fundamental bass was to

progress primarily by f i f th s , Basic to the f if th progression was the

dominant-tonic re la t ionship which created the tona l i ty , and,

inherent ly , modulations abound in chromatic music.

In response to a need for a be t t e r means of evaluating notes ,

Hugo Riemann provided a theory of functions, which reduced a l l chords

singly to ton ic , dominant, or subdorainant. Riemann's contribution

allowed for a l t e red chords within the tona l i ty , but s t i l l did not

allow for the p o s s i b i l i t y that ident ical chords might have different

meanings according to the context in which they move. This theor>'

was concerned with chord to chord re la t ionsh ips .

I t was Heinrich Schenker who f i r s t revealed a more d i rec t

re la t ionship between the horizontal and the ve r t i ca l and supplied the

energy necessary for a broader understanding of the whole. His

3 See p a r t i c u l a r l y Hugo Riemann, Harmony Simplified, or The Tonal

Function of Chords, t r ans . H. Bewerunge (London: Augener and Con^jany, 1895).

theories evolved over a period of more than t h i r t y years in various

books, a r t i c l e s , and other publ ica t ions . His Harmonielehre (Harmony)

was published anonymously in 1906 under the t i t l e Neue musikalische

Theorien und Phantasien (New Musical Theories and Fantasies) . 11 .vas

the f i r s t of a long ser ies in which his theories were revealed as

they were developed. Oftentimes these concepts were f i r s t revealed

in immature, embryonic forms which underwent subsequent development

before t h e i r f inal presentat ion in Der freie Satz (Free Composition),

in 1934, a few months af ter his death. I t is th is f inal work which

reveals Schenker's ideas in the i r f inal form and is his most important

work.

Schenker's theories are tonal theor ies . Living at the end of

the nineteenth and into the f i r s t th i rd of the twentieth centur ies ,

he exhibi ts in his theories the culmination of tona l i ty as the prime

organizing factor of musical uni ty. Like Rameau and many others

before him, Schenker refers to the t r i ad as the only musical en t i ty

t i ed to na ture , a re la t ionship that can be seen in the f i r s t five

overtones of a harmonic s e r i e s . He purports that each tonal work

( ea r l i e r music was as yet imperfect by his standard, as was modem

music) was a unique in te rp re ta t ion of the t r i a d , the tona l i ty , and

was an "unfolding" (Auskomponierung) of that t r i a d over the course

of the composition.

^See Heinrich Schenker, Harmony, ed. by Oswald Jonas, t rans . Elisabeth Mann Borgese (Chicago: The University of Chicago Press , 1954) and Free Comoosition, ed. Oswald Jonas, t r ans . Ernst Oster (New York:""Longman', Inc . , 1979). For a complete l i s t i n g of Schenker works, see David Beach's bibliography in Yeston's Readings.

s

15

Although t h i s concept i s d i f f i c u l t for many to accep t , i t i s

l i t t l e d i f f e r e n t from saying simply t h a t the t o n a l i t y i s e s t a b l i s h e d

over the course of the composition and t h a t a l l sounds r e l a t e in one

way o r another to t h i s t o n a l i t y . Even the main s t r u c t u r a l harmonic

component of sona ta form i s suppor t ive of the t o n a l i t y , or the ton ic

t r i a d ( I — - ^ v ||«i».uA^v I- H). Using a l i t t l e of the t heo r i e s of

Rameau and Riemann, one can say t h a t I-V-I i s a l l t ha t i s needed to

e s t a b l i s h the t o n a l i t y . Such a t o t a l l y harmonic explanat ion i s not

r e a l l y what Schenker says a t a l l , as h i s i s a combined cont rapunta l

and harmonic exp lana t ion . I t i s , n o n e t h e l e s s , what r e s u l t s in the

music and i s a l o g i c a l at tempt to expla in Schenker in funct ional

harmonic thought .

In the course of the unfolding of t h i s ton ic t r i a d a s t r u c t u r a l

framework emerges. The harmonic aspect of t h i s framework i s r e f e r r ed

to by Schenker as the Ursa tz , t r a n s l a t e d by various w r i t e r s as " p r i

mordial s t r u c t u r e , " " p r o t o - s t r u c t u r e , " "arche typal s t r u c t u r e . " Tliis

s t r u c t u r a l framework i s the unfolding of the t r i a d . I t i s the " h o r i -

z o n t a l i z a t i o n " of the t r i a d . Consequently, i t i s not d i f f i c u l t to

conceive of the t r i a d as being prolonged. Since h o r i z o n t a l i z a t i o n i s

the concept , one must approach the music in terms of v o i c e - l e a d i n g s ,

i . e . , con t rapun ta l p r i n c i p l e s . The top-most s t r u c t u r a l vo ice , not

n e c e s s a r i l y corresponding to melodic tones , produces a s tepwise

^These and o the r t r a n s l a t i o n s are on page 170 of S l a t i n , "Heinricn Schenker ' s T h e o r i e s . "

Refer to Adelle Katz d e f i n i t i o n , page 22.

14

descending l ine from any member of the tonic t r i ad to the tonic p i t ch .

Consequently, there are three forms of the Url in ie , as Schenker ca l l s

th i s top l i ne : 3 2 1 , 5 4 3 2 1 , or 8 7 6 5 4 3 2 1 . This Urlinie

i s st5)ported by a bass voice which arpeggiates among the members of

the t r i a d , with a goal of the f i f th scale degree imjnediately preceding

the ton ic . This t o t a l s t ruc tu ra l level (the Ursatz, of which the

Url inie is the top-most voice) i s referred to as the background

(Hintergrund) .

Just as the background is an unfolding and consequently a

prolonged tonic t r i a d , any or a l l of the resu l tan t consti tuents in

the background level can be prolonged through various techniques of

prolongation to produce an intermediate level called the middleground

(Mittelgrund). Prolongations of various consti tuents of the middle-

ground wi l l produce the foreground level (Vordergrund), which now

very closely resembles the actual surface sound.

.An analogy with archi tecture may provide a useful i l l u s t r a t i o n

for further c l a r i f i c a t i o n . Architecture i s concerned with f i l l i n g

three-dimensional space with a usable s t ruc tu ra l e n t i t y . Two

buildings side by s ide , one very ornate , the other extremely simple

and p la in , may seem to be t o t a l l y different from each o ther , yet

s t r ipped of the finish-work, they could very well reveal iden t ica l

s t r uc tu r a l designs and construct ion. As i s the case with any

7 Following the prac t ice of Schenker, the scale degrees of the

Url in ie are indicated with carets to dis t inguish them from other Items indicated with Arabic numbers.

15

s t r u c t u r e , the s t ruc tu ra l framework is usually not v i s i b l e . Much of

what i s seen i s purely ornamentation.

/ Schenker has often been misinterpreted regarding the Ursatz,

tlie ult imate s t ruc tu re . I t i s not inportant that a l l music can oe A A A

, , 3 2 1 8 .

reduced to j y I 1°^ one of the other limited types) , but i t i s

important that the s t ruc ture be secure and adequately support the

music which res t s on i t . I t i s not of significance to the viewer or

user , that there are only a limited number of a rch i tec tura l types

( rec tangles , t r i ang l e s , cubes, pyramids, e t c . ) , but i t is v i t a l to

the users of the building that i t be s t ruc tu ra l ly sound. What

probably wi l l have the most immediate appeal to the bui ld ing ' s occu

pants wi l l be the finish-work and ex t ras , the decorations, the

u sab i l i t y of the space, e t c .

Implici t in th is description of music as an unfolding, i s the

concept of constant motion. Schenker has often been c r i t i c i zed for

a t t r i bu t i ng a s t a t i c qual i ty to music in the concept of prolongation.

Nothing could be more foreign to the concept. The musical work i s in

a constant s t a t e of motion, with di rect ional goals, both raelodically

in the tonic goal of the descending Ur l in ie , and harmonically in the

tonal i ty-def in ing s t ruc tu ra l dominant of the Ursatz. Upon reaching A

2 9 y, the most intense motion completes the inevitable return to tonic.

8 A A A

A background consist ing of an Url inie of 3 2 1 which is supported harmonically by tonic with a movement to the dominant upon the a r r iva l of 2, coming to a full close on 1 supported again by tonic .

9 ' As described previously, th i s symbol represents the Urlinie 2

supported by the dominant in the background leve l .

16

The motion jus t described is that effected by the background.

Also present within the music are more immediate, detai led motions,

the motions which prolong any or a l l par ts of the background. I t i s

here , in these more immediate l eve l s , that the concept of prolongation

becomes paramount. Once again a reference to archi tec ture may aid in

the c l a r i f i c a t i o n of the concept of prolongation.

As one approaches from a dis tance, he sees the whole edif ice of

a church in i t s rura l s e t t i n g , and real izes the upward projection of

space the s t ruc ture crea tes . As he comes nearer , he can no longer

see the open countryside, but does begin to notice individual windows,

doors, and various other aspects of design. As he walks up the s teps ,

he can no longer see the steeple above his head, but notices the

beaut i ful carvings on the huge wooden doors. And, as he turns the

door knob, he can no longer see the top of the doors, but focuses

very in ten t ly on the r ight wing of the angel in this minute par t of

the carving.

This same l ine of thought, from the general to the spec i f ic ,

from the whole to i t s p a r t s , i s p a r t i a l l y analogous to that of back

ground to one prolongation in the middleground, to spec i f ica l ly one

chord in the foreground, one that may not even appear in the general ,

as ce r ta in ly the wing of the angel does not . However, the analogy is

only p a r t i a l l y complete. The act of focusing in on the wing t e l l s

nothing about the function of that wing in the s t ruc ture of the church

bui ld ing. To complete the analogy, the function of each par t and the

re la t ionship of the par t s to each other and to the whole must be

considered.

17

The door f i l l s a space. Although i t i s cer ta inly functional,

p r a c t i c a l , and even aes the t i c , i t i s not s t r u c t u r a l . The building

would not lose any support and coherence in s t ruc tura l design, were

the doors not there . What i s more, to the so l ida r i ty of the s t ructure

i t matters not what materials are used in the construction of the

doors; they could be made of wood, cast i ron, chrome and g lass , or

even papier-mache. Doors of each of these mater ia ls , however, would

serve a different function, and each would be f i l l i n g the door-space

d i f fe ren t ly . The door-space is par t of a larger space, one that i s

def in i te ly s t ruc tu ra l - - t he wall space. Without a beam at the top of

the wall-space, there would be no support for the roof, and conse

quently no church. The s t ruc tu ra l framework is on the perimeter of

the wall-space and the pa r t i cu l a r materials and design of the wall

could have been of a different s o r t . However, this wall with th is

design f i l l s th i s wall-space. In other words, the carvings are space

f i l l i n g in the wood; the actual doors are space- f i l l ing in the door-

space, and a l l are space- f i l l ing in the wall-space, a l l of which in

turn , i s space - f i l l i ng , but i s s t r u c t u r a l , to the ent i re ed i f ice .

In music, many of the motions on the surface are s p a c e - f i l l e r s .

They are unfoldings on the foreground level of an en t i ty which exis t s

on the middleground level , in which that en t i ty may very well be only

a pa r t of the unfolding of an even more s t ruc tu ra l en t i ty on the back

ground l eve l . I t i s in th i s regard-- that of the rea l i za t ion of

function or significance of an en t i ty or motion to the s t ructure of

the phrase , sec t ion , or work--that the layered approach offered by

Schenker is vastly different from and, in th i s w r i t e r ' s opinion, an

18

improvement Lq)on tha t developed by the Rameau-in flue need t h e o r i s t s .

The approach of the l a t t e r i s seemingly overly concerned with the

chord at the moment only in re la t ion to i t s e l f , the sca le , the harmonic

s e r i e s , and to only the chord immediately before i t and af ter i t . This

concern i s much l ike examining the angel 's wing without rea l iz ing i t s

re la t ion and function within i t s se t t ing and, consequently, i t s s ign i

ficance to the whole s t ruc tu re .

The work of Hugo Riemann was an in^rovement upon the Rameau

method. His attempt to delineate the functions of tonal i ty and to

carry those functions to increasingly broader areas was cer ta inly an

advancement towards understanding the relat ionships within the larger

contexts . However, the primary deficiency in the Riemann approach

was the fa i lure to acknowledge variable chord signif icance. With

Riemann, in a given key, the tonic t r i ad was always tonic function,

regardless of i t s posi t ion within the phrase, and hence, carr ied the

same weight at a l l t imes.

These comments regarding Rameau and Riemann are in no way meant

to underrate the contributions of these two great theor i s t s to the

f ie ld of music theory. I t i s highly l ikely that they were, indeed,

aware of the larger re la t ionships within music, as i s evidenced by

Riemann's generalized conception of t ona l i t y - - t ha t a l l features of a

tonal composition must express the content of a single underlying key.

Moreover, i t i s th i s conception of tona l i ty , as Robert Morgan so aptly

develops in his a r t i c l e , " tha t forms his [Riemann's] most important

contr ibut ion to the theore t ica l atmosphere in which Schenker

developed--an atmosphere which Riemann shaped . . . to a remarkable

19 ,,10

extent . Morgan also points out t ha t , although one would be

mistaken to contend tha t Schenker consciously adapted the theories

of h is predecessors to f i t his theore t ica l framework, there is some

indicat ion tha t he was at leas t p a r t i a l l y cognizant of them. In fact

i t would have been most unlikely that Schenker's work would have even

been possible had these two great theor i s t s not preceded him, for, as

Morgan again surmises, Schenker's contribution i s

both more and less or ig ina l than i s generally assumed: less in that i t does not offer a t o t a l l y unprecedented way of looking at musical s t ruc tu re ; but more in that i t rad ica l ly transforms inher i ted theore t ica l ideas, lending them a t o t a l l y unforeseen new meaning and unexpected l i f e . Schenker then has maintained t r a d i t ion in the very moment of a l te r ing i t . ^ l

I t should be qui te apparent by now that th is unfolding i s

s t re tched out through time and motion, and that th is en t i ty space

f i l l i n g i s effected through the technique of prolongation. Prolon

gation i s defined by Adelle Katz in her excellent a r t i c l e as "the

means by which the genius t rans la tes th i s primordial material [Ursatz]

into a Foreground that i s the resu l t of his own fantasy and imagi-

1?

nat ion ."* Thus prolongation i s the means by which the Ursatz undergoes organic growth. I t i s the embellishment, the working out , and

Robert P. Morgan, "Schenker and the Theoretical Tradi t ion: The Concept of Musical Reduction," College Music Symposium, 18, No. 1 (Spring 1978), p . 94.

Morgan, pp. 95-96.

^^.Adelle Katz, "Heinrich Schenker's Method of .Analysis," .Musical Quarterly, 21 (1935), pp. 511-529.

20

the he igh ten ing to c e r t a i n s i gn i f i cance of var ious aspec ts of the

b a s i c s t r u c t u r e . P ro longa t ion , in the Schenkerian sense , does not

imply making a note or passage temporally longer , but "can be

descr ibed as something r e l a t i v e l y complex which serves as an e l abo ra

t ion of something t h a t i s r e l a t i v e l y simple.""^"^ Fe l ix Sa l ze r r e f e r s

to p ro longa t ion as the " l i f e - g i v i n g force" of a conpos i t ion , as he

s t a t e s .

I t remains f u t i l e knowledge unless we recognize the d i r e c t e d motion wi th in the framework with i t s l i m i t l e s s p o s s i b i l i t i e s of v a r i e t y , de tou r s , and delays c a l l e d p r o l o n g a t i o n s , and which are the l i f e - g i v i n g force of a composit ion. I t i s t h i s i n t r i c a t e i n t e r p l a y between the i n f l e x i b i l i t y of the s t r u c t u r a l framework and the e l a s t i c i t y and reproduct ive a c t i v i t y of the pro longa t ions t ha t expla ins a most s i g n i f i c a n t f a c t o r in the a r t of composition: the purpose and meaning of d i r ec t ed motion. ^^

Severa l of the means by which pro longat ion i s accomplished are

descr ibed by Katz. The following examples are offered by her in the

p rev ious ly mentioned a r t i c l e . In Exan^le 1-a the space of the t h i r d

(5 to 3) in the C major sonor i ty i s f i l l e d in with a pass ing note F. ^

Gerald Warfield, Layer Analys is : a Primer of Elementary Tonal S t r u c t u r e s (New York: Longman, I n c . , 19 78, f i r s t pub. 1976 by David McKay).

14 Fe l ix S a l z e r , "Di rec ted Motion: The Basic Factor of Musical

Coherence," American Musicological Socie ty J o u r n a l , 3 (1950), p . 157.

.As p r ev ious ly p re sen t ed , in Schenkerian theory music i s the unfolding of a t r i a d . Consequently the var ious i n t e r v a l s of the t r i a d may be sounded h o r i z o n t a l l y over a t ime-span--henee , the concept of 3rd-span , 4 th - span , 5 th - span , 6 th -span .

21

Example 1. Dissonant pass ing tone harmonized as consonance

^

h. e. J.

-jsn

r i^T T

^ ^ F ^ 5/1 i

r fi 3z: I

In 1-b t h a t pass ing note i s harmonized to become consonant, al lowing

both melodic and harmonic generat ion of the C major s o n o r i t y . Not

only are the same conponents p re sen t in 1-c as were in 1-b, but a l so

another space f i l l e r has been inc luded- - the C-sharp chromatic pass ing

note which f i l l s the space from C to D. (The function of the D i s

t h a t of e l a b o r a t i o n of the C.) The harmonic movement of I - I I - V - I i s

as firm and convincing a h o r i z o n t a l i z a t i o n of the C major t r i a d as i s

p o s s i b l e to e f f e c t . The d issonant pass ing tone C-sharp could be

harmonized to become p a r t of a secondary dominant ( e . g . , V ' / i i ) , in

which case another leve l of p ro longa t ion has been e f f ec t ed , as in

( 1 - d ) .

Exaii5)le 2 . Octave t r a n s f e r .

22

Another means of prolongation s tated by Katz is by changing the

r e g i s t e r of a note to i t s octave by horizontalization."^^ In Example

2-a, the beginning pi tches have been displaced an octave each by

arpeggiation in contrary motion. In 2-b, the space of the upper voice

t h i r d (3 to 5) and the lower voice fourth (8 to 5) have been f i l l ed

with passing no tes . In the remainder of the arpeggiation, the th i rd

(8 to 3) has been f i l l e d in with a passing note , the E (5) s p l i t s into

two voices to f i l l with passing motion the fourth (5 to 1) , and the

lowest voice also f i l l s a th i rd (3 to 1) with a passing note . All i s

an elaboration of the octave displacement of the i n i t i a l t h i rd - - a

prolongation with other prolonging motions within.

Example 3. Exchange of voices.

To c la r i fy hor izonta l iza t ion as used by Katz, her Schenkerian def ini t ion of tona l i ty i s offered: " I t i s necessary to d i f fe ren t ia te between the na tura l p r i n c i p l e , which is Simultaneity (as expressed in the Klang), and the a r t i s t i c adaptation of that p r inc ip l e , which is Succession. In other words, the t r i ad represents a form of na tura l Coherence. Tonality then, i s the form of Coherence obtained by sh i f t ing the raw material—the natural tr iad--from i t s ve r t i ca l pos i t ion to a horizontal one, and by extending i t by means of Succession or Horizontal izat ion. In shor t , tona l i ty i s a t ransformation of the t r i a d . " (Katz, "Heinrich Schenker's Method of Analysis ," u. 313. Caps are Katz ' . )

1 Prolongation can also be accoii Dlished by exchange of voices. I:

Example 3-a, the top voice moves stepwise 4-3-2, while the bottom voice

seems to skip and spli t . This skip is actually brought about by the

transfer (or split t ing, in this case) of the C to two octaves. In

3-b the top and bottom voices invert, with the E continuing back to F,

the G back to A, producing a sixth inverting to a third, then proceed

ing on stepwise to the tonic triad which then moves functionally to

the dominant. In 5-b the first two notes of the bottom line, A-G,

are continued in the notes of the top line, A-G-F-E-D, producing the

line A-G-A-G-F-E-D, while the other line, F-E-F-E-D-C-G, begins in

the top voice and shifts to the lower voice. Through the exchange of

voices, the space between the notes of the first and second chords of

1? 3-a is filled in, thus prolonging the 3 upon i ts arrival.

A final means of prolongation given by Katz is "by the Brechung

or skip in the chord line," This particular means she describes as

the use of "the tones of the Klang in Succession, thus stretching out

18 the melodic line by means of various intervals of the chord." As

an exan^le, she uses the opening measures of Beethoven's Sonata. Opus

2, No. 1, reproduced as Example 4.

In this example, several aspects are revealed. The surface

melodic content is that of the intervals of the triad--the triad

intervals as the basis for a melodic motive. Very few real functional

17 Note the slur connecting the two E's in 5-b.

18 Adelle Katz. "Heinrich Schenker's Method," p. 516.

24

harmonies are used here--primari ly tonic over s ix measures (embellished

by a neighboring chord and passing through another to the f i r s t

inversion) before moving to the SLroertonic which leads to the dominant.

Example 4. Beethoven's Sonata, Opus 2, No. 1 (mm 1-8)

The t r i a d has been s tretched over s ix measures by moving through the

members of the t r i a d in both soprano and bass (5 to 5 in the soprano

and 1 - 3 - 5 in the bass) while arpeggiating the chords on the

surface level a l so . One other aspect of the arpeggiation is the

var ie ty in i t s manner of a r t i c u l a t i o n . In the f i r s t measures, the

t r i a d i s arpeggiated, s t re tched out , beginning on C, through F, A-f la t ,

C, F, u n t i l in the f i f th measure i t i s contracted into C as a grace

note plus A-f la t . In measure 7, the t r i ad of the tona l i ty is mani

fested in a broken f minor t r i ad immediately before the move to the

s t r u c t u r a l dominant. .Arpeggiation i s one of the most important

_ 0

p r o l o n g a t i o n a l means a t work in t h i s passage .

In h i s tex tbook. Layer .Analysis, Gerald Warfield r e f e r s to th ree

agents of p ro longa t ion which he c a l l s "p ro longa t iona l o p e r a t o r s . "

These ope ra to r s a re a rpegg ia t ion , pass ing motion, and neighbor motion.

These same motions are d iscussed in S a l z e r ' s S t r u c t u r a l Hearing, where

they are r e f e r r e d to as i n t e r v a l o u t l i n i n g , i n t e r v a l f i l l i n g , and

ornamental types of motion, i l l u s t r a t e d below as Example 5 _ 20

Example 5 .

#

Tir~cr I •JOH I lac l a : •JOL

in4Ti»\ ySilM^ omfrmfrrt. /?/ \t{*r*9\ •tt^/*'*'"'*^

These t h r ee types of motion are combined in a c t u a l music to produce

l ayers of p r o l o n g a t i o n s , as in Example 6.

Example 6.

The motion from E to G (A) is an interval outlining motion, while

that in (B) from G to E is the interval filling type. All of the

19 Gerald Warf ie ld , Layer .Analysis, p . 4 4

" F e l i x S a l z e r , S t r u c t u r a l Hearing: Tonal Coherence m Music, 2v. (New York: C. Boni, 1952), v, 1, p , 119,

26

mot ions , however, depar t from and re tu rn to E, thus c r e a t i n g an

ornamental motion which cons i s t s of the o ther two tv^es .

Based on the previous d i s c u s s i o n s , one might c o r r e c t l y surmise

t h a t Schenkerian theory i s predominantly a l i n e a r concept. Conse

q u e n t l y , i t s roo t s are in s t r i c t counte rpo in t . These cont rapunta l

l i n e s are b e s t observed in the middleground reduc t ion . (See Chapter

I I I for a d i scuss ion of the reduct ion technique . )

The con t rapun ta l element i s , however, only ha l f of the theory .

The remaining h a l f i s rooted in funct ional theory . This harmonic

aspec t i s c l e a r l y i n d i c a t e d by the concept of the Ursa tz , which i s a

harmonic s t r u c t u r e . In the unfolding of the t on i c t r i a d , the bass

w i l l i n e v i t a b l y reach the dominant, the "octave d i v i d e r . " This

concept i s e s s e n t i a l l y t h a t of a t o n a l i t y ' s being e s t a b l i s h e d by the

dominant, which in func t iona l thought , i s the function of the dominant.

Schenker supp l i es every p o s s i b l e Ursatz formula with a l l th ree forms A A A A A A

of the U r l i n i e (3 - 1, 5 - 1, 8 - 1) in Der f r e i e Sa tz , according to

the a p p l i c a t i o n of h i s r igorous contrapuntal-harmonic p r i n c i p l e s .

Any harmonic s t r u c t u r e wi thin the Ursatz may subsequent ly be

pro longed, thus prov id ing the concept of harmonic p ro longa t ion .

Consequently, not only a note may be prolonged, but an e n t i r e harmonic

e n t i t y (chord, o r even tonal area) may be prolonged. This concept i s

based on a p r i n c i p l e revea led in c o u n t e r p o i n t - - " t h a t s eve ra l tones 21

can s tand for the one tone t h a t dominates a group of t o n e s , " Thus,

*• Fe l ix S a l z e r , S t r u c t u r a l Hearing, v, 1, p , 106,

harmonic prolongation also has as i t s bas i s , counterpoint, as evidenced

in Sa l ze r ' s statement:

I t i s one of the greates t achievements of Western music tha t the development of the harmonic concept has not overpowered the contrapuntal concept. The former has been applied instead in such a way as to allow the contrapuntal concept to develop fully i t s own charact e r i s t i c function, so that i t i s even possible for whole phrases and uni ts to be dominated by counterpoint and i t s progressions.22

Oswald Jonas, in the introduction to his edit ion of Schenker's

Harmony, refers to these two aspects as he describes, "the chief merit

of Schenker's early work consists in having disentangled the concept

of sca le-s tep [Stufe] (which i s par t of the theory of harmony) from

the concept of voice-leading (which belongs in the sphere of counter

p o i n t ) . " He further s t a t e s , "the theory of Auskomponierung shows

voice-leading as the means by which the chord, as a harmonic concept,

i s made to unfold and extend in t ime." " He then summarizes qui te

adequately, the dual aspect of music (harmonic/contrapuntal):

The chord is s imultaneity. To use a metaphor, i t has a dimension in space; and the nature of music, which flows in time, demands i t s t rans la t ion in to a temporal sequence. This process i s . . . "compositional unfolding" or Auskonponierung. I t could find i t s f inal expression, however, only a f te r an incursion into the f ie ld of counterpoint, since the goal of creation in time, of Auskomponierung, can be reached only via voice-leading.^^

* Salzer, v. 1, p. 109.

23 Oswald Jonas in Heinrich Schenker, Harmony, p, xvi.

24 Oswald Jonas in Heinrich Schenker, Harmony, p. xvi.

28

And Leo Kraft r e f l ec t s Schenker's ideas when he s t a t e s .

The opinion has already been expressed that the term harmony i s v i r t ua l l y useless . Supposedly, harmony deals with the study of chords, counterpoint with l i n e s . But such a statement overlooks the basic fact that l ines flow together to make chords, and the only reason that chords follow in a certain order i s that the l ines lead them there . If harmony books make any sense i t i s because they deal with musical motion--that i s , counterpoint. . . . There is much more to learning about chords than writ ing Roman numerals under them. The way to learn about chords i s through learning about the l ines that generate the chords.25

Underlying the concept of musical motion or directed motion,

are bas ica l ly two kinds of chords- -s t ruc tura l , harmonic chords (those

which underl ie the basic s t ructure) and prolonging, contrapuntal ones.

In discussing chord prolongation, Salzer describes two kinds of motion,

Direct motion he describes as "contrapuntal chords between two

harmonic chords," whereas ind i rec t motion is that created by "contra-

puntal chords prolonging a single chord." Rhythmic posi t ion as

such, i s not necessar i ly indicat ive of a chord's function. The factor

which wil l actual ly determine whether a chord has harmonic or contra

puntal function "wil l always be i t s posit ion within the voice-leading ? "7

pat te rn and the purpose i t f u l f i l l s within that p a t t e r n . " " '

25 Leo Kraft, Gradus: An Integrated Approach to Harmony, Counter

point and Analysis (New York: W. W. Norton and Company Inc . , 1976), p . 30.

Salzer, St ructural Hearing, v. 1, p . 100.

^^Salzer, v. 1, p , 100-101,

29

Example 7, from the Bach c h o r a l e , "Der Tag, der i s t so freunden-

r e i c h , " i l l u s t r a t e s the d i f ference between harmonic ( s t r u c t u r a l )

chords and con t rapun ta l chords .

Example 7. Bach Chorale No. 158, Der Tag, der i s t so f reundenreich.

^ ^ n i

i 1 iS

«=4

^ ^ m

r TO 1 r

The f i r s t five chords perform a contrapuntal function. They prolong,

or spin out the s t ruc tu ra l tonic t r i a d , as evidenced by the melodic

bass l ine which descends stepwise from tonic in one octave to tonic

in another, and by the soprano which moves from the root of the tonic

t r i a d to the th i rd during that same time span.

A look at th i s example from a more t r a d i t i o n a l , functional

approach wi l l reveal the same r e s u l t s . A t r ad i t i ona l Roman numeral

analysis i s given below in Example 7-a.

Example 7-a.

r^

\M\m^=^^ Vi sL v ' -L

i

jr I I

;o S u b s t i t u t i n g T for a l l t o n i c function chords (in the exan^le , I and

v i ) , PD for a l l pre-dominant function ones (IV and i i ) and D for a l l

dominant funct ion chords (V and v i i " ) , the ana lys i s would be t h a t of

Example 7-b.

Example 7-b.

^ f T PD P I PP P T

From the above " reduc t ion" (the pass ing tones have been omi t t ed ) , the

f i r s t p ro longa t ion i s r evea led . S ince , according to the concept

which allows the s u b s t i t u t i o n of a secondary t r i a d for a primary one,

the vi chord prolongs the t on i c t r i a d , as i l l u s t r a t e d in Example " - c .

Example 7-c.

Vi ' T SO

The funct ion of the pre-dominant (subdominant) group of chords i s to

lead to the dominant. They provide harmonic movement whose motion i s

d i r e c t e d to the dominant. The function of the dominant, of course ,

i s to e s t a b l i s h , or lead t o , t o n i c . Hence, I - IV-V-I , or T-PD-D-T, i s

a f u l l y completed motion which begins a t t o n i c , moves i n t o an area

whose funct ion gives d i r e c t i o n to complete the motion where i t began.

In o t h e r words, the motion T-PD-D-T, i s a type of p ro longa t ion t h a t

51 extends a chord by moving away and back. A more extended view of the

above passage provides the analysis of Exanple 7-d.

Example 7-d.

^ * ^

J IT PP — v

ot -vn 1

PI K X I

?DD I or KOfi^LlTt)

T j v \;(i 1 n Y 1 'J

EYI From e i t h e r of the analyt ica l approaches above (that of the

t r a d i t i o n a l Rameau-Riemann chord function or that of the Schenkerian

contrapuntal/harmonic) one extremely s igni f icant point i s revealed:

that a l l chords are not of equal significance in generating di rect ion

within the music--that i s , musical s t ruc ture exis ts on various a rchi

tec ton ic l eve l s .

I t i s perhaps in th i s realm, tha t of h ierarchic s t ruc tu re , tha t

Schenker made his grea tes t contribution to musical theory. Through a

se r i e s of reduct ions , wherein progressively more ornamental, prolonging

de t a i l s are systematical ly eliminated, the various " layers" of the

music are revealed.

52

CHAPTER I I I

THE REDUCTION PROCESS

Prolongat ion was p rev ious ly descr ibed as "something r e l a

t i v e l y complex which serves as an e l a b o r a t i o n of something t ha t i s

r e l a t i v e l y s imp le . " One might think of reduct ion as the reverse

of p r o l o n g a t i o n . I t i s something t h a t i s r e l a t i v e l y s inp le which

s tands for something r e l a t i v e l y complex and e l a b o r a t e . Reduction

i s the s i n ^ l i f i c a t i o n of a foreground passage to a more fundamental

l e v e l . The s i m p l i f i c a t i o n s are " i n t e r p r e t a t i o n s of the s p e c i f i c

d e t a i l s of a p i e c e , and thus add to our ove ra l l view of the p i e c e . " "

The f ac t should remain c l e a r , however, t h a t reduct ions are the r e s u l t

of a n a l y s i s . They e x i s t by v i r t u e of the conscious and sys temat ic

ac t of e l i m i n a t i n g the ornamentations and e l abo ra t i ons from a passage

or l eve l of music. Reduction i s c lose ly akin to v a r i a t i o n . In

desc r ib ing t h i s r e l a t i o n s h i p . Forte s t a t e s :

In b r i e f , the a n a l y t i c a l technique of reduct ion der ives from the composit ional technique of v a r i a t i o n , as i t developed during the tona l pe r iod . .At the r i s k of over s impl i fy ing , I po in t out t h a t reduc t ion i s approximately the reverse of v a r i a t i o n . By means of v a r i a t i o n techniques a b a s i c s t r u c t u r e becomes more e l a b o r a t e , in terms of i n c r e a s i n g number and v a r i e t y of me Iodic-rhythmic

^See page 20.

2 Gerald Warf ie ld , Layer Ana lys i s , p . 42.

:>j>

54

events . Reduction accomplishes the reverse; de t a i l i s gradually eliminated in accord with the t r a d i t i o n a l d i s t inc t ion between dissonant and consonant tones (made with reference to the tonic t r i a d , the elemental consonance) so tha t the underlying, control l ing s t ructure is revealed. ^

Although Schenker i s universal ly associated with the reduction 4

technique, i t i s not t o t a l l y his innovation. He, however, more than

any o ther , refined and developed the technique through i t s use in his

many analyses. Regretfully, Schenker never explained the actual

method. However, he le f t a wealth of examples in his many analyses

of musical works.^ He also used the reduction technique as the

vehicle through which he a r t i cu la ted his unique conception of tona l i ty

as ul t imately revealed in Der freie Satz. From these reductions (and

to some extent from those of subsequent users of the technique such

as Salzer , For te , Travis , and Berry) the method of reduction in the

present work i s derived.

Although i t i s beyond the scope of this study to evaluate the

various works based on Schenker, i t should nevertheless be pointed out

tha t at the present time there ex is t s only one published work whose

^Allen Forte , "Schenker's Conception of Musical S t ruc ture , " Journal of Music Theory, 3 (1959), p . 18. Reprinted in Yeston's Readings in Schenker Analysis.

'^Forte mentions a few pr io r examples and Morgan develops the h i s tory of the technique very thoroughly in his a r t i c l e .

^For a complete l i s t i n g , see Larry Laskowski, Heinrich Schenker An .Annotated Index to His Analyses of Musical Works. (New York: Pendragon Press , 1978).

J O

primary purpose i s to develop a methodical approach to the reduction

process . In most of the older l i t e r a t u r e , the wri ters approach the

subject of reduction by explaining a Schenker reduction, never by

actual ly reducing a passage of music. Recently, publishers have

released several textbooks in which the authors use reduction as a

tool in explaining basic theore t ica l concepts. Even these authors,

however, do not separately and systematically approach the technique

of reduction.

In a se t of reduction graphs, the hierarchic s t ruc ture of the

music i s revealed in both harmonic and l inear re la t ionsh ips . In the

f i r s t " l eve l" or " layer , " the most obvious ornamentations and

arpeggiations are eliminated, revealing a more l inear composition. In

each subsequent layer more prolongations are replaced with the ind iv i

dual notes instead of the s tretched out passage, un t i l ult imately the

most fundamental s t ruc ture i s revealed, (Schenker's Ursatz). As

previously pointed out, Schenker referred to only three l eve l s - - the

foreground, middleground, and background—each represented by a

separate reduction graph. Some analysts today use fewer (or more)

reductions to ar r ive at tha t level which displays the most basic

re la t ionships within the music; the number of reductions or layers

i s often determined by the complexity of the music. Schenker himself

Leo Kraft, Gradus; William Duckworth and Edward Brown, Theoretical Foundations of Music (Belmont, California: Wadsworth Publishing Company, I n c . , 1978); Edward Aldwell and Carl Schachter, Harmony and Voice Leadings (New York: Harcourt Brace Jovanovitch, 1978) ;' Peter Westergaard, Introduction to Tonal Theor>^ (New York: W. W. Norton and Company, I n c . , 1975); Robert Cogan and Pozzi Escot, Sonic Design.

56

often used four to five separate reductions in deriving these three

l eve l s .

Beyond the foreground leve l , rhythmic values of notes lose t he i r

temporal associat ions in a reduction and instead indicate re la t ive

s igni f icance , or s t ruc tu ra l weight. Rather than the reader ' s f i r s t

being referred to a glossary of graphic symbols, in the following

discussion he wi l l encounter the symbols as they are needed while

rea l i z ing several reductions.

Example 1.

^m ^m : « :

3Sfc

S i ¥

The f i r s t example for reduction (Example 1) , i s a standard four

measure phrase length imparting an element of f ina l i ty in harmonic,

melodic, and rhythmic d i rec t ion . A t r ad i t i ona l Roman numeral analysis

inp l i es equal i ty among the cons t i tuen ts : I I V I . All are

primary t r i ads of equal duration and metric placement. In approaching

the phrase, one must rea l i ze tha t the sonority resul t ing in the second

measure i s brought about by melodic motion in the bass and soprano

through the exchange of tones. Since there i s no change of chord in

57 me asure 2 —only arpeggiation of the same chord (3 to 1 in the soprano,

1 to 3 in the bass) , the f i r s t two measures combine into the contents

of Example 1-a. By the same process , measure 3 resu l t s in the contents

of Example 1-b.

Example 1 (a, b , c) .

A concept v i t a l to reduction i s that octave r eg i s t e r i s of l i t t l e

consequence and most thought can be in terms of pi tch class only. ' .As

a r e s u l t , octave duplications can be eliminated from the contents of

1-a and 1-b. The G in 1-a i s doubled as i s the F-sharp in 1-b;

without the doublings the re su l t i s the contents of 1-c,

The two primary con^onents of the voices are the top-most (as

expressed in the theory of the Urlinie) and the bass (as expressed in

However, the f inal Ursatz wil l be shown in what Schenker refer red to as the "obligator>' r e g i s t e r , " which in a much si iqj l i f ied explanation is tha t octave r eg i s t e r in which the progressions of the Ursatz take p lace . Excursions in to different octave reg i s t e r s r e su l t from arpeggiat ions, out r ight octave t r ans fe r s , and a leap of an inner voice in to a much higher r e g i s t e r into what seems to be the top voice. These concepts will become c learer as the reduction process continues.

58

the theory of the "grundbrechung" aspect of the Ursatz) . The B of

measure 2 (of Example 1) i s an inportant tone while i t s soprano (G)

i s not so inpor tan t . The B is more important because i t is an aspect

of the tonic arpeggiation in the bass. The top-most voice of the

reduction so far produces a 3-2-1 descending l i ne , one of the Urlinie

forms defined by Schenker. Tlie f i r s t reduction now looks l ike tha t

in Example 1-d.

Example 1-d.

m I r r

In Example 1-d the descending top voice is indicated in open

note heads where the inner l ines are less s t ruc tu ra l ly important;

therefore they are shown in black noteheads. The notes of this bass

are a l l s t r u c t u r a l l y inportant to the Ursatz form, with the B of

l e s se r import since i t does not si:5)port a new s t ruc tu ra l chord. This

example cannot be reduced any fur ther ; i t i s one of the Ursatz forms

of Schenker's Per f re ie Satz. The notat ion, however, can be inproved

to show more c lear ly the contrapuntal aspects and spec i f ica l ly the

s t r u c t u r a l weights. The notes of the Url inie are to be indicated

39 A A A

with Arabic numerals and carets (3 2 1) above the corresponding notes .

The G in the inner voice af ter moving to the leading tone, resolves

to the tonic at j . The other inside voice (the D) merges with the

bass upon i t s a r r iva l upon the D at y and resolves to G in t.he }. The A

presence of the B at the i i s superfluous since the whole piece i s

the hor izonta l movement through the members of the tonic t r i ad to

t h e i r convergence upon tonic at the end. The final reduction to the

Ursatz form i s tha t of Example 1-e.

Example 1-e.

I l l

I t should be pointed out that these four measures were approached

as though they were a whole conqposition. However, since th is i s more

than l ike ly the f i r s t phrase of a more extended work, the Ursatz form

reduction above i s only the f i r s t reduction of a more extended

reduction. The bass notes of the Ursatz are indicated in ooen

g An Ursatz form of a p a r t i a l composition such as th is one i s

referred to as a "f igurat ive Ursatz ."

40

note-heads with stems and beamed toge the r with a balken (broad beam).

The o t h e r note values i n d i c a t e r e l a t i v e s ign i f i cance of weight .

Always the top voice (Ur l in ie ) and bass a rpeggia t ion are the most

impor tan t . The U r l i n i e i s i n d i c a t e d here in white n o t e s , the l e s s e r

l i n e s in black n o t e s . The B of the bass a rpeggia t ion i s i nd i ca t ed in

a r a t h e r s t r ange way--the flagged h a l f - n o t e . In r e l a t i o n to the o the r

n o t e s , i t has almost equal weight with the o t h e r three tones of the

bass a r p e g g i a t i o n ; they , a f t e r a l l , are "f lagged" h a l f notes a l s o .

However, i t i s detached from the o the r s because only the t o n a l i t y

def in ing roo t s are c o n n e c t e d - - i . e . , t on i c and dominant, and there i s

no harmonic change over the B.

Tliere are s e v e r a l ways to i n d i c a t e the same meanings in t h i s

r educ t ion . Schenker himself was not c o n s i s t e n t , sometimes beaming

no tes of the U r l i n i e (as in the above b a s s , and as t h a t used in

Exan^le 2 and subsequent reduct ions) and sometimes i n d i c a t i n g them

as those of t h i s U r l i n i e above have been i n d i c a t e d , with s i n g l e white

n o t e s . In any case one fac t remains — t h a t s t r u c t u r a l weight and

coherence are i n d i c a t e d by the type of note and groupings, r e spec

t i v e l y . S a l z e r and many of h i s followers would i n d i c a t e the meanings

above in the fol lowing manner (Example 1-f) . Obviously, in Example

1-f, weight i s i n d i c a t e d by length of stem on the white n o t e s .

As a f u r t h e r explana t ion of the technique of r educ t ion , cons ider

Example 2 . The example w i l l immediately be recognized as a minutely

ornamented vers ion of Example 1. Pro longat ion i s a t work he r e .

Reduction i s the r ep lac ing of the extended passage with t h a t for which

the extended passage s t a n d s , and in the process revea l s the

41

con t r apun ta l r e l a t i o n s h i p s and the s t r u c t u r a l harmonic framework. In

Example 2 the melodic soprano and bass of measures 1 and 2 have an

even g r e a t e r melodic i m p l i c a t i o n : stepwise motion. The t h i r d s and

roo t s of the soprano and bass have been connected through pass ing

t o n e s , while the t enor has prolonged the G through neighbor note

9 movement. These ornamenting motions are l ess s i g n i f i c a n t to the

s t r u c t u r e than the t r i a d members they prolong and are ind ica t ed in

s temless black n o t e s , as in Example 2-a, (The Ur l i n i e r e p r e s e n t a

t i o n a l method here i s t h a t of connecting the members with broad beams

(balkens) and w i l l be used through the remainder of t h i s work.)

Example 1-f.

*

h

pk

I n ^Recal l the p ro longa t i ona l o p e r a t o r s : (1) a rpeggia t ion (only one

a t work in Example 1) (2) pass ing motion and (3) neighboring motions ( a l l a t work in Exan^jle 2 ) ,

Exajnple 2.

4- X r' l ' T 1

Example 2-a .

r 1 1 As p rev ious ly c i t e d , coherence i s i n d i c a t e d by groupings. In

the example above, the " t h i r d - s p a n " or "progress ion through the i n t e r

val of the t h i r d , " the Schenker "5-Zug" (3rd span) i s i n d i c a t e d by

10 See footnote 15, p . 20.

45

the s lu r s connecting the B and G in the soprano and the G and B in

the bass . They are the outside boundaries of a meaningful musical

motion and r e l a t ionsh ip . A s imilar type of re la t ionship exis ts in

the motion out of and back into G, implying a retained tone the whole

time. The individual re la t ionships within these broader coherences

are also indicated: the s lurs connecting the small stemless notes to

t h e i r goals of motion.

Example 2-a can be reduced further to exactly the same Ursatz

as Exaji^le 1, through eliminating the most immediate prolongations

in the next reduction. When the prolongations of the f i r s t

coherences are eliminated the arpeggiations can be dealt with. The

elimination of those f i r s t prolongations resu l t s in the level which

i s the same as tha t of Example 1 in the beginning.

Example 2-b.

Ill I I I Example 3 offers a much more in t e res t ing problem of reduction.

Example 3.

44

^' r x ^ t ]!' T' V{ I," X X

Again i t s re la t ionship to Example 1 i s apparent. The f i r s t prolon

gation i s exactly that dealt with above, except that the motions do

not stop on the th i rd beat . Instead the top voice reverses direct ion

and ends where i t began. I t defines the in terval of a th i rd (within

the tonic t r iad) while re ta ining the i n i t i a l tone. This coherence

i s notated in such a way as to express these motions, as seen in

Example 3-a.

Example 3-a.

The bass , instead of re ta in ing the i n i t i a l tone, re ta ins i t s i^per

l imi t note within the th i rd , the B, but with a neighboring no te , C.

The "meaning" of the f i r s t one and one-half measures i s expressed m

th i s reduction (Example 3-b):

Example 3-b.

^ <Ct2ig,»^

m ^ •^^ »->F

n^,,',^

The notation above requires some further explanations. Retained

tones are usually indicated with broken slurs. As a matter of fact,

notations connecting any identical pitches (i.e., PC) are indicated

in a broken manner, such as the broken beam indicating a retained

A

Urlinie tone (the B [3] in the above exan^le). In representing only

a port ion of a graph, such as above, the p a r t i a l beam (bass note) i s

used to indicate that the note i s beamed to something which i s in the

omitted por t ion . The p a r t i a l beam i s also used to indicate coherences

where the so l id beam would add to confusion and det ract from c l a r i t y

(for ins tance , the absence of the next connected note over the next

several staves or even pages) . In such a case, the i n i t i a l note has

a forward indicat ing beam, the next one a backward indicat ing beam. with a forward one i f there i s s t i l l more to come.

46

Returning to Exanple 3 , one finds the remaining melodic l i n e

e x a c t l y as in Exan^les 1 and 2. However, there are d i f fe rences in

the bass and harmonic s t r u c t u r e . At the appearance of G in measure 2 ,

the bass leaps t o E and begins a motion whose goal i s the C bass tone

of the i i c a d e n t i a l m a t e r i a l . Consequently, the motions are

pro longing mot ions , which ac t as a springboard i n t o i i ^ , and would be

i n d i c a t e d as in Example 3-c .

Exan^le 3-c,

*

m 3E

<? '^ / . « _ ^ ^

^

^

I

V*,g g

ii 1 1 The f i n a l r educ t ion , Exanqjle 3-d, produces the same U r l i n i e as Examples

In a Schenkerian reduct ion only the s t r u c t u r a l l y important harmonic p lanes (his s c a l e - s t e p ) are i n d i c a t e d with Roman numerals , and not the l e s s e r chords wi thin p ro longa t i ons . Schenker 's Roman numerals did not i n d i c a t e the type (major, minor, e t c . ) of the t r i a d ; a l l were i n d i c a t e d with the same c a p i t a l Roman numeral. Today, however, many ana ly s t s i n d i c a t e var ious o the r harmonic c o n s t i t u e n t s and use both i ^pe r and lower case Roman numerals . In a d d i t i o n , v a r i a b l e p h y s i c a l s i z e of numerals are used to i n d i c a t e r e l a t i v e harmonic s i g n i f i c a n c e , a p r a c t i c e in which Schenker sometimes engaged. In Example 5-c the only Roman numerals Schenker would have i n d i c a t e d are I I I V I .

1 and 2 but is a different Ursatz.

Example 3-d.

-^4- ^^w=p^

1 iitr

An examination of the f i r s t phrase of Bach's Chorale No. 158,

Der Tag, der ist so freundenreich (first encountered in Chapter II ,

provided again now as Example 4) will further clarify the reduction

process.

Exan^le 4,

={=?=•

I ,51 mm - zz

2=?:

T=T=T i raj

* •

48

The extended tonic t r i ad (through the whole f i r s t measure) is brought

about through two direct ions of motion within the bass G prolon-

12 gat ion. The f i r s t i s the passing note motions, f i l l i n g the th i rd

space between the consonant notes as can be seen in Example 4-a.

Exan^le 4-a.

The second i s the resu l tan t neighbor motion, G-A-G, through octave

t r ans fe r , as shown in Exan^jle 4-b.

Example 4-b.

L_„J A new representa t ional symbol i s encountered in the middleground

reduction of 4-c-- the curved arrow. The extended tonic i s in tens i f ied

at the end of the f i r s t measure to create a dominant re la t ionship to

the s t r uc tu r a l IV in measure 2, which consequently adds even more

en5)hasis to the pre-dominant IV. The understanding of the G

12 This prolongation, as such, i s discussed more fully in Chapter I I , pp. 29-52

49

major-minor seventh in measure 1 i s dependent upon the IV chord m

the next measure. The arrow r e l a t e s t h i s dependence.

The nex t problem in reducing Example 4 occurs in the f ina l

measure. Since the U r l i n i e i s a descending stepwise l i n e , a ques t ion

a r i s e s regarding the C on the f i r s t bea t of the measure in the soprano.

One might be i n c l i n e d to accept the C as the most s t r u c t u r a l tone here

r a t h e r than the B. Admittedly a C i s s t r u c t u r a l - - t h e bass root of the

IV leading d i r e c t l y to the dominant. Regarding the top vo ice , however,

one must remember t h a t the theory of the Ur l in ie arose from Schenker 's

concept of t o n a l i t y : t h a t a composition i s an unfolding (or hor izon

t a l i z a t i o n ) of the t on i c t r i a d . The spaces between the members of

the t o n i c t r i a d are f i l l e d in as pass ing notes which are harmonized

t o become consonant to produce the harmonic s t r u c t u r e , the Ursa tz .

I f the C in the top voice were considered s t r u c t u r a l in the f ina l

background reduct ion with the B having previous ly been e l iminated as

a pass ing motion from C to A, the Ur l in ie concept i s v i o l a t e d . (A

s tep-wise voice connecting a member of a t on i c t r i a d to the f ina l

t o n i c would not e x i s t . ) Consequently, a more orthodox view (in the

Schenkerian sense) i s t h a t the B (the 3) i s prolonged through

7 ne ighbor ing motion as i t becomes the seventh of a IV , which m turn

2 moves p rope r ly to y, as in Exan^le 4 -c . El iminat ion of a l l the

p ro longa t ions r e s u l t s in the Ursatz of 4-d.

As the f i n a l exaii5)le for r educ t ion . Example 5 i s an extens ion

of Example 2.

lO

Example 4-c.

T T' T I Example 4-d.

A 3

A A 2 I

^

If ^

^ TT?? l E ' E I Exaii5)le 5 .

4; jr*i' T r -• :?% X '

Example 5 cont 'd .

(0 ^ ' ^

1 X' r VI It 1/ r i

The Ursatz form of Exaii5)le 2-c is now understood as only another

prolongation since more music follows. The space ber^een the 3rd and

roo t , over the f i r s t two measures, has been f i l l ed in with passing

motion, and has been harmonized in the foreground level to produce a

13 consonance, resu l t ing in the reduction of 5-a.

The motions of measure 3 are obviously moving to a goal of the

dominant, the 5, in measure 4, which actually is the f i r s t note of

the Ur l in ie . The motion p r io r to the 5 i s considered "space-opening"

motion. (Schenker's German term i s Anstieg.) The presence of the

C-sharp leading tone and the secondary dominant re lat ionship elevates

the s t a tu re of the D to that of the Urlinie note seen in the reduction

of 5-b.

^•^This "consonant passing tone" i s an aspect of the concept referred to as "dissonant prolongation," i . e . , a dissonance of a more remote level i s prolonged while being harmonized with consonance and i s often even " ton ic ized ," which i s Schenker's explanation of what is t r a d i t i o n a l l y conceived as modulations.

Exan^le 5-a .

O.-

rn , ff. ^

a^'^f- a Example 5-b

U'^f, • ft L

Were the C-sharps of measure 3 only C-na tu ra l s , the inner voices would

only be r i s i n g from wi th in t o produce a long i as in 5-c .

An i n t e r e s t i n g ques t ion a t hand now i s which C i s the next

s t r u c t u r a l U r l i n i e note? Considering the vo ice - lead ings in measure 3 ,

i t soon becomes apparent t h a t t h i s C performs a l i n e a r function

connect ing the D to B, supported by the same type motion in the b a s s ,

O J

resu l t ing in a t o t a l l y contrapuntal passage (Example 5-d)

Example 5-c,

f)^

A t

^ ^ 1 - '*

d^^^^^

Example 5-d.

The motions produced by the vi chord in measure 6 are of the

same function as those in Example 3, a springboard into the s t ruc tu ra l

bass i i , which in turn becomes basic to the s t ruc ture as dominant

prepara t ion . I t i s the C of the supertonic t r i ad that resumes the

descending motion from 5 to I of the Ur l in ie , as in Example 5-e.

Exan^Jle 5-e. A

^ 3 ft I

\.* g>"^-K£»^ ' J i g-^

,<, / * t»» /If ,p i

T- • \tt-^l

54

Example 5-e, which is actual ly a middleground reduction, reveals

many aspects of organization. The prolonged tonic t r i ad at the

beginning, which encon^asses five and three-quarters measures,--in

fact a l l the music up to the cadential i i I4 V I - - i s organized in

p a r a l l e l tenths resolving to octaves between the outer voices,

r esu l t ing in a contrapuntal l i ne . This p r inc ip l e , tenth between the

voices, surfaces again at the cadence (G-B) as i f to unify the whole.

Jus t as the tenths during the f i r s t are created by an "inner voice"

(since the top-most voice is on D the en t i re t ime), the B at the end

i s also created by a r i se from the inner voice while the s t ruc tu ra l

voice i s the G. The most remote level , the Ursatz, i s shown in

Example 5-f.

D O

Example 5-f.

The preceding examples have been approached from the point of

view that there are coherencies within music, which when recognized

both conceptually and pa r t i cu l a r ly percept ively, give direct ion and

produce sound, secure, and unified s t ruc tu re . The coherencies are

re la ted and effected by tona l i ty . The ultimate s t ructure wil l be the

tona l i ty defining en t i ty and such s t ructure exis ts on a remote level

in a l l tonal music. All pi tch occurrences within the music perform

e i t h e r a s t ruc tu ra l function or a prolonging function, or both, alw.iys

project ing towards the tonic- - the one and only tonic .

As a f inal example in which the concepts of tonic iza t ion

( ton ica l iza t ion) and in terrupt ion wi l l be revealed, the f i r s t p a r t ,

the minuet por t ion , of Schubert 's Moments Musicaux, Opus 94. No, 6

(D, 780) i s presented as Example 6 (p, 57) . .At f i r s t perusal , a

o 6

6

modulation to E major seems to take place within the middle of the

work. Upon further analys is , through reduction, other explanations

are offered.

The i n i t i a l four measures are , in ef fec t , an extended tonic

t r i a d which over th i s period of time, is arpeggiated from root

pos i t ion with the th i rd in the soprano to the f i r s t inversion with

the f i f th in the soprano. During th is arpeggiation, the chord and

individual members of the chord are embellished by a neighboring i i ^

upon resolving a suspension. This tonic t r i ad in f i r s t inversion,

a f te r an octave transference in the bass through arpeggiation, returns

to i t s i n i t i a l posi t ion in measure 5 af ter passing and neighbor note

motions. In measure 6, the dominant i s actual ly arrived upon and

embellished by i t s dominant during the arpeggiation from f i r s t

inversion to root pos i t ion . In re t rospect , the f i r s t eight measures

are a l inear movement from tonic to the functional dominant.

An immediate problem l i e s in the meaning of the E-f lat soprano

note in measure 8. Is the i n i t i a l C the f i r s t Urlinie note, or i s a l l

the i n i t i a l motion merely space-opening motion to the E-f lat as the

f i r s t Url inie note? Several factors SL5)port the choice of E- f la t ,

not the leas t of which i s the secondary dominant immediately preceding

i t . However, the tonic prolonging motions were completed in measure

6 and the dominant was reached in the next measure with 2 in the

soprano and the th i rd of the V in the bass , which then f i l l e d the

space to the root with passing motion. Upon reconsidering, the

secondary dominant i s a contrapuntal chord, not a harmonic one, a

Example 6: Schuber t , Moments .Musicaux, Opus 94, No. 6 (D. "80)

-^-4 ®

\

h ^ ^ A M ^

/

'-N^rh^-^.

? r^ p

* i^i^ =p»

^ ^ * 1 ' I ^

i ' - ' ;

cJzi @ I ~ 1 1 i ^ VllSUJ:

'i ^ ^ ^ ^

^

m P

t^w~ 3-s"• • " —\'— ~zX— —T—'

- « ^ 4^7=^^^-^^ - fn ?^:^E:E3

®

k iK

-#-^ =>i:"Tr ' S i -b U ' g—»-

JU»-

! i i i : ^ . 3 f — ' — * — - —

*y-^

-^-(5-

r/ isi-.

- ^ - ^ :^3 4

^3

i «

t ^ ®

!/J { *

S 2?ft: a E

r ^f.

Zr^

^^t ^ r"

^ < — I -

^ ^ ^ # -

S :

vc?

^ £±^±% 1 = ^ SJ^ ^ . t—r

rr^zt iE^

^

@

i i k S -5—*#a ^1 !;.'ir'''j S L-:ii'a g t ^ ^ - j - f T r J - i I Ii j lii - ^ t*-

I rr 1

act i ^

^ %!]Vn*< l^'W^ ^ ^ ^

i ^ :a= ie? -5-* w ZTT iw:^

®, , ^irV < q j 9#t

4 , , , _ - • ,

- t . • a — • v " • f t ..', » , • . . L-—^

^

^ mr^s

0 0 0

\

fp PP

s ^ SE-: •Ji a es V - t — r - ; — ) — T T T : — ^ -

^Me >:^ t » — : i - i — t — S L i 5 ^ —* —. "i"^* •9 •*• -

59

f a c t o r s t r o n g l y suppor t ing C as the f i r s t Ur l in ie n o t e . The f i r s t

r educ t ion would be t h a t of Example 6-a.

Example 6-a .

^ ^ ' • I" * ^ I 1

^

T Tlie second phrase begins l i ke the f i r s t . Hence, a re tu rn to

A

the i n i t i a l 3 i s q u i t e expected. A ques t ion here might have to do

with the descending U r l i n i e concept . Is t h i s concept v io la t ed? The

answer i s no , for in i t s descension the U r l i n i e may experience i n t e r

n a t i on when supported by the "octave d i v i d e r , " the dominant, a f t e r

which the re i s a r e t u r n t o a t o n i c t r i a d tone and a resun^t ion of i t s

descen t . One should r e a l i z e t h a t for t h i s in ter r tqpt ion to occur, t h i s

dominant must be extremely i n p o r t a n t s t r u c t u r a l l y , such as the h a l f cadence h e r e , a f t e r which i s a second p a r a l l e l - c o n s t r u c t e d ph ra se .

A 2

(When desc r ib ing t h i s y as an i n t e r r u p t i o n , cons ide ra t ion i s given

only t o these f i r s t two p h r a s e s . These phrases w i l l be r e i n t e r p r e t e d

p r e s e n t l y in r e l a t i o n to what fo l lows . ) The interriqDtion i s often an

f^ 60 14 -

agent m delineating form, such as the V at the end of the develop

ment section of the sonata-form in which the recapitulation begins ^ A A

again with 8, 5, or 3. The in terrupt ion is indicated with two

p a r a l l e l v e r t i c a l l ines as seen in Example 6-a.

In considering the second phrase, measures 9-16, one notices

more chromaticism. This chromaticism i s actually the r e su l t of even

more ornamented prolonging motions. In the arpeggiation of the two

pos i t ions of the tonic t r i a d , the B-flat neighbor note passes through

a B-natural passing note in returning to C; the F neighbor note passes

through an F-f la t (written as E-natural) in returning to E-f la t . The

C i s , of course, also embellished with an upper neighbor D-flat and

the A-f la t , a neighbor G.

In measure 13, ra ther than the soprano returning to C, here, i t

remains on the E-f la t that was brought into the top by an exchange of

voices; i t came from an inner voice and merges with the Urlinie note

only at the end of measure 14, These motions are shown in Example 6-b.

The Roman numeral I I I i s indicat ive of the fact that the

chromatic mediant i s en^loyed here in a ra ther s t ruc tu ra l pos i t ion .

The bass drops the octave; i t i s harmonized as a root , not a th i rd ,

as in the f i r s t phrase. I t i s par t of a tonic arpeggiation in the

At the time of his death Schenker was working on a study of form.

bass : I I I I i i ^ v I . (1 3 [4] 5 1)

15 61

Example 6-b.

m m^

( i ' l l The remainder of the minuet i s graphically notated in Example

6-c. The German Augmented s ixth chord appears in measure 16 to begin

the second sect ion or the digression. With the resolution of th i s

chord, the minor th i rd scale degree i s retained to effect a change

of mode. The effect of the German Augmented sixth chord as an inten

s i f i ed pre-dominant chord i s weakened by a retrogression to a weaker

pre-dominant within th is context, iv , as the embellished dominant i s

t ransfer red to an inside voice in measure 20. From this point un t i l

the l a s t beat of measure 41 , where i t i s t ransferred back to the bass

Notice that another r e l a t i ve ly important factor in bringing about the s t r uc tu r a l significance of the I I I i s the French Augmented s ix th chord which precedes i t . The voice leadings of the upper and lower leading tones are resolved in a most intense way in a s t r a t e g i c pos i t ion within the phrase.

62

Example 6 -c . Schuber t : Moments Musi caux No. 6

A

3 A.

z

p ^ :C2 ^ '

^ •X. £ $S

3g^^^==e 2 :

^^ ^ •

:22: is:::^ S3: O.

x\

3 2 :

(Jr^

•, ^

4rV

= ^

^

!7^ f> ^ y ; ? 2 : . ^J,^"

m '' * 5 ^

^ « : :2=s: zr

vO: _x

CZr E=3a o ^

A

3 A

A/AA/

^'* O- :Zt ^O ^^ ^:fei=^ JOL

T

64

where the German Augmented s i x t h function r e t u r n s , the dominant and

i t s upper l ead ing t one , F - f l a t (most of the time s p e l l e d enharmoni-

c a l l y as E ) , remain in the middle vo ice , only occas iona l ly emerging

as the bass (but always a t s t r a t e g i c p o i n t s ) . These twenty-f ive

measures a r e , in e f f e c t , a prolonged German Augmented s i x t h upper

lead ing tone to the dominant as i t i s moving to the dominant towards

the end of the d i g r e s s i o n . After i t s r e s o l u t i o n to the dominant in

measure 42, the dominant i s embell ished again by i t s o the r neighbor ,

the subdominant over the dominant peda l . The pre-dominant funct ioning

submediant leads i n t o the leading tone diminished seventh chord, which

" t h i n s ou t" i n t o a f i r s t invers ion dominant t r i a d in measure 52 where

the d i g r e s s i o n ends . The seventh i s added to the dominant in measure

53 where the r e s o l u t i o n begins the r e tu rn to "A" a f t e r what can be

viewed now as a d ig re s s ion "around" the dominant, not as a modulation

to the chromatic submediant key of E major, as i s most f requent ly the

ana ly s i s of t h i s work.

Through v o i c e - l e a d i n g s , one can now view these measures as an

i n t e n s e movement to the dominant through the German Augmented s i x t h

embell ishment. In the process of moving to the dominant, the aura l

root of the German Augmented s i x t h chord, the upper leading tone to

the dominant, i s prolonged through a t o n i c i z a t i o n brought about by i t s

own dominant and extended usage. There i s no new t o n i c ; the re i s but

one t o n i c in a tona l work because, according t o Schenker, a l l the

music i s an unfolding of the t o n i c t r i a d , the t o n a l i t y . The function

o r s i g n i f i c a n c e of E major in t h i s work in these measures i s to

prolong and heighten the s i g n i f i c a n c e of the dominant E - f l a t ; and in

65

the process becomes prolonged i t s e l f through tonic iza t ion .

A s imi la r but much less extended s i tua t ion exis ts in measures

65 through 73, except here the pre-dominant function is being

prolonged, spec i f i ca l ly the Neapolitan chord on i t s way to the

dominant ( s ix- four , f ive-three f igura t ion) . These motions too, are

shown in Exan^le 6-c.

The examples in th i s chapter have been provided as a presen

ta t ion of the primary tool with which the Brahms Opus 118 has been

analyzed. The presentat ions of the analyses and findings from these

analyses comprise the remainder of t h i s work and wil l be found in the

sect ion following the glossary of graphic symbols.

CHAPTER IV

A GRAPHIC ANALYSIS OF BRAHMS, OPUS 118

Glossary of Graphic Symbols

The various rhythmic values of notes have no rhythmic a s s o c i a t i o n s . S t r u c t u r a l s i g n i f i cance of a p i t c h i s r e l a t i v e to the i n d i c a t e d rhythmic va lues . Decreasing rhythmic values r ep resen t decreas ing s t r u c t u r a l s i g n i f i c a n c e .

Upward stemmed, open noteheads connected by a broad beam i n d i c a t e the notes of the top s t r u c t u r a l l i n e , or U r l i n i e . Arabic numbers with superimposed ca re t s are placed above those n o t e s . (Uncapped Arabic numbers i n d i c a t e an Ur l i n i e motion of the same s o r t on a more immediate l e v e l . )

by Downward stemmed open noteheads connected

a broad beam i n d i c a t e the s t r u c t u r a l ba s s .

' • , . •

The slur denotes contexts of structural relationships (for example, the third-span). It is used when beginning and ending pitches of the context are of different pitch classes. The first and last notes are structural, there fore some kind of stemmed note. Sometimes the slur is in the form of an ess, when octave transfer is employed.

The broken slur is used to connect notes of the same pitch class in a context, and denotes the return to or the retention of a single pitch. It, too, may be in the form of an ess.

66

• , ! . • •

Tlie beam often replaces the s lu r when indicat ing more intermediate and remote re la t ionsh ips . As with the s l u r , the beam may be sol id or broken,

r 1 # # ^ #

r-f

Over an extremely long context, the middle portion of the beam may be omitted. Often a direction is interpolated in the omission (for example, to meas. 80).

Crossed lines indicate exchange of voices.

fif Curved arrows indicate dominant

r e l a t ions , with the arrow pointing to the re fe ren t ia l tonic .

I -E-E'J Roman numerals denote areas and/or

points of harmonic s ignif icance. Relat ive size denotes re la t ive s t ruc tu ra l s ignif icance.

r IT r JT

T- » J

A horizontal brace denotes a succession of local harmonies essent i a l l y prolonging and embellishing one of broader, s t ruc tu ra l s ignif icance. The same aspect may also be shown by an arrow following a s ingle Roman numeral.

£-'(0' S-'L, ite. Figured bass type .Arabic numbers

denote the employment of techniques of voice-leading, or the l inear or contrapuntal functions of a ser ies of sonori t i e s .

Pa ra l l e l l ines indicate the location of a break or in ter rupt ion in the s t ruc tu re .

68

The Work as a Whole

The s i x p i eces of Opus 118 e x h i b i t a remarkable degree of uni ty

wi th in each and are un i f i ed as well as a whole. Each revea ls a

mastery of tona l o rgan iza t ion with utmost economy.

Each of the s i x p r o j e c t s an Ur l in i e of 3 2 1, r e s u l t i n g in

compatible s t r u c t u r e s . The t o n a l i t i e s a lso con t r ibu te to the sense

of un i ty in t h a t they are r e l a t e d by s t e p , as demonstrated in Example

1 below.

Example 1,

I g ^ »' 4" * « j . ^" a J j"" a ^ ia r.^ ^ &a-

» L J L J L J L J L J L

Addi t iona l aspec ts of u n i t y revealed in the diagram above are

shown in Figure 2 .

1. An element of palindrome:

m I—?=^—1 M m m .M m

2. Step p rog re s s ion :

A G ^ _ ^ F ^ ^ ^ ^ - f l a t

3. R e p e t i t i o n :

a. A, g moved down a 3rd = f, F, e - f l a t

4. Change of mode:

a - A and F - f

Figure 2 . Aspects of un i ty in Brahms, Opus 118.

69

These face t s are a lso supported by express ive a spec t s . The

p i e c e s f lanking e i t h e r end, Nos. 1 and 6, are the most harmonically

o r i e n t e d , whose piano t ex tu r e s are b a s i c a l l y a rpegg ia t ion , and whose

t o n a l i t i e s are most ambiguous. The two major t o n a l i t i e s , Nos. 2 and

5 , are the most l y r i c a l , whose subs t ruc tu re s involve submediant

p r o l o n g a t i o n s . The i n t e r i o r ones, Nos. 3 and 4 , are the most

u n s e t t l e d , and end with the coimnon r i s e of the dominant tone from an

i n n e r vo i ce , a prominent aspect of each.

The mot iv ic connection of the pe r f ec t fourth and a long extended

s t r u c t u r a l dominant are prominent. The vo ice- lead ing graphs reveal

o rgan iza t i on and tona l coherence within a work whose cont rapunta l and

express ive q u a l i t i e s have long been recognized. They also revea l

aspec ts of o v e r a l l s t r u c t u r e , aspects which con t r ibu te to the under

s t and ing of a t r u l y remarkable work of u n i t y .

No. 1, Intermezzo

The Commentary

The f i r s t " In te rmezzo ," only forty-one measures in l eng th , i s

perhaps the l e a s t complicated of the s e t . The f i r s t ten measures are

a mediant p ro longa t ion e f fec ted by a top voice movement from C (5)

through p a r a l l e l cons t ruc ted s o n o r i t i e s (chords of the s i x th ) to i t s

octave t r a n s f e r p r i o r to the t o n i c i z a t i o n of C ( I I I ) in measure 8.

Problemat ic in t h i s passage i s the B-f la t of the second measure. The

sound i s t h a t of a major-minor seventh chord. However, the chord

does not r eso lve as such, and upon examining the v o i c e - l e a d i n g s , i t

becomes apparent t h a t p a r a l l e l s o n o r i t i e s are a t work in t h i s passage ,

r a t h e r than func t iona l movements. These chords of the s i x t h are

70

a r t i c u l a t e d through the occurrence of an appoggiatura .

The middle p o r t i o n of t h i s work, measures 11 through 2 8, i s the - >

s t r u c t u r a l dominant prolongation, r i s ing from the y in measure 13 to

G as pa r t of the C major sonority and bearing the same material as

the opening measure. This material is at tained af ter three measures

of chromatic bass motion up to the dominant E, The effect of a l l th i s

r i s e out of the chord i s that of an upper neighbor embellishment.

The rea l cadence, tha t i s , the resolution of th is eighteen-

measure dominant, i s in measure 28. From here un t i l measure 39 i s 9

tonic prolongation. Measure 31 appears to be vii/V resolving to V

in measure 34. One might believe this progression i s preparing the

f inal cadence to tonic . However, the directed melodic ac t iv i ty

reached i t s goal in measure 28, and the tonic chord of resolution

becomes a secondary dominant headed towards the subdominant embellish-•7

ment of tonic (vi i° / i v over dominant peda l ) . The bass a r r iva l upon

tonic i s not so strong as might otherwise be because of the subdorai

nant t r i a d above, f i r s t major then minor, with obvious melodic ac t iv i ty

producing the embellishment shown in the middleground graph.

The bas ic material of th is "Intermezzo," is harmonic arpeggia

t ion . An inportant aspect of the harmonic-tonal s t ructure is the

beginning of the bass arpeggiation on 3 ra ther than on 1, creating an

impression as though the work begins between tonic and dominant,

progressing immediately to dominant, as indeed i t does. (Refer to

the commentary of No, 6 regarding the i n i t i a l ambiguity of that p iece . )

The melodic span of the perfect fourth i s also of importance, as i t i s

in numbers 2, 3, and 5.

hc_j\n ajj^ s i s

Ursat;

Background:

I z- X

itftrs -*.;f^ 1

^ ' jO

I 1 T

J 2 A 1

^ ^ I ^ I

^ f

Middleground

? ?-

^

; ^ ^ . ^ ' ^ • r " ^ - < . -

A 7 -2 1

* • ^9 s ^ - 13

^ nr ' 0^ ¥=^ * ^^ r- 7 f;: ' ' - ' ' . ^ ^

II

*^*- i^ p' ^

J

Foreground / -

± -1 W i 32:

: ^ 2=s; ^ e: 4ba ^

^

^

i 4—L

= ^

^

#

s ^ 12^ :g ' :£ ' ^ ^

^ # = g Ipc

VI ir ^ r T^

IE

, J

^ » ^ ^

^

s 5?=t :xt g»^ g m

rr

? ^ iLfiL

^

^

^ ^

* •

I I in'" H i g

ITT

w :a=±

:CC

^T ' ^

^ ±e:

%

No. 2, Intermezzo

The Commentary

The second of Opus 118, also an "Intermezzo," is s t ructured on A

a background of a prolonged x foi" forty-eight measures before a

submediant (and consequently, continued tonic) prolongation un t i l

measure 76. At th i s po in t , with the obvious return of the beginning

mater ia l , the prolongation continues only un t i l measure 84, where the

s t r uc tu r a l dominant i s heard. The resolution of the s t ruc tura l domi

nant i s heard at measure 106, af ter which i s a final tonic prolon

gat ion.

The i n i t i a l tonic prolongation reveals a substructure of A A A 3 2 1 p a r a l l e l construction to the overall s t ruc tu re , i . y . j . Following

th i s prolongation i s that of the submediant during which time the

descending perfec t fourth (the melodic material of measure 1) i s

e s sen t i a l l y the only mater ia l . Brahms presents th is material in

counterpoint , change of mode, and inver t ib le counterpoint during th i s

prolongation. This same fourth, which both opens and closes the

"Intermezzo," also serves as the material for the high points of

measures 1 through 48 and measures 76-end, The climax occurs within

a dominant prolongation on the middleground level , within a neighbor

ing subdominant ornamentation. I t is further enhanced by the use of

hemiola (the only instance of such rhythmic use on the foreground

level in the "Intermezzo.") (See measures 29 and 97.) At work within

t h i s piece i s extensive use of prolonged, and consequently s ign i f i can t ,

subdominant and supertonic harmonies, (See measures 50 through 37.)

TIic Analysis

Ursa tz :

^ ^ ^ ^CX.

'0}\^^ *^Li 1

l / t

r x~^

Background:

A

2

^ i

A

# tf €>^^- r ^ ~ 7 -»' ^

A i

^^IP ^' 1 ^r* ^ r

^ ^ ±*

l e t i

7 ;

t s IS v/'j'r

I vi X 1

Foreground

i * ; 2z: ' ' ' . , ^ _ ^ V'# g ^

3 E ; be?: *«•> ^ ^ # K # f * ^

7"

^ ^ 32: ^ « = fl"^

Middleground, Level 1

5E c \< "i^^

^ 3fc

r U

2 2 : •^— 1 a

M V

? • r - g -

)4Ji m XT-

^^m

^ ~*~Y* -VT

ir:^

- ^

^ ^ ^ ^ ^ ^ ^ E ^ ^^€> ^ ' - ^ — ^ r f—

31 ^

;•'/'• T _ « ^

= = = ^ « % ^

jr^

i • ^ ^

^ ^ y g

« - « ?8gg ^ * > • • '

; V * -

^

t J -T

p 3 - » * -

dfct iirV= 2 E

s r - : 5 v _

79

W ^

1 s ^

'•'. .-'- !a -»-. _« _

^ ^

' i ''l^i^'*^-jrzr

" g ^ ^

S

jg ,^

5 ^ 1 ^ ^

i £ f atac

^ ^

80

^ d ^ 0 ^ » ^ ¥ * t ^ ^ O^' -n

i^zza: ^ ^ ' t ^ ^ ^i

S ^

1351

• - ^ - ^ ^ : - y ^ = »

s

: ^ St

^

81

'¥ r^t^

^

^ 5 E 0 9 M ^

^ 0 ei

m m g #

:?2: #-3"

r. 3

82

p^tti ^ ^ \ r\ - p ^

i( J- ^T- IV %) J

M g ^

f* ^

: i=^ * ^ ^ -

f

85

Middleground, Level 2 :

i k

{0 f '^' ^UjT^ *• ' ' ' ^

SB

^ 3 ^ i ] ^ :?c

221 :©:

1 ^

i ^ i! ^ ^ f f m^

'J)' 'k/ -tt-

84

^ \\v \'

^S^'^^

^ ^ 0 p =#=^^ 3 ;

T

^

^ ^ r J^^^«^^i^.\', ^ f a g ^

^ s:; ^

^

85

U f i^^j, ^s vt t=»=¥--/i,*'^7r^-^^^ ^ ^^

T*^^ s f^-er

jjj^i b t^^^ U 4 L - ^ ^* ^0r ' ' ^ ^ ^ ^ 2z:

/ I / - ^

I 4i i g » =F

^ 3a: : E : izz:

36

m t- [ (

3 , . ^ = ^

-^0 7*

< I

— — ^

^

^ vl^^^> '''11 ^''"T^^ •:z=zz==z=B=^ ^ ^ t.

5(fcZE

3 t

V

g k 32:

1

^ ^-^^

"31 D"

87

^

I si

T-'-g fi II ~ ^

-o—•-tr, ' ^

^

I r- '^ ^

. *> 6

2S5:

^ ' 6^

^ 3S?

^ ^ ape:

88

i Uf <\ . <f r'^ ' ^

0 §0 it ^ ^

SB

, ^ #

' ' .i- ^ ^ ^ E 5 = • * - . -

f = ^ ^ ^ "H ^ ' ^ rr '

I ! \ iti g ^

'^'M' 9 ^ m - T ^

89

J' i:lf

A^ ^ u^ ^ ^0 ^ 1 1 ^ ^0 0f* ^

^ ^ — , •*

r / i ^

:2z:

i ^ ^

^

^ k

i/i--^

-e-

.-hli

^

i.'> iff-e-

^

i : s = 3 j ^ . f i^.$- i - ^ ' ^ ^

:«?: 122: : ^

iT ' I . ^ jy. I K I " JL

90

\¥ ,'' ' . ^ # ^

^

i -

= 2 5 = ^

f"

p 4 *

te ^ t * lg

fj^m^ yi> /o f

91

yi I i

^

2s: 2z:

^

^ ^

9;

• ^ ^ ^ ^ '• - -

^ g zsn

r

az2^ ^ ^ i ^ ^ ^ ^ i ^ - r - ^ ^ X < V=

s J

^

4. ^

* * » k

M in

'^•4f(^ ^

ff

iJ^ S

^

0 "2^ ^ 1

_ •_ ^- - 'f

94

No, 5, Ballade

The Commentary

The "Ballade," the third piece of Opus 118, has a somewhat

extraordinary prolongation within the center of the work, after a A ^ A 3 2 1 complete s t r u c t u r a l prolongation of i_y_x> of the opening tonic

(measures 1-37). At th is point (measure 38) the bass arpeggiates to

the major th i rd scale degree, which is then prolonged for thirty-two A A A

3 2 1 measures, producing i t s own substructure j . y . j , af ter which i s a

restatement of the f i r s t prolongation (measure 77), The bass

arpeggiation i s that of a major tona l i ty while the Urlinie is that

of a minor tona l i ty embellished by the upper neighbor major 5. An

in t e rp re t a t ion i s that the tona l i ty of G i s unfolded in both i t s

major and minor forms, as indeed the foreground modalities do f luctuate

between major and minor. Also of i n t e r e s t i s the inner voice D, 5th,

t ha t r i s e s to importance by i t s ornamented prolongation at the end,

a c h a r a c t e r i s t i c common to No. 4.

Tlie Analysis

Ursa t z :

P 5E

k I^^^P^ Sz^Eu^

^ (g # I ^

r TTT - ^ X

Background:

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A

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1 Z '

l-^J ii ^ ^ l a i ^ i d - t J > -

4-$" J

ITU' , : f f n- rTTf iiEj: X

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Foreground: 96

m f,t, g"ifc

Middleground, Level 1:

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98

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^ - ^ ^ - ^

:^=^' V ' ' i ^ ^

I h J = z m — ^ :

m w. "ZITT^

t ^

a. »

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4S^ 4 » •^—m 0-zs: H i f ^ A ^

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^ ^

r v^


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db* 'f ii / - / _ ^ ^ e. ^ * -T^-t T

^m^ -XMl

^ a ^ i • '•

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101

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106

No. 4, Intermezzo

The Conmientary

The " In t e rmezzo , " Opus 118, No, 4, i s a v i r t u a l canon from

beginning to end. I t i s not as harmonically adventurous as the o ther

f ive in t h a t the only s t r u c t u r a l pro longat ions are those of t on i c and

dominant. (There i s , however, an i n t e r e s t i n g aspect to the s t r u c t u r a l

dominant p ro longa t ion beginning in measure 16.) Although the re

appears to be a s e c t i o n in A - f l a t , upon fu r the r examination and

l i s t e n i n g , the ea r i s led through a motion out of and back i n t o the

dominant, e f f e c t i n g p a r t of the dominant pro longat ion shown in the

v o i c e - l e a d i n g graph of measures 5 3 through 85. The s t r u c t u r a l

dominant i s reached in measure 16, followed by an ornamentation

through the German Augmented s i x t h (measure 35) with a not so obvious

r e s o l u t i o n to the t o n i c s i x - f o u r a t measure 39 which f i n a l l y becomes

dominant f i v e - t h r e e in measure 47. The music following i s the p r o

longat ion of measures 53-84, d iscussed above. Following these

measures i s motion out of V, to 14 in measure 98, through the I t a l i a n

Augmented s i x t h in measure 109, back to the ton i c s i x - fou r with i t s A 2

f ive- three resolut ion in measure 109 as the y, which resolves to the

s t r u c t u r a l tonic prolongation in measure 110. This tonic is prolonged

through subdominant ornamentation, f ina l ly effecting what i s commonly

cal led a plagal cadence, which i s obviously a f inal tonic prolonga

t ion sending a middle voice to the top for a 5th to r i s e from the

inner voices . (See discussion of No. 5.)

.V

Tlie Analysis IC

Ursa t z :

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^m ^ i

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Background

108

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109

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114

No. 5, Romance

The Commentary

Although a l l of these pieces are very t i g h t l y - k n i t , economically

constructed works, the "Romance," No. 5 of the Opus i s perhaps the

most economical. The i n i t i a l tonic prolongation is created through

the statement of four phrases. The i n i t i a l halves of these four

phrases are i d e n t i c a l , with the second halves resul t ing in a half

cadence in F major in the f i r s t and th i rd phrases and a half cadence

in d minor in the second and fourth phrases. Variety is created

through a technique of " inver t ib le counterpoint" where the f i r s t

Url inie tone i s actual ly revealed as the top-most voice in measure

9, a f t e r i t s previous occurrence as an inner voice in the preceding

two phrases .

The middle section i s not only a prolonged submediant, but a l so ,

and more importantly, a prolonged 5 (Urlinie note) reharmonized and

suspended over the V/vi. This middle section is the ornamentation of

a three-voice s t ruc ture through rhythmic var ia t ion , which becomes

increasingly complex and ac t ive . These phrases, l ike those of the

f i r s t sec t ion , are bas ica l ly a repeated four-measure phrase. They

are " c i r c u l a r " in nature in that they move to a V'/V which resolves to

a V melodically and often harmonically, but a l l over a D pedal.

Pa r t i cu l a r ly i n t e r e s t i n g in th i s piece is the r i s e from the

inner voice which occurs repeatedly in measures 40 through 44. Also

of i n t e r e s t i s the ornamentation pat tern of the neighbor note f igure ,

a pa t t e rn whose basis i s in the f i r s t notes and i s the whole manner of

ornamentation in the middle sec t ion .

Thc__An^j.2^^is

115

U r s a t z :

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128

No. 6, Intermezzo

The Commentary

The most t o n a l l y unusual of the s e t i s tne " In te rmezzo ," No. 6.

The t o n a l i t y of E - f l a t minor i s not s u b s t a n t i a l l y e s t a b l i s h e d u n t i l

towards the end. The most p r e v a l e n t soinid during the f i r s t p a r t i s

t h a t of the diminished seventh chord, A-C-E-f la t -G-f la t . , Four r e so -

l u t i o n s of t h i s chord ' a re explored within the work. The f i r s t i s to

t o n i c s i x - f o u r , which then becomes absorbed as a pass ing chord in to

the C h a l f diminished seventh chord, as in measures 3 through 8. The

second r e s o l u t i o n i s t h a t found in measure 11.. Here the chord i s not

r e a l l y reso lved a t a l l but i s extended downward to become a dominant

n i n t h chord. The F dominant n in th chord resolves to a B- f la t minor

t r i a d which becomes prolonged through measure 19. I t i s a t the end

of t h i s p ro longa t ion t h a t the t h i r d and fourth r e so lu t i ons are

encounte red . The diminished seventh chord of measure 17 resolves as

though i t were an apparent C diminished seventh , reso lv ing to what

appears t o be a D- f l a t major t r i a d . By the end of the measure,

however, the e a r has r e a l i z e d t h a t the chord was an A diminished

seventh chord a l l along and did reso lve to B-f la t minor. I t i s t h i s

ambiguity of roo t t h a t enables the ea r to hear these two r e s o l u t i o n s ,

one an apparent r e s o l u t i o n , the o t h e r perhaps the r e a l r e s o l u t i o n .

Although one might expect to hear a t o n i c i z a t i o n of G-f la t from

measure 41 on, B- f l a t minor i s heard as the tonal area for t h i s e n t i r e

s e c t i o n , r e v e a l i n g a con t inua t ion of the pro longa t ion of the s t r u c

t u r a l dominant. This B- f la t minor evolves i n t o a B- f i a t dominant

t h i r t e e n t h chord which r e so lves i n to the f ina l t on ic pro longa t ion in

129 measure 55 , a f t e r which i s a r e t u r n to the nebulous tonal impl ica t ions

of the A diminished seventh chord. These nebulous q u a l i t i e s , however,

are no t e x p l o i t e d now, for there i s a movement to the embel l i sh ing

subdominant s i d e - - t o the submediant, then to the Neapoli tan before

a r r i v i n g iq)on the dominant, which i s weakened througli the r e t r o g r e s s i o n

t o the s u p e r t o n i c ha l f -d imin i shed seventh before moving to t o n i c .

There then follows a double s ta tement of the motivic top t h i r d of the

beginning diminished seventh chord, t h i s t ime, however, without i t s

diminished seventh ambiguity.

The Analysis

Background:

s i

mi h^

\f n^ I p* p- ^

Ursa tz :

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CHAPTER V

CONCLUSION

Schenker's conception of tonal music--that a tonal work is a

unique i n t e rp re t a t i on of the t r i ad and is an unfolding of that t r i ad

over a period of time--has profound implications for the teaching of

music theory in the college curriculum. Since music theory is con

cerned with developing avenues of understanding for the ent i re a r t of

sound, i t i s responsible for developing a framework within which one

can expectantly approach a l l music. Tlie framework should be fashioned

from re la ted or compatible p a r t s , from par ts that grow out of or

con^lement each o ther- -not from those of such to t a l divers i ty that

each piece of music or each s ty le period has to be approached from

such a t o t a l l y new direct ion that any sense of coherence or i n t e r

re la t ionsh ips i s lacking. The Schenkerian concept of s t ruc tu ra l

levels can provide a basis for approaching a l l music.

Although Schenker never intended for his concepts to apply to

music other than tonal music through the nineteenth century, these

bas ic concepts regarding tona l i ty are applicable to a l l tonal music--

t e r t i a n , t r i a d i c , or otherwise. The emergence of tonal i ty in music

stands as a milestone in the h is tory of the development of music,

much as the emergence of perspective in the development of paint ing.

Perspective may be at work in a paint ing regardless of whether or not

the pa in t ing i s represen ta t iona l . Likewise, tona l i ty may be at work

146

14'

within a musical composition, regardless of whether or not the music

i s in a "key." Through the elimination of non-essential tones by

considering such factors as r epe t i t i on , doubling, duration, dyna^mcs,

r e g i s t e r , recurrence, rhythmic pos i t ion , posit ion within motion, e t c . ,

a reduction of a post - tonal work may reveal a manner of growth and

elements of un i ty , whose presence otherwise might not have been

revealed. The r e su l t s wi l l not be an Ursatz of the Schenker var ie ty ,

but i t i s j u s t such a r e su l t that might il luminate another aspect of

s t y l e . Several t heo r i s t s are presently expanding these theories in

th i s d i r ec t ion . (Notable are the works of Forte, Katz, Travis, and

Morgan.)

These concepts are equally compatible with pre-functional modal

music. Since t h e i r basis i s p a r t i a l l y in counterpoint, they are as

eas i ly applied to that music in the reduction process as to post-

tonal music. The reductions wil l reveal backgrounds of types other

than Schenker's Ursatzen, but again, i t i s th is very fact that

va l ida tes the applicat ion of the p r inc ip les .

Admittedly, Schenker's concepts are d i f f i cu l t for the beginning

freshman to fully comprehend and appreciate. But i s i t necessary to

know the source of the g i f t in order to use i t ? .An invest igat ion of

recent undergraduate theory textbooks will reveal Schenker's wide

spread, inescapable influence. The r e su l t of his influence can be

seen in works as ear ly as P i s ton ' s Harmony, through Salzer ' s

S t ruc tura l Hearing, Kliewer, e t a l . (Materials and Structure of

Music), For te ' s Tonal Harmony in Concept and P rac t i ce , and numerous

others un t i l f ina l ly his influence is openly acknowledged in such

148

p u b l i c a t i o n s as K r a f t ' s Gradus, and Aldwell and Schach te r ' s Harmony

_gnd Voice-Leading, and i s the foundation from which they sp r ing .

The study of music has t r a d i t i o n a l l y been approached on the

freshman l eve l from p r i m a r i l y a harmonic s tandpoin t . After a cursory

s tudy of melody (often wi th in the span of th ree to s i x weeks i f

undertaken a t a l l ) , the long and bewilder ing study of chords i s begun.

This s tudy commences with the memorizing of ru les of p a r t wr i t i ng

(not_ vo i ce - l ead ing ) through the app l i ca t i on of those ru les to four-

voice s t r u c t u r e s and ends with the f r u s t r a t i o n r e s u l t i n g from the

seeming i r r e l e v a n c e of those ru l e s to the s t y l e s of the l a t e n ine teen th

and t w e n t i e t h c e n t u r i e s . How much more exc i t ed the s tudents (and

t e a c h e r s , fo r t h a t mat te r ) would be i f the music could be approached

f i r s t from a broad view—a view po in t which allows the use of terms

a p p l i c a b l e to v i r t u a l l y a l l music. Most music c rea tes a sense of

t ens ion and r e l e a s e , with tens ion sometimes crea ted through i n s t a b i l i t y

dur ing tona l movement to a d i r e c t i o n a l goa l , such as the movement to a

h a l f cadence, the movement to the r e l a t e d key area during the br idge

pas sage , or the v i r t u a l l y cons tan t movement in a Wagnerian passage .

Sometimes t h a t movement i s r a t h e r s t rong and/or a b r t ^ t (as in some

Schubert s o n g s ) , o t h e r times r a t h e r weak and/or sub t l e (as in some

Debussy P r e l u d e s ) . During t h i s broad-view approach, the s tudent

could become f a m i l i a r with terms such as l i n e a r , v e r t i c a l , s p a t i a l ,

d imens iona l , p ro longa t i on , background, e t c . , terms appl icable to a l l

music.

To support the s t u d e n t s ' conceptual growth, the aura l work

must be aimed in the same d i r e c t i o n . I t i s here—in the area of the

149

a u r a l sk i l i s - - t h a t much innova t ion , exper imenta t ion , and research are

needed. Schenker ' s t h e o r i e s were based in h i s percept ion of musical

works, and by imp l i ca t i on can be the b a s i s for o t h e r s ' p e r cep t i on .

In an i n v e s t i g a t i o n i n t o the aura l aspect of harmonic rhythm in an

e a r l i e r s t u d y , the au thor found t h a t s tudents seemingly heard the

o v e r a l l t ona l d i r e c t i o n of a phrase more c l e a r l y than the ind iv idua l

harmonic changes w i t h i n . I t i s h ighly probable t ha t most l i s t e n e r s '

p e r c e p t i o n of music i s more in l ine with Schenker 's middleground than

t h a t of the sur face harmonic rhythm anyway. There i s a l ready some

a c t i v i t y in t h i s d i r e c t i o n with the recen t pub l i ca t i on of Gerald

W a r f i e l d ' s Layer D i c t a t i o n . This work i s , admit tedly , only a

beg inn ing , and paves the way for more i n v e s t i g a t i o n .

A program so s t r u c t u r e d would r equ i re t h a t the i n s t r u c t o r be

ab le to hear and d iscuss music from these vantage p o i n t s . Although

Schenker ' s concepts have inf luenced most t h e o r e t i c a l s t u d i e s , there

i s s t i l l some t h e o r e t i c a l thought which has co-ex i s ted v i r t u a l l y

untouched. I t i s t h i s a u t h o r ' s opinion t ha t although Schenker 's

t h e o r i e s are no t wi thout f laws, they do offer a way of understanding

a musical work in i t s e n t i r e t y and i t s c o n s t i t u e n t r e l a t i o n s h i p s and

consequent ly should be a t the core of a l l graduate s tud ies in theory .

One f i n a l conclusion and area for fu r the r i n v e s t i g a t i o n should

be r a t h e r obvious —tha t an unders tanding of a work derived from a

^James Lamb, "Aural Harmonic-Rhythmic Percept ion of Theory Students a t Sam Houston S t a t e U n i v e r s i t y , " Master ' s Thes i s , Sam Houston S t a t e U n i v e r s i t y , 1970, p . 100.

150

reduc t ion process y i e l d i n g a background s t r u c t u r e wi l l have d e f i n i t e

performance i m p l i c a t i o n s . Being cognizant of the s t r u c t u r a l dominant

can only heighten the p r o j e c t i o n upon i t s a r r i v a l with a r e s u l t a n t

response in the l i s t e n e r .

Heinr ich Schenker developed a theory of t o n a l i t y and a method

of comprehending and pe rce iv ing t o n a l i t y within music. His method

involves reducing the surface a r t i c u l a t i o n s to reveal the underlying

s t r u c t u r a l design and coherence. Applying the method based on those

p r i n c i p l e s to the s i x p ieces of Brahm's Opus 118, one discovers

o rgan i c un i ty and i n t e r r e l a t i o n s h i p s . Also discussed i s the

p o s s i b i l i t y t h a t Schenker ' s t h e o r i e s have far - reaching impl ica t ions

which can a f f e c t t h e o r e t i c a l study and should be the source of

f u r t h e r i n v e s t i g a t i o n in these d i r e c t i o n s .

BIBLIOGRAPHY

Aldwel l , Edward and Carl Schachter . Harmony and Voice Leading.

2 v o l s . New York: Harcourt Brace Jovanovi tch, 1978.

B a b b i t t , Mil ton. Review of S t r u c t u r a l Hearing: Tonal Coherence in

Music, by Fe l ix S a l z e r . American Musicological Society Jou rna l ,

5 (1952), 260-65.

Ba t s tone , P h i l i p . "Musical Analysis as Phenomenology." Perspec t ives

of New Music, 8 (1969), 94-110.

Beeson, Roger A. "Background and Model: A Concept in Musical

A n a l y s i s . " The Music Review, 32, No. 4 (1971), 349-359.

Boatwright , Howard. Review of Contemporary Tone S t r u c t u r e s , by

Allen F o r t e . Journa l of Music Theory, 1 (1957), 112-118.

. "Re: Contemporary Tone S t r u c t u r e s . " Journal of Music

Theory, 2 (1958) , 85-92.

Broder, Nathan. Review of S t r u c t u r a l Hearing: Tonal Coherence in

Music, by F e l i x S a l z e r . Musical Qua r t e r ly , 39 (1953), 126-8.

Burkhar t , Cha r l e s . "Schenker ' s 'Mot ivic P a r a l l e l i s m s , ' " Journal of

Music Theory, 22, No. 2 (Fa l l 1978), 145-175.

Campbell , Bruce. Review of Layer Ana lys i s : A Primer of Elementary

Tonal S t r u c t u r e s , by Gerald Warfield. Journal of Music Theory,

22 , No. 2 (Fal l 1978), 313-16.

Garner, Mosco. Review of S t r u c t u r a l Hearing: Tonal Coherence in

Music, by F e l i x S a l z e r . Musical Times, 94 (1953), 261.

151

15.

C i tkowi t z , I s r a e l . "The Role of Heinr ich Schenker." Modem Music,

11 (1932), 18-23.

Cogan, Robert and Pozzi Escot . Sonic Design: The Nature and Sound

of Music. Englewood C l i f f s , New J e r s e y : P r e n t i c e - H a l l , I n c . ,

1976.

Cone, Edward T. "Analysis Today." Musical Quar te r ly , 46, No. 2

(Apri l 1960), 172-88.

• "Musical Theory as a Humanistic D i s c i p l i n e . " J u l l i a r d

Review, 5, No. 2 (1958), 8.

Cooper, Grosvenor and Leonard B. Meyer. The Rhythmic S t ruc tu re of

Music. Chicago: Univers i ty of Chicago P r e s s , 1960.

Dahlhaus, Ca r l , "Schoenberg and Schenker." Proceedings of the Royal

Musical Assoc i a t i on , 100 (1974), 209-15.

Deutsch, Ot to E. "Reply to Mann's 'Schenker ' s Contr ibut ion to Music

T h e o r y . ' " Music Review, 10 (1949), 248.

Drabkin, William. Review of Music Forum IV, ed. Fel ix Sa lze r . Music

and L e t t e r s , 59, No. 1 (1978), 79-82.

Duckworth, William and Edward Brown. Theore t ica l Foundations of

Music. Belmont, C a l i f o r n i a : Wadsworth Publ ishing Company,

I n c . , 1978.

Dunsby, Johnathan M. "Schoenberg and the Writings of Schenker."

Journal of the Arnold Schoenberg I n s t i t u t e , 2 (1977), 26-33.

F o r t e , Al len . Contemporary Tone S t r u c t u r e s . New York: Columbia

Univers i ty P r e s s , 1955.

. "Re: A Review in Our Issue of March, 1957." Journal

of Music Theor>-, 1 (1957), 201-5.

155

F o r t e , Al len . "Schenker ' s Conception of Musical S t r u c t u r e . " Journa l

of Music Theory, 3 (1959), 1-30.

G e i r i n g e r , Kar l . "Heinr ich Schenker." Grove's Dictionary of Music

and Musicians , 5th ed. , ed. E r i c Blom. New York: S t . Mar t in ' s

P r e s s , 1955. Vol. VI I , pp . 477-78

G e i s s l e r , Fred. Reviews of Layer Analys is : A Primer of Elementary

Tonal S t r u c t u r e s , by Gerald Warfield; In t roduct ion to Tonal

Theory, by P e t e r Westergaard; Gradus, by Leo Kraft ; and

Sonic Design: The Nature and Sound of Music. Notes, 34

(1977) , 330-34.

G e t t e l , Will iam D. "Re: Analysis and Elementary Harmony." Journal

of Music Theory, 2 , No. 2 (1958), 240-49,

Guck, Marion A. , e t a l . "Analysis Synposium: Brahms, 'Der Tod, das

i s t die kuhle Nach t , ' Op. 96, No. 1 ." In Theory Only, 2 , No. 6

(Sept . 1976), 16-45.

Hopkins, Robert G. Review of The S t r a t i f i c a t i o n of Musical Rhythm,

by Maury Yeston. Notes , 34, No. 1 (1977), 77-80.

J o n a s , Oswald. Review of S t r u c t u r a l Hearing: Tonal Coherence in

Music, by F e l i x S a l z e r . Notes , 10 (1953), 439,

. "The Photogram-Archives in Vienna." Music and L e t t e r s ,

65 (1934) , 344-47.

Joseph , Charles M. Reviews of An In t roduc t ion to Tonal Theory, by

P e t e r Westergaard and Layer Ana lys i s : A Primer of Elementary

Tonal S t r u c t u r e s , by Gerald Warfield. The American Music

Teacher (Feb.-March 1979), 46-48.

154

Kal ib , Sylvan. "Thi r teen Essays from the Three Yearbooks 'Das

Meisterwerk in der Musik' by Heinrich Schenker: An Annotated

Trans l a t i on (Vol. I - I I I ) . " Ph.D. Diss. Northwestern Un ive r s i t y ,

1973.

K a s s l e r , Michael . "Exp l i ca t ion of the Middleground of Schenker 's

Theory of T o n a l i t y . " Miscel lanea Musicologica, 9 (1977), 72-81.

' "A T r i n i t y of Essays: Toward a Theory That i s the

12-note Class System; Toward Development of a Construct ive

Tona l i t y Theory Based on Writings by Heinrich Schenker; Toward

a Simple Programming Language for Music Information R e t r i e v a l . "

Ph.D. Diss . Pr ince ton Unive r s i ty , 1967.

Katz, Ade l l e . Challenge to Musical T rad i t i on . New York: A. A.

Knopf, 1945.

. "Heinr ich Schenker ' s Method of Ana lys i s . " Musical

Q u a r t e r l y , 21 (1935), 311-29.

K e l l e r , A. R. "The Syntax of Prolongat ion (within Context of

Theor ies of Heinr ich Schenker ) . " In Theory Only, 2 (Aug. 1977),

3-27.

K e l l e r , Hans. Review of Contemporary Tone S t r u c t u r e s , by Allen For te .

Music and L e t t e r s , 37, No. 2 (April 1956), 187-89.

K e s s l e r , Hubert . "On the Value of Schenker ' s Ideas for the .Analysis

of Contemporary Music." P e r i o d i c a l of Theory-Composition,

I l l i n o i s S t a t e Music Teachers Assoc ia t ion , 1 (1958), 1-11.

Komar, Ar thur . " L e t t e r to the E d i t o r . " Journal of Music Theory,

5 (Apri l 1961) , 152-56.

15o

Komar, Ar thur . Theory of Suspensions. P r ince ton , N.J . : Pr ince ton

Univers i ty P r e s s , 1971.

Kraf t , Leo. Gradus: An I n t e g r a t e d Approach to Harmony, Counterpoint ,

and Ana lys i s . New York: W. W. Norton § Company, I n c . , 1976.

Krueger, Theodore Howard. ' "Der f r e i e Sa tz ' by Heinrich Schenker:

A Complete T r a n s l a t i o n and Re-ed i t ing . Vol. I : The Complete

Text . Vol. I I : Supplement of Musical Exan^Dles." Ph.D. Diss .

Un ive r s i t y of Iowa, 1960.

Kudlawiec, Dennis Paul . "The Applicat ion of Schenkerian Concepts of

Musical S t r u c t u r e to the Analysis Segment of Basic Theory

Courses a t the College Level ." Ed.D. Diss . Univers i ty of

I l l i n o i s a t Urbana-Champaign, 1970.

Lamb, James. "Aural Harmonic-Rhythmic Percept ion of Theory Students

a t Sam Houston S t a t e U n i v e r s i t y . " Masters Thes i s , Sam Houston

S t a t e U n i v e r s i t y , 1970.

Lang, Paul Henry. E d i t o r i a l . Musical Quar te r ly , 52 (1946), 296-302.

Laskowski, Lar ry . Heinr ich Schenker: An Annotated Index to h i s

Analyses of Musical Works. New York: Pendragon P re s s , 1978.

Lerdahl , Fred and Ray Jackendoff . "Toward a Formal Theory of Tonal

^4usic." Journal of Music Theory, 2 1 , No. 1 (Spring 1977),

111-171.

Lloyd, Norman. Review of S t r u c t u r a l Hearing: Tonal Coherence in

Music, by Fe l ix S a l z e r . Notes , 10 (1953), 458.

Mann, Michael. "Schenker ' s Cont r ibut ion to Music Theory." Music

Review, 10 (1949), 3-26.

156

Mel l e r s , Wi l f r id . Review of S t r u c t u r a l Hearing: Tonal Coherence in

Music, by Fe l ix S a l z e r . Music and L e t t e r s , 54 (1955), 329-52.

Meyer, Leonard B. Emotion and Meaning in Music, Chicago: Univers i ty

of Chicago P r e s s , 1956,

M i t c h e l l , W. J . "Heinr ich Schenker 's Approach to D e t a i l . " Musicology,

1 (1946), 117-28.

• Review of Harmony, by Heinrich Schenker, ed, and t r a n s .

Oswald Jonas . Musical Quar te r ly , 41 (1955), 256-60.

Morgan, Robert P. "Schenker and the Theore t ica l T rad i t i on : The

Concept of Musical Reduction." College Music Symposium, 18,

No. 1 (Spring 1978), 72-96.

Narmour, Eugene. Beyond Schenkerism: The Need for A l t e rna t i ve s in

Music Ana lys i s . Chicago: Univers i ty of Chicago P re s s , 1977.

O s t e r , E r n s t . "Re: A New Concept of Tona l i ty?" Journal of Music

Theory, 4 , No. 1 (Spring 1960), 85-98.

P l e t t n e r , Ar thur . "Heinr ich Schenker 's Contr ibut ion to Music Theory. ' '

Musical America, 56 (1936), 14.

Regener, E r i c . "Layered Music--Theoret ic Systems." Perspec t ives of

New Music, 6 (Fa l l 1967), 52-62.

Reynolds, William H. "Re: Analysis and Uni ty ." Journal of Music

Theory, 3 , No. 1 (Spring 1959), 140-47.

. "Unity in Music ." Journa l of Music Theory, 2, No. 1

(1958), 97-104.

Riemann, Hugo. Harmony S imp l i f i ed , o r The Theory of the Tonal

Function of Chords. Trans, H. Bewerunge. London: Augener

and Company, 1895.

. 0 /

Rothgeb, John. "Design as a Key to S t ruc tu re in Tonal Music."

Journa l of Music Theory, 15,No. 1 (19"1) , 230-255.

. " S t r i c t Counterpoint and Tonal Theory." Journal of

Music Theory, 19, No, 2 (1975), 260-84.

S a l z e r , F e l i x . "Direc ted Motion: The Basic Factor of Musical

Coherence." American Musicological Society Jou rna l , 3 (1950),

157.

. S t r u c t u r a l Hearing: Tonal Coherence in Music. 2 vo l s .

New York: C. Boni, 1952.

S a l z e r , F e l i x and Carl Schachter . Counterpoint in Composition:

A Study in Voice Leading. New York: McGraw-Hill, 1969.

Schach te r , C a r l . "Rhythm and Linear Analys is : A Prel iminary Study."

The Music Forum, 4 (1976), 281-334.

Schenker , He in r i ch . Free Composition. Ed. Oswald Jonas . Trans.

E rns t Os te r . New York: Longman I n c . , 1979.

. Harmony. Ed. Oswald Jonas . Trans . El izabeth Mann

Borgese. Chicago: Univers i ty of Chicago P r e s s , 1954.

S e s s i o n s , Roger. "Escape by Theory." Modem Music, 15 (1958),

192-97.

. "The Function of Theory." Modem Music, 15 (1958),

257-62.

. Harmonic Practice. New York: Harcourt, Brace and

World, 1951.

. "Heinrich Schenker ' s C o n t r i b u t i o n . " Modem Music, 12

(1935), 170-78.

15 8

Ses s ions , Roger. "New Vis tas in Musical Educat ion ." Modem Music,

11 (1934), 115-20.

Simms, Bryan R. "New Documents in the Schoenberg-Schenker Polemic."

P e r s p e c t i v e s of New Music, 16 (1977), 110-24.

S l a t i n , Sonia . "The Theories of Heinrich Schenker in P e r s p e c t i v e . "

Ph.D. Diss . Columbia Un ive r s i ty , 1967,

Smith, Charles J . "The Nota t ions of Ana lys i s : An Approach to a

Theory of Musical R e l a t i o n s . " In Theory Only, 1 (Dec. 1975),

9-18.

. " R e g i s t e r i n g D i s t i n c t i o n s : Octave Non-Equivalence in

Chopin 's B u t t e r f l y E tude ." In Theory Only, 3, No. 5 (1977)

32-39.

. "Rhythm R e s t r a t i f l e d . " Pe r spec t ives of New Music, 16,

No. 1 (1977) , 144-76.

S o l i e , Ruth A. Review of Beyond Schenkerism: The Need for A l t e r

n a t i v e s in Music Ana lys i s . Notes , 34 (1977), 857-59.

T r a v i s , Roy. "Towards a New Concept of Tona l i t y?" Journal of Music

Theory, 3 , No. 2 (1959), 257-84.

Vander Weg, John. Review of Harmony and Voice Leading I , by Edward

Aldwell and Carl Schachte r . In Theory Only, 3 , No. 12 (1977),

31-35.

Walker, Alan. A Study in Musical Ana lys i s . New York: The Free

Press of Glencoe, 1963.

Warf ie ld , Gerald. Layer .Analysis: A Primer of Elementary Tonal

S t r u c t u r e s . New York: Longman I n c . , 1978. ( F i r s t pub. 1976

by David McKay.)

Warf ie ld , Gerald. Layer D ic t a t i on . New York: Longman I n c . , 1978.

Well , Alfred R. Review of Layer Analys is : A Primer of Elementary

Tonal S t r u c t u r e s , by Gerald Warfield. Piano Quar t e r ly , 25

(1977) , 53-54.

Westergaard, P e t e r . In t roduc t ion to Tonal Theory. New York: W. W.

Norton and Company, I n c . , 1975.

Yeston, Maury, ed . Readings in Schenker Analysis and Other Approaches

New Haven and London: Yale Univers i ty P r e s s , 1977.

. The S t r a t i f i c a t i o n of Musical Rhythm. New Haven: Yale

Un ive r s i t y P r e s s , 1976.

Zuckerkandl , V i c t o r . "The Inportance of Heinrich Schenker 's

Teach ing . " Musical Times, 76 (1935), 705.

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