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1973 Rational Structures in the Late Works of Anton Webern. Judith Marie Fiehler Louisiana State University and Agricultural & Mechanical College
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Recommended Citation Fiehler, Judith Marie, "Rational Structures in the Late Works of Anton Webern." (1973). LSU Historical Dissertations and Theses. 2539. https://digitalcommons.lsu.edu/gradschool_disstheses/2539
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FIEHLER, Judith Marie, 1939- RATIONAL STRUCTURES IN THE LATE WORKS OF ANTON WEBERN.
The Louisiana State University and Agricultural and Mechanical College, Ph.D., 1973 Music
University Microfilms, A XEROX Company, Ann Arbor, Michigan
THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. RATIONAL STRUCTURES IN THE LATE WORKS OF ANTON WEBERN
A DISSERTATION
Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College In partial fulfillment of the requirements for the degree of Doctor of Philosophy
In
The School of Music
by Judith Marie Fiehler B.A., Louisiana Tech University, 1961 M.Mus., Louisiana State University, 1965 December, 1973
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PREFACE
One of Che most interesting questions presently open to musi-
cological study is that of tracing the development of Webern's
mature style. This style is remarkable for its high degree of
logical organization, richness of structural resources, and
ingenuity of developmental procedures, as well as its inventive
musicality.
Webern's insistence on the validity of the application of logical
organization to music has rarely been discussed in the context of his
intellectual and musical background. Many of his post-war adherents
venerate him for this insistence, implying he was a logical positivist.
Well-informed, conscientious musicians and aesthetes who oppose him
generally do sojon this point. Some have found Webern's music to
be a summit in a long line of musical and humanistic tradition, while
others have considered it to be a parody of that tradition. Although
the reasoning put forth by these groups is important both musically
and philosophically, it is possible that none of them assesses Webern's
intentions as they were formulated.
It seems that the problem of the use of logic in music pre
occupied Webern for most of his adult life, and that the compositional
algorithm which he finally adopted was based on both philosophical
and musical principles. These principles are similar to certain
trends of philosophical thought current in the first decade of the
i i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. twentieth century, when Webern was attending the University of Vienna.
The process of abstraction seems to be particularly crucial to
an understanding of Webern's use of logic. This process has a special
meaning in the context of early twentiech-century Viennese thought.
Webern's contemporaries architects Adolf Loos, journalist Karl Kraus, Loo's friend and pupil, philosopher Ludwig Wittgenstein, and Webern's
teacher and lifelong friend, Arnold Schoenberg, shared a deep interest
in the implications of this process.
It seems that these men thought that abstraction implies a
generalization of perception of configurations occurring in the real
world. This generalization is conceptual in nature, for the perception
of configurations depends upon the individual who produces the
generalization. Abstraction is a means of looking behind appearances,
hypothesizing the causes for their formal characteristics. These
characteristics can be divided into those which make their causes clear,
and those which confuse the perceptibility of these causes by intro
ducing irrevelant material. With regard to the creation of .new-works
of art, it was thought that the elimination of the latter type of
characteristic improved the configuration by permitting clarification
of its meaning or function. This somewhat neo-classic view of the
role of abstraction in art seems compatible with certain passages in
Webern's published writings.
Webern's mature style presents an additional problem. The tech
niques of structure and development which he uses are certainly derived
from those of the past. However, his style cannot be said to display
logical continuity with traditional styles such as those of J. S. Bach,
i i i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Beethoven-, Brahms, and Mahler. Webern adopts the logical procedures
of these styles, but generally forms systems out of them which are
isomorphic to mathematical cyclic groups of finite order. These
systems, unlike those appearing in earlier works, are closed, and can
be constructed to cover all desired configurations. The use of these
systems seems to be an extension of the technique of pitch serializa
tion developed by Webern's teacher, Arnold Schoenberg. Whether the
formation of such systems in music is defensible from a musical
standpoint seems to rest on one's subjective musical insight. The
present study contains analyses which are observations of the structural
utility of these systems, without judging their moral rectitude.
For practical reasons, the present study is based only upon
material in print at the time of its formation. Unpublished documents,
particularly those in the recently formed Webern archives, undoubtedly
contain information of immense import to the conclusions drawn here.
Similar documents of Webern's contemporaries are gradually becoming
available, as are reprints of seminal periodicals such as Per Fa eke 1*~ 2 and Per Brenner, with which Webern was apparently familiar. The
study of these materials should open a productive field for further
study of topics sketched here.
Two important studies of Webern's Vienna have recently been 3 A published: Wittgenstein's Vienna and The Austrian Mind. Both
studies are broad in scope, discussing social and intellectual trends
of an entire era in an illuminating manner, but both are hazy with
regard to specific musicological developments of the time. These
iv
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. studies appeared too late to be included in the formulation of the
first three chapters, although they generally support hypotheses
advanced there. The studies are used in the fourth chapter, which
relate Webern's philosophy to that of other twentieth-century thinkers.
This study was made p o ssib le through the help of many persons.
The author would particularly like to thank Dr. Wallace McKenzie for
his patience, insight, and enoouragement, Dr. Kenneth Klaus for
introducing the author to the humanistic nature of Webern's style,
and Dr. Frederick Crane, whose scholarly approach to musical criticism
generated the nucleus of the study. In addition, mathematicians
Dr. Gordon Pall, Dr. Richard Anderson, and Dr. Pasquale Porcelli
provided indispensible clues to Webern's compositional procedures
and personality traits, and Dr. Burtis Casler bravely ventured into
regions justly dangerous to mathematicians to verify the conclusions
reached in the first chapter. Dr. Robert Chumbley of the French
department provided the catalyst which gave the study its intent and
final configuration. The School of Geoscience and the School of
Forestiy provided the financial means with which to study and write.
Susann Finley, that rarest of beings, an intelligent typist, provided
indispensible assistance.
Most of all, however, Webern himself must be thanked — my
unfailing Virgil, a true guide through many uncharted areas of thought.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. FOOTNOTES
PREFACE
^Der Faeke1. ed. Ludwig Ficker, (Nendeln, Liechtenstein: Kraus Reprint, 1969), reprint ed. 2 Per Brenner, ed. Karl Kraus, (Nendeln, Liechtenstein: Kraus Reprint, 1972), reprint ed. 3 Allan Janik and Stephen Toulmin, W ittgenstein's Vienna (New York: Simon and Schuster, 1973). 4 William M. Johnston, The Austrian Mind (Berkeley, Los Angeles, London: frniversity of California Press, 1972).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS
PREFACE...... i i
LIST OF TABLES...... x
LIST OF FIGURES...... x i
ABSTRACT...... x li C hapter I . THE COMPATIBILITY OF LOGICAL STRUCTURE AND MUSIC .... 1
Introduction ...... 1 Section 1. Musical Analysis: Basic Assumptions . . . 3 Section 2. On Systematic Musical Analysis ...... 10 Section 3. Some Observations on the Use of Logic in Criticism of the A rts ...... 25
I I . PHILOSOPHICAL AND LITERARY INFLUENCES ON WEBERN'S MATURE STYLE ...... 40
Introduction ...... 40 Section 1. Sources Cited in Webern's Published W r i t i n g s ...... 41 Section 2. The Influence of Goethe: Metamorphosis . . 47 Section 3. Kandinsky: The Natural Law of the Sense of S i g h t ...... 53 Section 4. Plato: The Melody Gives Out the Law . . . 57 Section 5. Hypothesis: The Philosophical Basis of Webern's S ty le ...... 65
I I I . DESCRIPTIONS OF WEBERN'S MATURE STYLE ...... 87
Introduction ...... 87 Section 1. Descriptions by Composers and Critics . . . 87 Section 2. Descriptions by Webern ...... 96 Section 3. Description by the Author ...... 102
IV. WEBERN IN THE CONTEXT OF TWENTIETH-CENTURY THOUGHT . . . 117
Introduction ...... 117 Section 1. On Whitehead's Discussion of Musical A n a l y s i s ...... 117 Section 2. Conceptual Sim ilarities in the Late Writings of Webern and Wittgenstein . . . 125 Section 3. Conclusion ...... 140
v i i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDICES
Introductory Remarks to the Appendices ...... 151 A. Large Form: Q u artet, Op. 28, F ir s t Movement ...... 163 B. S e ria l C ontrol of P itc h : T rio , Op. 2 0 ...... 190 C. V a ria tio n Technique: V a ria tio n s , Op. 30 235 D. K langfarbe: Second C an tata, Op. 3 1 ...... 325
BIBLIOGRAPHY ...... 370
VITA ...... 378
SUPPLEMENTARY MATERIAL 0 1. Score, Quartet. Op. 28 attached packet 2. Score, Trio. Op. 20 attached packet 3. Score, Variations. Op. 30 attached packet 4. Score, Second Cantata. Op. 31 attached packet
Note: Due to copyright regulations, the supplementary material does not appear in the microfilmed copy of this study.
v i i i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF TABLES
Table Page
I . Row-Form M atrices fo r Q u a rte t, Opus 2 8 ...... 155
I I . Row-Form M atrices fo r T rio , Opus 20 ...... 156
I I I . Row-Form M atrices fo r V a ria tio n s , Opus 3 0 ...... 157
IV. Row-Form M atrices fo r Second C an tata. Opus 31 .... . 158
ix
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LIST OF FIGURES
Figure Page
1. Subject and Countersubject of First Exposition, Quartet, opus 2 8...... 170
2. Subject and Countersubject of Second Exposition, Quartet, opus 2 8...... 175
3. Subject and Countersubject of Third Exposition, Q u a rte t, opus 2 8...... 182
4. Statements in Stretto, Quartet, opus 2 8...... 185
5. Dyadic Invariant Relationships, Prime Row Forms, Trio, opus 20...... 204
6. Dyadic Invariant Relationships, Inversional Row Forms, Trio, opus 20...... 205
7. Tetrachordal invariant Relationships, Trio, opus 20 . . . 206
8. Rhythmic and Articulative Patterns, Variations, opus 30 . 238
9. Cycles Based on Type 2 Tetrachords, Variations, opus 30 . 239
10. Relationships of Type 1 Tetrachords, Variations, opus 30. 240
11. Pitch Contour Variants, Variations, opus 30 ...... 241
x
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABSTRACT
An investigation of the logical, philosophical, and musical
background of the use of rational structures in the late works of
Anton Webern is undertaken. The significance of these structures
is also considered.
Rational structures are defined, for this purpose, as sets of
entities and relationships over a symbolic language, which are
sufficiently rigorous to be logically definable. The logical require
ments of the existence of such structures are given. The conditions
under which they can be applied to music are also discussed, in
conjunction with the limitations of schematic representation of the
music to be analyzed.
A model for the application of these structures to music which
resembles a model which may have been known to Webern is constructed.
This model is tested by four analyses of Webern's late works, using
different schematic reductions of musical structure.
Possible reasons for the existence of rational structure in Webern'
mature style are investigated. An hypothesis of Webern's personal
philosophy regarding such structures is developed, and compared with
similar philosophies of some of his non-musical contemporaries. These
philosophies have bearing on the analytical method developed in the
study.
If the discussion presented is used within its given limitations,
it may provide a basis for generalized investigation of the capacity
x i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. and credibility of all musical analysis which is systematic. The
procedures used can be expanded to non-Webernian musical analysis,
so long as the results obtained yield musical insight.
The study, then, assumes two functions. It provides and assesses
a procedure by which the rational structures found in Webern's late
works can be analyzed, observing the function and derivation of these
structures. It also explores the implications of this procedure,
indicating further work to be done in many connected areas of study.
x i i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER I
THE COMPATIBILITY OF LOGICAL
STRUCTURE AND MUSIC
Introduction
A foundation for analytical procedures suitable to Webern's
highly logical late works is postulated in this chapter. The musical
and logical requirements for this foundation are also discussed, so
that its reliability can be known.
The approach taken in this chapter is suggested by a lecture
given by Webern on February 20, 1933.
Just as a researcher into nature strives to discover the rules of order that are the basis of nature, we must strive to discover the laws according to which nature, in its particular manifestation "man," is productive. And this leads us to the view that the things treated by art in general, with which art has to do, are not "aesthetic," but that it is a matter of natural laws, that all discussion of music can only take place along these lines.
The conceptual nature of these laws is clarified by one of Schoenberg's
students as follows:
"Fundamental principle" means "fundamental law." Though the attempt to deduce the laws of art w ill probably always be futile, we never give up searching fo r them. What we u ltim a te ly fin d are but the obsessions, or the prevailing concepts of a period or of an individual. "Fundamental principles" may be defined as obsessions which have been so long maintained as to seem universal.
In retracing the steps by which Webern arrived at his mature
style, hypothetical underlying "laws" for the general use of logical
forms in music are postulated in this chapter. This 1b accomplished
1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2
by study of the assumptions upon which current practices of analysis
and criticism of the arts, systematic musical analysis, and standard
logical practice are based.
The recognition of these premises seems necessary to a non-
superficial discussion of rational structures in Webern's music.
It is assumed that Webern thought through most, if not all, of
these premises before imbedding such structures into his music.
The knowledge of lim itations and powers of logical procedure in
music also enable one to assess wisely the results of musical
analyses which cope with rational structures, as any analysis of
Webern's mature style must do.
In the first section, some basic concepts are outlined which
seem to .underlie contemporary musical analysis. These.concepts
can be used to help insure the compatibility of logical procedure
and musical practice.
In the second section, specific problems are examined which
arise when logical structure is applied to a general musical sit
uation. In particular, a general structure which pertains to cur
rent types of musical representations is shown.
In the third section, a model for imbedding logical structures
in the arts from a logical standpoint is constructed and discussed.
The information of this section is included to insure that analysis
done in later chapters makes sense logically as well as musically.
It seems that if both logical and musical requirements are not met,
attempts to handle rational structures in analysis will be futile.
The chapter as a whole is not primarily concerned with
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3
artistic or musical manifestations of structure, but rather with the
conditions which the use of logical procedure requires when that pro
cedure is applied to the arts, and music in particular. These con
ditions seem to be underlying laws by which one is able to compose
or analyze in a consistent manner.
Section 1. Musical Analysis; Basic Assumptions
For the purposes of the following discussion, analysis is de
fined as the process of gathering information from one's perceptions
of a given object, such as a musical work. Criticism is defined as
the process of passing judgement upon the results of analysis. The
section is primarily an examination of the fundamental assumptions which seem to underlie the procedures of analysis, It seems that
these assumptions can be defined most precisely by showing the pat
terns of thought from which they spring. These patterns of thought
apply to all kinds of loosely or tightly organized systems, not
just musical systems or procedures.
The first of these assumptions may be stated as follows: an
analysis is only a modelling of an actual, perceived object. It
is a reconstruction of the object whose configuration probably does
not duplicate that of the original object in every respect. For
example, even an exhaustive analysis of a randomly selected musical
work tends not to yield all the information which might be obtained
from the work by playing it, listening to it, or thinking about
it in relation to one's own personal life.
A discussion of the procedures of musical analysis is also a
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4
modelling. It is not claimed that this discussion or any other of
a similar nature is anything more than an approximation of the
actual process of analysis. Thus, unconditional acceptance of its
results is not thought to be justifiable.
The second assumption is that the object amounts to more than
its perceivable characteristics, and that the meanings associated
with these characteristics are not completely separable from the
meanings associated with the rest of the object. For example, the
results of a harmonic analysis of a musical work gain greatly in
meaning if these results are examined in the context in which they
occur. Although one can consider these results independently,
that is, one can generalize the function of certain chords, the
actual significance of the chords with relation to the musical work
can only be understood if one looks at the way in which they occur
in the work itself.
Suppose that these perceivable characteristics actually formed
a closed, independent system for all musical works such that their
realization in music was determined only by factors internal to
that system. Then no programmatic, textual, psychological, or other
such considerations could affect the way in which that music could
be put together. But, it is a matter of historical fact that these
considerations have had such effect. It is indeed possible to
compose music which is not affected by such considerations. However,
its analysis consists of its identification with an abstract
structure without a direct musical meaning. Such an identification
would be complete and final, and would yield little or no information
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of value to the musician.
It seems that the second assumption implies that there does
not exist a comprehensive analytical system in which the whole of
musical form can be imbedded. This conclusion is compatible with
a similar one in formalist logic. But it seems that the only
formal systems which can be apprehended completely are those
within a formalist logic, and then, only with relation to the
logic which contains them.
The th ir d assum ption has been th e su b ject of much controversy
in this century among critics and analysts in the arts, such as
Nelson Goodman, Rudolph Carnap, and the members of the French 3 structuralist movement. It seems that the use of the first two
assumptions implies that the traditional position in this
controversy be taken.
This assumption is that unless the creator of a work of art
is working completely within a formal system such as that described
on page 2, his work w ill not be contained in any rigorous formal
system. On the contrary, the analyst must anticipate the possi
bility that the work may be a conglomerate of contradictory systems,
exhibit ambiguity within a single system, or imbed a consistent
system within an illogical framework. Such exceptions are not
consistently thought to be bad in the arts. They may be thought
of as clues to the creator's intentions. For example, the dissonant
chord occurring in Beethoven's Ninth Symphony immediately before
the first entry of the baritone soloist, fourth movement, may have
been w ritte n in e r r o r , sin ce i t v io la te s commonly accepted ru le s
of harmony. On the other hand, the chord may be an expression of
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Beethoven's feelings at that point In the music, contrasting with
the consonance of the theme which Is to be Introduced In a few
m easures.
The fourth and fifth assumptions serve as the link between
musical analysis and logical procedure. The fourth assumption Is
that the analyst uses an a priori set of expectations with which
to measure the work. This set may consist of the analyst's prior
experience, his musical, Intellectual, emotional, and other
capacities and knowledge, as well as a specific set of anticipations
based on his prior knowledge of the biographical and musical
context of the work at hand. His analytical intentions are
interdependent with the content of his set of expectations.
By the fifth assumption, analytical procedures are divided into
systematic and intuitive categories. By means of well-established
logical principles connected with this division, some observations
can be made concerning the capacity of a given procedure to obtain
knowledge of a created object. The systematic method presumes
that events which are not precisely identical are called identical.
For example, a certain set of notes is called a tonic chord regard
less of its voicing or its position in the temporal flow of the
work, provided no modulation has occurred. However, the choice of
which events will be called identical is entirely up to the person
formulating the systematic procedure. For example, if he happens
to decide that a modulation has occurred in a work where key re
lationships are not clear, he may thereby imply that a certain
chord is tonic when it might not otherwise be thought to be so.
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While some choices may prove to be more fruitful than others, It
Is sometimes difficult to show that one particular choice Is the
best possible one to make.
A systematic procedure has certain advantages. It can ex
tend one's perceptual and interpretative ability. On the 6ther
hand, like all a priori expectations, it can bias one's apprehen
sion, and its use results in an apparently inevitable loss of
information. For example, if one hunts for a previously decided
pattern in one of Webern's mature works, he is likely to find
it whether or not Webern was aware of using it and overlook
p a tte rn s which may be much more im portant s tr u c tu r a lly . The
strategy of looking for pattern repetition, however, is generally
useful in the analysis of these works.
A strictly intuitive approach to analysis has the advantage
of letting one use the totality of his experience and knowledge
to bear on a given situation, meeting the requirements of situations
as they change. However, this approach seems to suffer from a lack
of quantative reliability. It lacks permanence, and automatically
excludes the recognition of rational systems. For example, it it
p o ssib le to perform th e F ourth Symphony of Brahms w ith th e fe e lin g
that one is experiencing it to the greatest of one's musical
capacity, and afterwards be unable to remember a single one of
its themes, let alone the intricacies of its form.
The sixth and last assumption seems to be supported by the
other five. Although this assumption was fundamental to metaphysics
for at least five hundred years, it is no longer generally accepted
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in all disciplines, especially those with rigorous foundations. It may be stated: the perceptible characteristics of a created
object depend directly upon its creator. Then, these characteristics
are known to him in a different and more complete sense than they
can be known by anyone else. One's knowledge of this object can
only be called "true" if it is complete. Since the creator's know
ledge of this object at least surpasses anyone else's knowledge
of it, no one else can claim an entirely "true" knowledge of it.
For example, it may be assumed that the composer of a work knows
why he wrote it as he did and would recognize the slightest devia
tion from his intentions, or from its score, in a performance.
This statement is probably more accurate for extraordinary composers
than for composers selected at random.
By this assumption, the analyst can know the created object
only through circumstantial evidence presented by the configuration
of the object and historical information about the object and its
creator. It seems that the result of such analysis must remain
hypothetical except where it is quantitative, and that quantitative
measurement per se is not likely to yield more than indirect ap
proaches to "true" knowledge of a work. For example, we can only
guess at the precise intentions of Dufay. Quantitative analysis
of his works may suffice to distinguish them from the works of
his contemporaties, but does little to illuminate our search for
those intentions.
These assumptions might seem to deprive the analyst of ultimate
purpose. "True" knowledge of music is noL obtainable by analytic
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procedures alone. The reduction of music to a formalist system
Is, by definition of such a system, meaningless in itself. System-
ization as a procedure leads to a reduction of meaning, as does the
rejection of systemization. The interpretation of the results
of analysis, which may be called criticism, cannot be more rigorous
and complete than the results, and the results are ambiguous.
However, these procedures and results which have little value
in themselves may be used as a means of obtaining information.
This information can enlarge the musical thought and capability
of the analyst, not only as a person interested in the structure
of music, but also as a performer and listener. The very am
biguity of interpretation of the results of analysis enables
one to postulate varied meanings which may generate fresh musical
ideas. These ideas can in turn motivate one to expand one's
understanding of what the totality of music is and can be.
If criticism could be made rigorous and complete, there
could be a complete, definitive explanation of Beethoven's Ninth
Symphony, correct for all time. Then, that work would never again
stimulate fresh production of music. It seems that the ultimate
result of such analysis would be the end of music itself.
The discovery of information which expands one's concept of
music can be called the acquisition of insight. It may be said
that accumulated insight is a musician's "true" personal knowledge
of music as a whole which enables him to hear, perform, and create
it. It seems that insight is gained directly or Indirectly through
all contacts a musician makes with music. Systematic analysis is
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only the most rational of these contacts.
By the sixth assumption, the musician cannot hope to gain
"true" knowledge of a particular work which corresponds exactly
to the composer's knowledge which Is "true" relative to his own
musical insight. A musician seeking Insight may choose the pro
cedure of analysis which helps him achieve his goal. If he also
has a clear understanding 6f the powers and limitations of the
various means of analysis at his disposal, he can select an
analytical method which is likely to be helpful to him. In the
author's opinion, the ultimate aim of musical analysis is to aid
the musician in this manner.
Section 2. On Systematic Musical Analysis
The author's views on the nature and scope of systematic
musical analysis are given in this section. The roles of tra
ditionally acceptable systematic methods of musical analysis
are also discussed. The ideas expressed are to be regarded as
explanations of solutions applicable to music in its present
state, subject to change should the course of music change. The
aim of the section is to find the functions underlying present ways
of forming a priori configurations of thought suitable for
musical analysis.
Music is tentatively defined as the totality of organized
sound existing within the conceptual thought of musicians, mani
fested through representations of music such as composition, per
formance, and analysis. These representations are primarily
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. interesting as devices for remembering precisely what the totality
of a work represented, or the forces generating the work represented,
are or can be. Analysis of a representation seems to Involve the
postulation of a conceptual ordering of one's thought before ex
amining the representation. The use of such an ordering can yield
musical insight which seems to prove the musical validity of a
particular analysis. The value of this insight does not seem
to be systematically clear. However, it may be observed that such
Insight is valuable if it aids a musician to generate music exhibiting
new conceptual structures.
It seems that the totality of music can only be examined in
directly, through representations. The configuration of a represen
tation may be said to be a statement by the musician who produced
it, that all forms, events, and relationships within that repre
sentation are "true," so far as he is able to make them "true" with
his musical insight, his ability to control the medium of repre
sentation, and the capacity of that medium. It seems that the
purpose of examining such a representation may be to try to
determine why the musician considers that configuration "true,"
not to measure its "truth" against a model, which itself would be
merely a representation. This purpose may often be better served
by observing how structures are harnessdd to give coherence to a
representation than by determining exhaustively how these structures
are played out within the representation. Sometimes it appears,
however, that one cannot know exactly how the structures are used
for coherence without finding out in detail how they relate to the
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rest of the work.
Some methods of systematic musical analysis, such as the
study of harmony, of large form, and of various types of con
trapuntal devices, are widely used by musicians. However, the
Im portance and v a lid ity of the use of even th ese commonly accepted
methods may be open to question when they are applied to works
which are not scholastic models. It appears that these methods
are a set of tools whose usefulness depends on their appropriate
application. The value of other methods which might be used In
musical analysis seems to depend, similarly, on whether their ap
plication is appropriate and yields meaningful musical insight.
The author's experience is that automatically useful results do
not seem to happen in musical analysis from the general use of
any systematic method.
The discussion of systematic analysis in the first section
shows that a consistent a priori means of organizing information
yielded by the work studied is required. This means seems to act
as a preparation of this information so it will be compatible
with the abstract system which is applied to the object. This
common ground enables the analyst to make a consistent organization
of the information yielded which reflects his aims at the outset
of the analysis.
Perhaps the most familiar example of su:^ organization of in
formation is notation of sound into score. The score is not a
complete description of a musical work, since differing interpre
tations can exist, each faithful to the score. Yet the score
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provides a means by which the work can be reproduced In detail
with some fidelity to the composer's original specification for
th e work.
The Information to be organized can be Imbedded as sound In
a measureable basis — a bounded, three-dimensional continuum of
pitch, Intensity, and time. The notation of the principal pitch
of any note Is given by the score within flexible lim its, depending
upon the specific tuning situation in performance. Timbre, or the
complex of pitches associated with the principal pitch, is not
completely determined by score notation, but is to a degree de
pendent on aural tradition and the insight-guided decision of the
performer. It appears that clarinet players agree on-:the timbre
of a characteristic clarinet sound associated with specific
directions in the score, at least within rather narrow limits.
However, the exact timbre given to that sound by a given player
is his decision.
The dimension of time is mapped through functions of tempo
onto a scheme of measurement which makes comparison of durations
of events possible. Specified exceptions such as ritards, arti
culation markings, rubato and slight tempo variations may or
may not be adequately represented in score notation. These ex
ceptions are to some extent dependent upon the inflection and
phrasing components of the intensity dimension. Dynamic level
and the "shape" of a note can be suggested by the score. However,
it is the individual player again who makes the final decision as
to the exact intensity of any given note.
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Score representation, then, varies In the degree of exactness
with which It represents sound. Several extensions of the capability
of the score to represent sound have been attempted In this century.
Nevertheless, the degree of inexactness still present in the score
Implies that the real task of realization of a musical score depends
upon the capability and Insight of the performer.
Ihe score may be considered as a model of the measureable
basis of sound, lacking some capacity to represent diverse sounds
or organizations of sounds. It Is an orderly means of classifying
and comparing sounds, simplifying the musician's task of finding
coherence among the sounds represented. The notatlonal require
ments of the score permits musical events to be recognized as
Identical with respect to that notation which may not be precisely
the same when the work Is performed. In addition, musical events
which may have common characteristics but have slightly differing
notations may be considered as Identical or not Identical at
the will of the person Interpreting the score. For example, one
can distinguish between middle C and the C an octave above it,
or merely call them both C's.
The score then appears to be a rudimentary systematic
analysis of music as sound, with certain fixed limitations and
properties. It may be called a mapping of the three-dimensional
continuum which is the measureable basis of sound into a fixed
system of symbolic notation. This mapping procedure enables one
to take a specific work as it is represented in sound, and represent
it in score. The score representation can then be mapped back into
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sound, in an almost unambiguous fashion. Mappings of music from one representation to another can be
generalized. Some of the properties of such mappings are now
discussed.
Certain properties appear to be necessary to systematic
analysis. These properties enable the musician to carry out
his a priori intentions in examining, composing, or performing
music. The mapping used must have provision for the recognition
of repetition of events or aspects of events.^ It must provide
enough information to distinguish representations of sounds from
each other clearly enough to serve the musician's purpose. It
must provide enough evidence so that the musician can postulate
relationships among these representations. The mapping must be
consistent throughout its domain and range, so that ambiguity or
misinterpretation is minimized relative to the a priori intentions.
A p articu lar mapping may have at least four additional
properties. Firstly, the mapping can preserve all information
of the original representation. Such a mapping could place the
sounds represented in a more useable format for interpretation.
An ideal example of such a mapping would be an exact tape recording
of an actual performance, which would permit the musician to re-hear
sections of that performance. He could then obtain more information
about that particular performance than if he could hear it only
once.
Secondly, the mapping may omit certain d istin ctio n s and
possible relationships of the original representation. For example,
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the score distinguishes shades of timbre crudely in comparison
with the way in which a responsible performer must distinguish
them. Even if it were possible to extend the capacity of score
notation to permit such fine distinctions, the score might be so
cluttered with additional markings that it could not be used
e ffic ie n tly . A mapping with th is second property condenses and
codifies Information so that distinctions and relationships
of the original can be more easily comprehended. Other mappings
or the musician'8 memory can supply missing information lost in
the mapping process. For example, aural tra d itio n and the perform er's
memory help him reconstruct musical works from their notation in
score.
Thirdly, the mapping process may impose an organizational
structure in the information mapped which permits easier analysis.
For example, the pitch notation of the score is particularly well
adapted to aid one's recognition of triad occurrences, or in a
broader sense, groups of notes which reinforce each other's
harmonic partials. This reinforcement will occur in a responsible
performance no matter how the information for performance is
given. However, a notation sympathetic to recognition of this
characteristic helps one to anticipate its effect.
Fourthly, the mapping may impose an organizational structure
on the information given which generates an analytical system. For
example, the score traditionally recognizes durations of musical
events as integral or fractional multiples of each other within
a given time segment. Actual performance practice might or might
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17
not reflect such accuracy, depending on style, aural tradition, and
other factors. However, a score with this property invites
analysis of duration properties in a manner which closely parallels
well-known processes of elementary arithmetic, and is even usually
explained in terms of these processes.
The first three properties place the- Information in a more
useable format, but do not affect that information'a distinctions
and relationships except by omission. The fourth property does
change distinctions and relationships, and hence affects possible
interpretations of the score.
Specifications of a musical event may be said to be well-
defined relative to the means of representation used. For example,
a note in score notation is unambiguous with respect to th at
notation, even though its specification's not as detailed as
that of an actual sound. It appears that results of mappings in
general from one representation to another ar£ ambiguous — th at
is, do.not give completely identical results time after time.
However, specific maps restricted to a single type of representation,
such as score to score, or actual sound to actual sound, may be
well-defined, and may even assume the rigorous properties of
mathematical functions. Since mathematical functions must be
well-defined, these observations seem to preclude the unrestricted
use of such functions in describing the mappings under consideration.
It does not seem that proof of the existence of well-defined
representations and mappings suffices to determine the processes
by which they are obtained. Sufficient counterexamples can be
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found to elim inate such a conclusion. For example, a work may
exhibit a certain logical property which is not intended by its
creator, but results from chance. Then the creative process which
formed that work cannot be assumed beyond question to have included
awareness of that property.
At present, the musician is free to use any consequence of
his imagination, knowledge, insight, logical or illogical thought
to determine the configuration of a musicial representation. To
restrict this freedom to processes definable within any presently
existing, unambiguous, consistent system would re su lt in a lim i
tation of the possibilities of musical development — a high price
to pay for an analytical property which has no specifically musical
connotation. On the other hand, the musician is free to use
systematic processes if they can help him.
Mappings and representations may be expressed in logical,
linguistic, or metamathematical terminologies. The uses of such
terminologies are subject to certain reservations if they are to
retain their utility.
None of these terminologies seem to be flexible enough or
capable of sufficient extension to be generally applicable to
all musical mappings and representations. It seems that a musician
using these terminologies should be aware of the precise limitations
involved in their use. He must particularly know just how well
they express abstract concepts, whether they are meaningful outside
of the context of their original discipline, and how appropriate
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their application is in relation to music. It must be noted that
any terminology can apply only to those portions of the mapping
or representation which are constrained to conform to the limi
tations of the terminology used.
Despite these reservations, it seems that such terminologies
are a potentially powerful source of technique for the musician
who is not content to depend on his intuition. They can express
some aspects of musical structure far better, and warn of possible
pitfalls more reliably, than any strictly musical terminology
now in common use.
The most accessible terminology seems to be that of applied
logic as it is expressed in mathematical notation. The purpose
of this terminology is to describe general types of well-defined
structures independently from their application to actual objects.
Its lim itations and powers are well known. I t is re stric te d to
well-defined systems, some of which are known to occur in existing
musical works. By an abuse of the language, the present study
will call the processes of applied logic "logical processes,"
and the structures defined by its terminology "rational structures."
If and only if the distinctions and relationships of a
system within a musical representation can be shown to be ab
stractly identical with those of a rational structure, properties
of the rational structure will also be properties of the original
system. This statement implies that the configuration of the
rational structure, which can be exhaustively determined by
techniques implicit in applied logic, can be used to predict the
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possible configuration of the original system in music.
This configuration will be abstract, and its manifestation
in music w ill not necessarily have any musical value. Then the
musician's proof that the configuration exists is only a first
step. He must also show that its recognition is of musical
significance. Some ways in which applied rational structures
can have musical significance are now discussed.
A common application of rational structure within a musical
work is the generation of formal skeletons of varying lengths
and importance to reinforce the coherence of the musical form.
The manner of reinforcement varies.
Sometimes the applied rational structure is used as a
starting point for musical thought which may, in the end, bear
little direct relation to the structure. For example, music
may be written in 4/4 meter without utilizing the accent pattern
which distinguishes that meter from other meters.
The applied rational structure may be a nearly independent
component of the to ta l musical form. For example, the harmonic
voice-leadings of the music of Rimsky-Korsakov are usually
scholastically accurate. In his orchestral works, however, a
large portion of the musical structure depends upon his control
of timbre and intensity, not harmonic progression. The areas in
which harmonic progressions are prominent, such as the last
movement of Scheherezade. seem generally to show a support of
those progressions with changes of timbre and intensity.
The applied rational structure may be used ns a generating
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force within the total structure, maintaining its internal con
sistency while producing structures which depend upon i t . For
example, a fixed ground bass is a well-defined sequence * of musical
events which can be used to generate variations whose sequential
patterns are not well-defined except with relation to the ground
bass.
The configuration implied by a rational structure may be used
or ignored in its musical application. For example, the cycle
of fifths is isomorphic to the algebraic cyclic group of twelve
elements. This structure can be invoked casually without affecting
the musical form greatly. It can appear briefly but strongly,
as in a II-V-I cadence. The full power of the cycle of fifths
can be used to generate chains of modulations with strong
voice-leadings, as it does within the style of Bach, where it is
used to strengthen sequential patterns.
If the full rigor of the applied rational structure is not
found musically necessary, the structure may appear in an incom
plete or contradictory form. There are several conditions under
which incompleteness or contradiction can occur within a musical
work.
Lack of rigor can result from the use of conflicting logical
systems. For example, a composer might find that scholastically
defined harmonic relationships conflict with an effect of timbre
necessary to the musical form of his work. For example, the
previously cited dissonant tutti chord in the last movement of
Beethoven's Ninth Symphony violates scholastic harmonic practice
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while it prepares the ear for the entry of the baritone soloist's
words, "0 Freunde, nlcht dlese Tbne!" 5 In such a situation, the
composer Is forced to choose between contradictory solutions
according to his insight.
Lack of rigor commonly results from conflict between the
requirements of an applied rational structure and the composer's
Intuitive insight. Berlioz's Svmphonle Fantastlque can be said
to exhibit a number of rational structures of harmonic, coloristic,
rhythmic, and other types of patterns. However, all of these
patterns are subject to rupture whenever Berlioz's seemingly
capricious programmatic ideas must be served. The codas of the
third and fourth movements of this work may serve as examples of
this sort of rupture.
Deliberate contradiction, of an applied rational structure
may be used, especially if that structure is a powerful force in
the work. For example, the rhythmic ambiguity of the minuet of
Haydn's Oxford Symphony gains effectiveness from the momentum of
the metric pattern which is contradicted when the principal
accent of the measure is shifted to the second beat.
Lack of rigor may re su lt from an extension of an applied
rational structure which is inconsistent with its logical require
ments. The introduction of secondary dominants into the system
of chords generated by a given key implies that the key will be
contradicted by one of the notes contained in the secondary
dominant chord.
Inconsistent extensions can eventually destroy the configuration
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of the applied rational structure. The chord sequences opening
the "Prelude" of Wagner's Tristan and Isolde may be said to be
the end product of many successive extensions of chord relation-
hips belonging to a given key, by Wagner and his predecessors.
These chord sequences do not seem to be analyzable uniquely to
any key, because It Is not absolutely clear from the chords given
to which key the sequences belong. Then the original rational
structure, the key, Is no longer the basis of the derived structure
of chord relationships. The latter structure can then survive
only on Its own merits.
Lack of rigor can be a signal to the analyst that a situation
In which the composer's insight is observable has occurred. The
analyst may observe the conditions surrounding the situation, and
arrive at some tentative conclusions regarding the reasons for the
choices made by the composer.
Applied rational structures may serve to define only points
or areas In the representation, while influencing segments between
these points or areas In d irectly or not at a ll. For example a
figured bass defines chord progressions, but does not specify what
embellishments may appear between chords.
These segments, not well-defined by applied ratio n al structures,
may be used as areas for testing extensions, contradictions, and
independent structures. It seems that one of the hallmarks of a
fine performer is his ability to make such segments musically
interesting in themselves as well as in relation to obvious points
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of structural coherence. He may do so Intuitively or In accordance
to his Interpretation of rational structures which he recognizes
or hypothesizes In the notation of the work.
The more or less standard Interpretations of works In the
current repertoire and conventions of performance practice seem
to be the end result of the work of many such performers. The
musician should distinguish between what he surmises Is the
composer's Intention and the often beneficial consequence of
filtering that Intention systematically land Intuitively through
the minds of many other musicians. The latter consequence may
have Its own analytical significance. I t Is the means by which
musicians relate music from another time and realm of Ideas to
their own, keeping the music In the living, developing repertoire
as they apply and develop their musical Insight.
If a musical work is to maintain Its Identity, the composer's
original intentions must be notated clearly. It seems that such
a notation, forming a representation of these intentions, implies
that sounds be defined as entities. These entities seem to be
defined in relation to each other. They may be further organized
into systems of relationships for the sake of clarity.
The necessdry requirements of the more common logical systems
are clearly defined sets of entities and relationships. It seems
that definition of entities and relationships occurring in music
need not be restricted to those corresponding to events in the
measureable basis. Such a restriction would make musical analysis
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more manageable logically. However, it would make certain musically
valid mappings logically nonsensical. Configuration of ratio n al
structures in music seem to be limited only by one's powers of con
ceptualizing them. There seems to be no strictly musical reason why
any rational structure based on entitles and their relationships can
not be realized in music. Many such structures have been postulated
in the twentieth century, notably by Hindemith, Schilllnger, and
Webern, and these structures have produced interestin g music.®
Section 3. Some Observations on the Use of Logic in Criticism of
the Arts
The application of logical models to concrete situations is
a delicate and perilous undertaking even for persons skilled in
logic. A complete theory of applications of this nature is beyond
the scope of the present study, although it may be implicit here.
This section points out some of the possible dangers and
advantages which could influence the formation of such a theory as
it might apply to analysis of the arts. A restricted demonstration
of such a theory is given which happens to correspond to a procedure
with which Webern may have been familiar. The consequences of
using this theory to interpret information relative to musical
analysis are also discussed.
The second section of this chapter investigates possible
processes underlying systematic music analysis. Similar investi
gations have been made in areas of applied logic. The elegant
solutions which have been obtained in these areas sometimes appear
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to cope simply and directly with critical problems which may be
insoluble within the realm of art. It is easy to forget that the
intuitive insight upon which the arts rely is neither expected
nor sufficient in stricter realms of thought. This insight depends
upon conclusions which may well be unprovable in a given deductive
system. On the other hand, logical solutions need not be value
less to the critic, but they are not to be had for the asking.
The critic who wishes to take advantage of logical solutions
cannot do so naively. He must understand in a rational manner the
conditions by which they are obtained, and the implications of
their use within their own discipline. He must be able to deter
mine whether their application in the arts is artistically accept
able, useful, or even possible. He must therefore have a thorough
understanding both of applied logic and of the arts.
Many words belonging to logical terminologies express musical
concepts with far greater precision than any words belonging ex
clusively to the discipline of music, especially if they are
used in a somewhat looser fashion than in the original discipline.
But to use these words loosely is to abuse th e ir original meaning,
and impair their logical power to a serious degree. Such abuse
cannot be tolerated in logical disciplines. The musician who uses
such words loosely must make it clear that he does so only in a
musical context, and only because the results he obtains from
their use is fruitful with reference to music. On the other hand,
if he describes systems in music which have strictly logical
ch arac te ristic s, he must use these words in th e ir original c larity
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and restricted meaning, or he will not gain control over the musical
system described. These precautions are necessary because the
language of applied logic is an artificial one, independent from
any other language, especially English.
No discussion of applied logic is meaningful syntactically
unless it takes place within constraints. The author knows of no
example of a ratio n al structure which is thought to hold under
all conditions. Then it seems that the critic cannot assume that
he can find such a structure in the a rts unless he can find
suitable constraints for the arts as a whole. It does not seem
that such constraints are desirable at this time. Certain critical
theories have postulated such constraints, but these theories seem
to hold only for a certain set of works, those constructed
deliberately within these constraints. For example, the full
rigor of the twelve-tone system, used as a critical tool, cannot
be assumed to be applicable to any musical work selected at random.
If the scope of art cannot be limited, the application of a
logical system to art must be limited to a portion of that scope.
The following discussion is limited to only one type of logical
structure with unambiguous properties, applied w ithin a model
which seems to be a special case of the use of rational structure
with relation to information of a certain type. It is assumed
that the use of th is model w ill concern only a portion of the
information available, that portion which can be made to correspond
to the logical system used.
The results obtained from the examination of the model arc
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assumed to hold only for the specific case outlined. These resu lts
cannot be generalized within a deductive framework to fit all
cases of application of logical systems. Although the model may
reflect all critical systems somewhat, It does not seem to define
them a ll completely.
The terminology Is used In Its customary strict meaning.
Short, non-rigorous descriptions of these meanings are given for
the convenience of persons reading this study who have no logical
or mathematical background. These descriptions are not to be
considered sufficiently strict to define the terminology within
its original, artificially constructed language.
The purpose of the model is to apply rational structures
to schematized infomation. The exact rational structure used,
the scheme by which the information is organized, and the precise
manner in which ratio n al structure and schematized information
are linked are chosen by the person using the model. He must
stay within the restrictions given for the- use of the model when
he chooses them.
The primary sources for concepts and terminology used in
the course of this discussion are Schoenfield and Curry.^
The concepts have been somewhat broadened for the purposes of the
present study. A complete investigation of the implications
of concepts presented in Curry as they apply to musical analysis
would be f r u itfu l, but is outside the scope of th is study.
Admissible rational structures are based upon a first-order
language consisting of distinct entitles. These entities may
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represent words, sounds, numbers, or any other objects when stru c
tures are applied. As far as the first-order language and the
rational structure are concerned, however, the entitles are only
meaningless symbols.
' Each rational structure consists of a set of these entities
together with a set of relationships among them. The structure has
three logical axioms, or conditions upon the structure as a whole,
the entities, and the relationships. It may well be that the
exact configuration of these axioms is somewhat determined by the
definition of entities used and implied requirements of relation
ships assigned, as well as certain properties of the structure as
a whole. The names assigned to the logical axioms by Curry are
"negation," "quantification," and "alternation." Schoenfield
refers to them by their usual mathematical symbols, commonly read
as "not," "there exists," and "union."
"Negation" is a condition on the definition of entities and
relationships. It may be stated thus: relative to the requirements
of the first-order language, every part of the rational structure
must be so strictly and unambiguously stated that anyone versed in
logic can show beyond doubt that hypothesized entities or relation
ships either belong or do not belong to the structure. Further,
the boundaries of any entity are such that the entity is distinct
from the rest of the structure. The result of any combination of
relationships and entities is always the same. This result cannot
contradict the configuration of the structure as a whole. This
condition guarantees necessary properties for the logical stability
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of the structure. Systems in which th is condition is relaxed so
that an entity does, does not, or might belong to the structure
are also potentially valuable to the purposes of this study, but
are omitted here.
"Quantification" restricts the scope of entities and relation
ships and links them to the first-order language. This condition
may be stated thus: The entities and relationships of the structure
exist only in relation to the requirements of the first-order
language, the structure as a whole, and the solidarity of linkage
among entities and relationships. Further, these requirements
give a means of a complete, unambiguous logical d efin itio n of any
portion of the structure from which the intra-structure properties
of that portion can be deducdd. This condition also enables one
to study portions of the structure with like logical properties at
the same time, obtaining information which relates equally well
to all of these portions.
"Alternation" is a condition on combinations of entities
and relationships. It may be stated thus: If a pair of entities
or a pair of relationships is itself an entity or relationship
of the structure, at least one member of the pair is an entity
or relationship within the structure in its own right. For the
purpose of the present study, this condition will be strengthened
to read, both members of the pair are entitles or relationships
within the structure in their own right. This condition is
necessary to the deductive property of the structure. The first
statement produces a condition which results in more flexible
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stru ctu res, which may be promising In musical analysis. These
structures are omitted here for the sake of logical brevity.
These three conditions guarantee the logical stability,
definability, and deductibility of the rational structures used.
The conditions also serve to make the properties of these structures
definable within the artificial language of logic, so that this
language can be used to determine the structure's exact configur-
ation.
This language can be used to observe changes in these
structures under application, if further conditions are met. In
particular, the language can verify that the properties of the
structure remain intact when meanings are assigned to its abstract
entities and relationships. This verification is a necessary
part of the model under consideration, since these properties
represent patterns of organization that are important to the
re su lts obtained from the use of the model.
The information to be analyzed must be so organized that the
application of the rational structure is possible. An example
of such organization is that of a musical work in sound, mapped
into its representation in score notation, given in the second
section of th is chapter. This example is used to illu s tr a te the
properties which the model requires of the organizational procedure.
The method of score notation assumes a format, or defined
space, within which the work may be represented. This format is
a set of staves whose vertical direction represents pitch level,
whose horizontal direction represents duration, together with
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various conventions and markings representing Intensity and timbre.
It happens to be subject to the three previously cited conditions
of negation, quantification, and alternation, as all such defined
spaces must. Entities described within this format are distinct
from each other, subject to the conceptualizations of the person
Interpreting the work. The format has no properties which prohibit
Imbedding ratio n al structures within i t . These la st two character
istics must also be exhibited by all such defined spaces admitted
to the model.
The schematic organization of a given musical work into
score notation has properties discussed in detail in the second
section of this chapter. Schematic mappings admissible to the
model must preserve structurally important details of information
taken from the object, subject to the conceptualizations of the
person mapping the information. Schematic mappings may have
any or all of the additional four properties previously cited with
relation to such maps in the second section of this chapter.
Beyond these properties, the schematic organization of the work
need have no logical re stric tio n s upon i t . The analyst is
directly concerned only with the representation, or image of the
information, as it appears in the defined space.
The rational structure must also be mapped into the defined
space, but in a more restricted manner. Since the configuration
of the structure must be exactly duplicated in the structure's
image, the structure, the defined space, and the mapping o f'th e
structure to the defined space must a ll be controlled by means of
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the artificial logical language. This mapping is identified in
the present study as the symbolic mapping.
The necessary conditions for the symbolic mapping are as
follows: 1) Every entity of the original structure must map
into an entity of the defined space which has exactly the same
properties as the entity of the original structure. These
properties are the ones defined relative to the first-order
language and the conditions of negation, quantification, and
alternation. 2) If there is a set of entities which generate
the original structure, this set must map into a set of entities
which generates the image of that structure. 3) The associations
among entities and relationships of the original structure must
be exactly preserved in its image. 4) Any conditions upon the
relationships of the original structure must also hold for the
images of these relationships.
If these conditions are met, the results of the relationships
of the image can be predicted from a knowledge of the configuration
of the original structure. These conditions insure that the con
figuration of the image will be either identical to that of the
original structure, or else to a reduction of it.
The symbolic mapping associates the images of the e n titie s of
the original structure with the entities produced by the schematic
mapping existing in the defined space. The defined space acts as
a common ground in which the resu lts of these two mappings can
be made compatible, so that the symbolic entities of the original
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structure are assigned definite meanings. The relationships among
these meaningful objects are assumed to be identical to those among
the meaningless entities in the original structure. It is the
analyst's responsibility to choose a rational structure which fits
the configuration of the schematized information in the defined space
reasonably well.
The results of this association of schematized information and
rational structure in the defined space is a description of a
postulated realm. This realm is assumed to have some relatio n to
a configuration of a portion of the original Information. The
function of this configuration within the original work is not
determined by the model, although clues to its function may be
supplied by characteristics of the realm.
The properties of the schematic mapping are su fficien tly
flexible to permit such a realm to be obtained from either a
lo g ically constructed musical work, or one that is not so con
structed. These properties also permit several such realms to
be obtained, either linked or not linked by sequential applications
of the model. These realms may be compared by the analyst to ob
tain further clues to the configuration of the original work. None
of these realms can be considered unique or of permanent value
so far as the original work is concerned, although some may be unique
and permanent with relation to the requirements of the model.
Some observations on the interdependence of the major portions
of the model are now discussed. The generality of these portions
is also shown.
The major portions of the model subject to logical restrictions
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are constructed according to the will of the analyst within
these restrictions. These portions are the rational structure,
the symbolic mapping, and the defined space. The other portion
of the model, the schematic mapping, depends on conceptualized
Interpretation of given information, and on the requirements
of the defined space. Then all portions of the model are under
the direct control of the analyst. It seems that the result of
using the model cannot be more accurate than the construction
and definition of these portions permit.
The schematic mapping, alone of these portions, is logically
ambiguous. Its organizational method of transforming perceptions
into manageable data has a crucial effect upon the interpretability
of the re su lts obtained. For example, i f the schematic mapping
imposes a system of measurement on the given information, the
result will consist of measurements of a chosen aspect of that
information. These measurements can be examined according to
standard methodology relating to measurement, such as statistical
procedure. However, these measurements are immediately meaningful
only in relation to their position within a numerical framework,
no m atter what the ratio n al structure and symbolic mapping are.
Further meaning depends on schematic interpretation of the re
sults. In particular, information not included in the chosen
aspect can be examined only by inference, as far as the' numerical
framework is concerned.
The defined space has two sets of properties. The first
set, determined by the symbolic function, contains logical and
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additional structural properties of the rational structure. The
second set, determined by the schematic mapping, contains non-
logical properties specified by the organizational method used
in that mapping. The defined space can assume the properties
of almost any presently existing mathematical space. It may be
algebraic, topological, or a function space. If necessary, it
may contain an infinite number of dimensions. It appears best
to make the properties of the defined space as minimal as
possible relative to the rest of the model, so that results ob
tained are not obscured by detail irrelevant to the purposes of
the analysis.
The defined space must have provision for distinguishing
the exact type of defined information that the schematic mapping
provides. If the mapping transforms information into integers,
the defined space must contain a well-ordered set of places where
points can be mapped. If real numbers are to be imbedded, the
defined space must contain a sufficiently long portion of the
real line upon which to map them.
If the image of the schematic mapping in the defined space
consists of numbers to be calculated, computational processes
must be obtained. The usual method of obtaining these processes
is compatible with the model discussed here. The generalized
rational structures for these processes consist of negation,
quantification, and altern atio n . The symbolic mapping makes
the configurations of these structures specific by assigning
definite meanings to the entities and relationships in a defined
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tneasureable space.
The same structure can yield more than one computational
process. For example, the same structure is used to obtain the
system of integers under addition and the system of integers
under multiplication. Sets of structures can be generalized
further. For example, all algebraic groups can be expressed
as a single type of structure of entitles and relationships,
no matter how many elements they may contain. Then the specific
rational structure selected may have been obtained from a pre
vious symbolic mapping of a generalized structure into an
intermediate defined space, conforming to the axioms of a
system such as algebra, topology, or functional analysis. The
model discussed here does not exclude th is p o ssib ility . The
structure used need not have been obtained in this manner, since
it is defined with relation to the first-order language. However,
the use of an intermediate space to clarify the structure's con
figuration is often useful to the analyst.
It may be rightly observed that the model described here is
nothing but a codification of the analyst's a priori conclusions.
Contemporary logical thought seems to imply that one can expect
nothing else of such a model in a deductive framework. The
author knows of no logical system which claims to have its basis
in reality, or anything else than the interpreted perceptions
and concepts of the person formulating the logic. Logic, applied
logic, and mathematics are considered to be certain only because
the persons using them have a common linguistic contract regarding
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a ll symbols and procedures used. The model discussed here attempts
to serve as the basis for such a contract for those reading the
present study.
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FOOTNOTES
CHAPTER I
THE COMPATIBILITY OF LOGICAL STRUCTURE AND MUSIC
*Anton Webern, The Path to the New Music, edited by W illi Reich, translated by Leo Black from Per Wee zur neuen Musik (simul taneously published Bryn Mawr, Pennsylvania: Theodore Presser Company in conjunction with Uhiversal-edition, 1960), p. 10. 2 Adolph Weiss, "The Lyceumof SchHnberg," Modern Music IX no. 3 (March-April, 1932): 99. 3 The controversial work of Rudolf Carnap is perhaps most safely approached through the critique by Alan Hausman and Fred Wilson, Carnap and Goodman; Two Formalists (Iowa City: University of Iowa, 1967). Nelson Goodman, Languages of A rt: An Approach to a Theory of Symbols (Indianapolis: Bobbs-Merrill, [1968]), is a useful study whose re su lts can be generalized. Perhaps the most in terestin g of the works by critics influenced by the French structuralist movement is by Roland Barthes, Le degre zero de l'e c ritu re (P aris: Editions du Seull, [1953]).
^The present study follows Wittgenstein's definition of "aspect" as recognition of an attribute or portion of the subject at the will of the observer, as given in the work, Ludwig von Wittgenstein, Philosophical Investigations, translated by G. E. M. Anscombe (Oxford: Basil Blackwell, 1953), bilingual edition, pp. 208e-209e.
^The dissonant chord mentioned here appears in measure 267, the beginning of the Presto. The baritone entry is in the ninth bar of th at Presto, measure 276.
^Paul Hindemith, The Craft of Musical Composition, translated by Arthur Mendel (New York: Associated Music Publishers, 1945); Joseph Schlllinger, The Schillinger System of Musical Composition (New York: Carl Fischer, Inc., [1946 J), 2 vols.; a rigorous definition of pitch serialization as Webern knew it is given in the work, Ernst Krenek, Studies in Counterpoint: Based on the Twelve-Tone Technique (New York: G. Schirmer, Inc., [1940]). 7 Haskell Brooks Curry, Foundations of Mathematical Logic (New York: McGraw-Hill Company, Inc., [1963]); Joseph Robert Shoenfield, Mathematical Logic (Reading, Massachusetts: Addison-Wesley Publishing Company, [1967]).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER II
PHILOSOPHICAL AND LITERARY INFLUENCES ON WEBERN'S MATURE STYLE
Introduction
Philosophical Ideas mentioned In Webern's published writings are
discussed In this chapter. These Ideas seem to have had considerable
Influence on Webern's formulation of principles underlying his
mature style. In particular, a philosophical justification for the
deliberate use of new rational structures In music Is shown.
Several schematic organizational methods appear among these
Ideas. Webern's use of transformal and metamorphlc techniques may
have been based upon the botanical Ideas of Goethe. His use of
timbre as a stru c tu ra l determinant may have been suggested by the a rt
and writings of Kandinsky. The value which he placed upon form for Its
own sake, as well as his Idealization of logical process, may have
been due to his readings of Plato and Rant. The specific requirements
for logical process In music, as discussed In the third section of
the first chapter of the present study, are paralleled In Houston
Stewart Chamberlain's book on Kant, which Webern owned.
Webern's approach to these Ideas was undoubtedly shaped by his
thorough scholastic training at the Gymnasium at Klagenfurt, which
enabled him to qualify for the University of Vienna. The progressive
intellectual climate of the University itself must have also altered
that approach.^ Since exact information about Webern's education was
unavailable at the time of writing, the present study assumes only 40
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that Webern read the sources cited in an unbiased manner, and does
not attempt to draw inferences about their relation to the Intellectual
G eatalt in which Webern encountered them.
Section 1. Sources Cited in Webern's Published Writings
At the time that the present study was written, Webern's published 2 writings were: Per Weg zur neuen Musik. a collection of notes taken
at his lectures of 1932-3, with letters to Willi Reich; the foreward
to his edition of Isaac's Choralis Constantinus II. which was his 3 doctoral thesis; an essay, reprinted with’a quotation and an excerpt 4 from a letter; diary entries and miscellaneous short passages quoted
in Reich's Anton Webern;5 le tte rs to the Humpliks;*’ to Roberto
Gerhardt;^ excerpts of letters and diary entries in Freidrich Wildgan's 8 9 Anton Webern; and le tte rs cited in a rtic le s by W illi Reich.
Some of these sources mention books which Impressed Webern, and
theee books are also mentioned below. A partial listing of his personal
library is available.The texts which he chose to set to music are
cited as indirect clues to his philosophical and aesthetic leanings.
The author mentioned most frequently in these sources is Goethe.
In 1911, Webern read Wilhelm M eister; he owned Farbenlehre and an edi- 12 tion of Goethe's conversations with Eckermann. During 1918, he is
said to have carried Faust around with him, as many German-speaking 13 intellectuals have done. He read the Goethe-Schiller correspondence
in 1928 and the Goethe-Eckermann conversations in 1936.*^
Goethe is quoted twice in connection with the concept of meta
morphosis in the correspondence with the Humpllks. In the le tte r
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of May 26, 1941, the V ariations, opus 30, are discussed as follows:
Imagine this: 6 notes are given, and In a shape determined by the sequence and the rhythm, and what follows . . . Is nothing other than this shape over and over again.' Naturally in continual "Metamorphosis" (in musical terms this process is called "Variation") -- but It is nevertheless the same every time.
Goethe says of the "Prime Phenomenon": "ideal as the ultimate recognizable thing, real when recognized*, symbolic, since it embraces every case, identical with every case**". * In my piece, that is what it is, namely the shape mentioned above.1 (The comparison serves only to clarify_the process.) ** Namely in my piece.' That is what i t does.'
Josef Folnaur, the editor of the Humpllk correspondence, gives the
source of the quotation as "Naturwissenshaft in Allgemeinen, einzelne
Betrachtungen und Aphorismen," and notes that the lines also appear
in Goethe's "Maxims und Reflections."^ The letter of July 25, 1942
to Hildegard Jone quotes Goethe's poem, "The Metamorphosis of Plants,"
lin es 5-8, in connection with the form of the Second Cantata, opus 31.
What went before is now repeated backwards. "Repeated": . . . "All shapes are similar and none are the same: thus the chorus points to a secret law, to a holy riddle."
This poem contains one of Goethe's most concise descriptions of his
"primeval plant" concept.
Webern's preoccupation with this concept is shown in his letter
to Willi Reich, August 23, 1941.
As with Goethe's "primeval plant" -- "with this model, and the key to it, one can straightway invent plants ad infinitum . . . the same law will be found to apply to all other living m atter.'" I s n 't that the meaning of our law of the row, at its deepest?-*-”
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The quotation Is from Goethe's letter to his teacher, Herder, May 19 17, 1787. Webern would have had to have read eith er Goethe's
early correspondence or the Italian Journey to have known it.
The "primeval plant" concept reappears in Webern's lectures of
February 19 and 26, 1932.
You'll already have seen where I am leading you. Goethe's primeval plant; the root is In fact no different from the stalk , the stalk no d ifferen t from the leaf, and the leaf no different from the flower; variations of the same idea .... The same law applies to everything living; "variations on a theme" — th a t's the primeval form, which is at the bottom of everything. Something that seems quite different is really the same. The most comprehensive unity re su lts from th is.
Goethe's full explanations of the "primeval plant" concept are found
in his journal, Natural Science in General; Morphology in P a rticu la r,
and in his booklet, "Metamorphosis of Plants." The author is of
the opinion th at Webern would have had to have read one of these
sources to obtain the excellent grasp he had of Goethe's rather
unorthodox scientific thought. Webern is known to have had a per
sistent interest in nature and botany, and at one time carried a 21 botanical lexicon with him on excursions. Webern's comments on
Nature are much like Goethe's, and are further discussed below.
The lecture of February 20, 1933 shows that Webern was also in
terested in Goethe's work on visual perception, Farbenlehre. There
are two quotations, both central to Webern's musical philosophy, cited.
And he says, "But perhaps those of a more orderly turn of mind will point out that we have not yet even given a definite explanation of what colour in fact is . . . < Here again there is nothing left to repeat: colour is
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natural law as related to the sense of sight." Since the difference between colour and music Is one of degree, not of kind, one can say that music is natural law as related to the sense of hearing.^2
According to the lecture notes, the following quotation is from the
introduction of Farbenlehre. but it is not.
Goethe speaks aphoristically of "the impossibility of account ing for beauty in nature and art . . . We want to sense laws . . . one would have to know them." But Goethe sees th is as almost impossible — but that doesn't make it less a neces sity "to get to know the laws according to which nature in general, in the particular form of human nature, tends to produce and does produce when she can ..." What was that? Goethe sees art as a product of nature in general, taking the particular form human nature. That is to say, there is no essential contrast between a product of nature and a product of art, but that it is all the same, that what we regard as and call a work of a rt is basically nothing but a product of nature in general.
[We] must strive to discover the laws according to which nature, in its particular form "man," is productive. . . . [it] is a matter of natural laws, . all discussion can only take place along these lines.
This passage seems to reflect the interpretation of Goethean prin
ciples by the philosophical school of German idealism. It seems
interesting that Webern does not quote from writings of this
school, but from earlier sources, and the present study consequently
follows Webern's practice in this regard.
Webern makes only two specific comments on the w ritings of his
contemporaries other than Schoenberg and Berg in currently published
w ritings. The le tte r to Alban Berg, December 21, 1911, links him
directly to the early expressionistic painters who experimented
with visual color at the time that Schoenberg experimented with
sound color, Klangfarbenmelodie.
Kandinsky's book is excellent. I do not think I have
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already w ritten to you about J±; or have I? It is called The Spiritual in Art.
The publication of one of Webern's songs in Per Blaue Reiter, which
was edited by Kandinsky, was probably due to Schoenberg's influence.
The Schoenberg-Kandinsky correspondence of 1911-1912, which is not
published, should give more indirect information about Kandinsky's
influence on Webern.
Webern wrote to his cousin Diez, November 5, 1902, that he was
"attending lectures . . . given by Dr. Mflller about 'Practical
Philosophy' — a fine chap who talks more about literature than 25 philosophy. The author has been unable to find any more information
about Dr. MUller. An official listing of the doctoral dissertations
in philosophy written at the University of Vienna during Webern's years
there shows that favorite topics were the philosophies of Leibnitz, 26 Kant, and Schopenhauer. Webern was personally acquainted with the 27 28 writings of Kant, Schopenhauer, and Nietzsche.
Webern's matriculation at the University of Vienna implies that he
passed the Matura, a s tr ic t entrance examination requiring knowledge
of Greek and Latin, as well as ancient texts and mythology. 29 In 1941,
he noticed, while reading Plato or a Plato commentary, that the Greek
word Nomos meant melody as well as law. He was su ffic ie n tly impressed
by this incidence to write to both Willi Reich and Hildegard Jone about
it. In the letter to Willi Reich, he shows that the idea underlying the
dual meaning of Nomos is characteristic of his mature works.
A voice gives out the law — in this case the soprano so lo ist — th a t's to say "melody" — but the Greeks had the same word for that as for law: "Nomos." So the "melody" has to "lay down the law."
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46
That's how it's always been in music by the masters! Whether 1 shall bring it off as they did, only God knows, but at least I've recognized what's involved.' Naturally, the "row" in Itself consititufts a law, but it needn't also be the "melody!" But since in my case it in fact is. the row takes on a quite special importance. The foundations of our technique in general are there, but I think I'm returning to them in a quite special sense.30
Plato discusses the double meaning of Nomos. as far as the author
knows, only in his dialogue, Laws. In th is work, the concept of law
in general is developed as an analogy to musical law, and the double 31 meaning its e lf is twice mentioned sp ecifically . The passage des
cribing Greek music in th is work would probably have interested
Webern from a musicological standpoint.
I t may be inferred from Webern's le tte r to Berg on December 21,
1911, that Webern read Kant in depth.
I am giving you Kant's letters because I wish you to become acquainted soon with this splendid, remarkable mind. I do not know very many of his works eith er. But I am striving towards a very exact knowledge of him.32
Webern's respect for the writings of others, probably a result
of his classical education and his musicological training under
Guido Adler, is shown in his le tte r to Hildegard Jone, September 3,
1933.
The examples you sent me from translations of Virgil made me -- I can't; put in any differently -- extremely sceptical. Is there any sense in trans lating so unllterallv? What is left of the thought? It becomes that of the translator. For in the last analysis it is the words that make the thought! For example: 'dicite.’ That doesn't mean 'sing.' It means 'say,' 'speak' . . . hasn't the thought been considerably falsified thus? . . . The passage from the 'T illag e' section . . . appears to me to have
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absolutely no connection with the original. 1 am sh o ck ed 33
There is enough evidence In Webern's published w ritings to show
that his interest in philosophical and literary works was lifelong,
and that it affected his musical thinking. He seems not to have been
content with superficial knowledge of the ideas involved, but strove
to obtain deep understanding of them.
Section 2. The Influence of Goethe: Metamorphosis
It is dangerous to quote Goethe. His range of interest was so
universal, his output so v ast, and his lif e so long that one can not
only find passages, but even contradictory passages in his work on
almost every subject. * This point is illustrated by*^oel£htr,-&^qninents on the structure
of his Faust. He worked on Faust almost all of his productive life,
leaving it unfinished at his death; the development of Faust as a
lite ra ry work p a ra llels Goethe's own development. Eckermann gives
Goethe's comments thus, recorded in 1827:
But what strange people the Germans arej They make life so much more difficult than it need be by their profound thoughts and ideas which they look for in everything and read into everything. Why on earth w ill you never have the courage to surrender yourselves to be taught something new, to be inspired and emboldened to some great achievement! Why must you always assume that nothing is any good unless it is some sort of abstract thought or idea? They come to me for instance and ask: what idea did you try to embody in Faust? As if I knew the answer myself and could put it into words' The life I portrayed in Faust is rich and many-coloured and very various, and a fine thing i t would have been, I must say, if I had attempted to thread that on to the thin
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string of a single pervading Idea.' 34
Twenty-one years e a r lie r , however, according to Luden, Goethe said:
Faust does after all possess Interest of a higher kind -- the idea, that Is to say, which Inspired the poet and binds all the Individual parts of the poem Into a whole, furnishing the law for each and every one, and apportioning to each Its due and proper Im portance. 35
The widely respected Goethe scholars, Wilkinson and Willoughby, solve
this particular contradiction with the explanation that, in the first
quotation, Goethe equates "idea" with abstract thought, whereas in
the second, "idea" is more nearly equivalent to center or Mittlepunkt.
The explanation of Mittlepunkt continues:
And the words [of the second quotation] . . . which . . . determine the climate of i t s meaning are not derived from the sphere of abstract thought at all, but from that of organic growth .... The unifying -principle he has here in mind is not a philosophical 'idea' at all, not one which can be abstracted from the poetic structure and formulated in other terms. It is rather the principle which is active in the living processes of the poem itself, the formative tendency, or Bildungstrieb. which organises a ll the p arts, however diverse, into a meaningful whole. 'idea' here signifies 'organic centre' . . . — the point from which all the parts radiate and 'out of which, mutually replenishing and completing each other, they all have grown and could well go on growing. . . . The poetic tendency of the individual part, ' he insists, 'points at all times to necessary connection, that is, to a conmon centre, to a primary idea. ... . the fragments # . .. . will ap pear in that same whole as organic parts, and then, and only then, will they assume their true significance.'
There is, perhaps, a further explanation for these contradictory
passages. In 1806, Goethe was en th u siastically developing his
botanical theories, and felt that his ideas were valid not only in
scientific fields, but also in literature. The second quotation
re fle c ts his botanical theories. By 1827, he had resigned himself
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to the indifference of scientists to his work, and was perhaps dis-
heartened about his theories. 37
Goethe was hampered in his s c ie n tific work by the very talen ts
which enabled him to write powerful literature — his strong, intui
tive creative impulse, and his keen powers of observation. He was
in the habit of relying upon his subjective judgement because it was,
for the most part, accurate. If his judgement was contradicted, he
would alter or enlarge his hypotheses instead of starting over. He
would attempt to gain a conceptual, intuitive understanding of a
given phenomenon as a whole, later linking its components to the
whole.u 1 38
This procedure was directly opposed to that of the scientists
of Goethe's time, which was based on a strict application of the
methods outlined by Newton and Kant. The incompatibility of Goethe's
method with that of Newton is shown by th is passage from Newton's
Principa
But hitherto I have not been able to discover the cause of these properties of gravity from phenomena, and I frame no hypotheses. For whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical . . . have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction .... And to us it is enough that gravity does really exist, and acts according to the laws we have explained.
As Leibniz had before him, Goethe placed him self in opposition to
Newton, and in spite of a great deal of honest effort, was unable
to accept the scientific method wholeheartedly.^® Although his
scientific work was unacceptable to his contemporaries, it is
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maintained today that it anticipated Darwin's theory of evolution
and the methodology of psychological studies of perception. ^ It
will be shown in the next section of this paper that Kandinsky's
ideas of perception are much like Goethe's. Both viewpoints of
perception can be supported from passages in Kant's works.
The concept of the "primeval plant" was developed by' Goethe
on his first journey to Italy. The concept itself resulted from
his observations of plants under non-experlmental conditions, and
is that the process by which he thought the universe was formed
would be reflected in each part of i t , whether that part be cu ltu ral, 42 a r t i s t i c , or s c ie n tific . This process he called metamorphism,
and it is the process referred to by Webern in connection with his
own music. The passage in which Goethe comes closest to an outright
statement that metamorphosis holds the key to both nature and art is
the very passage cited by Webern when he describes the qualities
determine the art he considers great.
I have hit upon a fcVtfftx’TTA.V (single law which is valid for a ll) , in botany especially, which amazes me . . . - The principle, by which I interpret works of art and unlock the secret which artists and art experts since the Renaissance have been laboriously trying to discover, seems to me sounder every time I apply it. It is verily the egg of Columbus .... One thing is certain: all the artists of antiquity had as great a knowledge of Nature and as unerring a sense of what can be represented and how, as Homer .... These masterpieces of man were brought forth in obedience to the same laws as the masterpieces of Nature. Before them, all that is arbitary and imaginary collapses: there is necessity, there is God. 43
Goethe defines metamorphosis as follows:
The metamorphosis of plants is the basis 6f the physio logy of plan ts. I t shows as the laws by which plants are formed ....
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In plant study we assume a beginning point of lif e that eternally reproduces itself. And in very few cases is the reproduction achieved by mere rep etitio n . Furthermore, in the more perfect organisms it is done through progressive development and transformation of the basic organ into more and more elaborate and effective organs, to achieve ultimately the highest point of organic activity; individuation and release of Individuals from the organic whole through generation and birth. ^
The basic organ referred to is the leaf, which Goethe thought was
the building block from which a ll parts of the plant were formed.
This formation was supposed to have taken place in a manner
exactly analogous to Webern's practice of formulating all parts of
a musical work from a single idea.
By 1823, Goethe decided that the concept of metamorphosis
alone did not explain the workings of the universe.
The concept of metamorphosis is a highle estimable gift . . . but a dangerous one. It leads to formlessness, destroys knowledge, disintegrates it. It is like centrifugal force and would lose itself in the infinite if a counterweight were not provided. I am referring to the specification force [which the translator clarifies as the tendency to assume specific form], that tenacious capacity for persistence inherent in whatever has attained existence, a centripetal force that can not be disturbed in its deepest nature by anything external
We should need to have recourse to a discussion of art. A symbolism would have to be created. But who is to achieve this? Who is to acknowledge it after it has been d o n e ? ^ 5
A description of an equilibrium between metamorphosis and the
specification force is found in Faust.
When Nature spins with unconcern The endless thread and winds i t on the spindle
Who divides the Flowing changeless line, Infusing lif e , and gives i t pulse and rhythm?
Who braids from undistinguished verdant leaves A wreath of honor as a mark of merit?
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Who safeguards Mount Olympus, who unites the gods? Man's power which in the poet stands revealed 46
Another is recorded by Eckermann.
The artist has a twofold relation to nature . . . he is her slave, inasmuch as he must work with earthly things; but he is her master, inasmuch as he subjects these earthly means to his higher intentions.
In Webern's mature works, an equilibrium seems to exist between
the s tr ic t logic to which the work must comply in i t s smallest de
tail, and the free, natural way in which the music itself develops.
In the light of the above passages, it seems that this equilibrium
represents a balance between the high purposes of man, who wishes
to bring Nature to realize her fullest potential, and the generating
processes of Nature, from which all is born and grows. It seems
that Webern consciously developed both aspects of this balance
as far as he dared, producing on the one hand a logical system of
intrinsic beauty and utility, and on the other hand, a concise
expression of the means by which growth seems to occur in all
living beings.
The formal principles of the epic style, as described by
Goethe, bear a strong resemblance to techniques important in Webern's
later works. Since Webern mehtions reading the volume in which
they occur, they may well have influenced him directly. They are 48 as follows: (1) progressive motives which further the develop
ment of the story; (2) retrograde motives which keep i t back from
its goal; (3) retarding motives; and (4) motives which introduce what
is to happen after the end of the poem. The first two principles
are central to his technique of development. The last two principles
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illustrate Webern's method of linking separate movements of a multi
movement work.
As the last section of this chapter shows, Webern does not
share Goethe's aversion of the purely abstract idea. From a
philosophical standpoint, Webern's reconciliation of the philosophies
of Goethe and Kant in musical structure seems to be a major achieve
ment.
Section 3. Kandinsky: The Natural Law of the Sense of Sight
Webern was only one of many to find creative inspiration in
Goethe's scientific work. Goethe's study of the appearances of
color, Farbenlehre. was an influence on German painters during
the Romantic era. 49 One of its central concepts is that color is
the result of the eye's interaction with visual phenomena, rather
than a quality of the phenomena themselves. This concept provided
aesthetic justification for the work of pre-expressionist artists
such as van Gogh and Gaugin, and their followers, such as the
Blaue Reiter group, with whom Kandinsky was associated.
Applications of specific passages in Farbenlehre can be found
in the paintings of the Blaue Reiter group. For example, Goethe
claims that an overabundance of a strong color would cause the 50 retina to see its complementary color on adjacent surfaces.
Alexij Jawlensky's Peonies, painted in 1909, shows a girl dressed
in vivid red, holding red flowers; her flesh in tinged with red's
complement, g re e n .^ Goethe also states that colors are capable 52 of stimulating emotions in a more or less predictable manner.
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without page(s) 54
UNIVERSITY MICROFILMS.
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Van Gogh had been one of the first painters of the nineteenth
century to re je c t the academic discipline of a rt. 58 His example
and that of many others give meaning to Kandinsky's statement,
"The a r tis t must have something to communicate, since mastery over
form is not the end but, instead, the adapting of form to internal 59 significance." These painters felt that the artist should gain
control over his medium only to increase his power to produce art.
The purpose-of painting became a matter of self-expression
rather than reproduction of Nature. Kandinsky saw two powerful means
of self-expression in art -- form and color.^ He held that neither
was necessarily dependent upon the appearance of the subject one
wished to paint. In fact, a concrete subject was no longer neces
sary; conceptions of form and color could serve as the means by
which the work of a rt would communicate to the observer.
To carry out th is idea, i t became necessary to examine the
intrinsic properties of form and color. Farbenlehre is an excel
lent subjective investigation of one's reaction to color, and even
discusses the allegorical and symbolic possibilities which could be
obtained by its use.
Kandinsky, like Goethe, finds analogous contrasts in warmth and
cold, yellow and blue, light and dark, proximity and distance, 61 repulsion and attraction as possible attributes of color. Such
oppositions may be generalized to qualities of timbre in music,
particularly Mahler's.
Goethe attempted a similar examination of the properties of 62 sound in Tonlehre. which was not published until the appearance
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of his complete works. Tonlehre presents a classification of the
elements of music by rhythm, timbre, form, acoustical properties, and
melodic contour. At the time of writing, no evidence was available
that any of Webern's contemporaries were familiar with this work.
However, fa m ilia rity with Farbenlehre may have prompted them to
formulate a similar classification of musical material. Schoenberg's
Harmonielehrt1,. as well as the early atonal works of Webern, seems, to
show an intent to use musical timbre according to previously unex-
ploited means, based on its apparently intrinsic qualities.
The work of the French symbolists was known to Kandinsky and 63 to Webern's contemporaries. The early expressionists followed
the Symbolist method of formulating new a rt by reducing th e ir re
spective mediums to the simplest possible components, letting structure
be determined by the natural generative power of these components.
These components were to be understood as consequences of perception;
that is, not as phenomena with objective artistic characteristics,
but as objects and qualities whose existence depended on the
subjective reaction of the artist to his environment. The Symbolists
felt, in addition, that perceptions are a stimulus to one's creative
power, enabling one to produce art transcending perception. It
seems that Webern held the expressionist view of perception when
writing his early atonal works, and moved toward the Symbolist
position in his later years. Either position would have enabled
him to produce a realm of a rt whose only laws would be the laws of
the mind, heart, and perception of the artist.
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Section 4. Plato: The Melody Gives Out the Law
Many of Plato's ideas on art seem directly opposed to those of
the expressionists discussed in the preceding section. Plato de
nounces free expression in art as dangerous to the state, and would 64 censor all poets, including Homer. He approves of the Egyptian
practice of strict regulation of music according to traditional
styles.^ Art for its own sake has little value . ^ Although
sound and color can be beautiful in themselves, they are not suf
ficient to generate meaningful a rt.^
These ideas, however, re fle c t P la to 's reaction to the music
of his own time. He has a noble concept of what it might become.
We shall never be true musicians . . . until we are able to recognize the forms of soberness, courage, liberality, and high-mindedness .... When there is a coincidence of a beautiful disposition in the soul and corresponding and harmonious beauties of the same type in the bodily form — is this not the fairest spect&cle for one who is capable of its contemplation? Surely the end and consummation of culture is the love of the beautiful.**®
Music is given to man that he might better understand the harmony
of the universe.
And harmony, which has motions akin to the revolutions of our souls, is not regarded by the intelligent votary of the Muses as given by them with a view to irra tio n a l pleasure . . . but as meant to correct any discord. . . in the courses of the soul, and to be our ally in bringing [the soul] into harmony and agreement with herself ....
The harmony of the universe is itself music.^
To Plato, the highest aim of man was to know "that place beyond
the heavens [of which] none of our earthly poets has yet sung, and
none shall sing worthily .... [it] is there that true being dwells,
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without color or shape . . . reason alone, the soul's pilot, can
behold i t , and a ll true knowledge is knowledge th ereo f." 7 1
Knowledge, even of th is Imperfect earth, tends toward a single
goal.
To the man who pursues his studies in the proper way, all geometric constructions, all systems of numbers, all duly constituted melodic progressions, the singly ordered scheme of all celestial revolutions, should disclose . . . a single bond of natural interconnection between all these problems.72
Similarly, the man who searches for beauty in nature, learning,
and "the special lore that pertains to nothing but the beautiful
itself" finds in the end one single form of knowledge, the vision
of beauty that transcends all existence. 7 3
The universe is moved by an entity which corresponds to a
human soul, and is called, simply, soul. 7 4 All human endeavor is
a result of the forces emanating from that soul. For this reason,
the "grand primal works and deeds . . . prove to be those of a rt;
those of nature £of this imperfectly created earth) will be secondary
and derivative from art and mind." 7 5 But it is only as the human
brain is put into motion in the manner which is felt to be natural
to it — that "akin to . . . the thoughts and revolutions of the
universe" — chn one "correct the courses of the head which were
corrupted at our birth, and should assimilate the thinking being to
the thought, renewing his original nature, so that having assimilated
them he may a tta in to that best life which the gods have set before
7 fi mankind, both for the present and the future."
The matter out of which plant and animal life was to be generated
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at first "presented a strange variety of appearances, and being full
of powers which were neither sim ilar nor equally balanced, was never
in any part in a state of equipoise, but swaying unevenly hither and
th ith e r" u n til i t was organized by form and number, or to be exact,
into infinitesmal triangles. 77 The triangles are made out of the
four elements, and come in various geometrical configurations which
help determine the manner in which they are fitted together.
One could say that the abandonment of to n ality would put the
raw materials of music in a similar chaotic state. The triangles
would be a means of giving order where no order seemed possible.
The process resembles Goethe's metamorphic concept, but has the
additional capacity of organizing entities which are dissimilar and un
equally balanced. ' A larger system of order modeled on the order
of the universe was the next logical step. One could create a
logical universe, motivated by an ideal of that universe, and postulate
worlds within it. The order of these worlds would reflect that of
the universe as a whole.
It seems that, in Webern's mature style, a work is just such a
world. Its generative elements are put together by means of :
"triangles" of a very specific configuration, namely that of the
row. This configuration governs the shape of the generated elements,
just as the shape of the triangle in Plato's image of the earth
determines the qualities of the object of which it is a part. The
generative elements, or that out of which "plant and animal life"
will be made, are the sounds available to Webern, including their
perceived aspects of rhythm, register, timbre, and so on. The
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universe itself is the set of all permutations of the chromatic
scale, and all possible perceptual combinations of the aspects of
sound. The soul of th is universe, that which sets i t into motion,
is shown by the operations of inversion and retrograde upon the set
of permutations, together with the procedures for motivic develop
ment. By setting this soul, universe, and generating process in
motion, i t might be hoped that one could achieve an approximation
of the perfect knowledge and beauty which was considered to be the
ultimate good by Plato.
The world which is created by Webern in the process of composi
tion bears many resemblances to Plato's ideal state as outlined in
the Laws. Both are well-ordered (completely hierarchially arranged)
and tig h tly organized; randomness is frowned upon, since a l l should
contribute to the achievement of the greater good, namely perfect
order. The smaller elements of form and the motives in Webern's
work, like the inhabitants of Plato's state, refledt the structure
of the larger organization. Their every action is ruled by the 78 laws of the state or world. One of the primary laws of Webern's
world is that all pitch organization is subject to the specific
permutation, or row, selected for that world. In a very real
sense, the melody does lay down the law. In English as well as in
German, the term "canon" or Kanon preserves the double meaning of Nomos. law as well as melody. This double meaning is made obvious
in several of Webern's works in which actual canons are used, notably
the pre-twelve-tone serial song, "Fahr hin, o Seel," opus 15, no. 5,
and the f i r s t movement of the Symphony, opus 21, which is w ritten
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In Webern's mature style.
The Inclusion of all notes of the chromatic scale in the row form
reflects the completeness of the work's "universe" on a smaller scale.
In the passage in Plato's Republic describing the music of the spheres, 79 all seven notes of the scale are sung at once, in concord. The 80 only dissonance is dissension against the universal laws. But in
Webern's realm of order, as in Plato's state, "No law or ordinance 81 whatever has the right to sovereignty over true knowledge."
In almost all of Webern's work, choice of pitch affects and
restricts voicing possibilities, which in turn affect and restrict
choices of timbre. In Webern's mature style, there is an interplay
on the structural level between the plan which governs rational
patterns and the actual sound desired. The development of sound,
however, is ultimately subordinated to the design of the whole, as
Plato's citizen is subordinated to the laws of the state.
The explanations of Plotinus, the neo-Platonist, may clarify
the nature of Plato's thought as it was understood by the authors
of the texts of the songs, opera 15-17. Plotinus speaks of the 82 world, or the domain of living man, as "being." "Being" is in te r
mediate between the ultim ate unity, the humanly incomprehensible
supreme good which might be called God, and nonbeing, or formless
matter. "Being" is divided into three stages: "soul," which is the
closest stage to the ultimate attainable by living man, in which he
possesses rational insight; "spirit," next in rank to "soul," in which
man is able to categorize information from other stages in an intel
ligible manner; and "nature," ranking below "spirit," the sensory
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world into which man Is born.
Thus the world is a place of transition, situated at once in light and darkness. It is beautiful and divine, because i t originates in the One. It is a shadow, a reflection, incomplete and full of failings, because it is everywhere vitiated by orderless matter, the untruth of nonbeing. In so far as Being is formed, i t is beauty, truth, good; but in so far as every existent, even the best, contains a vestige of unfg^med matter, it partakes of ugliness, untruth, and evil.
Plotinus advises man to strive to reach the beauty of the One, the
ultimate, by transcending the world in which he finds himself. He
considers order and logic to be both means of transcending and ex
pressions of the One in forms in te llig ib le to humans.
The sense-perceptions of the stage "nature" are not as true or as
beautiful as those of the higher stages. In "nature," man can only
perceive the real world; in "spirit," he perceives glimpses of the
One.
What we have called the perceptibles of that realm [of the One] enter into cognisance in a way of their own, since they are not material, while the sensible sense here -- so distinguished as dealing with corporeal objects — is fainter [in perceiving the true and good] than the perception existing in a less true degree and taking only enfeebled images of things There — perceptions here are Intellections of the dimmer order, and the Intel lections There are vivid perceptions. ^
Then the apprehension of beauty of logical insight based on concep
tio n of inner meaning is greater than that of natural objects based
on objective perception of outward form. The ultim ate must take
shape to be perceptible to the soul; these shapes may be thought
of as variations of the ultimate, and reflect to some degree its
beauty. The less the shape d iffers from the higher stage of which
it is a variant, the more beautiful it is.
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Shape is an impress from the unshaped; . . . Matter, in the nature of things, is the furthest away, since of itself it has not even the lowest degree of shape. Thus lovableness does not belong to Matter but to that which draws upon Form; the Form upon Matter comes by way of soul; soul is more nearly Form and therefore more lovable; Intellectual Principle, nearer still, is even more to be loved; by these steps we are led to know that the First Principle, principle of Beauty, must be f o r m l e s s . 35
But music must deal with sound, which is by its very nature an
aspect of Matter. Then music can only approach the First Principle,
and to do so must take shape. The more orderly the shape, the
greater beauty the music will exhibit. The sensory perceptions of
sound must then be subordinated to logical Insight. Yet these
sensory perceptions are beautiful in their own right, and can be
used to engender beauty by means of the motivic development technique.
This technique may be said to give meaning to sensory perceptions in
a way analogous to the way that Goethe's process of metamorphosis
brings unformed m atter into the higher stage of Nature. But th is
technique can only work in this fashion if the sensory perceptions
are reduced to their simplest forms. Otherwise their use would
endanger the precision, hence the beauty, of the logical insight
which is the goal of the composer.
Webern's correspondence with Hildegard Jone reveals his belief
that the beautiful must be made simple, so that i t can be universally 86 understood. His selection of poetry for his songs seems to support
this belief. Abstraction, as the simplification of music to its
vital elements, is equated with transcendence in the following
passages:
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It's important that Bach's last work was the "Art of the Fugue," a work that goes wholly into the abstract, music lacking all the things usually shown by notation--no sign whether it's for voices or instruments, no performing indica tions. It's almost an abstraction--or I prefer to say the highest reality.' All these fugues are based on one single theme, which is constantly transformed; a thick book of musical ideas whose whole content arises from a single idea!87
And yet, to be heard, such music must manifest it s e l f in sound.
Webern's extensive performing indications show his preoccupation with
the manifestation itself. It seems that these indications clarify
a pre-existing abstract structure so that it can be heard. Although
the resulting sounds are beautiful in themselves, it seems more
important to Webern that the ultimate order of the work be made
clear through these sounds. Apparently, Webern considered sound'
aggregates both as collections of discrete pitches and as single
configurations of timbre, whose value in a composition is determined
by the relation of such pitches and timbres to other aggregates in
the work. A single pitch may then be considered an aggregate of
one pitch, with a specific timbre configuration. Then choice of pitch
is subject to other logical orders, which it enhances through careful
assignment of timbre and re g iste r.
Plotinus considers man most free when he willingly submits to
logical restrictions in pursuit of the ultimate. Some of the texts
which Webern chose for the songs, opera 15-17, glorify the restric
tions of Christ's cross, because the cross makes the salvation of man
possible. Similarly, the restrictions of serialism enable the
composer to reach a higher stage of logic which brings him closer to
abstraction and transcendence; hence, closer to uncreated beauty.
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[Christ on the cross comforts his mother:'] "Oh, Mother, cry no more, tfy sufferings are slight; The Kingdom of Heaven is mine."
Ascend, fair soul, to thy God, Who made thee of nothingness, Who redeemed thee with His death, And who holds open the gates of Heaven. Go forth to Him, who, in baptism, Gave thee innocence; May He mercifully receive thee Into that better life.
F aithful cross above a ll others one and only noble tree, none in foliage, none in blossom, none in f r u it thy peer may be. Sweetest wood and sweetest iron,gg sweetest weight is hung on thee.1
In the last verse of the last chorus of the second Cantata, the last
text of Webern's published work, there is a vision of the beauty
brought through Christ, or if one can maintain the previous imagery,
through the restrictions of logic:
(Christ) holds Heaven like a flower, and leads to greatest lig h t, in perfect peace moved our will, by a child's sweet might, by “bold love's great power.-
Section 5. Hypothesis: The Philosophical Basis of Webern's Style
During Webern's formative years, the mainstream of German
philosophical thought was idealistic, vigorous, and pragmatic. To
a great extent, it developed according to the principles of Goethe
as presented in his works Faust and Wilhelm M eister.
Both works portray men whose purpose is the search for the
ultimate secrets of life, which is carried on by living and reading
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as fully as possible, observing in an unprejudiced manner. Goethe's
philosophical development can be described as such a search. Although
as he admitted, this procedure at times led him astray, he felt
i t superior to more rig id methods of acquiring knowledge of the
world. Wilhelm Meister is a self-educated man who does not strive
for excellence in any one discipline as an end in itself, although
he does attain a fair degree of competence as an actor and surgeon.
His goal seems to be to generalize all that he learns into a
macro-knowledge that w ill enable him to comprehend a ll of Nature.
The validity of the search for this macro-knowledge seems to
have been one of the fundamental assumptions made by the German
id e a lists who followed Goethe, such as Fichte, Schilling, and Schopen
hauer. From Kant they inherited the idea that logical systems
could have universal validity only with reference to manifestations
of Nature, where Nature comprises the total of man's conceptual
izations and perceptions of the world. Such logical systems might
not explain the causes of these manifestations, which might be due
to the influence of the World-Spirit which transcended manifestation.
The Hegelian dialectic, the rejection of musical stylistic
tradition by Wagner, and the basic premises of nihilistic thought
seem to have means of limiting the scope of rational thought to
its proper province. It was assumed that only close contact with
the causes of Nature could yield fruitful results to the search for
the foundations of intellectual thought, and that rigid a priori
systems of thought could blind one to these causes.
A man's deed was a true expression of the spirit which transcends
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Nature if it waa made in harmony with that part of the spirit which
dwelled in him. Such a deed would take precedence over any a r tif i c ia l
condition which contradicted it. The constant exercise of one's
will in performing such deeds seemed to imply a continuing renewal
of the World-Spirit in the world of men. The stifling of this will
was held to be a denial of life and the creative process. It was
not thought that such exercise of will could be anything but
beneficial to the human race, because of Goethe's premise that a
return to Nature was a return to the highest good for all men.
A revolution to break down constricting systems was thought to
benecessary before man's will could be exercised freely. Then man
could build a new system which would be in accordance with Nature.
Wagner's Art and Revolution opens with a quotation from Garlyle,
Goethe's friend and translator, which portrays both the inevitability
of revolution and the problems which follow.
There is the next milestone for you, in the History of Mankind.' That universal Burning-up, as in hell-fire, of Human Shams. The oath of Twenty-five Million men, which has since become that of all men whatsoever, 'Rather than live longer under lies, we will die! . . . unappeasable revolt against Sham-Governors and Sham-Teachers, — which I do charitably define to be a Search, most unconscious, yet in deadly earnest, for true Governors and Teachers ...» world in anarchic flame for long hundreds of years . . . before the Old is completely burnt out, and the New in any state of sightliness? Millennium of Anarchies; — abridge it., spend your heart's-blood upon abridging it. ye Heroic Wise that are to cornel^0
It was thought that the new system, if properly constructed,
would permit a ll human actions which were in harmony with the causes
of Nature. If constrictions of the natural will still existed,
they would serve to point out flaws in the new order, and thus as
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signals for its correction. The unfortunately incorrect premise made
was that Nature would not contradict herself in her motivation of
man's will.
The Heroic Wise referred to by Carlyle were those men capable
of constructing such an order, men who had developed through the
Goethean search. They were to question all prior systems of thought
for validity with respect to the causes of Nature. Only that which
developed and grew was held to be living, hence part of Nature;
then the study of growth processes was necessary to separate man's
imperfect understanding of Nature from a true perception of Nature.
An analogy was drawn between biological and intellectual growth.
The creative process was felt to be the highest expression of the
causes of Nature. The thinker's duty was to observe with an open
mind all of Nature, inferring ultimate secrets which would enable
him to set up the order which would be the salvation of mankind.
Wagner states that the development of Art parallels that of
man.
The real man will therefore never be forthcoming, until true Human Nature, and not the arbitrary statutes of the State, sh all model and ordain his lif e ; while real Art w ill never liv e, u n til i t s embodiments need be subject only to the laws of Nature, and not to the despotic whims of Mode. For as Man only then becomes free, when he gains the glad consciousness of his oneness with Nature; so does Art only then gain freedom, when she has no more to blush for her affinity with actual Life. But only in the joyous consciousness of his oneness with Nature does Man subdue his dependence on her; while Art can only overcome her dependence upon life through her oneness with the life of free and genuine Men. ^
Schopenhauer finds a natural affinity between music and the sort of
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philosophical thought then current.'
[Music] expresses in a perfectly universal language, in a homogeneous m aterial, mere tones, and w ith the g reatest determinateness and truth, the inner nature, the in- itself of the world, which we think under the concept of will, because will is its most distinct manifestation. Further, . . . philosophy is nothing but a complete and accurate repetition or expression of the nature of the world in very general concepts, for only in such is it possible to get a view of that whole nature which will everywhere be adequate and applicable . . . supposing it were possible to get a view of that whole nature which w ill everywhere be adequate and applicable ...» supposing it were possible to give a perfectly accurate, complete explanation of music, extending even to particulars, that is to say, a detailed repetition in concepts of what i t expresses, th is would also be a sufficient repetition and explanation of the world in concepts, or at least entirely parallel to such an ex planation, and thus it would be the true philosophy.92
This passage would seem to imply that the Goethean search could be
realized through music, and that its results could be made com
prehensible to all who understood music — a much greater number
than those who understood philosophy. In addition, music would
have the advantage of showing these resu lts d ire c tly , in a way
analogous to the manner in which they occur in nature. Philosophy
is limited to explanations of these concepts.
Wagner's Art-Work of the Future outlines a means of optimizing
the power of music to express such concepts;93 Previous constraints
had to be destroyed or weakened, so th at the composer's w ill would
be unhampered. In particular, fashions and stylistic mannerisms
would be suppressed as unnatural. Art should arise from the heart,
and speak to the heart, as an overflowing of man's union with
Nature. The foundation of musicis not melody, rhythm, or laws
of harmony and counterpoint, but tone its e lf . Tone is said to
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encompass a ll other aspects of music and link music to the s is te r
arts of dance and poetry. Harmony Is a means of shaping, and Its
laws are a constriction of its limitless domain. Absolute music
is frowned upon; but Beethoven's Symphony No. 5 is not absolute
music, since its determinism reflects moral will. Music should
be a universal drama, not merely a collection of sounds; the
composer should be a poet in tone.
Parallels between this outline of Wagner's musical thought and
the course taken by Webern and his colleagues in the early twentieth
century can be drawn. Egon Wellesz, Webern's fellow classmate at
the University of Vienna and under Schoenberg, published an article
in 1911 which echoes the revolutionary cries of Wagner for a new
music, and stresses the importance of tone as a determining factor
in musical structure, cited on page 88 of the present study.
The underlying principle of Schoenberg's Harmonielehre. first
published in 1911, is that the motivating causes behind musical laws
are more important than the laws themselves. This edition of
Harmonielehre postulates musical structures based on the character
istics of sound itself rather than t r i a d s . 94
When Webern was a young man, the traditional structure of music
was weakened by the dissolution of structures based on key. The
Viennese artistic world favored the deft use of style and fashion
rather than expression of one's honest enjutional reactions, producing
at best movements such as the Jugendstil and writers such as
Hofsmannthal, and much more trivially , the Viennese waltz. Non
musicians of Webern's c irc le , such as Adolf Loos and Oskar Kokoschka,
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revolted actively against this tendency.
The precise means of reconciling and using these ideas seems to
have presented a considerable problem to Webern as a young man. It
seems that the basis of his first serious attempt to bring a new order
out of anarchy was manipulation of perceptual aspects of tone, notably
in the Quartet, opus 5, or the Six Pieces for Orchestra, opus 6.
Webern's mature style may be said to emerge with opus 19, although
much of its characteristics still had to be developed. The songs pre
ceding this work, opera 15-18, seem to show both by the musical tech
niques used and the texts a rather painful struggle to achieve mastery
of the complexity of structure implied. If so, it might be possible to
date the period of postulating, planning, and completion of the style as
circa 1921-6.
Two major events took place near the beginning of this period
whose significance depended upon a mastery of form sim ilar to that
which Webern would eventually achieve. These took place in such circum
stances th at Webern would probably have known about them.
In 1921-2, Rilke translated the poetry of Paul Valery into
German. In doing so, he was exposed to a literary style of rigorous
c la rity which was, nevertheless, able to communicate strong poetic
feeling. Under the influence of this style, he was finally able
to write the works which all but eclipse his earlier poetry: the
Duino Elegies and the Sonnets to Orpheus. Webern's interest in Rilke's
works had previously manifested itself in his choice of texts for
the songs, opus 8. I t is possible that Webern might have also
read works by Rudolf Kassner, in whose company Rilke worked
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out much of his creative philosophy.
In 1922, Wittgenstein's Tractatus appeared In a bilingual
edition. Tractatus explores the limitations of logic, philosophy,
and by Implication, art In a manner which Is not only similar to the
way In which Webern's structure took shape, but Is also a clarifi
cation of some aspects of that structure. Moreover, Tractatus Includes
a self-contained primer of the sort of formalistic logic that
Wittgenstein had absorbed In his previous study with Bertrand
Russell. At the time of its publication, Wittgenstein was living
in Austria, from time to time maintaining contact with his teacher,
Adolf Loos. Tractatus had been submitted to Karl Kraus for publi
cation. in 1919 and some of Kraus's writings on syntax seem to
show its influence. Both Loos and Kraus were among Webern's friends
during this period. Kraus's writings are cited in The Path to the
New Music. ^5
These two events may well have provided the syntactic catalyst
that enabled Webern to venture into rigourous structural techniques.
Both Rilke and Wittgenstein had the same sort of philosophical
background that Webern had, and attempted to integrate it with the
requirements of rigorous structure. Wittgenstein came to the con
clusion that such structure was only a tautology, meaningless in
itself without a specific application. Rilke was able to apply
it to produce poetry of high artistic quality. In the author's
opinion, Webern decided that such structure was an expression of
the deep laws of Nature and Art, and thus particularly suited to his
technical needs.
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Webern used- the poetry of Symbolists Stephen George and Rainer
Marla Rilke for his early songs, and eventually adopted an aesthetic
position which has much in common with that of the Symbolists, who
seem to have thought that a carefully structured form is a window
through which one glimpses the infinite. Extraneous elements in
the form tend to obscure the in fin ite , which is unknowable except
through the use of such "windows."
If the infinite can be equated with the ultimate truth of
Nature and Plato's soul of Nature, rather close agreement can be
reached among the Platonistic, Goethean, Kantian, and Symbolistic
positions. The structure of Plato's universe as described in
Timaeu8 and The Republic is a manifestation of its soul. Goethe's
hypotheses on the principle of metamorphosis imply that life can
best be understood as a transcendental aspect of rigorous form.
Kant endeavors to show that one's capacity to develop intellectually
rests upon application of rigorous forms of a .priori thought, as
do the Symbolists. It might seem that such an idea, within the
Intersection of otherwise divergent philosophies, might be thought
to be a fundamental truth at a time when philosophers thought
fundamental truths existed.
Houston Stewart Chamberlain's book on Kant, which Webern o w n e d ,96
is almost entirely a discussion of an interpretation of the approaches
of various thinkers to this idea. He shows that their honest search
for the ultimate truth seems to have led them all from contradictiory
premises to this idea. He thinks that no seeker after truth should
accept the conclusions of former thinkers as final. However,
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certain procedures and Ideas seem to be Inevitable, In consequence
of Kant's Investigation of methods that the thinkers are lim ited to
using.
Chamberlain discusses the processes linking perception and
comprehension at length. He calls the generalization of perception
Into sets of Interpretable objects "Scheme." The organization of
abstract thought which applies to these sets is called "Symbol."'
The Symbol, In fullest acceptation of the word, is the perceptive demonstration of that which is thought: the Scheme, In its widest sense, is the rendering into thought of that which has been perceived.97
"Scheme" and "Symbol" seem to be incompatible unless some sort of
"commutator" or medium of translation is found between them. In
the following passage describing the interpretation of ordinary
experience, "Time" is said to be a commutator.
That the invisible comprehension is powerless till the actual visible object has been offered to it by per ception, and that, on the other hand, this same per ception remains blind, unless comprehensions transfer this visibility into the invisibility of the world of thought -- this, combined with the doctrine that it is Time which schematically and symbolically cares for the hither and thither of the transformations: this it is which taken together makes up the essenc^gof Kant's perception in regard to human knowledge.
The commutator seems to parallel Peirce's "ground" in its function.
A more comprehensible name for this medium of translation might be
"common ground," and that term will be used in the remainder of
this section.
Without the common ground, perceptions cannot be comprehended
and comprehensions are only abstract forms. The common ground has
no meaning in itself, but if it is not adaptable to the requirements
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75
of the material it transmits, it can distort information. For this
reason, it should be as minimal and powerful as possible.
Chamberlain quotes Leonardo da Vinci and Diirer to show that
the combination of "Scheme," "Symbol," and common ground is essential to art, dfespite differences of time, place, and circumstance.
Our soul is composed of harmdny, and harmony is never bred save in moments when the proportions of objects are seen or heard.
The outer work must be the indication of the inner understanding .... The art of mensuration is* the true foundation of all painting.99
The force of art is identified with "Scheme." It is subjected to
organization by "Symbol" through the comnon ground. The common
ground does not determine the precise form of the work, but contains
the laws or tendencies which generate th at form.
These terms may be linked to those used in the discussion in
the first chapter, third section. "Scheme" may be said to correspond
to the schematic mapping, and "Symbol" may be said to correspond to
the symbolic mapping. The common ground is the set in which these
mappings meet, the defined space. "Scheme" prepares information
for logical study, and "Symbol" organizes th is information into
logical patterns.
The Symbolists, at this point, assert that the force of art
acting through "Scheme" arises from the unknowable in fin ite , and that
a we11-organized common ground is the only means of momentarily
glimpsing that force. Chamberlain, on the other hand, asserts
that the infinite is approachable to the industrious Weltanschauer
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using this method. Webern's correspondence seems to imply that
Webern thought that the infinite was not only approachable, but part
of his daily life.
It would be presumptuous to infer that a man of Webern's
scholastic training and independent turn of mind would have read and
accepted the work of any philosopher without reservation. However,
certain passages from his lectures seem to reflect this method.
His defense of the twelve-tone technique seems to imply that
he considered it to be a sort of common ground.'
So what has in fact been achieved by th is method of composition? What territory, what doors have been opened with this secret key? To be very general, it's a matter of creating a means to express the greatest possible unity in music. .... Unity, to be very general, is the establishment of the utmost related ness between a ll component parts. So in music, as in all other human utterance, the aim is to make as clear as possible the relationships between the parts of unity; .... Until pow, tonality has been one of the most important means of establishing unity. It's the only one that has disappeared; everything else is still there .... So: what is music? Music is a language. A human being wants to express ideas in this language, but not ideas that can be translated into concepts -- musical ideas. . . . Comprehensibility is the highest law of all. Unity must be there. . . . Men' have looked for means to give a musical idea the most comprehensible shape possible.^®
Unity as it relates to "Scheme" and diversity as it relates to
"Symbol" are described in terms of the common ground, which relates
diverse elements to express the fundamental unity of the work. The
success of the common ground is the measure of the comprehensibility
of the finished work to an enlightened perceiver.
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Something comprehensible is something of which I can get a complete view...... So a smooth, f la t surface also makes comprehension impossible. Things alter if something at least is given, a start. But what constitutes a start? Here we come to differentiation. . . . Broadly speaking, the intro duction of divisions.' What are divisions for? To keep things apart, to distinguish between what is principal and what is secondary. This is necessary, to make yourself intelligible, so it must also happen in music.
Composition with twelve notes has achieved a degree of complete unity that was not even approximately there before. It is clear that where relatedness and unity are omnipresent, comprehensibility is also guaranteed. And all the rest is dilettantism, nothing else, for all time, and always has been. That's so not only in music but everywhere. In the pictoral arts, in painting, I can only sense, not prove, that there are similar relationships insuring unity, but I know above all that it's so in language.
The common ground of the compositional algorithm of Webern's mature
style seems to meet the aims of the Symbolists and the requirements
of Chamberlain's method. I t can assume s iffic ie n t rigor and d e ta il
to satisfy the requirements of any conceptual pattern of "Symbol,"
yet retain enough flexibility to follow the fluctiations of
perception-guided "Scheme."
Webern's common ground is also compatible with the processes
of modular development which Goethe thought constituted Nature's
logic. The importance of these processes to Webern is shown by
passages from the lectures speaking of deriving art as directly as 102 possible from Nature. He seems to have thought that the best
expression of natural creative thought would correspond to Nature's
logic, hence the best possible creative procedure was based on it.
Although Webern's lectures stress comprehensibility, he does
not seem particulaly concerned that his hearers be aware of the
common ground used to produce his music.
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If an untutored ear can't always follow the course of the row, there's no harm done — in tonality, too, unity was mostly felt only unconsciously, . . . Something will stick in even the nalHvest s o u l . 103
Perhaps he f e lt that i f the common ground were adapted to transmit
accurately an expression of Nature, the resultant work would be
perceived as schematic as well as symbolic by the listener. He may
have thought that the results of using his common ground were more
important than its machinations.
Chamberlain quotes Goethe as saying that colors are the deeds 104 of light, from which one hopes to obtain disclosures about light
itself. In a similar sense, compositions can be thought of as deeds
of the natural creative force, from which one might infer the
characteristics of that force. In a sense, every composer who is
not content to duplicate the music of the past forms his own method
of "Scheme," "Symbol," and common ground. The specific value of'
Webern's method in its mature form is that i t is unusually precise
and powerful, well adapted to his creative urge and his intense in
tellectual and musical convictions. For this reason, Webern's
mature music reveals much more of the natural creative force than
the great bulk of music seems to reveal.
His method includes his conception of the motivating principles
underlying all of music rather than their traditional manifestation.
The common ground is made as efficient and small as possible, to
make the "Symbol" - "Scheme" relationships clear. Unity is imposed
through organization of sound material on several logical levels,
as shown in the third chapter of the present study.
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It seems that Webern thought that he had based his compositional
method squarely on the most valid philosophical thought, the best
intellectual procedure, and the most accurate generalization of the
motivating forces of music that he could obtain. He seems to have
thought that his work was in accordance with a way of reflecting
Nature valid not only in music, but in all disciplines.
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FOOTNOTES
CHAPTER II
PHILOSOPHICAL AND LITERARY INFLUENCES ON
WEBERN'S MATURE STYLE
^The Austrian educational system of Webern's youth is discussed in The Austrian Mind, pp. 66-73. 2 Anton Webern, Per Weg zur neuen Musik. ed. W illi Reich (Vienna: Universal-edition, 1960), also trans. Leo Black, The Path to the New Music (Bryn Mawr: Theodore Presser Co., 1960). This publication; contains a rendering of a stenographic transcript of the two lecture series given by Webern in the early 1930's, "The Path to Twelve-Tone Composition" and "The Path to the New Music," as well as various letters to Willi Reich. The present study principally follows Black's translation, referring to this publication as Path. Where the author's translation is used, the work is referred to as Weg. 3 Anton Webern, ed., Heinrich Isaac: Choralis Constantinus II. Denk- mal.er der Tonkunstler O sterreich. vol. 32 (Graz: Academische Druck-u. V erlagsanstalt, 1959, rep rin t editio n ), pp. v i i - x i i i . 4 Anton Webern, "Schoenberg as Teacher," from the Symposium Arnold SchBnberg. 1912, cited in: Composers on Music, trans. and ed. Sam Mbrgenstern (New York: Pantheon Books, Inc., 1956), pp. 455-7.
^W illi Reich, Anton Webern: Weg und G estalt: Selbzeugnisse und Worte der Freunde (Zurich: Verlag der Arche, 1961).
^Anton Webern, L etters to Hildegard Jone and Josef Humplik. ed. Josef Polnauer, trans. Cornelius Cardew (Bryn Mawr: Theodore Presser Co., 1967). •j Suzanne K. Langer, "Letters from Webern and Schoenberg to Roberto Gerhardt." The Score XXIV (November 1958): 36-41. g Freidrich Wildgans, Anton Webern, trans. Edith Temple Roberts and Humphrey Searle (London: Caldar and Boyars, 1966).
^Willi Reich, "Anton Webern Uber Alban Berg," Neue Zeitachrift fUr Musik CXXIV (1963): 143ff; "Aus unbekannten Briefen von Alban Berg an Anton Webern," Schweizerlsche Muslkzeitung XCIII (1953): 49ff; "Berg und Webern schreiben an Hermann Scherchen," Melos XXIII (1966): 225; "Briefe aus Weberns letzen Jahren," Osterreichesche Musikzeitschrlft XX (1965): 407ff.
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Hans Moldenhauer, comp., Anton von Webern: Perspectives (Seattle: University of Washington, 1966), pp. 156-159. Webern's own catalog of his personal lib rary is liste d in the Moldenhauer Archives on p. 139.
^Q uotations from texts in th is chapter are taken from the booklet accompanying the record, "Anton Webern: The Complete Music," Columbia Masterworks # K4L-232. This booklet was apparently prepared by Robert Craft and Kurt Stone, although only Stone's name appears as editor.
12WeJL und Gestalt, p. 10; Perspectives, p. 157.
^^Wildgans, p. 92. 14 Jone, pp. 11, 12.
^3Jone, p. 44. The ita lic s in th is and other quotations from Webern's writings are as they appear in the published sources.
^Jone, p. 87.
*^Jone, p. 47; Johann Wolfgang von Goethe, Gedenkausgabe der Werke. Briefe. und GesprHche. ed. Ernst Beutler (ZUrich: Artemis Verlag, 1949), vol. 1, p. 516. 1 ft Path, p. 63. 19 Johann Wolfgang von Goethe, Ita lia n Journey (1786-1788). trans. W. H. Auden and Elizabeth Mayer (Ita ly : Pantheon Books, 1962), pp. 305-306. 20 Path, p. 53. 21 Weg und G estalt, p. 22. 22 Path, p. 11; Gedenkausgabe. vol. 16, p. 21.
23Path. p. 10. 24 Weg und G estalt, p. 21.
23Wildgans, p. 30. 26 Dissertations-Verzeichnis der Philos. Fakultflt der Universitflt in Wien (Vienna: Gerold & Co., 1935), vol. 1, pp. 8-13. 27 Weg und G estalt, p. 22.
O f t Path, p. 13. 29 The Austrian Mind, pp. 67-68, 245.
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Q _ Jone, p. 48; Path, p. 63. 31 Edith Hamilton and Huntington Cairns, ed., The Collected Dialogues of Plato (New York: Pantheon Books, 1961), pp. 1312-1313, 1371. The translation of Laws is by A. E. Taylor; the lines referred to are 4.722d-e and 7.799e.
32Weg_ und G estalt, p. 22. 33 Jone, p. 22. A/ David Luke and Robert Pick, ed. and trans., Goethe: Conversa tions and Encounters (Chicago: Henry Regnery Co., 1966), p. 215; John Oxenford, trans, Conversations of Goethe with Eckermann and Soret (London: George Bell and Son, 1882), p. 258. Conversation of May 5, 1827. 35 Biedermann, ed., Goethes Gesprache. Vol. 1, p. 427, conversa tio n of August 19, 1806, cited in: Elizabeth M. Wilkinson and L. A. Willoughby, Goethe: Poet and Thinker (London: Edward Arnold, Ltd., 1962), p. 96.
■^Wilkinson, pp. 96-97. 37 Oxenford, pp. 47-49. Conversation of December 30, 1823. 38 Johann Wolfgang von Goethe, "Influence of the New Philosophy," Natural Science in General; Morphology in P articu lar. Vol. 1, no. 2, cited in: Bertha Mueller, trans., Goethe's Botanical Writings (Honolulu: University of Hawaii Press, 1952), pp. 229-230. 39 Isaac Newton, Principa. cited in: H. G. Alexander, ed., The Leibniz-Clarke Correspondence (Manchester: University Press, 1956), p. 170. 40 Oxenford, p. 49; Mueller, pp. 230-231.
^M ueller, p. 16. 42 . Italian Journey, p. 383; Schiller's letter to Goethe, August 23, 1794, cited in: M. von Herzfeld and C. Melvin Sym, trans. and ed., Letters from Goethe (Edinburgh: The University Press, 1957), p. 227. 43 Italian Journey, p. 383; Path, p. 11.
^Johann Wolfgang von Goethe, "Preliminary Notes for a Physiology of Plants," published posthumously, cited in Mueller, pp. 85, 94.
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45 Johann Wolfgang von Goethey "Problems," Natural Science In General: Morphology in P articu lar. Vol. 2, no. 1 (1823), cited in : Mueller, p. 116.
^Johann Wolfgang von Goethe, Faust, f i r s t p art, trans. by Peter Salm (New York: Bantam Books, Inc., 1962), pp. 8-11, lines 139-157 of the prelude in the theater. 47 Oxenford, conversation of April 18, 1827, p. 248. 48 Uber epische und dramatische Dichtung. cited in Letters, p. 270. The Goethe-Schiller correspondence of 1797, read by Webern, contains many passages discussing the structure of the epic. 49 Bernard S. Myers, The German Expressionists: A Generation in Revolt (New York: McGraw-Hill Book Company, n .d .), p. 160.
50Eastlake, pp. 25-6; Beutler, vol. 16 (Schriften zur Farben- le h re ). pp. 41-2.
^^Myers, plate 23, facing p. 240. 52 Eastlake, p. 304; Beutler, p. 206. 53 tfyers, plate 19, facing page 208. 54 Eastlake, pp. 311, 307, 318; Beutler, pp. 210, 208, 214. 55 Wassily Kandinsky, Concerning the Spiritual in Art. trans. Michael Sadlier and others (New York: Wittenborn, Schultz, Inc., 1947), p. 73. Kandinsky cites the complete works, ed. by Heihemann. 56 Oxenford, p. 248, conversation of April 18, 1827. 57 Italian Journey, pp. 104. 58 The Complete L etters of Vincent van Gogh. Vol. 1 (New York: New York Graphic Society, n.d.), pp. 112-113. 59 Kandinsky, p. 75.
^Kandinsky, p. 39.
^Kandinsky, pp. 60, 64; Eastlake, p. 276; Beutler, p. 188. 62 Beutler, pp. 906-11.
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63 Kandinsky, p. 33; Egon Wellesz, "Die jUngste Entwicklung der neufranzBsischen Musik," Der Merker II no. 16 (May, 1911): 660, 664. 64 Plato, Republic i i i , lines 396c-397d, e78d-379d; pp. 641-642.
^Plato, Laws, ii, lines 657a-b; p. 1254.
^ P la to , Republic x, lines 603b; p. 828. 67 Plato, Laws ii, lines 669a-670a; p. 1266. 68 Plato, Republic iii, lines 401c-402d; pp. 646-7. 69 Plato, Timaeus. 47d; p. 1175.
7^Plato, Republic x, lines 616d-6l7d; pp. 840-841.
7*Plato, Phaedrus. lines 247c; p. 494. 72 Plato, Epinomis. lines 992a; p. 1532. 73 Plato, Symposium, lines 210d-211c; pp. 562-563. 74 Plato, T im aeus/43ff; pp. 1171-3; Laws x, 892-f£; pp. 1447-1448.
7^Plato, Laws x, 892b; p. 1447. 76 Plato, Timaeus. 90d; p* 1209.
77Plato, Timaeus. lines 49-61c; pp. 1176-1186. 7 8 Plato, Laws v, lines 726-727; p. 1314. 79 P lato, Republic x, lines 617b; p. 841. 80 Plato, Laws i i i , lines 689c, 691c-d; pp. 1284, 1286.
®1Plato, Laws ix, lines 875c, p. 1434. 82 Jaspers, Karl. The Great Philosophers: The Original Thinkers. ed. Hannah Arendt, trans* Ralph Mannheim' (.Har court, .Brace,- ana woria, Inc., 1966), pp. 40-47.’ 83 Jaspers, p. 47. 84 Plotinus on the One and Good. Being the Treatises of the Sixth Ennead. trans. Stephen MacKenna and B. S. Page (London: The Medici Society, Ltd; Boston: Hale, Cushman & F lin t, 1930), p. 171; section VII, 7-8.
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Q e Plotinus. p. 200; VI.7.32; p. 201; VI.7.33. 86 Jone, p. 10, le tte r of August 6, 1928.
^ Path. p. 34. 88 Craft, p. 21, opus 15, no. 1; opus 15, no. 5; p. 22, opus 16, no. 3, trans. Leroy. Llnlck. 89 C raft, p. 27, opus 31, no. 6, trans. Eric Smith. 90 Thomas Carlyle, History of Frederick the Great. Book XXI, chapter 1, cited in: Richard Wagner, Art and Revolution, reprinted in Richard Wagner's Prose Works, ed. and trans. William Ashton Ellis, C arlyle's original English cited here (New York: Broude Brothers, 1966), vol. 1, pp. 23-24. 91 Art-Work of the Future, ib id ., pp. 71-72. 92 Arthur Schopenhauer, The World as Idea, cited in: Schopenhauer: Selections, ed. DeWitt H. Parker (New York: Charles Scribner's Sons, 1928), p. 186.
"Art-Work of the Future, pp. 72, 82, 88ff, llOff, 115£f, 123, 126, 129. 94 Arnold Schoenberg, Harmonielehre. 3rd ed. (Vienna: Universal- edition, 1922), pp. 596-597.
" p a t h . pp. 9-10. 96 Perspectives, p. 158. 97 Houston Stewart Chamberlain, Immanuel Kant: A Study and a Comparison with Goethe. Leonardo da Vinci. Bruno. Plato, and Descartes. tran s. Lord Redesdale (London: John Lane Co., 1914), vol. 1, p. 230. n o Ib id ., p. 305.
" i b i d . , pp. 99, 113.
10°Path. p. 42ff. 101 Path, pp. 17-18.
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102 On page 14 of Path. Webern demonstrates that he considers a musical Idea to be an organization of sound, not a fortuitous musical event. He also shows that he wishes to eliminate elements from the common ground which would transmit the creative force in terms of non-musical ideas.
103Path. p. 53.
^^Chamberlain, p. 94.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER I I I
DESCRIPTIONS OF WEBERN'S MATURE STYLE
Introduction
This chapter contains technical, as opposed to philosophical,
descriptions of the way in which Webern's compositional algorithm
operates in his late works. These descriptions serve to give a
musical setting to the logical and philosophical premises of the
first two chapters.
The first section contains descriptions by Webern's contemporaries
of the musical situation which generated the beginnings of Webern's
personal style, the emergence of his mature sty le, and also post-war
explanations of the configuration of the mature style. The second
section draws from Webern's doctoral d issertatio n and Per Weg zur
neuen Musik to provide Webern's own explanation of his compositional
algorithm. The third section consists of hypotheses by the author
which prepare the musical foundations for the techniques used in the analyses accompanying the present study.
Section 1. Descriptions by composers and c ritic s
Some of the characteristics of Webern's mature style seem to be
understandable only as consequences of his deliberate break with the
past. This break seems to have begun in the years 1909-11, with opera
3-8. The first descriptions given show some of the ideas of Webern's
close friends and contemporaries during this time.
Egon Wellesz, who studied with Webern under Guido Adler and
87
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Arnold Schoenberg, describes the effect of the Viennese performance
of Debussy's Pelleas and Mellsande as follows in a 1911 article:
Seldom does one feel so strongly that in one work a new art emerges, that tradition is broken .... What does this new style consist of? F irstly , a new conceptualization of melody and harmony; secondly, a new representation of form; thirdly, a changing interpretation of dramatic elements in music. . . . [in the short piano works of the Impressionists] a melodic line is given which permeates the entire work. The a r tis t gives a suggestive sketch which portrays an entire world of tone. This is not thematic development, but cohesion produced by flowing, constantly renewed melody . . . mysterious sounds, deeply affecting the soul . . . detached from all technical considerations, so that one does not think in terms of themes, voices, or counterpoint, but only of the limitless musical impression.
Wellesz notes that the style of the Impressionists violently disrupts
an established, rigorous compositional tradition in French music,
and says that a similar disruption should take place with regard to
the existing Germanic musical practice. The specific ways cited by
Wellesz in which Debussy breaks with French musical practice seem to
parallel certain stylistic characteristics of Webern's opera 2-8.
Abandonment of the thematically based structure . . . establishment of a new harmonic system . . . . the beginning of construction of new forms .... renunciation of program matic music.
In 1911, almost an entire issue of Per Merker. a leading
musical journal of the time, was devoted to Schoenberg's theory and 3 music. In a later issue, Hugo Fleischer carefully discusses the
pros and cons of Schoenberg's ideas, and judges the effect of
Schoenberg's music as follows:
When the true path of music consists in the discarding of all conventions, leaving only the element of sound (in the broadest sense of the word), but musical compre hension has developed to the point that the hearer is
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able to analyze a complex phrase by means of the melody, harmony, polyphony, dynamics, timbre, Ideas, and feelings which produce It, the musical purist may feel completely excluded. The Interplay of possibilities of association produce the legitimate area In which musical content Is produced, [in Schoenberg's music^ the Idea of the Absolute cannot be apprehended clearly. All seems remote; only the Impression of perceived sound remains (as In the vocal music of Debussy.') and the emotional meaning or fantastic garb of Schoenberg's sound structure Is rejected by the New Aesthetic as a boundless mixture and a diminution of the principle of clear musical content.4
The above passage seems to have been in part a reaction to
Schoenberg's Harmonielehre. f i r s t published in 1911. In th is work,
Schoenberg postulates sound structures based upon timbre, which
at that time meant conceptualized tone color rather than scien
tifically measured wave-form configuration. He generalizes the
function of pitch in musical context so that it applies to timbre
in an analogous manner.
I cannot consider pitch as a separate e n tity from timbre [Klangfarbel. unlike most musicians. I find that the tone's character is a result of its timbre, of which the pitch is a dimension. The pitch is a component of the large domain of timbre; the pitch is nothing but timbre measured in a certain direction. If it is possible at this time to make logical progressions out of chords differing only in pitch content, it should also be possible to create similar progressions out of timbre [measured in3 another dimension [thaft that of the fundamental tone 3 . . . such that the sounds in the progressions will have relationships to each other governed by a logic similar to that which rules harmonic progressions. This notion seems to be, and probably is, a fu tu r is tic dream, but I believe that i t w ill be realized .... Progressions on timbre fKlangfarbenmelodienl .... who dares to present such a theory now?
An examination of the structural configuration of Webern's
works seems to imply that his development as a composer was somewhat
dependent on generalizations of various functions and aspects of
tra d itio n a l music. Sometimes these functions and aspects were
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broadened in definition, as in the above passage. They could also be
narrowed, so that relationships belonging to a key or a scale could
be used independently of that key or scale.
Wallace McKenzie lists several relationship patterns occurring
in the Passacaglia. opus 1, which seem to be at least partially
derived from the somewhat scholastic style in which the work is
written. This style dictates adherence to key and to an established
large form whose units are melodically and harmonically determined.
McKenzie points out that Webern's structural control surpasses the
requirements of that style by relating the derived patterns not only
to key and large form as stipulated, but also to his own complex
system of organization.
However, the careful attention to many different levels of structure, i.e., intervallic relationships within the motives, interrelations of the motives themselves, motivic development, thematic metamorphoses, and formal relationships which sometimes have m ultiple significance, is a characteristic of Webern's compositional technique which remains through all subsequent changes of style.
When key restriction is dropped in opus 3, these patterns are related
only to Webern's plan for the work in which they appear. In opus 3
and later works, their function in that plan seems to result from
progressive generalizations of traditional musical practices, as
exemplified in the organ fugues of J. S. Bach and the late string
quartets of Beethoven.
George Perle discusses the function of these patterns in
opus 5 as follows:
The integrating element is frequently a minute intervallic cell, which may be expanded through the permutation of its components, or through the free
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combination of Its various transpositions, or through associa tion with Independent details . . . . [ which may be used to] generate a larger, thematically significant pattern, whose rhythm, contour, melodic in terv als, and pitch may then be treated as separable components.7
Ferle also notes the significance of fixed individual notes as micro
cells, a compositional habit which does much to define relationships
among e n titie s in the late works of Webern. The metamorphic process
of variation particularly depends on the relation of these micro
cells to each other.
GyHrgy L igeti describes the manner in which Webern builds a new
kind of formal structure, replacing traditional patterns with gener
alized ones. The formation of this structure seems to have been a
continuing development of compositional technique, so that each work
in the Webern canon has an individualistic organization.
Webern changed this [traditional] basis of hierarchal structure. He made no distinction between consonance and dissonance. ... . The vertical and horizontal dimensions were meshed; melody and chord were placed on an interchangeable basis . . . Therefore, the form appears to be static — as though the work stood s t i l l in time, while its components rotated within it — without an unique beginning or end. . . . The form is no longer based on the d istin ctio n between musical events of greater or lesser importance. The terms melody and accompaniment lose th e ir meaning .... There is a distinct decline of polyphonic functions; contrapuntally, because of the interlacing of vertical and horizontal networks of sounds; on an imitative level, because [clearly audible] voices in the traditional sense no longer exist .... What remains, and constitutes the musical form, is a multicolored weaving of sounds intertwined about each other, simultaneously and successively, which permeates all musical dimensions.®
Numerous exceptions to the above observations can be found in the late
works of Webern. For example, the V ariatinns. opus 30 contains passages
in which melodic and accompanying configurations appear. The "multi
colored weaving of sounds" can be found as early as opus 4. Otherwise,
the above passage describes the basis of Webern's mature style well.
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Walter Kolneder observes that the adoption of serial technique
In opus 17 does not mark a sudden sh ift In Webern's style.
Attentive listening to . . . opp. 15-20 reveals no esse n tial differences; a t the most there can be heard an Increasing concentration In which systematic chromatic penetration of the writing certainly does play a part.®
However, the mastery of twelve-tone technique seems to have
enabled Webern to broaden his compositional algorithm in non-pitch
directions. In the following passage, one of Webern's early
supporters compares the songs of opus 23, which may be said to belong
to his mature style, with his earlier songs.
Considered only from a musical standpoint, they are of much broader scope than Webern's previous songs. No longer does he sketch the whole world in a single stroke; no longer does he express everything that may be said, in one measure, in one tone. This procedure was once necessary perhaps, for in extreme concentration a counterpoise was found to the resolution of the old musical harmony and to the forms which were inextricably bound up with it. But the twelve-tone system opens the possibility, under certain circumstances the necessity, of expanded musical form. Webern exploits th is p o ssib ility with happy assurance, and fulfills the necessity with the rigorous observance fittin g to a great composer.
Wolfgang Fortner discusses Webern's mature style thusly:
He constructs, horizontally or vertically, upon rhythmically differentiated, carefully timed entries, a quasi molecular structure dependent only on its own internal relationships for coherence. The corresponding variation technique links these basic molecular structures to the whole by simple or retrograde symmetry, through augmentation or diminution, through interlaced contrapuntal technique, etc., generating larger structures out of these molecules, that in their turn are linked to generate entire movements .... When listening to Webern's music, one must catch hold of the significance of the sound and its relationships to neighboring sounds. . . . The comprehension of the molecular structural organization in the first fraction of a second is the basis on w^ich all following musical entries are comprehended.
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The role of serial technique In the structural processes discussed
in the above passage is clarified by Pierre Boulez as follows:
We take as a point of departure a fundamental series, and attribute to each component of sound a pattern selected by analogous characteristics; [the configuration of] each component will be determined from a fundamental ordering, but the patterns used w ill be determined by the properties of th at component. Thus, we do not have to consider literal patterns in each of many separate domains [of sound], but patterns extending through the en tire domain of musical thought. With respect to the row forms of Webern, we are able to say that the series w ill be considered as a structural un ifier which can mediate among the individual components and among complexes of components. The se le c tiv ity conferred by appropriate functions to each component of sound, which can determine and be determined by the other components, follows from the selective power which deploys the components by means of th eir interrelatio n sh ip s. The game of balancing can only be played properly when structures are thus.organized; one calculates, then, the possibilities. . .
What are the possibilities to be calculated? Roger Sessions,
who has been influenced by Webern, speaks of the "color" of a
sound as being determined by the following considerations:
. . . the way in which the tone is attacked and set into motion; the speed with which i t develops its fu ll strength; the kind and amount of control that the player can exercise once it has been sounded; the way it is specifically modified by an increase or decrease in loudness or intensity, or by a rise or a fall in pitch; and the degree to which the player can modify one or the other of these elements, Including some that I have not mentioned here. ^
Any or all of these considerations can be serially controlled, and
can be made subject to the structural processes given in the above
passage by Boulez.
Sessions codifies possibilities of interrelationship thus:
As far as the question of contrast, and unity in terms of contrast, is concerned, an infinite number of
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possible procedures can be subsumed under one or the other of two headings ... . , associative and contrasting.
Jan La Rue defines these possibilities in terms of the change that
takes place from one musical event to another:
Variation, mutation; extension; alteration, contrast; diminution/augmentation, inversion, reversion, density (concentration/dilution); inflection, deflection, interruption; dynamics, color, texture; rate of change. All of these potential changes should be considered as flexibly as possible in framing analytical questions. 5
Boulez also uses change as a means of describing these p o s sib ilitie s:'
Similar organization: repetition, simple transformation, complex transformation, with p arallel structuring. Dissimilar organization: contrast rather than rapport. Transformation of eith er of the above in a rig id or a free manner. Overlapping of the two events in such a way that their endpoints cannot be distinguished.^
These conceptually based p o ssib ilitie s of in terrelatio n sh ip s can
also be serially organized.
The role of these possibilities and their interplay is discussed
by Webern's colleague, Herbert Elmert."
This brings us, finally, to the idea of a rhythm of connections. The time elapsing between the sounding of the antecedent and consequent of a chromatic [non-tonal, deliberately constructed pitch] relationship is felt as a period of expectation, as a silence fraught with tension . . . only chromatic relationship can counteract, or balance, the polarizing tendency arising from recalled impression of a sound, and negate that impression. Such negation is felt as a necessity in Webern's musical organism, and it gives particular vitality to the intra~connecting durations. These durations condition the underlying rhythm of musical development [in Webern's music]. This rhythm is seldom simple, since every single moment is filled out by the expectation of several such connections, since several relational tempi are woven together in a pervasive counterpoint . . . < The actual rhythm springs from mutual interaction of the parameters pitch and duration 'to which one must to a small degree add the parameter dynamics . . . The slightest alteration of these parameters' respective
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positions will exert a retrospective effect on the entire structure and cause a change in the folding of the en tire acoustical web.”
A powerful aspect of Webern's compositional algorithm lies in
th is a b ility to change the en tire course of a work by a slight
alteration. As a good chess player would, he calculates the effects
of his moves in such a way that all possible consequences are under
his control, obtaining the precise musical results which he intended.
The following passage was written about composers in general, but it
seems to describe Webern's attitude toward controlling devices.
His musical thought is governed by the object he has envisaged and that he wishes to bring into being. If he writes, let us say, a canon, it will not be for any reason other than the fact that a canon belongs in his design. In other words, he is pursuing a creative goal, not one which he can achieve by simply pursuing a line of rational thought.
One of the most complete summaries of Webern's mature style is
th at by Gundaris Pone.
Webern's compositional syntax reflects his attraction to the concept of monogenesis as a fundamental universal law underlying various manifestations in nature. This concept, one of the key tenets of German Romanticism, came to Webern primarily from two sources: the natural philosophy of Goethe and the aesth etic views of his teacher, Arnold Schoenberg, especially the latter's Grundgestalt theory. To derive everything from a single idea, to re ta in the essence of the idea and to change only its forms of appearance, to create a context by deploying these forms of appearance in time and space — these are the procedural problems with which Webern's compositional syntax are concerned. The methods which Webern employs to generate new forms of appearance of his basic idea, the motivic cell, are well known in traditional composition: inversion, retrogression, augmentation, diminution, subtraction, addition, and various combinations thereof. However, the contextual disposition of motives varied by these methods reveals a wholly new orientation .... Whereas there is a general consensus that pitch levels represent
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the vertical and durations the horizontal coordinate, it is seldom realized that dynamics, articulation, and timbre are Important factors in suggesting the depth of fi61d. In bringing this new dimension [of sonority] to the fore, Webern took two important steps. First, he de emphasized the linear force of the two primary parameters, pitch and duration, by isolating the motive from a linear context. This explains the illusion of the "spacial" functioning of Webern's motives and their seemingly elliptical relationship within larger syntactic units. Second, Webern accentuated the new dimension of depth by assigning structural functions to the spacial parameters which formerly had been relegated entirely to the role of emphasizing thematic gestures. Thus, Webern became the f i r s t composer in whose works timbral and dynamic symmetries, m irrors, and canons appear as consciously applied structural determinants. In light of the foregoing discussion, a persistent misinterpretation of the function of the so-called Klangfarbenmelodie technique should be corrected. Contrary to firmly entrenched beliefs, Klangfarbenmelodie is not a kaleidoscopic embroidery of linear functions, that is, melody; rather it is an important compositional method of revealing a sonorous depth of field. There is no better proof of this than an aural comparison between a conventional version of Bach's Ricercare and Webern's orchestration of it.19
Section 2. Descriptions by Webern
Two descriptions of musical style of substantial length
by Webern are currently in print. The first is the introduction
to his doctoral dissertation, an edition of the second book of 20 Heinrich Isaac's Choralis Constantinus II. completed in 1906. The
second is Per Weg zur neuen Musik. whose contents are liste d on page
80 of the present study in the sebond footnote.
The introduction to the dissertation is interesting in that it
reveals which aspects of Isaac's style caught Webern's attention
at the time when he began to formulate his own style. He sees Isaac's
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97
style as the result of the union of two great near-rational music
stru ctu res, polyphony and harmony, at the h isto ric a l moment when
harmony began to replace polyphony as the decisive structural
factor in music.
Isaac occupies a position of balance within the period of development of polyphonic vocal music from the second half of the fifte e n th century to 1550. The vivacity and independence of Isaac's individual voices is more masterful than that of Okhegem or Obrecht. The inflexibility of the phrase, a consequence of the note-against-note procedure applied persistently and equally so that the voice appears to be the resultant only of the contrapuntal procedure, Is altogether concealed in Isaac's masterworks. We can observe here a wonderful display of polyphonic art so achieved that, even though the individual voice completely satisfies the requirements of well-defined counterpoint, the surface impression is that the contrapuntal procedure could be discarded, and another procedure begun through subtle vertical organi zation of the voices. The followers of Heinrich Isaac do not adhere to his polyphonic principles. Isaac developed the purification of the phrase to its limits, and this purification was inflexibly invoked by his followers, as a means of solving the problem of verticalization of pitches. Out of this purification came the possibility for the solution of all the requirements of harmony . . . He has fulfilled the ideal of animated and independent voice-leading in a wonderful fashion. Each voice has its own development and is complete in itself, wonderfully and inspriringly shaped. This care is shown in each detail . . . voices interwoven in such a way that the individual existence of each voice is clearly prominent. The whole is propelled in a wonderful flux of the highest art; the euphony of the whole is indescribable.22
The above passage can, for the most p art, be applied to Webern's
attitude toward polyphonic,, or linear, organization, and vertical,
or timbre-dependent, configurations.
The following discussion of the breakdown of church modes
in the face of emergent harmonic structure could be taken to refer
to the breakdown of tra d itio n a l harmony in the music of Wagner,
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Wolf, and Schoenberg prior to 1906.
The character of the church modea [in Isaac's music] is . . . often unclear through lack of adherence to their strict use. . . . This forced interpretation of churhh modes, influenced by the emerging major-minor breakdown of the system of modes, is a notable consequence of polyphony. When one is no longer content with one voice but must have more voices sounding together, he has taken notice of harmony. Then one's work is no longer rooted in the base of the old [linear] church modes, but rather in that of [vertical] tonality. The cadences of Isaac and his followers are entirely based upon harmonic requirements, with th e ir connections with the f if th below and above, to express the key of the cadence as clearly as possible once more through the marking out of its boundaries.
The above passage suggests th at even in 1906 Webern was aware that
the breakdown of tra d itio n a l structures implied that new structures
must be formed.
More than twenty years later, after he had developed his mature
style, he returned to this subject of replacement of church modes by
to n ality to demonstrate the breakdown of to n ality in his youth.
Summing up, I'd say: just as the church modes disappeared and made way for major and minor, so these two have also disappeared and made way for a single series, the chromatic scale. Relation to a keynote — tonality — has been lost. . . . It helped to build the form, in a certain sense it ensured unity. . . . [it].was the essence of tonality. As a result of all the events mentioned, this relationship first became less necessary and finally disappeared altogether. A certain ambiguity on the part of a large number of chords made it superfluous. And since sound is natural law as related to the sense of hearing, and things have happened that were not there in other centuries, and since relationships have dropped out without offending the ear, other rules of order must have developed...... Harmonic complexes.arise, of a kind that made the relationship to a keynote superfluous. 24
He gives historical documentation of the break with tonality as
occurring shortly after his dissertation was completed.
With all this we approach the catastrophe: 1906, Schoenberg's Chamber Symphony (fourth-chord s.'); 1908,
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music by Schoenberg that's no longer In any key. . . . Schoenberg's Song op. 14;•. . . a key — but no cadence . . . . Schoenberg's George Songs op. 15 . . .: no more return to the tonic, everyone feels the end anyway.
This moment [when tonality was felt to be unnecessary] happened in about the year 1908. 25
The discussion accompanying the above passages implies th at,
according to Webern, the relationship to the keynote gradually
receded from the surface of the musical structure, to be replaced
by principles of unity and repetition of musical materials. This
situation seems to parallel that which he outlines in his discussion
of the music of Isaac with regard to well-defined counterpoint and
harmony. To prevent the re-emergence of the tonic as a stru ctu ral
force, duodecaphonic concentration was d eliberately enqsloyed, but
it would be fourteen years before strict twelve-tone technique would
provide a pitch-based structure capable of replacing tonality.
If the discussion of Isaac's development of tonality is to be
taken as semi-autobiographical, there should be a similar development
of some compositional technique in Webern's early work anticipating
the mature style. The generalization of musical function to the
principles of unity and repetition, applied to variation techniques
already established, seems to develop in this way.
The lectures included in Per Wee zur neuen Musik discuss,
primarily, the clarification of natural causes of musical structure.
One of the early amplifications of this clarification is based on ideas
of Goethe.
In non-technical terms, man is only the vessel into which is poured that which the totality of Nature wants to make manifest .... just as the naturalist strives to discover the legality upon which [the manifestations of]
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Nature are founded, our aspiration must be to find the laws under which Nature in the specific form of humanity is productive. It follows that the object of which the tonality of art speaks, its substance, is not "aesthetic," but a matter of coping with the laws of Nature, and that ^ all discussion of music can follow only from this understanding.
Serial technique is shown to be a manifestation of these causes
which reflects them clearly, because the language of the process used
is logically constructed.
The supreme principle of all manifestation [Darstellung] of thought is the law of intelligibility. . . . something in telligible is something which I can perceive as an entity [Uberbllckbar], whose boundary I can define. . . . thus we come to the classification of entities [Gliederung]. ..Composition with twelve notes has attained a degree of completion of structure [Zusammenhang] which was not even approximately available before. Clearly, when cohesiveness of structure and relatedness apply everywhere, intelligibility is secure. . . . It is thus not only in music,'but'in all fields. I can only sense, not prove that in the [other] fine arts such relationships guarantee cohesiveness of structure: however, I know that this condition holds in language.2?
The sort of relatedness which secures structural cohesiveness,
or rigor, in serial technique is shown to be the consequence of
historical development. Webern defines the term "motive" as "the
smallest division of a musical idea which is treated independently. 28 But how do we recognise one? Because i t 's repeated.'" He speaks
of developmental techniques of the past applied to the motive:
In one case the repetitions are literal and without gaps, like the links of a chain, whereas later one became freer and left out certain intermediate stages, thinking — metaphorically — " I t 's happened once already, so I can jump to something else without carrying on the development any further." Things were more immediately and abruptly juxtaposed, which of course made them harder to understand. But what else plays a part? The fact that repetitions were carried out with ever-increasing freedom -- one pro ceeded by variation, for the development resulting from varying a single motive led one further and further from the point of origin. Curves became longer, ever more broadly spun o u t .^
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Serial technique provides a means of reconciling the formal
advantages of strict and free repetition of motlvic configuration
with contrapunctal structure. In Webern's mature style this
reconciliation is made simpler by the possibility that notes can
be added or subtracted at w ill from a given motlvic configuration
by judicious selection of the original row form, use of particular
rows in a given situation, and voicing of these rows.
Serial technique is a means of achieving efficiently a
compositional structure which uses the natural laws (as described
by Webern) to advantage.
. . . When that kind of unity is the basis, even the most fragmented sounds must have a completely coherent e ffe ct, and leave hardly anything to be desired as far as "comprehensibility". i8 concerned.30
However, serial technique is not considered as the final, perfect
expression of these laws. It's up to future times to discover the stricter laws of structural coherence that are already present in the works. When this true comprehension of art is achieved, then there will no longer be a distinction between science and inspired creation. The further one presses forward, the greater becomes the identity of everything, and finally one has the Impression of being faced by a work not of humanity but of Nature. . . . I know how I invent, and how it continues, and then I look for the right place to fit it in.
It seems to the author that Webern used rigorous structure in
order to obtain the framework necessary to sustain his compositions,
and that he did so to obtain a musical space which would facilitate
a specific sort of developmental technique based on relatedness of
selected entities, or motives. This technique seems to display
efficiently the natural laws of order which he felt music should
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exhibit.
Section 3. Description by the author
The model discussed In the third section of the first chapter
Is used as the means of obtaining descriptions of Webern's mature
style. These descriptions serve as bases for the analyses accompany
ing the present study.
Four hypothetical organizational schemes are developed and
associated with rational structures. The resulting realms are put
into a hierarchy of logical levels. Webern's mature style, as
interpreted here, is thought to resemble the resulting complex of realms
and their interaction. This resemblance is but a provisionally useful
means of determining formal aspects of Webern's late works.
A single general procedure is followed for these schemes. An
entity is identified with the musical term "motive," the smallest pos
sible particle of a musical idea, recognizable by its repetition. It
seems that the definition of an entity may be arbitrary, and that the
results obtained in consequence need not be final. In Webern's
mature style, relationships among such entities seem to resemble those
typical of algebraic structure when they affect the position of the
entity relative to its context, and to resemble those of topological
structure when they affect the content and length of the entity.
Support for this generalized procedure is given by the following
passage, written in 1932 by an observer of Schoenberg's teaching
methods, well after Webern's mature style was established.
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Coordination or relation of parts to the whole Is an essen tial factor In form. Coordination In organic forms Is assured through mitosis, or the continual subdivision of the original germ c e ll (cytldes). In music th is germ-cell Is, for Schtinberg, a single motive. The forms of variation which the motive undergoes might be called musical mitosis. Even in his analysis Schtinberg refers a ll musical occurrences In a composition to a single motive. Methods of varying a motive are: 1. Changing the intervals or notes and holding the rhythm; 2. Changing the rhythm and using the same tone or intervals; 3. Simultaneous combination of both these methods; 4. Inversion; 5. Elongation; 6. Contraction; 7. E lision (of one or more notes); 8. The crab form (motus canzicrans. repeating the motive backwards). All these devices for variation are coordination factors in the construction of a piece of music.
The e n title s to be examined in Webern's music are the re su lts of
v ariatio n of the original e n tity or e n titie s by these and other means.
The relationships among these entities are these means of variation,
which transform the entities into their variants. The configurations
of entities and relationships are largely determined by Webern's
definition of his musical domain, and the specific form chosen in
turn is a factor in the d efin itio n of the domain of a specific work.
A number of aspects of these entities and relationships can be
examined. Each such aspect can be used to generate a possible logical
level for analysis.
Webern's mature compositional algorithm seems to contain four such
logical levels, and possibly more. Within each level, selections are
made from the possible configurations-of entitles with regard to the
aspect to which the level relates. The selected material is treated as
generating entities, and their distinctive characteristics are used to
form a structural design with relation to the logical level. No entity
which does not function in this way is permitted in the work.
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The manner of development choaen In each logical level derives
from the possibilities offered by the characteristics of the entitles.
The manner of development Is Itself a generative factor In the cumu
lative development of the work as a whole. The Interplay among
logical levels Is also generative, and derives from charaterlstlcs
Inherent In combinations of selected entitles and relationships.
Although the characteristics of logical levels and their entitles
are rigidly determined at the outset, they are subject to free develop
ment within a priori constraints. Thus, a balance between a coherent,
detailed large formal design and freely unfolding content Is
maintained.
The logical levels discussed In the present study may be ordered
in a hierarchy. From "highest" to "lowest," they are: 1. large
form; 2. twelve-tone serial pitch organization; 3. metamorphic and
tranaformal, or strictly algebraic, variation technique; 4. Klang-
farbe organization, including parameters which influence timbre direc
tly or indirectly, such as voicing, dynamics, nuance, and so fort!
The "higher" the level, the more abstract its structure seems, the
larg er its e n titie s are, and the more firm ly its logic must be pre
served through the "lower" levels. The "lower" the level, the more
power it has to affect the note-by-note course of the work, interacting
with the m eta-logic of the domain of sound Its e lf.
The level of large form is the only one which has global control
over the work. Particularly in the instrumental works, it is an ab
stra ct scheme whose s p ir it must be obeyed in a ll other logical levels.
Its entities are large temporal divisions of the work, bound together
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by interrelationships similar to those which give balance and coher
ence to traditional large forms. Often, traditional forms will be
used in an abstract rather than a literal sense in this level, or
the processes which generate them w ill be employed to produce new
m anifestations of them. Sometimes, as in the f i r s t movement of the
Quartet, opus 28, two or more large forms are used simultaneously.
The design of entities and their relationships tends to be
stricter and more modular in the mature instrumental works than in
the mature vocal works. In the instrumental works, the boundaries
of entities are made clear by adherence to formal breaks throughout
most, if not all, logical levels. The relationships among entities
tend to be employed in a manner th a t exhausts the desired possi
bilities of combination, returning to the content of the original
entity. In the v^cal works, as in most of the works from opus 14
to opus 18, d e fin itio n of e n tity is usually text-dependent, and
relationships reflect those displayed by the text.
The complex element of this level is the large division of the
form as a whole. Its place in the large form determines its shape,
and thus the configuration of all lower levels.
The logical level of twelve-tone serial organization exists within
a purely formalistic domain, deliberately planned to cover systematic
ally possibilities of pitch relationship. The precise algebraic con
figuration of this domain is discussed in the following analysis of the
Trio, opus 20. This configuration has several desriable properties.
It is a completely predictable means of organizing entitles of pitch
p attern s w ithin the row, e n titie s consisting of the rows themselves,
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and of postulating Interrelationships between row forms.
This method of pitch organization permits this predictability
without making i t the sole controlling factor of the work. Thus,
one may have a rigid ratio n al structure on th is level which does
not necessarily affect the course of the large form, the metamorphic-
transformal development of the phrase, or the timbre characteristics
used. However, th is structure may be used at w ill to reinforce any
of these other structures.
In particular, this method of pitch organization enables the
composer to construct v e rtic a l aggregates in a systematic manner which
will sound not as a set of overtones of a present or implied fundamental
tone, but as an individualistic timbre (i.e., not as a chord with
added notes, but as a sound whose ch aracteristics of timbre are more
important than its actual pitch). Then the resources of timbre can
be exploited as an Independent parameter, instead of a component of
to n ality .
The relationships of row forms and portions of row forms with each
other can generate a structure which may complement other formal
structures. This complementation may be obvious only after exhaustive
analysis, although it is sometimes audible as well. The author thinks
that Webern postulated general schemes of row progressions, but that
the exact choice of row within a progression depended on consideration
of the requirements of other logical levels at that point of the work.
The metamorphic-transformal level contains musical ideas whose
boundaries are chosen at Webern's will. The significant portion of
their content, that is, the part which is subjected to metamorphic or
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transformal variation, Is also chosen at Webern's will. Either
variation technique can control the level at any given moment. The
entitles of the level of large form obtain much of their internal
developmental configuration with relation to this level.
One may compare the two variation techniques by observing that
a transformal variant Is a repetition with changed orientation,
whereas a metamorphic variant Is a repetition with internal change.
The transformal process Is prismatic, refracting musical Ideas
through the restricted domain without changing their ldentlflability.
The metamorphic process Is a direct borrowing of Goethe's botanical
theory, developing a musical Idea from a tiny seed, or generating
entity, into a large, flowering plant "leaf by leaf," or as a
b o tan ist would now say, cell by c e ll. The complex element of the
metamorphic-transformal level is a phrase made up of superposed
variations of entities.
Both these processes occur according to a logic almost as strict
as that governing se ria l technique its e lf . Development by these
processes must reflect past development in the work. Entities must
maintain their Identity, and to some degree, internal relationships.
Transformal structures are as strfctly algebraic as twelve-tone serial
ones are. Metamorphic structures must maintain consistency of the
same sort that a growing plant displays -- techniques of expansion,
linkage, and contraction are carefully controlled.
The Klangfarbe level has no internal validity but sound itself.
It preserves all higher logical levels, but determines precise events,
as well as voicings and vertical correspondences, Many of Its proc
esses interact with those of the metamorphic-transformal level.
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In this level the final choices of the definition of each note are
made. No "truth" which violates the metaloglc of the ear is permitted.
Yet, of the choices available, Webern seems, almost Invariably, to
choose the most essential, simplest alternative — that which disturbs
the higher logical levels least, yet serves the ear best. In some of
his non-technical correspondence, Webern equates simplicity with truth
and the capacity for transcendence. In this level, this simplicity
is made manifest.
In the Klangfarbe level, a statement of a musical idea seems to
invoke a consequence or resulting statement, which in turn gives rise
to another consequence. This pattern is followed until silence is
itself a possible response to the previous material (either the total
material preceding, part of it, or only the immediately preceding
statement), at which point the section or movement may end.
The consequence may have any of several relationships with preceding
material. Commonly, its relationship is metamorphic, expressed as an
expansion and/or contraction of sound characteristics of the preceding
material. The author finds the following alterations common when an
expansion is indicated: increase of range or intervallic span; use
of more extreme, brighter, or more colorful register and timbre;
variation; increasing connections among ideas; longer durations
(except for written-out accelerations); more attackB within a time
span; added notes; added contrasts; increasing or higher dynamic
level; acceleration. Corresponding alterations occur when a contraction
is indicated: decrease of range or intervallic span; use of duller
or more commonplace register and timbre; repetition; disintegration of
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relationships among Ideas; shorter durations; fewer attackb, fewer
notes, fewer contrasts; decreasing or lower dynamic level; severe
vertlcalization, a tendency to sum up material which was previously
linear in character.
The consequence may repeat some of the material used in the
preceding statement. In Webern's mature style, repetition, permutation,
inversion, and retrograde of material of the preceding statement
is often an indication of slackening expansion or oncoming or actual
contraction. Although voicing of pitch content is frequently used to
accomplish an impression of expansion or contraction, it seems to be
generally an accessory rather than the controlling factor in the
determination of the consequent's configuration.
The consequence may contrast with the preceding statement. In
such a case, its content balances and opposes that of the preceding
statement. The calculation of this balance and opposition reveals
much about Webern's conceptual organization of sound.
The consequence may be a continuation of the preceding statement.
In such a case, it is like a realization of the Klangfarbenmelodle
concept — a tra n sfe rra l of a melody from voice to voice without an
intensity discontinuity of sufficient importance to break the line.
A given consequence may display any or all of these relationships
with the preceding statement. A statement may generate more than one
consequence, especially when an expansion is taking place. Similarly,
when the formal structure is contracting, a single consequence can
satisfy more than one preceding statement.
It is the author's opinion that almost every significant pattern
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In the works of Webern's mature style can be analyzed re la tiv e to these
logical levels. The potential uniqueness of such analysis can only be
shown If one proceeds from the complex result to the simple cause, for
the causes given may generate many results. It seems that this quality
of one-directional potential uniqueness is the factor which gives the
style i t s power and unity, but permits free development.
The functions of these levels as they interact with one another will
now be discussed. The following statements, like those referring to
the logical levels, are thought to have only provisional validity, and
are made only to clarify the structure examined.
The motivation' for using these structures and the way in which
they are manifested appears to be pragmatic. If a structure is given
in a fragmentary form, it is likely to have a secondary function in
the total structural configuration. On the other hand, if a structure
is complete and supported by similar structures in other levels, it
is probably important to the total structural configuration. In
general, a structure appears to be used and emphasized when its
characteristics are essential to the musical requirements which it
meets -- the time, place and circumstance of its appearance.
All logical levels seem to depend heavily upon the linkage of
structural entities used in a modular fashion. The configuration
of the entity and its relationship to its surroundings is an index
to the structural happenings of the moment in which it occurs; but
these happenings are made obvious through that configuration. The
flow of the work and the entity-relationship network are potentially,
then, interdependent. Their actual interdependence is subject to
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Webern's decision.
Linkage of entitles can be Internal or external. Internal linkage
is shown through similar configuration of content, produced either
metamorphically or transformally. External linkage.is free, and
refers to the function of the entity as a whole in the structure or
structures in which it is imbedded. Such structures provide a basis for
relationships among entities, and the structures themselves are made
manifest through the relationships generated by juxtaposing entities.
The motlvic contents of entire divisions of the large form often
appear to derive from metamorphic and transformal application of
variation techniques to a single musical idea. The pitch organization
of entire works is similarly based on strict transformal variation of
twelve-tone row; but the precise row form used in a given situation
may well be determined by metamorphic consideration.
It seems that Webern sometimes wishes to use only a portion of
a given rational structure as a strong formal generating device, but
for the sake of completeness wishes to present the whole structure.
In such a case, he appears to de-emphasize the portion of the structure
which is non-essential to the matter at hand by bringing in structures
from other logical levels as formal generating devices. The non-
essential material is not wasted, but used to create other formal
details. This procedure is especially evident when he wishes to
emphasize certain pitches, and must bring in entire row forms to get
the pitches he wants.
A musical idea which is a strong generating entity will often be
almost strictly repeated: same voicing, same pitches, same durations
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and volumes. Variations of that musical idea may be slight, but are the
more striking because the idea becomes a strong point of reference in
the flow of the work. The use of serial technique enables Webern to
imbed such ideas in similar surroundings. For example, a retrograde
of such an idea can be easily presented in a retrograde of its original
setting. An idea which appears in two forms in a slightly different
way can be varied by using one or the other form. Pitches can be
added to the idea by adding another row form to the texture; they
can be subtracted by introducing the extra notes into the accompani
ment. Since twelve-tone technique controls only the pitch component of
a tone, its sound can be varied freely in the Klangfarbe level with
out disturbing the row-form structure.
Configurations of rhythm, timbre, voicing, dynamics, and
combinations of these aspects may also consititute a musical idea.
These configurations can be varied in the same way that a musical
idea based on pitches is varied.
This sort of variation is as close as Webern comes to total
serialization. In the author's opinion, the breakdown of sound
aspects into a definite, limited number of parameters, and the complete
serialization of these parameters, would not have served Webern's
compositional intent. This procedure would have resulted in a
determinism which would not have permitted him to emphasize or
de-emphasize a rational structure when it suited him to do so. In
addition, the metamorphic variation technique would have lost a great
deal of its freedom. Serialization loses its rational power when
subjected to non-canonic variation techniques; for the results are
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then no longer predictable, and the structure no longer holds, as
explained In the third section of the first chapter*
It seems that the emphasis on discrete pitch of a tone, which
applied in pre-Webernian music, shifts to an emphasis on its total
sound, described by its pitch, dynamics, voicing, and volume, in
Webern's mature sty le . Traditional harmony is based upon pitch
only. The organization of Weberi ’s mature style is based on the
relations between characteristics of all portions of the sound of
a tone. Then exact repetition of a musical idea takes the place
of a tonal center. It can function as a point of origin for an
entire structure or set of structures.
A phrase, or complex of phrases, can then be described as
moving toward such a repetition. The further the relationships within
entities are from that repetition, the further away the entities
themselves are from the point of origin of the structure. Structures
whose relationships suggest cadential patterns seem to occur before a
return to the point of origin.
In the author's opinion, the nature and function of these
entities and relationships is similar to the nature and function of
chords and chord relationships in trad itio n al harmony. The process
is used in such a way that it is logically independent of the means
by which it is manifested. Although some pitch patterns function in
a manner which seem to reflect the old tonal structures, these
pitch patterns are not the primary controlling factor in the process
the way they are in tonal music. In Webern's mature style, no aspect
of sound has such power.
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Webern's mature style seems to have been constructed to provide
an efficient, elegant vehicle for his compositional Intent. It
should be considered as a means by which he is able to achieve a
refined, supple structure capable of expressing whatever sort of
beauty he wished to communicate.
These logical levels are used in the analyses accompanying the
present study. Appendix A contains an analysis of the Quartet, opus
28, f ir s t movement, according to the structure of its large form.
Appendix B consists of a generalized discussion of twelve-tone
technique as it related to the conclusions of Chapter I, and an analysis
of the application of th is technique in the T rio, opus 20, where it
dominates musical events perhaps more than in any other of Webern's
late works. Appendix C contains a generalized discussion and analysis
of Webern's variation technique as a transformal, or strictly logical,
and metamorphic, or not strictly logical, developmental technique, in
conjunction with the Variations, opus 30. The voicing patterns of
the Second Cantata, opus 31, are discussed in Appendix D.
The results of these analyses with regard to one's musical insight
should change in time and circumstance, if the premises of Chapter I
are taken as valid. As a re s u lt, no conclusions are drawn from them,
and it is hoped that they will lead the reader to investigate these
works and reach his own conclusions about their structure.
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FOOTNOTES
CHAPTER II I
DESCRIPTIONS OF WEBERN'S MATURE STYLE
Unless otherwise Indicated, all translations of sources cited
in this chapter are by the author.
*Egon Wellesz, "Die jUngste Entwlcklung der neufranzBsischen Musik," Der Mericer II (May, 1911): 660-661.
^Ib id ., p. 664. 3 Per Merker II (June, 1911). Articles by Arnold Schoenberg, Rudolf Reti, Paul Stefan, Karl Linke, and Richard Specht.
^Hugo Fleischer, "Fllr und wieder Arnold SchBnberg," Der Merker III (June, 1912): 922.
'’Arnold Schoenberg, Harmonielehre. 3rd ed. (Vienna: Uhiversal- edition, 1922), pp. 506-507.
^Wallace McKenzie, "The Music of Anton Webern," d isse rta tio n reproduced by University Microfilms, Inc., Ann Arbor, Michigan, submitted to North Texas State.College, 1960, p. 78. -j George P erle, "Atonality and the Twelve-Note System in the United States." The Score XVII (July, 1960): 53.
^GyBrgy L igeti, "Weberns Melodik," Melos XXX (1966): 117-118. 9 Walter Kolneder, Anton Webern: EinfUhruna in Werk und St11 (Rodklrchen am Rhein: P. J. Tonger, 1961), p. 104.
^David Josef Bach, "New Music by Berg, Webern, Krenek," Modern Music XII (November-December, 1934): 32.
^H/olfgang Fortner, "Anton Webern und unsere Z e it," Melos XXVII (1960): 326. 12 Pierre Boulez, Penser la musique aulourd'hui (Mainz: C. B. S chott's Sohne, 1963), p. 119. 13 Roger Sessions, Questions about Music (Cambridge, Massachusetts: Harvard University Press, 1970), p. 33.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 116
14Ibid., p. 101.
^"\jan La Rue, "Basic Analytical Procedures,11 unpublished manu scrip t, p. 5a.
■^Boulez, p. 143.
^Herbert Eimert, "Die notwendige Korrektur," Die Reihe II (1958): 59. Translation based upon the English edition.
18Sessions, p. 110. 19 v Gundaris Pone, "Webern and Luigi Nono: The Genesis of a New Compositional Morphology and Syntax," Perspectives of New Music X no. 2 (Spring-Summer 1972) : 114-115. 20 Anton Webern, ed ., Heinrich Isaac: Choralis Constantinus II. Dpnkmfller der Tonkunstler Osterreich. vol. 32 (Graz:Academische Druck-u. V erlagsanstalt, 1959, reprint edition).
21Weg. 22 Isaac, p. viii. 23 Isaac, p. xii. 24 Path (i. e., transj Leo Black), pp. 36-37.
2^Path. p. 48. 26 Wee (i. e., trans. author), p. 11.
27Weg. pp. 17-18, 19.
28Weg. p. 26. 29 Path, p. 31. 30 Path, p. 64; le tte r to W illi Reich, August 6, 1943. 31 Weg. p. 56. 32 Adolf Weiss, "The Lyceum of SchBnberg," Modern Music IX no. 2 (March-April 1932): 99.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER IV
WEBERN IN THE CONTEXT OF TWENTIETH-CENTURY THOUGHT
Introduction
Webern's supposed philosophy is compared .with that of three
other twentieth-century thinkers in this chapter, so that it can
be clarified. In the first section, Webern's approach to musical
thought is compared with that of Alfred North Whitehead. Some
differences between Webern's philosophy and the premises of
logical positivism are also noted.
Similarities between the late writings of Ludwig Wittgenstein
and Webern are shown in the second section. These two men were
close contemporaries with similar backgrounds. Their mature work
seems to imply the acceptance of corresponding underlying premises.
The third section, concluding the portion of the study not
containing musical analyses, sums up certain observations regarding
the use of rational structures in the arts. Certain concepts held
in common by Webern and Paul Valery are used as a point of
reference.
Section 1. On Whitehead's Discussion of Musical Analysis
An important challenge to the model outlined in the first chapter
is found in the w ritings of Alfred North Whitehead, perhaps the most re
nowned mathematician-phllosopher of the first decades of the twentieth
century. In the course of a book which is a lengthy exposition of the
117
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boundaries of logical thought, he argues that systematic analysis of
music Is Impossible.
. . . the audition gains complexity of subjective form by Its Integration with other feelings. Also, though we can discern three patterns, namely, the pattern of the [acoustically measureable ] datum, the pattern of emotional quality, and the pattern of emotional intensity, we cannot analyse either of the latter patterns in complete separation either from the pattern of the datum or from each other.
This conclusion seems to be a consequence of the premises which
Whitehead assumes to be categorical for all systematic thought.
These premises are now shown to differ from those outlined in the
first chapter of the present study, and from those implied in the
second chapter by the philosophical writings discussed there. Space
limitations dictate that this study must do Whitehead the injustice
of presenting these premises in summary form. The premises which
differ chiefly have to do with schematization of data. It appears
that Whitehead's view of schematization is a defense of the validity
of Newton's approach to science, based on unbiased perception rather
than conceptualization, cited in the second section of the second
chapter of the present study. He wishes to extend that approach to
all application of logic.
The objects of sc ie n tific study are assumed to present an
appearance to the perceiver which is entirely consistent with their
actual form. Regardless of the method of perception or the perceiver,
their boundaries, internal configurations, and relationships with
each other are invariant. The universe of such objects is "atomic;"
that is, if the objects are divisible, the division is always the
same, and they are composed of a fin ite set of d iscrete components
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whose sum comprises the whole.
This invariance is considered to be a physical property, subject
to physical causes or laws. One's knowledge of these properties and
laws is assumed to be exact and objective. Then th is knowledge does
not depend upon conceptualization of interpreted appearance, but
apprehension of appearance which is identical to the physical
characteristics of the object. Such knowledge is then also invariant,
and is assumed to be as stable as logical systems themselves.
This stability is a rigorous constraint upon the schematic
function discussed in the third section of the first chapter of the
present study. Only one such function can exist for given data, and
it is associated with some rational structure so precisely that one
may say that the rational structure is generated by the schematized
data. One may then assume that the foundation of rational systems is
found in the observable characteristics of the real world.
Objects which cannot be schematized unambiguously and associated
with rational structures in a well-defined manner are not admissible
to logical analysis, according to these premises. In particular,
musical e n titie s as sounds have variant boundaries and components even
with regard to the preceived measurable basis according to the auditory
acuity of the listener. Structural ambiguities compound the confusion.
Even works w ritten in commonly agreed upon forms such as sonata allegro
can display these ambiguities; for example, it is not clear whether
the first theme of the first movement of Beethoven's Pathetique Sonata
begins on the downbeat, or on the fourth beat of the first measure
of the exposition.
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A way out of this problem is suggested by the existence of the
measureable basis of sound, the three-dimensional continuum
of pitch, duration, and Intensity. Objects In this basis are ob
jectiv ely measureable mechanically, but as Whitehead points out,
their causes cannot be described as accurately as physical laws can,
nor are the resu lts of hypothesized causes unambiguous. It also
seems that perception by mechanical means generally does not yield a
great deal of information to a musician which helps him understand
the conceptual configuration of a musical work.
Since schematized data is assumed to be precisely associated
with only one rational structure, only one analysis of that data is
logically possible. However, even schematized musical data is subject
to multiple in terp retatio n s. Then, even i f an unambiguous method
of perception were obtainable for music, the result would still be
inadmissible to a logical system.
The unique analysis of the data is assumed to give a complete
knowledge of that data, as a determinate component of the universe.
Whitehead implies, and the logical positivists state, that no other
knowledge of the real world is possible. That is , if one cannot
find unambiguous means of defining what one knows, one does not know.
Since one of the premises of the second section of the first chapter
was that fin al knowledge of a musical work is neither possible nor
desireable, musical analysis cannot yield the sort of complete knowledge
that Whitehead requires. By im plication, such analysis can yield no
knowledge at a ll. Varying interp retatio n s of a musical work can only
be falsehoods.
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With regard to a rt, Whitehead takes the Romantic position that
a created work Is generated by the whole universe, a fusion of
divinely Inspired conceptualization with physical manifestation,
ultim ately unknowable as God and the universe in unknowable. Since
it cannot be objectively known, it cannot be judged according to a
value system. If it cannot be so judged, it cannot be found to be
"true" or "false" as a whole. Whitehead apparently sees no other
motivation for analysis of art. It may be mentioned, in passing,
that Whitehead is not renowned for his creative output in the fine
a rts .
Whitehead appears to assume that ultimate truth, represented by
the totality of possible thought or by God, exists in a potentially
logical sense. If so, he takes on the fundamental premise of the
German idealists — that Nature is not self-contradictory, and that
reality is ultimately rational, although we may not be able to prove
that it's so. He differs from the German idealists in that he knows
that all schematizations of Nature do not produce logical results of
consistently fine quality.
His position seems to be that only the scientifically proved
methods of determining logical systems from reliable data will give
the strong re su lts desired, and that methods based on conceptualization
of data and application of pre-existing rational structure are per se
unreliable. He does not seem to admit the possibility that
scientifically proved methods may rest on consistent a priori
interpretation of data which may have tautological foundation.
Certain passages in Der Weg zur neuen Musik seem to parallel
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Whitehead's premises. This apparent similarity Is probably largely
due to the common influence of the mainstream of European philosophy
on both men. It seems that the divergent result which they obtain
is largely due to Whitehead's adherence to the absolutist foundations
of sc ie n tific method as outlined by Newton, Hume, and Mach, whereas
Webern's position is close to that of the German idealists and to 2 Wittgenstein's, which, according to Janlk and Toulmin, resembles
the scientific pragmatism of Hertz and Bolzmann.
Webern's lectures show that he thought of music as conceptually 3 based rather than having fixed premises based on physical reality.
The boundary between consonance and dissonance is especially cited as 4 conceptual rather than absolutely determined. The shift of emphasis
from the principal pitch of a sound to its complex of pitches which
compose its timbre is a change of conceptualization.
Webern's definition of a motive as the smallest particle of a
musical idea, recognizable as an entity not by its own unique
characteristics, but only because it is repeated, seems to imply
that he does not think, as Whitehead does, th at the division of en
t itie s is unambiguous. Examination of Webern's music seems to bear out
this assumption. But if the universe in which Webern works does not
have this property of being "atomic" with regard to its physical
basis, the logic upon which the music depends cannot hold uniquely
with relation to that physical basis. This statement, if true,
uncovers a substantial gap between Webern's musical practice and many
contemporary explanations of that practice.
The cause of the structural configuration of Webern's music,
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which in turn determines its physical realization, seems to be based
not on causes which are physically determinable but on his need to
express ideas which can 't be expressed any other way.^ These ideas
may well take logical form, but the impression given by the lectures
is that Webern considers music to be a language uniquely suited to
express his ideas.^ This statement is again at variance with many
contemporary assumptions about Webern's style, but it is consistent
with the ideas about language of Wittgenstein and Kraus, Webern's
Viennese contemporaries. Kraus's ideas of language, in fact, are
discussed in the first lecture of the series given in 1933.^ g Language is a means of presentation of ideas. The configuration
of language may reflect natural laws, which, if adhered to, clarify 9 and give expressive power to the language. The search for these
natural laws preoccupied many thinkers in the first decades of the
twentieth century -- Whitehead himself, Wittgenstein, Kraus, and the
members of the Vienna Circle who took Wittgenstein's Tractatus
as their starting point. At the time that Webern formulated his
mature style, he could have come in contact with some of these
thinkers. However, i t seems possible that the ideas which prompted
these men to search for the foundations of language may have
prompted Webern to reconsider the foundation of music as well.
The stability of mathematics as an "eternal object" was one of
the goals of Whitehead's work, and much of his writing: must be
assessed with respect to his wish to make this stability permanent.
Webern assumes no such stability for music, but rather shows that it
changes in accordance with the need for expression of musicians.
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He seems to think that his style Is the perhaps inevitable historical
cumulation of progressively stronger means of handling musical material.
However, his sty le is not the fin a l such means, even though i t has
attained rational form.
According to Janik and Toulmin, the Viennese generation to which
Webern belonged sought the foundations of thought from a strong,
flexible intellectual base, in a manner which was both generated and 12 constricted by the society in which they found themselves. The
preoccupation with language was perhaps suggested not only by the large
number of languages and dialects which made communication nearly
impossible, and by the constant prevarication not only of the press,
.but also by daily contact among people in daily life. Vienna seems
to have been a city in which free conceptualization was a comnonly 13 played game in all human action. The thinkers and artists of Webern's
circle were in constant opposition to all inept or■misleading uses of
conceptualization or of language, and Webern's insistence upon the
rightful use of language should probably be regarded in that context.
Webern's generation was the last to receive the full impact of
accumulated European philosophy'and strict classical education. After
World War I, education in philosophy and classics degenerated sharply,
not only in Austria but in other European countries as well. The
post-war generation seems to have been content to build on the
foundations laid down by Webern's generation without examining them
very thoroughly. Janik and Toulmin show that W ittgenstein's
Tractatua was misinterpreted to serve as the foundation for the 14 Vienna Circle and the logical positivists. They note that this
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trend was general.^
Whitehead himself did not escape this fate. For many years,
mathematicians seem to have accepted cn faith the mathematical
foundation which he and Russell Intended to last for all time. It
Is only In the last few decades that reconsideration of Its assumptions
have led to serious challenges to Whitehead's philosophy.
Similarly, Webern's musical ideas have been interpreted from
a positivistic standpoint — that is, that music is only a language,
tautologically defined; its ultimate meaning is not within the
language, hence does not exist; thus, its structure is its whole
meaning. This structure is realized in a physical basis, therefore
it can be physically described uniquely according to the procedures
of Whitehead. However, Whitehead shows in the chapter accompanying
the quotation cited above that these procedures do not apply.
This interpretation was unfortunately strengthened by Webern's
isolation in Vienna before and during World War II, and his death in
September, 1945. His only non-musical reb u ttal is found in the lectures
published in Der Weg zur neuen Music.. For the re s t, he followed
Wittgenstien's maxim that that which cannot be said can only be
shown, by using the schematic process as a means of displaying in
music that which cannot be expressed any other way.
Section 2. Conceptual Similarities in the Late Writings of Webern
and W ittgenstein.
Although Webern and W ittgenstien were both in Vienna for most
of the period 1919-1928, it has not been shown that they had any
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contact with each other. There are several possibilities for contact:
Adolf Loos, Wittgenstein's teacher in architecture and a friend of
both, could have introduced them, or discussed ideas of either with
the other; Webern, who had a strong in terest in philosophy, could have
read Tractatus. which was first submitted to Karl Kraus, who influenced
both men; W ittgenstein, who had a strong in terest in music, could have
heard about or attended the Verein fUr privat Musik Auffuhruneen.
with which Webern was closely connected, perhaps at the suggestion of
Loos or Kraus; Wittgenstein and Webern may even have discussed the
role of logic in music in unrecorded conversation.^^
This period was crucial in the intellectual development of both
men. W ittgenstein seems to have le ft the profession of philosophy
temporarily during this period, but he was rethinking the principles
of the Tractatus and formulating the ideas which underly his later
work. His work after this period shows a concern with the boundaries
and limitations of the predicate calculus, its schematic relations to
the world, and a preoccupation with non-numeric logical and logic-like
structures. During these years, Webern's style developed from the
rather intuitive structure of opus 15 to the deliberately planned con
tro l of the musical domain ch aracteristic of works a fte r opus 20.
It is the author's opinion that the strongest support for the
notion that these men did have some contact during the period of 1919-
1928 is that each produced statements about thought processes at a
later time unobtainable to the other, in which influences of the other's
late work seem to appear. These statements are: the lectures
contained in Der Wee zur neuen Musik. given by Webern years a fte r
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Wittgenstein had left Vienna, and preserved only through a stenographic
transcript which was not published until after World War II; and
Wittgenstein's Remarks on the Foundations of Mathematics^ and 18 Philosophical Investigations. written in England during World War II,
when in te lle c tu a l communication between England and Austria was almost
impossible. No discussion of serial technique published before the end
of World War II seems to show as fine a perception of the foundations
and idiosyncracies of Webern's stylistic orientation as Wittgenstein's
latter works do, in their investigation of the characteristics of
logic and language; no such discussion has the logical scrupulousness
and breadth of structural insight that the Path does, and these
qualities seem to be more closely akin to Wittgenstein's thought than
to that of any other musician of Webern's circle.
It cannot be claimed without further evidence that Wittgenstein
and Webern had any influence on each other. However, the similarities
between the logical problems which they both faced, and solutions which
they found for these problems, are so close that a study of the work of
eith er seems to illum inate the work of the other. These sim ilarities
are to some extend the result of the thorough philosophical education
which both men had in Austria at about the same time. Still, the most
striking parallels occur not in their acceptance of the philosophical
tradition as it was presented in their youth, but in their reactions
to it. Some of these similarities are discussed below.
Parallel Passages in the Late Writings
Both men faced the question, "To what extent is some sort of logic
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Inescapable in the communication of coherent thought?" Webern re
stricted the question to musical thought. Perhaps the most concise
of the passages In the Path which allude to this question Is the
following:
Presentation of a musical Idea: what is one to understand by that? The presentation of an idea by means of notes. With this object -- to try to express an idea — universally valid laws are assumed. Every thing that has happened, been striven for, aims at f u lf illin g these laws. Something Is expressed in notes — so there is an analogy with language. If I want to communicate something, then I immediately find it necessary to make myself intelligible. But how do I make myself Intelligible? By expressing myself as clearly as possible. . . . The highest principle in all presentation of an idea is the law of comprehensi b ility . Clearly th is must be the supreme law.^9
A great part of Philosophical Investigations deals with the
characteristic problems arising as a consequence of using language
as a means of presentation of one's thought. One fundamental
premise of the work is that the purpose of language is to express
thought. There are many passages close to the one cited above from
Path, among which is the following:'
1.97 Thought is surrounded by a halo — Its essence, logic, presents an order, in fact the a priori order of the world: that is, the order of possibilities. which must be common to both the world and thought. But this order, it seems, must be utterly simple. It is prior to all experience, must run through all experience; no empirical cloudiness or uncertanity can be allowed to affect it — It must rather be of the purest crystal .... We are under the illu sio n that what is peculiar, profound, essential in our investigation, resides in its trying to grasp the incomparable essence of language. . . . we are not striving after an'ideal, as if our ordinary vague .sentences had not got a quite unexceptional sense, and a perfect language awaited construction by us. --On the other hand, it seems clear that where there is srnse there must be perfect order.
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Webern discusses the necessity of using music as language:
There must have been a need, some underlying necessity, for what we c a ll music to have arisen. What necessity? To say something . . . ; to express an idea that can't be expressed In any way but sound. . . . [Music! tries to tell people something, by means of notes, that couldn't be said In any other way. In this sense music Is a language.**
W ittgenstein uses musical structure as an example of a non-verbal
construction which has some of the characteristics of a language.
1.527 Understanding a sentence Is much more akin to understanding a theme In music than one may think. I mean that understanding a J.ing4stlc phrase lies nearer than one thinks to what Is ordinarily called under standing a musical theme. Why Is just this the pattern of variation In loudness and tempo? One would like to say "Because I know what It's a ll about." But what Is it all about? I should not be able to say (I.e., verbalize). In order to explain I could only compare It with something else which has the same rhythm (I mean the same pattern) .... 1.528 I t would be possible to Imagine people who had something not quite unlike a language: a play of sounds, without vocabulary or grammar .... 1.529 "But what would the meaning of the sounds be in such a case?" — What is it in music? Though I don't at all wish to say that this language of a play of sounds would have to be compared with music.22
The idea that art, the product of man as a part of Nature as a
whole, is b u ilt on laws of Nature is Goethe's. Both men are intrigued
by the idea, but refuse to take traditional interpretations of these
laws as final. Wittgenstein writes: '
I l .x i i If the formation of concepts can be explained by facts of nature, should we not be interested, not in grammar, but rather in that in nature which is the basis of grammar? -- Our interest certainly includes the correspondence between concepts and very general facts of nature- . . . if anyone believes that certain concepts are absolutely the correct ones, and that having different ones would mean not realizing something that we realize — then let him imagine certain very general facts of nature to be different from what we are used to, and the fermentation
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of concepts different from the usual ones will become In te llig ib le to him. Compare a concept with a style of painting. For Is even our style of painting arbitrary? Can we choose one at pleasure? (The Egyptian, for Instance.) Is It a mere question of pleasing and ugly?23
Perhaps the most Important question discussed In the Path Is the
validity of the replacement of tonality by the twelve-tone technique.
Webern's argument is based on a train of thought similar to that cited
above, which may be due to Loos rather than to eith er Webern or
Wittgenstein. The natural characteristics of the overtone series are
said to generate major and minor chords, which in turn form the basis
for traditional tonal system. This system is related directly to
music itself, which is an application of language. The natural
laws of unity and comprehensibility, however, are inherent in the
form of language itself, and thus take precedence over the natural
laws based on the overtone series. By recognizing this precedence,
the composer can postulate the existence and expression of more
powerful musical ideas than formerly.
In this musical material new laws have come into force that have made it impossible to describe a piece as in one key or another. ^
To Wittgenstein, the consequence of superseding previous
organizational structures is not trivial. In the midst of a section
in which he examines a possible correspondence between music and
mathematics, there is a passage which might almost be a recollected
conversation.
11.77 I have invented a game — realize th at whoever begins must always win: .so it isn't a game. I alter it; now it is all right.
That is to say, the player should not be assured of winning. An
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analogous situation in composition might be that, if one composed in
a given style, the requirements of the style should not be so strict
th at the outcome of the composition is autom atically determined. The
passage continues:
Did I make an experiment, whose result was that whoever begins must always win? Or that we are inclined to play in such a way that this happens? No -- But the result was not what you would have expectedi 0: course not; but that does not make the game into an experiment. ^
In the context of the Remarks, one experiments when he performs an
action with no idea as to how it will turn out. When one performs
an action within a logical system, he is able to predict the outcome
of that action if he understands the system properly. But what if the
system itself changes, as it has done many times in the history of
music, according to the Path? Wittgenstein says:
But what does it mean not to know why it always has to work out like that? Well, it is because of the rules. -- I want to know how I must alter the rules in order to get a proper game. — But you can e.g. a lte r them e n tire ly — and so give a quite different game in place of this one. — But th at is not what I want. I want to keep the general outline of the rules and only eliminate the mistake. -- But that is vague. It is now simply not clear what is to be considered as the mistake.
Webern would have replied, according to several passages in the lec-
turesj that whatever interferes with unity and comprehensibility
should be considered as a mistake, and that music history can
be viewed as a progressively firmer grasp of those two principles
as structure-generating components. Serial technique is not the
final stage; "It's for a later period to discover the closer
unifying laws that are already present in the works themselves." 28
Wittgenstein continues:
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I t Is almost like when one says: what is the mistake In this piece of music? It doesn't sound well on the Instruments. — Now the mistake Is not necessarily to be looked for In the Instrumentation; It could be looked for In the themes. Let us suppose, however, that the game Is such that whoever begins can always win by a p articu lar simple trick. But this has not been realized; — so It la a game. Now someone <&aws our atten tio n to I t ; — and I t stops being a game.
The "simple trick," as far as the tonal system was concerned,
was the possibility of free modulation. "I can exploit the double
meaning of all those chords so as to move elsewhere as fast as possible.
In fact there was no longer any reason to return to the basic key, 30 and that meant the end of to n a lity ." For the ju s tific a tio n of
tonality was that the basic key provided the fundamental unity of
the composition; "tonality . . . was an unprecedented means of
shaping form, of producing unity. What did this unity consist of? 31 Of the fact that a piece was written in a certain key." But
when free modulation negated the unifying force of the principal key, 32 "something had to come and restore order."
Tonality is then abandoned as a unifying force, not because it
has no validity or usefulness, but because more powerful unifying
forces supersede it. Wittgenstein continues:'
What turn can I give this, to make it clear to myself? — For I want to say: "and it stops being a game" -- not: "and we now see that it wasn't a game." That means, I want to say, i t can also be taken like this: the other man did not draw our attention to any thing: he taught us a different game in place of our own. — But how can the new game have made the old one obsolete? — We now see something different, and can no longer naively go on playing.^
Webern sums up his fdeas on to n ality thus:
The relationship to a keynote gave these structures an
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essential foundation. It helped to build their form, In a certain sense It ensured unity. This relationship to a keynote was the essence of tonality. As a result [of free modulation and expansion of tonal relationship]' . . . this relationship first became less necessary and finally disappeared completely. A certain ambiguity on the part of a large number of chords made tt superfluous. And since sound Is natural law as related to the sense of hearing, and things have happened that were not there in earlier centuries, and since relationships have dropped out without offending the ear, other rules of order must have developed . . • • double gender has given rise to a higher race."'34
One of the lectures In the Path reveals that the early efforts
of Webern and his colleagues to form these new rules of order were 35 "experimental." However, the adoption of serial technique Implies a
conscious structuring of a new "game.," in the author's opinion, by
its musically unprecedented rigor. It is extremely difficult, if
not impossible, to say that a given musical work is or is not
rigorously tonal because of the varied interpretations that exist
of tonality, even among theorists. But one can say without fear of
contradiction that a given work is or is not twelve-tone serial, even
in the group of works which perhaps display the greatest continuity
between non-serial and serial technique: Webern's opera 15-17. Webern and his follower Leibowitz insist that the twelvA-tone 36 technique is strongly related to the past. Nevertheless, the
composer must enter the realm of se ria l technique through a conscious 37 acceptance of its consequences. In the lectures, a somewhat analogous
situation is pictured: the introduction of an additional part to
monophony. "The first person who had this idea — perhaps he passed
sleepless nights -- he knew: i t must be so.' . . . absolute necessity
compelled a creative mind; he couldn't manage without . . . one part
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couldn't express the Idea any longer." 38 And In this way a dis
continuity with the game of the past Is reached, although remnants
of the old game may appear in the new game.
If a musical work is tonal, a given note has a definite relation
ship to any other note which may occur, defined by the unifying
force of key. Free modulation implies that this relationship is
ambiguous. But i f th is relationship can be ambiguous, the natural
law of the overtone series is not sufficient to determine the
relationship, or key structure as a whole. Then tonality as a
theoretical system must be, at least in part, conceptual rather than
a wholly natural phenomenon.
W ittgenstein shows a figure of an animal head which can be
interpreted as either a duck with a long bill or a rabbit with long
ears, and points out th at the figure has meaning only through one's 39 interpretation of it. He then shows a more abstract figure, and
shows that the recognition of various aspects of it also occur at 40 w ill. He comments:
One kind of aspect might be called 'aspects of organization.' When the aspect changes parts of the picture go together which before did not .... "Now he's seeing it like this." "Now like that" would only be said of someone capable of making certain applications of the figure quite freely. The substratum of this experience is the mastery a technique .... Such a concept [i.e., means of perception.] would be comparable with 'major' and 'minor' which certainly have emotional value, but can also be used purely to describe a perceived structure . ^
Wittgenstein's usage of the word aspect differs from the
accepted usage of the word parameter. A parameter is a measure
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o£ the physical characteristics of a phenomenon In a direction
determined a priori; whereas
The concept of an aspect Is akin to the concept of an Image. In other words: the concept 'I am now seeing It as . . . 1 Is akin to '1 am now having this Image.' Doesn't It take Imagination to hear something as a variation on a particular theme? And yet one Is perceiving something in so hearing .... Seeing an aspect and imagining are subject to the w ill. There is such an order as "Image t h i s ." and also: "Now see tfye, figure like t h i s but now: "Now see this leaf green.
"Now see the figure like th is" could be expanded as "Conceptualize
the given phenomenon by associating it with this image,” whereas
"Now see this leaf green" would imply "Distort your perception of
an objectively measurable parameter to coincide with your subjective
expectation of its value."
Webern asserts, "Music is natural law as related to the sense
of hearing." 43 The acoustical result of sounding two or more pitches
together is objectively measureable; and if music is natural law, it
might seem that this result must be treated as a parameter rather
than an aspect. If so, "Now hear this interval as consonant" would
be a meaningless statement. Webern is careful to explain his solution
to th is problem.
The overtone series must be regarded as, practically speaking, in fin ite . Ever subtler d ifferen tiatio n s can be imagined . . . ; the only question is whether the present time is yet ripe for them. But the path is wholly valid, laid down by the nature of sound. . . . Dissonance is only another step up the scale, which goes on developing further [By scale, he here means overtone series 3* • • • But any one who assumes that th ere's an essen tial difference between consonance and dissonance is wrong, because the entire realm of possible sounds in contained within the notes that nature provides -- and that's how things have happened. But the way one looks at i t is most im p o rtan t.^
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Although the acoustical result of sounding two or more different
pitches together Is objectively measureable, the Interpretation of
this result Is not; then consonance, which gives the tonal system
much of its coherence, Is at least In part a conceptualization.
It Is part of a language-game, and therefore subject to higher
conceptualizations, If they exist.
The recognition of variation, according to Wittgenstein, is
also a conceptualization.
Doesn't it take imagination to hear something as a variatio n on a p articu lar theme? And yet one is per ceiving something in so hearing .... Take a theme like that of Haydn's (St. Antony Chorale) — take the part of one of Brahms' variations corresponding to the first part of the theme, and set the task of constructing the second part of the variation in the style of its first part. That is a problem of the same kind as mathematical problems are [in an accompanying note, Wittgenstein stipulates, that is, a problem within a proof-system, subject to contradiction]. If the solution is found, say as Brahms gives it, then one has no doubt; -- that is the solution. We are agreed on this route. And yet, it is obvious here that there may easily be different routes, on each of which we can be in agreement, each of which we might call consistent.
Webern regards the variation technique as one of the primary
ways of achieving unity through repetition, and considers it a 46 function of the structural domain chosen. The forty-eight row forma
derived from the original row form are considered variants of it, 47
with equal structural importance; that is, it is immaterial which
of them is 'th e original row form chosen to generate the work, because
their interrelationships remain invariant under global operations of
retrograde, transposition, and inversion. Wittgenstein seems to argue
this equality of row forms by claiming that inversion and retrograde
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are not simple changes of order.
Can one row of letters have two reverses? Say one acoustic, and another, optical, reverse. Suppose I explain to someone what the reverse of a word on paper Is, what we call that. And now it turns out that he has an acoustic reverse of the word, I.e., something that he would like to call that, but It does not quite agree with the written reverse. So that one can say; he hears this as the reverse of the word. As if, as it were, the word got distorted for him in being turned round. And this might perhaps occur if he pronounced the word and its reverse fluently, as opposed to the case of spelling it out. Or the reverse might seem d ifferen t when he spoke the word forwards and back wards in a single utterance. It might be that the exact mirror-image of a profile, seen immediately after it, was never pronounced to the same thing, merely turned in the other direction .... But I want to say that . . . we know that the word has only one reverse. "Yes, but i f i t is supposed to be a reverse in this sense there can be only one." Does 'in this sense' here mean: bythese ru les, or with th is physiognomy? In the first case the proposition W^uld be tautological, in the second i t need not be true.
Webern does not say that the forty-eight row forms have equality ex
cept with regard to pitch order in the context of the music. It
seems to the author that such a statement would imply that the
optical and acoustical properties of the row were identical in
practice. If so, Webern's use of the row would imply a synthetic
structure which would have little or no relation to the through-
composed or polyphonic forms of the past. Yet Webern's purpose is
not to build such a synthetic structure.
. . . this is music (mine) that's in fact based just as much on the laws achieved by musical presentation after the Netherlanders; that doesn't reject the development that came then, but tries on the contrary to continue it into the future, and doesn't aim to return to the past. What kind of style, then? . . . building a tonality, but one that uses the possibilities offered by the nature of sould in a d ifferen t way, namely on the basis of a
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system that does "relate only to each other" (as Arnold has put it) the 12 different notes customary In Western music up to now, but doesn't on that account (1 should add to clarify things) Ignore the rules of order provided by the nature of sound . .. . .
His purpose, It seems to the author, Is to let the structure generate
or assist In generating music.
The row forms are called "kinds of variation,"^0 and variation is 51 equated with the process of metamorphosis. In metamorphosis, the
entity varied retains its identity, but its shape is changed. As there
is an infinity of plants generated by t he process of metamorphosis (at
least within Goethe|s concept of it), an infinity of variations of a
musical idea are possible by the same process. If retrograde and in
version are means of metamorphosis rather than operations existing
only within a synthetic structure, their results may well differ,
acoustically, from the original row form in other respects than pitch
order.
A somewhat analogous situation of dual analysis occurs in the
tonal system. When one considers the acoustical properties of the
pitch complex generated when two or more sounds occur together, it makes
a considerable difference whether these sounds are taken to consist
only of the principal pitches (without accompanying partlals), as is
done in most tonal analysis and hypothesizing about to n ality as a
structure; or whether these sounds are themselves complexes of over
tones, as they usually are in the course of performed music. In the
f i r s t case, i t would be a simpler matter to draw a d istin c tio n between
consonance and dissonance; in the second, it would not be, because of
the possibility of dissonances generated by overtones (for example,
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139
the overtones of bells). And yet It is possible to describe systems of
tonality consistently and meaningfully by adhering to the first case.
Wittgenstein continues:'
51. Think of a machine which 'is so constructed1 that it reverses a row of letters. And now of the proposition that is the case of
A B E R (German original) OVER (English adaption) the result is REBA REVO.
The rule, as it is actually meant, seems to be a driving power which reverses an ideal sequence like this. — whatever a human being may do with an actual sequence.
A more extensive rebus, SATOR AREPO TENET OPERA ROTAS, was in fact
used by Webern as a notational convenience when he investigated the
interrelationships among the row forms used in his Concerto, opus 24.
He put the row in a musical context before casting it in its final
form; however, his final choice was determined by the interrelationships
it generated under strict applications of inversion and retrograde.53
Wittgenstein continues:
This is the mechanism which is the yardstick, the id eal, for the actual mechanism. And that is intelligible. For if the result of the reversal becomes the criterion for the row's really having been reversed, and if we express this as our im itating an ideal machine, th e ^ th is machine must produce this result infallibly.
Webern quoted HBlderlin thus:
"Again, other works lack infallibility, compared with those of the Greeks; at least until now they've been judged by the impressions they make, rather than by their ordered calculus and all the other procedures by which beauty is produced." Need I even say why I was so struck by the passage?"*-*
In the author's opinion, the key words in the above passage are not
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"judged . . . by their ordered calculus" but "judged . . . by their
ordered calculus and all the other procedures by which beauty is
produced." Webern's music is not beautiful because serial technique,
as he uses it, is a strict logical calculus. It is, rather, beautiful
because this technique produces beauty when Webern uses it as a means
of structural organization. The calculus is meaningful only in the
context of sound; but then, so is the tonal system. Wittgenstein
wrote, "Only in the stream of thought and life do words [that is,
language-components’] have meaning.
Wittgenstein is wary of facile solutions to philosophical questions,
and continually searches for important concepts overlooked by accepting 57 such solutions. Webern adopts a similar viewpoint:
Here is Karl Kraus: "The practical application of the theory, which affects both language and speech, would never be that he who learns to speak should also learn the language, but that he should approach a grasp of the word-shape [corresponding to Wittgenstein's "aspect?'.'], and with it the sphere whose riches lie beyond what is tangibly useful. . . . I t is b e tte r to dream of plumbing the rid d les behind her rules, the plans behind her pitfalls, that of commanding h e r...... To teach people to see chasms in truisms -- that would be the teacher's duty toward a sin fu l generation."
Section 3. Conclusion
The application of logical models to concrete situ atio n s is a
delicate and perilous undertaking even for persons skilled in logic.
A complete theory of applications of this nature is far beyond the
scope of this study. The discussions above are only concerned with
the possible dangers and advantages which could influence the
formulation of such a theory in the specific context of musical
analysis.
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Why should persons whose principal concern Is the arts even
consider becoming Involved In such an Intricate and possibly hazardous
area? Before this century, criticism of the arts usually contented
Itself with the description of concrete examples. Models which were
abstracted from these examples, such as fixed literary and musical
forms, were for the most part made explicit only by constant
reference to the works from which they were drawn. Such criticism
Is still possible, and Its validity usually Is not questioned. How
ever, Its results apparently do not satisfy many persons who are
presently active In the arts.
The twentieth century has seen a tremendous expansion of the
arts, which has been characterized by annihilation and redefinition
of former procedures, by an unprecedented Inslstlnce that every
artist must do battle at the very frontiers of art, and by an un
willingness to deify the resultant works of art. At the same time,
the critic has attained a vantage point from which he can attempt to
Interpret the whole of the history of the arts panoramically, and In
particular, try to account for the art which Is contemporary to him.
The tools of artistic analysis and criticism which served In the
nineteenth century no longer suffice, either for the artist who must
be his own severest critic, or for the critic who wants to under
stand what the a r tis t is doing.
The developments of twentieth-century art have also forced a
re-examination of the art which engendered them. Some criticisms which
have long been taken for granted now may appear inadequate (such as
previous deifications of certain works) as their results are compared
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with the results obtained through application of one's Intuitive In
sight, developed through contact with contemporary arts.
In some Instances, twentieth-century critics evaded coping with
the breach which has consequently appeared between actual artistic
development and Its criticism, perhaps in the hope that It would
eventually go away. This evasion was often disadvantageous to the
development of the arts, as well as unnecessarily painful to the
artist. It seems to the author that this breach has, in some cases,
almost nullified the value of the critical process in its application
to these works and forced the artist to choose either hermeticism or -
the sacrifice of the dynamic thrust of the art.
This breach has been spanned, to some extent, in the area of
French literature, as a consequence of re-examination and evolution of
the critical process to meet the critical demands of works produced.
It seems significant that the impetus for this evolution yas produced
principally by critics who were themselves not merely spectators but
participants in the arts to some degree. This evolution appears to have
reacted against, as well as sprung from, a strong pre-existing critical
foundation which apparently served the cause of French literature well
in its own time.
The author thinks that similar re-examinations and evolutions
of the critical process as a whole might serve the cause of all the
arts. It would be helpful to understand what the critical process
as we use it involves; what it is able to do, and what we cannot
expect it bo do; what forms it has taken in the past, and how effective
these forms have been; and how i t can be extended from i t s present
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configuration. It appears that the need to find some answers to these
problems is so great that the critic cannot afford to overlook any
means through which he may be able to provide them.
One of the immediate crises facing the critic is that of the
difficulty of understanding some of the manifestations of the twentieth-
century arts. It appears that these arts have been a battleground of
concepts and ideas, with each artist finding, as best he could, means
of bringing them into existence as works of art. It seems that the
arts have always been in this situation to some degree, but never to the
extent that the very survival of the arts rested upon the outcome. It
seems to be at precisely this point that many contemporary critics find
themselves helpless. A deliberate extension of the analytical process
to cover th is situ atio n seems cru cial; but such an extension seems to
presume an abstraction of the process itself. It is interesting to note,
in passing, that the development of French literary criticism has tended
in this direction.
The critic is encouraged to pursue this course of action by the
example of the apparently independent work of two of the great seminal
figures in early twentieth-century arts — Paul Valery and Anton Webern.
Both men were conscientious a r tis ts who produced exceptional works of
wide influence. Both were knowledgeable in the history of their
respective arts, as well as in logical forms and philosophy; and both
used this knowledge as a springboard from which to develop deep, logical
theories of the processes possible in art. These theories enabled them
to resolve the artistic crises which they faced while maintaining strong
personal styles.
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It seems that both men accomplished this end by patient examination
of the nature and possibilities of art as they found It, and of their
own mental processes. They both searched the art of the past for
manifestations of similar processes, noted the development of such
manifestations over the centuries, and postulated their further
development. Neither seems to have accepted any prior concept relating
to art or mental process, including their own, without subjecting it to
thorough examination; and neither ceased to develop his theories of art
or style of art throughout a long lifetime.
Although the critical processes developed by Webern and Valery
apply chiefly to their own work, the author thinks that these processes
may be generalized with some safety to apply to the arts in general.
Their strengths and limitations are particularly valuable for the
purpose of this study, since these processes displayed from their
inception some degree of abstract thought.
Some generalizations that could be made from the critical work of
Valery and Webern are: 1) Criticism as the study of the creative
process in art deals primarily with configurations of a language in
that art. One examines these configurations and sometimes, as a
consequence, catches an intuitive glimpse of ideas behind the configur
ations. 2) Art is a means by which the creative process is made
manifest. If its language is found to be inadequate for this purpose,
the artist is free to extend or reorganize that language to fit his
needs. 3) Consequently, the arts are subject to evolution, and the
c r itic a l process must be flex ib le enough to cope with that evolution.
4) There may well be deep, constant laws governing the creative
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process and the languages of art, but we don't know them now, and we
may never know them.
If the artist or critic is free to postulate suitable realms
within a work of art, he neither has to affirm nor to deny the
existence of an ultimate configuration of the language of art. This
result supports a notion which underlies much of twentieth century
art — that an artist is free to invent configurations and realms in
which to place these configurations; he is motivated in this inventive
process by the search to find the appropriate means to make his ideas
manifest.
The processes described in the first chapter hold only so long as
the structure of the logical model used remains reliable under appli
cation. Artists and critics have shown the capacity for sudden,
capricious change; the art that they have produced has also tended
to change rath er than to remain stable. I t would seem th a t a rigid
application process would probably not yield results of lasting value.
This apparent disadvantage of the application process can imply
two results which, in the author's opinion, support the hypothesis
that the process used can be compatible with present methods of
criticism .
First, it seems apparent that the process described above can
only be used in direct connection with some configuration of a
symbolic language. Such a language depends largely upon some sort
of linguistic convention for its usefulness and permanence.
Relative to that convention, the language, its configurations, and the
study of the structure of those configurations w ill be stable enough
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to permit a span of reliability which Is long enough to serve the critic.
A configuration of this type is bound to a particular manifestation
of art. This process limits the critic to the examination of specific
cases, while permitting him sufficient flexibility to note the
differences between them, and thus to postulate the changes which have
taken place. The process also permits the critic to make successive
studies of a single work in order to better approximate its actual
structure. Since the process is hypothetical rather than deductive,
contradictions arising from the comparison of different studies need
not prove fatal to the critical results.
Secondly, the critic does not have to bear the unreasonable burden
of finding results which will be valid for all time. He is free to
accept or reject any result at will, depending on its coincidence with
his a priori judgments- at a given time, under given circumstances.
Then, the critical result need only be reliable so long as it serves
the artist or critic; its very disintegration may serve as a symptom
that its usefulness is over.
These results are compatible with the results generalized from
the work of Valery and Webern. I t is not presumed th a t these re su lts
explain the whole of the critical process as it is presently used,
or that they limit the further evolution of that process. They do
seem to indicate that further investigation into the possibility of
using tools based upon the methods of applied logic in a r t i s t i c
criticism might prove to be profitable to the artist, critic, and
to the arts themselves.
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FOOTNOTES
CHAPTER IV
WEBERN IN THE CONTEXT OF TWENTIETH-CENTURY THOUGHT
^Alfred North Whitehead, Process and Reality: An Essay on Cosmology (The Free Press: New York, 1969; f i r s t edition published in 1929), pp. 273-274. o Wittgenstein's Vienna, pp. 186-201. 3 Path, p. 19. 4 Path, p. 16.
~*Path. p. 17-19. g Ibid., passim.
7Path. pp. 9-10.
^Path. p. 17. 9 Path, p. 16. 10 Path, p. 19. 11 Path, pp. 20-37, p. 56. 12 The Austrian Mind, p. 73.
^The Austrian Mind, pp. 115-119.
^W ittgenstein's Vienna, pp. 202-218.
15Ibid.
^Frederick Englemann, Letters from Ludwig Wittgenstein with a Memoir (New York: Horizon Press, 1968), pp. 123, 144-146.
*7Ludwig Wittgenstein, Remarks on the Foundations of Mathematics, ed. €. H von Wright, R. Rhees, and G. E. M. Anscombe, tran's. G. E. M. Anscombe (Cambridge, Massachusetts and London, Endland: The M. I. T. Press, 1967), bilingual edition. 18 Ludwig Wittgenstein, Philosophical Investigations, trans* G. E. M. Anscombe (Oxford: Basil Blackwell, 1953), bilingual edition.
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19Path. p. 17. 20 Philosophical Investigations, pp. 44-45e.
2*Path. p. 16. 22 Philosophical Investigations, p. 143e.
23Ib id ., p. 230e. 24 Path, p. 51. 25 Remarks, p. 99eff.
26Ibid.
27Ibid.
23Path. p. 56. 29 Remarks, p. lOOe; loc. c l t .
3^Path. p. 46.
31Path. p. 43.
32Ib id ., p. 43. 33 Remarks, loc. c l t .
34Path. p. 37.
35Path. pp. 44-45.
3^Path. pp. 40-1.
37Path. p. 54.
OQ Path, p. 19. 39 Philosophical Investigations, p. 194e.
40lb Id ., p. 207e.
41Ibid., pp. 208e-209e. 42 Philosophical Investigations, p. 226e.
43Path. p. 11, 15.
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44 Path, p. 16. 45 Philosophical Investigations, loc. c l t . ; Remarks, p. 166e.
46Path. pp. 35, 52, 53.
47Path. pp. 53-56. 48 Remarks, pp. 128e-129e. See also Philosophical Investigations. pp. 198e-199e. 49 Path, p. 61; le tte r to W illi Reich, May 3, 1941.
~^Path. loc. cit.. p. 62.
~^Jone. p. 42, 44; Path, pp. 52- 53. 52 Remarks, loc. c i t .
53Anton von Webern, Sketches (1926-1945). commentary by Ernst Krenek, foreward by Hans Moldenhauer (New York: Carl Fischer, 1968), plates 33-34. 54 Remarks, loc. c i t . 55 Path, pp. 65-66; letter to Willi Reich, February 23, 1944.
^Ludwig Wittgenstein, Zettel. ed. 6. E. M. Anscombe and G. H. von Wright, trans. G. E. M.' Anscombe. .Berkeley and Los Angeles: University of California Press, 1967), p. 31e.
~*7Z e tte l. p. 82e; Remarks. 130e-131e.
CO Path, pp. 9-10.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDICES
ANALYSIS BY LOGICAL LEVEL
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. INTRODUCTORY REMARKS TO THE APPENDICES
The four logical levels outlined in the third section of the
third chapter of the present study are applied to actual analyses
in these appendices. The general properties of the manifestation
of each level within the work as a whole are discussed first. The
way in which it is used in the course of the music is then discussed,
in the sequential order of the music. Structures relating to other
logical levels are mentioned when they affect the level under
discussion.
For each level, a work is chosen which seems to exemplify
Webern's use of that level. The large form of the first movement of
the Quartet, opus 28, is a powerful component of the total structural
configuration of that work. The row forms of the Trio, opus 20,
Webern's first large-scale serial work, seem to dominate the handling
of musical material. The developmental and variation techniques
used in the Variations, opus 30, seem to provide the bulk of that
work's structural coherence. The text of Webern's last completed
work, the Second Cantata, opus 31, is made musically comprehensible
largely through the use of articulation and timbre in the Klangfarbe
level of organization.
The definition of these logical levels, their entities, and
relationships with regard to the work analyzed constitutes no more
than the defined space postulated by the author, in which the
ratio n al structures occurring in Webern's late works can be examined.
151
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I t Is not presumed that Webern had these four levels consciously
in mind whenever he composed In his mature style.
Specialized terms are used In the appendices to clarify analytical
results. Their definitions are designed to make the employment of
these terms efficient In analysis, and may not correspond to meanings
associated with them In common usage.
"Large form" Is the overall stru ctu ral design of a work or
movement, usually conforming In some degree to a large traditional
structure such as fugue or sonata allegro. The components of such
structures, when used In Webern's late works, seem to determine the
work's configuration by motivating the formation of musical material
In ways which p arallel the functions of sim ilar components of
tra d itio n a l form.
A "motive" is a small musical entity which is used to generate
other entities. It may be subjected to "variation," or repetition
with some change in configuration. If the change affects the internal
configuration of the motive, it is called "metamorphic;" if it affects
the position of the motive in the context of the work, such as
retrograding, transposing, inverting, or otherwise shifting it about,
the change is called "transformal." When the motive is used with
its re p e titio n or with other motives to form a complex e n tity , i t is
said to undergo "superposition." Superposition can be used to
describe overlapping, simultaneous use, or sequential linking of
motives. "Intraversion" is a partial re-ordering of the motive; for
example, if the motive consists of two pairs of notes, reversing the
order in which the pairs appear.
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A "pattern" Is an aspect of a motive restricted to some portion
of sound such as duration, pitch, articulation, timbre, nuance,
Intensity, or some combination of such portions. This restriction
Is thought to be subject to conceptualization rather than to
measure of either the notated score or some manifestation in sound,
although such measure can serve as a basis of restriction. The
terms "variation," "metamorphic," "transformal," and "superposition"
apply in the same way to patterns as they do to motives.
The "voicing" of a pitch or group of pitches is its assignment
of octave, duration, articulation, and timbre. Voicing often
determines the structural prominence of pitches and motives, as well
as providing a basis for contrast and linkage among them. The
octave assignment of a pitch is its "registration." A pitch without
registration is called a "pitch class."
A "pitch aggregate" is a set of notes which are not defined by
sequential order, although they may appear in sequence. The "normal
form" of a pitch aggregate, as the term is commonly used, is its reduc tion, exclusive of registration, to an unique intervallic description.*
Fitch aggregates with the same normal form are related by transposi
tion, inversion, or inverted transposition.
An "adjacency" is a set of two notes occurring in close prox
imity. The term adjacency is also used to describe neighboring
pitch classes in a row form; for example, a "semitone adjacency"
in a row form would be two pitch classes, adjacent in the sequence
of the row form, whose smallest intervallic distance is a semitone.
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A "hexachord" Is a pitch aggregate of six notes; a "tetrachord,"
of four notes; a "trichord," of three notes; a "dyad," of two
notes. "Dodecaphonic concentration" is a complete set of the twelve
distinct pitch classes of the chromatic scale occurring in a
relatively small area, not given sequential definition. A "row
form" is such a set with sequential definition. The operations of
retrogression, inversion, and transposition link row forms together
in sets of forty-eight, as described in the preliminary remarks
of Appendix B.
Tables 1, 2, 3, and 4 provide row-form matrices for the works
analyzed in the appendices. Both numeric and alphabetic matrices
are given, in a one-to-one correspondence. Read left to right,
these matrices give the original row form; right to left, the
retrograde form; top to bottom, the inverted form; bottom to top,
the retrograde of the inverted form. To find a particular trans
position of these row forms, start with the numeric or alphabetic
pitch class desired to the left or to the top of the matrix. The
top line of each of these tables is thus both F 0 and R 0, and the
leftmost column of each matrix is both I 0 and RI 0. These tables
are included only for the convenience of the reader. With practice,
one should be able to proceed without their help.
The resemblances of the Quartet, opus 28, to Beethoven's
Grosse Fuge. and of the Variations, opus 30, to Brahms1s Variations
on a Theme by Havdn are striking and yield much structural informa
tion. For example, the fourth variation in the Brahms Variations
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TABLE I . ROW-FORM MATRICES FOR QUARTET, OPUS 28
0 11 2 1 5 6 3 4 8 7 10 9
1 0 3 2 6 7 4 5 9 8 11 10
10 9 0 11 3 4 1 2 6 5 8 7
11 10 1 0 4 5 2 3 7 6 9 8
7 6 9 8 0 1 10 11 3 2 5 4
6 5 8 7 11 0 9 10 2 1 4 3
9 8 11 10 2 3 0 1 5 4 7 6
8 7 10 9 1 2 11 0 4 3 6 5
4 3 6 5 9 10 7 8 0 11 2 1
5 4 7 6 10 11 8 9 1 0 3 2
2 1 4 3 7 8 5 6 10 9 0 11
3 2 5 4 8 9 6 7 11 10 1 0
Bb A GB Eb E C# D F# F Ab G
B Bb C# C E F D Eb G F# A Ab
Ab G Bb A C# D BCE Eb F# F
A Ab B Bb D Eb 0 C# F EG F#
FE G F# Bb B Ab A C# C Eb D
E Eb F# F A Bb G Ab CBD C#
G F# A Ab C C# Bb B Eb D F E
F# F Ab G BCA Bb D C# E Eb
D C# E Eb G Ab F F# Bb A C B
Eb D F E Ab A F# GB Bb c# C
CBD C# F F# Eb E Ab G Bb A
C# C Eb D F# G E F A Ab B Bb
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TABLE I I . ROW-FORM MATRICES FOR TRIO. OPUS 20
0 1 5 4 11 10 6 7 2 3 8 9
11 0 4 3 10 9 5 6 1 2 7 8
7 8 0 11 6 5 1 2 9 10 3 4
8 9 1 0 7 6 2 3 10 11 4 5
1 2 6 5 0 11 7 8 3 4 9 10
2 3 7 6 1 0 8 9 4 5 10 11
6 7 11 10 5 4 0 1 8 9 2 3
5 6 10 9 4 3 11 0 7 8 1 2
10 11 3 2 9 8 4 5 0 1 6 7
9 10 2 1 8 7 3 4 11 0 5 6
4 5 9 8 3 2 10 11 6 7 0 1
3 4 8 7 2 1 9 10 5 6 11 0
Eb E Ab G D C# A Bb F F# BC
D Eb G F# C# C Ab A E F Bb B
Bb B Eb D A Ab E FC C#F# G
B C E Eb Bb A F F# c # D G Ab
EF A Ab Eb D Bb BF# GC C#
F F # Bb A E Eb B CG Ab C# D
A Bb D C# Ab G Eb E B C F F#
Ab A C# C G F# D Eb Bb BE F
C# DF# F C B G Ab Eb E A Bb
c c # F E B Bb F# G D Eb Ab A
G Ab C B F# F C# DA Bb Eb E
F#G B Bb F E c c# Ab A D Eb
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TABLE I I I . ROW-FORM MATRICES FOR VARIATIONS. OPUS 30
0 1 4 3 2 5 6 9 8 7 10 11
11 0 3 2 1 4 5 8 7 6 9 10
8 9 0 11 10 1 2 5 4 3 6 7
9 10 1 0 11 2 3 6 5 4 7 8
10 11 2 1 0 3 4 7 6 5 8 9
7 8 11 10 9 0 1 4 3 2 5 6
6 7 10 9 8 11 0 3 2 1 4 5
3 4 7 6 5 8 9 0 11 10 1 2
4 5 8 7 6 9 10 1 0 11 2 3
5 6 9 8 7 10 11 2 1 0 3 4
2 3 6 5 4 7 8 11 10 9 0 1
A Bb c # CBD Eb P# F E G Ab
Ab A c B Bb C# DFE Eb F# G
FF# A Ab G Bb BD C# C Eb E
F# G Bb A Ab B C Eb D C# EF
G Ab B Bb A C C# E Eb D F F#
EF Ab G F# A Bb C# C B D Eb
Eb E G F# F Ab A c B Bb C# D
C C# E Eb DF F# A Ab G Bb B
C# D F E Eb F# G Bb A Ab B C
D Eb F# F E G Ab B Bb A C C#
BC Eb D C# E F Ab G F# A Bb
Bb B D C# c Eb E G P# F Ab A
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TABLE IV. ROW-FORM MATRICES FOR SECOND CANTATA. OPUS 31
0 9 1 2 10 3 11 7 8 A 5 6
3 0 A 5 1 6 2 10 11 7 8 9
11 8 0 1 9 2 10 6 7 3 A 5
10 7 11 0 8 1 9 5 6 2 3 A
2 11 1 A 0 5 1 9 10 6 7 8
9 6 10 11 7 0 8 A 5 1 2 3
1 10 2 3 11 A 0 8 9 5 6 7
5 2 6 7 3 8 A 0 I 9 10 11
A 1 5 6 2 7 3 11 0 8 9 10
8 5 9 10 6 11 7 3 A 0 1 2
7 A 8 9 5 10 6 2 3 11 0 1
6 3 7 8 A 9 5 1 2 10 11 0
A F# Bb B G C G# E FC#D Eb
CA C# D Bb Eb BG G#E FF#
6 # FA Bb F# B G Eb E C C# D
GE G# A F Bb F# D Eb B c c#
B G# Bb C# A D Bb F# G Eb E F
F# Eb GG# E A F C# D Bb BC
Bb G B C G# c # AF F#D Eb E
D B Eb E C F C# A Bb F# G G#
c # Bb D Eb B E C G# A F F# G
FD P# G Eb G#E C C# A Bb B
E C# F F# D G Eb B C G# A Bb
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Is In a minor key, while the remainder of the work Is In a major key;
the fourth variation of the Variations, opus 30 f is in a realm of
pitch relationships which is largely an inversion of the realm which
pervades the remainder of the work. Careful examination of such
resemblances is beyond the scope of these analyses, but it is hoped
that the reader will not disregard them as a consequence.
All of the works analyzed in these appendices have a common
characteristic which impedes strict analysis: certain shifts in pattern
which appear aurally to result from free composition can be shown to
derive from strict methods of construction. It seems that one cannot
always determine whether the apparently free result or the strict
method is the important factor of such a shift with relation to the
design of the entire work. The author thinks that a clear line
cannot be drawn between free and strict aspects of these works unless
it be drawn somewhat arbitrarily.
The analyses given here are not presumed to give a complete
description of the bewitching labyrinth of rational structure
characteristic of Webern's late works. The power of rational struc
tures to engender systems of relationships beyond those stipulated
by their creator is used in these works in form a multitude of
possible-structural conceptualizations. It is fascinating to
postulate a rational structure and trace its course through Webern's
late wbrks, with little regard as to whether Webern was conscious
of its presence. Sometimes, though, such a structure recurs so
prominently and with such persistence that one feels that its
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appearances cannot be accidental, or merely a consequence of some
other formal plan. The structures discussed here seem to be of
that type. However, other definitions and structural interpretations
of these works are always possible.
Certain structures in these works are given short shrift for
lack of space. For example, the highly interesting rhythmic patterns
of the Quartet, opus 28, are not discussed at all, and the ways in
which phrases are built in the Trio, opus 20, are mentioned only
in passing. The row-form relationships of the Variations, opus 30,
are somewhat disregarded in favor of those of smaller units, and
the discussion of the Second Cantata, opus 31, is principally
restricted to clearly audible structures.
Much of the formal design on these works is difficult to hear
in performance. Row forms do not, as a rule, coincide with audible
areas of dodecaphonic concentration or with motivic boundaries.
Many structures are masked deliberately by other structures, or
given multiple functions. Webern's music has been called "eye music,"
music not intended to be heard.
The author thinks that the existence of formal structures is
sufficient to provide the possibility of their audibility if the
performer chooses to emphasize them. Webern's late works provide
the performer with many opportunities for subtle interpretation by
the selection and balancing of these structures as a means of
expressing their intense musicality.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. These works seem to reveal themselves only gradually as one
patiently works with them and lives with them for many years. One1
appreciation for them seems to develop as one matures musically
under their influence, and this maturation appears to clarify and
enhance one's knowledge of the music of Webern's predecessors:
Isaac, Bach, Mozart, Beethoven, Brahms, and Mahler.
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FOOTNOTES
INTRODUCTORY REMARKS TO THE APPENDICES
*For a complete discussion of this and other terms In current use In the somewhat hermetic field of serial analysis, see George Perle, Serial Composition and Atonalltv: An Intro d u ctio n to the MUsic of Schoenberg. Berg, and Webern. 3rd edition, revised and enlarged (Berkeley: University of California Press, 1972) ; Milton Babbitt, "Set Structure as a Compositional Determinant.11 Journal of Music Theory V (1961); 72-94. For another example of the sort of arithmetic manipulation which is shown in Appendix B, deriving from the above discussions, see Donald Martino, "The Source Set and Its Aggregate Formations," Journal of Music Theory V (1961), pp. 224-73, and Hubert S. Howe, "Some Combinatorial Properties of Pitch Structures; Perspectives of New Music III (Fall-Winter 1968): 103-109.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX A
LARGE FORM: QUARTET. OPUS 28, FIRST MOVEMENT
Preliminary Observations:
The first movement of the Quartet, opus 28, appears to satisfy most
of the formal requirements of a triple fugue with countersubjects. Its
large form deviates significantly from that of scholastic fugue in two
ways. The pitch relationships of subject and answer entries are based
upon Intervals built on minor thirds Instead of perfect fifths. The
countersubjects are given such structural power that the expositions
appear to display not one set of subjects and answers, but two.
The term "subject" is applied to the first entry in each exposi
tion. The term "countersubject" is given to the first entry following
the subject which is neither the subject nor the subject's answer. The
third entry of the countersubject consistently anticipates rather than
follows the third entry of the subject. A good case could be made for
a reversal of this identification, or for the assignment of a term such
as "second subject" to the countersubject. Successful analysis of the
expositions does not seem to depend on assignment of terms, but upon
recognition of the clear manner in which subject and answers fu lfill
a strict, preconceived plan.
Rhythmic correspondences among the entries in the expositions do
not seem to be determined by the large form, but by immediate require
ments of complex entities, vertical intervallic correspondence, and
Klangfarbe structure. The free linear use of entries permits multiple
163
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structural Interpretation of the expositions on many levels. This
analysis Is principally concerned only with the level of large form.
The structures of all other logical levels seem to be subordi
nated in the large form. Row forms are used linearly, four at a time,
In the expositions, packed densely in the stretto, and used successively
at a time almost everywhere else. Strict imitative techniques are
used in the expositions, and metamorphlc variation prevails in the
Introduction, episodes, and coda. The stretto is characterized by in
tensive superposition of almost all of the motives which appear in the
work. The voicing In the expositions is such that the subjects and
answers are heard independently of each other. In other parts of the
movement, voicing tends to blur distinctions among motiv.ic entities,
especially in areas where canonic structures are dissolved.
The row form is highly degenerate. The retrograde inversion at
the major sixth is the exact equivalent of the original form. The
row i t s e l f c o n sis ts only o f th re e statem en ts of the B-A-C-H m otive.
As a consequence, every tetrachord of the row consists of four adjacent
semitones, and the set of forms is divisible into four sets, each con
taining six row forms with tetrachords of identical pitch content.
The B-A-C-H motive occurs only once in the e n tir e q u a rte t in i t s
customary form within the lim its of a minor third, in the third move
ment, measure 16.
A similar economy of means is used in the construction of other
small-scale structures. The lim itation of number and length of ideas
permits Webern to display the interrelationships he gives them with
great force and clarity. Rhythmic, lntervallic, and articulatlve
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patterns tend to be Interdependent. Expansion techniques occur princi
pally by elaboration of aspects already present in the motivic entity
instead of by insertion of new material, or by superposition and con
catenation of motivic entities. The introduction contains fragments
relating to all of the subjects, countersubjects, and the distinctive
features of the stretto and coda. The small patterns occurring in the
first measures anticipate all of the motives presented in the rest of
the introduction.
In the following discussion, the movement is divided into
six major sections: introduction, the three expositions together with
the episodes following them, stretto, and coda. This division should
clarify the reasoning which seems to govern the finely detailed con
struction prevailing throughout the movement.
Introduction (measures 1-32)
If, in this hall . . . a tuning fork or a well-tempered instrument began to vibrate, you would at once, as soon as you were affected by this pure and exceptional noise that cannot be confused with others, have the feeling of a beginning, the beginning of a world; a quite different atmosphere would immediately be created, a new order would arise, and you yourselves would unconsciously organize yourselves to receive it. The musical universe, therefore, was within you, with all its associations and proportions — as in a saturated salt solution a crystalline universe awaits the molecular shock of a minute crystal in order to declare itself ....
The first twelve measures of the movement constitute such a
declaration of a musical universe. They are knit into a large, fore
shortened arch. The rest of the introduction develops from the position
established by this arch to a state of musical intensity which can serve
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166
as a springboard for the first exposition.
The large arch Is divisible into three smaller arches of four
measures each. The second arch develop? and varies the patterns given
in the first arch, and the third arch bears a similar relation to the
second. Progressively shorter durations, and more frequent entries, and
more abrupt pitch extremes increase the intensity of the texture of
the third arch.
From a serial standpoint, the first arch is economically construc
ted. The second set of the twelve chromatic notes (Which does not cor
respond to the second row form, which overlaps the first) is so construc
ted that it is a retrograde, tetrachord by tetrachord, of the first set.
Only one note of the second set, Bb, occurs in a different part than
it does in the first set; all notes occur in the same octave in both
sets. The notes in the third set of twelve chromatic notes appear in
the same order, in the same parts and octaves, as they do in the first
set, in rhythmic dimunltion. Of ten simultaneous attacks occurlng in
the first arch, seven are minor thirds or tenths. /
Several new patterns are derived from superposition of the three
articulation patterns of the first four measures — two separated
notes, one separated note plus two slurred notes, and two slurred
notes. These patterns are superposed on each other to provide still
more patterns. For example, the articulation pattern occurring in
measures 7-8 anticipates the first countersubject; measures 10-11,
the second subject; 1-4, the pattern which will detrelop into the
third subject. The summation of the entries in measures 1-4 present
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a simple up-down melodic contour; In 5-6, the same contour In diminu
tion; 7-8, the contour In inversion; and In 9-12, the contour becomes
a zigzag, and potentially a source for the derivation of more Involved
melodic contour — for example, that of the first subject. The contrast
of pizzicato with sustained half notes recurs In the first exposition.
The superposition technique also provides for greater precision
in the voicing of combination of notes than might be obtainable from
other rational structures present. The viola's entry in measure 5
coinciding with the second of two slurred notes in the violoncello
completely changes the character of the slur and the effect of the last
note of the slur. Simultaneous pizzicati and slurred notes in measure
10 gives subtle emphasis to the traditional tendency of a downward
slur to give an impression of slackening tension. In measure 4, the
violoncello entry gives such an emphasis to the second slurred note
in the second violin part. In measure 11, in the corresponding portion
of the third row form, this emphasis is increased by the simultaneous
attack of the two entries. The simultaneous attack also serves as the
point from which the last small melodic curve of the large arch can
rebound.
These superposition techniques depend upon flexibility of vertical
correspondence; that is, unconstrained juxtaposition of motivic entities,
and free adaption of their internal rhythmic configuration to a given
situation. The possibilities of retrogression and inversion are also
assumed for motivic entities. It might be noted, in passing, that such
techniques are characteristic of polyphonic music during the time of
Heinrich Isaac, and that Webern had a thorough acquaintance with that
m usic.
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The large arch is followed by a short 'episode, measures 13-15, which
breaks the up-down melodic curve pattern.. Measures 16-32 are develop
mental in character and provide a musical and structural transition
to the first exposition.
The first row form of this developmental area maintains the
voicing of pitches established in the arch. However, the remainder
of this section contains only one more duplicate voicing (a span of
six row forms and seventeen measures). An almost constant forte pre
vailed throughout the arch, but in the developmental area piano,
sforzando, and fortissimo are used. The range of each part is increased.
Striking contrasts of range (measures 17 and 26), echoing the pattern
of slackening downward slurs, anticipate effects which will be prominent
in the stretto and coda.
New articulation patterns are developed through superposition.
Their length increases in preparation for the six-note first subject.
A striking new pattern, accented half note followed by two accented
quarter notes, is linked to both the first counter-subject and the
third subject. Parallel slurs (measures 19-31) anticipate those of the
second and third countersubjects. Reversals in intervallic direction
(measures 21 through 22), reflecting the melodic curve of the arch form,
will contribute to the development of the second subject.
Measures 16 through 21 anticipate the polyphonic form of an ex
position. The articulation pattern of a separated note followed by
two slurred notes, which played an important role in the arch, occurs
in all parts at least once. However, it is foreshortened rhythmically
in its last entry (second violin), and is followed by an unrelated
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passage of much lesser density. The pitch relationships among the
entries are not particularly promising. The first countersubject re
sults from the concatenation of this pattern with its retrograde.
The passage following this little exposition-like section anticipates
the first subject in its contour and texture.
The choice of series seems to anticipate the pitch relationship
of subject and answer in the first exposition. Motives are frequently
repeated or varied, the entry occurring at a minor third below the
original pitch level of the original motive, or a major sixth above
(violoncello, 17-20; second violin, 22-24; violoncello and first
violin, 29-30).
By the end of the introduction, the structural materials which
will be used in the fugue itself have all been presented. Wallace
McKenzie has pointed out to the author that this feature of the in
troduction might lead one to consider it as analogous to the exposition
of a classic sonata allegro form, where the arch represents the first
theme, and the developmental area with its small exposition as the
second theme and codetta.
First Exposition and Episode (measures 33-47)
In the following discussion, the subject is identified as . .
that pattern appearing in the second violin part, measures 33-34.
The countersubject i& then identified as that pattern in the viola
part, measures 34-37. These statements appear in Figure 1-.
The pattern of statements of the subject and its answers is as
follows: first statement of subject, second violin, measures 33-34;
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 1. Subject and Counteraubject of First Exposition, Quartet, opus 28
First Subject:
First Countersubject:
& b
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171
Its answer, first violin, measures 36-37. Second statement of subject,
altered, first violin, measures 39-40; Its answer, exact, violoncello,
measures 42-43.
The pattern of statements of the countersubject and its answers
is as follows: first statement of countersubject, viola, measures
34-37; its answer, second violin, measures 37-40. Second statement
of countersubject, violoncello, altered, measures 37-39; its answer,
viola, exact, measures 40-42. The second statement of the counter
subject precedes the entry of the first answer by a half note. Each
answer of the countersubject overlaps the countersubject by a half
n o te.
The countersubject's second statement precedes the second statement
of the subject. Neither the subject nor the countersubject appears in
all voices.
The subject and countersubject are strongly related. Their pitch
contents have the relation of retrograde inversion to each other. The
countersubject is an exact rhythmic augmentation of the subject. They
differ', principally in timbre and nuance pattern, the countersubject
being given a much more prominent effect by the articulation, timbre,
and other considerations of voicing assigned to it. For this reason,
the countersubject overbalances the subject when they are played to
gether. Because of the pattern of entries, subject material predomin
ates up to measure 37; countersubject material dominates measures
37-40; and subject and episodic material dominate the remainder of the
exposition. An up-down curve of Intensity results, which recalls the
intensity curve of the initial arch (measures 1-4).
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Subject and countersubject and answer pairs have a clear pitch
relationship. The answer always occurs a minor third below the sub
ject or countersubject which it answers. Since subject, countersub
ject and answers all have beginning:;and final notes separated by the
interval of a tritone, a diminished seventh aggregate is formed by the
beginning and final notes of each pair. Further, the exact pitches of
this aggregate are the same for the first subject-answer and first
countersubject-answer pairs, and also (a major second below) for the
second subject-answer and second countersubject-answer pairs. This
pattern of pitch relationships stands out particularly sharply because
tritones are not available from adjacencies in the row form itself.
The pitch content of all subjects, countersubjects, and answers
is six notes -- a B-A-C-H motive plus two additional notes, separated
by a semitone, at the distance of a major third from the last note of
the B-A-C-H motive. The first subject and first countersubject comprise
a single row form; so do the first subject's answer and the first
countersubject's answer, the second countersubject and the second sub
ject, the second countersubject's answer and the second subject's answer.
Entries belonging to the same row form are automatically hexachordally
combinatorial. Since the subject and countersubject are related through
inversion, it was not possible to make entries hexachordally combina
torial without losing the diminished seventh aggregate which provides
the fundamental pitch relationship. For this reason, entries which do
not belong to the same row form are not hexachordally combinatorial.
Slight alterations appear in the second entry of the subject and
countersubject, but the answers remain exact in every respect. The
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row forms used maintain the serial relationships set up In the arch.
The third row form retrogrades the first tetrachord and maintains the
order of the other two tetrachords of the first row form (P0- II ) .
The second and fourth row forms have the same relationship
(?9- I 10), where the last of the pair is the Inversion up a
semitone of the first of the pair. The transposition of the answer
to a minor third below Introduces an opposing tetrachord content to
that of the row form of the subject.
Throughout all expositions of the movement, row forms are used
linearly, one assigned to a part, with some voice-crossing. This
linear use is not found In other sections of the movement. At no
point in the first exposition do all four instruments play simultan
eo u sly .
As the small episode following the large arch broke up the
patterns of that arch, the episode following the first exposition
dissolves the structure of that exposition. The episode also prepares
the material for the second exposition by developing complex entities
and increasing the general intensity of the texture. The articulation
pattern which was used lm itatively in the introduction is developed
and used lmitatively here also.
The articulation pattern is used canonically, appearing in all
voices. Its first half, three strongly separated quarter notes,
derives from the subject. Its second half, two slurred notes followed
by a detached single note, derives from the countersubject. Its pitch
relationships vary greatly in the imitation, but rhythmic, articulative,
and dynamic configurations remain constant. Since it is linked
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structurally to material from both the first and second expositions,
It Is well suited to serve as transitional material between them.
The tail of the exposition and the eposode's opening is marked by
a rhythmic displacement of the meter, which is continued through the
episode. This displacement contrasts with the straightforward metric
pattern of the first exposition, and prepares one for the rhythmically
free second exposition.
A strong motivic statement in the second violin, answered in the
first violin, gives the impression of a false start to the second
exposition (measures 45 through 47). The first entrance of the second
exposition overlaps the answer (measure!47).
Second Exposition and Episode (measures 47-65) The subject of this exposition is identified as that pattern
appearing in the second violin part, measures 47 through 49. The
countersubject is then identified as the pattern appearing in the viola
part, measures 49 and 50. This identification yields an analytical
result which is consistent with the one obtained for the first expo
sition. These statements appear in Figure 2.
This exposition contains four subject-answer pairs instead of
two. They can be separated into two sets; the first set contains
answers at the pitch level of a fifth below, whereas the second set
contains answers a minor third below.
The entries for the first set of subject-answer pairs are as
follows: first statement of the subject, second violin, measures
47-49; its answer, violoncello, measures 49-52. Second statement
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 2. Subject and Countersubject of Second Exposition, Quartet, opus 28
Second Subject:
m
Second Countersubject:
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of the subject, first violin, measures 51-53; its answer, first violin,
measures 55-57.
The entries for the second set of subject-answer pairs are as
follows: first statement of subject, second violin, measures 51-54;
its answer, viola, measures 53-55. Second statement of subject, viola,
measures 57-60; its answer, first violin, measures 60-62. The imitation
in this set is varied by inversion of the pitch contour in the first
answer and in the second statement of the subject and its answer.
The entries for the countersubject-answer pairs are as follows:
first statement of the countersubject, viola, measures 49-51; its
answer, violoncello, measures 53-56. Second statement of the counter
subject, second violin, measures 55-58; its answer, violoncello,
measures 58-60. Both answers are pitch contour inversions of the
countersubject. The first answer is a minor tenth above, and the
second answer is a minor third below.
As in the first exposition, the countersubject's second statement
precedes the second statement of the subject (first set of pairs).
Every entry of subject, countersubject, or answer is covered by a
simultaneously occurring attack in another voice.
The subject and countersubject both consist of four notes,
slurred two by two. In the subject, the slurs are downward, then
upward; in the countersubject, both slurs are upward. The pitch
content is the B-A-C-H tetrachord for both subject and countersubject.
The rhythmic pattern is reversed in all answers thusly: the
duration of the first note of the subject or countersubject is assigned
to the third note of the answer; the duration of the second note, to
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the fourth; the duration of the third note, to the first; the duration
of the fourth note, to the second. In short, the second half of the
rhythmic pattern of the subject or countersubject appears as the first
half of the answer, and the first half appears as the second half of
the answer.
Fitch content of subject or countersubject and answer is not
duplicated. Where the answer is at the fifth below, the total pitch
content of subject or countersubject and anwer is disjunct; where
it is at the minor third, it li conjunct. The second statement
of the subject-answer pair of the first set is a major second above
the first statement of that set. The second statement of the counter
subject is a major second below the first statement of the counter
subject. This relationship parallels the major second distance between
first and second statements in the first exposition. The second
statement of the subject of the second set is a major fourth below,
and the answers of that set both begin on the same pitch but continue
in inversion to each other.
All row forms in this exposition are used tetrachord by
tetrachord. Thus, each form contributes three statements of subject,
countersubject, or answer. The choice of row form seems to be de
termined by the entry pattern and Internal configuration of statement
d e sire d .
The row form used consists of six pairs of adjacent semitones.
The row forms used can therefore be separated into two sets of
twenty-four forms each, with a distinct semitone adjacency pattern in
each set. Throughout this exposition, at least one row form from each
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of these sets Is present. Then, at any point, Webern has access to
any semitone adjacency he may wish to use. There Is a heavy concen
tration of neighboring E's In measures 55-57, adjacent F's In
measures 57-58, simultaneous C#'s In measure 58, and adjacent G#'s
In measure 60. This deliberate favoring of pitches anticipates
serial techniques used In the stretto to come.
The B-A-C-H m otive which Is the b a sis fo r a l l su b je c ts , co u n ter
subjects, and answers Is used In the original form and retrograde.
Inversion of the motive yields the retrograde form, and retrograde
Inversion yields the original. The two adjacent semitone groups of
the motive are Invariably voiced as slurred major sevenths or major
ninths. When the slurs are In different directions, the Intermediate
minor third Is usually voiced as a third. When the slurs are In the
same direction, as they are In the countersubject, the minor third
Is usually voiced as a sixth.
The first statement of the subject, first set, is the only
subject or answer statement of the first set which is not a retro
grade of the B-A-C-H motive. All statements in the second set are
the original form of the motive. Countersubject statements are
original form, and their answers are retrogrades.
The first and second statements of the subject in the first
set end on the same note; so do the first and second statements of
the countersubject. The beginning and ending notes of the subject
statements of the second set, and the first answer, are adjacent.
The second answer of this set has the same beginning and final
notes as the first statement of the subject, first set.
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The sustained, fluid nature of the subject and countersubject
lends itself well to varied superpositions. One of the most effective
of these is as follows: a half note or a whole note, of more than
usual intensity and quite often the upper note of a two-note slur,
is reinforced at another pitch a beat after its entrance by a some
what lower, similarly Intense note which is the first note of a
two-note slur. The result is that the weight of the first note,
which would naturally diminish after its initial attack, is main
tained or even increased without a crescendo on that note. The
steadily increasing frequency of entries, together with this device,
results in a building up of intensity throughout the section.
Superposition of sustained notes results in a particularly
striking pair of phrases in measures 51-54. The vertical cor
respondence given are so planned that these phrases are set off from
the rest of the material not by the boundaries of entries, but by
rests occurring in the middle of entries. Fitch intervals of major
thirds and minor sixths predominate. The major ninth in measure 52
i s g ra c e fu lly "re so lv e d " to a compound minor th ir d , and th e second
phrase ends with a minor third.
The contour inversion of the subject-answer entry appearing in
the viola, measures 53-55, is apparently a consequence of the pitch
contour and voicing requirements of the second phrase. The first
note of this entry completes G-Bb-D and D-F£*A triads, and its
second note, and F^A-C# triad. The harmonic implications of these
triads are masked by unusual voice-leading relying on common tones
and large leaps, low dynamic level with unartlculate pitch changes,
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and resolution to a harmonically unrelated tone at a lower pitch level
In measure 54, the Eb In the violoncello part.
The preceding phrase, measures 49-50, and the following phrases,
measures 54-58, show a similar construction but are more dissonant in
intervallic content. The last entry of the exposition, in the
violoncello, measure 58, is masked by a sustained note at the same
pitch in the viola. This masking is one of the first appearances
of a doubling device which gains in structural importance in the rest
of the movement.
Like the first episode, the second episode fragmentizes the
material of the preceding exposition and develops it in preparation
for the following exposition. Statements of the subject and counter
subject appear in rhythmic alteration. A steadily decreasing dynamic
level, a massive ritardando, and smooth texture reduce the overall
effect of intensity considerably. Thus, an intensity curve for the
division consisting of second exposition and episode again reflects
the intensity curve of the initial arch (measures 1-4).
The statements in the episode do not appear in clear canonic
sequence. The first such statement occurs simultaneously with the
last answer of the exposition, has identical pitch content with
that answer, and reverses its beginning and final notes. The author
thinks that it cannot be established definitely from structural
relationships alone which of these two statements is in fact the
real answer of the exposition.
The episode ends with the first rest in all parts since the
beginning of the first exposition. The quiet entrance of the subject
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of the third exposition Is thus prepared.
Third Exposition and Episode (measures 66-79)
The subject Is Identified as that pattern occurring In the first
violin part, measures 66-68. The countersubject Is then Identified
as that pattern In the second violin part, measures 68-69.
These statements appear In Figure 3.
The pattern of subjects and their answers Is as follows: first
statement of subject, fist violin, measures 66-68; Its answer,
viola, measures 67-68. The second statement of the subject, first
violin, measures 68-70; its answer, viola, measures 68-69 (altered).
Third statement of the subject, first violin, measures 71-73; its
answer, viola, measures 72-73.
3Vo additional subject-answer pairs appear in the third episode
as follows: first statement of the dubject in episode, second violin,
measures 73-75; Its answer, viola, measures 74-76. Second statement
of subject in episode, second violin, measures 76-77; its answer,
measures 77-78. These additional pairs duplicate the pitch content
of the first two pairs of entries of subject-answer in the expo
sition. The pitch contour of the pairs in the episode closely dupli
cates that of the exposition pairs; the second note is transposed
down an octave in two entries and the first note is transposed up an
octave in another, so that each entry in the episode begins with
either the interval of a major seventh or a minor ninth.
The pitch level of the subject-answer entries in the exposition
and episode appears to be significant. Three cycles of major third
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 3. Subject and Countersubject of Third Exposition, Quartet, opus 28
Third Subject:
A | qrco______«pVfff o t-1 p^ I=j=&
Third Countersubject:
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progressions appear, and the episode concludes with the completion
of the last cycle. The first cycle begins with the first note of
the first entry of the subject, Bb, Is followed by the F# entry In
measure 68, f i r s t v io lin , D entry In measure 71, f i r s t v io lin ,
concluded by the first note of the first entry of the episode, Bb
In second violin, measure 73. The other two cycles are C-G#*E-C,
and Eb-B-G-Eb. The notes missing from these cycles, F-A-C#, do not
appear to have structural significance In this division.
The pattern of countersubject-answer pairs Is as follows: first
statement of countersubject, violoncello, measures 67-68; Its answer,
second violin, measures 68-69. Second statement of countersubject,
violoncello, measures 70-71; Its answer, second violin, measures
71-72. Third statement of countersubject, viola, measures 72-73;
if an answer exists, it is defined by pitch content only, for no
additional motivic entity corresponding to the configuration of the
countersubject follows.
The end of the third statement of the countersubject may be
said to mark the end of the exposition. If so, the quarter rest in
all parts at the beginning of measures 74 divides the exposition and
episode.
This section displays the most varied pattern superposition yet
incountered in the movement. Dynamic contrasts of brief duration ap
pear for the first time since the introduction. Of particular interest
is the manner in which p iz z ic a ti notes in the subject in teract with
slurs in the countersubject. They reinforce the low note of the
two-note slur, a retrogression of the effect noted in the second
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exposition; but here the p iz zica ti can only give an added punch to
the attack, instead of intensifying the duration, as it did pre
viously. The pizzicati mock the effect of the falling and rising
slurs, preparing material for the stretto. Like the second episode,
the third episode is dissolved not by less frequent events, but by
a slackening of tempo and decrease of dynamic level. The final
pianissimo "am Steg," muted, recalls a similar effect in measure 65,
I at the end of the second episode. Nearly two measures of silence
following the episode contrast with the sudden changes of Intensity
and rhythm which characterize the stretto.
Intensity curves for the three expositions and episodes could
be described as follows: first exposition, up-down curve; first
episode and second exposition, steadily increasing in ten sity ; second
episode decreasing intensity; third exposition and episode, decreasing
intensity, through an up-down curve. The intensity curve pattern for
the expositions and episodes then parallels that of the introduction.
Stretto (measures 80-96) The subjects and countersubjects appear only as superposed
patterns. The first four measures contain the original pitches of
the first entry of the first subject in correct sequence, beginning
with the pizzicato A in the viola part, measure 80, and extending
from one part to another to the Db in the viola part, measure 83.
The original pitches of the second subject are,presented, beginning
with the A in the violoncello part, measure 81, extending to the B
in the second v io lin , measure 82. The pitch content of the third
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Fig. 4. Statements in Stretto, Quartet, opus 28
First Subject:
-6 — e - i m i ^ v fc m ik ;
Second Subject: vl< vln 3iz : £
vln I
Third Subject: m Sp m m
_ First Cpuntersub ject: vln ^ vln 1 J/Jnl f e r p i /3 jy I ------3 - v 1 J .
v k I v ? — — b p * 1 - .....-
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subject overlaps that of the second subject. The third subject's
original pitches are stated, beginning with the Bb in the first
violin part, measure 81, extending to the same B in the second
violin part which ends the presentation of the second subject.
A statement of the original pitches of first countersubject
begins with the Bb in the violoncello part, measure 87, ending with
the E, measure 92, in the same p art. The pitches of the second
countersubject appear, beginning with F# in the first violin part,
measure 91, continuing to the 6 in measure 93, second violin part.
The third countersubject is not as clearly stated as the others;
its original pitch content may be said to begin with the Eb,
viola p art, measure 83, continuing to the D, second v io lin p art,
measure 85. These statements appear in Figure 4.
Although it is possible to find configurations corresponding
to'the original pitch content of the answers, these configurations
are not clear. Their presence may be due to the extreme degeneracy
of the row form used, and excessive overlapping of row forms in th is
section.
Single pitches are given emphasis by repetition within a short
time span, or by doubling. In measure 81, A is repeated; in the
following measure, C; the following measure, D; measures 85-86, F;
measure 87, Bb; measure 88-89, B; measure 90, unison C; measure 92,
unison F; The author sees no pattern in this sequence of pitches
which relates to the pitch structure of the movement.
The complete absence of slurs makes it possible for a given
note to belong to not only one, but many statements of subject,
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countersubject, or answer. As the stretto progresses, there Is a
complete absence of disjoint thematic patterns. The device noted
previously of sustaining intensity with fresh attacks in another part
is used again, but now reinforcements are themselves reinforced.
Notes are not merely separated, but forcefully attacked to emphasize
their separation. Falling and rising intervals are canonically
imitated at close range, which exaggerates contrasts of range. The
density and intense voicing of the section contrast with the muted
passages which surround it.
Coda (measures 96-112)
This section differs from the rest of the movement in several
respects. The texture is almost completely homophonic. Hie tetra-
chords of the row are not emphasized, and at most three consecutive
notes of the row form appear in any given voice. Control of pitch
content is not directly related to statements of subjects, counter
subjects, or answers. Voicing, dynamic level, and nuance seem to be
unconstrained by rational schemes.
The pitch content in measures 96-99 is a retrograde of that
in measures 2-4, the last half of the initial arch. The final bars,
measures 110-112, repeat this pitch content in the same order as in
measures 96-99. This pitch content also appears in the opening
measures of the th ird movement.
Doublings and repeated notes are frequent. In measure 98, C#
is doubled; 99, E is doubled; 100, F repeated; 101, F# doubled;
103, A and C doubled; 105, B repeated; 106, D repeated, 107, F
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repeated; 110, Bb repeated; 111, C# repeated. In th is sequence of
repeated or doubled pitches, Intervals of a minor third predominate.
One could possibly say that the nuance pattern of the first
countersubject opens the coda, and that the pitch content of that
pattern Is reminiscent of that countersubject. However, the author
thinks that this relation Is not sufficiently definite to be asserted.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. FOOTNOTES
APPENDIX A
1Paul Valery, The Art of Poetry, trans. Denise Folliot (Princeton: Princeton University Press, 1958), p. 67. This book is volume 7 of The Collected Works of Paul Valery, edited by Jackson Mathews, Bollingen Series XLV, various dates.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX B
SERIAL PITCH ORGANIZATION: TRIO. OPUS 20
Preliminary Remarks:
An Investigation of the motivic structure and the ordering of row
forms Indicates that the Trio, opus 20, consists of two movements
whose large forms have some resemblance to sonata allegro form. The
first movement may also be Identified as a rondo, or as a sequence of
arches, and Its adherence to the sonata allegro form Is not rigorous.
The second movement Is an almost completely orthodox sonata allegro
movement. It displays a slow Introduction, correct pitch relation
ships, contrasting thematic material, and even a device corresponding
to the traditional "pounding of the dominant" just before the
recapitulation. The last measures of the first movement anticipate the
beginning of the second movement, and the la st measures of the second
movement recall the beginning of the first movement. The tetrachordal
structures emphasized are used to strengthen this interrelationship.
In the first movement, row forms are used successively, never
simultaneously. Their ordering suggests strongly that they were chosen
for their properties of interrelationship. In the second movement, row
forms are used simultaneously and in linear combination. The choice
of row form seems to depend on properties of small portions of i t which
permit repetition or variance of pitch aggregates or sequences, or
which can be combined with other forms to produce pitch patterns not
obtainable from the row forms permitted.
190
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In the first movement, motivic patterns are interdependent,
derived rather obviously from common material. In the second move
ment, the motivic patterns are much more highly developed, contrast
strongly with each other, and exist in a much wider variety than in
the f i r s t movement.
One could almost make the generalization that the first move
ment is the primitive working out of the ideas which give the Trio
its coherence. On the other hand, the second movement presents
these ideas on a more sophisticated, more intricate level. The pitch
structure.of the work seems to provide an opportunity to observe the
ways in which Webern attained mastery over twelve-tone technique.
Interrelationships of the Row Forms Used In order to understand what is actually happening on the pitch
serial level in the Trio, the author thinks it is essential to in
vestigate the possibilities inherent in the basic row form itself,
and i t s relationship to the other forty-seven permissible row forms
which are relatedaunder the operations of retrogression, inversion,
and transposition. To simplify the process of computing these
relationships, the following notation is used:
Each pitch' class is represented by a residue class of N/(12)
as follows:
Eb = 0, E = 1, F = 2, . . . , D = 11.
Note that the integer representing each pitch-class measures its
distance from Eb in semitones; thus, the interval of Eb to A can
be represented as 6.
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A row form Is then notated as a sequence of twelve numbers
from 0 to 11, each number appearing only once. To transpose a
row form, add a number corresponding to the number of semitones
contained In the musical interval of transposition. Thus, If one
wants to transpose P 0 up a major th ird , he would add 4, since
a major third contains four semitones, to each number of P 0.
All addition, of course, must be subject to modulo 12; that la,
If a number greater than 12 la obtained, 12 or multiples of 12
are subtracted from I t u n til a number between 0 and 11 Is obtained.
Similarly, if a number less than 0 is obtained, 12 or multiples
of 12 are added until a number between 0 and 11 Is obtained.
Inversion of a row form takes two steps. First, every number
of the row form Is subtracted from 12. Then, one must add twice
the number value of the f i r s t number of the transposed row form
desired. Thus, I f one wanted to obtain I 4 from P 2, I 10 would
be obtained f i r s t by subtraction, and then the re s u lt would be
transposed to the level of I 4. Alternate algorithms for Inversion
e x ist, and can be found with a l i t t l e practice.
The process of retrograding the row form reduces Itself to
w riting down the numbers In reverse order. Then P 0 and R 0 are
Identified with the same numerical sequence.
It can be shown that If any two twelve-note series have a
certain relationship or similarity, this relationship will remain
relatively the same If both forms are Inverted, retrograded, or
musically transposed to the same degree. This statement carries
an additional condition that the axis of Inversion be specifically
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193
defined.
In ahort, this statement says that, given any two row forms, soy
R I 1 and R 6, successive operations w ill not change th e ir re la tiv e
sim ila ritie s. Retrograding both forms yields I 1 and P 6, and
transposing both to the same level yields I 7 and P 0. If the basic
row form of the Trio is used for these row formg, a ll of these pairs
are hexachordally combinatorial.
The mathematical proof of this remarkable property can be per
formed e ith e r by considering a row form to be a permutation of integers
modulo 12, or by considering i t as a step function. In e ith e r case,
the proof rests on two characteristics of the system of classic
twelve-tone technique. The first of these characteristics is that
any of the permissible operations or any combination of these opera
tions,, applied to any set: of forty-eight row forms generated according
to the rules of this technique} yields precisely the same forty-
eight forms. The second characteristic is that all variants produced
by any one of these operations form a mathematical cyclic group. The
group consisting of the products of these operations is one of
relatio n sh ip s, not of elements, for no row form need be taken as
an identity element. The operations of retrograde and inversion each
haver period 2, and the operation of transposition has period 12.
The operations do not commute under ordinary conditions, although
the row form sequence generating the set of forty-eight forms may
be such that some of the forty-eight forms are duplicates of each
other, and the structure of the large group is, as a result,
degenerate.*
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Transpositions of the basic row form are called Prime, and are
represented by the Symbol P n, where n equals the Integer value of
the first pitch class of the row form. Thus, P 0 Is the first row
form of the Trio; P 6 Is Its transposition by a tritone, beginning
on A.
Transpositions of the retrograde are called R n, where n equals
the Integer value of the last pitch class of the row . This system
of numbering simplifies identification of row characteristics,
because R 0 will have similar invariant and aggregate patterns to
P 0 as is so clearly evidenced in the opening measures of the Trio ..
Further, P 0 retrograded is exactly R 0, and R 0 retrograded is
exactly P 0.
Transpositions of the inversion are called I n, where n equals
the integer value of the f i r s t p itch class of the row. This number
ing, as will be shown later, presents some computational problems,
but the ease of spotting relationships between row forms is more
than ample compensation. The inversion of I n is, of course, P n.
R I n is considered the retrograde of any I n, and is numbered,
as are the other retrograde forms, by the last pitch class of the
row. The retrograde inversion of R I n is P n; its inversion is
R n; and its retrograde is I n.
It can be shown that if the row numberings are so defined, and
a relationship can be proven to exist between two row forms, and
these forms are operated upon in the same manner by the above
operations, or if they are transposed by the same integer value,
the relationship will hold. For example:
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It is known that P 0 is hexachordally combinatorial with I 7.
In the second movement, R I 1 and R 6 occur simultaneously. Is
this latter pair of rows hexachordally combinatorial?
R I 1 : R 6 as I 1 : P6 as I 7 : P 0.
And R I 1 is shown to be hexachordally combinatorial with R6.
It is then immediately apparent that it is of the utmost
importance to discover the relationships of all the permissible
row forms to one of them do that these.relationships can be applied
to all possible pairs of these row forms. It is immaterial which,
rowform is taken as the point of origin, but to .po designate the
f i r s t row form of the work has become customary.
The first row statement of the Trio is as follows:
0154 11 10 672389
Eb E Ab G D C# A Bb F F# B C
The following semitone adjacencies occur:
01 23 45 67 89 10 11
Eb E F F# 0 Ab A Bb B C C# D
All of these semitone adjacencies have the same normal form,
0 1; and all are the result of transposition by an even integer.
As a m atter of fa c t, a ll the residue classes modulo 12 which are
even integers transpose the form 0 1 into one of these adjacencies.
We can thus deduce that the adjacency 0 1 appears in all even
transpositions of prime (P 2 n) if the ordering of the adjacency
is disregarded. The retrograde of 0 1 is 1 0, which has the normal
form of 0 1 also; thus, by a similar process, it is deduced that,
order disregarded, 0 1 also appears in all even transpositions of the
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retrograde form. The interval (2 3) or T 2: (0 1) then appears in
all even transpositions of prime and retrograde; and one can eventu
ally deduce that all these and no other semitone adjacencies will
be found in all even transpositions of prime and retrograde. Any
odd transposition of (0 1)will produce a semitone adjacency that
does not fall into that pattern: 1 2, 3 4, 5 6, 7 8f 9 10, 11 0.
Since it is known that all even transpositions of prime and retro
grade contain like semitone adjacencies, it is clear that those
row forms produced by transposing all of the even transpositions
of prime and retrograde by the same integer will have the same
semitone adjacencies, and that these adjacencies, in the case of
an odd transposition, are
12 34 56 78 9 10 11 0
E F F# G Ab A Bb B C C# D Eb
Therefore, it can be generalized that all odd transpositions of the
prime and retrograde have the same semitone adjacencies, but none
of the semitone adjacencies present in the even transpositions of
prime and retrograde.
On the other hand, the inversion of the row presents the same
intervals as the prime, with their order reversed; that is a rising
semitone becomes a falling semitone. Thus, the inversion of our
row form must have the same characteristics of semitone adjacency
as the prime; and also,
P 0 : P 2 as 10:12 and P O : R 0 as I 0 : R I 0.
Thus it is inferred that all even transpositions of the inversion
and retrograde inversion contain the same semitone adjacencies;
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but which? The first two pltch-classes of I 0 are (0 11); It Is
Inferred as In the case of the prime set, that (0 11) appear In
all even transpositions of the Inversion and retrograde Inversion,
and similarly, that even transpositions of (0 11) also appear In
these forms. Thus, the pattern of semitone adjacency In the even
transpositions of the Inversion and retrograde Inversion Is the
same as It Is In the odd transpositions of the prime and retrograde,
further, since
P 0 : ? 1 as I 0 : I 1, P 2 : F 3 as I 2 :I3, . . .
that Is, containing the opposing semitone adjacency, odd trans
positions of the Inversion and retrograde Inversion contain the
semitone adjacency of the even transpositions of the prime and
retrograde. Each of the forty-eight row forms thus conforms to
exactly one of these semitone adjacency patterns. One need find
only one semitone adjacency within a row form to know what the other
five must be, since the two sets of semitone adjacencies are •
mutually exclusive. In fact, even transpositions of the prime form
and odd transpositions of the inversion, with their retrogrades,
are mathematically speaking even permutations of the basic row form.
Odd transpositions of the prime, even transpositions of the inver
sion, and their retrogrades are odd permutations of the basic row
form.
Next, possible trichordal structures are examined. When they
are reduced to normal form,
015 016 045 056 (pitch order disregarded)
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the third Is an inversion of the first, and the fourth is an in
version ofthe second. Therefore, some inversion row form exists
in which thecontents of the first trichord of F 0 is found in the
third hexachord, and the contents of the second trichord similarly
w ill be found in the fourth hexachord of some inversion row form.
The actual pitch-class content of the trichords of P 0 is now
examined:
0 1 5 10 11 4 2 6 7 3 8 9
Eb E Ab C# D G F A Bb F# B C
(pitch order disregarded)
The last two trichords of I 0, found by taking the inverse, modulo
12 of each pitch class, are:
10 6 5 9 4 3
C# A Ab C G F#
(In ascending order: 5 6 10 3 4 9)
Now, if the content of the third trichord is to equal the content
of the f i r s t hexachord of P O, 7 must be added to each pitch-class
(that is, transposed by a perfect fifth): 5 plus 7 is 0; 6 plus 7
is 1; and 10 plus 7 is 5 (addition modulo 12). Adding 7
to the fourth trichord of I 0 yields the same result, and in inves
tigating trichordal relationships one stumbles upon the more im
portant hexachordally combinatorial relationship. The operations
that were used were inversion and transposition by the integer 7.
Thus, I 7 is the form desired:
17: 7 62 389 105 4 11 10
Bb A F F# B C E Eb Ab G D C#
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P 0: 0 1 5 4 11 10 6 7 2 3 8 9
Eb E Ab G D C# A Bb F F# B C
Moreover, with the exception of the intraversion 1 0, the pitch-
class ordering of the second hexachord of 1 7 duplicates that of
the first hexachord of P 0; similarily the pitch-class ordering of
the first hexachord of I 7, excepting the intraversion 7 6, duplicates
that of the second hexachord of P 0. The content of trichordal as
well as hexachordal pitch aggregates is unchanged.
P 0 is always hexachordally combinatorial with R 0, regardless
of the basic row form selected. Are there any other such relation
ships between our P 0 and another form?
The normal form of the hexachords of P 0 is:
0 1 2 3 6 7 01238 9.
Since the normal forms are unequal, no transposition of prime can
reverse the content of the first and second hexachords.
The normal form of the hexachords of R I is :
012367 01238 9.
Since the normal form of the f i r s t hexachords of P and R I are
equal, the normal forms of th eir complements (the second hexachords
of P and R I) are also equal. Again, there is no transposition of
R I in which the content of the first hexachord of P 0 can appear
in the second hexachord of the new row form.
Therefore, it is concluded that the only hexachordally c o m b in
atorial relationships among our selected row forms correspond to the re
lationships P 0 : R 0 and P 0 : I 7. The following analysis shows
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that these relationships are of great structural Importance in the
Trio. They are generalized as the arch concept, and give reason for
transposition of entire sections at the interval of a perfect fifth.
The tetrachords of P 0 have the normal form,
0145 0145 0167
Since the normal form of the inversion of O 1 4 5 is also
0 1 4 5, it is apparent that the pitch-class content of the
first tetrachord can be found in the second tetrachord of a trans
position of P 0, and also that of some inversion. In this case,
the retrograde and retrograde Inversion row forms with this property
w ill be retrogrades of the prime and inversion row forms which
are sought.
The actual pitch-class content of the second tetrachord of P 0
i s :
6 7 10 11
A Bb C# D
Transposition by the addition of the integer 6 (tritone) gives the
desired result; and, since the actual pitch-class content of the
first hexachord is 0 1 4 5, this transposition also results in
the contents of the second hexachord of P 0 being transferred to the
first hexachord of the new form; moreover, transposition by the
integer 6 will not change the content of the third hexachord:
P 6: 6 7 11 10 5 4 0 1 8 9 2 3
A Bb D C# Ab G Eb E BC F F#
P 0: 0 1 5 4 11 10 6 7 2 3 8 9
Eb E Ab G D C# A Bb F F# BC
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Using the same procedures as used in investigating trichordal
structure, it is determined that I 11 gives a similar distribution:
11 10 6 7 0154 9832
D C# A Bb Eb E Ab G C B F# F
Note that the ordering of the first two tetrachords is preserved
in this form, and that the last tetrachord is retrograded.
Another tetrachordal grouping is of importance in the Trio,
the normal form being as follova by tetrachordal grouping:
0 1 0167 0145 0 1.
The third tetrachord of P 0 may then appear as the first full
tetrachord of the new form, while the first or the second tetra
chord of P 0 would appear as the second full tetrachord of the
new form:
P 4: 4 5 9832 10 11 67 01
G Ab C B F# F C# D A Bb Eb E
Using this grouping, P11 can be arranged as follows:
P 6: 67 11 10 54 0189 23
A Bb D G# Ab G Eb E B C F F#
Obtaining new pitch-class values for the stressed tetrachords, we
can "modulate" through this form to
P 8: 8910 7623 10 11 45
B C E Eb Bb A F F# C# D G Ab
Obviously, the same result can be obtained with pitch-class content
transposed to different tetrachords by regrouping P 0 and "modulat
ing" to P 2. Further, one could regroup P 2 and "modulate" to P 4,
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repeat the process from P 4 to P 6 and thus return to the original
tetrachordal pitch-class content. Thus, the relationships among
the even transpositions of the prime which are discussed above
in a broad sense are more sharply brought into focus. Under the
same conditions of transposition and regrouping, these relationships
will also hold for any series of odd or even transpositions of a
prime, retrograde, inversion, or retrograde inversion.
The closest relationship of tetrachordal ordering is found
between a row form and its inversion transposed up a major seventh
(integer value 11) :
P O : 0154 11 10 67 2389
P 11: 11 10 67 0 154 9832
The first two tetrachords occur, in reverse order, with the same
pitch class content and ordering; the third tetrachord is exactly
retrograded.
The tetrachordal and semitone adjacency systems of odd and even
permutations of the basic row form used in the Trio exhibit pre
cisely the same internal relationships, as described above, but are
mutually exclusive. Tetrachordal links between these two systems
exist, based on the presence of dyadic invariants other than that
of a semitone within the tetrachords considered. Within either
system, such a dyadic invariant will imply tetrachords of like
content, because each pitch class is uniquely, inevitably associated
with another pitch class a semitone away. A dyadic invariant of
this type between two row forms which do not belong to the same
system implies unlike tetrachordal content:
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P 0: 5 4 11 10 P 8: 10 11 4 5 but
P 7: 3 4 11 10
yet the two common members of the tetrachords of P 0 and P 7 can
be used as a link between these row forms, If the pitch-classes in
volved are favorably voiced.
In Figures 5, 6 and 7, adjacent dyadic invariants are not
enclosed in parentheses; dyadic invariants occurring within a
tetrachord, but whose members are not adjacent but occupy correspond
ing positions in the row forms considered, are enclosed in
parentheses.
Figure 5 shows following intervals which occur in P 0 and
th e ir invariants under the above conditions: 1 5, 4 11, 10 6,
7 2, 3 8, and the tritone (3 9) which is not an adjacency but
generates one of the basic tetrachordal forms. Retrograde forms,
of course, contain identical adjacency patterns with reversed pitch
order; they are, therefore, omitted from this table.
The tetrachordal structure relationships occurring among even
transpositions of prime forms, discussed above, are supported by
the evidence of this table; P 6 has four possible tetrachords in
common. The interval 3 9 is not considered here, because
is inevitably related to 3 8 in even permutations, as an examination
of the possible row forms shows. The relationships of inversion
row forms tp P 0 is shown in Figure 6.
Dyadic invariants which are adjacent between two row
forms which are both odd or both even imply not only identical
pitch-content of the tetrachord aggregates involved but also that
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Pig. 5. Dyadic Invariant Relationships, Prime Row Forms, Trto, opus 20
P 0: 1 5 4 11 10 6 7 2 3 8 (3 9)
P 1: (1 5) 8 3 (3 9)
P 2: (4 11) (2 7)
P 3: (10 6) 7 2 (3 8)
P 4: (10 6) 8 3 (9 3)
P 5: (4 11) 6 10 (7 2) (9 3)
P 6: (5 1) (11 4) (6 10) (8 3) (9 3)
P 7: 5 1 (9 3)
P 8: 11 4 (7 2)
P 9: 4 11 - (2 7) (8 3)
P 10: (5 1) (3 8) (3 9)
P 11: (5 1) (11 4) (10 6) 2 7 (3 9)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 6. Dyadic Invariant Relationships, Inversional Row Forms, Trio, opus 20
P 0: 1 5 4 11 10 6 7 2 3 8 (3 9)
I 0: (1 5) (6 10) (7 2) (9 3)
I 1: (1 5) (4 11) (6 10) (2 7) (8 3) (9 3)
I 2: (3 8) (3 9)
I 3: 11 4
I 4: (4 11) 6 10 (2 7)
I 5: (5 1) (6 10) (3 8) (3 9)
I 6: 5 1 11 4 2 7 (3 9)
I 7: (1 5) 4 11 (7 2) 3 8 (3 9) I 8: (8 3) (3 9)
I 9: (4 11) 2 7
I 10: (11 4) (10 6) 7 2 3 8
I 11: 1 5 10 6 8 3 (9 3)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 7. Tetrachordal Invariant Relationships, Trio, opus 20
p 0, I 1, R 4, R I 9 0 1 4 5 (0 1 8 9)
p 2, I 3, R 6, R I 11 0 1 6 7 (2 3 8 9)
p 4, I 5, R 8, R I 1 0 1 4 5 (4 5 8 9)
p 5, I 6, R 9, R I 2 0 1 3 4 (5 6 8 9)*
p 6, I 7, R 10, R I 3 0 1 2 3 (6 7 8 9)
p 7, I 8, R 11, R I 4 0 1 1 2 (7 8 8 9)*
p 8, I 9, R o, R I 5 0 0 1 1 (8 8 9 9)
p 9, I 10, R 1, R I 6 0 1 1 2 (8 9 9 10)*
p 10, I 11, R 2, R I 7 0 1 2 3 (8 9 10 11)
p 11, I o, R 3, R I 8, 0 1 3 4 (8 9 11 0)*
*used as tra n sitio n s between odd and even permutations.
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their ordering be identical or retrogressively related, in which
case the pitch order of the adjacency is reversed between the two
forms* It is clear that only I 11 maintains tetrachordal pitch-
content while maintaining the exact order of the first two tetra
chords and retrograding the third tetrachord, as previously
shown. These relationships are shown in Figure 7.
It must be clearly understood that these Figures can be so
read only because of the unique semitone-adjacency structure of the
basic row form. The results obtained cannot be generalized to
apply to pitch structures generated by other basic row forms.
Five distinct tetrachords containing two semitone adjacencies
each can be derived from any of these row forms. Their normal
forms are:
0145 0145 0167
0167 0145
Note that only two normal forms are necessary to describe any of
these tetrachords. The ordering of pitch classes within these
tetrachords are:
0154 5401 0167
6701 4501
Not only are each of these orderings unique, but their retrogrades
are also unique. Then ten possible tetrachordal pitch-class order
ings exist among the row forms: six for the normal form 0 1 4 5,
and four for the normal form 0 1 6 7. In the f i r s t movement
of the Trio, a given row's appropriateness in its context may be
determined as much by the ordering of its tetrachords as their
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pitch content and order of appearance.
Unlike tetrachords containing non-semitone dyadic invariants,
.occurring only between row forms with the condition that one is
an odd permutation of the other, serve as a structural link between
the systems implied by the odd permutations and the even permutations.
Another means of such "modulation" is the emphasis placed on the
tetrachord formed by the la st two members of a row and the f i r s t
two members of the succeeding row; obviously, any tetrachordal
structure containing two semitone adjacencies can be constructed.
Similarly, the pitch distribution among the various parts can have
the e ffe ct of skipping over part of the row, making i t possible
to construct a tetrachord of, say, the first and third semitone
adjacencies.
The first semitone adjacencies of each tetrachord of the
basic row form yield the normal form 0 1 2 3 4 5, which is ,
of course, hexachordally combinatorial with its complement.
P 0: 0 1 11 10 2 3
4 5 6 7 8 9
Since the last pitch-class of P 0 is an odd integer, the retro
grade inversion form which contains the same first and last pitch-
class as P 0 is alsoan even permutation and preserves not only the
direction but the content of each semitone adjacency:
PO: 01 54 11 10 67 23 89
R I 9: 0 1 67 23 11 10 54 89
Further, since the two falling semitone adjacencies of the basic
row form are a tritone apart, which implies that the other four
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can also be grouped In a similar manner, the transposition o£ a
row form at the trltone (Integer value 6) also preserves semitone
adjacency direction. Thus, P 0, P 6, R I 9, and R 1 3 have the
same semitone adjacency interval content and direction; their
retrogrades R 0, R 6, I 9, and 1 3 reverse the direction of each
such adjacency.
Another relationship involving the first two and last two
pltch-classes is that of the tetrachord formed by the juncture of
any two row forms; for example, the sequence P 0 -- P 2 forms the
tetrachord 9 8 (P 0) — 2 3 (P 2) with a normal form 0 1 6 7.
Obviously, any tetrachordal content may be formed at w ill under
this condition, but those with normal forms corresponding to those
of tetrachords of the basic row form are often used.
Since every semitone adjacency occurs at either the beginning
or end of some row form in either a rising or falling direction,
these tetrachords can have any of 4.' orderings; that is, all pos
sible orderings exist. If P 0 is the first of two rows, structurally
significant tetrachords (in normal form) occur as shown in Figure 6.
I 7 and I 11 gain added significance; the tetrachord 0 12 3
is often sought after, even in the first movement. The relationship
of R 4 and R 8 are perhaps a determining factor in the significance
of these row forms, especially the latter. R I 6 is shown to have
a definite pivoting function; the sub-relationship between P 11
and R 3 becomes clear.
»
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F irst Movement
1. Exposition ("measures 1-21)
Measures 1-3 comprise the Initial arch. The row forms used
are P 0 and R 0, and every pitch class is voiced in exactly the
same manner in both forms. Of significance is the prominence of
Eb-E as the first and last notes of the arch; F#-C at the juncture
of the two forms, and the introduction of the important semitone
adjacencies D-C# and Ab-G as motivic fragments.
Measures 4-7 comprise the second arch. Row forms used are
R I 6, I 11, and P 0. The first semitone adjacency of R X 6 and
the last of the P 0 form the tetrachord C-C#-B-C; further, R I 6
and P 0 are inversionally related about the axis C-F# in retrograde.
The relationship is emphasized by the identical voicing of C at
the beginning and end of the arch. As a reversal of the first arch,
C-F# begin and end this arch, and Eb-E occur at the midpoint. I 11's
strong structural affinity to P 0 has been discussed.
Measures 8-10 form a tran sitio n from what might be called
the first theme area, consisting of the first two arches, to the
second theme area. In measures 1-7, R I 6 is the only odd permu
tation, and its strong structural relationship to P 0 is specifically
exploited. The second theme area shows a dominance of odd permu
tatio n s, and measures 8-10 must provide a smooth link between these
two opposing systems.
The row forms used are I 1, R I 4, and I 10. I 1 forms the
tetrachord 8 9 0 1 (normal form 0 14 5) with the preceding form,
P 0; further, it begins with the pitches E-Eb. The juncture of
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I 10 and P 11 at the end of the transition la 2 1 11 0, (normal
form 0 12 3), and E-Eb Is specifically stated precisely at the
juncture. The trltone correspondence of R I 4 and I 10 Implies
a sub-arch, as F#-C occurs at the juncture as a consequence of the
tetrachord F/M»-C#-C (0 1 6 7) these two row forms are used to
stress the change of semitone adjacency pattern B-C, near the start
of I 1, which is changed to Bb-B at the s ta rt of R I 4. Sim ilarity,
I 1 ends with G#-G, R I 10 with F#-G. I 1 and R I 4 contain dyadic
invariant C-F, whereas I 10 contains its inversion F-Bb, precisely
the dyadic invariant of P 0 and P 11.
Measures 10-15 form the f ir s t section of the third arch.
While the pitch series occurring in individual parts is exploited
previously, notably in the link between the f i r s t and second
arches, v io lin s: C#-D, E-D#, C#-D, i t does not assume prominence
before this area. The rhythmic patterns of the second theme area
lend themselves easily to such techniques, and in the measures
10-15 a definite distribution of pitch classes is built up, reaches
a peak in 12-13 (violin, G#-A-Bb-A-G#) and is dissolved.
The row forms used are P ll, P 3, R I 10, R 8, and R 3, a ll
odd permutations except R 8. The section begins with E-Eb and ends
with C-F#, both dyads occurring at the juncture of row forms. The
P 3 - R 3 arch relationship is reinforced by almost identical
voicing. It can hardly be coincidental that the last pitch class
of P 3 is Eb (as is the first of R 3) implying still another,
smaller arch; for R I 10 and R 8 have an inversional relationship
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at the axis C-F#, as did P 0 and R I 6 in the second arch.
In measures 16-19, the row forms of the second arch are used
as the midpoint of the third arch: R I 6, I 11, and P 0. The as
sociation of C with Eb In the violin part perhaps Indicates a
temporary reconciliation of these heretofore separated pltch-
classes. A temporary transition back to the even permutation
system is achieved.
In measures 19-21, the row forms of the tran sitio n from f ir s t
to second theme area are repeated: I 1, R I 4, I 10, and P 11,
closing the third arch and the exposition. Odd permutations are
again dominant. Quasi-resolutions involving Eb are noticeable
in the violin part. Heavy use of harmonics and pizzicato in 21
seems to indicate a dissolution of pitch-class relationships
formed in the exposition.
Looking at the third arch as a whole, one notices several im
plied tetrachordal relationships, considering that P n, P n + 6,
I n - 1, In-7 contain the same tetrachords. The relationship
of P 11 and I 10 occurs at the ends of the arch. The P 3 system
is used as a transition from P 11 to the system of R 8, which im
portant row form is presented for the first time here. P 3 and
R 8 contain the dyadic invariant C - E, which occurs several times
in the violoncello part in this area. R 3 has a transitional
function, leading this time to R I 6, of P 7's tetrachordal system.
P 7 is related to P 0 as P 3 is related to P 8, and the midpoint
returns us to the tetrachordal system of the first arch (P 0).
The next form, I 1, contains five common adjacencies with P 0,
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the closest relationship possible between an odd and even per
mutation of the basic row form. R I 4 is related to I 1 as P 3
Is to F 0; I 10 is, of course, part of R I 4's tetrachordal
system, which is none other than that of P 11, our final row form
of the arch.
lurther, P 11 and P 3 are linked by the tetrachord Bb-B-F#-G
(normal form, 0 1.4 5), a variation of the F#-G-C#-C tetrachord
linking R I 4 and I 10, P 3 and R I 10 associate Eb-E as the
central members of the same tetrachord that introduced the second
theme area -- D-Eb-E-F (0123). R I 10 and R 8, because of the
held-over D, give a variant tetrachord D-C#-G/A-G (0167), instead
of the expected C-C#-G#-G. R 8 -- R 3 gives the pivotal form
C-B-Eb-D (0 1 3 4); R 3 -- R I 6 repeats the G-F#-C-C# (0 1 6 7)
tetrachord which linked R I 4 and 1 10, which appears at a crucial
transition point, just before the restatement of the second arch
m aterial.
The dyadic invariant of I 10 and P 11, Bb-F, also appears in
P 3, R I 10, also in conjunction with R 8, again occurs in R 3
and R I 6. Later Bb is paired with F#, and again with F in the return
of P 11. The interval A-D, appearing first in I 11 near the
midpoint of the second arch, occuring again in I 10, recurs
throughout this section. P 11 contains its inversion A-E; P 3,
R 1 10, R 3, the juncture of R I 6 and I 11 not only contain but
emphasize this interval.
Small structural arches, based on direction of movement rather
than actual pitch, abound in this area. Often, one side of the
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arch Is inversionally related to the other, as In measure 15, violon
c ello : C#-C-E-F-C#, where the normal form of C#-C-E is 0 1 4, and
that of E-F-C# Is also 0 14. Palindromes also appear: the G#-A-Bb-
A-G# sequence in measures 12-13 is immediately repeated. As the
exposition draws to a close, palindromes become more frequent:
measures 19-20, v io lin , C#-E-C#; G#-A -- G-Eb-G-Eb — G#-A. The
latter sequence is introduced shortly after A-C#, violoncello, which
links the two sequences. Thus one gets a glimpse of the interweaving
of arches and arch fragments which pervade much of the second
theme area. The overriding Impression, however, is one of forward
movement and of expansion of ideas, in contrast to the more static,
more carefully arched first theme area.
2. Development (measures 22-41)
The development consists of a sequence of seven row forms which
is repeated: R I 0, R 1, I 8, R I 5, R 2, R 4, P 4. These row forms
are strongly related.
R IO belongs to the tetrachordal family of R I 6, which is
the first odd permutation to appear in the movement, and recurs at
the midpoint of the third arch. Moreover, R IO ends on Eb, the
f ir s t pitch class of the movement, and begins with F#, whose struc
tural importance in the exposition is discussed above. R 1, the
next row form, is related to R I 0 as P 0 .: I 11, the closest tetra
chordal relationship. I 8 begins "modulating;" it belongs to
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the tetrachordal aystem of P 3, prominent in the third arch of the
exposition. R I 5 belongs to the tetrachordal system of P 0, and the
transition In the third arch from P 3 to P 0 Is recalled here In
abbreviated form as the row structure returns to a region of even
permutations. Ihe tetrachordal modulation from the system of P 0
to that of R 2 to that of R 4 takes place in a manner also recalling
the previous modulation. R 4 is immediately retrograded, ending
the series with an arch the size of the first arch of the exposition.
No member of the tetrachordal family of R 4 previously appears
in the movement, and this retrograde serves to emphasize its occur
rence here.
The first statement of this row form sequence comprises measures
22-30. The first statement of the sequence begins quietly, building
gradually in textural complexity and motivic intricacy to a climax
at the midpoint of the arch, R 4 -- P 4. Semitone adjacencies are
invariably realized as major sevenths in this area. Overlapping
tetrachords generated by superposition of row forms occur throughout
this passage. In measures 23-24, violin, the trichord F-E-Eb
appears, simultaneously with B-Bb, viola. This incidence is echoed
at once by the complex e n tity D (violoncello) -C#-C (v io lin ), -B-Bb
(violoncello), and D-Eb-E-F, v io la. The D-Eb-E-F aggregate is
inverted by the combination of elements of different row forms, Eb-E-C#-D,
and the inversion is permuted twice with added notes: D-C# (G) -Eb-'E,
also resulting from a combination of row forms, and E-Eb (A) -D-C#.
The literal retrograde of A-D-C#-G# (viola) -G (violin)
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from R 4 to P 4, identical even to voicing, must be noted. In the
violoncello part, C and F remain constant: in the violin, Bb remains
constant. Of the pitches interchanged, three are the crucial Eb,
E, and F#. The direction of Eb-E is reversed, and F# is inverted
in register; that is, instead of being a relatively high note in
the violin part, it is relatively low and in the violoncello part.
The sequence of seven row forms is repeated in measures 31-40,
beginning with an almost exact inversion of voicing of the first
row forms in the f i r s t part of the development. While th is section
is reminiscent of first arch material, it does not seem that the
material of the first theme area is really developed motivically.
Somewhat similar pitch-class handling to that of the first part
of the development occurs, along with a more and more free in
version of voicing. In measures 35-37, the violin part reads:
F-E-Eb-D-C#-D-D-C#, with each of these semitone adjacencies- given
a registration of a major seventh.
Beginning with measure 37, a definite recall of the second
theme motivic material takes over. The emphasis on A -r
a trito n e away from Eb -- may have been intended as a rudimentary
"pounding of the dominant." The juncture of R 4 and P 4 passes
without incident. One's attention has been drawn away from the
structural implications of the row forms, in strong contrast to
the situation of the first statement of the seven row series.
3. Recapitulation (measures 41-65)
The row forms of the exposition are almost literally repeated,
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Structual Implications are differently handled, however, and ex
ceptions are noted.
In measures 41-42, the row forms of the first arch are repeated.
Only one motlvic pattern Is used, consisting of only two notes. In
one sense, this pattern Is a diminution of the second theme motlvic
pattern, In another, a simple statement of the motlvic fragment
which Is the basis for the entire work. No Interval but that of
a major seventh occurs within the pattern. The distribution of
pitch classes among parts forms the link between the development
and the recapitulation: from P 4, F#-F-C#-D; from P 0, D-C#-F-F#; from R 0, F#-F-C#-D. This pitch-class sim ilarity is a deliberate
exploitation of the tetrachordal relationships of P 4 and P 0. This
sequence continues through the end of the second arch.
As far as voicing is concerned, R 0's pitch classes exactly
duplicate P O's. The fact that Tempo Primo does not occur until
the beginning of the recapitulation of the second arch would indi
cate the possibility that the first arch, in the exposition, is
actually an introduction. In the recapitulation, it may be a
transition to the recapitulation proper beginning in measure 4^
or the sort of premature recapitulation found in Beethoven's
Symphony No. 3. f i r s t movement.
Measures 44-48 contain the recapitulation of the second arch,
reaffirming the semitone adjacency pattern of the even permutations.
In R I 6, C# is paired with D in opposition to that row form's
natural tendencies, and that aggregate is predominantly displayed
in succeeding row forms. Once again, the identical voicing of C
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at the beginning and end of the arch reinforces its structural
characteristic, but this time C is voiced again in the same manner
near the midpoint of the arch, in conjunction with Eb, The inter-
vallic similarity between R I 6 and P 0, unlike the exposition's
treatment in this area, is not exploited. Moreover, the motlvic
fragments are shorter and more efficiently organized in relation
to each other. All these factors tend to de-emphaslze the arch
characteristic of R I 6 - I 11 ■■ P 0.
Measures 48-51 contain recapitulation of the transition to
the third arch. Since the third arch displays an inversion of
register of pitch-class voicings and de-emphasized .the semitone
adjacency characteristics strongly emphasized in the recapitulation
of the f i r s t and second arches, these measures have a d ifferen t
function than in the exposition. A quasi-canon is gradually devel
oped; the violin is the dux, the viola and violoncello, in that
order, are the comes. The motives used are much more similar to
second theme material than in the exposition, but, unlike the ex
position, semitone adjacencies are scrupulously kept in close
proximity with each other. The C whose voicing plays an important
role in the second arch reappears thrice, in the same octave as
before, but in the violin part, as the last note of each entrance
of the dux. The Eb which appeared in conjunction with C at the
midpoint of the second arch is prominently placed at the beginning
and end of these three row forms. Even though E is actually the
first pitch-class of I 1, its appearance is as a grace note,
whereas Eb is first bowed, then repeated pizzicato. Near the end
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of I 10, the grace note is D, an inversion of the semitone ad
jacency about the axis Eb. Numerous smaller arches appear, both
of actual pitch-classes and of aggregates used with their inversions.
The second theme area is marked both by a return to tempo and a
sharp contrast in dynamics. The actual ending of I 10, the E that
concluded this section in the exposition, is disguised by an
elision with the overriding entrance of P 11.
Measures 51-56 contain the recapitulation of the f i r s t section
of the third arch. Generally speaking, the pitch classes associa
ted with the violin in the exposition are in the violoncello part.
Those previously found with the viola are in the v io lin part, and
those of the violoncello are in the viola p art. The canon begun
in the transitional area is continued. Now it begins alternately
with D and B. F-Bb is prominently voiced; A-D less so. However,
A recurs^violoncello, with identical voicing, almost as a pedal note.
Several arches on a small scale which characterized this section
in the exposition do not appear here. As in the recapulation of
the second arch, the motives are shorter. The entrances in the
canon are permutations of the actual pitch-class content rather
than showing arch characteristics. In general, this section seems
to show greater stability from almost any analyzable standpoint
than the congruent area of the exposition does.
Measures 57-61 contain the recapitulation of the second
section of the third arch. The C which was prominent in the re
capitulation of the first theme area is now in the viola part. Its
function as an axis of inversion for register and for related pitch
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aggregates Is clearest In this area. For example, in measures
58-59, G#-G-F#, v io lin , is complemented by Eb-F-E, violoncello. Both
aggregates have the normal form 0 1 2 and the complex normal form
0 1 2 3 4 5.
This area shows a return to the techniques used in the small
arch. At the beginning of the area, G-F# from R 3 is answered by
F#-G from S I 6. In measure 58, G#-A-A-G#, v io lin , is one of the
most obvious of many small arches. The pedal in the violoncello
part is first D, then E. A general tendency to voice pitch classes
in the same manner as in previous areas, relatively little motivic
development, and a rather thin texture give an impression of
stability, a slackening of musical development in preparation for
the end of the movement.
Measures 61-65 contain the recapitulation of the last section of
the second arch. This area has a closing theme function in the exposi
tion. Here i t merges, w ith the added row form R 0, w ith a coda.
There is a continued association of C# and G# and D with A,
reflecting, in the first case, the linking tetrachord of the exposi
tion, and in the second, the prominend dyadic invariant of the
second theme. F#-G-C#-C reappears, here as a link between the row forms
R I 6 and I 10. There two row forms are so voiced that they exhibit
arch characteristics in combination. Bb-B, violoncello, is reversed with
the same voicing; Eb-D is reversed with an inversion of register.
The distribution of pitch classes in R 0 seems to be intended as an
inticipation of the tetrachord pattern of R 8, the first row fora of
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the second movement. The movement ends on E-Eb, the semitone .
adjacency which began It, which may suggest that the entire move
ment may be regarded as an arch.
C. Second Movement
1. Introduction (measures 1-9')
The row forms used in th is section are: R 8, RI 11, P 1,
R I 8, I 5, R 7, and R 9. The pitch distribution of each row
form is : f i r s t tetrachord, v io lin ; second tetrachord, v io la;
third tetrachord, violoncello. In addition,, all semitone
adjacencies are always kept together motivlcally. Then it seems
that the tetrachord pattern, the type of semitone adjacency
pattern, and the direction of semitone adjacency would seem to be
the controlling factors in choice of row form. Tetrachords
formed by the juncture of two rows can be invoked almost at w ill.
Although some departure from strict ordering of the row form in
time sequence has occurred in the first movement (measure 51, end
of I 10), row forms or parts of row forms are used simultaneously
here for the first time.
In the first measure, motlvic fragments occur almost in canon.
As in the first movement, measures 48-51, the order is violln-
viola-violoncello. The order is varied in the second entrance to
preserve a rather surprising relationship: the semitone adjacen
cies, in order of presentation, are in falling chromatic sequence.
Only two semitone adjacencies rise naturally in R 8. One of these
is realized as a major seventh, and thus falls. The only two
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semitone adjacencies that are realized as rising Intervals occur
In the violoncello part, one containing C and the other, Eb. The
relationship between R 8 and Its predecessor, the last row form of
the first movement, R 0, Is the same as P 8 : P 0, which Is dis
cussed In the material on tetrachordal relationships. R 8 also
ends with the same two pltch-classes that begin R 0, B and C.
Further, the violin and violoncello begin the second movement with
the same pitch classes with which they ended the f i r s t movement,
6# and Eb. The last four notes of the violin part In the first
movement are retrograded to form the first tetrachord of R 8, In
the first four notes in the violin part. Thus, an arch relation
ship between these two row forms is implied. The normal forms of
the tetrachords of R 8 are: 016 7, 014 5, 014 5.
R 1 11, again an even permutation, has the tetrachordal con
tent of P 0. Normal forms are the same as R 8. The same distri
bution occurs, except that the semitone adjacencies are presented
in rising chromatic sequence, although the majority of the semitone
adjacencies are realized as falling intervals. The last two
pitches in the violin part, B-C, are the end of R 8, violoncello
part; the last two pitches, violoncello, C#-D, are the end of R 8 in
the violin part. The juncture of R 8 and R I 11 produces the
tetrachords 0 1 6 7, 0 1 2 3, 0 1 2 3. The juncture of R I 11 and
P 1, a transition from an even permutation to an odd one, is
beautifully done. The viola's last two notes in R I 11 are E
accompanied by a D, violoncello. The viola's first two notes in
P 1 are Eb-D; the Eb tied over, the D voiced as the previous E,
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has identical registration, violin, beginning of R 9. The introduction
ends, then, on a rather indeterminate structural pattern which
contrasts strongly with the fairly clear statements of its beginning.
2. Exposition (measures 10-73 with repeat)
a. F irst theme (measures 10-39)
Measures 10-25 contain the first period of the first theme. The
row form sequence R 8, R 1, I 4, R 9, R 2, P2, P 8, R I 9, and I 4
is presented. Certain similarities between this area and the begin
ning of the first theme in the first movement can be noted. All row
forms are used successively, and there is no real pattern of pitch
distribution among parts. R 8 may play the same structuralrole
in this area that P 0 plays in the corresponding part of the first
movement.
Adjacencies and aggregates occurring in combinations of row forms
are emphasized. There is a surprising number of whole steps in measures
13-14, considering that this interval is unobtainable from the row
forms permitted. Semitone adjacencies appear as major seventh vertical
aggregates, whose pitch content tends to rise through this area. The
interval of a fourth is rather laboriously introduced in measures 10-11
and measure 25, the beginning and end of the area.
R 8, the first row form of the movement, is realized here quite
differently than there. It is prepared by the two preceding row forms,
R 7 and R 9, in the first appearance of a circling technique resembling
that of a turn. The first six pitch classes of R 8 are presented to
gether, then the next four, then the last two, a progressive diminishing
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of aggregate content. The entry of R 8 is emphasized by a change in
tempo, a change in the number of attacks per time interv al, and the
rather high voicing, violoncello.
On the whole, row form relationships appear to be of secondary
importance in this area. The only tetrachordal juncture which seems
noteworthy is in measures 15-16, between R 1 and I 4. Semitone
adjacencies voices as major seventh aggregates and repeated seem to
belong to larger aggregates. The repetition in measures 19-21 of P 2,
the only such re p e titio n of a row form in the work, seems to serve
the purpose of permitting the repetition of an aggregate in a
diminution of thematic material. In both occurrence of P 2, the row
form is divided into hexachords. The close proximity of R I 9, whose
retrograde is hexachordally combinatorial with'P 2, can hardly be
accidental, for it is also grouped by hexachords. P 2's close
relationship with R 8, the first row form in this area and of the
movement, and with P 8, the next row, seemP to be significant.
Measures 26-30 contain the transition to the second area of the
f ir s t theme. The row forms used are R 2, R I 1, R I 8, and R 9. A
deliberate attempt to move as much by semitones as possible, combined
with a triplet motive which tends to break down tetrachordal struc
tures, differentiates this area from its surroundings. R 2 and
R I l's tetrachordal affinity, that of P 0 : I 11, is not exploited.
R 2 is anticipated by the previous emphasis of P 2, but voicings here
do not resemble previous voicings, and the hexachordal division does
not appear. R 9 ends the introduction, and here it seems to serve
the same purpose, in conjunction with dissolution of ideas.
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Measures 40-44 contain the transition to the second theme area.
The row forms used are I 10 and R 5. This is the first area of the
work in which row forms are used lin early instead of successively
for an extended passage. The tetrachordal relationship between these
row forms is emphasized, for the first four pitch classes of I 10 are
Introduced before the beginning of R 5. F-E-B-Bb, R 5, occurs simul
taneously with D-Eb-G-F#, I 10 in measures 42-43. In measure 44,
B-Bb-F-E, and inversion of a previous tetrachord, I 10, appears with
Eb-D, R 5, hardly a complete combinatorial realization. Again, the
identifying pitch classes of the row forms are a perfect fourth apart.
b. Second theme (measures 45-73)
Measures 45-54 contain the f i r s t area of the second theme, con
sisting entirely of linearly combined forms. The sequence of rcw
forms used is R 5, I 10, R I 8, P 3, R 5, and R 7. The f i r s t two pairs
are tetrachordally combinatorial, and the last two have pivotal
tetrachordal relationships. A more sophisticated, freer motlvic pattern,
together with considerably more variant voicing, tends to minimize
invariant pitch classes among these forms. For the first time in the
work, tetrachords are used as melodic source material.
As in the preceding transition, combinatorial aspects are treated
rather loosely. Dodecaphonic concentration is not the controlling
consideration. Opposition of aggregates with sim ilar content in augment
tation and diminution prevails, so that in small areas certain pitch
classes occur much more often than others do.
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Measures 55-59 contain a return to the material of the beginning
of the second theme. Despite the similarity of texture between that
area and these measures, row forms are used successively here. The
sequence used is I 6, R I 7, and if X 5, with a circling pattern
reminiscent of that of the first two forms of the introduction. The
section ends with a rather pronounced aural ncadence,"•suggesting an
important point of structural articulation -- perhaps the end of
the second theme proper and the beginning of the closing theme of
the exposition.
Measures 60-73 display the working out of fragments of second
theme m aterial. The row form sequence used is I 2, P 6, P 10, R I 3,
P 6, P 10, RIO, and I 10. All row forms except for the f i r s t and
last two of this sequence are even permutations, SO' ordered that
there is a shifting back and forth between tetrachordal systems.
Row forms are used successively, with one exception, which exploits
the opposition of two tetrachordal systems. The junctures between
row forms are noteworthy: Ab-A-A-Bb, I 2 and P 6; a common 0 1 4 5
tetrachord, P 6 and P 10; A-Bb-A-Bb, P 10 and R I 3; a 0 1 2 3
tetrachord, entrance of P 6; P 6 and P 10, with the same relationship
as before; a common 0 13 4 tetrachord, P 10 and RIO; and a common
0 12 3 tetrachord between the last 'two forms. Inversions of normal
forms are paired. A general freedom of movement and voicing again
yields an impression of a dissolution of structure. The last notes,
violin, Ab-G-B, recall the opening of the exposition, Ab-A-B.
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3. Development (measures 73b-117)
Measures 73-83 contain the first period of the development, easily
subdivided at measure 80. The row form sequence used Is I 3, R I 3,
R 4, and 13. 13 and R I 3 are retrogrades of each other. R 4, 13,
and R I 3 are tetrachordally combinatorial. R 4 occurs near the end
of the first theme In the exposition, and R I 3 occurs near the end
of the second theme. The f i r s t four notes of the development proper,
measure 74, are the same as those which begin the exposition: G#-A-C-B.
The motive consisting of three repeated notes is probably a condensa
tion of the previous triplet figure, and considerably slows the rate
at which the row form is presented. On the whole, the last four meas
ures show a return to the technique of the first theme area.
Measures 84-87 contain a transition similar to that between the
first and second theme areas of the exposition. I 1 and F 2 are
used linearly, both forms jumping from one instrumental part to another.
Although the row forms used are tetrachordally combinatorial, the
grouping is by trichords rather than tetrachords.
Measures 88-101 contain the second period of the development, sub
divided at measure 96. For the first six measures, row forms are used
linearly. Afterwards, they are used successively. The sequence used is
R 6, R I 1, I 4, I 6, P 5, R 6, P 1, I 8, R 0, I 7, I 2, and P 7. R 6
and R I 1 are hexadordally combinatorial. R I 1 and I 4 are not at
all combinatorial, but have a pivoting relationship which is exploited.
In measure 90, F# is associated both with G and F, and a l i t t l e further,
C is associated with both B and C#. Eb-E is repeated across row forms.
These techniques serve to bring into prominence the pitch classes
which are significant in the exposition of the first movement of the work.
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Internal relationships of row forms are: R 6 ■ I 6 • R 6;
R 6 ■ R 0; 1 8 - 1 2; I 7 * P 7. The technique again resembles
first theme area; the major seventh simultanities are realized
col legno. Grouping is by tetrachord or hexachord, trichords
being relatively unimportant. The juncture of P 5 and R 6
pivots about F, R 6 - P 1 gives 0 1 3 4, P 1 ■ I 8 pivots about C.
I 8 - R 0 pivots about both C and D -- no mean featf that. The
combinatorial similarities of R 0 and I 7 are ignored. Perhaps
an arch might be inferred, but if it is intended, it is played down. Other row form junctures seem unremarkable.
Measures 102-105 contain the transition to the third "period"
of the development. The row forms used are P 8, P 6, and R 11.
Row forms are again used successively. The juncture P 8 - P 6
gives the normal form 0 1 2 3. Two semitone adjacencies are,
simply, repeated in P 6 -- C# 7D and E-Eb, both of which are
prominent in the first theme, first movement. The small arch C
(violoncello) - F# - (viola) - C - (violoncello) may have some
similar significance. The motivic material is apparently derived
from the second arch of the f i r s t theme.
Measures 106-117 comprise fin al area of the development.
There is a dissolution of previous material, ending with a quasi
"pounding of the dominant," in this case the beginning pitch-
class of the work, Eb. Row forms used are R I 2, R 3, I 11, R I 6,
R I 4, and R 8. R I 2 and R 3 have the familiar I 11 - P 0
relationship; R 3 and I 11 have no apparent link except that,
disregarding one duplicated pitch class, E, they are haxachordally
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combinatorial. I 11 - R I 6 is. of importance, in reversed
order, in the first movement, R I 6 and R I 4's tetrachordal
similarities are exploited. R I 4 and R 8's juncture pivots
rather neatly about G. R 8 is, of course, the firftt row of
the introduction and exposition, and its dominance is reasserted
by its appearance at the close of the development.
Motlvic m aterial is drawn from many sections, but the area
is perhaps most strongly reminiscent of the last portion of the
first period of the development. Tetrachordal groupings of
0 12 3 are common, and one can define certain trlchordal groupings
of 0 1 4 and 0 15. The general impression is of a slackening
of structure, a return to the more simple semitone adjacency
patterns which can be avoided, in this row form, only by the use
of considerable ingenuity. The pivot of the last row of the section,
R 8, and the first of the recapitulation, R 1, about the note B
is most obvious.
4. Recaoitulation (measures 118-180)
a. F irst theme (measures 118-148)
In measures 118-130, all row forms of the first period of
the first theme reappear, exactly as before. The head of the motivic
material starting the first theme, violin, the pitch order somewhat re
versed from the similar material in the exposition; disregarding
intervening pitches, G#-A-C-B is realizes as C-B-G#-A (normal
form, 0 14 5). There is a greater tendency to form small arches
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and rep etitio n s of the sort found In measures 124-126 In the violon
cello part: Eb, t r i l l C#-D, Eb, Eb, ,t r i l l C#-D, at the juncture
of P 2 and P 2. Trichords are little used; normal form 0 1 6 is
the most common. A lack of variety in voicing, and the use of
pitch classes within a part as temporary pivots violin, measures
130-131; Db-C, C-Db, C-B, contribute ,to a greater stability of
structure than in the exposition. Again, one senses a return to
the simpler semitone adjacency structure. All other dyadic
invariants are practically disregarded. The break at the end of
this area is quite pronounced.
In measures 131-134 a transition area, the row forms of the
exposition are again repeated literally. Much the same technique
and motivic material are used as in the congruent place. Again,
a greater stability of voicing is apparent, and the play on C and
C# in the violin part can hardly be accidental. There is a general
tendency to distribute pitches among the parts as in the second
theme area of the f i r s t movement.
In measures 135-143, row forms change quite rad ically from
those of the exposition: I 8, I 3, R 8, P 3, I 8, R 1, and R I 1.
The I 3 - P 3 (or R 3) relationship is found also in the exposition
in this area; the I 8 - R 8 relationship instead of I 10 - P 10
indicates a rising rather than a falling perfect fourth relation
ship to the I 3 - P 3 pivot. The substitution of R 1 - R I 1 for
R 8 - R I 8 is done to preserve the relationship of this area
with the next transition: R I 8: I 10 as R 1: I 3.
Measures 144-148 contain the tra n sitio n to the second theme area.
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Now, the modulation permitting the recapitulation of second theme
material a perfect fourth above Its level of transposition In the
exposition Is complete, and the row forms here, I 3 and R 10, show
such a relationship. The pitch classes appear In much the same
manner, the first tetrachord of the I form established before the
R form gets underway. However, the voicing of pitch classes Is
largely reversed.
b. Second theme (measures 149-179}
Measures 149-162 recapitulates the beginning of the second
theme. While the row forms are the same, transposed up a perfect
fourth, their handling is quite different. There is more of a
tendency to scatter notes among the parts, not hold to a line
made up of the row's pitch-classes in order. Motives are more
fragmentary, less well defined. The beginning of R 0 recalls
m aterial from the introduction, which in continued, in a frag
mentary fashion, to the end of this area, and even beyond. No
clear pattern of grouping emerges. At measure 159, the return
to the beginning of second theme material does not occur, as it
did in the congruent place of the exposition. The "cadence" is
not recapitulated, at least rhythmically.
In measures 163-174, the row forms of the exposition again
occur transposed up a perfect fourth. Thematic material and tex
ture are sim ilar to that found in the exposition* At measure
172, however, the pace begins to quicken, and a wider range and
greater variance of voicing-prepare one for a somewhat more
involved closing of the recapitulation than of the exposition.
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The motlvic patterns of these measures Is much like that of the
second theme of the recapitulation.
The row forms of measures 175-179, since the entire sequence
of exposition row forms has been recapitulated, are new: R 4,
I 9, R I 8, R I 4 in somewhat of a jumble, and R I 6. The I 3 - R 4
relationship is the familiar I 11 - P 0 in a variant form; R 4
and I 9 are tetrachordally combinatorial; R I 8 and R I 4 seem to
present the tension generated by the juxtaposition of the two
most important forms of the work, P 0 and P 8 (R 8), in a variant
fomr. These two forms "circle" R I 6, whose importance in the
first movement is discussed above.
5. Coda (measures 180-193)
The row forms used are R I 7, R X 10, R 8, P 1, R 9, P 2,
R 6, and P 8. The first four measures recall the introduction ;
The next six, second theme material; the last four, first theme
and opening of development.
The first tetrachord of R I 7 is the retrograde of R 8's
first tetrachord, and also appears in the violin part. The
secmd tetrachord, identical to that of R 8, is in the violoncello
part, while the third, also identical to R 8's second tetrachord,
is in the viola. R I 10, not R I 11 as previously, follows,
pivoting in the viola part about A. The pattern begins to break;
although tetrachordal partitions are realized as in R I 7, R I 10
considerably overlaps R 8. This important form is combined with
the last row of the introduction, R 9. These two row forms
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pivot every semitone adjacency in a sort of canon. P 2 has the
important rising perfect fourth relationship with R 9, and was the
only form to be repeated, perhaps because of its tetrachordal
affinity with R 8. R 6 provides a final tetrachordal variant
before the movement ends with P 8 — a perfect arch relationship
with the first row of the Introduction and the exposition. There
seems to be no correlation of voicing or pitch distribution be
tween the f i r s t and la st row forms of the work.
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FOOTNOTES
APPENDIX B
For a sound mathematical background to group structure, see Serge Lang, Algebra (Reading, Mass., and London: Addison-Wesley Company, 1965).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX C
VARIATION TECHNIQUE: VARIATIONS. OPUS 30
Preliminary Remarks:
The large form of th is work is described by Webern in a le tte r to
Willi Reich.* According to this letter, the work consists of a theme
and six variations in an Adagio form, such th a t the theme is also an
introduction, the first variation a presentation of a theme, the
second variation a transition, the third variation a presentation of a
subsidiary theme, the fourth variation a developmental recapitulation,
the fifth variation another transition, and the sixth variation a coda.
The configuration of each variation is thus determined not only by re
casting m aterial from the theme, but by its position in the Adagio
form. The variations are metamorphoses rather than embellishments of
the theme.
The letter also states that the work is derived from the initial
four-note motive. Every note of the work can be said to belong to a
four-note motive resembling the in itia l one in some way, and the exact
conditions of resemblance seem to be invariably of structural import.
Much additional musical material is derived from the initial motive
by a combination of strict and free developmental procedures. This
analysis is principally a study of these procedures and their role
in the construction of the large form of the work.
The letter stipulates that two kinds of variation technique 2 are used in the Variations, but does not describe them clearly.
Two species of variation technique, transformal and metamorphic, are
235
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presumed by the present study, which may correspond to the two that
Webern had in mind.
Transformal variation, or the re-orientation of an entity in
context without a change in internal configuration, can be applied
to rhythmic, articulation, pitch contour, pitch sequence, pitch
content, and dynamic patterns of entities. Retrograde, inversion,
verticalization, and transposition are considered types of trans
formal variation. The results of these operations may be meaningful
structurally either with relation to a fixed point, such as the
first pitch class of a work, or in themselves, for example, in the
row-form.relationships of the closing measures of the Variations.
Metamorphic v a riatio n , or the change of intern al configuration
of an entity, is applied to the above patterns in much the same
way that transformal variation is applied. When the change is so
slight that the result can be clearly identified with the original
entity, the metamorphic variation technique used is usually confined
to more or less regular augmentation or diminution of some pattern.
When irregularity occurs, especially with relation to rhythm or pitch,
the change in pattern often seems to resemble tendencies of variation
common to works written in fifteenth-century mensural notation.
Many of these tendencies can be found in the early sixteenth-century
works of Heinrich Isaac, which Webern transcribed. These tendencies
are discussed below in conjunction with the fourth variation, in
which they are prominent.
Metamorphic v a ria tio n which greatly a lte rs the patterning of an
entity may consist of irregular diminution or augmentation, permutation,
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or transformal operations applied to part but not all of the
pattern. Such variation links the initial statement of the work,
measures 1-2, contrabass, and the "subsidiary theme" statement,
beginning of the third variation, measures 74-5, flute. Like
transformal variation, metamorphic variation can be meaningful
structurally either with relation to a fixed pattern, or in itself.
These types of v ariatio n can be applied progressively to
entities to produce developmental sequences. In Webern's late
works, such sequences are either closed, so that their continuation
leads to a return to the configuration of the original entity, or
reversible, so that the direction of development can be retrograded
or inverted to obtain the configuration of the original entity.
Developmental sequences of both types occur in the Variations.
The fourth and sixth variations are imitative, each consisting
of a four-voice canon of pitch-classes, with metamorphic variation
of other patterns of the dux appearing in the other voices. The
remaining sections are homophonic and interconnected by several
structural similarities on many patterning levels. Their complex
e n titie s tend to be metamorphically related, but th e ir components
are usually transformally related.
The constraints imposed upon the musical m aterial seem to be
subordinated to the intuitive flow of the music, while supporting
and giving shape to that flow. The patterning of various aspects
of the initial motive does not seem to belong to a strict, logically
closed system, but to be an additional means of so organizing the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 8. Rhythmic and Articulative Patterns, Variations, opus 30
*• J J j f J 4fJ. - nx - U- > O , m
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Eig. 9. Cycles Based on Type 2 Tetrachords, Variations, opus 30
Cycle 1, first invoked in measure 3, oboe
from P 0 : B D Eb Gb
from P 4 : Eb Gb G Bb
From P 8: 6 Bb B D
Cycle 2, first invoked in measures 6-7, violoncello
from P I: C Eb E G
from P 5: E G Ab B
from P 9: Ab B C Eb
Cycle 3, first invoked in measure 32, pitched percussion
from P 2: C# E F Ab
from P 6: F Ab A C
from P 10: AC C# E
Cycle 4, first invoked in measures 40-2, horn
from P 3: D F F# A
from P 7: F# A Bb Db •
from P 11: Bb Db D F
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Fig. 10. Relationships of Type 1 Tetrachords, Variations, opus 30
original form inversion, about inversion, about first pitch class last pitch class
1. A Bb Db C A Ab F F# Eb DB C
2. B D Eb Gb B Ab G E C# C A Gb
3. Bb BD C# Bb A F# G E Eb C C#
4. FE G Ab F F# Eb D BCAAb
5. A Ab F F# A Bb Db C Eb E GF#
6. C Eb E GC A Ab FDB Bb G
Cycle linking tetrachords 1. 3. 4:
RI 11 ( tetrachord 1 ) = tetrachord 4
RI 8.( tetrachord 4. ) = tetrachord 3
P 11 ( tetrachord 3 ) = tetrachord 1
Cycle linking tetrachords 1 and 5 with the first two tetrachords of the fourth variation:
I 9 ( tetrachord 1 ) = tetrachord 5
RI9 ( tetrachord 5 ) = F# F D Eb, first tetrachord of variation four
RI9 ( above tetrachord ) = C C# E Eb, second tetrachord of variation four
P 9 ( above tetrachord ) = tetrachord 1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 11. Pitch Contour Variants, Variations, opus 30
Initial statement:
Retrograde
In v ersio n
Retrograde Inversion
"Subsidiary theme" ’ statem e n t:
R etrograde
In v ersio n
Retrograde Inversion
Observe that the last two operations yield no new pitch contours.
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musical material that its defined configuration strengthens the
total structure in a natural manner.
The entire work can be shown to consist of four-note groupings,
most of which are classifiable into six rhythmic and articulative
patterns, shown in Figure 8« Superposition of four-note groupings
sometimes reflects these patterns. When a four-note motive occurs
in a single instrumental part, or with the first two notes in one
part, and the last two in another, it is called a "statement" in
the following analysis.
Since statements almost invariably represent row-form segments
of the first four, the middle four, or last four notes, their
pitch content tends to fall into two pitch-aggregate classes:
those with normal form 0 13 4, and those with normal form 0149.
The first and last tetrachords of the row form are of the first
type, and the central tetrachord is of the second type. These
two types of tetrachords seem to have opposing structural roles.
The second type also occurs in four expanded cycles shown in Figure
9. The common use of several row forms at once permits construction
of these tetrachords and expanded cycles independently of the
requirements of the continuation of the row form. The frequency
of distribution of a single row form in several instrumental parts
also facilitates freedom of pitch selection.
Patterns consisting of three elements are significant
structurally in the third variation, the "subsidiary theme"
variation. These patterns are recapitulated in the fourth and
sixth variations, and in the fifth variation to a lesser degree.
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These sets of three are usually accompanied by a single fourth note
entry, completing the four-note grouping. The pitch content of
trichords commonly drawn from the row form are as follows (from P 0):
0 1 4; 2 5 6; 5 6 9; 7 10 11 j all of which have normal form 0 14.
Six tetrachords presented in the first half of the theme seem
to be structurally important in pitch-class sequence and content.
They are the six tetrachords of P 0 and P 1 and their retrogrades
R 0 and R 1. Since P 0 and P 1 are related both by transposition
and retrograde inversion, these tetrachords are closely linked.
Their configurations, relationships, and variants are shown in
Figure 10. They are numbered in order of appearance in the first
half of the theme.
Tetrachord 3 and tetrachord 6 are transpositions up a semitone
of tetrachord 1 and tetrachord 2 respectively. Tetrachord 4 is
an inversion up a minor sixth of tetrachord 1, and tetrachord 5 is
a retrograde inversion of tetrachord 1 about the axis of its first
pitch class. Tetrachord 2 is first presented after the last note
of tetrachord 1, thus in context it appears as (C) B D Eb Gb,
occurring simultaneously with tetrachord 3, Bb B D C#. Then the
direction of the intervals surrounding the central minor third in
tetrachord 3 are in opposing directions to the intervals surrounding
the same minor third in tetrachord 2. In the course of the
Variations, such partial transforms abound. This one serves to
. mark the interval B-D as structurally notable.
Figure 11 displays the variants of pitch contour derived
from the in itial statement and the "subsidiary theme" statement
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by transformal operation. The additional pitch contour of three
rising intervals is usually associated with the second type of
tetrachord, and may derive metamorphically from the pitch contours
shown in th is F ig u re.
The row form is degenerate, R 1 being the retrograde inversion
of P 0. Despite this degeneracy, the operations of retrograde,
and retrograde inversion have separate structural functions. The
retrograde operation provides palindromes which serve to mark
structurally significant events, whereas inversion becomes a
varying of material about a pitch axis which is thus emphasized as
a pivot. Retrograde inversion serves as a recapitulation device,
at its strongest when the last pitch-class of the resulting string
of notes is the same as the first pitch-class of the original
s tr in g .
The degeneracy of row form and the density with which forms
are used can produce varying analyses of the precise row forms
appearing in some passages. The author prefers the solution of
Heinrich Deppert, outstanding for its Webernian elegance, although 3 it is not the simplest solution possible.
The row form is hexachordally combinatorial at the transposition
of the interval of an augmented fourth. Four additional row form
relationships appear to be important: P 0 - R 5, relating to
transposition while preserving sequences of pitch classes;
P 0 - R 0, producing palindromes; P 0 - R 3, producing inversions
of tetrachords; and P 0 - R 1, producing retrograde inversions
of tetrachords.
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The relationship of P 0 and R 5 is as follows:
P 0: 0 14 3 2 5 6 9 8 7 10 11
R 5: 43012 11 10 789 65
The preservation in retrograde of the string 5 6 9 8 7 10 11 and
the intraversion of the tetrachord 0 14 3 are Important to the
structure of the Variations. This relationship is most obviously
invoked as P 3 - R 8, serving as a pivot at the center of the second
v a r ia tio n .
The relationship of P 0 and R 0 is, of course, that of simple
retrograde. It is prominent in the theme, serving to introduce the
palindronw device which serves to mark structurally important events
and to link the six major tetrachords of the work.
The tetrachordal relationship of P 0 and R 3 is as follows:
P 0 : 0143 2569 87 10 11
R 3: 21 10 11 0985 6743
yielding two sets of tetrachords with the same last two pitch classes,
a pair with the Interval 5-9, and two more pairs with identical
Initial pitch classes. The pitch content of the first tetrachord
of R 3 is an Inversion about the axis 1 of the pitch content of the
first tetrachord of P 0. The last tetrachords of the two row forms
have a similar relationship by inversion about the axis 7. The
trlchordal relationships of the two row forms also yield relation
ships of inversion. Every possible trichord of P 0 has at least
an inversion about its initial or final note in R 3 except 4 3 2.
0 14 and 5 6 9 have inversions in R 3 about every pitch class they
contain. R 3 is the "tonic" of variation 3, the subsidiary theme area.
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The relationship between P 0 and R 1 is as follows:
P O : 0143 2569 87 10 11
RI: 0 1189 10 763 452 1
or retrograde inversion about the axis of the first note. The pre
servation of the adjacencies 2 5 and 7 10 is important in the theme
as a means of "modulating" between the two types of tetrachords.
These two forms and their retrogrades are the only ones used in
the theme, and together they are used to generate nearly all the
structural procedures of the work.
A consequence of transformal variation of the row form which
has results with metamorphic implications is shown by the relation-,
ship of P 0 and P 2. First and last pairs of pitch classes within
tetrachords are interchanged.
P O : 0 1 4 3256 9 87 10 11
P 2: 2365 4 78 11 10 9 0 1
These row form relationships are so clearly associated with
the operations of inversion, retrograde, retrograde inversion, and
intraversion that they reappear when these operations become structur
ally important. In the sixth variation, these relationships rather
than specific row forms are recapitulated.
The structure of the theme is described by Webern as resembling
that of a period, and seems to correspond to that of a double
period. Double periods can be postulated in every variation with
varying degrees of credibility. The fourth and sixth variations
consist of such interlocked, sustained phrases that their divisions
into periodic segments are not unambiguous. Points of structural
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correspondence are marked by reappearance of events, or their variants,
found in the theme, such as operations, voicing sequences, superposition
techniques, and pitch content. The cycles of the second tetrachord
type seem to function in a manner opposing the way in which the
cycles of the first tetrachord type function, which sets up one of
many "dominant," or tonic-opposed, structural systems which further
serve to articulate the periodic structure.
The boundaries of phrases are often marked by changes of tempo,
fermatas, rests, and contrasts in timbre, dynamics, tessitura,
rhythmic and articulation patterns. Links between variations
sometimes appear. There is a general tendency for the second
period to be a complex variant of the first.
An alternate interpretation of the form of the theme might be
a set of nested sections about the initial statement, so that any
structural break within the theme or variation can mark the end of
a formally significant portion, which begins with the beginning of
the theme or variation. This interpretation seems to clarify the
plan of the fourth and sixth variations, and can be applied to the
o th e rs .
Still another interpretation of the structure of the theme
would be binary, with the second section an expansion of the first.
This form is observed in the present study in the introduction to
the first movement of the Quartet, opus 28, and the inter-movement
form of the Trio, opus 20. The first part could be restricted to
the first clear formal division of the theme. This Interpretation
does not seem to account for as much structural detail as the two
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mentioned above.
The tempo shifts back and forth' from 160 to 112 beats per
minute, a proportion of 10 to 7. This shift may reflect the pro
portions used in fifteenth-century mensurally notated works. The
author has been unable to find a significant rhythmic relation in
the Variations which would make this shift structurally meaningful
as an independent pattern, but the existence of such a relation is
not precluded. This shift insures phrases of unequal duration
almost everywhere except in the second variation, and facilitates
metamorphic rhythmic variation.
Unlike most of Webern's late instrumental works, the Variations
contains passages in which melodic lines are contrasted with ac
companying figurations. Phrases of melody can be identified
with prominently voiced sequential entities occurring either in
a single part or in parts linked by superposition, or close
sequential presentation with similar voicing characteristics. Ac
companying figurations appear to be either isolated notes which
counterbalance the melody in voicing and rhythm, or vertical pitch
aggregates. It is often difficult to distinguish melodic material
from accompaniment in this work. The following analysis presents
only one of many possible interpretations of the melodic structure
of the Variations.
Webern's large-scale variation technique can also be observed
in the Plano V a ria tio n s, opus 27, Symphony, opus 21, second movement,
and the Passacaglla. opus 1. The Passacaglla particularly seems
close in spirit to the work analyzed here. Both works consist of
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orchestral variations In which no part of the original theme Is
kept constant as the theme Is metamorphosed Into cumulatively more
complex, highly Individual variations. The large form of both
works Is not limited to a set of watertight repetitions with
alterations of the original theme, but contains contours of
density and of various aspects of sound which transcend single
variations, linking them into a single coherent entity.
Theme (measures 1-20)
The first major section of the Variations presents the source
material and variation procedures which seem to generate the rest
of the work. It also displays sequences of voicing, patterns of
structural events, and phrase divisions which appear in the varia
tions. Using only statements, It has a reasonably clear double
period structure with short coda.
The first phrase extends from measures 1 to 3; the second,
4 to 6; the third, 7 to 12; the fourth, 13 to 18; the coda, 19
to 20. Row forms flow freely from phrase to phrase, with complete
vertical discontinuity (rests in.all parts) only in the center of
the third and fourth phrases. The centers of the first and second
phrases are marked by contrast in timbre, dynamic level, tempo
change, and rests in some parts.
The first half of each phrase is simpler in construction than
the second half. In the first period, the first halves consist
only of single statements, and the second halves consist of two
superposed statements. The second half of the second phrase is
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extended by a retrograde of one of these statements, belonging to
the second tetrachord type, which might be considered to provide
a half-close for the double period.
In the second period, the first halves consist of two super
posed statements, and the second halves consist of three superposed
statements plus a vertical aggregate. The brief coda returns to
the simplicity of the Initial statement, consisting of a single
statement, the retrograde Inversion of the Initial statement ending
on th e same note as the f i r s t note of th e work. This coda may be
said to provide the full-close for the double period.
Generally speaking, the first phrase of the second period
appears to be an elaboration of the second phrase of the first
period. Similarly, the second phrase of the second period
parallels the first phrase of the first period. This structure
is similar to Webern's description of double periods in his 4 lectures. Inversions appear in the middle two phrases of the
double period, suggesting a developmental function; retrogrades
appear in the last two phrases.
All of the tetrachordal pitch aggregates in the theme are
structurally important in the variations, but those marked by
retrograde are particularly noteworthy. At the end of the first
period, tetrachord 6 is stated and immediately retrograded. In
the middle of the first half of the first phrase of the second
period, tetrachord 4 is presented and immediately retrograded,
tetrachord 3 is retrograded and then presented in its original
form, and tetrachord 1 is retrograded and then presented as a
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vertical aggregate. The flrat motive of the second period, tetrachord
3 retrograded, la Itself retrograded In the last phrase.
Retrograde Inversions of the Initial statement, with their
apparent cadentlal function, appear at the end of both periods,
and the end of the first phrase of the second period. At the end
of the first period, the axis of Inversion Is the first note of
the Initial statement; at the end of the first phrase of the second
period, and In the coda, about the last note of the initial state
ment.
Transpositions of tetrachords appear principally In the first
halves of phrases, and seem to have a developmental character.
They are generally linked to their context by pitch content by
pivoting adjacencies, often of a semitone or minor third.
When the pitch content of any of the tetrachords given in
Figure 9 is repeated in the second period as a statement, the
voicing of individual pitch classes is either identical to that of
their first statement, or the entire statement undergoes an inversion
of register. Of the repetitions and retrogrades cited above, all
duplicate original octave placement except for the following:
the first entry of the second period and its retrograde in measures
15-16 (tetrachord 3, retrograded) display register inversion;
as do the statements of tetrachords 4 and 5, also in the first
phrase of the second period. The alteration of tetrachord 5 is
not strict, marking the first occurrence of the new pitch contour
of three successive intervals in the same direction. The alteration
of tetrachord 4 introduces the first statement divided between parts.
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Some timbre changes also occur, notably in the statement of
tetrachord 2 in retrograde in measures 11-12, the end of the third
phrase, in which the original assignment of the motive to oboe is
expanded to include flute and clarinet. Other timbre changes
generally tend to be expansions of this nature. Changes of register
and timbre are concentrated in the third phrase.
The frequent tempo changes seem to serve to give added charac
ter to the motivic statements, and to heighten the expressiveness
of the section. The author sees no consistent structural reason
for their use, although in general they seem to reflect the shape
of the double period.
First phrase (measures 1-2)
The first half of the first phrase ccnsists of a statement
which is referred to in the following discussion as the initial
statement. Its patterns of registration, pitch, voicing, articu
lation, dynamics, and rhythm are taken to have the structural
function of tonic for the entire work. Its tetrachord pitch
content defines tetrachord 1; its rhythmic and articulation pattern,
pattern "a;" its pitch contour, the original form of pitch contour
for statements related to it, specifically a downward leap followed
by two upward leaps, so that the general pitch direction is upward.
The associated nuance markings give the motive a greater dynamic
level in its middle than its ends. It is stated piano, using a
compass of over two octaves, and appears in the contrabass part.
The second half of the first phrase contrasts with the first
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Second phrase (measures 3-6)
The first half of the second phrase is again a single statement,
muted trombone, recalling the tessitura, pitch direction, dynamic
changes, rhythmic and articulation patterns (in retrograde diminution)
and tempo of the first half of the first phrase. Its pitch contour
is retrograde inversion, so that all four transformal variants of
that pattern appear in the first four statements. Its pitch
sequence defines tetrachord 4, which belongs to the first tetrachord
ty p e.
The second half of the second phrase contains a pair of state
ments superposed, forming tetrachords 5 and 6. Unlike the motives
of the second half of the first phrase, these motives do not cross,
stay at a distance from each other, and conform to rhythmic and
articulation patterns "c." The pitch contour of the first motive
of the pair, first violin, measures 4-5, is retrograde inversion;
th a t of th e second, v io lo n c e llo , same p la c e , i s in v e rsio n . The
rhythmic patterns of both seem to be diminutions of "a," that of
the second statement a slight metamorphic variant produced by
shortening the last note.
This superposition is followed by a retrograde of the second
statement in the same octave and similar timbre, bass clarinet,
measure 6. This voicing is the first appearance of a frequent as
sociation of bass clarinet or clarinet with cadential areas; here,
with an area which seems to have a half-close function.
This statement resembles the initial statement in several
ways. This statement's rhythmic pattern is retrograde diminution,
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half In tessitura, timbre, dynamic level, pitch direction, rhythmic
and articulation patterns, and partially in tetrachord formation.
Some of its aspects have the structural function of a dominant,
or an opposing pole to the tonic. It consists of a pair of super
posed statements, the first appearing in the oboe part, and the
second in the viola part. Their rhythmic and articulation patterns
define pattern "b," an altered retrograde of "a" in diminution.
The first motive of the pair is a pitch-contour retrograde; the
second is a pitch-contour inversion. The tetrachord pitch content
of the first defines tetrachord 2, belonging to the second tetra
chord type; that of the second, tetrachord 3, belonging to the
first tetrachord type.
In superposition, the two motives form a complex entity whose
rhythmic and intervallic density is low at beginning and end,
and high in the middle. The general pitch trend of the complex
entity is downward, balancing the trend of the first half of the
p h rase. The f a llin g in te r v a l B-D, oboe, is repeated in th e same
octave by the viola, displaying a technique of singling out these
pitches for further attention later in the movement.
The Webern letter to Reich states that both of the tetrachords
in this complex entity are to be taken as variants of the initial
statement, and that they represent the results of the two kinds of
variation intended by Webern. The statement in the oboe part
seems generally to be metamorphically related to the intial statement.
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Its last note Is the first note of the Initial statement. Both end
on the same dynamic level and are notated In 6/8 meter; this dynamic
level and meter do not occur elsewhere In the first period.
This statement also resembles the second statement. Its tetra
chord type Is type 2; Its articulation pattern Is "b," and Its pitch
contour Is an exact Inversion of that of the second statement about
the axis Eb, which occurs In both statements. The. sim ilarities of
this statement to the Initial statement give it a cadentlal charac
ter; its sim ilarities to the second statement show that this cadence
is not a closure to tonic function.
The superposition and retrograde together form a complex
entity comprising the second phrase. The instruments used provide
a timbre closer to the central sound of the orchestra than the
timbres of preceding entities. Again, the complex entity shows more
dynamic and intervalllc density in its middle than its ends. Its
general pitch direction is downward, so that for the first period
the pitch direction pattern is up-down, up-down, ending with a
return to the original pitch and dynamic level.
As the second halves of phrases in the first period are ex
pansions of the first halves, the second phrase is an expansion
of the first phrase. The third phrase presents the greatest extent
of expansion in the section.
In the first period, the most complex structure is that of two
superposed statements, always occurring in the second halves of
phrases. In the second period, excluding the final statement area,
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two superposed statements form the simplest structure, and more complex
entities appear in the second halves of phrases.
Third phrase (measures 7-12,)
The first half of the phrase consists of two superposed statements.
The first, measures 7-9, first violin, resembles the initial statement
in rhythmic and articulation patterns, both retrograded, dynamic
level, and pitch relation, retrograded and transposed up a semitone.
However, its pitch content retrogrades that of tetrachord 3, its
pitch contour is a register inversion of the first statement of that
tetrachord, the B-D interval is prominently voiced again, and the
statement occurs at a higher pitch level and slower tempo than the
initial statement.
The pitch content of the other statement, measures 7-9, harp
and contrabass, retrogrades that of tetrachord 5, and its rhythmic
are articulation patterns are variants of "a." It is also a
register inversion of the first statement of tetrachord 5. The
complex entity formed by the superposed statement as a generally
downward pitch direction, a decreasing dynamic leve, and a rhythmic
and articulation pattern which is an extension of ”a" and a
palindrome.
The frequent use of varied initial statement patterns here
anticipates a similar use ifc congruent areas of the following
variations. Such use also reflects the tendency of the double
period structure to display similar material at the beginnings of
both periods.
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The second half of the third phrase contains three superposed
statements and a vertical aggregate. All of these entitles repeat
pitch content of previous statements. The first retrogrades
tetrachord 4; the second presents the recently retrograded tetra
chord 5; and the third retrogrades tetrachord 2 In Its original
registration with expanded timbre, and Its original rhythlmic and
articulation patterns. The vertical aggregate repeats the original
registration with expanded timbre of tetrachord 6. The first state
ment Is a register retrograde and pitch-contour Inversion; the
second Is a register Inversion and presents a new pitch contour.
None of these tetrachords has the character of a tonic in Its
original appearance. All of the tetrachords presented in the
second phrase are retrograded and/or inverted in the third phrase.
The rhythmic and articulation patterns of each of the three
linearly presented statements are variants of "a," in progressively
smaller diminution of the original statement. The pitch contour
of the first is inversion; of the second, a new variant; of the
third, the original contour.
The complex entity formed by these motives and the vertical
aggregate dontrasts strongly with the first half of the third
phrase in dynamic level, general pitch direction, rhythmic and
intervallic density, and timbre. The instrumental sequence is
violoncello, tuba, trombone (open), and a significant doubling of
flute, oboe, and clarinet, ending with a sforzando crescendo rein
forced by the vertical aggregate, sforzando pizzicato in all
s tr in g s .
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The third phrase as a whole can be taken to have the nature of
a palindrome variant, centered about the beginning of measure 10 at
the tempo change. The pitch sequence in harp-contrabass-tuba-trombone
in m easures 8-11 i s Gb-F-G/A-A-A-G/A-F-F#. The statem ent in woodwinds,
measures 11-12, has a pitch content which is a variant of that of
the statement, first violin, measures 7-9. The pitch content of
the aggregate in the strings, measure 12, is a verticalization of
that of the half-close statement, bass clarinet, measure 6.
The voicing sequence of this phrase reappears in some variant
in every variation with the possible exception of the last. The
woodwind voicing is generally associated with the intensity peak
of the section. The pitch content of the palindrome noted in the
preceding paragraph is also repeated in every variation, sometimes
with the added notes B-C. When these notes are adjoined, the re
sulting pitch content links the retrograde inversion of the initial
statement about its last note with the first statement of the third
variation, the "subsidiary theme" statement. In this section, the
pitch class B appears nearby, and C is obtainable from the following
aggregate in the strings, measure 12.
The aggregrate itself is the first appearance of the accompanying
material for variations 1 and 2. Its immediate variant, measure 15,
brass, develops through the work, culminating in prominent statements
in the sixth variation.
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Fourth phrase (measures 13-18)
The first half of the fourth phrase is constructed much like
the first half of the third phrase, but it marks a return to
tonic functions. It consists of two superposed statements, the
first in the tuba, a return to the tessitura of the original state
ment, and the second split between harp and viola.
The pitch sequence of the first statement is a retrograde.of
that of the original statement; the pitch contour is also a retro
grade, and the rhythmic and articulation pattern is in its original
form. The low dynamic level is a return not only to that of the
original statement, but to that of the first half of the third
p h rase.
The pitch sequence of the second motive is also a retrograde,
of tetrachord 3. Its timbre partially reflects its original ap
pearance; its registration is an exact repetition. It is much
slower and softer here, and is not prominently voiced as an entity
in i t s e l f .
The rhythmic and articulation palindrome effect resulting
from the superposition of these two motives repeats that found in
the first half of the third phrase. The tempo and dynamic level
also links these areas.
The second half of the fourth phrase, like the second half
of the third phrase, contains three superposed statements and a
pitch aggregate. The sequentially linked statement appears last
in the third phrase; there, it appears first. The pitch content
and sequence of the first motive is a retrograde of the immediately
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preceding last motive, tetrachord 3; the second, retrograde of
tetrachord 6; the third, retrograde of tetrachord 2. The rhythmic
and articulation patterns of the first duplicates that of the
original statement in diminutions of the other two, variants of
pattern "b." The pitch contour of the first is that of the
original statement; of the second, inversion; of the third, retro
grade. All registrations are those of the original statements,
and all timbres used resemble those originally used.
The timbres obtained by the use of violin-clarinet-oboe is
a reduction in intensity from that of the last half of the third
phrase. The general pitch direction is downward, and there is a
sharp reduction in dynamic level. Both phrases of the second
period are terminated by a fermata.
The trend toward tonic-associated material in the fourth
phrase culminates in the short coda, to the fourth phrase, which
is comprised of a single statement of the four-note motive. Its
pitch content and sequence is a retrograde of tetrachord 5. Thus
it is a retrograde inversion of the original statement's pitch
content about the axis of the first note of the work. Its pitch
contour is also a retrograde inversion; its rhythmic and articulation
pattern-is "a" in rhythmic diminution.
Variation I (measures 21-55)
This variation is a codification and thematic statement of
material introduced in the first section. It is principally
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homophonic in texture, with a clear division between melodic and
accompanying material. Row forms are used linearly in the first
period, and somewhat more freely and densely in the second period.
The statement commonly spans three or more measures, whereas in
the theme it extended to two measures at most. The phrases of
Variation I are also much longer than those of the theme, and their
divisions and relationships are clear. As in the theme, each phrase
is binary, and the second phrase is extended, this time with
developmental m aterial.
The presentation of tetrachords almost exactly duplicates that
of the theme, with some additions and variants. All of the tetra
chords marked by retrograde in the theme reappear in congruent
p o s itio n s .
Timbre and dynamic level changes occur only at structural
junctures. The sequence of voicing found in the theme is generally
followed in this variation. Accompanying chords appear in each
instrumental choir in turn.
Changes of register and pitch contour are more static in this
variation than in the theme. The first variation, in general, is
characterized by its static, predictable adherence to the double
period form.
The tempo is increased in the second and third phrases. As
in the theme, these two phrases contain a disproportionate amount
of non-tonic material, including inversions and transpositions, as
well as increased rhythmic and intervallic density. The fourth
phrase again returns to tonic material, cadential functions, and
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a slackened pace.
Transformal and metamorphic variation of the given material
produces new structures in the second, third, and fourth phrases.
An extended statement of six notes is introduced in the second
phrase, and reappears in the third and fourth phrases, with slight
alterations. Two important new tetrachords which provide links
between variations are first displayed in the extension of the
second period. The first palindrome of a dyad occurs in the last
half of the fourth phrase, and is displayed with the importance
elsewhere reserved for statements.
The four cycles shown in Figure 9 first appear together in
measures 29-42, an area which spans the break between the second
phrase and the third phrase, including the half-close area. The
tetrachord aggregate immediately preceding the extension, clarinet,
measures 29-31, is the first entry belonging th Cycle 1. Cycle 2
is represented in a statement, horn, measures 32-4. Cycle 3
occurs in the tetrachord aggregate, harp and celesta, measures 32-4.
Cycle 4 appears in the statement initiating the third phrase, horn
again, measures 40-42, accompanied by a tetrachord aggregate derived
from Cycle 1.
The four cycles reappear in the third aid fourth phrases.
They can be shown to be complete, although this completion is not
clearly delineated. The statement of subsets of Cycles 4 and 1
in measures 40-2 are noted above. The pitch classes necessary to
complete these cycles, F#-A and Eb-F# can be found in measures
43-4, strings aid woodwinds respectively. Cycle 2 is more than
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completely stated, beginning with tuba, measures 43-6, then trombone,
measures 46 (G), horn, measures 48-9, concluding with violoncello,
measures 49-50. Cycle 3 makes Its strongest appearance, harp and
celesta, measures 48-50, with nearby C#'s and E's, first.violin and
viola, to complete Its representation in measures 46-7* Representa
tives of the cycles can also be found in the last half of the fourth
phrase, measures 52-56 as dyads or trichords, anticipating the
structuring of the final measures of the work. Cycle 1 appears in
the Eb-Gb-G-B aggregate, measure 52; Cycle 2, Eb-E-G in the same
measure; Cycle 3, by C#-E-F in measures 54-5; Cycle 4, by C/A-D-F
in th s same m easures.
Observation of deliberately omitted pitch classes is interesting,
if not of provable structural moment. A tetrachord from Cycle 1
can be built from omissions from the first phrase: B-D from the
first half, Eb-Gb from the second half. The last half of the fourth
phrase lacks the pitch classes Ab-A-B-C, those of the initial state
ment of the third variation, the "subsidiary theme" statement.
First phrase (measures 21-26)
Each half of the first phrase of the first period contain a
single three-measure statement. The first half of the second phrase
is in a faster tempo and spans four measures, giving the effect
of a hemiola, and the last half of the second is extended. Each
statement is accompanied by a repeated four-note vertical aggregate,
whose rhythm probably derived from pattern "c." The pitch content
of the motives and aggregates present tetracliordal material related
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to that found in congruent areas of the theme. This material is
also extended in ways analogous to those used in the theme.
The timbre of the melodic statements progresses in weight of
color and volume from solo violin, solo violin reinforced by muted
violins, clarinet, to trumpet. The timbre of the accompanying
figure is assigned in turn to representatives of all four major
divisions of the orchestra: brass, woodwinds, low strings, and
celesta with harp beginning a new cycle with woodwinds in the
extension. The timbre of the whole is somewhat subdued, and the
dynamic level is low, at its peak in the extension.
The first entry of the first vertical aggregate comes before
the double bar marking the beginning of this variation, and dupli
cates the pitch content of the last motivic statement of the theme
(tetrachord 5) in a lower, more compact registration. This pitch
content thus provides a link between the first two major sections.
A further link across the double bar is the sim ilarity in voicing
and registration of the last motivic statement of the theme, and
the first motivic statement of the first variation. Both occur in
solo violin, pianissimo, with similar intervallic leaps. The
second of these statements begins with the last pitch of the first.
The pitch contours are identical. The second is a rhythmic augmen
tation and retrograde of the first.
The pitch content and sequence of the linearly stated motive
of the first half duplicates that of the original statement. Its
pitch contour and registration are retrograde inversion; its
general pitch direction is upward, its rhythmic-articulation pattern
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is a retrograde of "a," and its dynamic level is low, with greater
volume in the middle than than the ends. This statement is then
strongly linked to the original statement, which occupies the cor
responding place in the theme. The accompanying vertical aggregate's
pitch content is that of tetrachord 5, the pitch content of the
last motive of the theme.
The pitch content and sequence of the linearly stated motive
of the second half is that of tetrachord 3. Its pitch contour
is that of the original, as is its rhythmic and articulation
patterns. The pitch content of the accompanying tetrachord is
that of tetrachord 2, which also occupies the corresponding place
in the theme. Thus, the B-D doubling of the last half of the first
phrase of the theme is duplicated here. The general pitch direction
again upward.
Second phrase (measures 27-39)
The pitch content and sequence of the linearly stated motive of
the first half of the second phrase is again that of tetrachord 4.
This statement is extended in the manner previously noted in the
theme, third and fourth phrases. The pitch contour is that of the
original; the rhythmic-articulation pattern is an extension of
"a," perhaps a forecast of "f." The pitch content of the accompanying
vertical aggregate is that of tetrachord 1.
The pitch content and sequence of the next statement (measures
32-34) is that of tetrachord 6, which was the half-close tetrachord
of the theme. The pitch contour duplicates that of its first
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statement In the theme; it is more prominently voiced, and transposed
up an octave, and greatly augmented rhythmically. Its nuance pattern
retrogrades that of the second statement in the theme.
The vertical aggregate's pitch content results from the super
position of two row forms, and does not duplicate the pitch content
of previous tetrachords. It has the dominant normal form 0 14 9,
and contains the interval A-C in common with the first tetrachord.
It may then be said to be a transposition of the dominant tetrachord
pattern to the pitch level of tetrachord 1.
The statements contained in the extension (measures 35-39) .
present new, significant variants of the initial statement which
are used later in the work. The first is a transposition of the
extension found in the first half of the second phrase (measures
27-31), its rhythmic retrograde, and its register retrograde inver
sion. Thus these two statements frame the statement of the half
close tetrachord in measures 32-34.
The first four notes of the extended statement in measures
35-38, first violin, refer back to the initial statement, its
pitch content transposed up an augmented fourth, similar timbre
register inversion. The first two notes, Eb-D, held in common
with the pitch content of tetrachord 2, suggest that the tonic
tetrachord pattern is to be considered transposed to the pitch
level of the original dominant tetrachord. The structurally
important interval D-F is first presented here. The pitch content
of this statement is that of the "modulation" between variations
5 and 6 (measures 135-136).
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The pitch content of the statement, violoncello, measures 38-39,
superposed on the extended statement appears to be taken from three
row forms, and is also in the tonic tetrachord pattern. Its central
A-C interval (which appears as the outer pitch-classes of tetrachord
1 in the original statement) also suggests a shifted relationship
to the tonic. This particular variant recurs as the most prominent
link between variations 2 and 3.
Third phrase (measures 40-47)
The first halves of phrases in the second period, like those
of the first period, consist of a statement and a vertical aggregate.
The second half of the third phrase resembles that of the theme
in its construction. The second half of the fourth phrase presents
techniques used in the fourth phrase of the theme. Fitch .contours
rise in the third phrase, fall in the first half of the fourth
phrase, and rise in the last half of the fourth phrase.
The timbre intensity, as well as dynamic level, assigned to
motivic statements rises from horn, pianissimo, to a repetition of
the doubling of flute, oboe, and clarinet which appeared in the
congruent area of the theme, rapidly dropping off from this peak
back to pianissimo horn, and bass clarinet. This last instrument
had closing or cadential material not only in the congruent area
of the theme, but in its half-close area as well.
A tempo change with an increased number of measures in the
area of woodwind doubling may have been intended as a hemiola
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effect. The high point of intensity, however, was reached in the
extension at the end of the first period.
The vertical aggregates are once again assigned in turn to
representatives of the major divisions of the orchestra: pizzicato
strings, sustained strings, and harp with celesta, and brass,
completing the cycle outlined in the first period. The use of horn
for two motivic statements may parallel the use of tu tti muted
violin for two motivic statements in the first period. The sequence
of tuba, trombone, and doubled woodwinds in measures 43-46 exactly
parallels the sequence in the congruent area of the theme.
Rhythmic patterns are all augmentations of "a," with two
exceptions: the woodwind doubling, an augmentation of "b," which
also derived from "b" in the theme; and the first motivic statement
in the fourth phrase, also an augmentation of "b."
The pitch relation to the cycles of Figure 8 are discussed
above. Analysis of tetrachordal content yields specific links to
congruent events in the theme.
The first motivic statement has the pitch-classes Bb-C#
in common with its analogue in the theme. It also contains the
D-F aggregate introduced in the motivic statement immediately
preceding, in the extension of the half-close. Its accompanying
aggregate has D-Bb-B in common w ith the same analogue, so th a t
motivic statement and accompaniment may both be said to derive
from the same statement in the theme (measures 7-8).
The second half of the third phrase presents tetrachord 4
in the accompanying vertical aggregate. The appearance of this
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tetrachord here is preserved in the variations to come, and helps
provide evidence for locating this area of the form. The woodwind
passage contains the pitch classes F#-Eb in common with its analogue,
and its pitch-class content is inversionally related to that of the
analogue about the axis of F#-Eb.
The extended statement, measures 43-6, tuba and trombone, is a
transposition down a major third of the extended statement, measures
27-31, and is the third occurrence of the extended statement in this
section. The aggregate appearing in measures 46-7 is an inversion of
its analogue in the theme, about the axis C.
Fourth phrase (measures 48-55)
The pitch content of the statement and aggregate of the first half
of the fourth phrase appears to be defined by the requirements of cycle
completion. While there is a dim pitch relationship with the analogues,
it does not seem definite Enough to be asserted here. The pitch
relationships of the last half of the fourth phrase, measures 52-5, seem
to be new. The unequal voicing of pitch classes is evident; the
palindrome about the axis C#-D may anticipate the highest pitches
exposed in the first two measures of the second variation, C#-C-D.
The last half of this palindrome can be linked with E-F, viola, measures
54-5, to form the tetrachord C#-D-E-F, which inverts the pitch-class
content of tetrachord 1 about its highest pitch, C#. This inversion would
be consistent with the occurrence of tetrachord 5, an inversion of
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tetrachord 1 about its lowest pitch, A, in the congruent area of
the theme.
Variation 2 (measures 56-73)
Webern's letter to Willi Reich describes this variation as
a bridge passage between the first and third variations, the princi
pal and subsidiary themes respectively.^ It seems to serve as a
structural pivot or modulatory passage in many ways. Its form
falls easily into the double period framework previously established,
its first and third phrases are of exactly equal length, of 2 bars
each of 2/4 and 3/8 meter. Its second phrase is of that length
plus an "extension" of a measure of silence, and its fourth phrase
contains three bars of 3/8 meter and one bar of 2/4 meter, ending
with a transition into the third variation. Phrase endpoints seem
to be clearly defined, and the phrases strongly resemble one another.
A minimum of new m a te ria l w ith re sp e c t to v o ic in g , rhythm, and
articulation is introduced after the patterns are set in the first
p h rase.
According to Deppert,^ the row form sequence is determined by
two simultaneous, opposing cycles, one consisting of seven successive
transpositions of P 1 at the interval of a perfect fifth, the other
by seven successive transpositions of R 0 (RI 11) at the Interval
of a perfect fourth. The two original rows are prominent in the
theme, and their ultimate transposition to the level of the augmented
fourth with a return to their original relationships serves to both
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close out the section and prepare the pitch relationships for the
third variation.
Webern seems to have thought of the interval of the augmented
fourth as a possible replacement for that of the perfect fifth in g the serial use of tonally based forms. A large area of dominant
pitch relationships is established by this modulation, and the sub
sidiary theme may be said to have the proper "key" relationship to
the tonic. However, the situation may not be so simple. As noted
above, inversional relationships also are assigned a dominant
function in this work.
The texture consists of vertical presentation of aggregates,
w ith a minimum o f th em atic statem ent except in th e tr a n s itio n . The
summation of these aggregates, measure by measure, is invariably
symmetrical and follows a definite sequence of presentation and
retrograde. This property may be no more than a consequence of
the sequence of row forms used, but its obviousness may in itself
be significant.
The voicing of aggregates is invariably by instrumental
choirs, with the winds much more prominently displayed than either
the strings or pitched percussion. Except in the first phrase,
where two-note slurs occur, vertical aggregates consist simply of
sustained or short single sets. Rhythmic patterns derived from
complex entities formed from these aggregates are, relatively
speaking, simple.
The wide range of row forms used makes possible the presentation
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of tetrachords which have structural consequences later in the work.
These tetrachords often have three pitch classes in common with
previous tetrachords, are related to tetrachord 1 by the last cycle
shown in Figure 10, or appear in one of the cycles of Figure 8.
The aural result of apparent metamorphic variation is thus obtained
through transformal means. This relation of metamorphic manifestation
of transformal function is developed in the third and fourth variations.
The trichord relationship anticipates similar relationships in the
third variation. The pitch-class content of tetrachords is, perhaps
incidentally, often related to those of P 10, intraversionally
related to P 0.
The first two tetrachords of variation 4 appear in the more
intense part of the section, measure 60, the beginning of the second
phrase, and measure 65, the beginning of the third phrase. These
tetrachords have not appeared previously in the movement. Their
occurrence here is a jump in the sequential pattern of development,
which immediately retrogrades to the first two tetrachords of variation
3 (the first of which appears briefly in measure 63), measure 66,
closing the second variation.
The only statements in the variation are those in measures
72-3, presenting the pitch-class content of that of the first two tetra
chords of the third variation, inversionally related about the axis of
the first pitch class of the work, A. The second variation then
culminates its "modulation" from the pitch relationships of P 0 to
those of R 4, the retrograde inversion of the row form inversionally
related to P 0, P 3. These latter pitch relationships are thought to
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be characteristic of Invocations of the "subsidiary theme" material.
Other interrelationships between this complex entity and the first
complex entity of the third variation are discussed below.
The pitch contour of the first of the statements at the end of
the second variation, clarinet, is retrograde inversion, reflecting
that of the last statement of the theme. The pitch contour of the
second, solo violin, is a retrograde, and its register and timbre
seem to be inversions of the register and timbre of the initial
statement. Thus, the second statement is a retrograde and an in
v e rsio n .
The voicing of these statements reflects the voicing of the
last statements of the theme and first variation, solo first
violin and bass clarinet respectively. The pitch contours balance
each other, and the two statements intersect in time on a unison.
A, the pivot of their inversional relation. The manner of resolution
of this unison emphasized this relation. The rhythm of the complex
entity formed by the two statements consists of an eighth note
followed by seven consecutive sixteen notes, a probably expansion
in accelerated tempo of the rhythmic pattern of three successive
attacks found in measures 68, 70, and 71, the middle of the second
period, which also anticipates the rhythmic pattern of the three-
note motive of the third variation.
The rhythmic pattern of each of the two statements is a
fragment of pattern "b," repeated, original form in the first
statement, and retrograded in the second. This repetition forms
a new rhythmic pattern which is important in the third variation.
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The second statement Is divided into a pizzicato note and a short
phrase, arco, of three notes, possibly in preparation of the
figurations of the next section.
Variation 3 (measures 74-110)
This section, according to Webern, presents the subsidiary
theme. Three structural devices predominate here for the first
time: three-note motives, for clarity, referred to in this dis
cussion as "figurations," palindromes of two to five notes, and
inversions. Palindromes can sometimes be also interpreted as
tetrachordal permutations, if certain auxiliary notes are also
considered.
This is the first variation whose division into four phrases
is not clear. The division given in this analysis is principally
based on congruences with areas in the theme and first variation.
However, these congruences are prone to relative linear shifts,
similar to linear shifts possible in the realization of mensural
n o ta tio n .
The use of progressively lower transpositions of row forms
yields similar intervals with successively lower pitch levels,
resulting in a pervasive downward trend of pitch. This trend is
offset by strong, rising statements of the four-note motive,
usually portions of the cycles of Figure 9. Material not belonging
to these statements is usually rather delicately voiced, with
relatively few complex entities. Frequent shifts of tempo add to
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the generally Improvisatory character of the section.
The first two measures are linked to the last two of the pre
ceding section, and all three new structural determinants are shown.
Links to the fourth variation appear in the second phrase, and in
the closing measures of the section. The position of these links
is analogous to that of material in the second variation anticipating
the structure of the third variation.
Contrasts of dynamic level abound. There is a gradual buildup
of intensity and dynamic level to the end of the second phrase,
with some slackening in the third phrase, and clear vertical divisions
in the fourth phrase between pianissimo and fortissimo. Changes
of tempo, rhythmic pattern, and free vertical correspondence give
an illusion of free, almost improvisatory structure, in which pro-
menently voiced palindromes assume aural importance.
All phuases present inversions and retrograde inversions of
the tetrachords which appear in congruent parts of the theme,
sequentially and distinctly in the first period, and interlaced in
the second. The exact transformal method and the relation of
superposed tetrachords is important structurally, remaining con
sistent, usually, within each phrase. The first and last pairs
of four-note patterns on various levels are shifted, as are the
inner and outer pairs. The results of these transforms and
shiftings are used in the following variation.
The first notes of the initial statements of the second and
third phrases do not coincide with the tempo changes which might
be taken to mark the head of these phrases. Voicing patterns do
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not always appear In the areas which their appearance in the theme
might lead one to anticipate them. These structural changes seem
to be symptomatic of a general loosening of the vertical correspon
dences established in the theme. The phrases as defined here are
of nearly equal length and seem to be internally consistent
structurally.
Tetrachord pitch content is often related inversionally to
tetrachords of the theme and first variation. The axis of inversion
is generally significant. Dyads and trichords with pivotal pitch
functions occur frequently. Motivic fragments often have multiple
structural functions.
First phrase (measures 74-81)
Inversions of the three tetrachords presented in the first
phrase of the theme are given here, superposed upon themselves
according to a consistent scheme of transformal relationship to
the original statements. The first phrase contains three complex
entities, each consisting of a motivic statement with an accompanying
figuration with isolated note.
The first statement of the variation, flute, measures 74-5,
closely parallels the last one of the preceding section, solo
first violin, measures 72-3. This first statement is called the
"subsidiary theme" statement in this analysis, and it has almost
as much structural significance in the work as a whole as the
initial statement does. Its patterns are closely related to those
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of the last statement of the preceding section. Its attacks are
rhythmically an exact augmentation at an increased tempo; its pitch
content is identical, the order shifted so that the previous
positions of inner and outer pairs are reversed, an intraversional
technique important to this variation. The dynamic pattern
sforzando attack — two note slur at a lower dynamic level —
sforzando attack is a repetition of that of the previous statement;
its pitch contour is a retrograde inversion, and its register is
very nearly a repetition.
The "subsidiary theme" statement's pitch sequence is a retro
grade inversion of that of the initial statement, about the axes
of the latter's two outer pitch classes,, A-C. Its tessitura seems
to invert that of the initial statement.
The "subsidiary theme" statement appears in conjunction with
an isolated note and figuration, violoncello and clarinet, which
together form a tetrachord with pitch content identical to the im
mediately preceding statement in the second variation, clarinet,
measures 72-3. The figuration forms a palindrome with the last
f two notes of that statement, at a lower dynamic level and increased
tempo. The pitch content of the tetrachord, an inversion of that
of the original statement about the axis A-Bb, is again inversionally
related to that of the "subsidiary theme" statement, and the axis
of inversion, A, the last pitch class of each, is again stressed,
this time as an exposed adjacency.
The complex entity displays a freer rhythmic pattern and more
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casual balance of pitch contour than that of the immediately preceding
complex entity to which it is so strongly related. Xhese two complex
entities form a structural pivot between the sections to which they
belong.
The first half of the phrase is completed by another complex
entity, consisting of two statements, both belonging to the second
tetrachord type. Cycles 1 and 2 from Figure 9 are represented, the
two cycles which are prominent in the theme. The tempo is slowed
at the beginning of this complex entity, reflecting the tempo change
at measure 3 of the theme.
The fir3t statement of this entity appears, first violin,
measure 76, closely followed by the second statement, oboe. The
two statements are in rhythmic canon; the rhythmic pattern is
precisely that of the second to last statement of the second variation.
They are inversionally related about their last pitch-class, Eb, an
augmented fourth from the axis of the preceding pair of statements.
This axis is again voiced as an unaccompanied adjacency. The voicing
in oboe and violin may be a variant of that which accompanies the
first statement of the second tetrachord type in the theme, measure
3. The pitch content of the first statement of the entity is a
retrograde inversion, or transposition, of the statement in measure
3 about the intervals Eb-Gb. The pitch content of the second
statement is an Inversion about the axis of Eb. The complex
entity is then strongly related to the first statement of the
second tetrachord in the theme.
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The last complex entity of the phrase is related to the first
statement of the third tetrachord in the theme, measure 3. The
complex entity, like the first of the section, consists of a
motivic statement with a grouping of Isolated note and figuration.
The voicing and register almost exactly duplicates that of the first
complex entity in retrograde, so that these patterns appear as an
enclosing palindrome about the second area, which contains only the
palindrome-like second tetrachord type.
The pitch content of the statement, flute, measures 78-81, is
an inversion of the first statement of tetrachord 3 about the axis
C#-D; that of the tetrachord formed by the figuration and isolated
note, clarinet and viola, a permutation of the pitch content of the
statement, with the first and second pairs of pitch classes reversed.
The overlap results in a quasi-palindrome with intraversion whose
center on unison F is again an unaccompanied adjacency. A silence
of two beats separates the first and second phrases.
Second phrase (measures 82-94)
The first two tetrachords of the fourth variation are intro
duced at the head of this phrase. They may be derived following
the method of the second cycle given in Figure 8, or they may be
considered to be inversions of tetrachord 4 about the axes resembling
those of the second complex entity of the first phrase. A dual
derivation would not be inconsistent with Webern's compositional habits.
Tetrachord 5fs inversion is presented without a break in
texture, followed by two superposed variants of tetrachord 6. The
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end of the phrase is marked by a fermata. The second phrase then
contains three areas, by tetrachordal analogy to the theme, but
its breakdown into complex entities is not as clear as that of
the first phrase of this variation. Elisions and double structural
functions assigned to the same event abound. Like the areas in the
first phrase, each subdivision of the second phrase presents
inversions and retrograde inversions of all tetrachords found in the
corresponding phrase of the theme.
The first area consists of the first three notes of a state
ment, flute, measures 83-5. The fourth note might be considered to
be isolated but appears in the next area, also flute, measure 87.
These three notes are accompanied by two isolated notes with asso
ciated figurations, violoncello, viola, bass clarinet. The pitch
sequence of the statement is a retrograde inversion of tetrachord 4
about the axis of its first pitch class, E. Its pitch contour is a
retrograde of that of the initial statement; its rhythmic pattern is an
augmentation of that of the "subsidiary theme" statement, disregarding
the increase in tempo at measure 85, and its pattern of dynamic level
is a variant in which the first sforzando is replaced by an accented
piano, giving the fourth note of the statement an added emphasis by
c o n tra s t.
The pitch content of the first grouping of isoltated note and
figuration is a retrograde of tetrachord 4 about the axis E, the second
pitch class of that tetrachord. The Intersection of the pitch-class
content of this grouping with that of the statement, Eb, the axis of
lnversional relationship, is disguised.
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The pitch content of the second such grouping is an inversion
of that of tetrachord 6, transposed up a major seventh so that the
axis of inversion is not contained in the pitch content. The
intersection of this pitch content with that of the statement,
D, is marked by adjacency with similar voicing occurring on the
isolated note.
The figurations are so constructed that their resemblance is
aurally clear. Both consist of three consecutive falling sixteenth
notes immediately following the isolated note with which each is
grouped. Their pitch contents are related by retrograde inversion,
again at an axis which is not contained in their common pitch
c o n ten t.
The first grouping, as well as the first note of the state
ment, is piano; the remainder of the area is forte and moves at
an increased tempo. The listner is thus prepared for an event
of structural importance, which takes place in the next area,
measures 86-9 — an aurally obvious palindrome followed by inter
laced two-note motives representing all cycles of Figure 9.
The center of the palindrome is the missing note of the
statement of the preceding area, flute, measure 87. The palindrome
itself is formed by the statement and retrograde of the pitch
sequence of tetrachord 5, with increasing dynamic level. The
resulting tetrachords intersect on the double center note of the
palindrome, sforzando, trumpet, measure 87, a striking complement
to the flutter-tongued note of the same pitch level in the flute.
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This registration of F Is anticipated, viola, measure 80. Both
tetrachords are realized as Isolated note-figuratlon groupings,
the last reversing the conventional downward pitch direction of
the figuration. The registration of these groupings is identical,
and their voicing nearly so, seemingly altered only to maintain
the increase of dynamic level which prevails through the second
p h rase.
The pitch content of the first tetrachord of the following
complex entity measures 88-9, first and second violin, is a retro
grade inversion of tetrachord 2 about its first pitch class, B;
that of the second tetrachord, a retrograde inversion of tetrachord
6 about its last pitch class, G. The two statements are inver
sionally related about the axis of these two pitch classes, the
interval G-B. It may be noteworthy that the first palindrome of
the work is in the congruent area of the theme, the extension of
the second phrase, and that its center is one of these pitch
classes, G.
The tetrachords are realized as two-note motives whose
rhythmic patterns derives from that of the first motivic statement
of the variation, and from that of the figuration device. The
axes of inversion are aurally evident as adjacent entries at the
same p itc h le v e l.
The pitch direction of the complex entity is strongly down
ward, and its rhythmic pattern is eight successive sixteenth notes,
like that of the last complex entity of the second variation. The
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entity is somewhat balanced by the following apparently isolated
note, which is actually the first note of the first state
ment of the third phrase. This note is separated from the. rest
of its statement by a fermata and contrast in dynamic level, in a
manner resembling the isolation of the note which centers the
palindrome, flute, measure 86. The continuity of both these notes
with their statements is maintained by assigning the entire state
ments to the same p a r t, f l u t e .
Third phrase (measures 90-99)
This phrase uses techniques introduced in the second phrase,
in that it presents inversions and retrograde inversions of the
tetrachords in a freely interlaced manner. Additional material
emphasized certain pitch relationships, and some notes have
multiple structural functions.
The phrase can be divided on the basis of texture, resemblances
to congruent areas of the theme, and tetrachordal entities, at
the last beat of measure 94. The area before that point resembles
the first half of the third phrase in the theme, and the area
after resembles the second half of that phrase.
The voicing of statements becomes more intense, preparing
for the strong statements in the fourth phrase, measures 105-6.
The tempo fluctuates at nearly equal periods of time. The im
portant tetrachords Eb-E-F/A*G and E-Eb-C-C#, respectively the
last tetrachord of the third variation and the first of the fourth
variation, are introduced together, measure 82-6.
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The pitch-class content of the first statement of the first
half of the phrase can be Identified with that of the initial
statement, or the inversion of tetrachord 5. The sequence of
pitches, however, is shifted so that the inner and outer pairs of
pitch classes are reversed. The last two pitch classes, C-C#,
serve to reinforce the appearance of the retrograde inversion of
tetrachord 3 about the axis of its last pitch class, C, in
measures 90-1. This last tetrachord is the one that might be ex
pected at the head of the phrase from examination of the congruent
area of the theme and the preceding events of the variation.
The pitch-class content of the tetrachord serves to reinforce
that of the next one, the inversion of tetrachord 5 about the axis
of its last pitch class, C#, which comprises a statement; and the
one after that, a retrograde of tetrachord 4. Tetrachords 3 and
4 appear in sequence in the congruent area of the theme, and are
followed there by tetrachord 5.
The statement, trumpet, measures 91-5, has the pitch contour
of the original statement. Its assignment to the trumpet may be
a voicing variant of its assignment to horn in the congruent area
of the first variation. As an entity in itself, its dynamic
level pattern is a variant of that of the first statement of the
variation — loud outer notes, subito piano for its third note.
Its rhythmic pattern is a new permutation of that of the first
statement of the variation. It is so imbedded in its complex
entity that its identity as a statement may be masked in performance.
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The configuration of the complex entity is such that the pitch
contour, pitch content, and dynamic level of the statement is
embellished. The two figurations are retrograde inversions of
each other about the axis of their respective last and first
pitch class, E. The register duplication of the voicing of that
note, occurring also in the motivic statement in the time interval
between the pair of figurations, implies that a palindrome variant
is probably intended. The imitation of the pitch classes G-F#
in the oboe with duplicate registration in the'trumpet .part is the
first appearance of an imitative procedure which is important in
the fifth variation. Its occurrence here is emphasized by the
timbre sim ilarity of the trumpet and oboe.
The second half of the third phrase is a non-rigorous palin
drome of structural events, the second half Inverted, about the
region of the fermata in measure 97. The tetrachords are again
interlocked in such a way that they reinforce each other.
The first tetrachord's pitch content sequence corresponds to
that of the inversion of tetrachord 5 about the axis of its first
pitch class, A; the second's, to the retrograde inversion of
tetrachord 1 about the axis of its last pitch class, C. The
retrograde inversion of tetrachord 6 about its first pitch class,
and that of tetrachord 2 about its last pitch class, follow. The
area concludes with permutation of tetrachord 4 and the Inversion
of tetrachord 5 about its last pitch class. Again, all tetrachords
appearing in the congruent area of the theme are presented.
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The principal statement, • trumpftt again, measures 96-9, its
dynamic level pattern an inversion of the imnedlately preceding
statement in measures 91-94. Its pitch contour is a retrograde
of that statement, its articulation and rhythmic patterns a return
to those of the "subsidiary theme" statement. It is again disguised
in the context of the surrounding complex entity, which this time
seems to balance rather than emphasize its characteristics. The
voicing sequence of the congruent area of the theme seems to be
spread out over the portion of the third phrase after the fermata
and the first half of the fourth phrase. A redefinition of phrase
boundaries to include this voicing pattern in the third phrase
drastically shortens the fourth phrase, and does not seem to be
consistent with the procedures of pitch relationships.
All palindrome relationships in this area are variants.
Axis of inversions between the memebers of the pairs of figurations
in measures 95 and 99 are given the same register. The pitch class
palindrome containing the figuration in measures 94-5, violin, and
97, violoncello-viola, is disguised by varying other patterns.
The statements of the second tetrachord type, meaaires 96-8,
yield memebers of cycles 3 and 4 (the inversions of cycles 1 and 2),
with representative dyads from all cycles. Fragments of the other
two cycles can be found in the neighborhood, but their appearance
may not be of c ru c ia l im portance.
Tetrachord 6 is voiced, harp and trumpet, measure 99, in
such a context as to suggest a clear C major chord, providing a
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cadential sound to the area concluding the third phrase. Such use
of previous half-close material seems to imply that the cycles of
Figure 9 have superseded it in importance as tonic-opposed material.
Fourth phrase (measures 100-109)
The first half of the fourth phrase presents a complex entity
of interlaced tetrachords, similar to those of the second and
third phrases, at a lew dynamic level, with figurations predominating.
The second half, in contrast, principally consists of distinct
superposed statements, some at a high dynamic level, and seems to
reflect in i^s structuring the processes used in the theme. The
tempo continues its almost regular fluctuations, The point of
division between the halves of phrases is made at the beginning
of measure 105, which coincides with a tempo change and two strongly
voiced imitative statments, trombone and viola.
The pitch content of the complex entity which comprises the
first half of the phrase begins with tetrachord 3, with its inner
and outer pairs of pitch classes reversed. The entity continues
with tetrachord 5, retrograded (which equals the inversion of
tetrachord 1 about its first pitch class), and concludes with a
further permutation of tetrachord 4 about its first pitch class F.
Tetrachords 1 and 3 appear in the congruent area of the theme.
The added tetrachords again appear ot support the characteristics
of these original ones.
The principal statement, solo violoncello, measures 100-2,
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is again somewhat disguised by its context. Its pitch contour,
rhythmic, and articulation patterns return to those of the first
statement of the variation, and its dynamic level drops the
established pattern of the variation.
The accompanying figurations are related by successive inver
sion. The axes of inversion are, in order, A, Bb-Db, and Eb-E.
Only the second of these axes appears in the pitch content of the
figurations, and it is marked by lnmediate repetition in the same
register. The pitch contour is preserved under inversion except
for the last motive, which does not present a clearly related
ptich contour. The notes left over from the figurations are
absorbed in context, except for the one which begins the cycle, F#,
horn, measure 100. The small cycle of progressive change may be
said to anticipate canonic technique found in the fourth variation.
The second half of the phrase contains two complex entities,
one consisting of two superposed statements, the second of a
statement and a grouping of an isolated note and a figuration.
The last note of the section is doubled and tied over into the
fourth variation.
The two statements in the first complex entity have pitch
content of the second tetrachord type, representing Cycle 1 and
Cycle 2 of Figure 9, as do the tetrachords of the congruent area
of the theme. The first is the tetrachord of Cycle 1 not repre
sented by the six tetrachords of the first half of the theme; the
other is retrograde inversion of tetrachord 6, about the axis of
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its last pitch class, 6. The two statements have identical rhythmic
patterns, both are fortissimo, and their pitch contour, a return
to that of the first statement of the variation, is inverslonally
related. They appear in canon at the interval of a quarter note.
The axis of inversional relation, G-B, is not stressed, so that
the linear rather than vertical correspondence between the state
ments predominates aurally. The last note of the entity is
somewhat isolated, and may imply a linked tetrachord with pitch
content of tetrachord 5, with a portion of the next statement
in the harp.
The final complex entity of the section serves as an inver-
sionally related link with the first statemtnt of the fourth
variation. This entity consists of a motivic statement in the
harp at a much lower dynamic level than the preceding statements.
The pitch content of this statement is that of the retrograde
inversion of tetrachord 5 about the axis F#, its final pitch
class. The tetrachord appearing at the congruent area of the
theme is the retrograde of tetrachord 5. It may be significant
that the final pitch class of the variation, the last of this
tetrachord, is Eb, an augmented fourth away from the first and
final pitch class of the theme, A. In any case, the doubling
of harp and muted contrabass provides a distinctive envelope for
this note — a decisive attack and pervasive sustained power
even at the pianissimo level.
The pitch content of the accompanying grouping is that of
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tetrachord 1, shifted so that the inner and outer pairs of pitch
classes are reversed. The two tetrachords are then inversionally
related, but the relationship is not made aurally obvious. The
variation thus concludes with an altered repetition of tonic-
associated material, combined with the inversional balance character
istic of the section. The appearance of clarinet in this area is
again an association of its timbre with cadential function.
The pitch content of the final statement of the variation
provides a link to the first statement of the fourth variation. The
statements are related by retrograde inversion about their inner
pair of pitch classes, E-Eb, providing a palindrome variant which
spans the sectional division.
Variation 4 (measures 109-134)
Webern'8 letter Identifies this variation as a developmental
recapitulation. Much of the structurally prominent material
introduced up to this point appears in it, varied with apparent
freedom. If division is made at measure 125, the first period
is at a slower tempo than the second, and contains one less measure
in compensation. Since smaller divisions of the structure are not
clear, they are not made in this analysis.
After the dux, each canonic voice's pitch class content is a
transposition up a semitone from that of the immdeiately preceding
voice. Then the four canonic voices present four simultaneous
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unfolding row forms so related that, by linear shifting, any of
the four pitch classes within the aompass of some major third are
available at any given moment. The only exceptions to this
relationship occur in the region following measure 127, and result
from varying overlaps of row forms within voices.
Each canonic voice consists of three overlapped row forms,
all inversions, with the relationship pattern I n — I n + 2 —
I n + 4, which allows the last two pitch classes of the In ending
row form to serve also as the first two pitch classes of a
beginning row form. The canonic voice is said, for the purposes
of this study, to be defined by this row form relationship. Each
canonic voice leaps freely among instrumental parts, as Figure
13 shows.
The numbering of the canonic voices must be somewhat arbitrary,
since the order of their entry in imitation does not always conform
to the entry pattern established in the first few measures. The
order used in this analysis is based on their pitch relationship.
The first to enter, and the lowest in pitch, is called the dux.
or 1; the second, and second lowest, is 2; the third lowest, 3;
the last, and highest, 4.
The juxtaposition of forms transpositionally related at the
semitone forces some duplication of semitone adjacency and dyads
with pivoting characteristics, as well as near adjacency of re
lated tetrachords.
P 0: A Bb C# C B D E Gb F E G Ab
P I : Bb B D C # C Eb E G Gb F Ab A
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The use of four such rows simultaneously allows shifting pitch
level through broad Intervals, as In measures 122-4.
The row form relationship also guarantees that three pairs
of forms related as P 0 : P 1, the retrograde inversion relation
ship, are always present; that two pairs related as P 0 : P 2,
the intraverison relationship, are also always present; and that
one pair related as P 0 : P 3, the inversion relationship, is
also always present. Further, the first row form of the section
is, according to the transformal relationships of the structure
of the work, the most remote from P 0 which can be obtained;
namely, its retrograde inversion at the augmented fourth.
The fixed tetrachord relationship in this section, as in the
sixth variation, seems to be secondary to the relative tetrachord
relationships forces by the canonic scheme. Nevertheless, a
pattern of relationship which is an inversion of the cycles of
Figure 8 connects the prominently voiced tetrachords. This re
lationship is shown in Figure 12.
The voices of the canon seem to be subject to free linear
shifting to facilitate construction of complex entities and
phrases. Tetrachordal identity is usually maintained, the exceptions
generally occurring in the region of row form overlaps. Almost
all previous patterns of rhythm and articulation appear. Clear
presentations of previous ideas, however, are seldom found, and
transformal means of variation of the dux are generally avoided
in favor of metamorphic means.
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The general means of building phrases and presenting voices
in simultaneous variation used here seem to reflect the means
used in Heinrich Isaac's sequence from the Choralis Constantinus. 9 transcribed by Webern, "De radice Jesse." A complete discussion
of the ways in which Webern's acquaintance with the music of
Isaac is beyond the scope of this discussion. A few of the more
obvious sim ilarities of this particular sequence with the fourth
variation can be mentioned briefly.
The sequence, like the fourth variation, is not audibly a
strict canon. It contains several close-range imitative passages,
usually presenting rhythmic and pitch variants of its initial
motive, a rising scalewise passage with which the tenor begins.
The means of varying this passage are similar to those used in
the fourth variation. Transformal means of variation are sparingly
used, although inversional and retrograde relationships can be
found. The wealth of proportions used in the sequence and their
apparent serialization do not serve, in themselves, as the con
trolling factor in the variation of the passage — it appears,
rather, that these proportions are used in order to produce
pre-conceived variation patterns which fit into a large formal
design. The variants of the passage are superposed to form a
single, long phrase of gradually increasing intervalllc and
rhythmic density. This phrase, viewed as an entity in itself,
can be seen as a summation of the effects produced by the four
voices, making musical sense without explicit reference to the
im itative techniques which pervade the whole.
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Similarly, the fourth variation presents variants of state
ments, freely imitated at close range. The statements are linked
to form two long phrases, here identified as the two periods of
a double period form. The large plan of these phrases can be
considered independently of;their canonic structure.
The author is of the opinion that the serial techniques used
in this variation are not to be taken as the sum of the variation's
structure despite the care with which they are worked out. As in
"De radice Jesse," the structure of the whole transcends the
intricate detail of the entitles which make it up, so that such
detail can be obscured by larger musical purposes.
The rhythmic manifestation of the canonic voices is so free
that no extended strict rhythmic imitation occurs, although
congruent tetrachords by row form often are associated with
similar rhythmic patterns.
F irst period (measures 110-124.)
If the dux of the canon is said to begin at the double bar,
measure 110, the first entries of each voice occur at the durational
distance of a half note. The assignment of contrabass - viola -
oboe to the first three of these entries probably reflects the
voicing of the first three tetrachords in the theme; that of
the clarinet to the fourth entry, the habitual association of
clarinet or bass clarinet with cadential situations in the pre
ceding sections.
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The dynamic level builds from pianissimo in all entries to
forte in measure 115f The F# measure 115, clarinet, marks the
first appearance of the second row form in a single voice. In-
tervallic and rhythmic density also increase throughout the pre
sentation of the first row form in all canonic voices. The only
prominently voiced unisons appear in measures 112-3, Cft, both
viola and trombone, followed by D, trombone and second violin,
emphasizing the chromatic upward trend in that area (B-C-C/A-D-Eb) ,
which, by the simultaneous unfolding of transposltionally related
row forms forces the voicing of three adjacent pitch classes, a
semitone apart).
The first tetrachordsi of the first three entries have pitch
contour inversional to that of the initial statement; of the last
entry, pitch contour inversional to that of the first statement
of the third variation. The exact transpositional relationship
of these tetrachords is masked by rhythmic and nuance variants.
The rhythmic and articulation patterns are permutations of those
of the initial statement. The tetrachordal pitch sequence
relation of these tetrachords to that of the rest of the work is
inversional, and shown in Figure 12.
The second tetrachord of the row form is presented as an
entity in all voices. It is of the second tetrachord type, thus
resembling tetrachord 2. The order of entry of the voices is
2-1-4-3, with the first and last pair entering at the durational
distance of a quarter note. The; rhythmic patterns are freely
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derived from "b," the pattern associated with tetrachord 2 in the
theme. The first two entries are audibly clear; the last two are
soemwhat covered. The first three entries have similar pitch
contour, inversion or retrograde inversion of that of the initial
statement; the fourth has that of the first statement of the
third variation. The increasing density aid dynamic level cul
minates in the unprecedented appearance of three motivic state
ments, simultaneously, forte, reinforeed by pizzicato harp in
measure 115. Brief unison A's and C's in that measure may reflect
the outer pair of pitch classes of the initial statement. The
contrast in sparse voicing in measures 110-3 with the complex
voicing in measures 114-5 may reflect a similar contrast between
measures 1-2 and 3 of the theme.
The pattern of entries for the third tetrachord yields
simultaneous pairs: 1-2, 3-4. This tetrachord involves a two-
note overlap of row forms in all voices, and it is accordingly
somewhat fragmented in its manifestations. The rhythmic pattern
of voices 2 and 4 seem to coincide, if rests are disregarded; it
is the retrograde of that of the previous tetrachord in the
voice 3, flute, measures 114-5, probably the most prominently
voiced tetrachord of those measures.
The two-note overlap results in an extension of this tetrachord
in all voices, and the loss of the first tetrachord of the new
row form. The extra notes are handled in various ways, but in
no voice does the entry of the new row form coincide with a new
statement. A slackening of texture results, measures 116-7,
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preparing for the quiet introduction of the second tetrachord of
the new row form, measures 117-121.
The pattern of entries in these measures is 2-3-4-1; after
the entry is covered somewhat, first, trumpet, measure 118, each
and the low dynamic level is maintained. The first three entries
occur a half-note apart. The voicing in brass and woodwinds may
be an elaboration of the voicing of tetrachord 3 in the theme,
or of the motivic statement in the trumpet in the second phrase
of the first variation, but the total effect here is much quieter
than it is in those areas. There is a general return to decreased
intensity despite the appearance in measures 119-120 of four
simultaneous motivic statements.
The pitch contour of the first and third entries reflects
that of the initial statement; that of the second and fourth,
of the first statement of the third variation. The. rhythmic
patterns seem linked to the initial statement, although that of
th e f i r s t e n try may be lin k ed to both.
Unisons of E, measure 118, E, measure 119 in the same register,
D in measure 120, and repetition of Bb, measure 121, combined
with the relaxed texture, seem to indicate a return to the context
of the head of the variation, measures 110-113. The prominence of
voicing given to A's whenever they appear may indicate a return
to altered tonic function. The F#, clarinet, and F, harp, in
measure 124, prepare the entries of unison woodwinds and violon
cello, respectively, in the next measure.
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Measures 122-4 contrast with the preceding portion of the
variation by a sudden tempo change and a sharp Increase In dynamic
level and intervalllc Intensity. These measures contain the
simultaneous presentation of the forces portion of the row form
which three adjacent semitone intervals, and that property is
exploited. Another two-note overlap follows the occurrence of
these three notes, resulting in another breakdown of tetrachordal
identity. These measures, then, like 116-7, are transitional
and do not contain clear motivic statements, with the exception of
that in measures 123-4, clarinet, an inversion of tetrachord 3
about the axis of its first note, Bb, in pitch contour and can
be seen as a register inversion of the initial statement. The
association of clarinet with this altered return to original
material is taken to represent a half-close.
The shifting adjacencies in the strings, measures 121-3,
present a succession of major sevenths at successively lower
pitch levels, reinforced by unisons. The effect is striking,
and may be a timbre and/or register inversion of the prominent
high woodwind voicing at the head of the second period.
Second period (measures 125-134)
The first tetrachord of the new row form having been absorbed
in the previous passage, the entries at the head of the second
period present the second tetrachord in the entry pattern 1-2-3-4.
The durational distance between the first and second entry is a
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quarter note; that between the other entries, a half note.
All four entries are prominently voiced. The first three
have a jagged pitch contour like that of the first statement of
the third variation; the fourth has a pitch contour of retrograde
Inversion to that of the Initial statement. All rhythmic
patterns In these statements are variants of those found In the
third variation. The voicing as a whole resembles a summation of
that of the third phrase of the theme, with the high unison wood
winds accompanied by a strong rise in pitch direction in the
strings, measures 125-7. There Is a return here, as in surrounding
areas, to return to the voicing by choirs procedure found in the
first variation. The fortissimo dynamic level is sustained
through measure 131, which, combined with the frequency and
strength of motivic statements, gives this area the greatest
weight of intensity of any in this variation.
The next statement, first violin, measure 127, is tetrachord
5 in original form. This tetrachord has previously been observed
in conjunction with the high unison woodwind passage. Its
appearance here is tu "'erstandably stressed; it is obtained by
disguising the actual first note of the tetrachord in measure
126 with pizzicato voicing. This tetrachord also marks the
last overlap of row form in voice 1.
Measures 128-130 might be expected to be transitional, from
an examination of the varying overlappings of row forms which occur
here. However, the voicing, dynamic level, and texture of the
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preceding area are maintained, and motivic statements and their
fragments give the area shape. The patterns of these statements
appear to be freely assigned with an eye to vertical correspon
dences such as the G-A interval stressed in measures 128-9,
second violin and violoncello. The fortissimo statement in
high unison woodwinds, echoing their previous entry, is the only
clear presentation of the central tetrachord of the last row form
as it passes through the four voices. The jagged contour is
widened; the rhythmic pattern is a retrograde of that of the
initial statement. While other motivic fragments follow, none of
them have such intensity and strength.
The row form area forcing three successive semitone adjacencies
is again exploited in the final measures of the fourth variation.
A semitone progression Initiated by a palindrome occurs in the
brass, measures 131-4, E#-D-Eb-E-F. More freely realized than
the similar passage at the end of the first period, it is accompanied
by the last motivic statement, first violin, masked somewhat by
accompanying notes, celesta, and by its resemblance to the
preceding fragm ent in th e same p a r t.
The intensity decreases rapidly in this area, the tempo
slackens at measure 132, and the area concludes with pianissimo
notes, harp. The presentation of disjunct dyads in the final
measures of the section, despite the transpositional relationship
of the voices, must be a deliberate anticipation of the final
measures of the work. The last tetrachord's pitch content betrays
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Its cadentlal function, for It Inverts the pitch content of the
last tetrachord of the theme about the axis of Its first pitch-
class, F#. The accompanying figuration Is significantly voiced
In the clarinet part, associated with cadentlal areas.
Cycles 3 and 4 from Figure 9 appear In complete form In
measures 131-4. The transpositional relationship of the. row
forms has guaranteed the appearance of representative tetrachords
from each cycle every time the tetrachord of the second type was
canonically treated.
The D-Eb sequence, c e le s ta , measure 132, may p a r tia lly
prepare the pivotal tetrachord which begins the fifth variation,
viola, measures 135-6. The variant D-C#, harp, measures 133-4,
may also serve this function. If the F#, violin, measure 132, is
included, a palindrome F#-D-Eb-D-C#-D-Eb-F# spans the double bar.
The high frequency of Eb's in measure 132 may serve to mark this
palindrome.
Variation 5 (measures 135-146)
This variation is identified as a transition by Webern. Like
the second variation, it verticalizes and condenses previous
relationships, an1 "modulates" from system of one tetrachord re
lationships to another. Like the second and the fourth variations,
the density of row forms is such that pivoting aggregates and
multiple structural meanings assigned to entities take precedence
over the presentation of the formal scheme identified with the
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theme. Entities of the second, third, and fourth variation are
presented here, varied in such a way that their identity fades.
Canonic imitation is brief and seems used for effect rather than
generation of large structures. The section is short, of low
dynamic level, and structurally fragmented. The few statements
which can be clearly defined then assume, in contrast, greater
importance than in the fourth variation.
The section can be fairly easily divided into four phrases
on the basis of contrast of texture, motivic integrity, and
tempo changes. Tetrachordal relationships with congruent areas
of theme are present, but incomplete. Voicing patterns may be
variants of those of the theme, but are not clearly thus definable.
The pattern of general intensity follows that of the theme.
First period (measures 135-141)
The f i r s t phrase co n tain s two statem en ts. The f i r s t i s
unaccompanied; the second, accompanied by aggregates resembling
those found in the second variation. The precise configurations
of these statements seems to be structurally important, for they
reflect specific variants of patterns which pervade the entire
work.
The pitch sequence of the first of these statements, viola,
measures 135-6, is particularly remarkable in context. It is
that of the first tetrachord of P 5, the row which has a string of
seven pitch classes identical to a string in P 0, and this
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. particular pitch sequence is the first four notes of that string.
Further, since R 5 is related to R 4, the last form of the fourth
variation, as P 1 is to P 0, the row form relationships of the
theme are also invoked. This tetrachord, then, serves as a
"common-tone modulation" between the system of inverted tetrachord
which pervades the third and fourth variations and the original
such system used in the theme and first variation. Its tetrachord
type, like that of the initial statement, is the first type.
The rhythmic-articulation pattern of this statement is the
retrograde of that of the original statement, in diminution.
Its pitch contour is a retrograde of that of the first statement
of the third variation. Its register is neither an inversion or
return to that of either of these previous statments, but some
what of a compromise between them. Its pattern of dynamic level
has characteristics of that of both. Its unaccompanied voicing
in a structurally exposed area accentuates its importance, and
recalls the similarly exposed context of the initial statement.
The second motivic statement more nearly recalls the first
statement of the third variation with respect to its register,
voicing, and rhythmic-articulation pattern. It is a retrograde
inversion about the axis of the first note, B, of tetrachord 2,
the analogous tetrachord in the theme. Its pitch contour, however
is a retrograde of that of the initial statement, and its falling
dynamic level is a retrograde of a variant previously encountered
in the second phrase of the third variation, flute, measures 83-7.
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The accompanying vertical aggregates resemble those found In the
second variation. Their rhythmic pattern Intersects that of the
statement in such a way that the rhythm of the complex entity consists
of an eighth, fourth sixteenths, and three eighths, possibly a variant
of the pattern of eight successive eighths, measures 69-71, second
variation. The vertical aggregates do not mask the identity of the
statement. The expected retrograde inversion of tetrachord 3 does
not appear as an entity in this area.
The second phrase consists of two statements, solo first violin,
measures 139-41, with a probable short extension. The four notes are
grouped two by two in each statement, and the rhythmic and articula
tion patterns are based on those developed in the third variation.
A dense knot of imitation at close range accompanies these statements,
blurring their audibility. Every dyad in these statements is imita
ted, either simultaneously in a different rhythm or at a durational
interval not greater than a dotted eighth beat. Additional entries,
pivotally related with identical or similar voicing and rhythmic and
articulation patterns, do not help to clarify the statement's configu
rations. The resulting intervallic and rhythmic density provides an
Impression of structural stress despite the generally low dynamic level.
The pitch-class content of the statements are, respectively, the
inversion of tetrachord 5 about its first pitch class, C, and a shift
variant of the original form of tetrachord 3, such that the first
and last pairs of pitch classes are reversed, while preserving
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their Internal relative sequence. No clear statement of tetrachords
4 or 6 appears. The rhythmic pattern of the statements taken
together is a palindrome which may be derived from the original
statement of tetrachord 5. The articulation pattern of the first
statement, and all accompanying fragments, consists of slurred
dyads, a fragmentation reflecting that found at the end of the
second phrase of the third variation. The articulation pattern
of the second statement and its accompanying fragments consist
simply of detached notes, which may reflect those of the accom
panying aggregates of the second variation, and here serves to
dissolve more complex articulation patterns. The change from
slurs on every eighth of the measure to detached notes on every
sixteenth of the measure brings about an almost immediate drop
of intensity, somewhat compensated by increased movement, at the
end of the first statement. In no preceding variation does an
intensity drop occur there. The articulation scheme of the phrase
as a whole may derive from that of the last motivic statement
of the theme, measures 19-20, first violin.
The pitches repeated in measure 141, the end of the second
phrase, include those of tetrachord 1, nearly in retrograde order,
oboe and harp, C#-C-Bb-A. The C-A interval is further emphasized
by a brief palindrome C-A-C, harp, first violin, celesta.
Second period (measures 142-5)
The third phrase combines material found in the extension
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of the second phrase and the voicing of the third phrase of the
theme in about about a third of the elapsed time taken in the
analogous area of the theme. The voicing is varied, compressed,
and retrograded (woodwinds, trumpet instead of trombone, strings).
The woodwinds present the inversion of tetrachord 6, the tetra
chord of the extension, inverted about its last pitch class, G.
The trumpet has a three-note fragment which may recall the/figur--
ations of the third variation, and the strings resort to the ac
companying vertical aggregates resembling those of the second
variation. The inversion of tetrachord 6 about the axis of its
first pitch class, C, appears in a motivic statement, first violin,
measure 142-3. The pitch content of this statement has three
pitch classes in common with tetrachord 5, which appears in the
congruent area of the theme. However,.it is of the second
tetrachord type, and its pitch content thus has a double meaning,
blurring the previous distinctive structural meaning of tetrachord
5. Its pitch contour is a retrograde of that of the initial
statement. Its rhythmic pattern corresponds to the figuration
plus isolated note grouping.
All four cycles of Figure 9 are represented in this phrase.
Its texture resembles that of the second half of the first phrase,
perhaps an indication of closing structural relationships. The
density of links with previous material, as well as the continued
drop in Intensity, also indicate closure in this area previously
associated with the intensity peak of the structure of the theme
or variation.
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The fourth phrase consists of four Interlocked statements, two
of which are so fragmented as to lack clear audible Identity.
Their rhythmic patterns are such that an attack occurs on every
sixteenth beat except the last of measures 144-5. A close variant
of the thythmic pattern of the initial statement is presented as
a canon with three entries: second violin, violoncello, clarinet,
viola. The rhythmic pattern of the statement, first violin, is
close to that of the "subsidiary theme" statement. Thus, the
rhythmic patterns alone recall those of the theme, third variation,
and the techniques of the fourth variation.
The pitch content of the statements is similarly a compression
of previous functions. The pitch sequence of the statement,
solo first violin, repeats that of the last statement of the'
theme, also solo first violin, the retrograde of tetrachord 5.
A shift of the original order of that tetrachord appears in the
statement, viola, in such a way that a palindrome variant by
dyada appears. The pitch content of the statement in second
violin and violoncello is a retrograde inversion of the same
tetrachord about the axis of its last pitch class, F#, so that a
palindrome variant by inversion can be found, recalling similar
palindromes in the third variation. The pitch content of the
statement, clarinet, the instrument associated with cadentlal
function, is a retrograde inversion of that of the statement
about the axis of its last pitch class, A. The tetrachordal
cycle by which tetrachords 3 and 4 are derived is thus shown.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. This time, the Initial tetrachord is the retrograde inversion of
tetrachord 1 about the axis of its last note, which is identical
to the retrograde of tetrachord 5.
The original, retrograde inversion, and inversion of the pitch
contour of the initial statement appear here. The fourth statement
first violin, has the original pitch contour of the first
statement of the third variation. The articulation patterns re
semble those found in the second phrase of this variation. The
relatively high tessitura of this passage may be a register in
version of that of the initial statement.
It is the author's opinion that this condensation and inter
locking of previous material with respect to several patterns
mark these two measures, 144-5, as the final cadence area of the
work as a whole with respect to fixed relationships. The coda
then serves the function of generalizing that cadence to resolve
the system of relationships Independent of fixed material, while
dissolving many of the other structural relationships of the theme
and first five variations.
Variation 6 (measures 146-180)
This variation, like the fourth, consists of a somewhat free
four-voice canon. Patterns not derived from pitch-class sequence
appearing in the dux are varied metamorphically in the other voices
Since no voice consistently leads the canon, the dux is here
assigned to that voice which begins with the trumpet entry in
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measure 146. This voice often anticipates the others, and Its
first raw form Is the retrograde of the first raw form of the dux
of the fourth variation.
The variation can be conveniently divided into two periods
at the beginning of measure 167, a textural as well as a structural
discontinuity. Before this point, row forms progress in a con
sistent fashion resembling that used in the fourth variation, and
any verticalizations within voices occur only at row form overlaps.
After this point, row form relationships are scrambled and redefined
to produce the desired configuration for the final measures of
th e work.
Techniques of pivoting configurations by presenting almost
simultaneous variants, of setting up palindromes and palindrome
variants, and assignation of multiple structural meanings to single
events are used here perhaps more frequently than in any oth er
area of the work. Frequent sustained notes functioning as
pedals, and repeated pitch classes, often surrounded by haloes
of similar events, provide local points of reference which occur
infrequently elsewhere. As in the fourth variation, complex
entities overlap and exhibit linear and vertical freedom of con
struction. There does not seem to be a consistent scheme for
presenting previous material, or to preserve its identity,
although every event: in this variation can be shown to derive
from some earlier configuration. Processes of construct! on used
previously, rather than their results, seem to have structural
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Importance here.
The principal function of the fifth variation seems to be to
recapitulate and resolve tetrachord-associated patterns, where
resolution is associated with clear restatement, wherever possible
in retrograde inversion.
The sixth variation similarly recapitulates and resolves
relationships which are not directly tetrachord-asaociated, or are
associated with tetrachads in a general rather than specific
way. These relationships include transformal methods which
generate tetrachord-associated patterns as well as metamorphic
methods applied to these patterns. The tetrachords themselves
appear, but generally vertically, and are dominant-associated
rather than tonic-associated. The last clear motivic statement
is that of tetrachord 6, which is dominant-associated and was
introduced as a half-close relationship. £hese relationships
are resolved through verticalization, condensation, and dissolution.
The sixth variation is also characterized by a use of the
Klangfarbe level as structural determinant. Phrases and breaks
in continuity are associated with that level rather than with
the other levels postulated by this study. To a greater extent
than anywhere else in the work, entities of voicing such as the
brass aggregate which opens the section are used to mark structural
points of articulation. Their structural effect may be far-
reaching within variations rather than immediate as in the preceding
variations. The duai interpretative possibilities of complex
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entitles as polyphonic or vertically planned areas are stressed.
The fourth and sixth variations display similar techniques
which are not standard throughout the work. The most obvious of
these seems to be simultaneous variation of the same entity.
Patterns of metric shifts, Isolated punctuatlve notes, and sus
tained pedals, and tetrachordal shifts seem to occur here more
then elsewhere.
Vertical aggregates, voiced In brass, measures 146-7, open
the variation. This event has been prepared by several subordinate
occurrences In structurally crucial areas of brass aggregates
such as measure 15, end of third phrase of the theme; measure 20,
first accompanying vertical aggregate of first variation; measures
52-3, first sustained occurrence, accompanying the last statement
of the first variation; measure 58, last half of first phrase,
second variation; and an important variant, woodwinds, measure 142,
the head of the third phrase in the fifth variation. Its appearance
at the head of the sixth variation, the place congruent to the area
which seems to set the tone for each variation, brings it into
prominenece for the first time. Its recurrence in measure 167
helps establish that measure as the beginning of a new section.
The voicing pattern for the variation as a whole reflects
that of the theme in a metamorphic fashion, with embellishments,
added material, and extensions of the original sequence. An
example of the extension technique is shown in the area following
measure 167, which might be considered congruent to the third
phrase area of the theme. The original sequence violln-harp-
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low strings-brass-woodwinds Is changed to brass-low strings-
woodwinds-harp-low strlngs-woodwlnds-harp-brass. The clarinet
does not appear as a solo Instrument In the final cadence. Its
doubling with flute and oboe, measure 179, appears to be a
repetition of previous woodwind doublings. A double meaning for
this event Is not precluded.
Three of the Imitative voices contain only transpositions of
the original row form, and begin with retrogrades of the firs row
forms of voices In the fourth variation. The other Imitative
voice, like the voices In the fourth variation, consists only of
retrograde row forms, and its first row form has the same hexachord
content as that of the first row form of the corresponding voice
in the fourth variation. Its second and third row forms have the
intraversional relationship with the second and third row forms of
the corresponding tmitative voice in the fourth variation. Row forms
are unfolded at a nearly simultaneous pace through the first period
of the sixth variation. The pitch content, and most of the pitch
sequence, is consequently related to that of three-fourths of the
fourth variation by retrograde inversion, row form by row form.
The row forms again overlap by two notes, so that the voices
using the original transposed row forms present successively lower
row forms, and the other voice presents successively higher row
forms. After the third set of row forms, the four imitative voices
would attain their original relationship transposed by an augmented
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fourth by means of these opposing sequences. This is precisely
the point at which the pattern is raptured and the first intra
voice verticalizations of entire tetrachords appear, measure 167.
Various previous relationships appear in the next measures.
The techniques of the second variation are shown briefly in
measures 167-9; a triple inversion relationship, P 1, P 4, and
P 7 begins in measure 169; a palindrome relationship across voices,
R 9 - P 9 appears, measures 171-180, extending to the end of the
work.
The last four row forms are P 1, P 9, P 4, and R 2. P I
has had many prior invocations of significance, but only in
relation to the missing form P 0. P 4's retrograde is the
important form of the fourth variation. The opportunity to
recall previous characteristics assigned to these forms is not
taken here.
P I : P 4 is the inversional relationship; P 4 : P 9 is
the relationships which preserves the sequence of a string of seven
pitch classes; P I : R 2 is the retrograde inversion relationship
P 0 : P 1. Since the intraversion relationship is invoked in
the first period, and the retrograde relationship R 9 : P 9
begins in measure 171, all major row form relationships are found
in this variation. Additional tetrachordal relationships are
discussed in sequence.
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First period (measures 146.-166)
All immitative voices begin simultaneously as members of the
brass vertical aggregate, measure 146. The second notes of all
voices comprise the following aggregate, measure 147. The third
notes occur at the durational interval of a quarter beat, beginning
with the Ab, violoncello, measure 148. In the first, third,
and fourth voices, the third and fourth notes are slurred down
ward; in the second voice, the two notes are detached and appear
in different instrumental parts. In the first, second, and third
voices, the third note is shorter than the fourth; in the fourth
voice, both notes have equal length.
In every voice, the rhythmic pattern is a metamorphic variant
of that of the initial statement. The pitch contour of the first
tetrachord of the dux is a retrograde inversion of that of the
initial statement; of the other voices, a duplication of slight
variant of that of the "subsidiary theme" statement. The pitch
sequence of the first tetrachord of the dux is a permutation of
that of tetrachord 4. The pitch sequence of the first tetrachords
of the third and fourth voices are Inversions of each other. Here,
as everywhere else in the first period, three tetrachords are
transpositionally related, and the fourth is related to the other
three by retrograde inversion.
The prevailing dynamic level is pianissimo, repeating that of
the last measures of the preceding variation. The fluid texture
contrasts sharply with that of the preceding variation. While
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some pitch classes of the brass aggregates appear In the last
measures of the fifth variation, no clear pitch relationship
spans the double bar.
The order of entry of the second tetrachord for all voices
is the same as that for the second half of the first tetrachord,
at the same durational interval, although the last note of the
f i r s t te tra ch o rd ends a t th e same time in a l l v o ic es. The p itc h
contour of the tetrachord in the dux resembles that of the initial
statement; of the other voices, that of the "subsidiary theme"
statement. The rhythmic pattern is generally a rather wide
variant of that of the initial statement. In the second and
third voices, the articula tion pattern is that of the "subsidiary
theme" statement.
The pitch classes G# and C#, which the choice of row forms
implies must be voiced three times each in this area, occur
in the same register every time, in instruments with closely
related timbre, in closely neighboring areas (G#, oboe, viola,
violoncello, measures 150-1); C#, flute, viola, violoncello,
measure 152). A small palindrome C# - double E - C# is a byproduct
of this procedure.
The complex entity produced by these entries begins forte,
on the stressed G#, and gradually decreases in intensity to a
pianissimo diminuendo. It ends, in all voices, on the last beat
of measure 152.
The sequence of entries of the third tetrachord breaks the
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established pattern. The dux enters an eighth beat behind the second
and third voices, which enter simultaneously; the fourth voice
enters an eighth beat behind the dux. Clear motlvic statments do
not appear, perhaps because the region of the overlapping row
forms has been entered. Some tendency to exhibit retrograde pat
terns from the Initial statement may be observed, however. This
area, measures 153-4, Is traversed quickly; Its entries consist
mostly of single sforzando attacks.
The high concentration of pltch-classes D and Eb Is again
exploited by repetition of register and similar voicing. The
first set of row forms ends nearly simultaneously in all voices,
the end of measure 155, although no break in phrasing can be
observed.
One statement and one partial statement, trumpet, measures
154-157, has pitch content of the second tetrachord type, pro
duced artificially by the overlap. Its steady Increase In
volume is supported by a similar Increase in all other voices
to the end of measure 157. Its steadily rising pitch contour
supports that increase. The partial statement, oboe and
clarinet, a timbre resembling that of the trumpet in the given
registers, can be said to belong completely to the new row form.
It consists of three sustained notes at successively higher
volume. The pitch class F is voiced similarly in both the
statement and the partial statement. An accompanying voice-
crossing in second violin and viola, tremolo am 8teg. a rather
brilliant effect, is comprised of two sustained aggregates which
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anticipate by a quarter beat the last two notes of the partial
statement. The author wonders whether the pizzicato G, first
violin, end of measure 157, can be played sufficiently strongly
to balance the resulting sonorities at this dynamic level.
Measures 158-160 m?y be the crown of a free arch comprising
the first period. The brass aggregate appears again, measures
158 and 160, this time with the fourth note delayed, first violin.
The tempo marking over measure 159 can refer only to the first
and fourth beats of that measure, insuring the durational distance
between the end of the aggregate and the violin - cello entry,
and the rhythmic precision of the repeated quarter notes in harp
and pizzicato strings with celesta spanning measures 159-60 —
a meticulous detail that may have some palindromic significance.
The entire area marks a sharp drop in intensity from the peak
obtained in measure 157.
The construction of measures 161-4 resembles that of measures
153-7. Both areas span row fora overlaps. The statement which
occurs here, measures 161-3, again is artificially obtained from
the row form overlap, and begins in the trumpet part. This time,
however, it is continued and extended by the tuba. The pitch
content of first tetrachord of the pitch sequence is an intraversion
of that of tetrachord.1; the last four pitch classes of the pitch
sequence, of the retrograde inversion of tetrachord 1, important
in the fourth variation: C-C#-E-Eb. The statement then links the
original and inverted tetrachordal systems in a rather sweeping re
p ris e .
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The accompanying sustained notes In measures 161-2 show no
voice crossing this time, but rather a chromatic slide resembling
that at the end of the first period of the fourth variation,
measures 121-4. The sharply attacked aggregates, harp, measure
163, recall those In measures 153-4. A brief partial statement
appears In second violin, measure 164, supported by another
chromatic slide, as well as the last two notes of the statement,
tuba, bringing about a sudden crescendo In preparation for the
climactic area of the first period.
Measures 165-6 present the second tetrachord of the third
row form, with clear statements in all voices, each confined to a
single part, all forte. The dux is the first to enter; the
fourth, third, and second voices follow in that order, at the
successive durational interval of a quarter beat. The pitch
contour is generally that of a metamorphosis of that of the
"subsidiary theme" statement; the articulation pattern in every
case is a close resemblance to that of that statement. The
rhythmic patterns are variants of the retrograde of that of the
initial statment. No statement in the first period, then, takes
all of its patterns from either of the two strongest statements
of the work, and few statements of the first period have patterns
which are transformal variants of those of the two principal
statements.
The complex entity has a high tessitura; its voicing may have
been intended to resemble that of the recurring woodwind doublings.
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The timbre effect is brilliant, and the bright sound is enhanced
by a tempo Increase at measure 165, and a "cut timftll'-jnetiric indi
cation at measure 166. The statements are so interlocked rhythmic
ally that a note falls on every eighth beat but three of these
two measures. The pitch class G# which appears in three voices
is placed in the same register and close proximity.
The retrograde relationship of the second and fourth entries
induces a palindrome, emphasized by identical registration and
articulation patterns. The characteristics of this palindrome are
enhanced by variant Imitations in the other voices.
Second period (measures 167-180)
The last tetrachord of the third row form in all voices is
concealed in the abrupt verticalization which marks the beginning
of the second period. Up to this point, at least two, and
generally three, measures are spanned by the canonic display of
each tetrachord. Two tetrachords are terminated here, each by a
single vertical aggregate; the other two are terminated in the
next measure.
The brass aggregate again begins the period, muted, piano,
contrasting with the brilliant finish of the preceding period.
Aggregates in the harp and syrings recall the accompanying
technique, as well as the row form procedures, of the second varia
tion. The important pizzicato G in measure 157, culminating the
first real crescendo of the variation, is recalled in the celesta,
too late to be of help to the crescendo in measures 165-6. Sustained
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notes in the woodwinds mark the first appearance of the notes
functioning as pedal tones which pervade most of the second period.
The function of these notes perhaps recalls that of the first
note of the fourth variation, contrabass, measures 109-10.
Measure 169 repeats in palindromic fashion the pitch content
of the harp aggregate, measure 167, in the celesta part, and the
B-Bb pedal notes, oboe and clarinet, measures 167-8, with reversed
voicing. Measure 169 marks the inception of the row form relation
ships which end the work.
The closely related row forms P 1, P 4, and R 9 dominate
measures 170-4, permitting repetition of events with slight
voicing variants. The doubling C//-D, violin and contrabass,
measure 170, reappears in measure 172, flute and bass clarinet.
The pizzicato aggregate, violoncello, measure 171, is slightly
augmented in a similar aggregate, harp, next measure, repeated,
harp, measure 176, initiating Cycle 2, completed by the statement,
first violin, measures 174-6. A similar aggregate, viola, also
measure 171, is expanded as the last appearance of the brass ag
gregate, measure 173. The sustained aggregate, second violin,
measure 170, on the other hand, is repeated somewhat less promin
ently with an added note, second violin, measure 174, and again,
celesta, measure 175. These frequent repetitions seem to represent
closure, especially since the palindrome relationship that was
obtainable is not invoked. The complex entity generated does
not seem to show more than a fragmentary patterning.
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The appearance of P 1 and R 2 in the final measures of the
work guarantees that all of the six tetrachords which begin the
work will reappear, transposed us a semitone, In their original
Interrelationships. These Interrelationships are thus made Inde
pendent of fixed pitch established In the theme. The further
appearance of P 4 and F 9 Insures that the lnverslonal pattern
of tetrachordal Interrelationships will also occur with relation
to the new pitch level. The choice of row forms also brings
about the tetrachordal and dyadic relationships of the last
measures discussed below.
The last two statements of the work are superimposed In
measure 174-7. Both are of the second tetrachord type, and they
are transpositionally related at the Interval of a minor third.
The first, violin, measures 174-6, has pitch content of tetrachord
6, the tetrachord associated with the half-close In the theme.
Its pitch contour Is a variant of that of the "subsidiary theme"
statement, and Its rhythm recalls that of the Initial statement.
It Is then related to three structurally Important statements. The
crescendo of Its first note prepares the entrance of the second
statement, muted trumpet, measures 175-7. The second statement's
pitch sequence Is a transposition of that of tetrachord 2, up a
semitone; its pitch contour is an inversion of that of the
"subsidiary theme" statement, and its rhythmic pattern resembles
a retrograde of that of the initial statement, with its last note
truncated. The articulation pattern of both statements Is, simply,
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detached notes, a complete dissolution of all previous articulation
patterns associated with statements. The tessitura of both state
ments Is relatively high, and their pitch contours balance. Their
common pitch class, Eb, Is repeated In the same register, same
duration, similar voicing. The dynamic level continues to drop,
to the measure of silence, 178, which sets off the last set of
tetrachords.
The last two measures display an abrupt change of density,
dynamic level, and general texture. All tetrachords are voiced
by dyads, a procedure anticipated only In measures 139-141 of the
fifth variation. All dyads but two, viola and first violin, con
sist of detached notes; each Is related to at least one other
dyad.
For the first time In the second period, the canonic
re la tio n s h ip among voices Is aud ib ly c le a r. The th ir d voice
leads, followed by the dux, then the fourth and second voices,
at the durational Interval of an eight beat. The first note
of every entry Is a quarter note; the second note Is either
a quarter or an eighth followed by a rest. All of the last dyads
consist of eighths. The rhythmic pattern of the whole Is such
that a note falls on every eighth beat of these two measures
except the first and last, which are silent.
Two pairs of dyads are related by pivots about a pitch class:
F-F#, flute; E-F, violoncello; IVC#, trumpet, D-Eb, trombone.
The rem aining two p a irs are re la te d by palindrom e: A»G#, v io la ,
G#-A, second v io lin ; B-C, f i r s t v io lin , C-B, horn.
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The relationship of the last set of tetrachords, although not
stressed in their realization, is also interesting. That of the
dux, belonging to P 1, has the pitch sequence of the retrograde of
tetrachord 5, the pitch sequence of the last statement of the
theme. The last tetrachord of the fourth voice, belonging to F 4
is automatically related to it by retrograde inversion about the
axis of its last pitch class, A, the first pitch class of the work.
The la s t tetrachords of the second and third voices, R 2 and F 9
respectively, are inversionally related about the axis of their
first pitch class, D. The inversional relationship of the last
tetrachords of F 4 and R 2 about the axis of their last two pitch
classes, B and C, link all four tetrachords.
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FOOTNOTES
APPENDIX C
^Letter to Willi Reich, May 3, 1941, cited in Walter Kolneder, Anton Webern: EinfUhrung in Werk und S til (Rodkirchen/Rhein: P. J. Tonger Musikverlag, 1961), p. 140.
2Ibid. 3 A complete listing of row form sequences for this work is given in the booklet accompanying Heinrich Deppert, Studien zur KompositiAns- technik im instrumentalen Spfltwerk Anton Weberns (Darmstadt: Tonos, 1962), p. viii.
4Path, pp. 26-27.
^Kolneder, p. 140.
6Ibid.
^Deppert, ibid.
8Path. p. 54. 9 Chorali8 Constdntinua. p. 194. An important discussion of the rhythmic structure of th is work is presented by Webern, p. 197.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX D
KLANGFARBE: SECOND CANTATA. OPUS 31
Preliminary Remarks:
This work is perhaps the most programmatic of Webern's mature
compositions. Its emotionally intense text reflects the difficult
times which Webern faced during World War II. He had lost public
acceptance in Vienna as a conductor and composer, as well as most of
his colleagues and friends. He had seen two pre-war Viennas vanish,
and with them the popular acceptance of the intellectual ideals of
his youth, and the aesthetic ideals of his middle age. He was
living in the privitation and danger of twentieth-century war in his
old age. In spite of these circumstances, he kept faith with the
Platonic ideals of logical form as means of transcending the mundane.
The use of voicing in this work seems to be largely motivated by
this programmatic impulse, serving to intensify the meaning of the
text. Voicing also seems to assume an independent structural function,
and the analysis below is principally concerned with the development
and use of this function. Since such an analysis from score notation
is necessarily somewhat conjectural, no portion of the discussion
below should be taken as unarguable. With this thought in mind, the
qualifications "seems," "appears," and "might" are dropped for the
sake of brevity, although their use would ordinarily be indicated for
each statement of the discussion.
325
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Only two of the six movements are analyzed, the third and
fifth. Their voicing patterns diverge, although they are both
written for soprano solo, chorus, and orchestra. The fifth
movement was the first part of the Cantata to be written, and
the third was the last. The fifth is therefore discussed before
the third, so that Webern's development of compositional pro
cedures can be shown in sequence.
F ifth Movement This movement contains four double bars which separate
structural areas. If the second and third of these areas are
combined, the movement can be said to be comprised of four sections
of approximately equal duration and structural weight: measures
1-16, 17-31, 32-45, and 46-60, with a general pattern A-B-B-A for
the large formal design. The middle two sections contrast with
the outer sections in many ways, and may be considered somewhat
developmental. The fourth section sufficiently resembles the first
the first to be considered a recapitulation. A letter to Hildegard
Jone from Webern implies that the large form is an arch, with
measures 25-31 as the structural center of the work.*
Throughout the movement, the parts which present the text
carry the weight of the structure -- in the first and last
section, the choir and solo soprano in antiphonal relationship,
and in the other sections, the solo soprano. The other parts
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embellish this principal line of the work, providing contrasts,
reinforcements, variants, and other reflections of its character
istics. The effect obtained is often that of a structural halo
about the principal line.
The rhythmic patterns and pitch contour of the principal
line are kept simple, and follow the inflection of the text as
it would sound if spoken. The technique used resembles that
developed in connection with Sprechatimme. The transformal
relationships which occur with relation to the principal line
appear to be of secondary structural importance.
The principal line always presents row forms linearly in
exact sequence. Row forms appear simultaneously in the accompanying
material, less exactly, as transpositions of the row form in the
principal line. The resulting pitch relationships are sometimes
made evident, but are usually played down.
If certain irregularities of procedure are permitted, the
row-form plan for the movement can be shown to consist of four
imitative voices whose transpositional relationship, 0 2 5 6 or
0 2 6 11, remains consistent. The pitch structure then resembles
that of the fourth and sixth variations of opus 30, cited above.
The row form itself is sonorous, with many intervals of a major
third and a perfect fourth, which invoke near-harmonic consequences.
These irregularities, and the use of such a row form, may be
deliberate reflections of Alban Berg'a free use of serial technique
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and his preference for row forms of this type. The movement itself
may be partially a memorial to Berg, whose death in 1936 was a
great personal blow to Webern.
Pitch intraversions within the span of a measure occur within
row forms. Pitch classes are repeated, as are dyads, particularly
in measures .51-2, c larin et and solo f ir s t violin. Row forms are
invariably overlapped, so freely that they lose much of their
distinctive identity. Transpositional relationships of simultaneous
forms fa c ilita te such overlap.
In measures 32-7, the pitch sequence of row forms appear to
be permuted, mostly by dyads. R 6 is presented in the vocal line
in its ordinary form, beginning with measures 31. The ordinary
sequence and the actual form used for the other three row-forms is
given below.
R 2: 2 1 0 4 3 7 11 6 10 9 5 8
B Bb A C# C E G# D# G F# D F
R 2 ': 2 4 3 1 0 6 10 7 11 8 9 5
B C# C Bb A M G E G# F F# D
(Actual form used)
R 5 ': 5 7 6 4 3 9 2 11 1 10 0 8
D E Eb C# C F# B Ab Bb G A F
(R 2' transposed, actual form used)
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R6’:6 8 7 5 4 10 2 11 3 0 1 9
Eb F E D C# G B G# C A Bb F#
(R 2' transposed)
R 6": 6 8 7 5 10 4 3 2 11 0 1 9
Eb F E D G C# C B G# A Bb F#
(Actual form used)
The permutation represented by R 2* supplies all intervals
missing from the original row form. I t also drops many of the
major third relationships which give the original rc*/ form much
of i t s fle x ib ility and character.
Although structures dependent upon pitch-class relationships
among entries are prevalent, properties of timbre seem to determine
the configuration of events. A tendency toward lyric improvisation
similarly overrides the sort of patterning of pitch contour, rhythm,
articula tion, and dynamics which pervades the Variations, opus 30.
The overall structure of the movement seems to be metamor-
phically rather than transformally realized. Its coherence rests
largely on programmatic content, made audibly clear by deliberate
specification of every musical event, not only with relation to
its context, but as a thing in itself. The sequence of major
thirds and the perfect fourth of the row form, a ll in the same
direction, seems to invoke and dissolve expected tonal feelings
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in such a way that every pitch of the sequence becomes a tonal
pivot, assuming independent Importance. The pitch structure of
the pre-tw elve-tone-serial song, "Fahr h in ," opus 15, may
anticipate this technique.
In any case, each event is provided with its own properties
of sonority, in which actual pitch content contributes to, and
is secondary to the sound of the whole. This sort of voicing may
be Webern*8 greatest contribution to the music composed during
the first two decades after World War II.
First section (measures 1-10
The chorus appears only in this section and the last. Each
part of the chorus is assigned an independent row form, and the
four row forms are always transpositionally related and unfolded
simultaneously. All parts sing the same rhythm, entering and
finishing together, one note per syllable of the text. The
resulting vertical aggregates invariably have the pitch-class
content 0 11 8 6 for bass, tenor, alto, and soprano respectively.
Some v ariety is obtained by change of reg istratio n , reflectin g
the inflection of the text. These procedures enable the chorus
to sing a cappella. usually a hazardous venture in serial music,
and rarely attempted elsewhere in the Second Cantata.
The resultant timbre of choir entries is rich and dense, with
a static, somewhat ponderous rhythmic pace. The bright, fluent,
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linear entries of solo soprano and solo Instruments provide an
opposing pole of voicing, embellishing the choral entries In a
fashion resembling the techniques used In mediaeval tropes, In
the Interludes between those entries.
Vertical or nearly vertical aggregates provide another realm
of voicing. Three Instrumental choirs are used In this section:
strings, winds, and pitched percussion. All three choirs are
assigned a four-part aggregate, and the strings are given two.
These aggregates also serve to embellish the setting of the text
in the interludes between choral entries.
The end of every entry is often followed by a new entry in
some other voice, a sixteenth beat behind its last attack of the
previous entry. The first entry begins on the second sixteenth
beat of the first measure. The rhythmic scheme is not clearly
bound to the metric pattern, but depends on the interrelationship
of the rhythms of various entries for its coherence.
Pitch-class and register links among entries also tend to
emphasize interdependence of parts. The solo violin entry,
measures 4-5, contains three pitch classes, B, F#, Bb, with identi
cal registration as in the preceding entry, same part, measure 3.
The last note of the solo violin entry, measure 5, Ab, is repeated
with almost identical voicing as the last note of the solo soprano
entry, measure 6, and also as the last note of the entry, same
part, measure 9, "Ich bin es." The dyad, solo violin, measure 6,
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Bb-A, is a repetition of register and voicing of these pitch
classes in measure 3 and measure 5, same part.
The v e rtic a l aggregates, winds, measure 5, and measure 6,
strings, contain a common pitch class with duplicate registration,
Eb, The first note of the bass entry, measure 8, duplicates the
pitch class and register of the lowest note of the aggregate in
the winds, F#. The last note of the soprano entry, same measure,
is also F#, duplicating the registration given it in the strings
aggregate, measure 6.
The initial pitch classes of the diagonally realized aggregate,
harp, solo soprano, and celesta, measure 9, are those of the first
chorus entry, measure 1. The general pitch contour but not pitch-
class content of the following entry, chorus, measure 10, is a
variant of that of the first chorus entry and perhaps marks the
beginning of a second phrase in this section. The Eb, first note
of next entry, solo soprano, measure 12, has been anticipated
in measures 5-6, solo soprano, and in both vertical aggregates in
those measures. F#-Bb is voiced, solo violin, measures 13-4, in
the same way as in measures 3 and 5. The Eb-G dyad, clarinet,
measure 13, previously occurring in the vertical aggregate, winds,
measure 5, is promptly inverted about the axis of its lowest
note in the next vertical aggregate, strings, measure 14. The
final pitch classes of the choral entry, measure 16, are the
same as those of the first notes of the first choral entry, measure 1.
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The structure of the section consists of four choral entries
separated by Instrumental Interludes of a largely linear nature.
The Interludes contrast with the somber, dense sonority of the
choral entries In tessitura, timbre, rhythm, articulation, and
many other respects.
The first interlude, measures 3-7, consists of a single
complex e n tity formed by the superposition of solo v io lin , solo
voice, and two vertical aggregates. The solo voice provides a
link in sonority to the sound of the choral entries, but Is higher,
more supple, and more varied than those entries are. The
aggregates, on the other hand, preserve the dense sonority and
static character of those entries, enlivened slightly by grace
notes. The solo first violin is even more supple, varied, and
bright than the solo voice, and provides an amplification of the
possibilities of sonority and articulation which can be assigned
to the human voice, framing the voice in time, in tessitura,
in rhythm, and pitch contour. The vertical aggregates follow
the second and anticipate the third entry of the solo first
v io lin , at an area of change of row form. They are voiced in a
subdued fashion, muted and in re la tiv e ly bland re g isters of the
instruments represented. The change of timbre from winds,
measure 5, to low strin g s, measure 6, together w ith the dynamic
markings indicated, yields a decrease in intensity as well as
a variation of sonority. Two eighth and one sixteenth beats of
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silence separate this interlude from the next choral entry.
The second Interlude consists of a single measure, a
diagonally realized aggregate in solo voice, pitched percussion,
harp and celesta, measure 9. The purpose of this aggregate
seems to be to mark the wordd, "Ich bin e s," as Important by
echoing them in a soft, brilliant cloud of rising notes.
The beginning note of each of the four entries is an over
lap of two row forms. The whole is so constructed that the
entries, at point of overlap, yield successively a perfect fourth,
minor third, and major third. This effect is accomplished by
voice-crossing of row forms, which is immediately rectified in
the next measure, choral entry. Harp and celesta are not used
elsewhere in the section, so their use here is particularly
striking.
The third and last interlude marks a return to the voicing
pattern of the first interlude. It may be considered as two
complex entities of considerably shorter durational span than the
complex e n tity of the f i r s t interlude. The f i r s t of these
entities presents solo first violin, solo voice, and solo clarinet
in rather loose imitation. The first note of each of these
entries is an overlap of two row forms, like the first notes
of the entries of the second interlude. The comparatively dark
sound of clarin et (three out of five notes are in the chalameau
reg ister) towards the end of- th is complex e n tity may mark a
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variant of the sound of the first vertical aggregate, winds,
measure 5.
The second complex entity, then, consisting of solo first
violin and low strings, would correspond to the area of the first
interlude in measure 6. Then, the f ir s t and th ird interlude have
similar voicing patterns, and the whole of the first section has
an arch form with relation to patterns of sonority.
The last choral entry of the section, measures 15-6, is even
darker and denser than the first choral entry, providing a point
of departure for the varied, changing voicings used in the middle
sections.
Second section (measures 17-31)
The elements of voicing presented in the first section are
here varied and placed into new relationships. Only one new
sonority is added -- piccolo, measures 25-7, which, since it was
not used earlier, has a striking, unexpected effect analogous
to the effect produced by pitched percussion, measure 6. Both
of these effects serve to mark as important certain phrases of
the text; here, the piccolo emphasizes the words stressed by
Webern in his letter to the person who wrote them, Hildegard
Jone, "Because it died upon the cross, we'll follow on; in all 2 bitterness of tears our sighing follows it." "It" is taken to be
an objectification of Christ as Freundselig. the love which is the
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ultim ate meaning of Webern's music, dying and transfigured on
the cross of that which translates it into higher purpose.
The sharp increase in tempo and change of row technique
bring about a distinct break of texture between the first and
second sections. The accompanying m aterial is not lin ear, but
consists of single events whose voicing similarities and contrasts
seem to be their major linkage. Pitch-class content of aggregates
is so severely limited that its change alone is sufficient to show
structural divisions. The row forms are so interlaced as to
become almost indistinguishable.
The double bar, measure 24, separates two phrases which may
be said to comprise the section. This double bar marks a change
in the handling of accompanying m aterial. In the f i r s t phrase,
only trichords of the normal form 0 1 4 are used. This normal
form is contained in the normal form of the aggregate used for
all choral entries. In the second phrase, an extended variant of
0 1 4, 0 1 5 9 is used. The aggregate, low strings, measure 24,
links the two la tte r normal forms with a pitch-class content
of 0 4 8; another aggregate, same parts, measure 31, summarizes
the two normal forms with a pitch-class content 0 1 4 5. The
choice of pitch content seems to be motivated by considerations
of timbre.
Up to the double bar, the accompanying m aterial is limited
to vertical aggregates on quarter beats of the measure, establishing
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the accelerated tempo and regular pulse beginning in measure 17.
After the double bar in measure 25, sustained notes and melodic
fragments are admitted, while the soprano solo continues to affirm
the ongoing pulse.
The soprano solo carries the principal line throughout the
section, pausing briefly only in measures 27 and 31. This is one
of the most supple vocal lines that Webern ever composed.
Measure 27, the word "nach," is a point of re s t of natural and
expressive effectiveness. The accompanying m aterial surrounds
this line with a frame of articulative, supporting sonority, in
a sort of im itation by v ariatio n and contrast ra re ly found in
pre-Webernian music. Register duplications of pitch classes
occurring in the soprano solo is generally avoided.
The first three entries of accompanying material, measures
17-8, exaggerate the pitch contour and vowel sounds of the solo
line and its tex t. The f i r s t three en tries of accompanying
material in measures 21-2 serve a similar function. The motivic
fragments, measures 26-8, piccolo and low strings, may derive
from portions of the solo line, measures 24-6. The point of rest
cited above, measure 27, is given further s ta b ility by sustained
aggregates, measures 27-8, low strings. Pitch contour is again
exaggerated, measure 29, and the decrease in activity of measures
30-1 is accentuated by a sameness of voicing of accompanying
aggregates, measure 31.
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Some close-range register and pitch-class duplication among
entries may be symptomatic of structural design. The dyad A-F,
harp, measure 19, recurs, second v io lin , measure 21, and again,
harp, measure 23. A ll voicing ch aracteristics except dynamic
level and duration of the vertical aggregate, winds, measure 18,
recur in the vertical aggregate, measure 21. The trichord,
celesta, measure 18, is exactly repeated, measure 23. These
correspondences may indicate a skewed palindromic structure whose
distortion is symptomatic of increasing development in the first
phrase of the section.
The falling dyad, D-F#, solo soprano, measure 27, is
anticipated, D, vio la, measure 26, and D-F#, c la rin e t, measure 27.
This duplication may be part of the total braking effect in
measure 27, preparing forthe setting of "nach." The same cause
may be served by the register duplications C#, solo soprano,
measure 28, and v io la, measure 27; also E, solo soprano and
violoncello, measure 28. The developmental pace is slower in
measure 28 than at the beginning of the passage of which it is a
v arian t, measure 25.
In measure 31, a cadential area and hence one in which
stability is needed, exact pitch-class and register duplications
occur: E, viola and celesta; Eb, harp and bell. There is also
some register duplication of pitch classes at the interval of a
semitone: viola, E-G#, harp, Eb-G; violoncello, B-C, harp Bb-B,
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violoncello, C-C#. The first two notes of solo soprano, A-Ab,
are anticipated by clarinet, measure 30, and celesta, measure 31.
Contrasts of te ssitu ra between the solo line and accompanying
material often result from a "follow through" by the latter of
the pitch direction of the former. Thus, the dyads, measure 19,
strings are a continuation in pitch direction of the falling
line, solo, measure 18. Similarily, the aggregate in low strings,
measure 24, end of first phrase, continues the fall of pitch
direction in the solo line, measure 23, and the piccolo entry,
measure 25 continues the rise in pitch direction of the solo
line, measure 24. Other contrasts of tessitura occur within
the accompanying material, and are so calculated that the solo
line provides a center of balance between opposing entries.
Such contrasts occur among the quarter-note aggregates, measures
21-3, the motivic fragments, measures 25-7, and all accompanying
entries, measures 29-31.
Accompanying material also adds depth the settins of certain
words by providing a wider range of pitch and timbre about
them, and by re fle c tin g the sound of vowels and consonants w ith
like sonorities. Such embellishment occurs on the word "Wort,"
measure 24; "Kreuz," measure 26; "Ernst," measure 29. "Bitternis,"
measure 30, is given minimal support, perhaps because of its
negative connotation.
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The accompanying material, taken separately, provides Its own
realm of sonorities, with some Independent structural patterns
of voicing. Up to the double bar at measure 24, a voicing sequence
and its variant emerges: celesta-winds-harp-atrings; winds-celesta-
winds-harp-low strings. The aggregate which coincides with "Bitter-
nis" serves as the center of a voicing sequence which is an arch:
measures 27-31, clarinet-celesta-harp; winds, sforzando; clarinet-
celesta-harp. A pattern which does not quite fit linearly with
that arch appears simultaneously, measures 26-31; rising slur-
half note-whole note; falling slur-quarter note-dotted half note.
The dynamic level up to the double bar at the end of measure
24 is mostly pianissimo. Measures 25-7, the setting of the
portion of the text associated with the word "Kreuz," have a con
siderably higher intensity level. The rest of the section is
generally pianissimo, with the exception of a passage associated with
the echoing of the material of measures 25-7, at measures 29-30,
at the words "Ernst der Bitternis."
The f i r s t use of accompanying m aterial consisting of more
than a single note, piccolo in conjunction with low strings, is
associated with "Kreuz," measures 25-7. The rising major sevenths,
low strings, should produce an effect of voicing equal in strength
to that of the powerful sound of solo, sustained piccolo, forte, in
its most comfortable range. This combination is reflected with
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less force at least three times In this section: measures 28-9,
solo violin, clarinet, and bass clarinet; measures 48-9, piccolo
solo violin, clarinet, and strings; and measure 51, clarinet and
solo violin. At each reflection, the text refers back to the text
of measures 25-7.
In measures 28-9, the solo violin repeats the piccolo entry
with nearly identical registration and identical pitch-class
sequence. The sevenths are replaced by minor ninths, voiced more
lushly and retrograded, in diminution, using all non-solo strings.
The fermata in measure 31 provides the first real break of
tempo in the section, and serves as a point of structural
articulation. The bell entry, same measure, is the only use of
that instrument in the movement, and may mark the precise center
of it. The pitch class and register of this audibly striking
entry duplicate that of the first note of the setting of "Wort,"
one of the key words of the text, measure 24, solo soprano. The
duplicate pitch class, Eb, is an augmented fourth from the pitch
class which may be considered as the tonic pitch class of the
movement, A, the first note of the first entry of the soprano
part, measure 1.
Third section (measures 32-45)
The general structural configuration of the third section
strongly resembles that of the second section. The differences
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between these sections seems to be due to programmatic content.
The second section describes how one follows the Word despite
"Ernst der Bitternis," whereas the third section describes the joy of receiving the inspiration of the Word.
The principal line is again in the soprano solo part, sup
ported by a frame of im itative and contrasting accompanying
material. Most of the general remarks made above with respect
to the structure of the second section apply here also.
The voicing pattern as a whole can be said to resemble that
of the second section, with some variance and embellishment.
Some of the small patterns of voicing, articulation, and pitch
contour previously established redur here. The tempo of the
previous section is maintained. Since it is well established,
there is little attempt to emphasize metric and rhythmic regu
larity. Measures 39-45 show some return to the interdependent
rhythmic structure of the first section.
The permutation of row forms discussed above occurs only in
accompanying m aterial, measures 32-6. The permutation does not
seem to change the actual sound of the accompanying m aterial,
for the previous pitch-class content, normal form 0 1 4 , is again
used for trichords here. The permutation only becomes necessary
with the realization of motivic fragments, measures 36-7, clarinet
and strings, which are a deliberate variant of the piccolo-strings
combination of measures 25-6 of the second variation.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The double bar between the second and third sections Is
flanked by a voicing pattern and Its vatiant. In measure 31, a
motive consisting of the last three notes of the soprano solo
part forms a small complex e n tity with the b ell sound, at a
lower pitch level, same measure. In measures 32-3, the motive
Is repeated with the same rhythm, transposed down a major fifth,
at a higher dynamic level, solo violin. The soprano entry,
measure 33, has exactly the same rhythmic relationship to the
motive as the bell sound did to the motive In measure 31. How
ever, here the Independent note Is at a higher pitch level than
that of the motive. The bell sound provides a cadentlal effect
In Its context, but the soprano entry In measure 33 is the first
note of a phrase in the principal line. Thus, closely related
voicing patterns are assigned quite different structural roles.
The voicing pattern of the accompanying m aterial, measures
34-5, may be a similar reflection of the voicing pattern in the
strings, measure 29. Both entities consist of three consecutive
quarter attacks, the first of which is, In timbre and tessitura,
contrast to the last two. In any event, the sequence of three
durationally equal notes recurs several times in the third
section, particularly in areas which recall measures 25-7. The
aggregate winds recalls the similarly voiced measure 30.
The first of these areas, measures 36-7, partially preserves
the pitch sequence of measures 28-9, also a variant of measures
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25-7. The clarinet entry, measure 36, is taken to correspond to
the higher pitched, slower solo violin entry, measures 28-9. The
vertical aggregates in strings, measure 36, are an inversion of
those of measure 29, with the second v io lin part held constant.
The final aggregate in the sequence, measure 37, has the same
outer pitch classes and registers as those of the first aggregate,
measure 29. ' The linear intervals of major seventh and minor third
which occur in a ll accompanying parts, measures 36-7, are also
found in the solo soprano part, same measures. The following
aggregates, measure 38, seem to be a variant of the solo violin-
strings pattern of measure 28, occurring ,in conjunction with the
complex entity just discussed in that area. The rhythmic pattern
of measure 38 is a retrograde of the one in measure 28, there is
a register inversion, and the pitch relationships are changed.
The aggregate, v iola, measure 38, is transposed down an augmented
fourth from its level in measure 28. The interval of the two-note
slur is changed from a semitone to a minor th ird . In measure 28,
the solo soprano line lies below this pattern, but in measure 38,
it lies above.
The pattern in measure 38 which recalls that of measures
25-7, is so varied that the material it presents seems almost new.
This m aterial is immediately imitated in a manner which suggests
development of the vertical aggregate voicing patterns, measures
17-24 and 33-34. ftie pattern and its development coincide with a
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falling line down the chromatic scale of pitch- classes from F,
soprano solo, measure 39, to F#, harp, measure 42. This lively
area is the loudest of the third section, and stresses the words,
"dann wenden wir uns a lle s e lig ," one's reaction to the appearance
of the Word.
Disregarding the grace-note, solo violin, measure 39, the
pitch-class content of the aggregates, bass clarinet and solo
violin, have the normal form previously identified with variants
of the material of measures 25-7: 0 14. The pitch sequence,
solo violin, is a transposition up a perfect fifth from that of
the clarinet entry, measure 36. However, the pitch sequence,
bass clarinet entry, measure 39, is a permutation of that of the
previous entry, strings, measures 36-7, and incidentally a return
to the order of the original row form. This entry then marks a
d e fin ite end to the area of permuted row forms.
The passage in which the bass clarinet entry is imitated,
measures 39-42, follows a voicing sequence clarinet-violoncello-
viola-second violin-solo violin-celesta-harp, which is a variant
of the sequence closing the area encompassed by measures 25-7,
clarinet-strings-celesta-harp-bass clarinet-solo violin. Here,
there seems to be a gradual lightening of timbre as the sequence
progresses. If the solo soprano line is included in the resulting
complex entity,. that entity has an attack on every eighth beat
of measures 40-2, except the last beat of measure 41.
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This passage resembles the diagonal aggregate in measure 9,
solo soprano, celesta, and harp, in several ways. Both entitles
are reactions to the immediately preceding words of the text:
"It is I," measure 9; "we all turn to it [the Word] gladly,"
measures 39-41. The effects of sonority and of rising, super
imposed short entries of these two passages are also similar.
The la st complex e n tity of accompanying m aterial is a con
tinuation of the imitation in measures 39-42. Its voicing sequence
may be a variant of that of measures 38-9, viola-bass clarinet-
clarinet. Here, these three instruments each appear twice, forming
two palindromes of voicing: viola-bass clarinet-viola; clarinet-viola-
clarinet. The motives imitated, like those of measures 39-42, are
linked by metamorphic variation techniques.
Close-range pitch-class and register duplications among
entries are again clues to structural design. Such duplications
occur much more frequently in the third section than in the
highly developmental second section.
The pitch classes C-C#, harp, measure 35, duplicate the
register of C-C#, violin, measure 33. Duplicate E's occur three
times in rapid succession in the same register, winds celesta,
and harp, measures 34-5.
The passage of measures 36-7 again recalls that of measures
25-7, but the frequent pitch-class and register duplication which
appear in it may indicate a Blower pace of development. The
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pitch class and register duplication which appear in it may indicate
a slower pcce of development. The pitch class C, clarinet, recurs,
solo soprano, measure 37, also bass clarinet, measure 39; Bb, second
violin, measure 36, is anticipated, measure 34, solo soprano; again
repeated, solo violin, measure 40, and solo soprano, measure 41.
The solo soprano part in measures 35-8 contains several pitch-
class and register duplications with surrounding material. The
pitch classes C-B, clarinet, measures 36, reappear, solo soprano,
measures 37-8, with the same pitch contour; the intervening
Eb is duplicated, viola, measures 37 and 38, and clarinet,
measure 39. The pitch classes C#, and E, solo soprano, measures
35-6, recur in the same order and register, same part, measure 39,
as the head of a phrase. This registration of these pitch classes
recurs often in the remainder of the movement.
The passage beginning in measure 39 seems to be more related
to previous pitch events than any preceding passage imitating
measures 25? 7• The following imitation, measures 39-42, contains
many pitch aggregates related at the semitone with nearly duplicate
registration. The immediate pitch-class and register duplication,
C#, violoncello and viola, measure 40, and Eb, solo violin,
measure 42, are the most obvious links. Although the passage pre
sents new material, the approaching cadence at measure 45 does
not permit stringly contrasting variation technique here.
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The closing measures of the section also show significant
duplication of pitch class and register. The first two notes of
the last phrase, C#-F, solo soprano, are duplications of the first
two notes the preceding prase, same part, measure 39. The C#
also duplicates the registration of the lust note of the next
chordal entry, soprano part, measure 47, as well as the first
note of the second section, measure 17. The last note of the last
phrase of the third section, in solo soprano, measure 44, has
the same pitch class and registration as the bell sound closing
the second section, measure 31. The f i r s t note of the accompanying
imitative material, viola, measure 44, is a repetition of the
preceding note, same part, measure 41. The associated dyad,
B-F#, viola, is closely imitated by Bb-F, bass clarinet, also
measure 44, and the Bb is immediately repeated, same measure,
viola, followed by A, measure 45, immediately repeated, same
measure, bass clarinet.
Fourth section (measures 46-60)
The tempo, techniques, timbres, and general formal design
of the first section are recapitulated here. There are five
choral entries instead of four, so that there are four inter
ludes of solo passages. This section shows a greater degree
of interrelatedness of musical events than the first section does.
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Four solo parts appear in the first Interlude. Each succeeding
Interlude has shorter and less florid solo parts than the preceding
ones. The timbre of Interludes also progressively lightens as the
text describes the effect of losing all-encompassing love. The
movement ends with a rather chilling use of harp and celesta,
markings of pianissimo and morendo, and a fin al choral entry whose
pitch contour seems scarcely to vary.
The first chordal entry of the section, like the first entry
of the work begins on the second sixteenth beat of the measure.
I ts dynamic level is lower, however, and i t is more closely voiced.
Although the pitch contour of the soprano part is identical in
both entries for the first measure, here the actual pitch level
is a major seventh lower than previously. The words of the text
are the same for both entries. The entry of the first section is
a proclamation, and the entry of the forth section is a meditative
repetition, a springboard for the setting of the intense text
which follows it.
The interludes seem to be musical and textual reactions to
the immediately preceding choral entries. Similarily, the
instrumental solos within the interludes seem to be reactions to
the text and configuration soprano solo beginning each interlude.
This sort of reaction is metamorphic rather than transformal,
psychological rath er than resu ltin g from precomposed design. The
effect of its use is an intensifying of an already emotional text,
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giving this section an impact of feeling rare in any of Webern's
work.
Several voicing patterns in the interludes recall previous
voicing patterns. The conjunction of piccolo, solo violin,
clarinet, and low strings, first interlude, measures 48-9, is
a durational contraction of the similar conjunction in measures
25-7. A further contraction of that pattern appears, second
interlude, measure 51, low strings, clarinet, and solo violin,
which seems to be the last clear appearance of the "Kreuz"
material which dominates the second and third sections.
The voicing pattern, second interlude, measure 51, can also
be shown to resemble that of the third interlude of the first
section, measures 12-3, and that of measures 40-2, one of the
variants of measures 25-7. The voicing pattern of the third
interlude, measures 53-4, reflects a negative word, "Feindseligkeit,"
and is related to the setting of "Bitternis," measure 30, also
accompanied by a sforzando brass aggregate, a rather stinging
effect. The voicing pattern of the fourth interlude, measures
.56-8, may be a reflection of that of measures 39-42, but is more
probably a result of the immediate demands of the text.
The pitch classes Eb and A seem to have the effect of a
tonic in this section. There is a tendency to voice certain
pitch classes, p articu larly Eb, F#, F, D, and C#, in rep etitiv e
ways, sometimes in ways which re c all events in other sections.
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Some close-range Inversion about a selected pitch class Is used:
measure 54, about G, harp and celesta; measure 57, A, celesta;
measure 58, D, celesta. Certain motivlc fragments are associated
with pitch classes. For example, the falling dyad from A in a
high register is used often: solo violin, measure 48 and 49;
piccolo, measure 49; solo soprano, measure 50; clarinet, measure
50, with a last weak occurrence, measure 57, solo violin. Such
dyads are inverted, measure 50, solo violin; measure 57, celesta.
A is, of course, the first pitch class of the original row form
of the entire work, and the first note of the soprano part of
the first entry of the movement.
Register duplication of pitch classes is prevalent, serving
to link neighboring entries. One of the most obvious duplications
serves to extend the first choral entry into the soprano solo
entry, C#, measure 46. In measure 49, the duplicate registration
of A and G#, piccolo and solo violin, may indicate that the
latter is a metamorphic variant of the former. Then the clarinet
entry, same measure, may be considered a transposed metamorphic
variant of the same pattern. A similar duplication implfes the
same relationship between clarinet and solo soprano, measure 51.
The G# is duplicated in the next choral entry, measure 50, as its
first note, soprano part, and measure 51, solo soprano.
Register duplication links the soprano entries in measures
47-9 and measure 51; C#, C. E, and F are the same in both. The C#
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. registration also appears, solo soprano, measure 53 and 56. In
the entry of measures 56-7, seven out of ten pitch classes are
duplicate registrations of previous ones in the soprano part in
this section. The registration of the first three pitch classes
of the first solo spprano entry of the movement, F#, C#, F, recur
permuted in the entry, measures 46-7, and retrograded, measure 56.
The last note of the alto part, measure 50, Eb, is duplicated
viola, measure 51. Eb recurs an octave higher, violin, measure 52
trumpet, measure 53, recurring as the last note of the tenor part,
fourth choral entry, measure 54, and last note of the alto part,
measure 60. This Eb is also the last note, solo soprano entry,
measure 49, and the highest note of the last occurrence of ac
companying material, harp, measure 58. The structural Importance
of Eb has been noted above with relation to the bell entry,
measure 31. At all times in this movement, two row forms related
at the augmented fourth are simultaneously unfolded, and the Eb-A
invocations here may be an allusion to that structural design.
Minor events in the accompanying material are linked by
duplicate F#: measure 51, last note of clarinet entry; measure 53
first note of next clarinet entry; and measure 57, last note of
last solo violin entry. The F# registration is the same as that
noted above, solo soprano.
This F# is associated with a duplicate Bb, clarinet, measure
51, and celesta, measure 54. This Bb is the first note of the
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soprano part of the fourth choral entry, measure 54; the laftt note
of the last entry of low strings, viola part, measure 56; recurs
twice, harp, measures 57-8; and Is In the last occurrence of ac
companying m aterial, celesta, measure 58.- The lower note of the
last note of the last entry of low strings, viola part, B, Is a
duplicate of the last note of the alto part, measure 55, fourth
choral entry, and the first note of the last tenor entry, measure
59.
The last note of the last solo violin entry, G, Is a register
duplication of the last note of the bass part, measure 60.
A occurs in duplicate registration, measure 57, solo violin
and celesta. G#-A, same measure, appear, celesta and solo soprano,
accompanied in each case with a pitch class which makes the
resulting trichords lnversionally related. Bb, B, and C occur in
duplicate registrations, measures 57-8, in accompanying parts.
The first and final notes of the last choral entry, soprano
part, measures 59-60, F# and C#, are given the registration which
they have customarily had in the solo soprano part In this section.
The F# is duplicated, solo violin, measure 57; and the C#, celesta,
measure 58.
Register duplication of pitch classes, then, increases as the
intensity of the section subsides. Transformal variation also
gradually takes precedence over metamorphic variation, and previous
patterns of voicing and pitch contour are phased out as the section
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progresses. Solo lines are vertlcalized. All of theae factors are
symptomatic of approach of cadentlal material In Webern's late style.
Instead of a deliberate return to tonic-associated patterns of
relationships, such as those found in the Variations, opus 30,
cessation of developmental activity suffices here to brake the flow
of the movement.
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355
Third movement
This movement Is also a four-voice canon of row forms, so
strict that even overlaps of row forms are almost always Identi
cal In all canonic voices. The order on entries of canonic
voices Is nearly always constant. As In the fourth variation
of opus 30, the dux is metamorphically and transformslly Imi
tated by the other voices.
The canonic voices jump freely among instrumental parts,
as in Webern's orchestration of the "Ricecare" from Bach's Musical
Offering, in which single melodically conceived lines are so
voiced that their inflection is enhanced by the timbre, registration,
articulation, and other properties freely asigned to each fragment.
The text appears to determine the inflection of the voice, and this
inflection is in turn amplified by the above technique. As in the
fifth movement, certain words receive special treatment, so that
their meanings as well as actual sounds are emphasized.
Three sections of the movement consist of imitative choral
passages, with two interludes of soprano solo with accompanying
material. In the choral passages, every vocal part is doubled
in some instrumental combination which colors it and extends its
characteristics, as well as providing security of intonation.
The one exception to this doubling is in measures 12-3, first
soprano and alto, where the words "des Klangs" are a cappella.
There are three choral parts, each assigned to a row form. In
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the third and fifth sections, soprano solo and first soprano
alternate. The fourth row form appears independently in the
accompanying parts, embellishing and balancing the other three.
The soprano solo is never doubled. In the interludes, it is
accompanied in a manner similar to that found in the second and
third sections of the fifth movement.
The row forms used simultaneously invariably have the trans
positional relationship in order of entry, 0 6 9 3. This relation
ship can be clarified as follows:
P 0: 0 9 1 2 10 3 11 7 8 4 5 6
P 3: 3 0 4 5 1 6 2 10 11 7 8 9
P 6: 6 3 7 8 4 9 5 1 2 10 11 0
P 9: 9 6 10 11 7 0 8 4 5 1 2 3
The first two pitch classes of all four row forms yield the
minor third cycle 0 3 6 9. The last three pitch classes yield the
entire chromatic scale. The dyads 1-2, 4-5, 7-8, 10-11 each occur
thrice, and the dyads 2-10, 5-1, 8-4, 11-7 occur twice. Trichords
11-7-8, 2-10-11, 5-1-2, and 8-4-5 occur twice. The major third
cycle which each row form contains is not duplicated in full in
other forms: P 0 contains 3-11-7; P 3, 6-2-10; P 6, 9-5-1;
P 9, 0-8-4. Partial duplications do appear, Pn • P n + 6j-for
example, P 0, 3-11-7; P 6, 3-7. The usual overlaps are of two
pitch classes, using Rn:In+9:Rn+ 10, which provides for
numerous duplication of dyads. As usual, Webern exploits or
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disregards these potential correspondences as it suits his larger
compositional purposes.
The movement is characterized by a lively, regular metric
pattern alternating between 6/8 and 3/8. This pattern is disrupted
only in the first interlude, and then only to shift the pattern
of accented beats in the solo soprano part. The rhythmic and pitch
contour patterns support the metric pattern of stresses. Brief
ritards appear at ends of sections or interludes.
The general impression which should be provided by the
performance of this movement is that of almost unbounded joy:
"Love shall ring like a storm-bell.'" (measures 29-31). The
transcendental love which is the subject of the entire Cantata
rings in this movement like a peal of bells — perhaps like the
changes traditionally rung in England.
First section (measures 1-12)
The choral parts, first soprano, second soprano, and alto,
appear in almost exact rhythmic and articulative canon, the only
vagaries occurring in the first soprano part. The pitch contour
patterns fall into small units and are usually identical or
exact inversions, with a tendency to limit major changes of
direction to the principal beats of the measure. The fourth,
accompanying imitative voice contains only isolated motives cor
responding to those found in the other three voices.
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The first and last of the initial choral entries are heavily
accented by doubling: second soprano, harp, muted trumpet; first
soprano, oboe, muted trumpet, celesta. The first two notes of
the accompanying voice occur, horn, and the next two notes of
that part constitute the only doubling of the alto entry.
In the first measures, there is a tendency for pitch
direction to be duplicated among parts. Thus, in the second
measure, an upward pitch direction is found in all parts,
accented on the last beat by the appearance of the highest pitch
yet encountered, 6, first violin. This upward swing is Immediately
counterbalanced by a downward trend in the first half of the next
measure. Similar alternating swings of pitch direction prevail
throughout most of the choral sections, sometimes several at once
in contrary, similar, or independent motion, adding to the aural
impression of pealing bells.
The trombone and trumpet generally appear in conjunction with
a stressed word of the text: "SchBpfen," measures 1 and 3;
"Worts,: measures 5-7; "LHuten," whose structural importance is
similar to that of "Kreuz" is accompanied by much joyous peal-
like motives in measure 8; "des Klangs," measure 11, the climatic
and concluding part of the section.
The strings appear in every measure of the section, reinforcing
the choral line and sometimes carrying the accompanying voice, as
in measures 1-2 and 8-9, first violin, and measure 10, pizzicato
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viola and violoncello. The string parts are pizzicato at "des
Klangs," measure 11, so that the timbres of pitched percussion,
trumpet, saxophone, and clarinet predominate.
A comparatively dark, rich timbre prevails through raeasuren
1-7, except for brief appearances of celesta, first violin in a
high register, and flute. The reaction to "L&uten," measures
7-8, consists of a brightening of general sonority as well as in
creased rhythmic and pitch contour movement. Measures 9-10
accomplish a lightening of the sonority without sacrificing
brilliance with the weight of the instrumental sound in high
woodwinds. The voicing in measure 11, "des Klangs," produces
a natural increase in intensity while maintaining the previous
level of bright sound. An ambiguity of the specifications
for mute in the brass parts might admit the possibility that the
trumpet entry in measure 11 is intended to be played open, and
an open trumpet would sound well here.
The doubling of the choral parts through the section gives
them highly individual sonorities. The first soprano part is
doubled in generally high, bright instruments: celesta-second
violin-oboe-clarinet, producing a momentary darkening, violon-
cello-flute-clarlnet. The second soprano part is at first as
sociated with the accompanying, middle parts of the orchestra:
viola and saxophone, gaining force at measure 8, oboe, then
trumpet and pitch percussion. The alto part is doubled in rich,
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dark, relatively low instruments: horn-Engllsh horn-trombone,
brightening at "LSuten" with the second violin-trombone-English
horn, saxophone in a low register. The words "des Klangs" are
unsupported in both alto and first soprano, so that these voices
almost seem to take flight from the momentum produced from the
section as a whole to provide the point from which the second
section can begin.
Second section (measures 13-28)
The solo soprano part continues the setting of the text,
ta k in g over from the choral p a rts in much th e same manner as in
the beginning of the second section of the fifth movement. The
first note of its initial entry overlaps the last note of the pre
ceding choral entries, 6, first soprano, with duplicate regis
tration and a similar vowel sound. This overlap of soprano parts
is almost the only direct link between the first and second
sections, for the texture, serial techniques, and nature of ac
companying material change with the solo soprano entry.
The first discontinuity of row forms in imitative voices
occurs here. The only row form spanning the sectional division
is that appearing in the alto part, whose last note is the second
note of the solo soprano entry, E, measure 14. The previous row
form pattern is inverted, so that original and retrograde inversion
row forms are introduced. The dux is assigned to the soprano solo
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part, all other canonic voices appearing In the accompanying
material In aurally clear Imitation.
The words of the text are not individually enhanced vertically,
but are set off imitative reactions in the accompanying material,
which appear in corresponding parts of the row form. The first
word of the section, "Alle," is followed by a vertical aggregate,
high strings, fortissimo, measure 14, and the stronger second
word, "Glokken,," sets off two such aggregates, pitched percussion,
sforzando, and relatively low woodwinds, also sforzando, both in
measure 15. "Die Herzen, wollen wir lHuten," again an especially
meaningful phrase with respect to voicing considerations, induces
the peal-like rhythmic, articulation, and pitch contour patterns
associated with "L&uten" in measures 7-8. Here, the three ac
companying voices are assigned to potentially bell-like instruments,
solo first violin, clarinet, and muted trumpet in exact pitch-class
and rhythmic canon with solo soprano as the dux, the durational
interval of entry invariably three eighth beats. The canonic pro
cedure reaches its height on the words "lHuten, o Menschen.'" One
of the intensity peaks of the section, measures 18-19. The beginning
of the next sentence of text, measures 20-1, "Nimmer durch RHume"
initiates three vertical aggregates, like the beginning of the first
sentence — this time, in a retrograde variant of the pattern in
measures 14-5; here, woodwinds, pitched percussion, and muted brass,
the strings reserved for the beginning of the next round of imitative
m otives.
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The pattern imitated, eighth note plus grace note, is intro
duced in its moat prominent voicing, measure 22, first and second
violins in a favorable register, fortissimo, as part of a larger
motivic statement. The following imitations are in relatively
tame instruments, in middle register: violoncello-bass clarlnet-
bassoon-flute-saxophone. The pattern is developed and Imitated,
fortissimo, measures 25-8, in strings only, in a short episode.
The syncopation at this pattern anticipates the rhythmic
characteristics of the opening measures of the next section. The
slight slackening of tempo, the emphasis on linear motion, and
the somewhat wiry sonority of strings in a passage with such
voicing and technical hazards maintains the momentum necessary
for the explosive entry of the next section, without detracting
from the letter's unexpected force.
Third section (measures 29-36)
This section begins at a peak of intensity matched in this
movement only in the concluding measures. The words used here,
"Sturml#uten muss nun die Liebe.1" set off another round of peal-
like imitation, this time heavily doubled, using all instrumental
parts, fortissimo. The peal-like figures and the syncopation
which give these measures much of their force are anticipated in
measures 7-8 in conjunction with the word "LHuten," and much of
this section can be shown to derive from those measures.
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There is a general return to the procedures of the first
section. The dux once again appears in the second soprano part,
followed by alto and solo soprano-first soprano, and finally,
accompanying voice (horn). Although there is an alteration of
the order of entry of parts, the imitative voices defined by row
form maintain their original entry pattern. The first and second
entries are heavily doubled: second soprano, oboe, muted trumpet,
celesta; alto, English horn, trombone, harp. The solo soprano
entry is unsupported and could conceivably be covered by the ac
companying fortissimos unless care were taken in performance.
When the first soprano takes over that line in measure 32, however,
it is doubled, muted trumpet.
The doublings assigned to each part again give that part
added characteristics of sonority. Excluding initial doublings
which give the properties of an attack to the first soprano is
supported by the high, bright•tirabres of muted trumpet and first
violin; second soprano, the somewhat more intense but lower
timbres of unison first and second violin, oboe, and second
violin; alto, by darker, lower sonorities of harp in its middle
low register, low strings, saxophone, and viola. These progres
sions of sonority reflect the decreasing voluem of the section.
There is an unusual amount of crosslng“of canonic voices
among parts in the neighborhood of the word "Liebe," measures
31-2. The rising lines, clarinet, flute, and first soprano
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 364
supported by trumpet in the immediately following measures may
reflect the upward leap associated with "Liebe" in all vocal
parts. This upward leap is in every case that of a perfect
fourth, an interval of the row form rarely stressed in this
movement elsew here.
After "Liebe," the instrumentation thins rapidly. The strings
are placed in the background, pizzicato, measures 33-5, as they
were at the end of the first section. The prominent timbres in
the final measures are flute and clarinet, the first time in
the movement that upper woodwinds have been used for such gentle
purposes, here associated with the words "trifge und mUde." The
motives appearing in these instruments introduce some of the
material used in the fifth section and provide an episodic link
to the fourth section. In three measures, the dynamic level
drops from rhythmic, accented fortissimo to pianto, with the
specifications "espr." and "zart" over quiet, slurred motivic
fragm ents.
Fourth section (measures 36-44)
This brief interlude consists of an accented, forte, but
unsupported soprano solo, together with seven separated vertical
aggregates in accompanying parts. The words "sie bewege die Luft"
may explain the apparent echoing effect of these aggregates.
The f.olo soprano entry, like that in the second section, is
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 365
linked to the immediately preceding material by pitch-class and
register duplication. Its first two notes appear in the first
soprano part, measures 35; its next two, flute, measures 35.
All four row forms span the sectional division. However, in every
other respect, this section returns to the techniques used in the
second section and is unlike the preceding one.
The text reaffirms the power of Love: "he must not come lazy
and weary.' No, he must stir all the air ..." Still, the level
of intensity must not rise to the extent that the beginning of
the next section, marked pianissimo, "sehr ruhig," is obscurred.
Hence, apparently, the solution: The momentum of the principal
line is carried by the soprano solo with almost no reinforcement
from the three imitative voices which accompany it. The most
economical way to accomodate these three voices is to compress
them into vertical aggregates.
It might be said that the whole of the third and fourth
sections are nothing but echoes of "StUrmlButen," measures
29-30. Similarly, the vertical aggregates of the fourth section
may be echoes of the first vertical aggregate, measure 37, the
only one which is sustained, and the fourth one, measure 41,
the intensity peak of the section. The voicing pattern of these
aggregates is: solo strings-celesta-harp-pizzicato strings-
all winds-pizzicato strings-celesta-harp-brass, nearly a palindrome.
The fourth vertical aggregate seems to be a reaction to the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 366
crest of a rather unusual melodic line with respect to Webern's
late style, measures 40-2. The soprano solo part contains three
consecutive rising Intervals, followed by four consecutive falling
Intervals, the whole spanning more than two octaves. The relatively
slow pace of the falling portion, successive quarter notes, makes
the line particularly noticeable aurally, accentuating the words
"innersten Schlaf," whose meafting with relation to the text of
the second movement makes their setting Important here.
The three following vertical aggregates are evenly spaced
rhythmically, and provide a short episode between sections.
During this episode the dynamic level drops, sharply, and there Is
again a slight ritard. The longest duration of silence in the
entire movement, that of an entire 6/8 measure, separates the
fourth and fifth sections.
Fifth section (measures 45-59)
This section consists of choral entries with accompanying
material. The first half of the section, measures 45-51, is
related to material in the episode at the end of the third
section. It is calm, with a preponderance of slurred dyads and
a low dynamic level. The second half of the section consists of
a crescendo to fortissimo, using the techniques and motivlc
patterns of the third section. The general form of the fifth
section can consequently be derlvdd metamorphically from a
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 367
retrograde of that of the third section.
The order of entries by imitative voice is again maintained,
although the order of entries by part is permuted. The. entry
pattern for the first half is as follows: second soprano, first
soprano, alto, accompanying voice (horn); for the second half,
solo soprano-first soprano, second soprano, alto, simultaneous
accompanying voice (first and second violins). The row forms
of the first section are invoked, with a return to the overlap
pattern In : Rn + 1 : I n + 10. There is a complete discontinuity
of row forms in all imitative voices at the beginning of measure
45, the only such discontinuity in the entire movement .
The words, "Komme durch dichtestes Dunkel" are accompanied by
relatively dark timbres, with an exact lightening, voice by voice,
of these timbres as the words, "und lege die Toten zur Ruhe,"
beginning near measure 49, appear. The change in timbre is marked
by two harmonics, harp, at the end of measure 48 and measure 49,
the first harp harmonics in the movement. Before this point, the
first soprano part is doubled by saxophone; afterwards, by clarinet.
The change in the doubling accompanying the second soprano is English
horn-oboe; the alto, muted trum pet-flute; the accompanying voice,
horn-violoncello-celesta-first violin.
In contrast to the rest of the movement, the rhythmic and
articulation patterns are nearly constant and do little to support
the metric pulse. The extent of pitch contours is relatively
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minimal ao that changes in direction are scarcely noticeable. The
three choral parts are in strict rhythmic and articulative canon,
at the durational Interval of three eighth beats. Similar parts
of the row form are treated almost Identically, so the canonic
use is aurally clear.
At measure 49, despite the lightening of sonority, the
dynamic level rises only slightly. The last appearances of the
words "Dunkel" and "Toten" are accompanied by brief solos,
violoncello and first violon, respectively. VToten" also occurs
simultaneously with the marking "morendo" in all parts. The next
important word, "Ruhe," measure 52, is accompanied by a pianissimo
high A in the trumpet, which immediately crescendos to molto
f o r te .
This A marks the beginning of the second half of the section,
the concluding measures of the movement. It is immediately
repeated in the same register by solo soprano on the word "wache,"
also molto forte, as the first of another round of entries.
The word "wache" invokes all the characteristics associated
with the word "SturmlHuten" in measure 29: high dynamic level,
heavily accented, driving meter, swinging changes of pitch direction,
strong doubling of all choral parts. The first occurrence of the
word "Leben" coincides with the entry of all strings, measure 54,
at which point the full strength of the orchestra is almost
attained; its last occurrence coincides with the first fortissimo
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marking, measure 55. The last phrase is realized and imitated
as an entity, with no one word receiving special attention.
The crescendo is helped by the order of entry of the various
instruments, measures 52-5: trumpet, saxophone, oboe-celesta,
flute-harp, pizzicato strings, arco strings, Engllish horn. The
re-entry of trumpet and the first entries of trombone and horn
are saved for the emphasis of the last phrase in the syncopated
pattern associated with "StUrmlHuten," measures 57-8, as is the
woodwind doubling, flute-oboe-clarinet. This last doubling is
the same as the one used in the Variations, opus 30, to mark the
peak of intensity in variations.
The trombone entry, measure 57, is apparently in error (plate no.
12461, page 32). If it were notated in tenor clef rather than
in bass clef, the row form structure which is consistent everywhere
else in the movement would be maintained, and the present parallel
fifths between trombone and harp in that measure which are not
typical of Webern's mature style would be avoided. A recent com
munication from Theodore Presser Company to the author supports this
supposition.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. BIBLIOGRAPHY
This bibliography contains only selected works which
were consulted specifically for this study and found to be di
rectly relevant to its subject. Omission of basic sources in
the area of study are not judgements of their value.
If primary sources are not given for works which dis
cuss music, they were not available. All translations of such
works are the author's, with the exception of some passages from
Per Weg zur neuen Musik. For this publication, the translation
of Leo Black is followed unless the author decided on a clearer
rendering of the original text. Footnotes to these passages
indicate the translated edition.
The translations of works which do not discuss music
directly are by authorities in the subject matter with which
these works are concerned. Particularly in the case of Goethe's
writings, it seems presumptuous to correct the translations
of those who have an intimate knowledge of the original language,
the ideas of the author, and the work itself. For this reason,
translated sources are given in the bibliography for those works
rather than primary sources, even though primary sources mire
usually available and were consulted.
370
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 371
BOOKS
Adorno, Theodore Wiesengrund. Dissonanzen: Musik in der verwalten Welt. Gottingen: Vendenhoeck und Ruprecht, 1956.
______. Prism s. T ran slated by Samuel and S h ierry Weber, Letchforth, Hertfordshire: The Garden City Press, Ltd. (for Neville Spearman, Ltd.), 1967.
Alexander, H. G., editor. The Leibniz-Clarke Correspondence. Manchester: University Press, 1956.
Barthes, Roland. Le degree z^ro de 1 'Iscriture. Paris: Editions du Seuil, [1953j.
Beitrage 72/73 Osterreichische Gesellschaft fiir Musik: Webern- Kongress. Vienna: Barenreiter, 1973.
Boulez, Pierre. Penser la musique aulourd'hui. Mainz: C. B. Schott's Sohne, 1963. Originally published as the fourth volume of the series Kontrapunkte.
Chamberlain, Houston Stewart. Immanuel Kant: A Study and a Comparison with Goethe. Leonardo de Vinci. Bruno. Plato, and Descartes* Translated by Lord Redesdale. London: John Lane Company, 1914, 2 v o ls.
Curry, Haskell Brooks. Foundations of Mathematical Logic. New York: McGraw H ill, [1963].
Deppert, Heinrich. Studien zur Kompoaitionstechnik im Instrumentalen Spatwerk Anton Weberns. Darmstadt, Germany: Tonos, 1972.
Dissertations - Verzeichnis der Philos. Facultat der Universitat in Wien. V ienna: Gerold und Company, 1935.
Englemann, Frederick. Letters from Ludwig Wittgenstein and a Memoir. New York: Horizon Press, 1968.
Ferm, Virgilius, editor. A History of Philosophical Systems. New York: The Philosophical Library, 1935.
Goethe, Johann Wolfgang von. Faust. Translated by Peter Seim. New York: Bantam Books, Inc., 1956.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 372
______. Gedenkausgabe der Werke. Briefe. und Gesprache. Edi ted by Ernst Beutler. Zurich: Artemis Verlag, 1949.
______. Italian Journey. 1786-1788. Translated by W. H. Auden and Elizabeth Mayer. New York: Pantheon Books, 1962.
Goodman, Nelson. Languages of Art: An Approach to a Theory of Symbols. Indianapolis: Bobbs-Merrill, [1968 j.
Hausman, Alan and W ilson, Fred. Carnap and Goodman: Two F o rm alists. Iowa C ity : U n iv ersity of Iowa, 1967.
Herzfeld, M. von and Sym, C. Melvin, editors and translators, Letters from Goethe. Edinburgh: The University Press, 1957.
Hindemith, Paul. The Craft of Musical Composition. Translated by Arthur Mendel. New York: Associated Music Publishers, 1945.
Janik, Allan, and Toulmin, Stephen. W ittgenstein's Vienna. New York: Simon and S chuster, 1973.
Johnston, William M. The Austrian Mind. Berkeley, Los Angeles, and London: University of California Press, 1972.
Kandinsky, Wassily. Concerning the Spiritual in Art. Translated by Michael Sadler et al. New York: Wittenborn, Schultz, Inc., 1947.
Kolneder, Walter. Anton Webern: Einfuhrung in Werk und St11. Rodkirchen am Rhein: P. J. Tonger, 1961, originally published as the fifth volume of Kontrapunkte.
Krenek, Ernst. Studies in Counterpoint: Based on the Twelve-Tone Technique. New York: G. Schlrmer, Inc~ [1940],
Lang, Serge. Algebra. Reading, Massachusetts and London: Addison-Wesley P u b lish in g Company, 1965.
Leibowitz, Ren^. L'evolution de la musique de Bach a Schoenberg. Paris: Editions Correa, n. d.
Luke, David, and Pick, Robert, compilers and translators. Conversations of Goethe with Eckermann and Soret. Chicago: Henry Regery Company, 1966.
Moldenhauer, Hans, compiler. Anton von Webern: Perspectives. Seattle: University of Washington Press, 1966.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 373
Mueller, Bertha, compiler and translator. Goethe's Botanical Writings. Honolulu: University of Hawaii Press, 1952.
Oxenford, John, compiler and translator. Conversations of Goethe with Eckermann and Soret. London: George Bell and Son, 1882.
Perle, George. Serial Composition and Atonalitv: An Introduction to the Music of Schoenberg. Berg, and Webern. Third edition, revised and enlarged. Berkeley: University of California Press, 1972.
Plato. The Collected Dialogues of Plato. Edited by Edith Hamilton and Hunt inton Cairns. New York: Pantheon Books, 1961.
Plotinus. Plotinus on the One and the Good. Edited and translated by Stephen MacKenna and B. S. Page. London: The M edici S ociety, L td ., and B oston: Hale, Cushman, and F li n t, 1930.
Polnauer, Josef, editor. Anton Webern: Letters to Hildegard Jone and Josef Humplik. Translated by Cornelius Cardew. Bryn Mawr, Pennsylvania: 1967.
Reich, W illi. Anton Webern: Weg und Gestalt. Zurich: H. Borsigs Erban, 1961.
Rognoni, Luigi. Expressionismo e dodecafonia. [Turin]: G. Einaudi, 1954.
Rufer, Josef. Composition with Twelve Notes related only to One Another. Translated by Humphrey Searle. New York: Macmillian C o., 1954.
Schillinger, Joseph. The Schillinger System of Musical Composition. New York: Carl Fischer, Inc., [1946].
Schoenberg,. Arnold. Harmonielehre. Third edition, revised. Vienna: Universal-edition, 1922.
______. Style and Idea. New York: Philosophical Library, 1950.
Schopenhauer, Arthur. Schopenhauer: Selections. Edited and. translated by DeWitt H. Parker. New York: Charles Scribner's Sons, 1928.
Sessions, Roger. Questions about Music. Cambridge, Massachusetts: Harvard University Press, 1970.
Wagner, Richard. Richard Wagner's Prose Works. Translated by William Ashton Ellis. New York: Broude Brothers, 1966.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 374
Webern, Anton, editor. Heinrich Isaac; Choralia Conatantinus II. Denkmaler der Tonkunstl'er Oaterreich. vol. 32. Graz: Academische Druck-u. Verlagsanstalt, 1959, reprint edition.
______. The Path to the New Music. Edited by Willi Reich, tra n s la te d by Leo Black. Bryn Mawr: Theodore P resser Company, 1960.
______. Sketches (1926-1945). Commentary by Ernst Krenek, forward by Hans Moldenhauer. New York: Carl Fischer, 1968.
______. Der Weg zur neuen Musik. Edited by Willi Reich. Vienna: Universe1-edition, 1960.
Whitehead, Alfred North. Process and Reality. New York: The Free Press (Macmillan Company), 1969.
Wildgans, Freidrich. Anton Webern. Translated by Edith Temple Roberts and Humphrey Searle. London: Caldar and Bowers, 1966.
Wilkinson, Elisabeth M., and Willoughby, L. A. Goethe: Poet and Thinker. London: Edward Arnold, Ltd., 1962.
Wittgenstein, Ludwig. Philosophical Investigations. Translated by G. E. M. Anscombe. Oxford: Basil Blackwell, 1953, bilingual edition.
______. Remarks on the Foundations ojfc Mathematics. Edited by G. H. von Wright, R. RHees, and G. E. M. Anscombe, trans lated by G. E. M. Anscombe. Cambridge, Massachusetts and London: The M. I . T. P ress, 1967.
. Z e tte l. E dited by G. E. M. Anscombe and G. H. von Wright, translated by G. E. M. Anscombe. Berkeley and Los Angeles: University of California Press, 1967.
Valery, Paul. The Collected Works of Paul Valery. Edited by Jack son Mathews, various translat rs. Bollingen Series XIV. Princeton: Princeton University Press, various dates, 14 vols.
van Gogh, V incent. The Complete L e tte rs of Vincent van Gogh. New York: New York Graphic Society, n. d., 3 vols.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 375
PERIODICALS
Adorno, Theodor Wiesengrund. "Form in der Neuen Musik." Darmstfldter Beitrflge zur neuen Musik X (1966): 9-21.
. "Vers une musique informelle." Darmstfldter Beitrtfge zur neuen Musik IV (1961): 73-102.
Babbitt, Milton. "Set Structure as a Compositional Determinant." Journal of Music Theory V (1961): 72-94.
Bach, David Joseph. "New Music by Berg, Webern, Krenek." Modern Music XII (1934): 31-38.
Berg, Alban. "A Word about Wozzeck." Modern Music V (November- December 1927); 22-24.
Boulez, Pierre. "Disziplin und Kommunikation." DarmstHdter Beitrage zur neuen Musik IV (1961): 25-27.
Castiglioni, Niccolo. "Sul rapporto tra parola e musica nella seconda cantata di Webern." Incontri Musical! Ill (August, 1959): 112-117.
DBhl, Friedhelm. "Die Welt der Dichtung in Weberns Musik." Melos XXXI (March, 1964): 88-90.
Eimert, Herbert, and Stockhausen, Karlheinz, ed. Die Rethe II (1958) ; entire issue devoted to Anton Webern.
F le is c h e r, Hugo. "FUr und w ieder Arnold SchBnberg." Der Merker I I I (1912): 919-923.
Hiller, LeJaren, and Fuller, B. "Structure and Information in Webern's Symphonie, Opus 21." Journal of Music Theory XI (Spring, 1967): 60-115.
Howe, Hubert S., Jr. "Some Combinatorial Properties of Pitch Struc tures." Perspectives of New Music III (Fall-Winter 1965): 45-61.
Jones, James R ives. "Some A spects of Rhythm and Meter in W ebern's Opus 27." Perspectives of New Music V (Fall-Winter 1968): 103-109.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 376
Kandinsky, Wassily, and Marc, Franz, ed. Der Blaue Reiter I (1911), presently available in a volume of the same name (Munich: Piper Verlag, [19651).
La Rue, Jan. "On Style Analysis." Journal of Music Theory VI (Spring, 1967): 91-107.
Langer, Susan K. "Letters from Webern to Schoenberg and Roberto Gerhard." The Score, no. 24 (November 1958),• pp. 36-41.
Lewin, David. "A Metrical Problem in Webern's Op. 27." Journal of Music Theory VI (Spring.1962): 124-132.
Ligeti, GyBrgy. "Weberns Melodik." Melos XXX (1966): 116-119.
Martino, Donald. "The Source Set and Its Aggregate Formations." Journal of Music Theory V (1961): 1 224-273.
Der Merker. vol. 2, no. 4 (1911). Almost the entire issue is devoted to Arnold Schoenberg and his music.
Nono, Luigi. "Die Entstehung der Reihentechnik." DarmstHdter Beitrage zur neuen Musik I (1958): 25-38.
Perle, George. "Atonality and the Twelve-Note System in the United States." The Score, no. 27 (July 1960), pp. 51-60.
Pone, Gundaris. "Webern and Luigi Nono: The Genesis of a Compositional Morphology and Syntax." Perspectives of New Music X (Spring-Summer 1972): 110-5.
Pousseur, Henri. "Music, Form, and Practice." Die Reihe VI 77-90.
Reich, W illi, ed. "Anton Webern zum 50. Geburtstag.11 Drei und Zwanzig: Eine Wiener M usikzeitschrift XIV (February 1934), entire issue devoted to Anton Webern.
. "Anton Webern Uber Alban Berg." Neue Zeitschrift fllr Musik CXIV (1963): 143.
. "Aus unbekannten Briefen von Alban Berg an Anton Webern." Schweizerische Musikzeitung XCIII (1953): 49-52.
. "Berg und Webern schreiben an Hermann Scherchen." Melos XXXII (1966): 225.
. "Briefe aus Weberns letzen Jahren." Osterreichesche M usikzeitschrift XX (1965): 407.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Rohwer, J. "Die Grundlagen der Musik." Muaikforschung IV (1967): 430-436.
Spinner, Leopold. "Anton Weberns Kantate Nr. 2, Opus 31; die Formprinzipen der kanonischen Darstellung." Schweizerische Musikzeitung Cl (1961): 303-308.
Stockhausen, Karlheinz. "Kadenzrhythmik bei Mozart." Darmstfldter Beitrage zur neuen Musik IV (1961): 38-72.
Weiss, Adolph. "The Lyceum of Schoenberg." Modern Music IX (March-April 1932): 99-102.
Wellesz, Egon. "Die jUngste Entwicklung der neufranzBsischen M usik." Der Merker I I I (May, 1911): 657-665.
Wolff, Christian. "Prinzipelles auf Musiktheorie." Schweizerische Musikzeitung LXXVI (1936): 204-208.
SCORES
Webern, Anton. Streichquartett. opus 28. Philharmonia no. 390. Vienna: Universal-edition, copyright assigned 1955.
•*____ . Streichtrio. opus 20. Philharmonia no. 175. Vienna: Universal-edition, copyright 1927, renewed 1955.
______. Variationen fllr Orchester. opus 30. Universal-edition:. no. 12417. Vienna: Universal-edition, copyright 1956.
______. II. Kantate. opus 31. Universal-eldition no. 12486. Vienna: Universal-edition, copyright 1956.
UNPUBLISHED MATERIALS
La Rue, Jan. "Basic Analytical Procedures." Mimeographed copy, p riv a te ly owned.
McKenzie, Wallace Chessley. "The Music of Anton Webern," disserta tion reproduced by University Microfilms, Inc., Ann Arbor, Michigan, submitted to North Texas State College, 1960.
RECORD BOOKLET Craft, Robert, and Stone, Kurt, editors. "The Complete Music of Anton Webern." Oolumbia Masterworks # K4L-232.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. VITA
Judith Marie Fiehler was born In Bonne Terre, Missouri, was
graduated from Louisiana Polytechnic Institute (now Louisiana Tech
University) with a Bachelor's degree In Instrumental music education,
and from Louisiana State University with a Master's degree In compo
sition. She is an experienced librarian, computer programmer, and
violist, and an enthusiastic amateur in almost all non-musical arts.
She is a member of the honorary societies Phi Kappa Phi and Phi
Kappa Lambda. She has co-authored three published articles and has
presented a paper at a regional meeting of the American Musicological
S o ciety .
373
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. EXAMINATION AND THESIS REPORT
Candidate: Judith Marie Fiehler
Major Field: Music
Title of Thesis: Rational Structures in the Late Works of Anton Webern
Approved:
Major Professor and Chai
Dean of the Graduate School
EXAMINING COMMITTEE:
(PoJUL
Date of Examination:
November 29, 1973
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.