CALIFORNIA STATE UNIVERSITY NORTHRIDGE
THE USE
, OF ANALYSIS IN TEACHING TWENTIETH CENTURY PIANO LITERATUHE
A graduate project submitted in partial satisfaction
of the requirements for the degree of Haster of J1.rts ·in
Music
by
Nancy Regnier
~shforth
The graduate project of Nancy Regnier Ashforth is approved:
CALIFORNIA STATE UNIVERSITY.
August, 1977
ii
NORTH~IDGE
TABLE OF CONTENTS
Abstract ·····················~·························
v
Introduction 8···················~······················
1x
PART I
CONCEPTS AND PROCEDURES
Chapter
I.
Expanding Concepts and Terminology...............
1
II.
Establishing Analytic Guidelines ·········•·······
10
PART I I
II I.
Berg:
ANALYSES Al"'D TEACHING POINTS
Sonata, Op. I-, { 1908)......................
19
Free Variations and Minor Seconds~ Major
Sevenths from Hikrokosm·2z._, (19215-1937) • .. • • • • • • • •
29
Messiaen: Noel, from Vingt Reqards sur L'Enfant
Jesus., ( 194ifT:7.
~ 8." .~:::::-,7-:·u ~ 7Ql·,. 7..
39
Conclusion ......•.....•....•.•.••.•....•.•.••.•-........
47
Bi~liography :··········································
48
Appendix: Musical Examples ••••••••••••••••••••••••••••
50
IV. Bartok:
V.
it • • • •
o ••
CALIFORNIA STATE UNIVERSITY, NORTHRIDGE
THE USE OF ANALYSIS IN TEACHING TWENTIETH CENTURY PIANO LITERATURE
and
GRADUATE RECITAL IN PIANO - PEDAGOGY
A graduate project sutmitted in conjun:tion
with an artistic performance presented in
partial satisfaction of the requ·irements
for the degree of Master of Arts in ~~usic
by
Nancy Regn·ier Ashforth
August, 1977
ABSTRACT
THE USE OF
A~ALYSIS
IN TEACHING TWENTIETH CENTURY PIANO LITERATURE
by
Nancy Regnier Ashforth
Master of Arts in Music
August, 1977
The purpose of this graduate project is to explore the uses of
analysis in teaching twentieth century piano music.
The project
includes both a recital of tWentieth century piano music and a
paper dealing with analysis in a studio teaching situation, with
mtls ka1 examp1es dravm from the reci ta 1.
~nong
the problems involved for a teacher are:
expanding a
traditional musical education to encompass evolving musical concepts
and terminology; finding a method of analysis that will be both
comprehensive and r·texible enough to produce immediate aural understanding in a studio teaching situation.
The paper is divid€d into
t~ro
parts.
The first two chapters
discuss evo1ving concepts and terminology and propose a series of
analytic questions to serve as a guideline for student/teacher ex-
p1or·at·tcn d1.a'i;1g the 1es$ons.. The guideline questions are grouped
into the categories of sectional structure; motivic structure,
tonal orders !i pi tr.h content 0 rhytl'm and texture.
v
The last three chapters contain analyses of three twentieth
century compositions: Berg, Sonata, Op. I; Bartok, Free Variations
and
~nor
Se.conds, Major Sevenths_. from VQlume VI of the Mikrokosmos;
and Messiaen's N~el from the Vingt Re~rds sur l'Enfant J~sus.
These analyses are presented in three steps: aurai analysis, based
on aural perception before study; theoretical analysis, based on
study of the scor:e; and teaching points, based on information gained
through the theoretical analysis.
FrL9~Yt-M~ 27,~.~19~7~7------------·~R-ec~i_t_a~J-H~a_1_1____________4_:_o_o~p_._m__
•
PROORAr~
MIKROKOS"10S ••••••••••••••••••••••••••••••••••••••••• o . . . . . . . . BELA BART6K
(1881-1945)
125.
Boating
144.
Minor Seconds,
~40.
Free Variations
r~ajor
Sevenths
SONATA NO. 5, OP. 38/135 ••••••• e••••••••••••••••••••••oSERGE PROKOFIEV
.
(1891-1953)
Allegro tr?.nquillo
Andantino
Un poco allegretto
----------·-·~-~----·-------------------~~~~--~-------
INTERHISSION
Vi
SONATA, OP. 1•••••• ••
Cl' . . . . . . . . . . . . . . . . • • • • • • • • • • . • • • • . • • • • • • • • •
ALBP,N BERG
(1885-1935)
,
VINGT REGARDS SUR L'ENFANT JESUS ••.••••••••••••••••••• OLIVIER MESSIAEN
{1908I
Regard de l'etoile ·
Regard de la Vierge
Noel
vii
)
The artistic performance of Nancy Regnier Ashforth is approved:
Dr. William Richards
Or. Charles Fierro
Committee Chairman
The abstract of Nancy Regnier Ashforth is approved:
.
Or. George
~kapski
Dr. -Charles Fierro
Califu~nia
State University, Nortrrridge
August, 1977
INTRODUCTION
The purpose of this graduate'project is to explore the uses of
analytic techniques in teaching twentieth century piano literature.
The project includes both a recital of twentieth century piano music
and a paper
dealing with the use of analysis .in a studio teaching
situation, with musical examples· drawn from the recital.
While the benefi.ts of -using analysis to aid in answering a
variety of musical questions or at least in suggesting approaches to
. find·tr;g solutions are unquestioned, the problem 1ies in the fact that
the majority of time spent in a college or conservatory in preparation
for a music teaching career is involved in the history, theory, and
performance practice of music written before 1900.
is, of
This preparation
course, indispensible in forming the critical and stylistic
acuity of the literate teacher.
However, in teaching t"'-er.tieth
century music, one must be aware of not only the continuing evolution
in the use of the materials of music. but also that the analytic
techniques describing the relationship bet\'Jeen materia 1s in earlier
music, remain viable only to the extent that these relationships
continue to function in the same or a similar way.
How can a studio teacher adapt a traditional education in music
to meet the problems in newer music?
Consideri~g
the expansion that
has taken place in all directions of musical thought since 1900, the
first step wo:.Jld be to re-examine our musical concepts and tenninology
in order to discover in which \'lays they have evolved or remained the
ix
same.
Next, a method for using analysis should
be
evolved which will
be sufficiently comprehensive and flexible to provide .immediate and
audible clarification with a variety of complex literature.
This paper will be presented in two parts: Part 1, (containing
Chapters 1 and 2), will discuss the expansion of musical concepts and
terminology, and will propose a series of analytic questions that can
be used as a guideline for teacherlstudent preparation of a new work.
Part II, containing Chapters 3-5, will consist of analyses from the
works of three composers, divided into three areas: aural analysis,
(the use of analytic guidelines, based on the student's aural perception of the work before any formal study); theoretical analysis,
(application of analytic questions to the musical scores); and
teaching points, (specific points to be discussed about the work as a
.
result of the theoretical study). The teaching points can include not
only the musical aspects of the work being analyzed, but also in
comparison with other works. thus broadening the frame of reference.
The examples: Sonata, Opus I, by Alban Berg; Free Variations
and Minor Seconds, Major Sevenths, from Bela Bartbk's Mikrokosmos
Volume VI; and Noel, from Olivier Messiaen's Vingt Regards sur
!:.:_En..f.!!!..!.Jg_ltJ.1_ were chosen because they
repr~sent three. differing
approaches to twentieth century composition.
The examples are all written in standard notation to
the
keyboard~
be
played on
the problems involved in the real fzation of graphic
notations or the tachnical requirements of non-keyboard perfonnance
(sounds created outside the keyboard) are outside the scope of this
papere
Since nona of the ?Xamples involve serial techniques, the
X
specific analytic methods used ·in serial analysis will not be discussed.
The goal of a consistent application of analytic tectmiques in
teaching should be to increase the independent ability of the student
to perceive, both aurally and intellectually, the shaping forces in the
music that he plays, and finally to achieve a more mature and intelligent
performance.
Xi
EXPANDING CONCEPTS AND TERMINOLOGY
In redefining for the twentieth century the concepts and
terminology commonly used in talking about music, one must take into
account the fact that musical contexts are constantly changing,
although the basic elements of pitch and rhyttm remain constant.
It
is confusing to find that in some cases the terminology has remained
the same while the meanings have subtly changed with the passage of
(One of the most obvious examples of this is the term
time.
____
·andantino,· the exact meaning of which is still debatable, both
.,..
among musicians and in reference sources.)
In other cases, such as
that of serial music, an entirely new terminology has been developed
to define the specific relationships within that system.
While there is probably no final solution to this problem, one
can often find a conmon thread in the usage of older terms that is
still. relevant and can be applied to new music. For example,
although historical
~ontext
has constantly altered
t~e
exact
boundaries of rooaning, one can still use "melodi1 or "melodic line",
in
m~ny
cases, to refer to the horizontal aspect of pitch succession.
The alterations in meaning,
from
the
Greek
and tonality, have dealt with melody as
modes through polyphony
constru~ted
within a certa.in
system or style, but not with the concept of melody as a horizontal
succession of
pit~h.
Given the variety of compositiona 1 techniques in current practice,
1
the standard twentieth century references are careful to avoid
referring to specific systems in their general definitions of
melody.
In the Harvard Dictionary of 1'-lusic v1e find:
11
a succession
of musical tones, as opposed to harmony, i.e. musical tones simulta1
neously ••• 11 ; in Grove's Dictionary of Music and t~usicians: "the
general tenn vaguely used to denote succession of single notes which
2
make musical sense ••• "
If one hesitates to use "melody11 or 11 melodic 1 ine" because in
earlier styles these terms implied a certain formal or tonal
structure as well as linear succession, than one can use simply
"1 ine, 11
11
1 inaar aspect" or 11 1 in ear connection; 11 the most appropriate
term depends on one's critical judgement of how that aspect functions
in the work being discussed.
Just as it would be ridiculous to refer
to. a melodic line in Prokoviev as a "linear succession of pitch class
.
events, .. it would also be inappropriate to talk about the "melodic
line" in the Hebern Y.?_riations, Op. 27_.
In using·any or all of these
tenns in teaching, the first consideration is that the student be
aware that the concept of horizontal succession obviously occurs in
all music, whether diatonic or chromatic, conjunct or disjunct, con•
tained within the span of a tetrachord or spread across the audible
range ..
The concept of harmony still retains its definition as the
vertical structure of a composition as opposed to the melodic or
l"Melody,t• Harvard Dictionary of ~·1usic, 2nd ·ed., (1969), p. 517.
2
c. Herbert H4 Parry, 11 Melody, 11 Grove's Dictionarv of Nusic and
Musicians, 5th ed., V (1954), p~ 66~--~-
horizontal structure.
However, since tonality is no longer
(necessarily) the controlling factor in hannonic succession, the
relationship of the harmonic aspect to the work as a whole must be
discovered in each work rather than assumed. One difficulty in
discussing harmony in twentieth century music is distinguishing
between contrapuntal lines that are only contiguously vertical and
vertical sonor·i tes \•/hose intervalli c structure defines than as
meaningful in the course of a work.
Certain terms have developed as
a result of this nonfunctional possibility of vertical structure:
1. aggregate: often used as a substitute for "chord, 11
(a.l though it has a more specialized meaning in serial
composition) .3
2. simultaneity: frequently used to refer to the simultaneous sounding of any pitches.4
3. vertical: a tenm used for the elements or components
of a composition that sound simultaneously and are notated
one above another on the score.S
\~hile
these tenms are useful, there is no reason that 11 chord 11 cannot
sti11 be used in referring to a simultaneity that has a specific
intervallic consistency within a work, if it is understood that the
intervall ic structure is not necessarily based on thirds as it was in
functional tonality.
3Robert Carroll Jones, A Glossarf of Theoretical Tenns Used in
Selected t~ritin s in English Aboutwentieth-Centur Music, doctoral
Cifss'ertation, Unw. of · owa, L65, Ann Ar or, ~1ic • : uriiversity
Microfilms, Inc., 1970} p. 8.
4Jones. Qp. cit., p. 281.
5Jones, oo. cit •• p. 351.
6
7
The concepts of extended tonality and suspended tonality (a
state where one basic tonality still exists in spite of various
melodic and harmonic f1gurations ~hich may have been added) can be
.brought up in discussing
~~rks
such as the Berg example in Chapter 3.
An example of vertical structure based on intervals can be seen in
8
Bart6k' s ~1inor Seconds, Major Sevenths in Chapter 4. The expansions
of basic harmonic concepts by
~lessiaen
are so specific to his music
that they vli11 be discussed \'lith the example of his work in Chapter 5.
All changes in the movement of sound through time must be
considered in a general definition of rhythm.
Howard E. Smither, in
9
his excellent article on rhythm in the Journal of Music Theory
defines rhythm as "order in time," the tenn "order" referring to a
harmonious relation rather than necessarily a regular arrangement.
While this broad definition is acceptable, there are still many
leve1s of rhythmic activity that should be differentiated in some way.
10
In his §l!:uctural Functions in Music,
Wallace Berry suggests the
following rhythmic aspects which are all related either to pace or
grouping:
6Jones,
pp. cit~.
p. 97.
7Jones, op. cil·• p. 305.
8Bela Bartok, Minor Seconds, Major Sevenths, from Mikrokosmos,
VI (London:
Boosey & Ha\"Jkes, Ltd., 1940), pp. 16-19.
9Howard E. Smither, 11 The Rhythmic Analysis o"f 20th,;.Century
Music~" ~.2!-l!!!al of r-1usic Theor.z', VIII. no. 1 (Spring, 1964), p. 56.
10wa11ace Berry, Structural Functions in Music, (Englewood Cliffs,
11 Inc., 1976'), pp. 447.
N••J.; Prenti ce-Ha11
-.: ,_·~
1. Tempo, which includes 11 .eo both the eventfulness of music
and the frequency of pulsation at some given level ... 11
2.
11
Pattern or motive, .~. as expressed in durational and
other strong-weak combinations which have, in a given context,
motivic significance at some level, or characteristics of
pattern by ~tthich a style, genre, or work can be identified ... 12
3. The profiles expressed in element changes (such as melodic
rhyt!tn, harmonic rhythm, textural rhythm) ..... as these
changes invo 1ve pattern, rate and degree of change. 11 13
Grouping, including meter, 11 • • • a portioning of music's
time span by associations perceived within and among
punctuated or articulated unit-orderings of events. 11 14
4.
While· rhythm in the majority of Western music has implied a
feeling of regular pulse and the organization of groups of pulses
into meter, these concepts have been both expanded and abandoned in
some twentieth century music.
Some terms in use to describe these rhythmic expansions are:
1. additive rhytt~: the grouping together or addition of
beats of unequal length. This is similar to the tenn
"asymmetric meters" Nhich refers to meter signatures V·lhich
indicate unequal groupings of beats such as 5/8, 7/8. 15
2. ametrical: (as used by Nessiaen) music with a free but
precise rhythmic pattern, in opposition to 'measured'
·(i.e. equally barred) music. 16
llserry,
oe.
cit., p. 305.
12Ibid., p. 305.
13serry,
Qp. cit •• p. 306.
14~.. p.
15Jones,
306.
op. cit., p. 6.
16Q1 ~vier Ness iaen! The Tech~ ig_~of r4y Must ca 1 Language,
trans.· by.
J~
Satterfleld, (Par1s:--IC[eauc, 1956),_!. 14.
•
u
3. metric modulation:
to another. 17
the gradual change from one pulse
4. polymeter: simultaneous use of two or more different
meters with two or more independent patterns of regular
accentuation used simultan·eously. 18
These terms will be useful in discussing the works of Bartok and
Messiaen and specific examples will be pointed out in the later
chapters.
The concept of texture in music has undergone a treJOOndous
expansion in twentieth century music.
As a term it defines both the
density and complexity of movement between musical lines, varying in
degrees from homophony to polyphony.
In earlier music texture was a
stylistic referent, being used with relative consistency within a
particular style.
Ho\'rever, as functional harmony disappears as the
controlling factor in creating form in twentieth century music,
texture assumes enough independence to be considered a separate
dimension of structural significance.
While the traditional terminology referring to texture, such
as "polyphonic11 and "homophonic, 11 needs no further definition, certain
other aspects of textural differentiation should be explored.
The
. tenn, "textural rhythn 11 can be used to describe the timing and nature
19
of textural changes, "textural activation .. describes the means
=I7Jones,
O_Q_.
citq p. 160
lBSmither, ~~· p. 77
19serry, oe. <:it. p. 201
·~·
I
the
w~ans
(dynamics, articulation, rhythm,) used to vitalize simpler
20
textures,· and "texture space 11 describes the boundaries of vertical
21
and horizontal in which the music moves,. It is possible to talk
about textural modulation (a term similar in its use to metrical
modulation) as a transition from one texture to another.
In teaching
twentieth century music, the awareness of textural modulation,
textural variation, how it is achieved and how Jt relates to the
structural whole is as important as the awareness of the pitch and
rhythmic organization.
Unlike the other musical aspects, which can be isolated for the
purpose of description and discussion, a definition of form or
structure in music must include all of the other elements and how
they relate to each other.
(While some twentieth century composet•s
work consciously to create random or formless sound experiences,
these sequences of sound events can only be described, not analyzed,
and
are therefore useless for the purposes of this paper.}
As a starting point, let us consider the following excerpt from
the Harvard Dictionary of Music essay on form.
"Music is not a chaotic conglomeration of sounds but
consists of elements arranged in orderly fashion according
to numerous obvious principles as well as a still greater
number of subtle and hidden relationships.22
zn.~erry, 2£· cit., p.22Z
21serry, op. cit., p.24~
·./
22
. "Form," !!,arva'1L_Dictionarx-_nf Musi£, 2nd ed, (1969) 326,
.
~lhile
the lack of a corrmon style practice creates a lack of
predictability in twentieth century music, the unifying techniques
used throughout the centuries are. still va1i d, though perhaps in
. different proportions or different guises. One must still look for
some kind of relationship between the polarities of motion and rest,
tension and relaxation, repetition and variation,_ density and
sparsity, small detail and large section, organic development and
stark juxtaposition.
Berry, in another sense, is also describing this balance when
he defines structure:
••• musical structure can be regarded as the confluence
of shaped lines of element succession which either agree •••
in intensity direction or d·isagree ••• in direction.
Within the range of musical elements subject to control
within these procedures, some are, of course, of greater
relevance to certain styles than others, but the underlying concept of the confluence of functional elementactions as fundamenta 1 to musi ca 1 structure and effect
is of crucial significance in all styles. 23
While one can assume some similarities in the quality of
confluence contributing to a coherent musical structure regardless of
style, certain traditional formal principles have been greatly
expanded.
For examp1e, the ide a of cadence has existed throughout
our musical history as one of the principal devices for delineating
structure. Without a clear definition of endings provided by the
harmonic unity of a tonal system, one finds both that the idea of
24
closure can be brought about by other means, ·such as textural or
23Berry, op. cit., p. 9.
24 ,Jones. op. _c)t,. s p. 46.
rhythmic changes or the completion of a motion in the pitch aspect.
or that in some cases, the concept is no longer relevent.
One assumes. logically that in any composition exhibiting a
perceptual unity of sound, there exists consistent fonnal relationships between the elements. It is up to the teacher to bring these
intuitive aural perceptions to the_ level of conscious
understanding
.
in the student.
ESTABLISHING ANALYTIC GUIDELINES .
Since music is an art which exists in time, it is impossible to
perceive the total structure of a work at once, as we can with other
art forms such as painting or sculpture.
The various methods of
analysis provide us with ways of looking at a composition as a whole
and uncovering the relationships between the parts.
Analysis has ahtays been a part of the teaching experience. The
process of cr·itical listening, whem not involved with specific
technical pt..oblemse constantly requires decisions based on analytic
knowledge.
Any comparisons one makes between phrases or sections. in
deta'il s of articulation • dynamics and rhyttrn are based on conc1 us ions
drawn from an awareness of the whole structure and not simply the
moment at
hand.
A most eloquent description of how a student benefits from
analysis is given in an article from a forum on theoretical training
in the Journal of Music TheprJ by Stanley Fletcher:
And all students should leam that the expressiveness
of music is not something they must learn to "put into
it" but something they must reveal by working out that
plastic treatment which makes most evident the textural
and structural nature of the composition. The study of
music must guide the study of its performance ••• He will
no longer be content to make a crescendo·because some
teacher or editor (or even the composer in the role of
editor) has indicated that he should, but will ask himself: "~lhat is happening in the music that should be
pointed up by an increase in this p?ssage? Or, if an.
accent is indicated, he will ask: ~~~!hat in the texture
or drama here calls for emphasis, and how much?" Such
a perfonner wi11 recognize. when his instinct or intuition
11
10
tells him to make the music sudden 1y softer, that the
treatment is justified because of a resolving dissonance
at that moment or because of a startling change of
direction in the harmonic progress, or a sudden retreat
from a previously asserted purpose in the structural
development of the composition. _
In sum the level of performance ••• is that of an
intelligent musical performer sensitized to music with
all his resources. He is not merely a highly trained
automation performing under the direction of blind
instinct, however refined blind musical instincts may
become. He is not merely a rational mind, dissecting
and analyzing the dead carcass of a musical composition
with a dry brain in a dry season. In this performance
the t\'10 have become one, a complete musical personality
with mind and imagination and intuition ~-;orking together
to\<.tard producing an enlightening and communicative
performance which shall engage not only the player but
the listener as well at this enriched level of experience. 25
However enthusiastic one is about the idea of using analysis in
teaching twentieth century music, several problems present themselves
at. once.
One is that the studio teaching situation is not the same
as a theory classroor.i and \'lhatever analytic techniques are used must
be immediately applicable to the music one is working on; i.e.
examples need to be audible and understanding must be achieved on an
aural as well as intellectual level.
The studio lesson is not the
place for graphs and charts.
Another problem is that specific analytic methods developed in the
past (such as those of Schenker) were the result of the study of a
specific kind of music.
One cannot impose an analytic method on music
which does not apply to that method, and certainly not all twentieth
century music is susceptible to the kind of hierarchical peeling which
25stanley Fletcher, "For the_ Perfonner." ~rnal_ of Music Theory,
I~I. no. 1 (April, 1959), p. 48. 49.
.....
Schenker's methods use.
However, Allen Forte, a theorist who has applied Schenker's
levels of reduction to the work of such composers as Stravinsky,
Sessions, Bartok and Schoenberg, claims no difficulty in reconciling
Schenkerian concepts to non-triadic music.
Forte's definition of
structure in music as a "complex of ordered and interrelated tonal
26
events which unfolds in time" does not eliminate non-triadic tonal
.wov·ks from consideration under this system, but rather insists that
other linear and hannonic events, to be uncovered through the levels
of reduction, fonn the basis of a hierarchical structure in a similar
way to the tonic-dominant function in tonal music.
Not \'.dshing to argue the possibility of using Schenkerian concepts
in analyzing some twentieth century music, one would also have to
state that the efficacy of using this technique in a studio teaching
situation
'from the
~uuld
scm~e
probably be limited to a teacher's ability to discern
(or fOi..eground 1evel \'/here perfonnance takes place •
after a11} the elements \<Jhich are structural as COlllJared to those which
are embellishing, or to point out how a musical event can function in
its immediate surroundings and also as part of a larger hierarchy,
and demonstrate these comparisons by audible example.
This continuing
insistence of the aural perceptibility _of the examples is backed up by
Forte in the conclusion of his chapter on analytic procedure:
The aural sense is basic to musical activity of any
kind, for music is an art in sound. The use of visual
'.,/
-------------·------
26A1len Forte, 9~nt~m~1r?!l-I£~ Structu~s. (New York: Columbia
University, 1955)
means (the analytic sketches) in this study does not
mean that the ear is considered secondary to the eye
in the analytic process. On the contrary, it should
be stressed that the sketches are valid and significant
only to the extent that they correctly represent structure
as abstracted by the ear. In all cases the ear is the
final arbiter. 27
Composer and theorist Philip Batstone, in his article
"~1us­
ical Analysis as Phenomenology" from Perspectives of New Music also
begins from the p·oint of view of 11 What is heard11 in music¥
He
points out that Schenker's theories are viable "because they are
pragmatically relevant, that they are relevant furthennore because
28
they stan from empirical examination of music as a "heard phenomenon."
Batstone' s argument is that in much twentieth century music, a
description of the means of a composition (which refers to the
techniques and compositional devices) does not always correspond to
a ~description of the aura 1 phenomena.
As an example he contrasts two
analytical approaches to a Webern work: the first, based on the
relationships of durational proportions; the second based on his
"ad hoc 11 analysis which uses perceptual assumptions such as extremes
of range, contrast, and repetition.
While not disparaging the
existence of complex relationships uncovered by the durational
analysis, since they are not audibly perceptible, he
c~1cludes
more important data exist on the aural phenomenal level.
Referring to the durational analysis, he writes:
27Forte 8 ~· cit., p. 24o
j
28Philip Batstone, "Musical Analysis as Phenomenology."
of Nev1 Music, VII, no. 2 (Spring-Summer 1969), 95.
P. ~_rspes_1j_y;;.;;
that
14
The above analysis is not viable with respect to
perception, and my reasoning involves a recognition of
·the fact that there is no opportunity to perceive the
creation of nonns of the kind \'lhich can allow the ear
to perceive 11 hierarchization 11 or movement or development on an order of complexity anything like that shm'ln
by this analysis. 29
Taking a similar viewpoint to Batstone is Charles Wuorinen, who
is known as a performer of twentieth century music, as well as a
theorist and composer.
Wuorinen writes concerning analysis and
performance:
••• it is extremely difficult to say just what goes
into the kind of analysis necessary for informed
performance. It is possible to observe, however, that
the type of analysis generally presumed to have value
in 11 theoretical" explication is often useless in the
preparation of a performance •••
From the performer's point of viewt such conventional analyses, while of course generally useful to
him outside of rehearsal, nevertheless fail to motivate his manner of playing. since the major part is
most often devoted to translating the information
into another (usually verbal) linguistic medium. The
performer, however, needs not translation, but direction and focusing. 30
Wuorinen goes on to cite examples from two contemporary scores
(Donald Marti no's Trio for viol in, clarinet and piano, and Peter
Westergaard's Variations for Six Players) to make the distinction
between when analysis is, or is not, useful for performance.
In
referring to the example from Martino's scqre he states:
29aatstone, op. cit., P• 104.
30char1es Wuorinen, 11 f.lotes on the Performance of Contemporary
Music," ~!.SE.ectives of New r~usic, III, no. 1 (Fall-~Jinter, 1964), 18.
It is not of crucial necessity to a successful
performance of this work, however, to know precisely which set segments are being presented through
this particular form of articulation - apparently
because given this knowledge, there is very little one
can do in the moment of performance to project it. 31
In contrast, Wuorinen writes, concerning the Westergaard example:
••• it is necessary to know that the timbral differentiations in this excerpt all have structural function.
But here a more detailed knowledge than is needed in
the ~1artino, is needed because it can be projected in
performance. 32
With these arguments as a conducive background, aural percep-
tibility remains foremost among the criteria to be used here in
establishing a series of analytic questions to serve as guidelines
in teaching.
Other criteria would be:
using familiar terminology
and concepts when applicable and expanding then when necessary;
stating possibilities as flexible and open-ended rather than restrictive in order to examine many different kinds of music. T.hese
ques~ions
are organized into discreet areas with the understanding
that in any creative discussion of a particular composition there is
bound to be a great deal of overlapping between areas •.
I.
Sectional structure
le Can the composition
be
divided into sections?
How are the sections articulated {by cadences,
rh.vthm 1 texture, harmony?)
2.
3.
vJhat are the general similarities or,. contrasts
31
wuorinen, ~·· p. 18-19.
32wuorinen, 2E· cit~· p. 20.
between sections?
4. How do the sections compare specifically in terms
of length. and general rhythmic and harmonic activity?
5. How do the larger sections break up into smaller
units or phrase groups?
6. How do these smaller groups interact to form the
larger sections?
II. Motivic structure
1. What are the smallest motivic units or ideas?
2. Is there an intervallic or rhyttrnic consistency
in their makeup?
3. How are the motivic units related or contrasted in
the different sections of the work?
4. How are the smaller units transformed and developed
into larger units or phrases?
III. Pitch material {linear aspect)
1. Is the linear aspect predominantly diatonic or
chromatic, conjunct or disjunct?
2. Is it possible to differentiate between structural
tones and embellishing tones?
3. What role does tessitura and register play in the
linear aspect? ·
4. How does the linear aspect interact with the other
elements in terms of texture?
IV. Pitch material {vertical aspect)
1. Is the overall sound tonal, bitonal, polytonal.
atonal, seri a1'!
·
z.
Are the vertical structures based on a consistent
intervallic content?
3. Is it possible to differentiate between a structural
and embellishing or coloristic use of harmony?
4. What is the rate of hannonic chanqe, and how does it
relate to the other musical aspects?
5. Is it possible to relate the harmonic motion to
the minimal structure? To the sectional structure?
V. Tonal orders
1.
Is there sane kind of tonal order?
On what is the tonal order based (one pitch center,
several pitch centers, an interval, an expanding inter~
vall i c pattern?)
2..
Can the tonal order be described by a system (tonal,
bitonal, polytonal, atonal, modal?)
3.
If not "systematic," as suggested above, is it
possible to describe a progression or development in
the area of tonal order?
4.
VI.
Rhyttrn
1. Is there a feeling of regularity at the level of
the pulse or beat?
Is there a feeling of regularity at the level of
meter?
.2;.
3.
Are there specific rhythmic motives?
4. How does the rhythmic structure of the work relate
to the other aspects, such as sectional structure?
5.
Is there rhythmic counterpoint?
Is it possible to describe various rhythmic levels
from motivic to structural upbeat and downbeat?
6.
7.
VII.
1.
Is there metric modulation?
Texture
Is the texture predominantly homophonic or polyphonic?
~Ihat and where are the contrasts in density, range,
and spacing?
2.~
How do the contrasts in texture relate to the motivic
and sectional structure?
·,·
3.
Howdoes the variety of texture relate to the linear.
vertical or rhythmic aspect?
4.
5.
Is there textural modulation?
This series of questions is designed, not to provide an in depth
analysis, but to serve as a starting point for discussion.
With the
guidance of the teacher, the student can learn to listen and evaluate
what he hears rationally as well as intuitively.
BERG:
SONATA, OP. 1 (1908)
Perhaps no other fonn since the beginning of the Classical
period has so expressed or exposed a composer 1 s unique view of
relating structure and content as the sonata form. The variety of
compositions that share this title is enormous; the concept to be
found in common is often no more than:
statement, departure or
development away from the statement 0 and some kind of return to the
statement.
In using sonata form, the composer has the choice of developing
whatever aspect seems most important to him. The element of contrast
possible with a sectional structure can be expressed by a variety of
means:
highly differentiated motivic and rhythmic materials; contrasts
of harmonic areas; dynamic, tempi and textural contrasts. On the
other hand the sectional structure of the form can be minimized in
favor of an organic unity of texture, motivic and rhythmic materials
'
and harmonic content, as Berg has chosen to do in his Sonata, Opus..l.
AURAL ANALYSIS:
1.
2.
3.
4.
5.
6.
7.
Sectional structure, differentiated by tempi.
No cadences; elision of sections.
No clear tonal center; chromatic use of harmony.
Complex texture; highly contrapuntal.
Use of meter; constant fluctuations$
Use of intervallic motives.
Use of rhythmic motives.
STUDY ANALYSIS:
33Albm Berg, Sonata, Op. I. (Vienna: Universal Editions,
1926) p. 11 ..
19
•• _. '!'.:"".' .•:~
33
The sectional structure is clearly related to the traditional
sonata fo nn:
I.
Expos-ition: m. 1-55.
M. 1-28, first thematic group,
M.29-48, second thematic group.
M.49-55, closing section.
!I.
Development: m. 56-109.
56-70, first section.
70-99, high point.
M.l00-109, restransition.
M.
M.
III.
Recapitulation:_ rn. 110-179.
M. 110-136, varied recapitulation, first thematic gr·oup~
M. 137-166, varied recapitulation, second thematic group.
M. 167-179, closing section.
Although the traditional sonata fonn is followed, including an
indicated repeat of the exposition, the continuous transfonnation and
development of the motivic material, both intervallic and rhythmic,
4
are so interrelated as to supercede or overlap the sections of the
form creating a work of continuous variation.
The sections dissolve
into each other rather than ending, with the only complete hannonic
cadences occuring in the opening and closing phrases.
The opening phrase, which can be considered a microcosm of the
work. -Introduces the intervallic and rhyttmic motives on which the
work is largely based, (ex.l).
The transformation of the first
rhythnic motive 'iJithin the first three measures, from upbeat to down
beat and in combination with its augmentation, is the first indication
of the continuous development, variation, and recombination which is
the compositional procedure of this work, (ex. 2) •.
One can also find sufficient reason to treat the hannonic material,
spe.cifica11y the series of altered chords which descend chromatically,
as the harrnonic motive of the work. Although lacking any particular
rhythmic character, this chromatic series appears throughout the
work, and is frequently developed in a motivic fashion: m. 6-7;
m. 40-41; m. 57-59; m. 147-149, (ex.3). There is a certain
ambiguity about whether this series can be considered solely in its
vertical construction.
m. 1-2 and
m~
When it moves in slow, even progression as in
8-9, it can be heard as supplying an harmonic (although
non-tonal} background; when it moves at the same relative speed as the
other lines, it can be heard as a doubled linear element
~ithin
a
polyphonic texture, as in m. 6-7. Thus, whether its function is
primarily vertical or
linea~
will vary according to the rhythmic
context of the passage.
Measures 3-10 develop the 'B' and •c• motive by fragnentation,
sequential repetition and rhythmic condensation, closing with an
elongation of the 'C' motive in m. 9-10 •
. To illustrate the economy of means which unifies this movement,
some of the various transformations of the •c• motive should be
illustrated.
Functioning 1ike an appoggiatura and occasionally a
suspension, this motive is frequently used to indicate the closing
of a phrase or section: m. 9-10; m. 15-16; m. 27-28; m. 4·5-48;
m. 54-56; inverted in m. 97-99; greatly extended in m. 130-136;
inverted in m. 161-164; m. 169-174; (ex.4).
rhythmic
augmentation"~
~lhen
combined \'lith
it takes the place of a functional cadence -
which is missing.
The same motive 0 inverted, is frequently used to initiate the
· phrases as in m.. 10, m. 13, in the closing section in m. 49, 51, and
in the final closing section, m. 167, 169. Occasionally the 'C' motive
appears as a phrase ending and immediately after as the beginning of a
new phrase as in m. 4-5, m. 77, m. 114. m. 143, and m. 169-171, a
device sometimes referred to as derivative continuation (ex.S).
The second phrase group introduces a new tempo· R,2scher ·al s Tempo I
as well as the triplet motive. 'D', which is a recombination of the
motives of the first phrase, (ex. 6).
The restatement of the first
phrase now includes the triplet motive and is developed in m. 16-28
to the first of a series of dramatic climaxes, which is built on a
. descending whole tone line derived from the descending major thirds of
the 'B 1 motive and first appearing in m. 7-8, (ex.7). The dissolution of,this phrase group, m. 26-29, is based on the inversion of
the 'D' motive.
The second thematic group is introduced by a new tempo,
L~p~~~er al~Eo-~
and a thinning out of the contrapuntal texture.
The motivic structure_ is again related to the opening phrase using a
recombination of the rhythmic and intervallic motives.
The 'C' motive,
previously used to begin and.end phrases is now enclosed within the
'A' motive and the 'B' motive is contained in a sixteenth note figure,
(ex. S). The accelerando which leads to the high point of this section
is built on a sextuplet diminution of the 'D' motive. The descending
1in.e, m. 43-44, although not consistently whole· steps as in m. 23-24.
relate-s to this- earlier
clima~
in
n~gi ster
ar1d dynamics as the high
point of an arch-shaped crescendo and accelerando, approached by a
--
similar sequential repetition.
t
While the closing section 1 m. 49-55 is based on an augmentation of
the sextuplet figure in m. 38, the development section begins with a
~recombination
of the 'A' motive and the descending line taken from
the climax of the arch shape.
The first section of the development
also features an increasing use of the triplet as the beginning of
the rhythmic accelerando which dominates the section. The hemiola in
the climax of this small arch shape acts as a
temporai~y
pulling back
of the motion, set against the augmentation of the descending line in
the bass.
The rhythnic complexity increases in the second part of the
development section which combines the 'D' motive set against the
sixteenth note motive in overlapping entrances.
In. m. 78. the
descending line phrase is added in rising sequential entrances, and
the
. climax of this arch shape in m. 91 for the first time combines the
intervall ic motives with the chromatic descending chords, now with
octave doublings, and extending the full range of an octave,
{e~.
9}.
If one relates the arch qesture which shapes the dramatic climax
of each section to the gesture of the opening phrase, the possibility
of another structure merges, in which the architecture of the movement is as much exposed by the hierarchical levels of enlargement of
this gesture as it is by the traditional functions of the various
sections of sonata form.
The similarity of the descending 1 ines at the high point of the
-arch shapes is too striking to be coincidental;· the derivation from·
the is• motive has already been suggested,
(e~
10).
It is the length of the preparation and dissolution of these
arch shapes v1hich detennines their level in the overall structure of
the work.
Berg fuses this dramatic idea with sonata form by varying
-the length and intensity of each .climax, reserving the most intense
for that point late in the development section \'/here the climax
would occur in a traditional sonata form.
A diagram for the arch shapes for-each section:
Preparation
Hi ghpoi!'~
Di sso1uti on
M. 5-10
m. 5-7
m. 8
m. 9-10
M. 18-28
m. 18-22
m. 23-25
m. 26-28
M. 38-48
m. 38-43
m. 44
m. 69-70
63-70
m. 63-66
m. 67-68
m. 93-99
M. 80-99
m. 80-91
m. 92
m. 93-99
123-136
m. 123-127
m. 128
m. 129-136
M3 150-166
m. 150-158
m. 159
m. 160-166
Lengt_!i
Expo.
e·[M.
Oeve1.
Recap.
By following the climax of the development with a retransition
based on the second thematic group, in the slower tempo, Berg again
undermines the sectional structure of sonata form by depriving the
recapitulation of any dramatic impact. The recapitulation is
introduced with fragments of the 'B' motive. m. 107-109, and when
the complete restatement of the first phrase occurs in m. 110, it
is already in a stage of redevelopment. which is characteristic of
the work.
Although all the elements of the exposition. return in the
recapitulation, there is no 1itera1 repetition. but again,
continuous recombination and variation of the motive materials.
For example, m. 3-5 are extended by sequential repetition in
m. 113-117 and m. 6-8 is now developed into another arch shape based
on the 'B' motive from m. 1Zl-130.with the triplet motive from
m. 11-16 combined with the
•c• motive in the dissolution, m. 131-136.
The Rasch, m. 38-44 is extended by sequentia 1 repetition into the
final climactic arch shape, m.. 144-166 which include.s a hemiola very
similar to the hemiol1a in m. 67-68.
The final closing section is varied by introducing the melodic
material from m. 167-168 in the bass line, m. 169-170 and inverted
in m. 171-175. The approach to the final cadence is similar to
m. 54-56, but in inversion; the right hand reaches the conclusion of
its phrase in m. 170, and reminisces one final time on the •c• motive
fJ
until the left hand has worked through its sequence to the F -b
cadence.
As the pitch material of the movement is so unified as to approach
being monothenatic, the element of rhyttln becomes increasingly
impo~tant
in providing both variety at the level of detail and co-
herence in the large-scale
stt~ucture.
Although the work is clear·ly
in 3/4 meter throughout, the continuous rhyttlnic develojlnent of the
pitch motives and the use of overlapping phrases and the hemiola give
the surface constant variety.
The transformations of the 'C' motive
have already been discussed; further examples of the transformations
of the 'D' motive are more extraordinary, (ex. 11}. The hemiola
appears throughout at points where tempo _changes are taking place: ·
m. 26-27; m.. 54-55; rn. 67-70-; rn. 159-160i and approaching the h·igh
point in the devel OJlilent section at m. 82-83 and 86-87.
ihe larger tempo changes, such as the ·Lanqsamer- al s ·rempo I
in m. 29 1 100, 137 and the Quasi Adaqio in m. 49 and 167 • are used
to clarify the structural sections, just as the accelerando followed
by
ritardand~
or ritenuto are used to delineate the arch shapes in
each section. Another rhythmic device used to set off these
dramatic climaxes is the use of the downbeat and the avoidance of
strong downbeats in the phrases preceding these high points.
Since
so much of the procedure of this work is built on continuations based
on some fonn of upbeat, (the first downbeat in the piece doesn't
appear until the b minor in m. 3!), the downbeats at these climaxes
definitely signify a point of arrival and assume a structural
significance.
In fact, what distinguishes the relative level of
importance of a particular arch shape in the hierarchical structure
is the intensity of the
do\~beat,
with the most intense high point in
the movement consistinq of a series of downbeats, the final one
occuring at that point where the overlapping entrances between the
hand~
join rhythmically, m. 91.
It is impossible to discuss texture separately from the element
of rhythm, since it is the constant rhyttm'ic variation at the motivic
level that is largely responsible for the complex, often contrapuntal texture.
As we have seen from the opening phrase, everything
is motivic, therefore an important element in the texture. There is
very little doubling, except for the octave doublings in the high
·,
points, and aside from the passages containing the chromatic chord
series, the voices move independently, both rhythmically and intervallica11y, creating a '<teritable thicket of sound. As a result, \'!hen
the texture is thinned, usually at a point where a new section is
beginning, such as in m. 29-32, at the Quasi Adaqio, m.·49 and 167,
or at the beginning of the development section in m. 56-60, it
becomes .a structural device, working in coordination with the·
tempo changes.
The focus of this analysis has been on motivic and rhyttmic
developnent.
Discussion of the harmonic content is more difficult
because there is often no more than a semitone connection to relate
one chord to the next. The intervall ic content of the chord structures
has a certain consistency in the use of fourths and tritcnes superposed
with thirds {which relate directly back to the opening motive
materia~;
but frequently the vertical structures are the result of voice leading
in several parts. As mentioned earlier, the sequence of chromatic
CQords from the first measures appears throughout the work as the
principal hannonic motive and is developed rhytllnically and
texturally.
Lvhile the chr0111atic voice leading, the use of
appoggiaturas, suspensions and resolutions constantly suggest an
harmonic direction, there is no root function, no real bass line
beyond a chromatic scale. There are suggestions of tonality in the
b minor cadences at the beginning and the end, and at certain points
such as the V-i progression in e minor in m. 32-32 (balanced by a
hint of b minor in a similar passage in the recapitulation, m. 139),
but these tonal references are temporary. A1though the framework
of sonata form is present, the lack of a unifying harmonic structure
necessitates that other aspects, in this case the intervallic
consistency of the pitch material, and the levels of rhythmic
development, from motivic detail to structural arch shapes, provide
the true coherence of the work.
TEACHING POINTS:
1. Development of intervallic motives.
2. Development of rhythmic motives.
3. Harmonic connection by chromatic voice leading compared
to functional hannony, by root motion.
4. Cadencing by changes of texture. rhythm, and motivic
dissolution •
. 5. Overlapping phrase structure.
6. Use of upbeat continuation; derivative continuation.
7. Structura 1 functions of the downbeat.
8. Comparison of the climactic arch-shapes.
9. Comparison of exposition and recapitulation.
10. Comparison of this sonata forms with other examples.
BARTOK: FREE VARIATIONS AND r.UNOR SECOND,
MAJOR SEVENTHS from
MIKROK0~10S,
(1920-1937)
FREE VARIATIONS (Vol. VI, 141) 34 ·
The first question one might ask in approaching an analysis of
this work is, 11 What is being varied?" Using the tenn, "variation 14
in the generic sense rather than specific, the Harvard Dictionary
of Music offers the following:
In the most general sense, a restatement that
retains some features of the original while others
are discarded, a"ltel..ed, or replaced. One of the most
fundamental techniques of composition, it takes such
forms as ornamentation, transposition, inversion,
retrograde motions augmentation, rhyttmic modification
t1·ansfonnation, etc. 35
·
AURAL ANALYSIS:
..
Using the analytic questions as a guideline for discussion, the
following areas could be examined in a preliminary way:
1.
2.
3.
4.
· 5.
6.
7.
Sectional structure.
Use of ostinato techniques.
Changes of texture.
Variety of rhythmic procedures.
Non-tonal pitch material.
Exchange or inversion of material bet\'1een hands.
Variation techniques.
STUDY ANALYSIS:.
In terms of variation technique, this work presents five varied
34sela Bartok, Free Variations from Mikrokosmos, VI, (London:
Boosey and Hawkes. Ltd. 11 .1940), pp. 2-5..
35nvariation, u Harvard Dictionary of MY2_i£, 2nd ed. (1969}, 89.
29
statanents of a sj1Tlmetrically expanding intervallic structure.
Variation 1. m. 1-12
2. m. 13-23
3. m. 34-43
4. m• 52-64
5. m. 65-72
Coda m. 73-82
Each variation is built on an expansion of a semitone to a tritone
and/or fifth combined with the ostinato principle, (ex. 12).
In the first variation the intervallic expansion occurs in the
left hand dyads» m. 1-7, which move from a-g# down to eb-d, using
the repeated 1 a' as the ostinato, (ex. 13). The right hand, which
is accompanimental at this point, completes the rhythmic ostinato
filling in the eighth note afterbeats4
In m. 7-12 following the
completion of the intervall ic expansion • the right hand continues the
ostinato on '.d', filling in the remaining pitches, ( •a' ascending
to 'd') much the same as it fills in the remaining afterbeats.
In the second variation the functions are reversed: .the
right hand has the intervallic expansion (in inversion at the octave)
while the 1eft hand fills in the afterbeat eighths, (ex. 14).
In
m. 20-23 1 the ostinato on 'a' is replaced in the left hand by an
ostinato surrounding the tritone: M. 20, c-f#; m. 21, g-c#; m. 22,
c#-9.
The temporary use of c-c# as the focus of the ostinato might
be understood; if c-c# is related to the fifth a-e as a similar
symmetrical center represented by d-d# -e, within the octave, (ex. 15}.
In m. 2.3, the left hand expansion parallels a similar expansion in
m. 11-12; both of these passages function as -a long upbeat to a new . .
section~
This short foray_a\'tay from the 'a' ostinato also introduces
-.1.1.
the tonal area to be explored in the fourth variation: the tritones,
gb-c. and c-f#.
The pitch material of the third variation is again based on the
•a• ostinato, but here the original statement and its inversion are
used simultaneously in a canonic displacement of four eighth notes.
·In this variation the tritone/fifth completion is divided between the
hands (ex. 16). The emphasis on the tritone is continued in the long.
upbeat passage (m. 46-51) which precedes the next variation and reaches
the fifth in the final chords in m. 51, (ex.17}.
The fourth variation is contrasted in a variety of ways., The
intervallic expansion is centered around the tritone:
in the r1ght
hand, m. 52-57, gb-c; in the left hand, m. 58-64. c-f#, (ex. 18). The
ostinato accompaniment to each of these statements has been transfanned from a rhythmic ostinato into a melodic figure which is also
.
built on a tritone.
The contrast is also apparent in the change to a
linear, melodic, tv1o-voiced texture and new tempo ( molto piu calmo,
lugubr~·
)•
The final variation returns to the pitch material, tempo,
register of the original statement, with the intervallic expansion
occuring simultanea,usly with its inversion in a stretto-1 ike passage.
The stretto effect is continued in the
coda~
which is built on the
accompanimenta1 afterbeat material first seen in m. 7-8, and
significantly absent in the last variation, (ex.19).
Since the pitch material of these variations is either identiCal
or, in the case of the fourth variationj very similar in construction,
the changes of character throughout the work are, to a large extent,
. the result of subtle variations in the use of rhythm. The first two
variations could be described as polymetric, VJith additive accent
groupings of
t~~·s
length (ex. 20)o
and three•s
cr~ating
rhythmic phrases of increasing
Note that the inversion at m. 13 is preceded by
nineteen J• s of upbeat.
In a similar way the third variation is
preceeded by eighteen J•s of upbeat, additionally strengthened by an
augmentation of the three J' accent _grouping into four in m. 22-23.
contra~t,
In
the section from m. 24-51 is characterized by the regularity
of accent groupings. The unaccented ostinato in m. 25-26 is given a
six ~pulse in m. 28-29 by the left hand punctuation; in m. 30-33
the accent grouping changes to three J and from m. 34-51 a regular
four
meter, coinciding
wi~h
the new variation.
The rhythmic preparation for the fourth variation_ is the most
e~tensive,
which is logical since the fourth variation presents the
greatest contrast in the \'fork, both in terms of texture, tempo and
pitch material.
again.
!1
doe~io
The ostinato is momentarily interrupted and begins
piu lento, accelerando. in a greatly extended
upbeat passage, a rhythmic gesture which has appeared earlier in the
work before new sections.
In spite of the contrasts in the fourth variation, there are
several
rhyth~ic
characteristics which relate this variation with
what has come before.
These are:
accent groupings {ex. 21), the three
the additive character of the
J
initiating each phrase, and
the filling in of the afterbeats with an· accompanying ostinato figure
{melodic here) in the alternate hand.
The final variation returns to the original material against its·
33
inversion, a stretto-1 ike passage which in effect telescopes the
first two variations.
The coda continues the overlapping entrances
between the hands, using the accompanimental material from the
opening statement, in the characteristic afterbeat position until
m. 77 and the appearance of the accented strong beats.
At this point, a telescoping of several parameters takes place.
There is
three
a rhythmic 2-CCelerando. from accent groupings of six
1' ;
p
to
at the same time the intervals decrease by semi tones in
each 1eft hand group.
The effect-is the reverse of interva11 ic
expansion featured throughout the work:
the 'a' tonal
~enter
a spiralling inward toward
and basis for all the ostinati.
Another point to consider in the process of variation is the
systematic use of register.
The unity of each variation is preserved
by the containment within one octave.
The entire work moves not
across the registers of the keyboard but in jt.nnps between the octave
regi stet·s. This procedure, \·lhich is necessary to preserve the
consistency of the ostinato, is established as a premise of the work
in the opening measures of the right hand accompaniment.
Octave
transpositions occur throughout the vmrk, usually after the completion
of the intervallic expansion, and function as a preparation, (just as
the extended upbeats), for the next variation.
Since the pitch
material in each variation develops in such a similar way, the changes
of register assume a structural role, and in the coda, the frequency
of registral sh·ifts, combine with the rhythmic
~to
provide
the motivating fm·ce of the conclusion.
It is ·irrelevant to discuss harmony in this work as there is no
vertical cons·truction for its own sake. The consistency of the
ostinato establishes 'a' as the tonal center, but the pitch
material moves in a synmetrical, _linear fashion in both directions;
what occurs vertically is the result of the contiguity of lines.
TEACHING POINTS:
1. · Principle of intervall ic expansion; its transfonnati on
throughout variations.
2. Relationships and contrasts between textureso
3. Structural use of register and extended upbeat.
4. Variation of ostinato principles.
5. Additive phrase structure (as compared to periodic phrase
structure).
6. Comparison of metric and polymetric use of rhythm.
7. Phrase completion: use of intervallic expansion in place
of cadence to indicate closing of phrase groups.
MINOR SECONDS, MAJOR SEVENTHS (VI, 144)
AURAL ANALYSIS:
1.
Relationships in the pitch material.
z. Overall metric feeling, fluctuation in pulse.
3. Variety of texture and register.
·4. Non•tonal hannonic structure.
5. Phrase structure, sectional structure.
STUDY ANALYSIS:
In contrast to Free Variationi,
~inor
Seconds, Major Sevenths,
(VI, 144), resists an easy division into discreet sections, but
r~ther,
another.
flows from the working out of one
comp~sitional
However, taking an overview of the
w~rk,
idea into
it is possible to
discuss it in terms of five sections, or phrase groupings, each of
which is characterized by its particular use of pitch material,
35
register and texture:
Section
I: m. 1-17; t\~ phrase groups, m. 1-8 (3rd beat),
m. 8 (2nd beat) - 17.
II: m. 18-34; two ·phrase groups, m. 18-22 (3rd beat),
m. 22 (4th beat) - 34.
III: m. 34 (3rd beat) - 43 (1st beat); two phrase
groups, m. 34 (3rd beat) - 38 (3rd beat),
m. 38 (4th beat) - 43 (1st beat) •
.
IV: m. 43 (1st beat) - m. 60; two phrase groups,
m. 43-47, m. 48-60.
V: m. 60-70; one phrase.
The final section might be described more accurately in terms of
a coda, since there is no further development of material.
Instead,
a single phrase returns to the opening register, pitches and
reiterating figuration used earlier in the work.
The relationship of section II to section lV is obvious:
the use
of a similar polyphonic texture and register. The expanding intervals
indicate that m. 43-60 are a continuation and completion of the motion
initiated in m. 18-25.
Aside from the coda, each of these sections, while varied in
other aspects, share a classical balance of two related phrase
groups.
In contrast to this balance is the continuous variation
and· development of the afterbeat, first seen in the major sevenths
in m. 2,4,5 and 6, into: 1. a phrase completion, m. 6-8, m. 25-34;
2. a registral punctuation, m. 9,12,16-17; 3.
m. 21-22, m. 37-38, m. 40-41.
~a
figural punctuation,
In m. 52-60, a combination of all of
the above techniques creates the high point of the work.
In a fashion similar to Free Variations, the pitch material in
.
~
.:
th'is work is derived from a S)ttlllletrical, expanding intervallic
structure:
a minor second, expanding in both directions to inter-
locking tritones which outline a major seventha
The entire work is
related both vertically and horizontally by the juxtaposition or
1 inear connection of minor seconds and major sevenths and the inter-
.
vallic
expansion of minor second to major seventh.
.
Section I presents this symmetrical expansion in the first two
measurest (ex.22).
In me 1-8 the minor seconds remain stationary
ciusters while the major seventh is developed from an afterbeat into
. a melodic cadential figure, m. 6-8, which reappears at the end of
section II and section IV, (ex. 23}.
In m. 8-17, the minor second,
now based on c# -d, expands into a nev.J seventh and the afterbeats,
although registrally expanded, are also built on minor seconds,
{ex. 24}.
Section II replaces the expanding clusters of minor seconds with
a contra punta1 texture.
c-b~
The minor second built on f-f# expands to
while the afterbeats horizontally outline two major sevenths a
tritone apart.
In the second phrase, (m.22, 4th beat - m. 25), the
. expansion from the minor second increases to a fifth, (ex. 25), at
which point, the motion is interrupted as the major seventh afterbeats take on the
pht~ase
completion in an augmentation of the
melodic, cadential sevenths in m. 6-8.
Section III introduces a new register while returning to pitch
material used in the opening section.
However,-this time the
positions within the phrase are the reverse of the opening section.
The major sevenths initiate the motion of the phrase and the minor
second clusters are used, in a horizontal figuration, as the
afterbeat, {ex.26}.
The polyphonic texture. returns in section IV, and in the first
phrase group, m. 43-47, the intervallic expansion from the minor
second extends to a fifth.
In the second phrase the motion is
completed when the expansion reaches the major seventh, {ex.27).
At
this point all previous developments of the afterbeat come into play:
the seventh as figuration, as a registral expansion, and finally as
a large canonic expansion of the cadential melodic sevenths seen at
the end of the opening phrase group.
The final section or coda returns to a figuration of the initicl
pitch material and rhythmic motion of the opening.
The major
seventh, also treated as a figuration, is repeated until the final
cadence which dup 1i cated the pitches of the first cadence.
Given the conscious restriction and consistency of the pitch
·material, the other compositional elements such as the rhythnic
activity, changes of texture, and use of register take on a structural siqnificance in shaping the work.
~Jhile
the variety of textural treatment of the minor second,
major seventh has already been discussed, a closer look at the
rhythmic motion is warranted.
The first contrast to be noted is that
between the metric consistency of the first phrase of each group,
and the rhythmic expansion of the poco strinqendo passages:
14-16, and 48-51.
m~
10-12,
Even more dramatic are m. 25-34, marked · poco a
Q.O£Q. acpgJ~ ~-- Jloepio moviment,£_ which, in effect, creates a
temporary metric modulation.
The section from m. 52-60 suggests,
first of all, a temporary suspension of meter (aided by the rest on
the downbeat in m. 52 and the ha 1 f note augmentation in m. 55-56),
followed by gradual return to the_ regularity of Tempo I.
The
poco a poco accelerando in the coda, considering the familiarity of
the pitch rnaterial 9 is predominantly a phrase of rhythmic and
registral emphasis.
In a similat· vmy one can contrast the restricted range which is
associated w-ith the balanced phrase groups, and the regi stral
expansion vJhi ch always coincides with the development of the afterbeat.
In the end, one can say that these rhythmic and registral
expansions are so interesting, not because they occur, but because
they take on the role,
(ofte~
assigned to the harmonic structure in
earlier periods), of defining the structural divisions and character
of the work.
TEACHING POINTS:
1. Exploration of the varying uses of the pitch material:
connections, expansions, changes of texture, horizontal
and vertical possibilities.
2. Sectional structure, relationships between sections,
3. Register as a structural element.
4. Rhythn as a structural element.
5. Comparison of the balanced phrases and expanding
afterbeat.
These two Bartok
' examples offer an interesting comparison of
compositional techniques with the Berg and
~1essiaen
examples.
In
contrast to the Berg, Bartok uses a variety of textures to delineate
his structures.
In contrast to the
r~essiaen,
there is a systematically
consistent relationship of the pitch material on all levels.
..
MESSiAEN'S NOEL (1944)
To extract an excerpt from a large cycle such as the Messiaen's
Vingt Regards sur L'Enfant J~sus
36
for the purpose of study or
analysis places certain limits on that analysis. The total participation of the excerpt and its function within the cycle cannot
be fully explained. However since the movements in this work are
not continuous, but rather, separated a-nd given individual titles
inferring a specific entity for each movement. it is possible to
make some observations on
r~essiaen • s
treatment of musica 1 materials
based on the excerpt alone.
The procedure used here for discussing Noel is somewhat
different from that used with the Berg and the Bart6k examples,
which referred almost
al~mys
directly to the scores.
While the
"
guideline questions still serve here to point out what and where
the contrasts, variations and repetitions take place in the score,
the student's understanding can be enriched by gaining some
familiarity with some of the sources outside the tradition of
Western music from which Messiaen draws musical inspiration. Thus
references
~Jill
be made to studies written on Messiaen's music as
well as his own work: The Technique of My Musical Language.
36Q1 ivier r;tessiaen, Noel from Vingt Regards sur L• Enfant J~sus,
Paris:
Durand, (1944) 9l)..:"g'jpp. -
39
40
AURAL ANALYSIS:
1. Sectional structure; three part structure with repeating
elements.
2. Ametrical rhythms.
3. Use of embellishing figuration.
4. Harmonic consistency of central section.
5. Contrast in tempo, and character of central section.
6. Non-tonal, highly chromatic harmony.
7. Coloristic use of harmony.
8. Use of ostinato technique.
9. Use of register.
STUDY ANALYSIS:
Before beginning a sectional analysis, several rhythmic concepts
that !·1essiaen uses ·in his search for variety should be brought out.
The first, as stated by Messiaen:
We shall replace the notion of "measure" and 11 beat"
by the feeling of a short value (the sixteenth note
for example) and its free multiplications, which wi11
lead us toward a music more or less "ametrical" ••• 37
The concept of the 11 added value" which Messiaen uses to avoid the
regularity of even meters arises from his study of the Hindu
rhythms or deci-tSlas as set do~TI by the thirteenth century
theorist, Sharngadeva, \<Jhich leads Messiaen to conclude,
11
it is
possible to add to any rhythm whatsoever a small brief value vthich
transfonns its metric balance...
38
The value can be a dot, a note
of small ·value, or a rest; the effect is tha.t of a brief augmentation (ex. 28) which destroys the feeling of exact symmetry or
regularity in the rhythmic flow.
With these ideas in mind it is
not difficult to explain the lack of a meter signature in much of .
37M
'
Tec hn1~
.
, ess1aen,
••• , p. 14 •
381pJ.Q_.
p. 15.
his music or the fact that the majority of rhythmic phrases contain
unequal groupings or an uneven number of beats.
-
In terms of the large sectional
structure NOel can be described
..
as a ABA form, with the A sections containing a smaller aha, thus
.incorporating elements of a rondo:
A ( 1-25)
.
· (a, 1-7; b, 8-ZO; a, 21-25)
B (26-52)
A (53-80}
(a, 53-57; b, 58-64; a,
65-8~
The first seven and last five measures of the A section employs
a rhythmic ostinato in the right hand cho.rds \'Jhich outlines the
•
.
ste_ci-t~,.! .vi.iav~nanda
39
(f f
J J))
to \'lhich Messiaen has added an
eighth value. offsetting the symmetry of the pattern.
In m. 5,
there is another example of an added value in the dot added to the
final chord.
.
The pitch materia 1 of the A section is based on the superposition
of perfect fifths and tritones, or augmented fifths and perfect
fourths, (ex. 29) in bell-like sonorities, {the subtitle of the
movement roughly translated is:
"The bells of Noel say with us the
40
sweet names of Jesus, Mary, Joseph ••• " ). The descending line
(m. 5-6) which is the first melodic idea in the work, closes the
ostinato pattern and continues to function as a phrase ending
through out the A section in m. 8, 13, and expanded in m. 18 and 19
(ex. 30).
In m. 8, 13, 18 and 19 we also see examples of embellishing
groups which are Messiaen's expansion of the CQncept of an
39Robert Sherlaw Johnson, Messiaen, (Berkele,y:
.Press, 1975)· p._198_.
40t•1essiaen. Noel, p. 90.
Univ. of Calif •
embellishing note. The section is shaped by these embellishing
groups and expanding phrase endings in the sense that they augment
the time space between the bell-chords in a similar way to the
'
<
concept of added values, but carried to a higher structural level.
There are two contrasting phrases which interrupt the bellchords and their cadenza figure in this section: m. 10-12 and
m. 15-17. The first, based on the chords in m. 6, outlines the
dec1-tala miga-varna (
J J} ~r. 111.1. JJJJ. J. J II J t J)
41
and the second, using the fifth and fourths in embellishing patterns
as well as in chords, outlines the deci-fala, ~: (
J J.] }J).
42
J 1 J.
J,.fll.
Although the pitch material of these t\'/O phrases
can be related intervallically to the rest of the section, the
juxtaposition of unrelated rhythmic elements brings up an interesting
.
point in Messiaen's treatment of rhythm which is described by David
Drew in his study on Messiaen:
For r~lessiaen on the other hand rhythm is an extensive
phenomenon that belongs more properly to the vtorld
of space and solids, since it consists of selfcontained units whose significance lies not in their
interpenetration, not in their development over a period
of time, but in their juxtaposition one with another,
and in their relative volume and position rather than
in their relative stress. As such, these units, like
their component parts of a mobile, are both reversible
and divisible, but never developable. 43
41Johnson, op. cit., p. 195.
42Ibid p. 198.
43oavid Drew, "Messiaen - A Provisional Study (II) "Score,
13, (Sept. 1955), p. 68.
The return to the rhythmic ostinato (m. 21-25) frames the 'b'
section and finishes with the fallinq melodic figure.
The central portion of the vrork, or B section, falls into
five periods: m. 26-30; m. 30-34; m. 36-40; m. 42-46; and in m. 48-52.
It is contrasted with the A section by tempo, dynamic level, consistency in the use or range and register, use of modal pitch
material and consistency of rhythnic patterns.
Looking at the rhythmic structure separately, a repeating
pattern can be seen in the first four periods which maintains
almost complete consistency in the antecedent phrases while
expanding slightly in the termination of the consequent phrases.
The
fifth period excerpts rhythmic cells from the earlier periods
and augments the consequent portion again by the use of added
va1 ues:
M.
26-30:
M.
30-34:
M.
36-40:
'r' {;, r. r. ~ n
lJ J'
M. 42-46:
1' 1 (t J. r.•'1}. t J 1
Ar
J' 1' J' (
J ffl ••
rl 1i ' ' im{
j~J
'-<!-'
M.
48-52:
The pitch material of the 8 section is based on two of
Messiaen's modes of limited transposition.
These modes are sym-
metrical arrangements of the chromatic scale in interlockinq groups
of half and whole steps which can be transposed a limited number of
times before a duplication of p-itches.
Describing the unusual tonal
characteristics of these modes Messiaen states:
They are at once in the atmosphere of several tonalities, without polytonality, the composer being
free to give predominance to one of the tonalities or
to leave th~ tonal impression unsettled. 44
Melodically, the modes are difficult to distinguish aurally
{except for mode I which is a whole-tone scale) since certain
characteristic intervals, such as the tri.tone which Messiaen uses
frequently, appear in all of them.
However the harmonic constructions
within a particular mode can be recognized by their consistency,
and supply a distinct unity of harmonic color to a passage without
implying either a specific tonality or a progressive function.
The two modes used in Noel are mode II and mode III (ex. 31).
The first two periods, m. 26-34, consist entirely of mode III, first
transposition.
In m. 36-38 the antecedent of the third period, the
lower two staves are mode II, second transposition, (ex. 32), with .
the upper staff in mode III, (fourth transposition)?functioning as
44 Messiaen, Technigu~, p. 58.
a pedal group, which Messiaen conceives as the expansion of the
principle of a pedal note:
"Instead of one sustained note, foreign
to the chords which surround it, we shall have a repeated music •••
foreign to another music situated above or beloVJ it, each of these
45
musics will have its own rhythm, melody, harmonies."
The consequent
half of the third period, m. 33.,.;40 returns to mode II I, first
transposition.
The fourth period, m. 42-46 continues mode III with
an inversion in the melodic line, (ex. 33).
The final period
alternates fragments of the mode II phrase, (m. 47 taken from m. 36;
m. 48, last group, taken from m. 37-38), with fraqments of the mode
III phrases, and finishes v1ith a long expansion in mode III of the
descending passage taken
fr~
the end of the first period.
The use
of an embellishing group appears throughout the 'B' sectione at the
end
of the second, fourth and fifth periods •
...
In tracing the use of the descending melodic group, which first.
appears as the closing of the ostinato in m.5, we find that it
appears with little development, but in different levels of
prominence throughout the musical texture:
A: m. 5-6; first linear statement, functions
as phrase closing.
(same function in m. 25).
m. 8, 13, 18, 19; functions as phrase closing; expanded by
added chromatic notes, rather than rhythmic augmentation.
B:
m. 26; functions as melodic motive of section; given a
modal inflection; both initiates and closes the period.
m. 34; appears in registral change in bass; also in m.
46 and 52.
m. 42; in inversion.
m. 49-50; together with retrograde.
~
m.; 50-52 expansion of phrase clos·ing, by repetition. {ex.34)
~--;t
_ _., --
45 Messiaen, T~chnig~~~ p. 55.
A: m. 57, 58, 61, 64, 69; similar treatment as first A section.
m. 70-74; final appearance; augmented by expanding the
descendinq chord construction from a series of three, to
four, five. six, and finally ten chords, together with
their inversion.
TEACHING POINTS:
1. Messiaen's concept of ametrical rhythm: unmeasured measures,
regularity of the small est note value.
2. Concept of added value.
3. Concept of embellishing group.
4. Concept of pedal group.
5. Introduction to Messiaen's modes of limited transpositions.
6. Hanmony as color (as with pedal group) as compared to
·
functional harmony.)
7. Musical ideas used in juxaposition as compared to se·
quential or organic development.
...
CONCLUSION
In order to facilitate the use of analysis in teaching twentieth
century piano literature, a series of analytic questions has been
proposed to serve as a guide1 ine in student/teacher preparation of
new works.
By grouping these questions into the various dimensions
to be explored, and by keeping them f1 exible' and openended rather
than restrictive, it is possible to apply them to music of widely
differing styles.
The application of these guideline questions to the Berg, Bartokt
and Messiaen examples has shown not only a number of aural perceptions
regarding structure, rhyttrn, and texture that can be discussed at the
outset of the preparation of the work, but also many teaching points
uncovered through the analysis.
By using these teaching points in
comparison with other works studied, the student's a'ttareness of the
functioning of musical elements can be expanded beyond the scope of
the individual composition, and applied with increasing independence
to new \'/Orks.
47
48
BIBLIOGRAPHY
Bartbk, Bela. Free Variations, from ~1ikrokosmos, Vol. VI, London:
Boosey & Hawkes ( 1940), 2"-5.
----Minor Seconds, Major Sevenths, from Mikrokosmos, Vol. VI,
_London: Boosey & Hawkes (1940), 16-19.
Batstone, Philip. "Musical Analysis as Phenomenology," Perspectives.
of New t4usi c, VII I, (Spring-Summer 1969) t 94-110.
Berg, Alban.
Sonata, Op. 1. Vienna:
Universal Editions, 1926, Fall
Berry, Wallace. Structural Functions in Nusicp Englewood Cliffs:
N.J.-: Prentice Hall, Inc., 1976, 447pp.
Carner, t4osco. Alban Berg, The M_an and the vlork.
Duckworth and Co., 1975 XV, 255pp.
Cone, Edward T., 11 Analysis Today,"
(April, 1960), 172-188.
London:
Gerald
The Musical Quarterlx, 46
_
Drew, David, 11Messiaen - A Provisional Study,"
1954). 33-49.
~~
10 (Dec.,
-----"Messiaen, - A Provisional Study, III'' $£ore, 13 (Dec., 1955),
59-73.
-----"~1essiaen,-
A Provisional Study, III," Score,
1i
(Dec., 1955),
41-61.
Elston. Arnold. "Some Rhyttmic Practices in Contemporary Music,"
· The N@i@] Quarter1 v., 42 (July, 1956), 318-329.
Fenyo, Thomas. "The Piano Music of Bela Bartok," PH.D. Dissertation,
UCLA 1956, 293 1.
-----"Form" Harvard D.ict}QDary. ?f Music, 2nd ed. (1969), 326-327.
Forte, Allano Contemporary Tone Structures.
University, 1955. v-xii, 194pp.
New York:
Columbia
--.. --uSchenker• s Conception of Musical Structure, 11 Journa 1 of Music
Lheory, 3 (April, 1959), l-31.
,
Johnson, Robert Sherlaw.
Press, 1975. 221pp.
Messiaen.
Berkeley:
~:
Univ. of California
Jones, Robert Carroll. A G].Q.§~sary of Theoreti ca 1 Terms Used J.n
Eng1J.?ll .•Jl..b2ttl_T\ventieth-Centur_y t!lusic. · Doctoral diss. • Univ. of
l~~a~ j9y~· Ann Arbor, Mich.: University Microfilms, Inc. 1970,
6
Katz, Adele T., 11 Heinrich Schenker's Method of Analysis," The
Musical Quarterly, 21 (July 1936), 311-329.
LaRue, Jan,"OnuS'tyle_Analysis," Journal of Music Theory, VI
(Spring, 1962), 91-106.
.·
.
"Melody," Harvard Dictionary of Music, 2nd ed. (1969), 517-519.
Messiaen, Olivier. The Technique of My Musical Lanquaae. Trans.
by John Satterfield. Paris: ~. leduc,
2 vo,s. 74 pp,
61pp.
rgss.
Messiaen, 01 ivier, Noel from Vingts Regards sur L1 Enfant J?sus,
Paris: Durand (T944), 90-97.
Parry, c. Herbert H., "Me lady," Grove 1 s Dictionary o..f._,~usi c and
Musicians, 5th ed., V (1954), bb6-S69.
.
Redlick, Hans.· Alban Berg. The r~an and His
Abelard-Schuman, 1957: 316pp •.
t~usic.
New York:
Smither, Howard, "The Rhythmic Analysis of 20th Century Music, 11
Journal. of t·1~s.i c Theor1,, VI II {Spring, 1964), 55-88.
Stevens, Halsey, !he Life and t~usic of B~la Bart~k, New York:
~ Oxford Univ. Press, Inc., 1953. 366pp.
Suchoff, Benjamin. Guide to Bart6k • s t~ikrokosmos, Rev. ed. London:
Boosey & Hawkes, t-1usi c Pub1 i shers Ltd., 19i!: ·152pp.
Troup, Halcolm, 11 Regard sur Olivier Messiaen - I," Composer,
(Autt.ann, 1970), 31-32.
----"Regards sur 01 ivier Messiaen - II," Comooser, 38 (\.~linter, 1970),
21-26.
Vinton, John, "Bartok; on His 0\'JI'l Music, 11 Journal of the American
~us.i cz.o 1og i ca 1..society, XIX (Summer, 19'56), 232-243.
Wuorinen, Charles, 11 Notes on the Perfonnance of Contemporary Music,"
Pers,p~ctiv,es o,f New ~·lusic, III (Fall-Winter. 1964), 10-21.
50
APPENDIX: MUSICAL EXAMPLES
B~rg:
Sonata Op. I
Example 2:
Example 3,:
51
-
---
.
-~---
~
....:>-7
~:." ~~·~t,. ~~ ~;;.
..
-~
..;/
*
·------
· - -
~
bn
... - ! . .
.-
1 I
• - =%-I J j;J 19: 1~-=f- ~
""'
~,5~.. ~ ~~~; qe '1~ t 'e, t. r *'·rs~.*"" . -r..·. ~-i:
~-=57= ~ E}. t i: E ~~-:£~~~
........s-
.__,...,
'wl
.. ,.
~
-~
·__
-
·-·
...
-
····-
..
..
.
.
.
.
-
-
.
..
~---·--
52
Example J:
53
ffij
A_
.
Example 9:
. . " bJ .'""J_~b~
b9:
~~~·
Example 10:
~T ~ •
~amp 1e. ,1,1:
~~! ~q:l b~-t:
-
-.
1.1 ..
,.,.,70
·~-
----------------------'·
Bartol<:
Free Variations
Example 12:
Example 14:
'
I
Examo 1e 15 :-
#Fj;: : ).
Example 18:
,...""'_ "i2-!i'1
$: ~~-::;s=:==ia~========:e~.l?==~~:~·
7
;j:i:r:;;~-;:::::!.1
-ri:£::.
'th\149-l-fi
~~~
~v
•
1\
·.
·~J j-#~!i}ti--SlJ
--,
•.
~
<4i
•
J.. =:=6
~==~
Exam.e..l_e 21:
·~--57--?l
·~~
~~-r-J?J
vA
1WVM
,
Bartok:
~·1ajor
Minor Seconds,
Example 22:
Sevenths
•·
Example 23:
--~~
=§~ cw4F~
Example 24:
--
b+
-
1"'1
ff1K
f5'--··
""
iii>:
v
-
.
·- -
,"""
..\
...;;
.
-
I
'f.
'l
If
IF
!'.i'U
A
...-
~.
~
--
--
Ia-
""
T
·loi...a.
ba
57
. Q<..arne) e 2§ :
-.... 1,
I
...
'MI;rO
~~~~~~~~g~~~~:..it~-
~:
""'""-'J-3 -~'1
"""~"-4- '6"-5)
t=;=~~I
Messiaen:
Noel
~ample
.?1:
-4
Example 30:
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