Schoenberg on Problems; or,
Why the Six-Three Chord Is Dissonant
M AT T HE W ARNDT
Arnold Schoenberg’s curious ascription of dissonance to the six-three chord in his Harmonielehre reveals
the positing of a unity of tonal and non-tonal music in their solving of problems of unrest in the tone, the
dissonance, and the musical idea, but neither his fragmentary theoretical writings nor his interpreters have
fleshed this connection out. On the contrary, the notion has arisen of a “tonal problem” as a distinguishing
feature of tonal music. Drawing on blending theory and metaphor theory, I elucidate this unity by explaining
Schoenberg’s dialectical conceptions of the tone, the means of art (made up of consonances and
dissonances), the musical work (as a presentation of the musical idea), and the evolution of perception
and music and by supplementing Schoenberg’s analysis of the first movement of Johannes Brahms’s Piano
Quartet No. 3 in C minor, op. 60. These findings shed new light on Schoenberg’s and indeed on Brahms’s
musical thought.
Introduction
We shall have no rest, as long as we have not solved the
problems that are contained in tones.
— Arnold Schoenberg
Arnold Schoenberg is known as the Great Emancipator of dissonance, the
confounding father of modernist music.1 It may seem surprising, then, to ind him fussing
in his Harmonielehre not only over the straight-jacketed six-four chord, but also over the
utterly domesticated six-three chord. In his opinion, “Both are actually dissonances”:
If the chord formed by the actual voices corresponds to the overtones of the bass,
then the effect is similar to that of any single tone: the total phenomenon is named
for the lowest tone, the bass, and is diagnosed as the fulilment of the necessities of
the bass tone….If, however, the actual tones and the overtones of the bass do not
correspond, then clashes are produced among the elements above the bass. These
clashes may be felt as barriers, as resistance….
If we now compare the sixth chord and the six-four chord with the triad [in root
position], the decisive question in this comparison (since the tones are the same) is
the position of the bass….And now we ind that the overtones of the bass tones…
are contradicted by the make-up of the chord.2 Consequently, neither the sixth
chord nor the six-four chord are as consonant as a triad in root position….
I thank members of the University of Iowa School of Music, the University of Colorado at Boulder College of
Music, and the College Music Society Great Plains Chapter for their comments on presentations of condensed
versions of this article. I thank Christopher Brakel for his assistance with assembling musical examples.
1
The make-up of the six-three chord and six-four chord contradict the overtones of a bass tone in that the sixth
and fourth above the bass are a step away from a perfect ifth and major third, which are equivalent to the third
and ifth partials respectively.
2
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The six-four chord, then, as well as the sixth chord, contains problems. Both are
actually dissonances. But the problem of the six-four chord has more prospects of
being solved, and is consequently more urgent, more conspicuous. The problem
of the sixth chord is no less real, but it is farther from solution. The movement
latent in it is not great enough to compel action and may be ignored. Nevertheless,
its problem was not completely overlooked; the chord was indeed felt to be less
suitable than the root position for deining the key….Since the ear has proved so
subtly discriminating in the problem occasioned by the overtones of chord tones, we
may well hope it will not disappoint us in the further development of music, even
if this development should follow a course of which the aestheticians can already
predict with certainty that it will lead to the end of art.3
If it seems odd to ind Schoenberg treating both of these chords dissonances, then it
is all the more remarkable to ind him contradict himself some twenty pages later by
denying that the six-four chord is an actual dissonance: “The six-four chord and the
actual dissonance have only this in common, that in both lies a conlict that attracts
attention” (HL, 76). Are the six-three chord and the six-four chord dissonant or not? Or
perhaps the question should be, how can they be dissonant, if they are consonant?
Something else sticks out in the irst quotation. Schoenberg describes the dissonant
six-three chord and six-four chord as containing problems and latent movement,
properties that he also ascribes to the tone and to the musical idea in Harmonielehre and
in later writings. Regarding the tone, he claims that it “is capable of continuation, i.e.
that movement is latent in it. That problems are concealed in it, problems that clash with
one another, that the tone lives and seeks to propagate itself” (HL, 313; see also HL, 25).
Regarding the musical idea, he refers to “the movement latent in an idea, through which
alone an idea acquires life” (HL, 289). More speciically, he notes:
The continuation of the musical idea...can only happen thus: that the unrest—
problem—contained in the Grundgestalt or in the motive (and formulated by the
“theme,” or not, if none has been stated) is shown in all its consequences. These
consequences are presented through the destinies of the motive or the Grundgestalt.
How the Grundgestalt changes under the inluence of the forces struggling within
it, in this movement to which the unrest leads, how the forces again attain a state of
rest, this is the realization of the idea, this is its presentation.4
3
Schoenberg [1911] 1978, 57–58; cited hereafter in the text as HL. German page number references are to the
irst edition except where otherwise noted. The other abbreviated sources are: Schoenberg’s Structural Functions
of Harmony ([1954] 1969), cited as SF; Style and Idea (1975), cited as SI; and The Musical Idea and the Logic,
Technique, and Art of Its Presentation (1995), cited as MI. Throughout the essay, a double citation separated by
a slash refers to the original German and the published translation for the purpose of comparison. A single citation of a translated work refers to the published translation. All translations are mine except where the German
is not cited or where noted.
“Die Weiterführung des musikalischen Gedankens kann nur...so erfolgen, dass das in der Grundgestalt, resp. im
Motiv enthaltene Unruhe - Problem (das durch das ,Thema‘ formuliert wurde, oder nicht; wenn ein solches nicht
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Matthew Arndt — Schoenberg on Problems
For Schoenberg, these three cases of problems and latent movement—in the tone,
the dissonance, and the musical idea—are linked because the problem or unrest consists in
an unclear relation of tones to ground tones, and the latent movement aims to clarify this
relation. These cases are distinguished according to whether “ground tone” (Grundton)
means fundamental, root, or tonic. Unclear relations of overtones to the ground tone
(fundamental) in the tone are problems that produce unrest in artists and lead them to
seek clariication and solve the problems through imitation of the tone:
Until a short time before [musicians] had been on the right track, as, following the
dictates of the material, they imitated the overtones. But then they tempered the
system, and the system tempered the burning urgency to search....We ought not to
forget that we still must account for the tones actually sounding, again and again,
and shall have no rest from them nor from ourselves—especially from ourselves, for
we are the searchers, the restless, who will not tire before we have found out—we
shall have no rest, as long as we have not solved the problems that are contained in
tones. (HL, 314)
“Dissonances” are unclear relations of tones to ground tones (roots of intervals or
chords) that produce unrest and demand resolution, and they are also “more remote
overtones” (HL, 46):
I will deine consonances as the closer, simpler relations to the ground tone,
dissonances as those that are more remote, more complicated. The consonances are
accordingly the irst overtones, and they are the more nearly perfect the closer they
are to the ground tone. That means, the closer they lie to the ground tone, the more
easily we can grasp their similarity to it, the more easily the ear can it them into the
tone as a whole and assimilate them, and the more easily we can determine that the
sound of these overtones together with the ground tone is “restful” and euphonious,
needing no resolution. The same should also hold for the dissonances as well.5
And in a particular piece of music, a problem of unclear relations of tones to ground
tones (tonics) produces unrest or imbalance, and the clariication of these relations or the
restoration of balance is the presentation of the musical idea:
Every tone which is added to a beginning tone makes the meaning of that tone
doubtful. If, for instance, G follows after C, the ear may not be sure whether this
expresses C major or G major, or even F major or E minor; and the addition of other
tones may or may not clarify this problem. In this manner there is produced a state
aufgestellt wurde) in allen seinen Konsequenzen gezeigt wird. Diese Konsequenzen sind dargestellt durch die
Schicksale des Motivs oder der Grundgestalt. Wie sich die Grundgestalt verändert unter dem Einluss der in ihr
kämpfenden Kräfte, in dieser Bewegung in die die Unruhe übergeht, auf welche Weise sie dann wieder zur Ruhe
gelangen, das ist die Durchführung des Gedankens, das ist seine Darstellung” (MI, 226/227).
5
HL, 19/21; translation of “Grundton” changed to “ground tone” and “Gesamtklang” to “tone as a whole.”
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of unrest, of imbalance which grows throughout most of the piece, and is enforced
further by similar functions of the rhythm. The method by which balance is restored
seems to me the real idea of the composition.6
Relations of tones to the ground tone (the tonic) can be more speciically relations
between tones, chords, or keys. Here again, the determining factor is whether the related
tones, as ground tones themselves, are fundamentals, roots, or tonics.
So the tone, the dissonance, and the musical idea are connected in that they contain
unclear relations of tones to ground tones (fundamentals, roots, and tonics), problems
that lead to movement in search of clariication. (I always translate “Grundton” as
“ground tone” to highlight the connections between its meanings.) This complex of
notions has far-reaching signiicance for Schoenberg’s musical thought, for in none of the
quotations cited above does Schoenberg limit his claims to music with tonality—that is,
music that employs “the art of combining tones in such successions and such a manner
of simultaneity that the relation of all events to a ground tone becomes perceptible.”7 On
the contrary, as the opening quotation from Harmonielehre about six-three chords and
six-four chords already makes clear, he connects the notions of problems and movement
to the evolution of music, which—as we have often heard it said—led to “the dissolution
of tonality” (HL, 196). What we have here, then, are the lineaments of a unity of “tonal
and...non-tonal music” in their solving of problems of unrest.8 But Schoenberg never
explains in detail how the musical idea in a piece of non-tonal music might involve a
problem along the lines described above. In a fragment entitled “Zu: Darstellung des
Gedankens” (one of three with this title), he even seems to say that in twelve-tone music,
relations of tones to ground tones are not a problem:
The question of tonality can only be decided in accordance with the laws of the
presentation of the idea.
Compositions that are in every sense made tonally proceed so as to bring every
appearing tone into direct or indirect relation to the ground tone, and their technique
aims to bring this relation to expression in such a way that doubt about how the
tone is related can never come up for long.
6
Arnold Schoenberg, “New Music, Outmoded Music, Style and Idea” (1946), in SI, 123.
“Die Kunst, die Töne in solcher Reigenfolge und solcher Art von Gleichzeitigkeit zu verbinden, daß ihre die
Beziehung aller Vorkommnisse auf einen Grundton wahrnehmbar wird.” Arnold Schoenberg, “Probleme der
Harmonie (Notizen)” (T23.03, January 13, 1927), Z7, in Jacob 2005, 2:788; see also HL, 29; and Arnold
Schoenberg, “Opinion or Insight?” (1926), in SI, 261.
7
“Tonale und...non-tonale Musik.” Arnold Schoenberg, “Aphorismen und Sprüche” (T50.08, 1916–36, 1949)
(Arnold Schönberg Center, http://www.schoenberg.at), 8.
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Matthew Arndt — Schoenberg on Problems
This way is not only how the individual tone is handled but also how all tone
progressions, harmonies, and progressions of harmonies are constructed.
Composition with twelve tones related only to one another (incorrectly called
atonal composition) assumes familiarity with these relations, does not see in them
a problem still to be solved and worked out, and in this sense works with entire
complexes, similar to how language works with comprehensive terms whose scope
and signiicance are assumed to be generally familiar.9
The problem that I am interested in, then, is how to understand Schoenberg’s
understanding of the unity of tonal and non-tonal music with regard to problems in the
tone, the dissonance, and the musical idea in light of his laconic and seemingly conlicting
statements on the matter.
Schoenberg’s writings on this topic have given rise to equally disparate
interpretations. Carl Dahlhaus, Charlotte M. Cross, Patricia Carpenter, Pamela C. White,
John R. Covach, Severine Neff, Alexander Goehr, Markus Fahlbusch, Christian Reineke
and others have shed much light on Schoenberg’s concept of the musical idea as a central
element of his musical thought, and Andreas Jacob (2001; and 2005, 1:126–73) has
traced its historical background and its development in Schoenberg’s writings.10 Partly on
the basis of the series of manuscripts known as the Gedanke manuscripts (which includes
“Zu: Darstellung des Gedankens”), Carpenter and Neff have explained Schoenberg’s
understanding of the musical work as a presentation of the musical idea and have called
attention to the problem in the musical idea. But despite recognizing the universality
of the musical idea for Schoenberg, they interpret its problem as being restricted to
tonal music, citing the quotation from “Zu: Darstellung des Gedankens” as evidence.11
Accordingly, they have called it the “tonal problem” and have applied this notion to tonal
“Die Frage der Tonalität ist nur nach den Gesetzen der Darstellung des musikalischen Gedankens zu beurteilen.
“Die im alten Sinn tonal gearbeiteten Kompositionen verfahren so, dass sie jeden auftretenden Ton in ein unmittelbares oder mittelbares Verhältnis zum Grundton bringen und ihre Technik ist bemüht, dieses Verhältnis so
zum Ausdruck zu bringen, dass ein Zweifel darüber, wohin der Ton sich [bezieht] niemals längere Zeit hindurch
aufkommen kann.
“So wird nicht nur der einzelne Ton behandelt, sondern auch alle Tonfolgen sind so konstruiert, alle Zusammenklänge und alle Folgen von Zusammenklängen.
“Die Komposition mit 12 nur aufeinander bezogenen Tönen (unrichtig atonale K. benannt) setzt die
Bekanntschaft dieser Beziehungen voraus, sieht in ihnen nicht ein erst zu lösendes und herauszuarbeitendes
Problem und arbeitet in diesem Sinne mit ganzen Komplexen, ähnlich wie die Sprache mit umfassenden Begriffen
arbeitet, deren Umfang und Bedeutung als allgemein bekannt vorausgesetzt wird.” Arnold Schoenberg, “Zu:
Darstellung des Gedankens” (T35.02, November 12, 1925) (Arnold Schönberg Center, http://www.schoenberg.
at), 1; bracketed alteration of transcription per Jacob 2005, 2:699.
9
See for example Carl Dahlhaus, “Schoenberg’s Poetics of Music” (1976), in Dahlhaus 1987, 73–80; Cross
1980; Carpenter 1984; White 1985; Covach 1992; Patricia Carpenter and Severine Neff, “Commentary,” in MI,
1–86; Covach 1996; Carpenter and Neff 1997; Goehr 1998; Fahlbusch 2006; and Reineke 2007.
10
11
MI, 14; see also Carpenter 1998, 219–20.
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analysis.12 Murray Dineen (1989; 1993; 2004; 2005a; and 2005b) and David Bernstein
(2003) have followed Carpenter and Neff in this regard, although Dineen (2000, 56–59)
has also pointed to evidence that several students of the Second Viennese School may
have understood twelve-tone music in terms of problems. In response to Carpenter and
Neff, Cross (2005; and Schoenberg 2007) has argued that the Gedanke manuscripts
are intimately bound up with Schoenberg’s twelve-tone composition, but she does not
attempt to explain how Schoenberg’s comments here on problems apply to twelve-tone
music. Jack Boss (2000; 2008; and 2009), J. Daniel Jenkins (2007, 35–92), and Bruce
Quaglia (2008) have analyzed Schoenberg’s non-tonal music in terms of the musical idea
and its problem (for Boss, one with a solution, for Quaglia, one without a solution, and
for Jenkins, one that does not necessarily have a solution), but they consider the structural
elements of this music to be fundamentally different than those of tonal music and do
not attempt to connect such a problem to those in the tone or the dissonance. Graham
Phipps (1984) and Hidetoshi Fukuchi (2004) have meanwhile analyzed Schoenberg’s
twelve-tone music in terms of the musical idea and relations of tones to ground tones, but
like many others who have applied tonal analytical techniques to Schoenberg’s non-tonal
music, they do not attempt to connect such a musical idea to a problem and its solution.
Norton Dudeque (2005, 132–72) and Christian Raff (2006) have offered presentations
of Schoenberg’s formal concepts that apply to both tonal and non-tonal music, but they
do not deal much with the musical idea and its problem.
What seem to be contradictions in Schoenberg’s statements on dissonance and
problems can be understood rather as symptoms of dialectical opposition, a thoroughgoing
characteristic of his musical thought that Michael Cherlin (2007, 45) has deined as
“the process wherein progress, change or some desired resultant is obtained through
antagonisms or other types of opposition applied to matter, ideas, values, emotions, etc.”
In this paper, I elucidate the elusive unity of tonal and non-tonal music with respect to
problems in the tone, the dissonance, and the musical idea by explaining Schoenberg’s
dialectical conceptions of the tone as an idea of nature, the means of art (made up of
consonances and dissonances), and the musical work (as a presentation of the musical
idea), which are elements of his dialectical conception of the evolution of perception
and music, all of these conceptions being components of his theory of composition, his
understanding of what it means to compose and how it has been done. In the irst part
of the paper, I lay out these conceptions through a reading of his theoretical writings,
drawing on conceptual blending theory and conceptual metaphor theory as interpretive
See for example Carpenter 1983; Carpenter 1984; Carpenter 1988a; Carpenter 1988b; Carpenter 1991; Neff
1993a; Neff 1994; Carpenter 1997; Carpenter and Neff, “Commentary,” in MI, 62–86; Neff 1999; and Carpenter 2005.
12
Matthew Arndt — Schoenberg on Problems
tools. In the second part, I supplement Schoenberg’s analysis of the irst movement
of Johannes Brahms’s Piano Quartet No. 3 in C minor, op. 60, demonstrating how
Schoenberg’s theory of composition applies to a particular piece, how Brahms’s music
catalyzes his theory, and how it is that the six-three chord is dissonant.
I. Theory
Method
As Carpenter (1998) and Neff (1993b) have argued, Schoenberg is occupied
throughout his career with the formulation of a comprehensive aesthetic-technical theory
of composition that encompasses and uniies harmony, counterpoint, instrumentation,
and form, although he only completes fragments of it. With respect to technique, his
theory is largely pedagogical and drawn empirically from masterworks. But especially
with respect to aesthetics or poetics, his thinking is speculative and auto-pedagogical; his
aim is “to make things clear to himself” about composition (HL, 417).13 Schoenberg irst
articulates his vision of an overarching theory of composition in a letter to Emil Hertzka
in 1911.14 Harmonielehre, published in 1911, represents the irst component; it not only
explains the laws of traditional harmony but also indicates their evolutionary origin
and artistic function. The fragment Zusammenhang, Kontrapunkt, Instrumentation,
Formenlehre, written in 1917, represents a sketch of the remaining components, with
the notion of coherence serving as a unifying element. The concept of the musical idea
plays the same role in the Gedanke manuscripts, which were written ca. 1923–36 and are
particularly concerned with the presentation of the musical idea, or form. Neff (1993b)
has demonstrated how the majority of Schoenberg’s theoretical writings are connected
with this grand project.
Although Schoenberg’s musical thought develops over time, and his writings
represent various degrees of completion, his fragmentary theory of composition also
exhibits a certain fractured unity. In order to explicate components of this theory,
I mainly treat his writings as a uniied corpus, but I also address a signiicant issure
regarding consonance and dissonance. This wide-angle view of Schoenberg’s thought is
not maximally ine-grained, but it reveals a certain wholeness that would not be visible
otherwise. As Schoenberg says, “We must be at some distance from an object if we are
13
According to Cross, this aim is foremost in the Gedanke manuscripts; see Schoenberg 2007, 164.
Arnold Schoenberg, letter to Emil Hertzka, dated July 23, 1911 (Arnold Schönberg Center, http://www.
schoenberg.at); see also Arnold Schoenberg, “The Musical Idea; Its Presentation and Elaboration” (T37.06,
n.d.), in Schoenberg 2007, 187. Cross (1994) has found that Schoenberg already sketches ideas for a theory of
composition at the turn of the century.
14
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to see it as a whole; up close we see just individual features, only distance reveals the
general ones” (HL, 330). To put things another way, I aim here at what Schoenberg
would describe as an artistic rather than a scientiic reading of his writings. He contrasts
science with art in that “science must explore and examine all facts; art is only concerned
with the presentation of characteristic facts.”15
To gain perspective on Schoenberg’s theory of composition, I avail myself, as I have
done elsewhere (Arndt 2011), of the theories of conceptual blending and conceptual
metaphor. Gilles Fauconnier, Mark Turner, and others have argued that conceptualization
involves a basic cognitive operation called blending or integration, which is the dynamic
combination of cognitive units called mental spaces.16 In a blend or integration
network, two or more input spaces, some of whose elements are connected by analogy,
representation, identity, or other relations, project structure into a blended space, where
the new coniguration of elements gives rise to emergent structure, which can in turn
be projected back into the input spaces or used for further blends. For example, Rafael
E. Núñez (2005) has analyzed the concept of an ininity as a blend of the notions of a
completed iterative process and an endless iterative process, as shown in Example 1.
These processes are nearly identical, except that the former has an end and a inal state,
whereas the latter has no end. An ininity combines these qualities, paradoxically having
a inal state but no end. George Lakoff and Núñez (2000, 155–80) originally analyzed
the concept of an ininity as a conceptual metaphor, which they understood as a mapping
of structure from a more concrete cognitive domain to a more abstract domain—in this
case, a mapping from the domain of completed iterative processes to that of endless
ones. Lakoff, Mark Johnson, and others have argued that all concepts are metaphorical
in this sense and ultimately based on image schemas, which are patterns of objects
and forces abstracted from bodily experience, such as part-whole, center-periphery,
or source-path-goal.17 Fauconnier and Turner (2008) acknowledge the importance of
conceptual metaphors and image schemas; however, they have shown that the notion
of cross-domain mapping cannot account for the full variety of emergent structure in
concepts. In the case of the concept of an ininity, it cannot account for the concept
itself as distinct from a modiied concept of an endless iterative process. In the ield of
music, Lawrence M. Zbikowski and others have applied conceptual blending theory to
15
Arnold Schoenberg, “Brahms the Progressive” (1947), in SI, 399; see also MI, 115.
See especially Fauconnier and Turner 2002; and Fauconnier and Turner [1998] 2010. See Turner 2012 for an
extensive bibliography.
16
17
See especially Lakoff and Johnson 1980; Johnson 1987; and Lakoff and Johnson 1999.
Matthew Arndt — Schoenberg on Problems
Completed Iterative Processes
(Perfective aspect)
Finite Processes
Endless Iterative Processes
(Imperfective aspect)
Potential Infinity
The beginning state
The beginning state
State resulting from the
initial stage of the process
State resulting from the
initial stage of the process
The process: from a given
intermediate state, produce
the next state
The process: from a given
intermediate state, produce
the next state
The intermediate result after
that iteration of the process
The intermediate result after
that iteration of the process
Process with end and
inal resultant state
Process with NO END
The beginning state
State resulting from the
initial stage of the process
The process: from a given
intermediate state, produce
the next state
The intermediate result after
that iteration of the process
Process with NO END
with inal resultant state
Blended Space
Actual Infinity
Entailment:
The inal resultant state
is unique and follows every
noninal state.
EXAMPLE 1
The basic mapping of infinity (Núñez 2005, 1730, fig. 5)
the analysis of musical meaning.18 Michael Spitzer, Janna K. Saslaw, and others have
analyzed conceptual metaphors and image schemas in historical music theories, including
those of Schoenberg.19
See for example Zbikowski 1999; Cook 2001; Zbikowski 2002; Zbikowski 2002–2003; Sayrs, 2003; Bauer
2004; Johnson 2004; Bhogal 2006; and Zbikowski 2008.
18
See for example Saslaw 1996; Saslaw 1997–1998; Urista 2001, 66–94 and 111–19; Zbikowski 2002, 126–30
and 317–18; Spitzer 2003; Spitzer 2004; and Gur 2008.
19
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The Tone as an Idea of Nature
For Schoenberg, the tone is an idea of nature that is only partially manifest in
the natural world through the artist’s partially conscious perception. This partial
manifestation constitutes a problem that the artist ideally solves by imitating the tone in
the musical work, thereby bringing it to consciousness.
As I have argued elsewhere (Arndt 2011), Schoenberg’s theory of composition, at
least at the time of Harmonielehre, is based in part on his conception of the tone as a living
idea of nature that manifests itself incompletely in the natural world and more fully in the
musical work. In essence, the tone is “a composite, made up of a series of tones sounding
together, the overtones; hence, it forms a chord” (HL, 23).20 (Note that Schoenberg uses
the term “overtones” as a synonym for “partials.”) But in its phenomenon, the tone is just
a tone, more or less. Consequently, the tone has a problem that is the source of all further
problems in music: how to manifest its true nature. In other words, there is a dialectical
opposition to be overcome between the tone in its ideality and in its reality.21
The tone’s manifestation for Schoenberg is mediated by the artist’s perception
of the tone—where manifestation corresponds with conscious analysis and latency
corresponds with unconscious perception—and by his imitation of the tone. The artist,
then, is distinguished not by his individuality but by his receptivity. Schoenberg says that
the artist “hears that which is common to all, and what it is that sets him apart from the
others is perhaps not how he hears it, but that he does in fact hear it” (HL, 413). The
artist perceives the tone only partially consciously: the closer overtones are consciously
analyzed as pitched tones, whereas the more remote overtones are perceived unconsciously
and leave a trace only as tone color. According to Schoenberg: “The world of feeling
somehow takes into account the entire complex, hence the more distant overtones as
well. Even if the analyzing ear does not become conscious of them, they are still heard as
tone color. That is to say, here the musical ear does indeed abandon the attempt at exact
analysis, but it still takes note of the impression. The more remote overtones are recorded
by the subconscious, and when they ascend into the conscious they are analyzed and their
relation to the tone as a whole is determined.”22 Tone color, then, is the primary mode of
20
Schoenberg reafirms the composite nature of the tone in “Problems of Harmony” (1934), in SI, 271; “Attempts of Writing a New Textbook of Harmony” (T38.04, ca. 1937), in Schoenberg 1998, 24; and “Tonality”
(T75.11–12, n.d.), in Jacob 2005, 2:817.
To a certain extent, this dialectic relects a modern hybrid understanding of the tone. According to Fahlbusch
(2007, 110), for Schoenberg “the musical tone is understood not as immediate sensation, nor as mathematical
measurement, but rather in the tradition of modernity, particularly since the eighteenth century, as harmonic tone
[Klang], wherein the mathematical moment is combined with the experiential moment.”
21
22
HL, 18–19/21; translation of “Gesamtklang” changed to “tone as a whole.”
Matthew Arndt — Schoenberg on Problems
appearance of the tone and pitch is simply the portion of tone color that is analyzed or
measured with respect to height. As Schoenberg explains, “The tone becomes perceptible
by virtue of tone color, of which one dimension is pitch. Tone color is, thus, the larger
domain, of which pitch is a region. Pitch is nothing else but tone color measured in one
direction.”23 The unclear overtones present problems to the artist; they demand further
analysis, which takes place in and through imitation of the tone. In Schoenberg’s words,
“Our relation to this prototype [the tone] is that of the analyst, of the seeker; in imitating
it we discover more or fewer of its truths. The creative spirit strives for more, more and
more; those who merely seek enjoyment are satisied with fewer. Between this More
and this Fewer the battles of art are fought” (HL, 319). More speciically, as Alfred
Cramer (2002) has demonstrated, imitation of the tone involves imitation of tone color
with pitched tones; for example, widely spread chords can produce “the image of...more
remote overtones” (HL, 418). While the artist struggles to analyze the tone, the tone is
perpetually revealing new depths of itself to the sensitive artist, new tints of tone color. In
this regard, Schoenberg speaks of “the tendency of the unheard to reveal itself.”24 In these
two ways, the artist’s perception of the tone evolves over time.
Throughout his career, Schoenberg continues to afirm the notion that the tone is
the content and substance of all music, including twelve-tone music, that “all musical
phenomena can be referred to the overtone series.”25 In the manifesto-like opening
of the essay “Problems of Harmony,” Schoenberg states that the tone offers ever-new
musical ideas, whose problems demand ever-new musical techniques (read: twelve-tone
composition):
The cause of music demands, as the history of art-battles shows, that the secret
of the sounding tone be always pursued anew. The development of music is
more dependent than any other art upon the development of its technique. A
truly new idea—at least as musical history reveals—is hardly imaginable without
signiicant changes in musical technique. The material of music offers inexhaustible
possibilities; but every new possibility in turn demands a new kind of treatment,
because it presents new problems or at any rate demands a new solution of the old
one. Every tonal progression, every progression of even two tones, raises a problem
which requires a special solution.26
23
HL, 471/421; translation of “große Gebiet, ein Bezirk davon die Klanghöhe” changed to “larger domain, of
which pitch is a region.”
24
HL, 450/403; translation of “des Unerhörten” changed to “the unheard.”
25
Schoenberg, “Problems of Harmony,” in SI, 271.
26
Ibid., in SI, 269.
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the tone as an idea:
the tone as a phenomenon
at the next stage of evolution:
the tone as a phenomenon:
EXAMPLE 2
The tone
This passage echoes Schoenberg’s statements about needing to account for the tone
again and again and ighting to discover its truths, as well as his remarks about every
progression of two tones presenting a problem.
Schoenberg’s conception of the tone is structured by the image-schematic complexes
shown in Example 2. The tone in its essence (shown at the top left of Example 2) is
underwritten by a combination of a container, a part-whole, a center-periphery, and
a source-path-goal schema, as well as a verticality schema. The ground tone (the
fundamental) is a central part (shown as the point) that produces and becomes the tone
as a peripheral container and whole (shown as the circle).27 Schoenberg refers to the
overtones as peripheral “emanations of the tone” (HL, 20), and he treats this periphery
as a container and whole: “In the tone,...which is indeed composite, the lowest tone
is recognized as the one that begets the whole complex, the one for which the total
phenomenon is named.”28 Procreation is movement along the path (shown as the arrow).
Since the ground tone encompasses its offspring, this procreation of the tone is also the
development or growth of the ground tone. This development is then also movement
along the path, “for life is: movement.”29 This path has a “vertical” orientation (HL, 23),
leading from the restful, close overtones to the unrestful, remote overtones.30 “The distance
27
According to Turner (1987, 27), the whole is often thought of as a container.
28
HL, 65/56–57; translation of “erzeugt” changed to “begets.”
29
HL, 365/326; translation of “Bewegung” changed to “movement.”
Candace Brower (2000) has pointed out how in tonal music in general, the verticality schema correlates
stability with height in the tone, the chord, and the key.
30
Matthew Arndt — Schoenberg on Problems
from the ground tone” is distance along the path.31 Procreation and development involve
contrasting interpretations of the source-path-goal schema. In procreation, the whole is
the trajector (the thing that moves along the path), whereas in development, the part is
the trajector. The tone as a phenomenon (shown at the bottom left of Example 2) adds to
this image-schematic complex a nested-container and a blockage schema. The manifest
or conscious portion of the tone, the portion “within reach of the ear”32 that the ear can
“assimilate” as “euphonious” (HL, 21), is contained by the inner circle, whereas the latent
or unconscious portion is contained by the outer circle. Manifestation, corresponding
with conscious analysis of tone color as pitch, is the actual movement (shown as the
solid arrow), working its way up through the overtone series, and latency, corresponding
with unconscious perception, is the potential movement (shown as the dotted arrow). A
problem in the tone is the blockage (shown as the inner circle), where the tone is unable
to manifest itself further and correspondingly “the ear...abandon[s] the attempt at exact
analysis” (HL, 20). At the next stage of the evolution of perception (shown at the right
of Example 2), the ear will “expand the conception of what is euphonious, suitable for
art,”33 and the phenomenon as a whole will also expand.
The Means of Art
For Schoenberg, imitation of the tone employs “the means of art” (HL, 413) in
accordance with their inherent laws of usage, “the real ones, not the exaggerations of
orthodoxy” (HL, 329). The means of art are made up of consonances and dissonances.
Through repeated exposure, problematic dissonances or unclear overtones can be
emancipated and become consonances, a process that Schoenberg describes in his earlier
writings as perpetual and in his later writings as completed.
As we saw earlier, consonances are the closer, clearer, more restful overtones,
whereas dissonances are the more remote, obscure, unstable overtones. It is important
to note, however, that while all the means of art are overtones, not all the overtones are
necessarily means of art at a given moment in history. The identity between tones and
overtones means that the dialectical opposition within nature of the tone to itself in
its ideality and in its reality reproduces itself within art in the dialectical opposition of
consonances and dissonances: in reality, consonances are “free” as to their appearance,
31
HL, 20/21; translation of “Grundton” changed to “ground tone.”
Schoenberg, “Attempts of Writing a New Textbook of Harmony,” in Schoenberg 1998, 24. Here Schoenberg
actually designates only the ground tone as within reach of the ear, but it is likely that he is simplifying matters
for pedagogical purposes.
32
33
HL, 19/21; translation of “erweitern” changed to “expand.”
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whereas dissonances are “restricted” in that they require resolution (HL, 320), but they
can ideally become familiar through their repeated appearance and so be “emancipated”
(HL, 323). Schoenberg writes, “Dissonances are nothing else but more remote
consonances whose analysis gives the ear more trouble on account of their remoteness;
but once analysis has made them more accessible, they will have the chance of becoming
consonances just like the closer overtones” (HL, 66). Accordingly, there is also a more
abstract dialectical opposition between nature and art: in emancipating dissonances,
art becomes more like nature while nature through art becomes more like its true self.
According to Schoenberg, the distinction of consonance and dissonance “simply depends
on the growing ability of the analyzing ear to familiarize itself with the remote overtones
and therewith to expand the conception of what is euphonious, suitable for art, so that it
embraces the whole phenomenon given by nature.”34
As Stephen Hinton (2010) and I have both pointed out (Arndt 2011, 122–23),
Schoenberg shifts from conceiving of the process of emancipating dissonances as
perpetual to conceiving of it as completed, in keeping with what Hinton describes as
a shift from writing music in which dissonances are expressive to writing twelve-tone
music, in which dissonances are constructive. Although Schoenberg aims at emancipating
all dissonances in the Harmonielehre, he evidently does not think that this has happened:
“Even today, I feel that here, too, there are certain conditions on which my choice of
this or that dissonance depends” (HL, 70). Emancipating dissonances or expanding the
class of consonances involves revealing the laws governing new harmonic means to be
“the same laws that obtained in the older harmony, only correspondingly broader, more
generally conceived” (HL, 70). Such systematization requires observation of the effects of
the new means in musical works over time; it cannot “go ahead of the works, prescribing
a path for them that they will perhaps never take” (HL, 331). Since “there are no limits to
the possibilities of tones sounding together, to harmonic possibilities” (HL, 322), there is
no end to the process of emancipating dissonances. This perpetuity is in keeping with the
inexhaustibility of the tone. To quote Schoenberg, “What is attainable in that which lies
outside us, in the tone, theoretically speaking, has no limits.”35 In his later writings dealing
“Hängt nur von der wachsenden Fähigkeit des analysierenden Ohrs ab, sich auch mit den ferliegenden
Obertönen vertraut zu machen und damit den Begriff des kunstfähigen Wohlklanges so zu erweitern, daß die
gesamte naturgegebene Erscheinung darin Platz hat” (HL, 19/21; translation modiied). Also relevant here is
Schoenberg’s aphorism: “Unnaturalness—that which is contrary to nature, beyond nature—is only disagreeable
when it becomes a habit: but then it is naturalness again.” “Nur wenn die Unnatürlichkeit—das Widernatürliche,
Übernatürliche—zur Gewohnheit wird, ist sie unsympathisch: dann ist sie wieder Natürlichkeit.” Schoenberg
[1909–1910] 2003, 160/65.
34
“Das Erreichbare im außer uns Liegenden, im Ton, hat, theoretisch genommen, keine Grenzen” (HL, 357/319;
translation modiied).
35
Matthew Arndt — Schoenberg on Problems
with twelve-tone music, however, Schoenberg introduces the term “the emancipation of
the dissonance” to refer to a completed process.36 As Robert Falck (1982) has pointed
out, Schoenberg describes this emancipation in conlicting ways, placing increasing
emphasis on his own role and the role of theory (prescribing a path for music) as opposed
to that of composition. At times, Schoenberg (1974, 83) describes the emancipation of
the dissonance as the equality of all dissonances under the law, based on the assumption
that they are equally comprehensible: “The emancipation of dissonances allows for their
completely free use by virtue of the assumption that they no longer today afford the
trained hearer any perceptual dificulties.” Although this description is at odds with his
earlier writings, it is nonetheless a consequence of the identity of tones and overtones:
if pitch is the mode of appearance of clearly perceived overtones, then consonances and
dissonances must be equally comprehensible, because they both have pitch. But at other
times, Schoenberg describes the emancipation of the dissonance as being based on the
assumption that “the comprehensibility of the dissonance can be ensured, given certain
favourable circumstances.”37 This description is more in keeping with his earlier writings.
In either case, “the law of the emancipation of the dissonance” is tied to twelve-tone
music,38 for it is through this law that “the appearance of dissonances is regulated” in
this music.39 The tangled issue of the emancipation of the dissonance is tied up with that
of tonality, so we will revisit the former when we address the latter.
Schoenberg’s conception of the means of art is structured by the image-schematic
complexes shown in Example 3, which are identical to those for the tone as a phenomenon,
for again consonances and dissonances are overtones. The consonant overtones are
contained by the inner circle, whereas the dissonant overtones are contained by the outer
circle. Schoenberg distinguishes consonances and dissonances as “close” and “remote” and
distinguishes amongst consonances as also amongst dissonances as “direct” or “indirect,”
which again means “more or less close” (HL, 320). The full or partial “accommodation
of...overtones” in the system (HL, 319) is the actual or potential movement respectively
(shown with the solid or dotted arrow). The consonances are fully accommodated, but
the dissonances are not; “they are only supericially annexed to the old system” (HL, 330).
According to Schoenberg, “the evolution of music” (HL, 21) has proceeded through the
36
Schoenberg, “Opinion or Insight?” in SI, 258.
37
Ibid., in SI, 261.
38
Arnold Schoenberg, “My Evolution” (1949), in SI, 91.
Arnold Schoenberg, “Composition with Twelve Tones (2)” (ca. 1948), in SI, 247. Twelve-tone composition
itself is not a law or a system but a method; see Arnold Schoenberg, “‘Schoenberg’s Tone Rows’” (1936), in SI,
213, and Arnold Schoenberg, “Composition with Twelve Tones (1)” (1941), in SI, 218.
39
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emancipating dissonances
as a perpetual process:
consonances and dissonances:
EXAMPLE 3
The means of art
overtone series more or less in ascending order, beginning with the unison (the ground
tone) and proceeding to the octave (the second partial), the ifth (the third partial), and
the third (the ifth partial) (see HL, 65–67). The limits of the system (shown with the
inner circle) “impede” this evolution (HL, 25). The system based on the major scale
accommodates the irst six partials, whereas the system based on the chromatic scale
accommodates the irst thirteen.40 The perpetual process of emancipating dissonances
(shown at the right of Example 3), wherein we “receive these sounds into the system
as members with equal rights and privileges” (HL, 322), involves expanding the nested
container so that more overtones are classed as consonances, while the introduction of
new dissonances involves expanding the whole. The completed process of emancipating
dissonances, the assumption that they are just as comprehensible as consonances, simply
involves regarding the potential movement of accommodation as somehow actual.
The Musical Work
For Schoenberg, imitation of the tone in a particular musical work is imitation of
one particular tone, the ground tone (the tonic), which is the musical idea in its material
aspect. Manifestation or presentation of the musical idea involves variation of the motive
or the Grundgestalt, an image of the musical idea, a process that solves a problem of
unclear relations of tones to the ground tone through the self-assertion or the self-denial
of the ground tone.
As I have argued elsewhere (Arndt 2011, 123), the musical idea for Schoenberg,
the idea for a “tone piece,” is a particular tone as an idea, which is the ground tone of
40
See Schoenberg, “Problems of Harmony,” in SI, 271.
Matthew Arndt — Schoenberg on Problems
the piece (the tonic).41 The reader may balk at this claim, because Schoenberg for the
most part stops writing tonal music around 1908, and because Schoenberg (1974, 77)
himself characterizes this development as “the abandonment of a tonal center,” or he
says that his music “renounces a tonal centre.”42 However, when Schoenberg speaks of
renouncing a tonal center, he is referring more speciically to “the negation of a tonal
centre’s domination,”43 not to the absolute absence of a ground tone. So while I agree with
Ethan Haimo (2006, 6) that most of Schoenberg’s post-1908 compositions do not feature
“referential tonal centers,” I would hasten to add that they do feature non-referential
tonal centers. To understand this subtle but vital point, we need to recognize that tonality,
the perceptible relation of all tones to a ground tone, is not opposed to atonality, a
concept that both Schoenberg and Haimo reject, but rather to the imperceptible relation
of all tones to a ground tone.44 More speciically, tonality, which can be “extended”
through the inclusion of more distant tones,45 lies at one end of a spectrum of effects that
leads through “luctuating tonality” to “suspended tonality,” incorrectly called atonality
(HL, 383), which is to say that one can “blur” “the relation to the ground tone,”46 or one
can “leave the question entirely open” of which tone is the ground tone.47 Schoenberg
says that luctuating tonality and suspended tonality “also permit the supposition of
an operative center, but they show how it is not necessary to help this center attain
externally a power that it has, at most, internally.”48 In other words, one can assume that
41
“Tonstück” (HL, 18/20).
42
Schoenberg, “Composition with Twelve Tones (1),” in SI, 217.
43
Ibid., in SI, 244.
44
See HL, 432, quoted below; and Haimo 2006, 1–6.
45
HL, 29; and SF, 76.
46
“Zu verwischen” “die Beziehung auf den Grundton” (HL, 146/128).
47
“Diese Frage ganz offen zu lassen.” HL, 146/128. I follow Carter’s translation of “schwebende Tonalität” and
“aufgehobene Tonalität” as “luctuating tonality” and “suspended tonality” respectively in his translation of
Harmonielehre. In Structural Functions of Harmony (SF, 111), Schoenberg renders “schwebende Tonalität” as
“suspended tonality,” and he does not mention aufgehobene Tonalität. With the exception of Jacob (2000, 13)
and Richard Kurth (2000; and 2001), Schoenberg’s interpreters seem not to have perceived the identity between
aufgehobene Tonalität and what has been called atonality. Roy E. Carter suggests that “what Schoenberg calls
‘roving harmony’ in his later book...conforms to his description here of aufgehobene Tonalität” (HL, 383n1).
But roving harmony features all kinds of chords, whereas aufgehobene Tonalität “will involve almost exclusive
use of explicitly vagrant chords” (HL, 384), that is, inherently ambiguous chords. Bryan R. Simms (2000, 24)
similarly suggests that Schoenberg found aufgehobene Tonalität “especially characteristic of music by Bruckner
and Wolf.” But Simms does not mention that in the same breath, Schoenberg says examples of aufgehobene
Tonalität “are easy to ind in the works of modern composers” (HL, 384)—that is, composers such as himself.
48
“Auch die annahme eines wirkenden Zentrums zulassen, aber zeigen, wie es nicht notwendig ist, diesem
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a piece of music is generated by a ground tone, even if one does not “prove the lineage
of the chords from the progenitor.”49 Schoenberg writes, “The postulate that everything
emanates from the tone can easily forgo demonstration, since one is constantly reminded
of it anyway by every tone.”50
Schoenberg’s spectrum of effects from tonality to suspended tonality maps roughly
onto the evolution of music from the adoption of major and minor keys to the adoption
of the chromatic scale and to the total emancipation of the dissonance and twelve-tone
composition, which, as Richard Kurth (2000, 154) has argued, is “a way of ensuring the
suspension of tonality.”51 The oppositions between the two ends of the spectrum and
between the two ends of the evolution relect a dialectical “contradiction” in the tone’s
urge for manifestation in harmony (HL, 116n).52 On the one hand, “in an earlier stage”
(HL, 116n), the tone seeks to “propagate itself” (HL, 313), to “impose its own overtones”
(HL, 385), “to become and remain the ground tone” (the root).53 But on the other hand,
at a later stage, the tone’s “most urgent yearning” (HL, 50) is to “lose itself in, to become
part of a higher entity” (HL, 116n), “to serve a cause greater than its own” (HL, 49), “to
be overpowered, to be overcome by a ground tone a ifth below.”54 And on a broader
level, the ground tone (the tonic) can assert its “sovereignty over the structures emanating
from it” (HL, 128), producing tonality, or it can see that “everything designated as good
for its subjects serves only its own interests” and sacriice itself (HL, 152), producing
suspended tonality. In the words of Andreas Jacob, Schoenberg derives “the negation of
one deinite ground tone from the essence of the ground tone itself, which here inds its
fulillment in annulment, so to speak.”55 Ironically, then, as the artist works to “fulil the
Zentrum äußerlich zu einer Macht zu verhelfen, die es höchstens innerlich hat” (HL, 440n/394n–395n; translation modiied); see also Arnold Schoenberg, “My Evolution” (1949), in SI, 86. Robert P. Morgan (2010) has likewise argued that luctuating tonality still involves a single main key, even though it can also feature a continual
conlict between two keys.
49
“Ihre Abstammung vom Urahnen...erweisen” (HL, 146/128).
“Diese Voraussetzung: der Ton ist es, von dem das alles ausgeht, kann ja ruhig in der Luft schweben, da man
bei jedem Ton ohnehin vom neuen daran erinnert wird” (HL, 146/128; translation modiied).
50
On the suspension of tonality in twelve-tone music, see Schoenberg, “Composition with Twelve Tones (2),”
in SI, 246.
51
In other words, “the conditions leading to the dissolution of the system are inherent in the conditions upon
which it is established” (HL, 29).
52
53
HL, 133n/116n; translation of “Grundton” changed to “ground tone.”
54
HL, 55/49; translation of “Grundton” changed to “ground tone.”
55
Jacob 2000, 14.
Matthew Arndt — Schoenberg on Problems
purpose...of creating the truest possible imitations of the [natural] material” (HL, 313),
“inference of the external stimulus is almost certain to be inadequate” (HL, 18); that
is to say, the particular tone being imitated becomes unidentiiable, because it thereby
fulills its urge to lose itself in a higher entity, and it becomes “a mere speck in the ininite”
(HL, 225), like one whose love extends across the universe.
Since tonality for Schoenberg is a matter of perceptibility, whether a piece of music is
tonal depends not on the presence of tonic-directed melodic and harmonic progressions,
as we might be inclined to think, but on the evolution of perception: “Tonal is perhaps
nothing else than what is understood today and atonal what will be understood in the
future.”56 Accordingly, Schoenberg also uses the term “tonality” more broadly to denote
“the particular way in which all tones relate to a ground tone,”57 regardless of whether
this relation is perceptible. In this sense, there is just a difference between pieces of music
“in the emphasis or non-emphasis on the tonality,” such that even twelve-tone music is
tonal.58 This point is evident in Schoenberg’s protest against the term “atonal”:
Everything implied by a series of tones (Tonreihe) constitutes tonality, whether it be
brought together by means of direct reference to a single ground tone or by more
complicated connections. That from this single correct deinition no reasonable
opposite corresponding to the word “atonality” can be formed, must be evident.
Where could the negation be introduced? Is it that not all implications of a series of
tones, or not any, should characterize atonality? A piece of music will always have
to be tonal, at least in so far as a relation has to exist from tone to tone by virtue of
which the tones, placed next to or above one another, yield a perceptible continuity.
The tonality may then perhaps be neither perceptible nor provable; these relations
may be obscure and dificult to comprehend, even incomprehensible. Nevertheless,
to call any relation of tones atonal is just as farfetched as it would be to designate a
relation of colors aspectral or acomplementary. There is no such antithesis. Besides,
there has been no investigation at all of the question whether the way these new
sounds go together is not actually the tonality of a twelve-tone series. It is indeed
probably just that, hence would be a phenomenon paralleling the situation that led
to the church modes, of which I say: “The effect of a ground tone was felt, but since
no one knew which tone it was, all of them were tried.” Here we do not even feel it,
but it is therefore probably present.59
56
Schoenberg, “Problems of Harmony,” in SI, 284.
Arnold Schoenberg, “Probleme der Harmonie” (T69.12, n.d.) (Arnold Schönberg Center, http://www.schoenberg.at), trans. as “Problems of Harmony,” in SI, [2v]/270; translation of “Grundton” changed to “ground tone.”
57
Ibid., in SI, 284. At times, Schoenberg uses the term “key” in an equally broad sense to mean everything
produced by the ground tone. In notes for “Problems of Harmony,” Schoenberg contrasts “a key-emphasizing
method of composition” with “a style that leaves the key unemphasized.” “Einer tonartbetondenenden Kompositionsweise” with “eines Stils der die Tonart nicht unbetont läßt.” “Probleme der Harmonie (Notizen),” in Jacob
2005, 2:782. In light of such statements, Simms (2000, 21) probably goes too far when he claims that Schoenberg
“repeatedly emphasized that [his post-1908 music] had no key.”
58
59
HL, 3rd ed., 487n–488n/432; translation of “Grundton” changed to “ground tone.” Carter inserts a bracketed
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Schoenberg’s claim that twelve-tone music is tonal, that all the tones relate to a ground
tone, seems at odds with his characterization of twelve-tone composition as “composition
with 12 tones related only to one another,” which he contrasts with “root-related and
tonally related harmony.”60 However, these descriptions concern the relations that the
music permanently refers to, not the relations that exist. As he puts it, “The method of
composing with twelve tones substitutes for the order produced by permanent reference
to tonal centres an order according to which every unit of a piece, being a derivative of
the tonal relations in a basic set of twelve tones, the ‘Grundgestalt,’ is coherent because
of this permanent reference to the basic set.”61 “The relation of all tones to one another”
in twelve-tone music is not really independent but is rather “assured by the circumstance
of a common origin,” which is the ground tone.62 Or again: “Tones are related through
their common relation to the ground tones that represent what is the same in them.”63
If the ground tone for Schoenberg is the musical idea in its material aspect, then
what are the other aspects? As Cross (1980) has pointed out, Schoenberg distinguishes
three levels of the idea. He also identiies three levels of its presentation:
The idea of a piece of music is
1) in its conception
2) in its presentation
a) purely material
c) psychological
b) metaphysical
a) logical
c) psychological
b) metaphysical (Schoenberg 1994, 5)
Materially or objectively speaking, the idea is the ground tone. Psychologically or
subjectively speaking, the idea is the perception of the tone with its ever-new depths of
tone color, which represents the artist’s unique being in the present historical moment.
According to Schoenberg, the artist must “express something new and [previously]
question mark after “therefore,” thereby indicating that it is unclear to him how the imperceptibility of the
ground tone can indicate its presence. It is clear enough, however, that the mark of a self-effacing ground tone
is a blank.
60
Schoenberg 1974, 73; capitals suppressed.
61
Schoenberg, “My Evolution,” in SI, 91; commas adjusted.
62
Schoenberg, “Problems of Harmony,” in SI, 284.
“Töne sind verwandt durch ihre gemeinsame Beziehung auf die Grundtöne, welche das Gleiche in ihnen representiert” (MI, 146/147).
63
Matthew Arndt — Schoenberg on Problems
unheard that moves him.”64 In this sense, the musical idea is an artistic “vision.”65
Metaphysically speaking, the idea, to be brief, “connects us with the universe, with
nature,” through the medium of “pure feeling” (HL, 401); it connects us with “the spirit
of mankind” (HL, 411). Schoenberg relates these levels as follows: “The material of
music is the tone; what it effects irst, the ear. The sensory perception releases associations
and connects tone, ear, and the world of feeling. On the cooperation of these three factors
depends everything in music that is felt to be art” (HL, 19).66
As a tone perceived at a particular historical moment, the musical idea for
Schoenberg has a certain limiting depth in the overtone series, and to reveal this depth
through imitation of the tone is in a sense the goal of the musical work. This depth
seems to be what Schoenberg has in mind when he writes, “It is indeed not improbable
(perhaps it is even certain) that inherent in every idea and in the way it is elaborated there
is something that indicates boundaries to be reached but not overstepped” (HL, 127).
Imitation of the tone takes place in (at least) the horizontal and vertical dimensions,
forming an image.67 In the abstract, these dimensions are illed out by scales and chords
respectively. As Schoenberg explains, “If the scale is imitation of the tone in the horizontal
direction, in succession, then chords are imitation in the vertical, in simultaneity.”68 Or,
since imitation is procreation, “Chords are the vertical product of the overtones, but the
scale is the horizontal product” (Schoenberg 1974, 83). In the case of a particular musical
idea, these dimensions are illed out by rhythmicized melodic and harmonic progressions
respectively. To quote Schoenberg, “A musical idea..., though consisting of melody,
rhythm, and harmony, is neither the one nor the other alone, but all three together. The
elements of a musical idea are partly incorporated in the horizontal plane as successive
sounds, and partly in the vertical plane as simultaneous sounds.”69 The planes here are
more precisely dimensions of a single plane. For him, “the task in the evolution of music”
is “presenting an idea in all its deepest and richest consequences in such a way that all
the individuality that arises from it becomes visible on a multiform surface: projected on
64
“Neues, Unerhörtes, das ihn bewegt, auszudrücken” (HL, 447/400).
65
Schoenberg, “Composition with Twelve Tones (1),” in SI, 215.
66
See also Schoenberg’s deinition of music given in Stuckenschmidt 1977, 383.
67
On the musical work as an image of the tone, see Arndt 2011, 129–34.
“Ist die Skala die Nachahmung des Tons in der Horizontalen, im Nacheinander, so sind die Akkorde Nachahmung in der Vertikalen, im Miteinander” (HL, 26/26).
68
69 Schoenberg, “Composition with Twelve Tones (1),” in SI, 220.
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a plane, so to speak.”70 The notion of the presentation as a multiform surface relates to
thinking of it in terms of the articulation of a body:
Articulation (Gliederung) is necessary for every idea, the moment it is expressed;
for, although we think an idea at once, as a whole, we cannot say it all at once,
only little by little: we arrange the different components in succession, components
into which we divide up the idea differently from the way we put it together, and
thereby reproduce more or less precisely its content. In music we regard melodic
or harmonic progressions as the components of an idea. That notion is correct,
however, only as it applies to what is visible or audible, to those aspects of music
that can be directly perceived by the senses; it applies only by analogy to that which
makes up the actual content of a musical idea. But we may still assume that the
image of the notes provides a successful symbol of the musical idea, and that the
form and articulation manifested by the notes corresponds to the inner nature of
the idea and its movement, as the ridges and hollows of our bodies are determined
by the position of internal organs—as indeed the external appearance of every wellconstructed organism corresponds to its internal organization, hence the native
external appearance is not to be regarded as accidental.71
Schoenberg describes not only the musical idea together with its presentation, but also the
presentation itself as “a living central and whole body that puts forth a certain number of
members, by means of which it is able to exercise its vital functions.”72 In both cases, the
ground tone is this central and whole body. The ground tone thrives and ideally manifests
its full depth by procreating and developing into a piece of music. But even if the ground
tone manifests its full depth, it almost never perfectly and conclusively manifests the
tone in general, which continues to deepen in the artist’s ear while he is composing.
As Schoenberg explains, “It is dificult, yes, almost impossible to fashion an absolutely
compelling and inal close,” because the “boundaries to be reached but not overstepped”
are “not in [the musical idea] alone, but in ourselves as well..., keeping up with the spirit
of the times” (HL, 127). There is almost always a sliver of tone color unaccounted for
by the music, which means that “the ratio of the artist to his work”73 is almost always
unequal. This circumstance lies behind the following aphorism: “A disheartening fact:
purity is impurity attenuated to the utmost degree. These are indeed all only approximate
“In der Entwicklung der Musik die Aufgabe, einen Gedanken in allen seinen tiefsten und reifsten Konsequenzen so darzustellen, dass alle die Einzelheit, die sich aus ihm ergeben an einer vielgestaltigen Oberläche sichtbar
werden: sozusagen auf eine Ebene projiciert.” Arnold Schoenberg, “Jede blinde Henne” (T03.42, n.d.) (Arnold
Schönberg Center, http://www.schoenberg.at), 3.
70
HL, 3rd ed., 346–47/289; translation of “das Notenbild ein glückliches Symbol für den musikalischen Gedanken abgibt” changed to “the image of the notes provides a successful symbol of the musical idea.”
71
“Einen lebendigen Zentral- und Gesamtkörper..., der eine gewisse Anzahl von Gliedern absezt, vermittelst
welcher er seine Lebensfunktionen auszuüben vermag” (MI, 120/121).
72
73
HL, 366/326; translation of “Verhältnis” changed to “ratio.”
Matthew Arndt — Schoenberg on Problems
values: 0 = x - x or ∞ - ∞ or even x / ∞, and if we take them as only partially real,
then there is always a remainder that compels acknowledgement: as little compromise as
possible is the utmost that we can attain.”74
For Schoenberg, presentation of the musical idea, articulation into members,
involves varied repetition, where one thing following from another signiies procreation
and one thing changing into another represents development: “Repetition in music,
especially when linked with variation, shows that different things can arise from one
thing, through its development, through the musical vicissitudes it undergoes, through
generating new igures.”75 More speciically, presentation of the musical idea involves
varied repetition of a basic motive or a Grundgestalt—a basic shape containing
the piece’s motives—which thereby seems to generate the parts and develop into the
whole.76 As he puts it, “Everything within a closed composition can be accounted for as
originating, derived, and developed from a basic motive or at least from a Grundgestalt”
(MI, 135).77 In this way, the motive or the Grundgestalt represents the musical idea
or the ground tone, which actually generates everything.78 The motive and its products
are thus images of the whole, and their logically ordered appearance ideally serves to
“show the idea from all sides” (MI, 97), translating the material aspect of the idea
into the logical aspect of the presentation.79 In other words, “Musical art...consists of
“Eine entmutigende Tatsache: Reinlichkeit ist bis ans äußerste verdünnte Unreinlichkeit. Das sind ja alles nur
Näherungswerte: 0 = x – x oder ~ - ~ oder sogar x / ~, und nimmt man es nur einigermaßen materiell, so bleibt
immer ein Rest, der zum Bekenntnis zwingt: möglichst wenig Kompromisse ist das Äußerste, was wir erreichen
können.” Schoenberg [1909–1910] 2003, 162/66.
74
75
Arnold Schoenberg, “For a Treatise on Composition” (1931), in SI, 266.
76
For a thorough discussion of Schoenberg’s concept of the Grundgestalt, see Schiano 1992.
In a well known letter to Federico Busoni, tentatively dated August 13, 1909, Schoenberg professes the intention to do away with “motivic work.” “Motivischen Arbeit” (Arnold Schönberg Center, http://www.schoenberg.
at). However, this intention is short-lived, and in any case, Schoenberg’s opposition may have been primarily to
an overly narrow concept of the motive, for as Raff (2006, 64) has pointed out, “alongside the retraction of the
notion of the ‘athematic’/‘amotivic’ and the concomitant rehabilitation of the motive and thus motivic work, at
the same time a broadening of the concept of the motive becomes visible, which brings it to its limits,” namely the
notion of a mere interval as a motive. On Schoenberg’s apparently athematic music, see Haimo 2010.
77
At one point, Schoenberg loats a distinction between the main motive or main theme in “the old symphony,”
which is identical with the musical idea and “functions as the seed of the whole,” and the main motive along with
other motives in “the modern symphony,” which are subordinate to the musical idea and “function as building
blocks,” in a sense paralleling the distinction between the referential ground tone in the old harmony and the
non-referential ground tone in the new harmony. Arnold Schoenberg, [Draft for a lecture] (T73.17, n.d.), in
Schoenberg 1993, 9 and 11. In general, however, Schoenberg denies that the main motive is fully identical with
the musical idea, and so he asserts that the motive is always more of a building block than a seed (MI, 109).
78
On the dialectical relation between the motive and the musical idea, see Carl Dahlhaus, “What Is ‘Developing
Variation’?” (1984), in Dahlhaus 1987, 128–33.
79
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producing large and small images, which cohere by means of this motive, which in their
individual contents likewise cohere with it, and which are assembled so that the logic
of the total image is as apparent as that of its single parts and of their combination”
(MI, 149). In variation, “that form of repetition in which a number of the constituents
are repeated without change, while a number of others are omitted and possibly replaced
by different components” (MI, 155), the repetition allows the ear to become familiar
with certain imitations of the tone, while the change brings further imitations predicated
on the previous ones.80 In this way, variation ideally effects a gradual imitation of the
full depth of the tone. Schoenberg describes two main methods of presenting the musical
idea through variation. On the one hand, polyphonic music employs “unfolding,” where
“a number of tones are brought into such a reciprocal relation in their succession and
simultaneity (i.e., counterpointed in such a way) that all Gestalten appearing in the
course of the piece, being already contained in this Grundgestalt, are reined, proven, or
determined (partially, according to their possibility).”81 On the other hand, homophonic
music employs “development,” where “simultaneously with the conception of an entire
tone piece, such simple but characteristic Grundgestalten are invented as are suitable
for fulilling the form conceived at the beginning in all its parts through interrupted
or uninterrupted stepwise accumulation of Gestalten (often also interrupted through
back-formations).”82 In a sense, this distinction between unfolding (releasing Gestalten)
and development (accumulating Gestalten) parallels the distinction between the tone’s
procreation and its development.
Schoenberg also names contrast as a way of introducing newness, but just as variation is a type of repetition,
so too “contrast represents a type of variation; in art there is only coherent contrast.” “Stellt sich der Gegensatz
als eine Abart der Variation dar; in der Kunst giebt es nur zusammenhangsvollen Gegensatz.” Arnold Schoenberg,
“Der musikalische Gedanke; seine Darstellung und Durchfuehrung” (T37.08, July 6, 1925) (Arnold Schönberg
Center, http://www.schoenberg.at), 6.
80
81
“Abwicklung,” where “eine Anzahl von Tönen in ein solches gegenseitiges Verhältnis des Nach und Miteinander gebracht (kontrapunktiert) werden, dass dadurch alle im Laufe des Stückes erscheinenden Gestalten in
dieser Grundgestalt bereits enthalten, ausgebildet vorhanden oder teilweise ihrer Möglichkeit nach bestimmt
sind.” Ibid., 5.
“Entwicklung,” where “werden gleichzeitig mit der Konzeption eines ganzen Tonstückes solche einfache aber
charakteristische Grundgestalten erfunden, welche geeignet sind, durch unterbrochene oder ununterbrochene
stufenweise Umbildung (oft auch durch Rückbildungen unterbrochen) die anfangs koncipierte Form in allen
ihren Teilen mit Gestalten zu erfüllen.” Ibid., 5. Schoenberg also names “stringing together” as a method of
connecting parts, but it is “the most primitive of the three methods,” because “its premise is a certain unproblematic quality or problem-solved quality, a certain restfulness between the combined parts of the elements.”
“Aneinander-Reihung,” “die primitivste der drei Methoden,” “ihre Voraussetzung ist eine gewisse Problemlosigkeit oder -Gelöstheit, einer gewissen Ruhe zwischen den zusammensetzenden Teilen der Elemente.” Ibid., 4. On
these methods of presentation, see Neff 1999; and Heneghan 2005.
82
Matthew Arndt — Schoenberg on Problems
According to Schoenberg, the motive or the Grundgestalt as an image of the musical
idea contains a problem of “unrest that will give rise to further motion” (MI, 153; see
also MI, 107),83 and a “theme will, so to speak, formulate the problem of unrest present
in the basic Gestalt” (MI, 181). As we learned earlier, this unrest consists in unclear
relations of tones to the ground tone (the tonic), just as the unrest in the tone consists in
unclear relations of overtones to the ground tone (the fundamental). Thus the dialectical
opposition of the tone to itself in its ideality and in its reality, something that is found
both within and between nature and art, works itself out within the musical work in the
dialectical opposition of the ground tone to itself in the guise of other tones. Without
such a “problem” (or without solving it), Schoenberg tells us, “everything that is said
about the motive is inapplicable”;84 that is, there would be no repetition, no variation,
not even any distinction between the motive and the musical idea, because the idea would
be immediately clear. But we need to be clear about what it means for a relation of tones
to be unclear. On the one hand, the very appearance of other tones calls the ground tone
into question, regardless of their particular relation: “Every succession of tones produces
unrest, conlict, problems. One single tone is not problematic because the ear deines it as
a tonic, a point of repose. Every added tone makes this determination questionable.”85 On
the other hand, new relations of tones—which to a certain extent means dissonances—
are unclear by virtue of their unfamiliarity. For example, Schoenberg says that there is “a
great number of more-than-ive-tone chords, the resolving tendencies of which have not
yet been systematically investigated,” and “the relation of which is dificult to account
for.”86 Such new relations are what we ind in the musical work as a presentation of the
musical idea: it is “to present new tone relations for discussion and to work out their
consequences,”87 because the musical idea for Schoenberg always involves new depths of
At one point, Schoenberg distinguishes between tonal and rhythmic unrest (MI, 103), but rhythmic unrest
would again be tonal, because he considers rhythm in music to be a property of tones. See Schoenberg 1994, 11;
and Schoenberg, “Composition with Twelve Tones (1),” in SI, 226.
83
“Problem,” “alles was über das Motiv gesagt wird unanwendbar ist.” Arnold Schoenberg, “Formungselemente” (T51.18, n.d.) (Arnold Schönberg Center, http://www.schoenberg.at).
84
Schoenberg 1967, 102. At one point, Schoenberg (1994, 28/29) suggests that even an individual tone could
be a motive that contains a problem, “because, without further ado, an individual tone immediately poses a
question concerning its harmonic signiicance (is it a third, ifth, ground tone, etc.?)”; translation of “Grundton”
changed to “ground tone.”
85
86
Schoenberg, “Problems of Harmony,” in SI, 281.
87
Ibid., in SI, 269. Here one may note Schoenberg’s pithy dictum: “Art means New Art.” Schoenberg, “New
Music, Outmoded Music,” in SI, 115.
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the tone.88 Taking both of these factors into account, Schoenberg distinguishes between
degrees of unrest: the weaker unrest produced by familiar relations of tones, as found
in self-contained melodies, only requires counterbalancing, whereas the stronger unrest
produced by new relations of tones, as found in themes, irst requires clariication in the
form of variation. To quote him (1967, 102), “A melody re-establishes repose through
balance. A theme solves the problem by carrying out its consequences. The unrest in a
melody need not reach below the surface, while the problem of a theme may penetrate
to the profoundest depths.”
Since the problem in the musical idea for Schoenberg involves new relations of
tones, conversely it does not involve familiar relations. When a piece of music solves a
problem, it is to a certain extent is solved for good, and the unrest is diminished:
A Gestalt will be interesting that presents a new relation of tones and rhythms to
one another.
Here an author is not independent of his time. He cannot leave unobserved what
others before him have presented for discussion, which problems are exhausted.89
As problems have been solved and weakened, “the evolution of music has taken the path
of producing ever new kinds of ‘unrest’” or “stronger unrests.”90 So when Schoenberg
seems to say in “Zu: Darstellung des Gedankens” that twelve-tone music does not ind
relations of tones problematic, he is only referring to familiar relations, whose free use
allows one to deal with the problems of new relations. This much becomes clear in the
remainder of the fragment, translated here for the irst time:
An example:91 at a certain stage of knowledge it could be necessary to write in the
following manner: “People live in houses. These are: (then follows a description of
For example, the “newness” in Mozart’s ‘Dissonance’ Quartet lies in “the cross-related entrance of the irst
violin with A against the Aß that the viola just left.” “Der Neuheit” “des querständischen Einsatzes der ersten
Geige mit ‚a‘ gegenüber dem ‚as‘, das die Viola gerade verläßt.” Arnold Schoenberg, “Zur Frage des modernen
Kompositionsunterrichtes” (T14.26) (Arnold Schönberg Center, http://www.schoenberg.at), Deutsche Tonkünstler-Zeitung 27/21 (1929): 695.
88
“Interessant wird eine Gestalt sein, welche ein neues Verhältnis von Tönen und Rhytmen zu einander darstellt.
“Hier ist ein Autor nicht unabhängig von seiner Zeit. Er kann nicht unbeachtet lassen, was andere vor ihm zur
Diskussion gestellt haben, welche Probleme erschöpft sind.” Arnold Schoenberg, “Kriterien des musikalischen
Kunstwerks (Notizen zu einem Vortrag)” (T41.04, 1927) (Arnold Schönberg Center, http://www.schoenberg.
at), MD4.
89
“Die Entwicklung der Musik, den Weg gegangen ist, immer neue Arten von ,Unruhen‘ herzustellen,” “stärkere
Unruhen” (MI, 106/107).
90
91
Schoenberg paraphrases this analogy in “New Music: My Music” (ca. 1930), in SI, 104.
Matthew Arndt — Schoenberg on Problems
the walls, the roof, the door, the windows and a discussion of its purpose, etc.)...If
several such houses stand together, this is...Between houses are found streets...From
the town to the next community leads the road...etc.” Today there are still authors
who when they speak of the railroad begin if possible with Adam and Eve in paradise,
or at least with Papin and Stephenson. But one can easily perceive that this is only
necessary when one is speaking to readers who do not know this. Where one on the
contrary may assume a certain knowledge, one speaks in conceptual complexes,
which include the phenomenon and everything that hangs together with it, and one
may rest assured that, out of the number of relations contained therein, the reader
will only ixate on those that have to be thought about and that the very intelligent
reader will call upon and think with all truly known relations. Otherwise the best
author cannot proceed, and at best he will have to resign himself to a limitation of
the concept, inasmuch as it destroys the path of his idea if desired associations are
not triggered, but on the other hand the view of the complete connections must be
revealed if he wants to have a concept brought into consideration in its entire scope.
Perhaps he will then sometimes need to make speciic reference to the unfamiliar
relations; in any case, however, he may in general, particularly where it is a question
of familiar notions, work with a concept in its full signiicance, without having to
give an explanation. In precisely this position music inds itself presently: if a tone
C appears, then its tonal (primary) relations are familiar to the understanding of the
listener, and this tone can immediately enter into new relations. Such old relations of
tones are, e.g., the relations of tones sounding together in which the one or the other
tone is a suspension or passing tone: C–D (resolution C–B [sic] or C–C), C–Fƒ (B–G,
etc.), C–Gƒ (C–A, etc.), C–Bß (C–A, etc.), C–B (C–A, etc.), C–Dß (Bß–Dß).
With 3 tones
With 4 tones
New relations already appear with more than 4 tones.
The question is merely whether the musical understanding is in a position to grasp
these relations and so draw consequences from them, as out of those long familiar.
Here the principle established by me becomes signiicant:
1. The chords are not presented for discussion.
2. The use of musical space in (so to speak) 2 dimensions (horizontal and vertical)
aims at accelerating the presentation of the musical idea and is thus a question of
artistic economy. (In the sounding of a tone [e.g., a melodic tone] together with other
tones [e.g., harmonic tones], it aims at immediately answering one the questions
that arise out of the use of this tone, before it has proceeded to the next melodic
tone: it is either a member of a chord appearing in a comprehensible progression
or only a passing phenomenon, a suspension or a passing tone.) The new music
with 12 tones sees the same thing in the vertical direction as in the horizontal;
simultaneity for this music is only an ininitely fast succession; this ininitely fast
(simultaneously sounding) series of tones is to be grasped just as the progression
in the horizontal, and the question can only be whether it is possible to invent a
technique that makes the comprehensibility of the “vertical tone progressions” as
easy as that of the horizontal, for which one has more time.
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Such a technique is given through “composition with 12 tones related to one
another” (or, briely: “CompW12T”).
With this technique the relation of the 12 tones is established once and for all for
an entire movement, indeed for an entire piece, and relations other than those given
through the Grundgestalt could never appear. The course of the piece thus serves to
bring nearer to the understanding everything that cannot be grasped with the irst
hearing through frequent repetition and many-sided presentation. The presentation
of the idea uses exclusively this material, and it is always the task of the composer
to bring everything that he has to say to this “common denominator,” as it were.
Roughly speaking, the following happened in tonal comp.:
The relation of every appearing tone to the ground tone was brought to expression
just as much in the vertical as in the horizontal, so that one can say: in a certain
respect, the same thing stands in the harmony as in the melody, or, expressed
differently: the presentation of the idea proceeded in such a way that certain
problems were worked out just as much in the one dimension as in the other.
The same can be said of “CW12T” (and therewith it is shown that the true laws of
art—correctly understood—are eternal): the relation of the 12 tones to one another
is brought to expression in such a way that the same thing is said in both of the
presently known dimensions of musical space.92
“Ein Beispiel: In einem gewissen Stadium des Wissens konnte es nötig sein, folgendermaßen zu schreiben: ,Die
Menschen wohnen in Häusern. Es sind dies: (folgt Beschreibung der Mauern, des Daches, der Tür, der Fenster
und Erörterung ihres Zweckes und dgl.)...Wenn mehrere solcher Häuser beisammen stehen, ist das...Zwischen
den Häusern beinden sich die Gassen...Vom Dorf zur nächsten Ansiedlung führt die Straße...etc.‘ Es giebt heute
noch Schriftsteller, die wenn sie von der Eisenbahn reden womöglich bei Adam und Eva im Paradies oder doch
wenigstens bei Papin und Stephenson anfangen. Aber man kann leicht einsehen, dass das nur in dem Fall nötig
ist, als man zu Lesern spricht, die das nicht wissen. Wo man hingegen ein gewisses Wissen voraussetzen darf,
spricht man in Begriffs-Komplexen, die die Erscheinung und alles was mit ihr zusammenhängt umfassen und
darf sich darauf verlassen, dass der Leser aus der Menge der darin enthaltenen Beziehungen bloß jene auswählen
werde, an die eben zu denken ist und dass der sehr verständige Leser alle wirklich bewussten Beziehungen heranziehen und mitdenken wird. Anders kann der beste Schriftsteller nicht vorgehen und höchstens wird er sich das
einemal um eine Begrenzung des Begriffes zu bemühen haben, soferne es seinen Gedankengang stört, wenn nicht
gewollte Associationen ausgelöst werden, andrerseits aber die Aussicht auf sämmtliche Zusammenhänge frei
legen müssen, wenn er einen Begriff in seinem ganzen Umfang in Betracht gezogen haben will. Vielleicht wird er
dann manchmal auf die ungeläuigen Beziehungen besonders hinweisen müssen: jedenfalls aber darf er im allgemeinen, insbesondere, wo es sich um landläuige Vorstellungen handelt mit der vollen Bedeutung eines Begriffes
operieren, ohne eine Erklärung geben zu müssen. In eben diesem Zustande beindet sich die Musik gegenwärtig:
Wenn ein Ton c auftritt, so sind seine tonalen (primären) Beziehungen dem Verstande des Hörers geläuig und
dieser Ton kann unmittelbar in neue Beziehungen treten. Solche alte Beziehungen des Tones sind z. B. im Zusammenklang die Verhältnisse in denen der eine oder der andere Ton Vorhalt oder Durchgang ist: c–d (Aulösung c–h
oder c–c), c–is (h–g etc.), c–gis (c–a etc.), c–b (c–a etc.), c–h (c–a etc.), c–des (b–des).
“Bei 3 Tönen
“Bei 4 Tönen
“Neue Verhältnisse entstehen schon bei mehr als 4 Tönen.
“Es kann bloß die Frage sein, ob das Ohr, ob der musikalische Verstand imstande ist, diese Verhältnisse zu
begreifen und aus ihnen so Konsequenzen zu ziehen, wie aus den längst vertrauten.
“Hier tritt das von mir aufgestellte Prinzip in Geltung:
“1. Die Zusammenklänge sind nicht zur Diskussion gestellt.
92
Matthew Arndt — Schoenberg on Problems
Earlier, we established that the relations of tones to one another in twelve-tone music are
still based on their relations to the ground tone. To put this another way, relations of tones
to one another represent relations to the ground tone, similar to how a chord on a circle
represents two radii. In the fragment under discussion, Schoenberg conirms that familiar
relations of tones and new relations are all of a kind by describing them quantitatively:
relations of two to four tones are familiar, whereas relations of more than four tones
are unfamiliar. The main difference, again, is that tonal music, using old relations,
refers to the ground tone, whereas non-tonal music, using new relations, does not. This
lack of reference is related to emancipating dissonances: the parenthetical explanation
or resolution of familiar dissonances is omitted, and with the total emancipation of
dissonance in twelve-tone music, the chords as such are “not presented for discussion,”93
“2. Die Benützung des musikalischen Raumes in (sozusagen) 2 Dimensionen (horizontal und vertikal)
bezweckt die Darstellung des musikalischen Gedankens zu beschleunigen, ist also eine Frage der künstlerischen
Oekonomie. [Im Zusammenklang eines {z. B. Melodie-}Tones mit anderen {z. B. Harmonie-}Tönen bezweckt
eine der Fragen, die aus der Benützung dieses Tones entstehen sofort zu lösen, ehe zum nächsten Melodieton
übergegangen wird: er ist entweder Akkordbestandtheil eines in einer fasslichen Folge auftretenden Akkordes oder nur eine durchgehende Erscheinung, wie Vorhalt oder Durchgang.] Die neue Musik mit 12 Tönen
erblickt in der vertikalen Richtung dasselbe wie in der horizontalen; das Gleichzeitig ist ihr nur ein unendlich
rasches Nacheinander, diese unendlich rasche (gleichzeitig klingende) Aufeinanderfolge von Tönen sind ebenso
aufzufassen, wie die Folgen in der horizontalen und es kann nur die Frage sein, ob es möglich ist eine Technik
zu erinden, die Auffassbarkeit der ,vertikalen Tonfolgen‘ so leicht macht, wie die der horizontalen, zu denen
man eben mehr Zeit hat.Eine solche Technik ist durch die ,Komposition mit 12 aufeinander bezogenen Tönen‘
(kurz: ,Komp. m. 12. T.‘ genannt) gegeben.
“Bei dieser ist das Verhältnis der 12 Töne ein für alle Male für einen ganzen Satz, ja für ein ganzes Stück
festgelegt und es können niemals andere Verhältnisse auftreten, als die durch die Grundgestalt gegebenen. Der
Verlauf des Stückes dient dazu, alles, was beim ersten Hören nicht erfasst werden konnte durch oftmalige Wiederholung und mannigfaltige Darstellung dem Verständnis näher zu bringen. Die Darstellung des Gedankens
benützt ausschließlich dieses Material und es ist stets Aufgabe des Komponisten, alles was er zu sagen hat
gleichsam auf diesen ,gemeinsamen Nenner‘ zu bringen.
“Grob gesagt geschah in der tonalen K. folgendes:
“Die Beziehung jedes auftretenden Tones zum Grundton wurde sowohl in der vertikalen als auch in der
horizontalen zum Ausdruck gebracht, so dass man sagen kann: in gewisser Hinsicht stand in der Harmonie
dasselbe, wie in der Melodie; oder anders ausgedrückt: die Darstellung des Gedankens erfolgte derart, dass
gewisse Probleme sowohl in der einen, als auch in der anderen Dimension verarbeitet wurden.
“Das gleiche lässt sich (und somit zeigt sich, dass die wahren Gesetze der Kunst—richtig erkannt—ewig
sind) von der ,K. m. 12. T.‘ sagen: Das Verhältnis der 12 Töne zueinander wird dadurch zum Ausdruck
gebracht, dass in beiden bis jetzt bewussten Dimensionen des musikalischen Raumes dasselbe gesagt wird.”
Schoenberg, “Zu: Darstellung des Gedankens” ; translation and emphasis mine, except the emphasis on the
word “all.” Used by permission of Belmont Music Publishers and the Arnold Schönberg Center.
Schoenberg is here echoing the essay “Komposition mit 12 Tönen” (1923): “In twelve-tone composition this
law operates: that one must not inquire after the more or less dissonant character of a harmony, because the
harmony as such...is absolutely not presented for discussion as a compositional element....In CW12T it is precisely the mentioned tone row that is presented for discussion.” “In der Komposition mit 12 Tönen bewirkt dieses
Gesetz, dass nach dem mehr oder weniger dissonanten Charakter eines Zusammengklanges nicht gefragt werden
muss, weil der Zusammenklang als solcher...als kompositionelles Element gar nicht zur Diskussion gestellt ist....
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not supposed to resolve, although the composer will “sometimes need to make speciic
reference to the unfamiliar relations” through the resolution of dissonances. This lack of
reference is also related to the concision that is facilitated by twelve-tone composition:
horizontal passing motions and suspensions can also be presented vertically, so here
again but in a different way the lineage of these tones is erased.94 So Schoenberg tells us
that new relations of tones in twelve-tone music are problems that require clariication
through variation, just as the familiar relations once did.95 In interpreting this fragment
as claiming that twelve-tone music does not have problems, Carpenter and Neff have not
yet taken into account the historical nature of the problem, the continuity of familiar and
new relations, and the need for assuming familiar relations versus explaining unfamiliar
ones. Further evidence of problems in twelve-tone music appears in a notebook entry by
Schoenberg that apparently refers to a problematic pair of tone rows as complexes of
unclear overtones desirous of procreation:
The problem of a musical idea consists of the tension in the overtones if 2 or more
tones appear simultaneously and....
A...desire for reproduction work [sic] in a musical idea, once one row of overtones
has met its contrasting companion.96
According to Schoenberg’s dialectical and metaphorical way of thinking—and this
is a crucial point—the lack of reference to the ground tone in non-tonal music transforms
the phenomenal natures of unrest and rest. In a piece of tonal music, rebellious tones
introduce unrest by calling the ground tone into question—in terms of both our
knowledge and its power—and the ground tone restores peace by crushing the rebellion,
although in truth the ground tone is also the instigator, since the rebels take after their
ruler. To quote Schoenberg, “Perhaps...the rebellious ambitions of the subjects spring as
much from the tyrant’s urge to dominate as from their own tendencies. The tyrant’s urge
is not satisied without the ambitions of the subjects. Thus, the departure from the head
Zur Diskussion gestellt ist in der K. m. 12. T. eben die erwähnte Tonreihe.” Arnold Schoenberg, “Komposition
mit 12 Tönen” (T34.10, May 9, 1923) (Arnold Schönberg Center, http://www.schoenberg.at), trans. as “TwelveTone Composition,” in SI, [1v]/207. The same idea again appears in Arnold Schoenberg, “Linear Counterpoint:
Linear Polyphony” (1936), in SI, 296.
This phenomenon of verticalized horizontal motions seems to be related to the added-tone chords that Simms
(2000, 16) and Haimo (2006, 253) have identiied in Schoenberg’s early non-tonal music.
94
For an interesting analysis of Schoenberg’s twelve-tone Variations for Orchestra, op. 31, in terms of a logical
development of relations, see Covach 2000.
95
Arnold Schoenberg, “Notizbuch III” (T67.02, n.d.) (Arnold Schönberg Center, http:/www.schoenberg.at),
[5–6].
96
Matthew Arndt — Schoenberg on Problems
tone is explained as a need of the head tone itself, in which, in whose very overtones, the
same conlict is contained on another plane, so to speak, as a model. Even the apparently
complete departure from the tonality turns out to be a means for making the victory
of the ground tone so much the more dazzling.”97 In a piece of non-tonal music, the
situation is more complex. Although other tones may still call the ground tone into
question, for familiar relations the answer is (in accordance with the metaphor of music
as language as given in “Zu: Darstellung des Gedankens”) assumed to be understood
and left unmentioned. It is paradoxically the imperceptibility of the ground tone that
represents clarity and rest, and the mere hint of the ground tone in new, unclear relations
of tones that represents unrest, an arousal of the ground tone’s lust for power. To solve
the problem, the ground tone must work through its megalomania. (One is tempted
to say, it must go through a twelve-half-step program.) This inding is consistent with
Jenkins’s claim (2007, 60) that deviations from tonally ambiguous interval cycles such as
the chromatic scale, the augmented triad, and the diminished seventh chord are a source
of unrest in Schoenberg’s non-tonal music. It is also consistent with Cherlin’s observation
(1993) that Schoenberg’s twelve-tone music does not just abandon but actively
represses tonality and with Kurth’s suggestion (2001, 246 and 247) that “moments of
apparent tonal function” in this music are “imbalances in the suspension of tonality.” As
Schoenberg notes with respect to twelve-tone music: “Even a slight reminiscence of the
former tonal harmony would be disturbing, because it would create false expectations
of consequences and continuations.”98 However, this inding qualiies Cherlin’s assertion
that “perfection...is abandoned” by Schoenberg’s non-tonal music (2007, 8): suspended
tonality can convey a sense of imperfection, but only insofar as the suspension itself is
perfectly achieved. This inding also allows us to make sense of Schoenberg’s seemingly
inconsistent statements regarding the comprehensibility of dissonances: if one can hold
the ground tone responsible for disturbing the peace, as indeed it has always been, then
one can assume that consonances and dissonances are equally clear—that is, regard them
as equal in the eyes of the law—even though they are not really. So, in short, a piece of
tonal music solves its problem by erasing all doubt about the ground tone, whereas a
piece of non-tonal music solves its problem by erasing all trace of the ground tone as
such.
Two concrete examples of problems in non-tonal music are in order: a non-twelve-
HL, 171/151; translation of “Ausweichung vom Hauptton” changed to “deviation from the head tone,”
“Grundton” to “ground tone,” and “sozusagen in einer anderen Ebene, vorbildlich” to “on another plane, so to
speak, as a model.”
97
98
Schoenberg, “Composition with Twelve Tones (1),” in SI, 219.
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tone example and a twelve-tone example. Schoenberg’s Little Piano Piece, op. 19, no. 6,
begins in a state of equilibrium with a two-measure introductory phrase, composed of
an incomplete B7 chord (A–Fƒ–B) balanced against a G fourth chord (G–C–F).99 In the
Grundgestalt (mm. 3–4), the equilibrium is complemented by Dƒ in m. 3, which together
with the ground tones B and G forms a symmetrical augmented triad. The problem is
the high E that enters in m. 3 as neighbor note against the held Dƒ. E forms a dissonant,
seven-tone chord whose high, wide voicing makes it resemble remote overtones. When
E resolves back to Dƒ in m. 4, it tonicizes B by following the model ^3–^4–^3 in B major,
disturbing the equilibrium. In a varied repetition of the Grundgestalt, mm. 5–6, the
unrest increases in that E reappears as the ground tone of an incomplete E9 chord (E–D–
Fƒ–Gƒ) after the incomplete B7 chord, initiating a descending-ifths progression, while the
G fourth chord similarly progresses by descending ifth to a C fourth chord (C–F–Bß). A
continuation phrase, m. 7, accelerates the harmonic motion by skipping the A implied by
the preceding E9 chord and going directly to a Daddß9 (D–Eß–Fƒ) that takes its root and third
(D and Fƒ) from the seventh and ninth of the E9 chord. A second continuation phrase, m.
8, arrests the rampant root movement by balancing the expected G chord, Gaddƒ4 (Cƒ–G–
B–D), against its T1, Aßaddƒ4 (D–Eß–Gƒ–C). Not only G but all the previous ground tones
reappear: B, C, D, and the problematic E, which again resolves to Dƒ (Eß). Through this
gathering together, E is illuminated together with a new means of reaching a balance.
At the cadence in m. 9, the incomplete B7 chord is balanced not only with the G fourth
chord, but also with a very incomplete Bß7 chord (Aß–Bß), recognizable by its similar
voicing, which follows the model of m. 8 in that B7 is T1 of Bß7. The Bß–Aß igure in m. 9
is developed from the neighbor motive Dƒ–E–Dƒ in mm. 3–4 through inversion, octave
displacement, and reduction, thus clarifying its coherence with the ostinato motive.100
Fukuchi (2004, 81–85, 170, and 186–89) has shown how Schoenberg’s
“Begleitungsmusik zu einer Lichtspielszene” op. 34, features a conlict between Cƒ and
Eß as tonal centers. The Grundgestalt, mm. 1–3, begins with a hexachord composed of a
harmonic dyad Eß–Gß, a melodic motive E–Cƒ, and a suspension motive D–C in mm. 1–2.
The resolution tone C and the dyad Eß–Gß suggest viio of Cƒ, but D also has the potential
to function as the leading tone of Eß. Fukuchi has further shown that in the coda, mm.
200–19, the E–Cƒ and D–C motives combine into a D–E–Cƒ–C motive that uniies the
Schoenberg suggests that fourth chords “refer to degrees according to the degrees by which they are introduced and by which they are followed.” Arnold Schoenberg, “A ‘Theory’ of Fourths” (T37.02, 1939) (Arnold
Schönberg Center, http://www.schoenberg.at), 2. Since the fourth chords here move by descending ifth, I simply
interpret the bass as the root.
99
100
I am indebted to Severine Neff for helping me think through this piece.
Matthew Arndt — Schoenberg on Problems
the problem of unrest:
the solution in a
piece of tonal music:
the solution in a
piece of non-tonal music:
EXAMPLE 4
The musical work as a presentation of the musical idea
row by appearing transposed, inverted, and vertically. He does not mention that the inal
cadence in m. 217 gives the entire irst hexachord as two simultaneous and overlapping
statements of this motive: D–E–Cƒ–C, focused on Cƒ, and E–Gß–Eß–D, focused on Eß. In
this case, the problem is D in mm. 1–2 or the dissonant hexachord made up of Eß–Gß, E–
Cƒ, and D–C, because when D resolves to C, the music tonicizes Cƒ. The solution, worked
out through motivic development, is the inal cadence, which clariies and stabilizes D
and its hexachord—i.e., conirms the hexachord as consonant—and keeps the music
perfectly poised between Cƒ and Eß.
Schoenberg’s conception of the musical work as a presentation of the musical idea
is structured by the set of image-schematic complexes in Example 4, which are very
similar to those in Examples 2 and 3, for again the musical idea is a tone. A piece of
music at the appearance of the problem (shown at the left of Example 4) uses a container,
a part-whole, a center-periphery, a source-path-goal, a nested-container, and a blockage
schema, as well as an attraction schema.101 The piece represents a trek through “musical
space.”102 As Carpenter (1988b, 345) has argued, this space is not only the horizontalvertical plane of the music but also, as is relevant here, the space of relations of tones, “the
domain of the ground tone.”103 But these relations are not, as Carpenter has suggested,
entirely a priori; rather, to reiterate, every musical idea establishes new relations. “The
ground tone, or the ground tonality” (the tonic, or the tonic region), is a central part
and source (shown with the dot) that produces and becomes the peripheral container
and whole (shown with the outer circle).104 Clear relations of tones are contained by
the inner circle, whereas new, unclear relations are contained by the outer circle. This
Saslaw (1997–1998, 22–23) has drawn attention to the irst three of these schemas, but only as separate things
and only with regard to tonal music.
101
102
Schoenberg, “Composition with Twelve Tones (1),” in SI, 220.
103
HL, 169/150; translation of “Grundton” changed to “ground tone.”
104
“Der Grundton, oder die Grundtonalität” (MI, 120–22/121–23).
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EXAMPLE 5
The chart of the regions for C major (SF, 20)
containing of clear relations may be what Schoenberg has in mind by setting off the
closest regions in the chart of the regions, shown for C major in Example 5, which
represents musical space during “the tonal period” (SF, 68).105 As with consonances and
dissonances, Schoenberg distinguishes relations of tones in general as “direct (closely
related)” and “indirect (distantly related),” and he distinguishes the regions as “I. Close
and Direct; II. Indirect but Close; III. Indirect; IV[.] Indirect and Remote; V. Distant”
(SF, 21).106 Returning to Example 4, the problem consists of “remotely related tones”
(shown with the outer circle) that present “an obstacle to intelligibility” (shown with the
inner circle); that is, they appear as dissonances that cannot be traversed freely.107 These
remotely related tones produce “imbalance”108 and unrest: a motion (shown with the
solid arrow) that will give rise to further motion (shown with the outward dotted arrow)
as their “centrifugal tendencies” (SF, 2) overpower “the attraction of the tonal center”
(HL, 150).109 In tonal music, this motion is troubling because it threatens to go too far,
whereas in non-tonal music, this motion is troubling because it does not go far enough.
The original versions of the chart of the regions that Schoenberg apparently used for teaching set off groups
of regions with ovals and/or colors rather than just a rectilinear outline, but in any case the impression of nested
containers remains. Moreover, Neff (2011, 200–1) has suggested that Schoenberg’s use of color also illustrates
the evolution of music in terms of the incorporation of balanced pairs of regions: irst the dominant and subdominant regions, then the relative and parallel regions, and then alternate inlections of scale degrees. The same
nested-container schema may be behind Schoenberg’s earlier description of close and remote keys in terms of a
series of circles (HL, 155).
105
“Unmittelbares (nah-verwandtes)” and “mittelbares (entfernt-verwandtes).” Schoenberg, “Probleme der Harmonie (Notizen),” in Jacob 2005, 2:784.
106
107
Schoenberg, “My Evolution,” in SI, 87; see also SF, 113.
108
Schoenberg, “New Music, Outmoded Music,” in SI, 123.
109
On centrifugal and centripetal tendencies, see Jacob 2005, 1:294–301.
Matthew Arndt — Schoenberg on Problems
At the ideal solution of the problem (shown at the middle of Example 4 for a piece
of music with tonality and the right for a piece without tonality), the complex adds a
removal-of-restraint schema.110 Clariication of the new relations, “penetrating to the
most remote consequences of an idea,” which corresponds with “penetration into what
is given in nature” (HL, 315), is the removal of restraint (shown with the arrow piercing
the inner circle).111 This penetration represents the illing out of the ground tone, and
it brings about the closure of the “form,” “the termination of the unrest of opposing
forces that occurs if these reach a balance with one another.”112 In a piece of tonal music,
reaching a balance entails “counterbalancing the centrifugal powers of some of the tones
by centripetal tendencies,”113 in such a way that there is “a cyclical harmonic motion,
which goes out from the ground tone and returns to it” (shown with the outward and
inward arrows).114 But in a piece of non-tonal music, reaching a balance entails restoring
an equilibrium, in which the music is equally disposed toward the ground tone and
toward the other tones (as shown with the double-headed arrow).115 In these contrasting
situations, the self-assertion or self-denial of the ground tone can be understood as the
music’s concentration at the center or its diffusion respectively.116
Instead of blockage and removal-of-restraint schemas, Saslaw (1997–1998, 23) has suggested that the problem and its solution in a piece of tonal music involve a counterforce schema, a head-on meeting of opposing
forces, which both initiates motion and brings it to a halt. However, as we have seen, opposing forces for Schoenberg pull the music in different directions; they do not meet each other head on.
110
111
Schoenberg, “Brahms the Progressive,” in SI, 439.
“Form,” “das Ende der Unruhe entgegenstrebender Kräfte, welche eintritt wenn diese einander das Gleichgewicht halten.” Arnold Schoenberg, “Form in Music” (T51.17, n.d.), 7, in Jacob 2005, 2:684.
112
113
Schoenberg, “Tonality,” in Jacob 2005, 2:817.
“Einer cyklischen Harmoniebewegung..., die vom Grundton ausgehend zu ihm zurückkehrt.” Arnold Schoenberg, “Entwicklung der Harmonie” (T36.01, n.d.), in Jacob 2005, 2:754. Centrifugal forces also balance one
another, paradigmatically the dominant and subdominant; see HL, 24; HL, 132; and MI, 311.
114
In this regard, Kurth (2001, 247) points out that Schoenberg’s twelve-tone music suspends tonality “through
the abstract counterbalancing of numerous tonal forces.”
115
Incidentally, blockage and removal-of-restraint schemas also structure Schoenberg’s conception of the resolution of dissonances. Here we can recall Schoenberg’s statement about the dissonant six-three chord being felt as
a barrier to the fulillment of the bass tone. In addition, he writes of dissonant melodic spans, “The ear resists dissonances (more distant overtones)...; it perceives them as obstacles and longs for their removal, for their resolution” (HL, 45). And in describing the resolution of a dissonant chord by means of a strong progression, he writes,
“If a barrier is set against the harmonic low through the insertion of the dissonance, somewhat comparable to
a dam in a brook, then this resistance should create an accumulation of energy that takes the obstruction, so to
speak, ‘in full swing.’ An energetic move should be used to get over the barrier” (HL, 49).
116
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The Evolution of Perception and Music
The integration network in Example 6 shows how Schoenberg blends his
conceptions of the tone in nature and the means of art in his conception of the musical
work: the mental spaces are linked primarily by the nearly identical sets of imageschematic complexes we have analyzed. The crucial emergent feature, by virtue of which
the musical work can work out the dialectical oppositions within and between nature
and art, is that the tone’s abstract movement of procreation and development becomes
the concrete movement of tones in musical space and time.
Example 6 also maps out Schoenberg’s dialectical conception of the evolution of
perception and music. At a certain moment in history, the tone as an idea of nature
becomes a musical idea. The tone as a phenomenon and the means of art together feed
into the presentation of the musical idea: the appearance of the problem and its solution.
Penetration of the tone in the musical work contributes to further analysis of the tone as
a phenomenon and to further development of the means of art and their laws, including
the emancipating of dissonances, if they are not already totally emancipated. At the next
moment in history, this cycle repeats, with newly revealed tone color, newly analyzed
overtones, and newly invented musical means. This conception emerges in the following
description of the historical evolution of harmony:
1. The historical evolution is different from the natural evolution it might have been.
According to a natural evolution structures would exist that correspond to the laws
of nature.
2. It is true, nevertheless, that the historical evolution has followed, somehow, the
will of nature, even if by troublesome detours; for our minds (Geist) can produce
nothing that is completely different from nature. And if we assume that nature has
laws, then even this human creation cannot be accidental, but must rather conform
to laws.
3. The historical evolution, after all, tells only in what order and by what route
those harmonies broke into music, but not how they relate to the principal aim of
our activity. Thus, whereas these harmonies may of course have arisen as accidental
harmonic structures, they could be, nevertheless, just as legitimate and basic as the
others, whose fundamental character we have already recognized.
4. Actually, all the other chords of our system came into being in a manner similar to
that in which these harmonies emerged. That is, those too were irst used sparingly,
and with caution, as inconspicuously as possible; but then, as soon as they were
familiar to the ear, they became everyday, self-evident events in every harmonic
composition. They were freed from the context in which they ordinarily appeared
and were used as independent chords, as I have shown with the diminished triad and
the seventh chord. (HL, 315)
Matthew Arndt — Schoenberg on Problems
means of art:
tone in nature:
idea
phenomenon
consonances and
dissonances
musical work:
musical idea
presentation
EXAMPLE 6
The integration network of the tone, the means of art, and the musical work
EXAMPLE 7
The evolution of perception and music
According to Schoenberg, the historical evolution of harmony involves new chords
breaking into music and new laws appearing that govern their usage, and it constitutes
a imperfect version of a counterfactual natural evolution that would have been “if
artists always had the courage to go back to the primary source” (HL, 315). In other
words, this natural evolution would exactly match the artist’s evolving perception of the
tone. New chords, like other musical means, are irst understood only in part and later
understood completely; in Schoenberg’s terms, they become “self-evident.” His use of this
term indicates that the fully known laws relect the consciously perceived portion of the
tone, which is equally self-evident. Schoenberg distinguishes the fully understood musical
means from the totality of means as those of handicraft and art: “Art and handicraft have
as much to do with one another as wine with water. In wine there is of course water, but
he who begins with the water is an adulterator” (HL, 410).
As shown in Example 7, Schoenberg’s conception of the evolution of perception and
music combines the container, part-whole, source-path-goal, verticality, nested-container,
blockage, and removal-of-restraint schemas found in the tone, the means of art, and the
musical work with an additional source-path-goal schema. What emerges is a composite
graph of depth versus time: the depth of the tone as perceived, both consciously and
unconsciously (indicated by the lower jagged line and the diagonal line respectively),
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the depth of the tone as relected in the means of art, both the fully understood and the
partially understood (indicated by the lower and upper jagged lines respectively), and the
depth of the tone as imitated in the musical work (indicated by the upper jagged line).
Here it becomes clear that there is a duality between penetration of the tone in the musical
work relative to what is perceived at a given historical moment (the ratio between the
heights of the upper two lines) and the ever-increasing penetration of the tone in absolute
terms over historical time (the height of the upper jagged line). The former is the measure
of the artist, whereas the latter is the measure of art. There is also a duality between the
profound analysis of the tone by way of its imitation in the musical work (the height of
the upper jagged line)—for “to grasp what happens in a piece of music means nothing
else but to analyse quickly”117—and the more restricted analysis of the tone in perception
(the height of the lower jagged line). According to Schoenberg, the series of musical
works that yield a “positive gain” (HL, 30–31) in “the degree of penetration into what
is naturally given” (HL, 414) through imitation of the tone traces out “the path of the
means of art” (shown with the jagged arrow).118 Schoenberg tells us that “the evolution
of music has followed this path: it has included in the area of the means of art ever more
of the harmonic possibilities lying in the tone.”119 The irst music, music with no depth at
all, is the source and is shown where the jagged arrow begins. Schoenberg speculates that
“the most primitive form of prehistoric music had at its disposal only a single instrument
capable of producing only a single tone” (MI, 107). The solution of all the problems
in the tone, “the precise accommodation of all overtones” (HL, 319), is “the ultimate
goal,” but this goal is a moving target on account of the perpetual expansion of the tone
as a phenomenon. The limitlessness of the tone implies the endlessness of evolution.
Schoenberg declares, “Evolution is not inished, the peak has not been crossed. It is only
beginning, and the peak will come only, or perhaps never, because it will always be
surpassed” (HL, 97).120 Schoenberg describes the path of the means of art as “the path to
the summit” of a mountain (HL, 70). Works of “genius,” which attain full “penetration
of nature” (HL, 325), form mountain peaks along the path (shown where the jagged
117
HL, 133; see also Schoenberg, “My Evolution,” in SI, 87.
118
“Den Weg der Kunstmittel” (HL, 459/412).
“Die Entwicklung der Musik ist den Weg gegangen, daß sie immer mehr von den im Ton gelegenen Zusammenklangsmöglichkeiten in den Bereich der Kunstmittel einbezogen hat” (HL, 19/21; translation modiied).
119
At times, Schoenberg suggests that we may solve all the problems in the tone: “Imitation...does not yet, will
not yet for a long time, go as far as the prototype” (HL, 225). But even if we do, the evolution of music will still
continue. He says that when we “have reached the utmost perfection in the imitation of nature,” we will be able
to “turn away from the external model and more and more toward the internal, toward the one within us” (HL,
263/239; translation of “aüßerste Vollendung” changed to “utmost perfection”).
120
Matthew Arndt — Schoenberg on Problems
arrow touches the diagonal line). To quote him, “The highest pinnacles, which are most
accessible to the observer, into which the capillaries lift the inest and best from the
depths, these alone set forth the spirit of mankind....One sees that they are related and
how they are related, that they are coherent amongst themselves” (HL, 411–12). Namely,
they are related in that “the ratio of the artist to his work,” the ratio between the heights
of the upper two lines, actually “equals one.”121
According to Schoenberg, the way to the path of art leads straight up from the
material: “There is only one direct way of connecting to the past, to tradition, to the
thinking of our forerunners: to start again from scratch, as if everything earlier were
wrong, to get in touch again with the essence of things, instead of merely expanding the
technique of handling the given material.”122 For the one who relies on systematic rules,
the way to the path of art is blocked, and his work only reaches the level of handicraft
(as shown with the short vertical arrow), but for the one who relies on his ear and his
feelings, the way is open (as shown with the long vertical arrow): “Does the pupil have
need for the laws, so that he can know how far he may go? I have indeed just said how
far he may go: as far as his nature drives him; and he must strive to hear his nature
precisely if he wants to be an artist! If he only wants to be a craftsman, then a barrier will
appear somewhere all of its own accord; the same barrier that keeps him from artistry
will also keep him from going all too far” (HL, 415). By way of contrast, “The master
proves his mastery by breaking through the barriers and becoming free” (HL, 396).
For the craftsman, the way to the path of art is blocked not only in terms of inventing
new musical means but even in terms of using them. According to Schoenberg, “There
is perhaps still a copyright on them, a quite arrogant right of ownership, that refuses to
open the road to those who will not make the effort themselves. Those who themselves
make the effort ind it anyway, ind it in a way that gives them right of use. To them the
road is open; to the others, who only want to try their hand at it, may it remain closed”
(HL, 413). Handicraft keeps half-pace with art in terms of its depth. Schoenberg insists,
“The ordinary person...must always keep equal the distance above and below himself;
and since those above him push forward, he must move along at a suitable interval
behind” (HL, 416). Accordingly, the depth reached by art at a given moment is eventually
open to handicraft, to systematization. Schoenberg assures us, “Whereas the distance
121
HL, 366/326; translation of “Verhältnis” changed to “ratio.”
“Es gibt nur einen direkten Weg des Anschlusses an die Vergangenheit, an die Tradition, an das Denken unserer Vorgänger: es noch einmal von vorne anzufangen, so als ob alles frühere falsch wäre; sich noch einmal mit
dem Wesen der Dinge in Verbindung zu setzen, anstatt bloss die Technik der Verarbeitung gegebenen Materials
zu erweitern.” Schoenberg, “Aphorismen und Sprüche,” 3. See also Arnold Schoenberg, “Die heutige Jugend”
(T03.55, ca. 1931) (Arnold Schönberg Center, http://www.schoenberg.at).
122
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between the onrushing, brilliant insight of the genius and the ordinary insight of his
contemporaries is relatively vast, in an absolute sense, that is, viewed within the whole
evolution of the human spirit, the advance of his insight is quite small. Consequently,
the connection that gives access to what was once incomprehensible is always inally
made” (HL, 30). Along the same lines, Schoenberg mentions that “ultimately, the newer
techniques will be in the public domain” (HL, 413).123
II. Analysis
Overview
As is well known, Schoenberg’s study of Brahms’s music plays a prominent role in
his development as a musician, and he comes to see himself as Brahms’s successor in the
struggles of art.124 In Brian Hyer’s words (2002, 750), “Schoenberg...depicted himself as
Siegfried to (paradoxically?) Brahms’s Wotan, the hero who shattered the sacred musical
spear (with its contractual obligations to the tonic) and blazed a path to the new world
order, rebuilt from the ruins of musical tradition.” By illing out Schoenberg’s analytical
sketch of the irst movement of Brahms’s Piano Quartet No. 3 in C minor, op. 60, in Der
musikalische Gedanke und die Logik, Technik und Kunst seiner Darstellung, it is possible
to demonstrate how Schoenberg’s theory of composition works and how Brahms’s music
prompts his theory. I examine here the music’s motives, harmony, voice leading, form,
and character, heuristically adopting terms from William E. Caplin’s theory of formal
functions (1998) and James A. Hepokoski and Warren Darcy’s theory of sonata form
(2006). The main thing that sets my analysis apart from analyses of a “tonal problem”
and from other analyses of this piece is how I show the problem in the musical idea to be
linked to problems in the tone and the dissonance and how I understand the working out
of the problem to be a musical event as well as a historical event.
Schoenberg presents his analytical sketch to illustrate his claim that not only motivic,
melodic content but also tonal, harmonic content on its own has a coherent structure.
His comments focus on E and more speciically on E minor in the key of C minor as a
Schoenberg’s mountain is strikingly similar to Wassily Kandinsky’s “spiritual pyramid, which will some day
reach to heaven” ([1912] 1914, 20). Kandinsky ([1912] 1914, 6) describes its proile as follows: “The whole
triangle is moving slowly, almost invisibly forwards and upwards. Where the apex was today the second segment
is tomorrow; what today can be understood only by the apex and to the rest of the triangle is an incomprehensible gibberish, forms tomorrow the true thought and feeling of the second segment.” Jeffrey Perry (2000) has
examined the phenomenon of linear evolutionary accounts of music history.
123
124
On Schoenberg and Brahms, see Budde 1978 and Musgrave 1990.
Matthew Arndt — Schoenberg on Problems
problem whose solution gives the piece structure (see Example 8).125 Referring to the irst
appearance of an E-minor triad in mm. 28–30 at the end of the primary theme and the
beginning of the transition, Schoenberg notes, “The minor form that then appears, the
∂iii Stufe, ...could also be understood as melodic-motivic coherence, but this would not
explain how the harmony after the ‘Reprise’ then brings the same chord (∂iii) with ∂VII.”126
He identiies the quarter-quarter, Eß–D motion in mm. 3 and 4 as the basic motive, which
I call m for motive. Like Jonathan Dunsby (1981, 29) and Carpenter and Neff,127 I pair
m with the accompanying C–F motion in these measures as a derivative motive, n. The
melodic-motivic coherence of the E-minor triad would then be that E is actuated by the
variant of n E–E in mm. 28–30 as well as by the inversion of m E–F in mm. 30–31, but,
as shown in simpliied form in Example 9, the same can be said of the parallel point in the
recapitulation (mm. 223–35). In this latter case, E is actuated by the variant of n E–E in
mm. 224–26, as well as by the transposition of n E–A, the transposition of m E–Dƒ, and
the inversion of n E–B in mm. 226–27. The melodic-motivic coherence does not explain
the different subsequent course: a i6–V7–viio7–V/iv–iv–i progression in E minor in mm.
224–30. Schoenberg writes that the different appearances of the E-minor triad clarify E
as an alternative, raised mediant of C alongside the diatonic mediant (in other words, E =
M C too): “Brahms found a possibility, by means of this minor triad on E∂, that allows the
V of C minor to be followed by a chord that in an equally surprising manner leads one
time back to I (C), and another to the V of C minor, carried out like a key (G). The point
of this surprise is that this E so stands between C and G as does the diatonic third Eß in C
minor, C E G instead of C Eß G” (MI, 321). Schoenberg then riffs on this point, explaining
that the clariication of E as the raised mediant involves the E-minor triad leading in an
engaging and elegant manner to successive tonicizations of C, E, and G: “This progression
thus has the purpose of accomplishing a double surprise; the irst time, the surprising
reentry of the tonic theme; the second time, during which the E minor is truly further
carried out, becomes a double surprise: a) of a different continuation (E minor), which
b) ultimately lows into G major by use of the harmonic progression from bars 21–27
transposed to E [i.e., in a varied form in mm. 230–34], thereby actually producing C E
G. This bespeaks a special constructive elegance!” (MI, 321). Thus the clariication of E
Apropos of this problem, Schoenberg says that “tones and harmonies whose relationship to the tonic is only a
third...can exert sometimes a centrifugal tendency. This tendency grows with the greater distance from the tonal
circle, especially if substitute tones are applied.” “Tonality,” in Jacob 2005, 2:818.
125
126
“Die dann erscheinende Moll-Form, der -III∂ Stufe...könnte ebenfalls als melodisch-motivischer Zusammenhang verstanden werden, was jedoch die Harmonie nicht erklärte, nach der „Reprise“ bringt dann denselben
Akkord (III∂) mit VIIƒ/ƒ/∂” (MI, 314/315; translation modiied).
127
Carpenter and Neff, “Commentary,” in MI, 67.
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THEORY and PRACTICE Volume 37/38 (2012–13)
introduction primary theme
antecedent
introduction (2 bars) basic idea (2 bars)
continuation (6 bars)
p
m
p
m
m
m
˙™ ˙™ m
b
3
& b b 4 ˙™ ˙™ œ œ Œ œ œ Œ œ œ œ œ œ œ œ œ
nœ
nœ
bœ œ
o
Allegro non troppo
f
p
!"#$
œ ˙˙
œ ˙
? bb 43 ˙ ™ ˙ ™ œ œ Œ œ œ Œ œ œ œ ˙˙
b
˙
˙™ ˙™ œ œ
œ œ
œ œ œ
n
œ ˙
œ ˙
œ
œ
n
failed consequent
b
&b b
%
? bb
b
˙™
˙™
˙™
˙™
f
!"#$
˙™
˙™
˙™
˙™
introduction (2 bars) presentation (4 bars)
œ ˙
˙™
˙˙ ™
™
˙˙ ™
™
bœ œ
p
Œ
Œ
Œ œ œ Œ
bœ b œ
œ œ
œœ œ
œ Œ
œ bœœ Œ bœœ bœœ Œ bœœ bœœ Œ
œ
HC
standing on the dominant (10 bars)
continuation (5 bars)
b
& b b œ nœ œ
+,
(')*(''$
p´
œ nœ bœ
œ b œœ œœ bb ˙˙
? bb nœ
b
m
m
œ œ bœ nœ œ bœ
n ˙˙ ™™
˙˙ ™™
!"#$&'(#)*( pp
œœ bn ˙˙ b œœ œœ nn
œ̇ œ œ œ
œ b˙ ™
bb ˙˙ ™™
HC
EXAMPLE 8
Brahms, Piano Quartet No. 3 in C minor, op. 60, I, the primary theme
and the beginning of the transition, mm. 1–32 (short score)
b œ bœ
œ b œ bœ
bœ
Matthew Arndt — Schoenberg on Problems
n
b
&b b ˙™
˙™
n ˙˙ ™™
b ˙˙ ™™
n ˙˙ ™™
pp
˙˙ ™™
? bb
b ˙™
˙™
˙™
˙™
#˙ ™
#˙ ™
˙™
˙™
Œ
˙™
˙™
&'
p
nœ Œ nœ
Œ Œ
n
œ
nœ
˙˙™™
˙˙
n
!"#$%
pp
nœ
!"##$
Œ Œ
Œ nœ
nœ
˙
˙™
˙
˙™
!"##$
6
c:
V
iii???
primary theme
.
b
œ
()
œ
b nb œœ˙˙˙ ™™œ œ bœ œ œ nœ
bœœ
b
œ œ œ
& b b ˙™™œ œ bœ œ œ
n œ œ œ œ œœ œ œ
œ .
f
%&'(
f.
œœ
? bb bœ˙˙ ™™ œ œ bœ œ œ nœ
œœœ œ
b
œ œ œ œ
b ˙™
œ œ œ
lead-in (2 bars)
7
transition
.
œœ
œœ
Œ
œ
.
.
œœ
œœœ œ Œœ œ
œ œ œ œ
V
EXAMPLE 8
(cont’d.)
also entails its stabilization, in part through its tonicization. By establishing C–E–G and
C–Eß–G as equivalent tonic triads, the music draws the major and minor modes closer
together, thereby furthering the evolution of music. According to Schoenberg, “Major
and minor have evolved historically, ...containing everything that appeared in the seven
old modes,” and “the remaining two will eventually be one” (HL, 96), “the chromatic
scale” (HL, 247).
In their extension of Schoenberg’s analysis, Carpenter and Neff claim that the
problem is “to make clear the network of relations to the tonic implied by...Bß minor
and E minor.”128 Schoenberg, however, only discusses E in his analysis; he does not even
mention Bß.129 Furthermore, after closing his analysis, he immediately goes on to say
128
Carpenter and Neff, “Commentary,” in MI, 68; see also Carpenter, “Schoenberg’s ‘Tonal Body,’” 43–46.
According to Carpenter, Schoenberg mentions a potential conlict between B and Bß in his Form and Analysis
lectures. Carpenter and Neff, “Commentary,” in MI, 67; see also Carpenter 2005, 43. But as I explain below, this
potential conlict only intimates the problem; it is not the problem itself.
129
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THEORY and PRACTICE Volume 37/38 (2012–13)
[primary theme transition]
[standing on the dominant]
b
&b b
!!"
n ˙˙ ™™
pp
? bb
b ˙™
c:
Œ Œ
˙˙™™
nœ
˙™
antecedent continuation (8 bars)
j
# œ˙ ™ œ œ œ™
œ
˙
& #˙˙ ™™
#˙˙ œœ n˙˙ ™™
˙™
7
G:
V/iv
nœ Œ
nœ
˙˙
˙
iv
i
nœ
n
#
nnn ˙ ™
#˙ ™
m
n
#
nnn ˙ ™
7
e: i
vi
!
V
˙˙ ™™
œ œ
œ b˙ ™
p
e: viio
œ
lead in (2 bars)
6
!!#
? # ˙™
n œ̇ ™
˙™
Œ
n
˙™
V
I
G:
n
b˙˙ ™™
dominant arrival (premature)
˙˙ ™™
˙˙ ™™
˙˙
˙™
˙
Œ
$%&'
œ bœ
b œ ˙™
6
4
5
Œ
3
V
EXAMPLE 9
Brahms, Piano Quartet No. 3 in C minor, op. 60, I, the end of the primary theme
fused with the transition in the recapitulation, mm. 223–35 (simplified)
that Brahms’s Piano Trio in C minor, op. 101 “perhaps...shows a similar problem,” and
he points out that in the primary theme, “the thirds C–Eß–G, the ground tones of the
Stufen, are replaced...by C–Eßm–Gß,”130 the implication being that this problem, which
involves an alteration of a mediant of C (as well as a dominant), is similar to that of
“C E G instead of C Eß G.” The uniqueness of E as the problem in the Piano Quartet
movement will become clear as we now examine six key moments in the music’s motivic
and tonal development: 1) the primary theme in the exposition; 2) the transition; 3) the
secondary theme; 4) the new theme in the development; 5) the primary theme fused with
the transition in the recapitulation; and 6) the closing zone.
130
MI, 320/321; translation of “Stufengrundtöne” changed to “ground tones of the Stufen” and “C–E 3ß–Ges”
changed to “C–Eßm–Gß.”
Matthew Arndt — Schoenberg on Problems
The Primary Theme in the Exposition
The mysterious, ominous music in mm. 1–30 (Example 8), with its bell-like tolls
and its sinuous, creeping lines, introduces all the signiicant motives and gradually unveils
the problem. In keeping with this sense of mystery, the music has an enigmatic form and
function, appearing to Jonathan Dunsby (1981, 25–26) as an introduction, comprised of
a period (mm. 1–10) plus a sentence (mm. 11–30), to Carpenter and Neff as a primary
theme in the form of a sentence (with mm. 1–10 being the basic idea, mm. 11–21 being
the repetition, and mm. 21–30 being the continuation),131 and to Peter H. Smith (2005,
209; and 2006, 63) as the irst part of the primary material, comprised of a pair of
sentences (mm. 1–10 and mm. 11–30). We can acknowledge some truth in all of these
functional designations if, following Janet Schmalfeldt (2011, 9), we allow for the
reinterpretation of formal function and say that mm. 1–30 begin with the suspenseful
tone of an introduction and become a primary theme, and that mm. 32–70 begin with
the assertive tone of a primary theme and become a transition. The unfolding formal
and tonal designs effect these transformations. Smith is correct that mm. 1–10 and mm.
11–30 are a pair of sentential thematic units related by varied repetition. Together they
are basically periodic, except that they both close with half cadences in mm. 9 and 21,
and they express the tonic minor region, albeit with a digression to the subtonic minor
region in mm. 11–20, so mm. 1–30 are relatively tight knit and take on primary theme
function. By way of contrast, mm. 32–70 do not it a conventional model of phrase
structure and are modulatory, so they are relatively loose and take on transition function.
Some readers may not hear a half cadence in m. 21 on account of the anomalous IVß7
pre-dominant in m. 20, but Schoenberg at any rate hears “a lingering on V” following
this point (MI, 315). Mm. 3–10 are the Grundgestalt, which contains all the piece’s
seminal motives: not only m and n but also motive o, comprised of two forms of m in a
descending line, Eß–D–C–B in mm. 5–6, and motive p, comprised of motive o in mm. 5–6
and an inversion (or retrograde) of m, B–C in m. 6. Motive p also appears in retrograde
inversion, B–C–Bß–Aß–G in mm. 7–9. This latter statement of p presents two different
versions of the seventh scale degree in C minor, B and Bß, which, as Carpenter and Neff
have pointed out, hold the potential for conlict.132 This potential conlict intimates the
conlict between E and Eß, which is introduced by a variation of the retrograde inversion
of p, p´: an inversion of m, E–F in m. 20, followed by motive m, Eß–D in mm. 20–21.
As we have seen, E then reappears as an E-minor triad in mm. 28–30. Brahms marks E
131
Carpenter and Neff, “Commentary,” in MI, 67; see also Carpenter 2005, 41.
132
Carpenter and Neff, “Commentary,” in MI, 67; see also Carpenter 2005, 43.
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THEORY and PRACTICE Volume 37/38 (2012–13)
for our notice here with the marcato marking. This reappearance of E involves the same
transposition of p´ in mm. 30–32 as the irst appearance. By repeating this motive but
presenting E in a more vivid and speciic way, the music formulates the problem.
As Smith (2006, 65–66) observes, the E-minor six-three chord in mm. 28–30 is
harmonically (and also metrically) ambiguous: E as a neighbor note or implied passing
tone resolves to F in m. 31 as the seventh of V7, but the E-minor triad could also conceivably be iii6. The relation of tones to ground tones (roots) is therefore unclear: a conlict
emerges between E and G as possible ground tones, a clash between E and the closest
overtones of G, which means that the six-three chord is dissonant. But since the six-three
chord is also consonant, it does not simply call for resolution; it also calls for recognition,
sometime in the future.133 As a dissonance, E in mm. 28–30 is also an unclear, remote
overtone of G, as is indicated by the high, delicate, intermittent, and shifting sound of E
in contrast to the low, resonant, continuous, and stationary sound of G. Thus E in mm.
28–30 palpably illustrates how the three kinds of problems—in the tone, the dissonance,
and the musical idea—all come together in the musical work. This convergence is so
striking that it may be this very E-minor triad that Schoenberg has in mind when he calls
the six-three chord dissonant.134
The Transition
The delicate but disquieting E launches the music by means of a lead-in (mm. 31–32)
into the transition (mm. 32–70), which begins in an agitated manner with driving eighth
notes, numerous sforzandi, and a full texture, and E also pushes the transition onward
toward the secondary theme and its region. The transition begins with a variation of the
Grundgestalt, mm. 32–42, shown in Example 10: m–m–p´´–p´´ and a liquidation of p´´
instead of m–m–p–p. Another variation of the retrograde inversion of p, p´´, C–Eß–D–C–
Bß–Aß in mm. 34–35, substitutes a variant of n (C–Eß) for an initial inversion of m. In the
course of a sequence, p´´ generates a variation of o, o´, G–D–F–Eß in mm. 36–37, which
substitutes an inversion of n (G–D) for an initial m. In the two statements of o´ in mm. 36–
38, Eß is juxtaposed with E more directly than in the primary theme. E shows itself to be
an instigator, initiating an ascending melodic sequence and a crescendo that leads to the
climax of the transition, an imperfect authentic cadence in m. 42. Following this climax,
Smith (1997) has shown how Brahms often introduces other regions by exploiting the potential of linear sixthree chords to be read as inversions and vice versa.
133
Joseph Dubiel (1994) has analyzed another disruptive six-three chord in Brahms, the Bß-major triad in the irst
movement of Brahms’s Piano Concerto No. 1 in D minor, op. 15, as an “abnorm” that is eventually integrated
with tonal norms, much like a Schoenbergian problem.
134
Matthew Arndt — Schoenberg on Problems
primary theme
transition
basic idea (2 bars)
continuation (9 bars)
p´´
b œ. œ.
m
b
&b b
!"
œ. œ.
m
Œ
n
p´´
p´´
o
o´
œ œ œ œ œ œ œ œ œ œ œ œ œ œ
J
œ
J
J
Œ
n
m
f
p´´
o´
œ œ œ nœ œ œ œ œ b œ œ œ n œ œ œn œ
œ
b
œ
‰
‰
‰
‰
&b b J
o´
o´
!(
o´
œ
#$%&#'
o´
œ
œ
œ œ.
‰J
o´ m
ff
IAC
EXAMPLE 10
Brahms, Piano Quartet No. 3 in C minor, op. 60, I, the beginning
of the transition in the exposition, mm. 32–42 (melody only)
the transition gradually recedes in dynamics and textural density as it modulates to the
mediant major by way of the mediant minor, reaching a half cadence in m. 52.
The Secondary Theme
The noble secondary theme (mm. 70–110), with its stalwart melodic gestures and
its sumptuous accompaniment, displays Eß as the honored tonal region of the mediant
major, and it displays E as an aspirant to the mediant status of Eß. The theme is a large
period, with an antecedent (mm. 70–77) that is repeated and varied (mm. 78–85, 87–93,
and 95–101) and a consequent (mm. 102–10), each comprised of a compound basic idea
plus a continuation. As shown in Example 11, the irst antecedent begins with another
variation of the Grundgestalt in mm. 70–73: n–m–m–p´–p´ instead of m–m–p´´–p´´. The
ascending sequence of the inversion of p´ (mm. 72–73) parallels the descending sequence
of p´´ in the transition. In the second antecedent, E appears once again as an appoggiatura
in the inversion of m E–F in m. 82 and—just in case we missed it—in mm. 84 and
85. The ascending melodic intervals, the rhythmic and metric accents, and the dynamic
swells indicate E’s ardent yearning. The fourth antecedent, shown in a simpliied form
in Example 12, quiets down and turns to the mediant minor, as if to indicate the music’s
apprehension—what’s taking the consequent so long? E, taking advantage of Eß’s
momentary lapse of conidence, surfaces in m. 99 as the enharmonic Neapolitan region
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THEORY and PRACTICE Volume 37/38 (2012–13)
secondary theme
first antecedent
compound basic idea (4 bars)
b œ
&b b
'(
n
m
œ
œ
p´
m
j
œ œ
Ϫ
p´
œ œ œ. œ. œ
œ œ œ. œ. œ
p!"#$%"##&
EXAMPLE 11
Brahms, Piano Quartet No. 3 in C Minor, op. 60, I, the beginning of the first antecedent
in the secondary theme in the exposition, mm. 70–73 (melody only)
[secondary theme]
fourth antecedent
compound basic idea (3 bars)
b bœ ™
&b b Ϫ
()
? bb
b ˙™
p!"#$%"##&
eß:
œ œ
œ bœ
J
!
œ œ œ bœ bœœ
œ œ œ œ
œ œ œ œ œ
œ œ œ bœ œ
continuation (4 bars)
'%"#'&
˙™
˙™
7
i
9
V
#œ
nœ
œ
bb nœœ nœ n#œœ n#œœ #œ œ bnœ˙ bœ bœ œ nœ n œ
b
n
&
#œ
œ̇ œ œ
'%"#'&
nœ
nœ
n˙
7
4
2
œ
6
5
7
eß: vii /V
o
I
V
#œ
iv
E: iii
((
? bb
b nœ
n œ #œ n œ
#œ n œ #œ
viio
V/V
˙™
7
V
HC
EXAMPLE 12
Brahms, Piano Quartet No. 3 in C minor, op. 60, I, the fourth antecedent
in the secondary theme in the exposition, mm. 95–101 (simplified)
œ œ
œ œœ œ
Matthew Arndt — Schoenberg on Problems
new theme
antecedent
basic idea (2 bars)
. .
#### œ œ
Œ
& #
m
!"#
continuation (4 bars)
p´´´
œ. œ.
m
n
œ. >œ ™™ œ. œ. >œ ™™ œ. œ œ œ # œ
R
R
n
Œ
p´´´
m
>˙
ff
>
œ œ œ #œ œ
n
HC !
EXAMPLE 13
Brahms, Piano Quartet No. 3 in C minor, op. 60, I, the beginning of the
new theme in the development, 142–47 (melody only)
of Eß, appropriating the music of the third antecedent in mm. 90–91 and transposing it
up an augmented unison in mm. 98–99. Eß quickly comes to its senses and recaptures
the music through an enharmonic pivot in m. 100 and an ascending melodic sequence in
mm. 100–101 that launches the long-awaited consequent.135
The New Theme in the Development
The development begins with another turn to the mediant minor in m. 122; once
again, this move affords E an opportunity to emerge as the enharmonic Neapolitan
region of Eß in m. 139. In order to establish the place of E in C minor, however, the
music must prove the lineage of E apart from Eß, and this proof is partially worked out
by the subsequent new theme. The irst statement of this theme begins on I in B major
in m. 142, pivoting from V in E minor, and it cadences on i in E minor in m. 154. The
second statement begins on I in G major in m. 164, pivoting from V in C minor, and it
fails to cadence on i in C minor in m. 176. Thus the theme articulates a mediant relation
between B major and G major analogous that between E minor and C minor. To trace
out the relation between the tonic C and the mediant E, the new theme combines the
forms of the Grundgestalt in the primary theme and transition, associated with the tonic,
and in the secondary theme, associated with the mediant. As shown in Example 13, the
form of the Grundgestalt in the new theme (mm. 142–47) starts like that in the primary
theme with two separated statements of m, B–Aƒ in m. 142 and Gƒ–Fƒ in m. 143, proceeds
like that in the secondary theme with two statements of a variation of the inversion of
p´, p´´´, E–B–E–Fƒ in mm. 144–145 and Fƒ–B–Fƒ–Gƒ in mm. 145–146, which substitute
n for the irst m, and ends like that in the transition by liquidating p´´´. The music’s
135
The arrival of Eß major in m. 102 hardly resolves the tonal conlict with E. As Smith (2005) has observed, the
climax is “somewhat brittle and forced” on account of the registral break and the agitated eighth notes.
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THEORY and PRACTICE Volume 37/38 (2012–13)
heroic calling in the new theme to solve the problem is projected by the major key, the
fortissimo dynamics, the full texture, and the predominance of ascending melodic motion
with metric, rhythmic, and articulative accents. In the transitional passage between the
statements of the theme (mm. 154–64), the music’s head-to-head struggle with E, the
initial local tonic, is projected by the minor key, the roving harmony, the forte dynamics,
the divided texture, the ascending melodic sequence of motive m with metric, rhythmic,
and articulative accents, the similarly accented ascending arpeggios, and the rhythmic
conlicts.
The Primary Theme Fused with the Transition in the Recapitulation
Having been intimated in the development, the mediant status of E is partially
realized in the recapitulation of the primary theme fused with the transition, mm. 199–
235. As shown in Example 9, E again appears as an E-minor triad in mm. 224–26 and
is tonicized in mm. 224–30. In this case, E minor is only indirectly related to C minor as
the submediant minor of the dominant major, because the surface tonicization of E minor
is enveloped by a deeper I–vi–V progression in G major in mm. 223–35. E also appears
as the third of a C-major triad in m. 206, an unstable V/iv chord in C minor, again
actuated by p´, E–F–Eß–D in mm. 206–9, just as it was in mm. 20–21 in the exposition.
This pattern repeats in mm. 210–13. Thus E is stabilized but in an unclear context and
clariied but in an unstable context. Contrary to Carpenter and Neff’s claim, balance is
deinitely not restored yet.136
The Closing Zone
As Dunsby (1981, 34) and Smith (2005, 76; and 2006, 69) have both pointed out,
the primary theme in the recapitulation may be in C minor, but its tonic chords actually
prolong the dominant from the development, and the secondary theme (mm. 236–88)
prolongs the dominant still further, because it is in the dominant major rather than the
conventional tonic major. Consequently, the task of producing a tonic-function passage
in C minor corresponding with the passage in E minor in the development (mm. 154–64)
and echoing the mediant relation between B major and G major falls to the closing zone
(mm. 288–326). The irst thematic unit of the closing zone (mm. 288–303) recalls the
sequential treatment of m, the vigorous arpeggios, the roving harmony, the conlicted
rhythm, the divided texture, and the strong dynamics of the earlier passage. But the
closing zone does not succeed in its task until the inal thematic unit (mm. 313–26); this
136
Carpenter and Neff, “Commentary,” in MI, 73; see also Carpenter 2005, 63.
Matthew Arndt — Schoenberg on Problems
unit parallels the closing zone in the exposition (mm. 110–21) by restating the primary
theme together with a closing countermelody in C minor.
E appears in progressively clearer and more stable ways in the closing zone as an
alternate mediant of C. The closing zone begins on I in C major in m. 288, pivoting from V
in F minor. As Smith (2005, 87) notes, a transposition of m, C–B, hints at an E-minor triad
in m. 288 and actualizes iii in m. 289 as the bass ascends from C to E. These triads further
stabilize E minor, though it is still only indirectly related to C minor as the mediant of the
tonic major. E similarly appears as the third of I in C major m. 300. Example 14 shows
how E appears in the run-up to the cadence in m. 313 that ushers in the inal thematic
unit: it occurs in m. 311 and m. 312, through a transposition of m, E–Eß, in an ambiguous
pedal six-four chord prolonging V9 in C minor. Since E or Eß can both be heard as a chord
tone, they are brought together as alternate thirds of a tonic triad, but one without tonic
function. Finally, during the concluding statement of the primary theme (mm. 313–26),
the forms of m F–Eß in m. 318 and F–E in m. 319 unambiguously juxtapose Eß and E as
alternate thirds of a tonic-function tonic triad in the repetitive harmonic progression i–
iv–viio7–i–iv–viio7–I in mm. 317–319: the problem is solved. Yet no sooner is the solution
reached than E disintegrates into F in the viio/iv–iv6 progression in m. 320: E still has a
long way to go in the evolution of music before it is truly reconciled with C in C minor.
Even just in the quartet as whole, in Smith’s words (2005, 17), “C∂ and E∂—the two pitches
that would need to come together to form a transcendent major tonic—seem always to
be at odds. Any attempt to bring them into unity creates the feeling of resistance ones
gets when trying to force the wrong ends of two magnets together. When one pushes
forward, the other is repelled.” And this resistance to transcendence contributes to the
tragic expression that Smith has traced in the music.
Bookended by the movement’s only perfect authentic cadences in C minor, the
solution to the problem of unrest coincides with the full manifestation of the ground
tone; after all, the problem and the incomplete manifestation of the ground tone are
one and the same condition. And the completion of these processes coincides with
the end of the piece because this completion is the goal; there is nothing more to be
said. In Schoenberg’s words, “We may well ask: Why, in what manner, and when does
a piece of music close? The answer can only be a general one: As soon as the goal is
reached” (HL, 126). At irst glance, the solution being at the end of the piece might
seem incompatible with Schoenberg’s intuition that the solution is seen in the E-minor
triad’s production of C–E–G instead of C–Eß–G, a process that is completed with the
beginning of the secondary theme in the recapitulation. But in the work of art, the whole
can be seen in the part, or, in Schoenberg’s words, “Every little detail it reveals its truest,
51
52
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in the recapitulation, mm. 311–26
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THEORY and PRACTICE Volume 37/38 (2012–13)
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Matthew Arndt — Schoenberg on Problems
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53
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EXAMPLE 15
The overall harmony and voice leading in Brahms, Piano Quartet No. 3 in C minor, op. 60, I
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THEORY and PRACTICE Volume 37/38 (2012–13)
development
exposition
Matthew Arndt — Schoenberg on Problems
inmost essence.”137 The E-minor triad’s production of C–E–G instead of C–Eß–G also
appears in the overall harmony and voice leading of the piece, shown in Example 15,
with increasingly dense layers of harmony being indicated with open noteheads, illed
noteheads, and stemless notes: the piece moves from C as the ground tone (the tonic)
in the primary theme and transition, through Eß in the secondary theme, through E
in the development, which displaces Eß, to G in the development and recapitulation,
all contained by C, heard again in the closing section.138 Through the integration of
processes witnessed here—the solution of the problem, the manifestation of the ground
tone, the development of motives, and the evolution of music—such that the essence of
the musical work appears in every cross-section, Brahms’s music serves as a prototype for
Schoenberg’s theory of composition.139
Conclusion
For Schoenberg, the tone is an idea of nature that the artist imitates in the musical
work, thereby ideally bringing it to full consciousness. The tone is a chord in its essence
but a mere tone in its phenomenon on account of the unclear relations of remote overtones
to the ground tone (the fundamental). This obscurity is a problem that prompts the artist
137
Arnold Schoenberg, “The Relationship to the Text” (1912), in SI, 144.
Dunsby (1981, 35) hears two misaligned large-scale arpeggiations that similarly feature both E and Eß as
alternate mediants: the harmonic progression I–V–I, resolving to C minor in m. 313, and the tonal progression
c[?]–Eß–G–C, resolving to C major in m. 288.
138
Although Janet Schmalfeldt (1991) and others have combined Schenkerian and Schoenbergian analysis, some
readers may question whether a Schenkerian notion of layers is compatible with Schoenberg’s understanding of
harmony and voice leading. Noting that Schoenberg emphasizes the generative role of the motive and only ever
shows a couple layers in his own analyses, Boss (1994, 210) has claimed that “Schoenberg’s structural levels,
unlike Schenker’s, only go up as far as necessary to reach an unornamented motive.” But, as we have seen, the
motive for Schoenberg is only a representation of the generative musical idea, not the idea itself, so it need not be
the limit of linear analysis. According to Schoenberg, “an attempt to recognize and deine the musical idea stands
in clear contradiction to the sentimental poeticizing notion that a composition might arise from the motive as
germ of the whole, as a plant grows from a seed” (MI, 109). Furthermore, the limits of Schoenberg’s own linear
analyses do not necessarily represent the limits of linear analysis in accord with his theories. Schoenberg writes
that “the harmonic plan of every musical composition” is “an extended cadence” (HL, 152), which can only
mean that harmonic progressions occur in different layers from a background cadence to the series of chords in
the foreground. It is important to note that in a sense the foreground is just as essential as the background, for
only the entire piece in all its details presents the musical idea, the essence. In the words of Dudeque (2005, 129),
“tonal structure presents a stratiied organization for Schoenberg, each level with its own importance within the
whole.” Even with Heinrich Schenker (1956 [1979], 12/68), “the content of the second and the subsequent layers
is directed by that of the irst layer, but at the same time it is directed by the goals in the foreground, which are
mysteriously sensed and pursued.” “Richtet sich der Inhalt der zweiten und folgenden Schichten nach dem der
ersten Schicht, zugleich aber nach dem geheimnisvoll geahnten und verfolgten Ziele im Vordergrund.”
139
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THEORY and PRACTICE Volume 37/38 (2012–13)
to act. The artist uses the means of art to imitate the tone. Dissonances as imitations of
remote overtones exhibit unclear relations of tones to ground tones (roots) and so require
resolution or at least clariication. Imitation of the tone in a particular piece of music is
the imitation of one particular tone, the ground tone (the tonic), which is the musical
idea in its material aspect. Presentation of the musical idea through variation of the basic
motive or the Grundgestalt solves a problem of unclear relations of tones through the
victory or the self-sacriice of the ground tone. This solution in turn contributes to the
evolution of perception and music. These dialectical conceptions make up an integration
network whose spaces are linked by a basic image-schematic complex that undergoes
variation as the tone takes on various guises. This network establishes the unity of tonal
and non-tonal music with respect to problems in the tone, the dissonance, and the musical
idea, which Schoenberg posits but never clearly articulates, and which has proven to be
equally elusive for Schoenberg’s interpreters.
Schoenberg’s theory of composition is illuminated by his analysis of Brahms’s music
as supplemented here, but also, as Michael Musgrave (1990, 136) and Smith (2005, 66)
have both pointed out, even though Schoenberg’s analyses relect his subjective concerns,
they nevertheless bring objective qualities of Brahms’s music into focus. Contemplated
with an eye to the musical idea and its problem, the parallel motivic and harmonic
structures in Brahms’s music merge into a deep, shimmering image, somewhat like the
stereographs that were so popular in the late nineteenth and early twentieth centuries.
In this image we see Schoenberg relected, of course, but we also see through to Brahms:
Brahms strives to penetrate the tone, just as Schoenberg does. And in doing so, Brahms
reluctantly heralds an incipient dissolution of tonality, as Elmar Budde (1998, 276) has
suggested. Whereas the conclusion of the Piano Quartet movement fuses major and
minor, the conclusion of Brahms’s melancholy Intermezzo in B minor, op. 119, no. 1,
fuses tonic and dominant in mm. 65–67. According to Budde, this process announces
a suspension of the dynamics of tonal music. As problematic as Schoenberg’s theory of
composition is, it speaks to his extraordinary powers as a composer and as a theorist
that he heard Brahms’s faint intimation of such a theory and answered it in such a singleminded and singular way, in word and in deed.
Matthew Arndt — Schoenberg on Problems
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