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L o h m a n , P e t e r N a t h a n

SCHOENBERG’S ATONAL PROCEDURES: A NON-SERIAL ANALYTIC APPROACH TO THE INSTRUMENTAL WORKS, 1908-1921

The Ohio Siate University Ph.D. 1981

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University Microfilms International SCHOENBERG'S ATONAL PROCEDURES: A NON-SERIAL ANALYTIC APPROACH TO THE INSTRUMENTAL WORKS, 1908-1921

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

P eter Nathan Lohman, B.A., M.Mus,

* * * * *

The Ohio S tate U niversity

1981 Reading Committee; Approved by Burdette L. Green William Poland Gregory Proctor Adviser School of Music ACKNOWLEDGMENTS

I wish to thank ray advisor, Dr, Burdette Green, for his many hours of patient work on this document. I am also grateful to Dr. William Poland and Or. Gregory Proctor for their careful reading and valuable insights.

ii VITA

September 24-, 1953 ...... Born - New York, N.Y.

1975 . . « ...... B.A., Oberlin College, Oberlin Ohio

1976-1978 ...... Teaching Associate, School of Music, The Ohio State University, Columbus, Ohio I976r ...... M.Mus., The Ohio State University, Columbus, Ohio

1978-1979 ...... University Fellow, The Ohio S ta te U n iv ersity , Columbus, Ohio

FIELDS OF STUDY Major Field: Music Theory Studies in Analysis. Professor William Poland Studies in the History of Music Theory. Professor Burdette Green Studies in Composition. P ro fesso r Norman Phelps Studies in Electronic Music. Professor Thomas Wells

iii TABLE OP CONTENTS

Page ACKNOWLEDGMENTS ...... - ...... i i VITA...... i i i LIST OP TABLES...... v i LIST OP EXAMPLES...... v i i INTRODUCTION ...... 1 Chapter I . BASIC APPPOACÎILS TO ATONAL MUSIC. . »...... 19 The A e s th e tic /H is to ric a l Approach- Theories cf Pitch Organization- The Conypn , Analytic Approach- The "Emancipation of the Dissonance" and its Theoretical Implications- Alterations in the Musical Language. I I . THE VERTICAL DIMENSION IN ATONALMUSIC... ?2 The Verbal Categorization of Atonal Simultaneities - New Symbol Systems for Categorizing Atonal Simultanei ties - i'he Application of Chord Quali ty Analysis to Schoenberg's Atonal Works - Some General C h a ra c te ris tic s of Chord Qualities - A Tabulation of Chord Qualities in Schoenberg's Atonal Piano Works - xiie Case A gainst In te rv a l- Class Equivalence as an Important Factor in Schoenberg's Atonal Procedures - Layers of Vertical Activity. I I I . ATONAL MELODY...... - ...... 13^ The Role of Chromatic Saturation in Melodic Organization - Types of Melodic Interval Succession - Local Variation Procedures - Idiosyncratic Peatures - Perpetual "Variation". IV. FORMAI RECURRENCE . «...... l68

i. The Melodic A rtic u la tio n of Form - C:-2 ':-5xtual Emphasis - The Role of Ccnt9%. cual in Aural Coherence - Types of Relatedness - The Categories of Formal Recurrence - Category Ai Polymotivic and Section- alized Movements - Category Bi Imita tive "Contrapuntal" Movements - Category 0 t Monomotivic Movements - Category D* Untransposed Pitch-strings or Transposed P/R Items - The Concept of Musical Prose - Local and Low-grade Congruities.

V. USE OF THE ANALYTIC CATEGORIES IN ANALYZING REPRESENTATIVE MOVEMENTS...... 229 Analyses of Athematic Movements (Cate gory F) - Analyses of Athematic Movements (Category E) - Analyses of Two Represen tative Monomotivic Movements (Category D) - Analyses of Two Representative Monomotivic Movements (Category C) - Analysis of a Representative Imitative "Contrapuntal" Movements (Category B) - Analysis of a Representative Polymotivic, Sectionalized Movement (Category A). VI. SUMMARY AND CONCLUSIONS...... 305 BIBLIOGRAPHY...... 320 LIST OP TABLES

Table Page 1. The total mtmber of p-c seta and their distribution into the total number of symmetrical CQ*s and i-c equivalent C Q 's,,.,.. 92 2„ A vertical/horizontal count for Op. 19/1 ...... 101 3. Raw data for the CQ count of Schoenberg's 0pp. 11, 19, and 23 ...... 105 4. Summary of results of the CQ tabulation in Schoenberg's 0pp. 11, 19, and 23, and Brahms' Op.76 piano pieces ...... 110 5. The ten most commonly appearing CQ^'s and CQ^'s in the Brahms and Schoenberg-^ sample s .... 112 6. The average number of different CQ's of each size appearing in a given movement in the sample ...... 115 7. A comparison of anagram and i-c relations 123 8. Some factors that give contextual, emphasis to melodic items ...... 177 9. Points of recurrence in 0pp. 11, 16, 19, 21, and 23...... 191 10. The six categories of formal recurrence, listed in order of the conventionality of their constructive procedures ...... 193 11. Two low-grade congruities in Op, 16/5 ...... 237 12. The form al c a te g o riz a tio n of each movement in Pierrot Lunaire. Op.21 ...... 254 13. Local congruities in Op. 11/3 ...... 270 14. Points of recurrence in Schoenberg's instrumental works, 1923-1936 ...... 317

VI LIST 0? EXAMPLES

Example P&6 1. Two contrasting Hauptstimne passages, a conjunct one from Op.21/3 (a) and a disjunct one from Op.21/17 (b) ...... T7 2. Perle's analysis of Op.11/1, mm.1-3, showing "cell” groupings ...... 40 3. Regers String Quartet, Op.109, I, mm.32-39, displaying fast harmonic rhythm...... o2 4. Two possibly analogous enharmonic spellings in Op. 19/1, mm.3 and H ...... 5. Two respellings of a single pitch in Op. 19/3, mm.7 -8 ...... «...... 67 6. Two more examples of enharmonic respelling from (a) Op.23/1, mm.1-2 and (b) Op.21/6, m.21...... 68 7. Op.11/2; Consistent spellings of motivic Dp in m.2 and C#'s in mm.5 -6 ...... 69 8. Op.21/5: "Seventh chords" at the end of m.11, spelled to show their distinct make-up ...... 69 9. Structures containing a major seventh in Op.16/1 and Op.2l/4 ...... 76 10. Three-note structures containing a major seventh and some inner interval ...... 76 11. Three types of chords; (a) tertian. |b) whole-tone, and (c) pandiatonic; ^d-g) are incomplete chords, with if) and (g) implying (h) and (i), respectively...... 79 12. Inversion related CQ’s in m.1 of Op. 19/5 ...... 88

- .. . ■ . ' ' 13. Instances of anagram (A) and inversion (I) relations in Op. 1 1 / 3 . ; ...... 124 - vii- 14. Inverted "counterpoint" in Op.23/2, creating a series of interval-class in v e rs io n s ...... 126 15. Layered>texture in Op.21/5, created by CQj's in each hand of the piano, beneath a canonic passage (*) ...... 129

16. Op.19/3: semitone displacement of each pitch in left hand from the augmented triad in right ...... , '31 17. Congruities of contour (a and b) from Op.16/5, and of i-c inversion (c and d), from Op. 19/1 ...... '37 18. Three examples of semitonal construction: (a) octave displacement in Op.23/1, (b) chromatic saturation in Op. 19 /l, and (c) chromatic saturation in Op.16/2 ...... 140 19. Three examples of direct and indirect identities and neighbors from (a) Op.21/2, (b) Op.21/5, and (c) Op. 11/3 ...... 20. Op.21/11, mm.23-24: The two hands exchange pitches in an application of indirect neighboring reminiscent of Stimmtausch.... 142 21. An arpeggiation of CQ 1425 in m.2 and its vertical representation in m .4 •• of Op. 11/2 ...... 143 22. The piano part in Op.21/13, m.13, showing a great deal of semitonal motion displaced by o ctav e ...... 145

2 3 . An octave reduction of the left hand of Ex.22, showing the degree of indirect semitonal motion ...... %5

24 . Examples of atonal quasi-sequences from (a) Op.11/2, mm.9-11, (b) Op.21/3, m .13, and (c) Op. 21/ 5 , mm.10-11...... 147 2 5 . A brief canonic passage in Op.11/1, mm.2 5 -2 7 ...... 149

V l l l 26. Three examples of metrically displaced ostinati from (a) Op,11/2, (b) Op.16/1, and (c) Op.21/2 ...... 152: 27. Examples of metrically displaced melodic items in (a) Op.11/1, mm.14-16, (b) Op.11/3, mm.2-3, and (c) Op.1l/3, mm.32-33.. 153 28. Op. 19/3: Displacement of a note-value pattern from m.2 to m.3 ...... 153 29. Three examples of rhythmic diminution in (a) Op.21/2, mm.25-27, (b) Op.16/2, mm. 177-78, and (c) Op.16/4, mm.265-67 ...... 154 30. Interval expansion and contraction in Op.11/1, m.13 ...... 155 31. Pitch elimination in Op.21/2, mm.21-22: The D# is eliminated before the second ...... 155 32. Two small recurring items (a and b) from Op.21. Imitation (c) involving the second item from Op,21/13, m.27...... 181 33. Two common melodic items as they occur in Op.2l/lO, m .1...... 162 34. Two florid passages (a) from Op,21/2, mm.30-31, and (b) Op,21/14, where the individual pitches become subordinate to the coloristic effect...... ,,.,..,...... 163 35. Nine motivic transformations according to Schoenberg's analysis of Op.22/1 ...... 165 36. Conventional connections between main and concluding themes in Mozart's (a) K.385, (b) K.550, and (c) K.551 ...... 173 37. Op,9: The "tru e p rin c ip a l tones" (mai&ed x) of the f i r s t theme (a ), when inverted, produce the first four notes of the second theme (b), according to Schoenberg's analysis ...... 174 38. A loud dynamic creating contextual emphasis of a non-reourring item in Op.11/3...... ■ 181 ix

r 39. An item heard once at fff near the end of . q . Op. 16/5 ...... — ...... 40. Three motives from Op,11/2, showing the congruity of CQ 1425 between A and C ...... I 98

41. An example of a recurrence with a change of note-values from Beethoven's Third Symphony, fourth movement ...... 202

42. An apparent instance of retrograde inversion in the final measure of Op. 2 3 /1 ...... 204 43. Op. 23/1 : The f i r s t fo u r p itc h e s of the motive in inversion, m ,7...... 204 44. The local congruity of direct repetition in Op.21/5, mm.33-34 ...... 21? 45. A highly varied canonic passage from Op.2 1 /8 ...... 217 46. Op,21/6: The contour congruity in the opening cello part ...... 219 4 7 . A CQ congruity in Op. 19/4, OQ 1416 ...... 221 48. Op.19/4: A congruity of OQ supported by a congruity of note-value pattern ...... 222 49. A contour congruity and an antecedent- consequent re la tio n s h ip in Op. 11/1...... 224 5 0 . A rep eated OQ in Op. 16/5...... 226

5 1 . Op.16/5: The re tu rn of the f i r s t th ree pitches of the Hauptstimme at m.447...... 240 52. Congruity lis t and diagram for Op. 16/5 ...... 240

, 53. A contour congruity in Op. 19/1 ...... 242

34 . Two points of imitation in Op. 19/1 ...... 243 55. Semitonal voice-leading in Op.19/1 ...... 244 56. Congruity list and diagram for Op. 19/1 ...... 245 57. A four-voice recluctiôn of the right hand in mm.1-4 of Op.19/3i showing melodic organization ...... 246

58. Op. 19/3 reproduced in its entirety to show CQ c o n g r u i t i e s ...... 247 59. Congruity list and diagram for Op. 19/3 ...... ^49

60. Op. 19/5 in its entirety, showing several congruities of CQ and a contour congruity... 252 61. Congruity list and diagram for Op.19/5...... 62. Congruity list and diagram for Op.21/4 ......

63. Op.21/6, m.20, cello part, shown in (a), and an octave reduction, showing chromatic saturation,in (h) ...... 25o

6 4 . Congruity list and diagram for Op,21/6,.,. „. 258 65. Idiosyncratic figures as they appear in Op.21/10 ...... 260 66. Congruity list and diagram for Op.21/10 ...... 260 6 7 . Congruity list and diagram for Op.21/12 ...... 261 68. The brief "Galgenlied," Op.21/12, consist ing of one continuous accelerando ...... 263 69. A contour congruity in the piano part. Op. 2 1 /1 9 ...... 264 7 0 . A contour congruity in the cello part. Op. 21/ 19 ...... 265 7 1 . Congruity list and diagram for Op.21/19 ...... 265

7 2 . Contour congruities between mm. 1 and 19 and 1 and 21 in Op.11/3. Also shown are the CQ^'s in the L.H; of m.1 9 ...... 266

73. O p. 11/ 3 , m.27: avoidance of octave doubling using only four different C Q j's...... 272 74. Chromatic saturation in Op.19/2, mm.6-7; only Bb and F are absent ...... 273

xi 75, Op.19/6 reproduced in its entirety to show the use of exploited chords CQ 273 and OQ 255.. 275 76, The opening of Op.21/9, which recurs inm. 13... ^76 77, Op,21/9, ram.4-6 and 13-16, showing multiple appearances of CQ 147...... 277 78,..The exploited chords of Op,21/14, which begin and end the movement ...... 278 79, Op,21/14, m,9: sequence of fourth chords, CQ 255...... 279 80, The pitc h -s trin g in Op, 19 / 4 , re c u rrin g in m,10. ^81 81, The very b r ie f motive in Op,21/2, mo2, and its recurrence in m ,7...... 282 82, A local pitch/rhythm item in m,8, transposed in m, 10 of Op,21/2 ...... 283

8 3 , Contour congruities in the violin Hauptstimme nf Op,21/2 ...... 283 84, A transposed pitch-string in the violin Hauptstimme of Op,21/2, ram,2-8 and 8-9 ...... 284 8 5 , The p itc h - s tr in g of Op.23/2, appearing in the first measure...... 285 86, The only horizontal restatement of the string of Op, 23/2 that does not include octave displacement of any pitches ...... 286 8 7 , A horizontal statement of the string in Op. 23/ 2 , with the F and A displaced an octave higher...... 286 88, A verticalized statement of the string in Op, 2 3 /2 ...... 287

8 9 , Another partly verticalized statement of the string in Op,23/2 ...... 287

90 , The stretto treatment of three inversions of the pitch-string of Op,23/2 ...... 288

91 , A local pitch-string in Op, 23/ 2 . with corre sponding groups labelled (a), (b), (c) and(d)., 289 xii 92. The motive of Op.21/13, stated in m.1 and restated in mm.8-9 and m.l? ...... 293 93. Op.21/13» mm.33-35: combined diminution in the clarinet and augmentation in the flute... 294

94 . The lengthy recurrence in Op.21/21, . in mm.14-16, appearing an octave higher a t OFL...... 295 95. Op.21/21: a contour congruity in the piano between mm.9 and 19 that is not supported by OQ congruities ...... 296 96. The motive of the "passacaglia" in Op.2l/8. „... 297 97. The motive of Op.21/8 in rhythmic diminution, also spelled out in the original by the first note of each group of eighths ...... 298 98 . A diagram of the distribution of the motive in Op.2 1/8 ...... 299 99. Op.16/2, motives a and b ...... 301 100. Op.16/2: Threefold ostinato in celeste, flute and bassoon ...... 302 101. A diagram of the six sections of Op.16/2, delineated by the presence or development of a, b and c ...... 302 102. Op.16/2: the Hauptstimme at m.130,’ whose first three notes also appear in the celeste ostinato, a major tenth higher 303

X l l l INTRODUCTION

This study deals with the music composed by

Arnold Schoenberg between 1908 and the early 1920's, a period defined by distinct and deliberate changes of style. The end of the tonal, "late; Romantic" period of his output was noted by Schoenberg in reference to his Buch der hëneenden Gflrten:

...I was inspired by poems of Stefan George, the German poet, to compose music to some of h is poems and, su rp risin g ly , w ithout any expectation on my part, these songs showed a style quite different from everything I had written before. And this was only the first step on a new path, but one beset with thorns. It was the first step towards a style which . has since been called the style of ’atonality.'

Much of this study deals with the change in idiom that Schoenberg has described in his own writings, the result of which is commonly referred to as "free atonality," or simply "atonality." While the corresponding works of Alban Berg and Anton Webern are in a similar atonal idiom, this study concentrates on the music of

*Arnold Schoenberg, "How One Becomes Lonely" ( 1937 ), in Style and Idea, ed. Leonard Stein (New York: St. Martin's Press, 1975, p.^9. Schoenberg, their mentor. Schoenberg's third phase was marked by the crystallization of the twelve-tone method. According to Josef Rufer, Schoenberg first disclosed the details of this method in July, 1921 :

It must have been about the time of the composi tio n of the Prelude [from Opus 25] (end of July, 1921 ) when Schoenberg to ld me, " ...to d a y I have discovered something which will insure the supremacy of German music for the next hundred years." It was the method of composition with twelve tones related only to one another.^

Of the three phases, the music of the middle period is, without question, the most difficult to analyze satisfactorily. The works composed before I 908 may be ana lyzed from a tonal standpoint, at least in terms of their basic organization. For the works after 1921, Schoen berg's own explicit presentation of twelve-tone prin ciples immediately supplied analyzers with some basic tools. The music of the intervening period, however, from

1908 to 1921 , lacks either clear ties with the past or a new systematic formulation comparable to that of the twelve-tone period. As a result, the analysis of atonal music has proven to be quite problematic. One might look

p Josef R ufer, The Works of Arnold Schoenberg, trans. Dika Newlin (London: Faber and Faber, 1962), p.*+$. 3 at the atonal period as an important precursor to the twelve-tone period, vrtiere serial techniques are the main feature. While there is some substance to this approach 1 (see p. below), an alternative view is at least as valid, although it has received far less treatment in the analytic literature. This alternative is to compare Schoenberg's atonal works to the preceding, "common-practice" period, to see wiiat specific elements contributed to the dramatic stylistic change. This approach can be taken only if one employs conventional analytic methods, i.e., those that have been known to yield meaningful re sults in the analysis of "common-practice" music. This study involves the description and the demonstration of techniques adapted to the analysis of Schoenberg's atonal music from conventional analytic methods. The present pur pose is to show.that these techniques can reveal more than serially-oriented analysis when applied to Schoenberg's atonal works.

Works to be Considered

No definite dates can be cited as the beginning or end of the atonal period, because it overlapped with the other two periods, the tonal period at the beginning and the twelve-tone period at the end. In both cases, Schoen berg continued to compose in the previous idiom, even H after works had been composed in the newer one. Neverthe less, a group of works can be assigned to the atonal period with reasonable certainty. The works composed during this middle period were: Three Piano Pieces, Op.11, Das Buch der hëneenden GSrten. Op,15, Five Pieces for Orchestra, Op.16,

Erwartung, Op. 17, Die glückliche Hand. Op. 18, Six Little

Piano Pieces, Op. 19 , Herzgewachse. Op,20, Pierrot Lunaire. Op.21, Four Orchestral Songs, Op.22, Five Piano Pieces, Op,23, and the Serenade, Op.24. Three works actually

overlap the period from 1920 to 1923 , 0 p p . 2 3 , 24, and 25. Schoenberg reported in his own words how he skirted the periphery of the twelve-tone technique in the Five Piano Pieces and the Serenade :

Time fo r a change had a rriv e d . In 1915 I had sketched a symphony, the theme of the Scherzo of vdiich accidentally consisted of twelve tones. Only two years later a further step in this di rection was taken..«When I took the next step in this transition towards composition with twelve tones, I called it 'working with tones.' This became more distinct in some of the piano pieces of Op.23...1 had at this time not yet discovered all the technical tools that furnish such abundance of variety as is necessary for expansive forms...The closest approach happened in the Serenade, Op,24, which, besides, already contains one really twelve-tone piece, the Sonnett Nr.217 von Petrarca. the fourth move- m ent.J

3Schoenberg, "My Evolution" (19^9) in Stvle and Idea, pp.88-90. 5 This transitional phase was described further in another place :

Before I wrote my first strict composition with twelve tones—in I 92 I--I had still to pass through several stages. This can be noticed in two works which I had partly written preceding the Piano S u ite , Op. 25—partly even in 1919, the Five Plano Pieces. Op.21. and the Serenade. Op,2^. In both these works there are parts composed in 1922 and 1923 vrtiich are s t r i c t tw elve-tone com positions, But the rest represent the aforementioned stages.

The combination of compositional techniques in both Op .23 and Op.24 makes it questionable whether either should be included in a study of the atonal works that preceded the twelve-tone period. Both of these particular works are actually transitional, preceding the first entirely

twelve-tone composition, the Suite, Op. 25. Of the eleven atonal works listed above, six contain vocal parts. Although these works appear to be composed in the same basic style as the purely instru mental atonal works, they differ from them in two major respects. First, although vocal parts offer a good op portunity to study the horizontal dimension of the music, they actually complicate the study of the vertical dimen sion. Schoenberg rarely doubles the voice part, making

4 Schoenberg, "Composition with Twelve Tones (2 )" (c.1948), in Stvle and Idea, p.248. 6 the already unfamiliar vertical combinations all the more difficult to assess» Also, a vocal tone affects the mu sical texture differently from an instrumental tone, be cause of timbre and the unique qualities of the lyrics. As a result, the decision of exactly how to include the vocal note in the vertical analysis is often arbitrary. These special problems warrant an exclusion of the vocal works from this study, but merit a separate study else where. Second, the vocal works differ from the instru mental works with respect to form. Schoenberg said that in the atonal period he discovered "how to construct

It c larger forms by following a text or poem. He reported very little , however, about form in the instrumental atonal works. Pierrot Lunaire, although it does have a text, contains only a spoken voice part, the pitch mate rial of which can be disregarded. It can be analyzed, at least vertically, as an instrumental work. Its twenty-one movements, while not displaying any clearly , programmatic forms, offer a wide range of examples from classically-influenced to quite unconventional formal procedures. It has, therefore, been included in this study. Of the transitional works, Op.23 and Op.24, the

^Schoenberg, "Composition with Twelve Tones (1)" ( 1941 ), in Stvle and Idea, p.217» 7 former is a set of piano pieces that has been included in this study because it may be directly compared with the other atonal piano works, Op,11 and Op.19, even though the last movement is a simple twelve-tone piece in which the prime form at original pitch level is used exclusively. The Serenade, Op.24, has one vocal movement as well as some fairly sophisticated twelve-tone applications. For these I ma sons, it has been excluded from this study. From the above evidence, the years 1908 and 1921 mark what Schoenberg considered to be the crucial transitions in his evolution. The completion dates for the purely instrumental atonal works, however, span the years ]909 to 1923» The chronology of these works, worked out by Rufer,° has most recently been revised by Jan Maegaard. According to Maegaard, the completion dates for the atonal instrumental >forks are; op.11 and

Op.16, August, 1909; Op . 19 (1-5) February, 1911 ; Op . 19

(6); June, I 91 I; Op.21, July, 1912; Op.23 (1-2), July,

192 O; Op .23 (3-5), February, 1923.

^Rufer, The Works of Arnold Schoenberg. ^Jan Maegaard, Studlen Zur Entvicklung des dodekaohonen Satzes bei Arnold Schoenberg (Copenhagen; William Hansen, 19 7 2 ).Volume 1 is a chronology that largely supersedes Rufer's. 8 The Establishment of an Analytic Approach

The variety of compositional procedures, even within each particular multi-movement work, requires that the movements of these works be treated individually. Careful examination shows that some movements fit quite closely into a conventional scheme, \diile others appear to be unrelated to any prior practice except for the use of discrete pitch and note-value notation. Such variety presents a formidable obstacle to the systematizing of any set of analytic approaches. In a discussion of conventional music, an intui tive grasp of basic concepts, such as harmony and melody, can usually be safely assumed. In Schoenberg's atonal music, many of these concepts appear to be so altered that the customary axiomatic assumptions become questionable. For example, one need not establish the fact that there are harmonies in a Beethoven sonata before proceeding to analyze them. One could certainly deny that Schoenberg's atonal works are even:part of the classical tradition, thereby avoiding these basic theoretical issues. If one is to proceed, however, on the assumption that they are part of the classical tradition (even as a first step toward testing the validity of that assumption)a thorough reexamination of terminology is required. 5 When one considers a list of the constituents of a composition, the reasons become clearer why the ana lysis of Schoenberg's atonal works has proven to be so difficult in the past. Apel provided a practical list in his definition of analysis as

the study of a composition with regard to form, structure, thematic material, harmony, melody, g phrasing, orchestration, style, technique, etc.

When applied to the atonal music, the notions of form, theme, harmony and melody are often less apt than vihen used in connection with the music of the eighteenth and nineteenth centuries. Only through expanded definitions may these terms become meaningful when they are applied to much of the atonal music. The word "structure" has come into increasing use in twentieth-century music theory. In light of this,_it is interesting to note that of the nine constituents specifically enumerated by Apel, only "structure" and "technique" do not receive separate entries in his dictionary. The first constituent mentioned in Apel's list is form. According to Rufer, form is inextri-_ cably related to repetition:

^Willi Apel, Harvard Dlctibnarv of Music. 2nd ed. (Cambridge: The Belknap Press of Harvard University, 1972 ), p .36. 10 Only things which belong together and possess affinity can cohere, that is, become a form. In music, repetition is the seedbed in which this coherence is developed* Repetitions of the smallest formal element, the motif, have a unifying effect, and ensure that all parts of a work can be related to one another and thus create the necessary conditions for the building of its form. Music is unthinkable without repetition.9

From this point of view, the following statement by Schoenberg is tantamount to an assertion that his music is formless: "Substantially, I say something only once, i.e., repeat little or nothing.in a c tu a lity , how ever, it would be an extremely difficult undertaking, even for Schoenberg, to demonstrate that "little or noth ing" is repeated in his music. Many cases may be found, not only in Schoenberg's atonal works, but in his tonal and twelve-tone works as well, in which his assertion is a great overstatement. On the other hand, a work such as the th ir d movement of Op. 11 does indeed appear to have "little or nothing" repeated in it. In describing works that appear to be governed by a principal of

9josef Rufer, Composition with Twelve Notes, trans. Humphrey Searle (London: Barrie and Rockliff, 1970), p.25. lOsohoenberg, "New Music: My Music" (c.1930), in Style and Idea, p.102. u non-repetition, George Perle observed that "special ele ments may be emphasized and isolated.. .not as a means of 11 establishing focal points, but for the opposite purpose." The difficult and crucial question is: what exactly is not being lapeated? Obviously, if the notation of dis crete pitches and note-values is being employed, some in terval and note-value patterns must eventually repeat. Therefore, one must conclude that the items not subject to repetition in the atonal works are of the very kind that formerly were expected to delineate form. Often, in music of previous periods, these items, generally referred to as motives, are short melodic units whose formal sig nificance emerges through their repetition in the course of a work. According to Charles Rosen, the dimensions of these items are a factor in their identification, but so is the context .in which they are presented:

...in music before Schoenberg each separate occurrence of a motif connects with the others, either as part of a larger continuity or by being placed in a context that clearly recalls... its other appearances...But this continuity and sim ilarity are both refused us by Schoenberg.

George Perle, Serial Composition and Atonal- ity, 4th ed. (Berkeley: University of California Press, 1977), pp.18-19. ^^Charles Rosen, Arnold Schoenberg (New York: Viking Press, 1975), p.4l. 1,2 In the above citation, Rosen is referring specifically to Erwartune. Op, 17, considered by many to be the quintessen tial non-repetitive work. An accurate measurement of how little repetition occurs in Schoenberg's atonal works requires a systematic search in these works for the types of items that delineated form throughout the preceding periods of music. Such an examination, including consir. deration of the various means and contexts of repetition, makes up the major portion of Chapter IV of this study. As a means of making explicit the range of formal possi bilities that Schoenberg explored, a hierarchy of formal recurrence is established in Chapter IV. Using melodic recurrence as the standard for formal conventionality, the six categories in the hierarchy range from a high degree of recurrence to none. In the analysis of many atonal instrumental movements, the main question is not the famJliar one of what sort of form can be discerned, but the less usual question of whether any form can be discern ed . The traditional terminology for referring to vertical structures requires reexamination in relation to atonal music. Two terms that take on especially new meaning are chord and harmonv. the latter of which appears in Apel's list of compositional constituents. 13 In terms of exclusiveness, "chord" refers to a greater num ber of vertical structures than the more restricted term "harmony," but neither applies unrestrictedly to all ver tical structures. A chord is normally the simultaneous occurrence of more than two tones, identifiable within some system. It is not a tone cluster, or, more generally, not a structure containing a "non-chord" tone. A "har mony" may be defined not necessarily as a vertical struc ture per se, but at least as the implication of one, or its effect, or function. For example, a minor seventh chord is a particular type of vertical structure vdiich, in a piece of music written in a major key could convey the harmony of II, III, or VI. On the other hand, by the preceding definition of "chord," Bach's Two-part Inven tions contain no chords (except at the final cadences), but plenty of harmonies. Use of the word "harmony" im plies other notions, such as function or progression.

On the subject of harmony in the post-tonal works, Schoenberg reported a total independence of the p a rts :

...in sounding together they need not be related to a common harmony.no sort of "registerable" harmony has to result from the way they sould together;...if possible they should produce dissonances when they sound to g eth er (to show Ik. how little they are w orried).there need he no attempt to produce harmonic proeresiona ("registerable") ones, such as cadences or any ._ other identifiable fundamental progressions.... ^

With reference to the later twelve-tone method he said: " ...in twelve-tone composition harmony is no longer in any sense under discussion, nor is even progression...."^^ The word "harmony" i s th erefo re to be avoided whenever the significance of a given vertical structure should not be implied. Since "chord" implies an identifiable vertical structure, it may be safely used in conjunction with a cataloging system. The system of chord analysis described in Chapter II, based on the conventional notion of chord quality, provides a label for every possible simultaneity, permitting all simultaneities to be viewed as discrete chords. In this way, one can measure the degree of verti cal regularity in conventional terms. Proceeding with Apel's list of constituents, the notions of "melody" and "thematic material" represent the horizontal counterparts of chords and harmonies. These distinctions, vAilch remain fairly clear in the tonal

^^Schoenberg, "Linear Counterpoint" (1931), in Style and Idea, p . 291 . I^Schoenberg, "Linear Counterpoint: Linear Polyphony" (1931), in Style and Idea, p. 296. 15 idiom, become problematic in atonality. Traditionally, a "melody" may be thought of as simply a succession of sin gle tones given prominence in the texture. A "theme" is then an extended melody having formal significance achieved through some kind of repetition and/or develop ment in the course of a work. A f'motive" may then be thought of as a short melodic item having formal signifi cance. In atonal music, melodic prominence was difficult to insure, because of the extremely variegated texture and minimal repetition. These problems eventually led to Schoenberg's notation of the primary voice as Hauptstimme, first included in the Five Pieces for Orches tra, Op.16. Schoenberg distinguished quite carefully between motive and theme, as Rufer's detailed explanation of his terminology shows : a motif is the smallest musical form, consisting of at least one interval and one rhythm. The next sized form is the Grundeestalt or phrase, "as a ru le 2 to 3 bars long" (th e number o f bars depend ing on the tempo, among other things), and consist ing of the "firm connection of one or more motifs and their more or less varied repetitions." The next sized form, the theme,"arises from the need to connect several shapes together" and consists of 16 "the connection (here he expressly does not say firm) of the Grundeestalt (basic shape) with its more or less varied repetitions > The characterization of a motive as possibly consisting of as little as two notes permits quite small elements of repetition. Rufer also explained that the motive is "recognizable through being repeated many times; in this repetition the motif may either be altered or may remain unchanged."16 It is questionable to vdiat degree an altered two-note motive may remain recognizable. A' wide variety of melodic treatment is given the Hauptstlmme designation in the atonal works. An extended, relatively conjunct passage such as Example 1 (a) has been marked as Hauptstlmme, and a line as disjunct as Example 1 (b) has also been so designated. The variety of treatment of melodic materials in the atonal works is discussed in Chapter III below. While a total composition combines the consti tuents enumerated by Apel above: harmony, melody, etc.,

1$Rufer. Composition with Twelve Notes, p .vii. Note that the quotation, actually from a letter to trans lator Searle by Rufer, contains two definitions of Grund gestalt, one as "phrase," the other as "basic shape." In twelve-tone composition, the phrase and the row by no means necessarily coincide. I^Ibid, p.26. 17

Used by Faraisslon of Belmont Music Publishers, Iios Angeles, CsJ-ifomia 90049

Ex. 1. Two contrasting Hauptstlmme passages, a conjunct one from Op.21/6 (a) and a disjunct onig from Op.21/17 (b). the process of analysis, particularly of music as inac cessible as many of Schoenberg's atonal works, may be simplified in the initial stages by the isolation of cer tain constituents. This study concentrates on those con stituents that relate most directly to pitch organization: the vertical dimension, the horizontal dimension..(melody), thematic material, and form. Each chapter below isolates a particular constituent, Chapter II dealing with regular ity in the vertical dimension. Chapter III with melodic organization, and Chapter IV with the issue of melodic recurrence. As might be expected, Schoenberg's disregard for harmonic function drastically altered the vertical dimension. The melodic organization proves to be slightly more conventional. Although lengthy themes are scarce. 18 many shorter recurring motives are shown to be present. Formal details of individual movements are discussed in Chapter V, While some movements display a large-scale formal plan, others are organized into only brief and scattered fragments. There remains no indication that a generalizable principle of pitch organization exists for Schoen berg's atonal music. Schoenberg wrote in 19^9* "One day there w ill be a theory which abstracts rules from these compositions."^7 He, too, was apparently incapable of formulating such a theory. If these works are to be viewed as a part of the classical tradition,.then it should be possible to measure the extent to which tradi tional kinds of relationships exist in them. The far- reaching alterations that Schoenberg made in the musical language from 1908 to 1921 should then be easier to assess. One can make many substantive observations about Schoenberg's compositional procedures without having to rely on structural principles that took shape only at the very end of the atonal period. The following chapter con tains a survey of theoretical approaches to Schoenberg's atonality and a description of the conventional methods used in this study.

I^Schoenberg, Structural Functions of Harmony. (New York: W.W. Norton, and Co. , 1969)» p. 19^. Chapter I

BASIC APPROACHES TO ATONAL MUSIC

The many d i f f i c u l t i e s of tr e a tin g Schoenberg's atonal music nay be seen from an examination of the criti cal and analytic literature. Because the technical de tails of the idiom are so elusive, many commentators have merely chosen to present the historical and aesthetic conditions that led to Schoenberg's development of the new style. Those have attempted to clarify the ele ments of atonality have encountered the problem of fit ting the idiom, into a continuum from tonality to twelve- tone seriallsm. Certain relationships between Schoen berg's atonality and twelve-tone seriallsm can be ob served, such as the absence of a tonal center in both. The relationship between atonality and nineteenth-cen tury tonal practice has not been treated as extensively in the literature. The following summary of the findr ings of the major commentators shows which of these Issues have been raised and which have not.

19 2 0 The Aesthetic/H istorical Approach

Schoenberg's atonality has frequently been characterized In negative terms, e.g., the avoidance of repetition, the avoidance of tonal sonorities, etc. George Perle wrote, "It Is Impossible to state the fun damental conditions of atonality In general, except In a negative way..."^ Erwartune, Op. 17 has represented the ultimate negation of musical conventions for sev eral commentators (see p.157 below). Some commenta tors, such as H.H. Stuckenschmldt and Charles Rosen, have made the newness of the Idiom appear as an asset, without attempting to offer an explicit theoretical explanation of It. Stuckenschmldt wrote:

This 'style of freedom* did not stop with the suspension of tonal ties and the emancipation of the dissonance. Schoenberg produced In quick succession a large number of very varied works, a ll of which are alive with the excite ment of discoveries such as European music had not known since ,1600.^

Stuckenschmldt did not go Into detail about the nature of the "discoveries" In the atonal period. Rosen was slightly more specific, placing Schoenberg, Debussy,

IPerle, Serial Composition. P.1. 2h.H. Stuckenschmldt, Twentieth-Century Music, trans. Richard Deveson (New York: McGraw-Hill, I969), PP* 33“3^» 2 1 and Scriabin in the category of those composers \dio renounced certain long-accepted conventions:

The renunciation of the symmetrical use of blocks of elements in working out musical proportions placed the weight on the smallest units, single intervals, short m otifs....The expressive values of these tiny elements therefore took on an inordinate significance; they replaced syntax.3

Rosen did not elaborate on how syntax can be replaced or how music can remain intelligible in such a case. Schoenberg's own aesthetic evaluation of him self and his pupils also makes the renunciation of cer tain conventions appear in a positive way:

True, new ways of building phrases and other structural elements had been discovered, and their mutual relationship, connection, and combination could be balanced by hitherto un known means. New characters had emerged, new moods and more rapid changes of expression had been created, and new types of beginning, continuing, contrasting, repeating, and end in g had come in to u se .^

Although this type of characterisation contributes to the understanding of atonality as a stylistic move ment it does not answer specific analytic questions. The difficulty of describing the new means as some thing other than a negation of previous practice is

^Rosen, Arnold Schoenberg^ p.21. ^Schoenberg, "My Evolution," p .88. 2 2 evident in the wrltinga of Perle and of Allen Forte, the two major authors concerned with pitch organiza tion in atonal music. Perle said, "The 'free' aton ality that preceded dodecaphony precludes by defini tion the possibility of a statement of self-consist ent, generally applicable compositional procedures."5 Forte succinctly stated, "The structure of this com plicated music has not been well understood."^ Boris William P illin, in a specialized study of Schoenberg's atonal "counterpoint," concluded that, in comparison to tonal counterpoint, "there is hardly less preoccu pation with the vertical element in atonal counter point ; the preoccupation is merely reversed."7 The idea that the effects of tonal counter point are precisely those to be avoided in atonal "counterpoint" is echoed in William Austin's four "rules of harmony," \diich, again, are thoroughly n e g a tiv e : 1.) Avoid octaves, whether as moIodic leaps or as intervals between simultaneous notes.

5perle, Serial Composition, p.9. ^Allen Porte, The Structure of Atonal Music (Mew Haven: Yale University Press, 1973)j p .i x . Tsoris William P illin , Some Aspects of Counterpoint in Selected Works of Arnold Schoenberg (Los Angeles : Western International Music, 1971), p .90. 23

2.) Avoid major and minor triads and dominant seventh chords, either broken or sounding to g eth e r w ithout some o th er n o te . 3.) When a melodic phrase exceeds an octave in range, avoid exposing equivalent pitches in both octaves. Rarely use phrases of smaller range. 4.) Rarely use more than three notes in succession belonging to any one major scale. Never com pose a whole phrase of notes from one major scale. After a series of notes from one majorg scale, avoid returning soon to the same scale.

Many writers, including Schoenberg, have not consistent ly distinguished between "free" atonality and twelve- tone seriallsm in making observations about vertical com binations. Often, statements about twelve-tone serialism apply equally well to atonality. Leon Dallin, for example, said of twelve-tone "counterpoint":

Sonority, as a phenomenon independent of linear combinations, is of so little importance in the style, that principles of harmonic structure and progression are not given by its theorists, nor are harmonic formulas detectable in the compo s i t i o n s . °

This remark echoes what Schoenberg himself said about atonal and twelve-tone "harmony." All of the above

^William Austin, Music in the Twentieth Cen tury (New York: W.W. Norton and Co., 1966)pp.204-205.

^Leon Dallin, Techniques of Twentieth-Cen tury Composition (Dubuque, Iowa: W.C. Brown, 1957)» p . 186. 24

views portray the atonal idiom, in general terms, as one of constant fluctuation, or possibly even appar ent randomness.

Theories of Pitch Organization

Neither Schoenberg nor any other theorist has proposed a complete theory of pitch organization for Schoenberg's atonal music. The most conservative view is that Schoenberg's atonal music is actually tonal music in "disguise," This view was taken by Hugo Leichtentritt, who believed he could discern tonality in as late a work as Op. 19, composed in 1911. ■As evidence, Leichtentritt formulated what he called a "law" for chord progressions in two atonal piano works. Op, 1.1 and Op, 19; "Any two or three chords, no matter how dissonant, which can be resolved into the same chord, may be played together."11 He illustrated how the few chords that comprise Op, I9/6 (see p, 275 below) could be resolved to adjacent tones of an £ major triad. He also claimed to have found tonal im plications in the melodic lines. He summarized the hidden sim plicity he saw in Schoenberg's atonality,

lOHugo L e ic h te n tr itt, M usical Form (Cam bridge: Harvard University Press, 1951/, PP.443-4$0, l^lbld. p. 444 25

saying that "Schoenberg does his utmost to disguise plain progressions and chords and to make them appear strange and enigmaticUnfortunately, L eich ten tritt did not elaborate upon how two chords can "re solve Into the same chord." In spite of his Illus trations, his hypothesis remains fragmentary and has. received little subsequent support.^3 The most futuristic view Is the one that In volves seeking serial characteristics In the atonal works. Perle and Forte have both discovered some small examples of serial organization In the atonal works. Those works leading directly Into the twelve- tone period, Op. 23 and the Serenade, Op.24, of course, contain more extensive examples of seriallsm. Forte, In his ambitious effort to "provide a general theoretical framework with reference to which the processes underlying atonal music may be systemati cally described,"1^ did not claim to have provided

IZlbid. p.426. 13Rob@rt Suderberg, in "Tonal Cohesion in Schoenberg's Twelve-tone Music" (Ph.D. dissertation, the University of Pennsylvania, 1.966), has attempted to examine Schoenberg's a to n a l "harmony" from th e point of view of constantly changing tonal Implica t io n s . ^^orte. The Structure of Atonal Music. p . l z . 2 6

a general theory of atonal music. Moreover, Schoen berg's atonal works make up only a small portion of the works Forte considered. He investigated a much larger body of atonal works including those by Bartok, Stravinsky, and Scriabin. As a result. Forte and Perle's findings do not represent any sort of hypoth esis about Schoenberg's compositional procedures in the period, because they only consist of scattered analytic conclusions about isolated passages. The fully substantiated findings of Perle and Forte concern small units that they both refer to as "un-ordered pitch-class sets" (see p.S3 below). Perle pointed out that any vertical representation of a pitch"collection eliminates order as a considera tio n : The verticalization of linearly ordered ele ments imposes certain compositional restric tions that quite preclude its exclusive de termination of harmonic relations. And even verticalization, the only harmonic procedure ostensibly consistent with the premise of linear ordering, does not unambiguously represent this ordering.15

15Perle, Serial Composition, p.SM-. 27

Vlhen tinordered pitch-class sets are used in analyzing a work, they may actually be distributed horizontally, vertically, or in a combination of both dimensions. ■Although th e prime forms o f th e se s e t s are rep resen ted as successions by Perle and Forte, the most useful con ceptual basis for their application may be vertical rather than horizontal, so that one eliminates order at the outset. In his book on atonal music. Forte offered few arguments for the view that pitch-class sets ex plain the basic structure of Schoenberg's music. The majority of assertions deal with the interrela tionships between pitch-class sets, rather than their exceptional applicability to existing compositions.^^

^^There is no generally accepted term for the combined vertical and horizontal applications of a basic set. Rufer, in Composition with Twelve Notes, calls it "two-dimensional," which is perhaps the simplest designation available. 1?For discussions of the theoretical im plications of The Structure of -Atonal Music, see Richmond Browne's review in the Journal of Music Theory, F all, 197^, PP-390-M-15, and Eric Regener's article, "On Allen Forte's Theory of Chords," in Perspectives of New Music, v.13/1 (197^), pp.191- 212. 28

Forte only really confronted the Issue of the signi ficance of this particular system of analysis for Schoenberg's atonal works in a later article entitled "Schoenberg's Creative Evolution."^® Here, he offered more pointed evidence for idiat he called "pitch-class set-consciousness•" Forte's system of pitch-class sets involves three concepts that first became widely known through Schoenberg's twelve-tone method, namely the notions of pitch-class, interval-class, and verticalization. The interaction of these elements may be referred to as "twelve-tone relations." All three concepts are im plied in Schoenberg's writings, teaching, and composi tions, but were more clearly systematized by later twelve-tone theorists, notably Rufer and Milton B a b b itt. By the assumption of the first concept, the equivalence of pitch-classes, all pitches with the same name or with an enharmonic spelling (i.e., two C#'s or G and F#) are equivalent regardless, of the ■octave in \diich they are stated. This principle assumes the equivalence of both octaves and enharmon ies, and is exhibited in the well-known provision in

IGMusical Quarterly, v.44/2 (April, 1978), pp.133-176. 29 twelve-tone composition that the pitches of the series may be stated in any octave. Schoenberg did not state this principle explicitly, although it is implied not only in its many applications in his twelve-tone com positions, but in his statement that the "basic set consists of various intervals."^9 If, as Schoenberg implies, the intervals are the essential ingredient of the set, then octave displacement and enharmonic spelling must be secondary considerations. By the second assumption, the equivalence of interva1-classes, all equal intervaH ic distances, usually expressed in semitones, are equivalent, regard less of direction, octave displacement, compound, or Inversion. That is, the ascending minor third and the descending minor third, and even the ascending major sixth are all reducible to a distance of three semi tones, and are thus equivalent interval classes, i-c3. Interval-class equivalence can also be in ferred from Schoenberg's twelve-tone compositions and is vaguely implied in Schoenberg's statement: "The employment of these mirror forms corresponds to the principle of the absolute and unitary perception of musical s p a c e . "20 "Mirror forms" meant, to

^9schoenberg, "Composition with Twelve Tones (1)," p .219» SOlÈlâ, p.225. 30

Schoenberg, any inversion or retrograde relations. The fact that they may be freely substituted for one another implies some sort of equivalence. It is im portant to note that inversions can be by octave (i.e., complements) or by interval-class (i.e., "mirroring"). Both types of equivalence are assumed in twelve-tone relations. By the third assumption, that of verticali zation, horizontal materials retain their identity T^en contracted into vertical structures containing equivalent pitch-class material. Verticalization appears to be implied in Schoenberg's statement :

The elements of a musical idea are partly incorporated in the horizontal plane as suc cessive sounds, and partly in the vertical plane as simultaneous sounds. The mutual relation of tones regulates the succession of intervals as well as their association into harmonies.. .a basic set of twelve tones...can be used in either dimension, as a whole or in parts.21 This passage implies that the same "idea" may be rep resented along either (or both) of the dimensions. This "mutual relation" apparently governs both types of combination. In another passage dealing with ver ticalization, Schoenberg explained:

21Ibid. p .220 31

The main difference between harmony and melodic line is that harmony requires faster analysis, because the tones appear simultaneously, while in a melodic line more time is granted to syn thesis, because the tones appear successively, thus becoming: more readily graspable by the Intellect.22

This implies that because the pitch content is the same, regardless of the dimension in \diich it occurs, there is an indisputable affinity between a melodic segment and its vertical representation. From the preceding discussion, it is evident that the notions of pitch-class, interval class, and verticalization are an integral part of Schoenberg's twelve-tone seriallsm. It is not as obvious, however, that they are a part of his atonal theory. Forte's ex tension of the notion of pitch-classes (vrihich are ordered in a twelve-tone series) into unordered sets has no basis in Schoenberg's writings. Since Schoen berg's theoretical writings on pitch-classes deal only with ordered rows or segments, only the music itself can supply what small evidence there is for the use of unordered p-c sets. In order to see the relation between unordered p-c sets and ordered row segments, it may be useful to think of unordered pitch-class

22schoenberg, "Ity Evolution," p.87. 32 sets as vertical structures that may be ordered dif ferently in each instance of horizontal representation. Two essential questions may be raised with regard to the effect of twelve-tone relations on atonal music. First, is there evidence, either in Schoen berg's atonal compositions or his writings, that twelve- tone relations (or idiat Forte called "set-consciousness") were operating prior to the formalization of the twelve- tone technique in 1921? Second, for the compositions before and after 1921, how significant are twelve-tone relations, to the compositional process, or to the co herence they afford a work? The evidence fo r " set-co n scio u sn ess" (i.e., the application of twelve-tone relations) before ,1921 can appear in two possible forms: historical and musi cal. The historical evidence comes from sources outside the actual atonal compositions: Schoenberg's writings and certain facts relating to the composition of the atonal works. Because Schoenberg so explicitly re corded his twelve-tone principles, one might expect to find the atonal principles laid out with some precision. The writings on atonal music give one more the im pression of aesthetic essays, than of descriptions of technical procedures. In one such essay, he wrote: 33

...I became the first composer in this period to write shorter compositions. Soon thereafter I wrote in the extreme.short form. -Although I did not dwell very long in this style, it taught me two things: first, to formulate ideas in an aphoristic manner, which did not require continuations out of formal reasons; secondly, to link ideas together without the use of formal connectives, merely by juxtaposition.

In another place, he referred to the atonal phase as a twelve-year transition to the twelve-tone period:

After many unsuccessful attempts during a period of approximately twelve years, I la id the foundation for a new procedure in musical construction...24

These passing references imply that Schoenberg did not have a broad constructive procedure during the atonal p erio d . It is important to consider \diether struc tural factors, such as vertical/horizontal relation ships and "mirror forms," eventually began to out weigh the musical surface, i.e., motives, phrases:^ :etc. » in compositional importance. There are at least two documented indications that the musical surface was s till paramount to Schoenberg, even after the develop ment of twelve-tone seriallsm. Alban Berg, tdio

23schoenberg, "A Self-Analysis" (19^8), in Style and Idea, p. 78. 2^Schoenberg, "Composition with Twelve Tones (])," P.218. 34

frequently acted as an apologist for Schoenberg, said of melody in atonal music:

In this music, as in any other, the melody, the principal voice, the theme, is fundamen tal...th e course of the music is in a sense determined by it.^^

On the same subject, Schoenberg described how coher ence could be maintained in an atonal composition, in spite of the absence of a tonic:

Coherence in classical compositions is based— broadly speaking—on the unifying qualities of such structural factors as rhythms, motifs, phrases, and the constant reference of a ll melodic and harmonic features to the centre of gravitation—the tonic. Renouncement of the unifying ^ower of the tonic still leaves all the other factors in operation.

The "other factors," rhythms, motives, phrases, appear to hcve a corresponding role to Berg's "melody," "principal voice" and "theme." Although Schoenberg did not imply in his writings that notions like pitch-class and interval- class were operating in the atonal works, he employed

^^"What is Atonality?" radio interview with Alban Berg (April 23, 1930), trans. M.D, Herder Norton, in Nicholas Slonimsky, Music Since 1900, 4th ed . (New York: S c r ib n e r 's , 1971 ) , PP.' /131 313. 26schoenberg, "My Evolution," p. 8?. 35 the device of verticalizatlon as early as the still tonal Kanaaersymphonie^ Op. 9 (.1906). I t seems that the horizontal conception of such elements almost "justifies" their use as vertical structures: the accompanying harmony came to mind in a

According to these statements, the notion of vertical materials being derived from horizontal materials (actually the reverse of arpeggiation) was operating at least as early as 1906. Another historical issue concerning the pos sibility of any sophisticaled system of pitch organi zation in the atonal music is the brief elapsed time of composition for many of the works. While occa sional instances of "set consciousness" «110 l^^gi- nable, it is unlikely that Schoenberg could have com posed so quickly if he were employing complex pitch- class set relations on a large scale. As Jim Samson sta te d :

27schoenberg, Harmonlielehre. 3rd ed, (Wien: Universal Edition, 1922), p. 484, my trans la t io n . 36

•••the reader mast judge for himself whether three movements from Pierrot Lunaire could have been composed in one day using these methods.^ or the whole of Erwartune in seventeen days 1

The historical evidence, both from Schoenberg's writ ings and the facts concerning the composition of the atonal works does not present a convincing case for Schoenberg's use of formalized principles of pitch organization in these works. It is also possible to seek evidence of "pitch-class set consciousness" within the atonal mu sic itself. Because "set consciousness" is not a generally accepted musical concept, it is unclear idiat forms such evidence might take, except perhaps that a requisite number of pitch relations in a given work be accounted for by twelve-tone relations among unordered p-c sets. Forte's book The Structure of Atonal Music was not intended to demonstrate "set consciousness" in Schoenberg's atonal music, since it deals with many other composers, some of whose music is not generally considered to be part of the atonal corpus, such as Debussy. Porte's article "Schoenberg's Creative Evolution^" however,/assumes the single purpose of demonstrating "set consciousness," not only in Schoen berg's atonal works, but in some earlier tonal works

28jim Samson, Music in Transition (London: J.M. Dent and Sons, 1977), p.220. 37 as well. In order to prove "set consciousness" in these works, Forte took Schoenberg's musical "signature" : Es-C-H-B-E-G and sought instances of it. Schoenberg flat ly stated that "private biographical hints" were of no interest to him during the period.Furtherm ore, only by the use of twelve-tone relations among unordered p-c sets can a great number of musical items be shown to be related to Schoenberg's "signature." The conclusion is left to be drawn that Schoenberg was conscious of such connections. " In his article, Forte first reduced the "signa ture" to the set of pitch-classes with the prime form (0,1,2,5,6,9), also called set 6Z-4^ in Forte's table.30 According to Forte's system of pitch-class set relations, sets reducible to the same prime form (by pitch-class and interval-class equivalence) are equivalent, although they may be inversions or transpositions of the original set. Thus, any set of six pitch-classes is "equivslent" to twenty-three other sets by transposition and/or inversion. Furthermore, in many of his analyses. Forte applied the notion of subsets, by which a great number of three-, fo u r-, and five-note sets were shown to be related to the six-note set 6Z-i+4. Because Forte still found only a

pQ Schoenberg, "New Music, Outmoded M usic, S ty le and Idea," (19^6) in Stvle and Idea, p. 120, SOForte, The Structure of Atonal Music, p .179. 38 small number of scattered instances of 6Z-kh and i t s subsets, the article does not offer convincing evidence of "set consciousness" in Schoenberg's early works. Probably the most conclusive sort of evidence would in volve an exhaustive count of pitch groupings and a tabu lation of the most frequently occurring sets. Such a count was conducted on the vertical structures of Schoen

berg's atonal piano works, 0pp. 11, 19 and 23 (see Chapter II below), using a less serially-oriented cate gorization system than p-c set analysis. Conducting an exhaustive count is preferable to selecting a specific set and then seeking evidence of its applications as Forte did. It might be interesting to note that ninety- one six-note "chords" occur in Schoenberg's atonal piano works, and that nine of these chords are reducible to

the same set as Schoenberg's "signature": Op.ll/ 3 , measures 1 and 2; Op. 23/2, measures 9; Op, 23/^, twice in measure 30 and tvri.ce in measure 3 I 5 and Op,

23/5? twice in measure 4 3 . None of these occurs at the pitch level of the original "signature," Although twelve-tone relations among unordered pitch-class sets have, at best, been visible in only small sections of atonal compositions, they continue to be used by some analyzers in the absence of any compre hensive analytic theory. Besides lacking demonstrated 39 applicability, p-c set theory also lacks precise rules for grouping notes into sets. Perle, who referred to p-c sets as intervallic "cells," remarked that the cell

...may operate as a kind of microcosmic set of fixed intervallic content, statable either as a chord or as a melodic figure or as a combination of both. I ts components may be fixed with re gard to order, in which event i t may be employed, like the twelve-tone set, in its literal trans formations; prime, inversion, retrograde and ret rograde inversion. (Where it is stated as a simultaneity the order is not generally defined, so that only, "prime" and "inversion" are meaning fu l terms.

The parenthetical remark also applied to unordered p-c sets. According to this account, pitch-class sets or cells may be distributed vertically, horizontally, or two-dimensionally. The main criterion for analytic groupings in any of the three distributions appears to be nothing more than contiguity on the printed page. Such sets are frequently constructed from pitches that are sounding across a time span during which pitches not included in the supposed set or cell are also

31Perle, Serial Composition, p.9- 40 sounding, often in the same voice. An instance of this sort of grouping by Perle is shown in Example 2.^2 The analogous pitches appear to be those occurring on beat two of mm. 2 and 3: - F - B and - A - D& . Only the major seventh is common to both.

P e r le *s a n a ly s is : I P

A pparently analogous p itc h e s:

Ex. 2. Perle's analysis of Op,11/1, mm.1-3, showing "cell" groupings.

There are cases in which analysis using un ordered pitch-class sets or cells reveals a definite organization. Perle found some examples in Schoen berg's piano pieces, 0pp.11 and 23. In Op.11/1, the first three notes form a basic cell that can be traced through various aspects and transpositions at several points in the movement. Perle draw a few more examples

^ Ibid, p.11. The circled notes represent ,various distributions of the "basic cell." 41 from Op, 23, 'Which is an immediate precursor of the twelve-tone period. Perle compared the conclusiveness of these kinds of pitch relations in atonal music with similar relations in twelve-tone music:

Many of the procedures discussed in connection with "free" atonal composition continue to operate, but with the important distinction that they may now be related to a single all- pervasive primary formation.

Thus, in "free" ato n ality , there are numerous c e lls, none . of which is pervasive, and large portions of a work are de rived" from no c e ll, making them even:"freer".than.the rest, Although a fairly conservative atonal work like Op.11/1 raises the issues of the grouping of notes and the organization that grouping reveals, the more inac cessible atonal works pose an even greater challenge to the discovery of pitch organization. The piano pieces of Op , 19 have proven to lack an identifiable formal plan. Rufer characterized these pieces as follows:

These are essentially pieces of an aphoristic brevity, which makes i t possible to comprehend and survey the whole of each one, both in form and content, in one breath, as it were; thus no p articu lar formal methods are necessary. In pieces of six to seventeen bars' length no development is possible; th is would naturally have required a more differentiated formation. Thus here the form is limited to the shape of the aphoristic thought.34

^^Rufer, Composition with Twelve Notés, p. 59 42

In spite of this absence of "formal methods," Perle included an example from Op.19/1 of idiat he called '.'the subtle interrelation of microcosmic elements in an athematic work..."^^ According to Rufer's description of these pieces, only minute details of organization are likely to emerge, and more intricate analyses are prone to appear even more contrived and far-fetched. From the preceding discussion, it should be apparent that twelve-tone relations play only a minor role in the pitch organization of Schoenberg's atonal music. Even in the twelve-tone music, where these re lations are known to be omnipresent, they treat only a single facet of a work's construction. Perle warned against placing too much emphasis on the row analysis of twelve-tone compositions!

A mere description of the set and the transpo sitions and transformations to idiich it is subjected cannot be advanced as an "explana tion" of the work itself, but only of the sub structure, the system of tone relations upon idiich the work is b a s e d .

Perle, unfortTinately, did not suggest \diat kinds of ob servation could contribute to a work's "explanation."

35perle, Serial Composition, p.21.. 36lbld, p.60. 43

Schoenberg made a very similar observation, but from the standpoint of composition, rather than analysis :

•••many composers working with twelve tones are mistaken when they expect too much from the mere application of a set of twelve tones*••This alone could not create music* Doubtless.••other forma tive forces which produce the configurations and variations are even more important*37

The views that twelve-tone relations do not "explain" a work and cannot crsate music by themselves imply that other means of construction must be in operation* In the atonal music, where even twelve-tone relations are largely absent, these "other formative forces" are the only potential organizational elements left* The q u e stio n v/as r a ise d above whether Schoen berg, in his twelve-tone music, was justified in rely ing on twelve-tone relations for the aural coherence they ostensibly promote* Some studies have been con ducted on the subject of the aural coherence contributed by twelve-tone relations*^® Bruce Thrall summarized

37schoenberg, "Composition with Twelve Tones (2)," p.246* 3®see Diana Deutsch, "Memory and Attention in Music," in Music and the Brain, ed. MacDonald Crltchley and P.A* Henson (London; William Heinemann Medical Books, .1977); also Edward James Largent, Jr., "An in vestigation into the Perceptibility of Twelve-Tone Rows," (Ph.D. dissertation. The Ohio State University, 1972 ). 44

results from the studies he reviewed as follows: (1) Subjects could not distinguish between ex amples using two different series. (2) Professional musicians and students did not differ significantly In their ability to distinguish serial structures. (3) Subjects were able to correctly Identify horizontal, monophonic statements of the three derivatives of a series. (4) The ability to Identify the derivatives of a series was Improved by training.39 If, as the first finding Indicates, examples using two different series are not distinguishable, then the series must play a much smaller role In the aural effect of the music than might otherwise be assumed. Also, If professional musicians could distinguish serial structures no better than students, then the type of "ear" required to hear serial structures must d if f e r In some way from the to n a l "ear." The aural coherence afforded by the use of twelve-tone relations Is an extensive topic. It should be stressed, however, that Schoenberg wished to make clear the limitations of these relations In contribu ting to a work's coherence. He frequently exhorted analyzers to investigate other aspects of a work's

^%ruce E. Thrall, "The Audibility of Twelve- Tone Serial Structures" (Master's thesis. The Ohio State University, I960). 45 construction, many of ^Aioh he felt could not be served by the twelve-tone method. In one of his later essays, he enumerated some of the insufficiencies of the method:

The method of composing with twelve tones pur ports reinstatement of the effects formerly fur nished by the structural functions of the har mony. It cannot replace a ll that harmony has performed in music from Bach—and his prede cessors—unto our time: lim itation, subdivision, connection, junction, association, unification, opposition,-contrast, variation, culmination, declination, ebbing, liquidation, etc. It also cannot exert influences of similar ways on the inner organization of the smaller segments of ;diich the,greater divisions and the whole work consists.40

Despite Schoenberg's personal jargon, one can see that the influences he referred to must be those elements of coherence associated with earlier, "common-practice" music. If these,elements are more important than twelve-tone relations, then, by Schoenberg's own evaluation, their effect in a ll of Schoenberg's works merits a thorough examination. Because this sort of examination, even v^en conducted for atonal music, fo cuses upon conventional "common-practice" procedures, it may be simply designated the "conventional analytic approach."

^Schoenberg, "Composition with Twelve Tones (2)," p.24$. 46 The Conventional -ABalr/tic ,Approach

■Although th e main fe a tu r e s o f a to n a l music appear to consist of the negation of various prior conventions, many analyzers have hoped to find some hitherto unknown means of organization it it (such as p-c set relations) that would account for its newness. The evidence for new means of organization can be sought in Schoenberg * s writings with mixed results. Because he frequently failed to make an explicit dis tinction between "free" atonality and twelve-tone serialism, it is often difficult to tell which he is referring to in a given statement. Nevertheless, many of his aesthetic statements appear to be equally applicable to both idioms. Both were atonal; serial ism apparently grew out of the need Schoenberg felt to organize his atonal materials. Schoenberg was aware of the expectations of the musical public of his day, and often tried to draw parallels between, his procedures and conventional nine teenth-century practice. S till, on some occasions, he nearly admitted that his style was fundamentally dif ferent from a ll prior music. Around 1930, he wrote:

Now, if I recall that I confessed to repeating little or nothing in my music, then you w ill rightly ask, 'Why? Vftiy make it so hard for the 4-7 lis t e n e r ; \Axy not make things easier for him, In the waj he needs; idiy say only once things that are hard to perceive and remember even 'vUien heard repeatedly, so that one completely loses the thread and.doesn't begin to compre hend a l l th e th in g s th a t come la te r ? ' To this I have to say* '1 can do It no other way, and It does not work any other way. Only, I did not choose to write like that, I do not go out of my way to write like that, and It would be a relief to feel I might do It differently.'

Because the differences between Schoenberg's music and preceding works are clear from his compositions and his commentaries, there Is a need to examine these differ ences In detail. Because the concept of aural surface coher ence Is widely recognized (by Schoenberg's school and his critics alike), It offers a useful frame of refer ence within which Schoenberg's atonal works may be analyzed. Although other terms may be redefined, our Intuitive notion of conventional aural coherence should be maintained, because It directly determines how music Is heard. Conventional, aural surface co herence served as the point of departure for the ex tensive study of Schoenberg's atonal works by Jan Maegaard, 42

^^■Schoenberg, "New Music: .My Music,'’ p.104. ^^Maegaard, Studlen, v.2. 48

The focal point for Maegaard's study was Schoenberg's succinct statement about twelve-tone com p o sitio n s

'You use the row and compose as you had done it previously#' That means: 'Use the same kind of form or expression, the same themes, melo dies, sounds, rhythms as you used b e fo re . '^3

Maegaard simply sought to establish the meaning of "as you had done it previously." If the row was the only new element in twelve-tone composition, then the idiom must be the same as "free" atonality in all other re spects. In other words, Maegaard conducted an exten sive search for those "other formative forces" (see p .^3 above) that Schoenberg claimed were operating in his twelve-tone works. Part of Maegaard's method involved a "dis tinction between the audible and non-audible, between motivic and structural relationships."^ By "audible" he explained that he meant "immediately audible," and apparently believed that "structural" relationships are not immediately or explicitly audible. For the

^3schoenberg, "'Schoenberg's Tone Rows'" (1-936), in Stvle and Idea, p. 213. With this rule. Schoenberg is quoting his own maxim, also stated in a later essay, "Composition with Twelve Tones (1)." ^Maegaard, Studien. v.2, p.7. 49 purposes of his study, Maegaard assumed an admittedly arbitrary standard for audibility, without providing a clear exposition of that standard. He reasoned: "In the typical case, the distinction Is not difficult; In the hundreds of Incidental cases, however, subjectiv ity must under any conditions prevail."^5 His study has a few additional flaws. First, his system of har monic analysis contains certain ambiguities, such as overlapping categories (see Chapter II below). He also excluded some essential atonal works from the set of detailed analyses, namely Pierrot Lunaire and the Plano Pieces, Op.l9. Although his analysis of Erwartune Includes a vast amount of raw data, he offered comparatively little interpretation of the d a ta . Maegaard did not succeed In standardising his criteria for "audibility," but they apparently have some relation to surface features. While "struct tural" features apparently create long-range, under lying connections, "audibility" more properly applies to Immediate, explicit, sonic events. Using Maegaard's someidiat vague notion of audibility as a point of departure, the present study deals syste matically with the specific constituents of pitch

^^Ibld. my translation. 50

organization: harmony, melody, and form, in a basic, surface-oriented manner. Other constituents: dynamics, phrasing, rhythm, texture, etc., are dealt with only as they come to bear on the three major constituents of pitch organization. The notion of aural coherence may extend to different levels of analysis. Recent "structural" theories have examined long-range harmonic and melodic coherence. More immediate aural levels are imaginable, such as a study of classical cadential procedures that might deal with specimens consisting of only a few chords each. Immediate aural coherence in, for example, a Mozart symphony, results from >diat might be termed "local" harmonic and melodic regularity. Local regu larity has long been taken for granted in Mozart's works, a fact responsible for the recent interest in more long-range structural theories; local regularity, however, often poses great problems in the analysis of Schoenberg's atonal works. Even the degree of regular ity is exceptionally irregular, lending unpredictabil ity to Schoenberg's atonal music. Generally speaking, composers give attention to large-scale structural considerations, but they also seek to compose an effective musical surface. In the common-practice 51 era, this dual interest meant creating a balance between unity and variety in the local patterns of melody, tone color, texture, registre1 distribution, etc. When Schoenberg purposefully upset this balance in his atonal works, he altered the aural surface coherence significantly. Although the appropriate methods of analysis were also thereby necessarily altered, there is no reason to assume that conventional analysis be comes useless as a result. 52

The "Emancipation of the Dissonance” and Its Theoretical ■Impllcatlona

The transition from tonality to atonality had many theoretical Implications. In his writings, Schoenberg offered aesthetic as well as more technical accounts of the transition. One concept he Introduced as part of his description of the new style was the "emancipation of the dissonance." He wrote :

The term emancipation of the dissonance refers to Its comprehensibility, vdilch Is considered equi valent to the consonance's comprehensibility. A style based on this premise treats dissonances like consonances and renounces a tonal centre. By avoiding the establishment of a key modula tion Is excluded, since modulation means leav ing an established.tonality and establishing another tonallty.^o

In this description, Schoenberg established two quali fications for the new atonal Idiom: (1) It treats dis sonances like consonances; and (2) It renounces a tonal center. While these two criteria alone do not thoroughly describe Schoenberg's atonality, they are probably sufficient for the judgment that a given work

*^%choenberg, "Composition with Twelve Tones (1)," 53 is atonal* B&th criteria have extensive theoretical im plications, unexplored in Schoenberg's commentaries, but essential to the understanding of the idiom* If dissonant sonorities are to be treated like consonant sonorities, then dissonance, as such, is no longer a factor in atonal composition* Schoen berg, in fact, gives no details of the effect this treatment may have upon the listener's experience* ■Are these dissonances to be treated like consonances even though they are recognized as dissonances? Schoenberg may have hoped that if they were treated equally they would eventually be perceived equally* The end result, however, the so-called "dissonant" style, meant that consonance, rather than dissonance, was eliminated* The true source of dissonance has been sought in nature and in the human psyche* The quality of the sound itself has often been considered part of the cause for its relatively dissonant or consonant effect* Dis sonance, on the other hand, may be viewed as a function of style, wherein a ll characteristics of dissonance and its resolution can be attributed to musical development from one era to the next. In any case, Schoenberg's personal declaration that dissonance was now as 5 4

“comprehensible" as consonance could' not have consti tuted a scientific, psychoscoustical or musicological assertion. He was merely informing the reader tdhat could be expected in his music. Previously, there was a practical distinction between consonances and dis sonances, idiich could be defined purely on the basis of the kind of treatment each received. Dissonances re quired preparation and resolution, and consonances did n o t. A composer idio no longer distinguishes be tween consonance and dissonance can probably be ex pected to treat all vertical structures equally. The equal treatment of vertical structures, when applied to the diatonic scales, has been referred to as oandia- tonicism. This device involves treating all vertical structures equally as long as they contain only pitches from a single major scale. This practice, when ex tended to the complete semitonal scale, could be re ferred to as Danchromatlclsm.^7 In Schoenberg's case,

^^According to Apel, the term uandiatoniclsm was first used by Slonimsky in Music Since 1900 (cf. 1949 edition, p.xxiv). The term panehromatlcism was proposed by William M itchell in "The Study of Chromati cism," Journal of Music Theory, v.6/2 (Spring, 1962) p.2. Both terms refer to the indiscriminate use of vertical combinations within a given field of pitches. 55 however, total equalization never took place, because, although dissonances were freely used, overly familiar or tonally obvious sounds were avoided Instead. The following passage represents one of Schoenberg's state ments about twelve-tone composition that apply equally well to atonality:

In twelve-tone composition consonances (major and minor triads) and also the simpler disso nances (diminished triads and seventh chords)— In fact almost everything that used to make up the ebb and flow of harmony—are, as far as possible, avoided...40

The essential details of the "emancipation of the disso nance" can be summarized as follows: (1) dissonance no longer requires preparation and resolution; and (2) a ll vertical structures are treated equally, except that the simpler consonances must be avoided. The renouncing of a tonal center has other Im plications, with regard to meaning and effect, than just the free treatment of dissonance. Various accounts of Schoenberg's Second String Quartet, Op.10 (I908), tra ditionally regarded as the first atonal piece, reveal the potential for differing Interpretations. According to Schoenberg, In a ll four movements, the key

^®Schoenberg, "Twelve-tone Composition" (1923), In Style and Idea, p.207. 56

Is presented distinctly at all the main dividing points of the formal organization. Yet the over whelming multitude of dissonances cannot be counterbalanced any longer by occasional returns to such tonal triads as represent a key. It seemed inadequate to force a movement into the Procrustean bed of a tonality without supporting it the harmonic progressions that pertain to

The minimal tonal references in the fourth movement were also observed by Samson-

Even in the finale, however, Schoenberg did not completely abandon tonality, though it clearly could not have expanded further with out collapse.50

Maegaard maintained that the introduction to the fourth movement was tonal in only the vaguest sense, and listed seven additional commentators who agree that the after- math of the breakdown of tonality, a "breakthrough to .atonality," took place in the same work:

^^Schoenberg, "My Evolution," p .86 50Samson, Music in Transition, p .105 57 It la instructive to confirm that this Intro duction, which is repeatedly cited as the breakthrough to atonality, is firmly supported by the most original tonal relationships..,51

The abandonment of tonality was acknowledged by Schoenberg and his followers. Some of the subse quent disagreement among theorists relates to vdiat, if any, factors, replaced the cohesive role of tonality. Negative characterizations of the new idiom were both recognized and objected to by Berg: "...this collec tive term ’atonality" is intended to repudiate every thing that has heretofore made up the content of m u s i c ."52 Schoenberg, and obviously Berg, objected

5lMaegaard, Studien^ v=2, p .107, my trans lation. He cited the following commentators as gen erally agreeing on the pivotal position of the Second Quartet: Paul Stefan, Neue Musik, p.60; René Lelbowitz, Schoenberg et son école, p.90, Dlka Newlin, Bruckner. Mahler. Schoenberg, p .235, H.H. Stucken- schmidt, Arnold Schoenberg, p.4-1, Egon Wellesz, Arnold Schoenberg, p .11^ and "Begegnung," in Melos, v.33/1, p.6, and W. Z illig, Variatlonen, p.72. 52"What is Atonality?" p.1312. This defen sive reaction to the term "atonal" is discussed in Stvle and Idea, p.210. There, Schoenberg refers to a sim ilarly polemical passage from the Harmonielehre, pp.447-^88 (1922 ed.). 58

to this term because they suspected it was being used

In a derogatory s e n s e . 53 The o b je c tio n was r e a lly one of trivial semantics, centering around the word "tonal," which can refer to either tones or tonics. Schoenberg apparently feared that the term "atonality" Implied the absence of tones rather than the absence of tonics, and so took It to be disparaging. Since "tonal" Is often used to mean "tonlcal" (i.e ., pos sessing a tonic), then "atonal" can simply mean "atonlcal," and "atonality" can simply mean "atonl- callty," I.e ., the state of possessing no tonic. The atonal composers might have dispensed with this parti cular facet of critical opposition by accepting this distinction. The relationship between Increased tonal am biguity and the eventual total dissolution of tonality should not be taken for granted. (There may be an analogous relationship between representational and

pSprom th e H arm onielehre. p .^8?: "I must definitely reject that term , because I am a musl- - clan, and have nothing to do with anyone who Is - atonal. 'Atonal^ can merely mean something which does not conform to the essence of tone.. . .But - one can no more call any relation of tones 'atonal' .. than one could call a relation of colors 'aspectral* or ' a complement a ry • • There Is no such contrast.” 59 non-representatlonal visual arts, notable in the term "abstract" art, which is a term unavailable to the music theorist.) The relation of tonality to atonality is not necessarily a simple matter of degree. Indeed, there is a difference between avoiding this or that tonality, and avoiding any tonality whatsoever. There is no reason why the introduction or possible existence of more and more keys need eventually result in the elimination of a l l keys® In his major theoretical work, the Harmoniel ehre (1922), Schoenberg discussed the expanding lim its of tonality in terms of what he called."vagrant chords" (vaeierende Akkorde). These were rather loosely defined as chords that (perhaps enharmonlcally at times) can strongly imply more than one key: augmented sixth, aug mented triad, diminished seventh, etc. While he drew a clear connection between vagrant chords and modula tion to distant keys, no^diere in the Harmonielehre did he discuss specific details of the total elimina tion of a tonic.5^ Schoenberg introduced the idea of vagrant chords in the following context :

5^Although the possibility of atonality is mentioned, the specific means of achieving it are not. One should also note that the composers he cites in relation to weakening tonality, Bruckner and Wolf among others, did not employ radically new vertical structures in their works, but merely increased modulation and tonal fluctuation. 60 If, however, as In modern music, chords foreign to the scale, or (as I call them) vagrant chords predominate, the necessity of tonal solidifica tion comes into doubt*55

In this sense of the term, Schoenberg almost seems to be referring to any non-diatonic chord* Any chord foreign to the key has the potential to accentuate some other key, or possibly bring out some modal inflection* A note or chord is "foreign to the scale" (leiterfremd) supposedly because it comes from another scale* Thus, unless a chord is foreign to all scales, it must con tribute to the establishment of some other tônality. In other words, the notion of a "vagrant" or "foreign" chord makes sense only in the context of tonality* Without a tonic from which to wander, a chord can be neither "vagrant" nor foreign* In a modulation, a chord merely changes its function, while in atonality it no longer functions at all,'except as an isolated simultaneity* Tonality and atonality have also been viewed as relative degrees of chromaticism* Many writers have implied that a continuum exists from diatonic tonality through chromatic tonality into atonality, with the last representing the ultimate state of chromaticism* As Grout said: "The change from tonality obscured by extreme chromaticism to anotality with free dissonance

55Schoenberg, Harmonielehre. p*16M-, my trans la t io n * 6 l

was a gradual process with Schoenborg."^^ Eric Salzman observed how, during this change, Schoenberg *s music "proceeds towards a linear chromaticism In which motives and Intervals assume the structural force exerted for merly by tonal expectation and function."^? Salzman clearly considered atonality to be an extreme form of chromaticism. Schoenberg also appeared to believe that enough "foreign" chords not only threatened the key, but perhaps tonality In general. This was achieved through the replacement of the diatonic scales with thé chromatic scale:

...I t Is obvious that a great number of chords which are apparently foreign to the key promote the formation of a new perceptual unity: the chromatic scale. It must be noted here that by the accumulation of such events, the solid edifice of tonality may be ruptured.58

Again, It Is unclear idiether a specific tonality or tonality In general Is threatened. It Is also unclear whether the "events" that accumulate are modulatory

56Donald Jay Grout, History of Western Music, revised edition (New York: W.W. Norton and Co., 1973)• p . ‘+ 5 t o

57Eric Salzman, Twentieth-Century Music (Englewood C liffs, N.J.: Prentice Hall, 1967)> p.33. 58sohoenberg, Harmonlelehre. p .299, my trans lation. For another account, see Webern, Paths to the New Music (New York: P re sser , 19 6 3 ). 6 2 chords and progressions, or whether they are series' of entirely new vertical structures, not formerly found In tonal music. Schoenberg's atonality Is characterized not merely by the more concentrated use of tonally am biguous and modulatory structures, but by the use of unfamiliar vertical structures which do not progress In the tonal sense. This distinction raises doubt about U.H. Stuckenschmldt's statement that "the flood- tlde of chromaticism brought music to the brink of to n a lity and b eyon d ."59 In the case of Increased modulation, tonali ties are still established, but for Increasingly brief periods of time, as In the passage by Reger In Example 3.

Alieqro Hoderq.]t>, , . ,

é 0 3C3C IP (P)3IC3:

Ex. 3* Reger's String Quartet, Op.109, I, mm. 32-39, displaying fast harmonic rhythm.

The statements cited above support the view that in creased chromatic activity for modulatory purposes can eventually lead to a breakdown In tonality

59stuckenschmldt, Twentieth-Century Music, p.31. 63 altogether* William Austin took an opposing position, however, that chromaticism can exist only in contrast to diatonicism, and that the notion of chromaticism is en tirely transformed in the context of atonality:

Schoenberg emancipates the twelve notes of the chromatic scale from dependence on a diatonic norm. Each note is enharmonieslly ambiguous* Until now we have defined and felt chromatic notes and enharmonic ambiguities in relation to one or more diatonic scales* Even in the late works of Scriabin, where no diatonic scale appears, the ambiguous chords are related to two or three such scales, through their dominant character* When there is no such relation, chro maticism means something new* To say that Tristan or Syrinx or gliktra is very chromatic means that mauy notes deviate from the diatonic norms; to say that Pierrot, is chromatic means that every note is as normal as every other. The difference is not a matter of degree, but a radical difference of meaning* To say that Pierrot is "more chromatic" than Tristan makes no sense, because the two kinds of chromaticism are not connected by more and l e s s*60

Perle was in basic agreement on this point:

Atonality originates in an attempt to liberate the twelve notes of the chromatic scale from the diatonic functional associations they still retain in "chromatic" music—to dissociate, so to speak, the chromatic scale from "chromati cism* "o1

60Austin, Music in the Twentieth Century. pp. 205-206* Glperle, Serial Composition* P*l. 64

•According, to these descriptions, hypertrophied modulation alone could not account for Schoenberg's "breakthrough." The c r u c ia l elem ent was th e in tr o d u c tio n o f many unfam il iar, non-tonally-derived simultaneities as normal and regular sonorities. These new structures were not in serted here and there as coloristic effects, but were in constant use as the basic compositional material. This means that the transition from tonality to atonality need not have been, as Schoenberg said, "merely a logi cal development of musical resources.If the change was truly a qualitative one, as Perle and Austin have suggested, then it is reasonable to expect many radical changes to result from Schoenberg's abandonment of tonality. '

Alterations in the Musical Language

The deviance of the atonal idiom and the ana lytic problems associated with it can be attributed to certain alterations in the musical language. Schoen berg's use of enharmonic spellings, for example, raises serious doubt about any latent tonal conception on his part. In atonality, since there are no tones of

^^Schoenberg, "How One Becomes Lonely," p .50. 65

reference, no note can be considered an alteration of any other. Enharmonies are identical, and since there are no conventions of spelling, It ceases to be a major consideration. According to Richard Hoffmann, Schoen berg may have composed some passages with more attention to the note names than to the specific accidental, adjusting the accidental at a later time:

In the event that the suspect note caused an alien stylistic sonority (outline of a triad, major or minor second proximity), Schoenberg might have adjusted the pitch by merely changing the accidental...^3

Hoffmann was discussing this practice in the specific context of row irregularities in the twelve-tone music, however, it is quite possible that the practice origi nated in the preceding period. In 1924, Schoenberg wrote an essay entitled “A New Twelve-Tone Notation, "64 in \diich he sought a way to give each chromatic pitch only one means of notation on a three-line staff, thus eliminating enharmonies. This essay confirms the fact that spelling eventually became a needless complication to Schoenberg. Frequent B#‘s, cb'3, and double sharp ard flats in the atonal

^3Richard Hoffmann, "Concerning Row Deviations in the Music of Schoenberg," lecture reprinted in Bericht aber den 1. Konaress der Internationalen Schoenberg- Gesellschaft. IWien: Elizabeth Lafite. 1974). p.98 ^In Style and Idea, p.354. 6 6 music may seem to be traces of some sort of tonal concep tion, but any pattern to their use remains obscure. If Schoenberg had put down the note B, but later decided to raise it a semi-tone, it was certainly simpler to add a sharp to the note than to change its position on the staff, especially because there were no conventions of spelling that had to bo followed. The inconsistent use of enharmonies in the atonal works can be seen in several examples. Three examples may be seen in the Piano Pieces, Op. 19. In the first of these, in measure 3? an A# is tied to a B , and in measure 1^, a G# is tied to an A (Example 4). There is no particular congruity between these passages, since the three-note item B-D-A# in measure 3 is not heard until measure 15, where it is transposed to D-F-C#.

M* molto rlt..

Used by permiaalon of aelmont Music Publishers, Los Angolas, California 90049 Ex. *+. Two possibly analogous enharmonic spellings in Op. 19/1, mm.3 and 1^.

Even if Schoenberg sought to retain the "motive” of the augmented fifth , this explains neither (1) vriiy the 0# is not tied to a D in measure 16 (it proceeds up by semitone just as the B in measure 3 , nor (2) why the 67 G# is tied to the A in measure 14. In the latter case, the A may have been reached by spelling upwards in thirds from B-D -F. This leaves the C unexplained. These notes are known to be authentic and not editorial, because they appear in the manuscriptIn the earliest draft of the piece, the B in the left hand of measure is a B . If this wac what Schoenberg originally intended, then the connection with measure 3 becomes clearer. Given the note A in measure 14, the pitches D and B would hold exactly the same intervallic relationship to it as the notes E and C hold to the tied over B in measure 3* Of cou rse, one could only speculate about which accidentals Schoen berg changed after the fact. Another notational oddity occurs in Op,

19 / 3 , where in measure 7, E is respelled as D#, then again as E in measure 8 (example 5)* A sim ilar change

Used by permission of Balmont Music Publishors, Los Angeles, California 90049

Ex. 5» Two respellings of a single pitch in O p.19/3; nim. 7-8®

^Shown in facsimile on p.vii of Arnold Schoen berg, Samtliche Werke, "Kritische Bericht," series B, V .4, ed. Rheinhold Brinkmann (Mainz: B. Schott's Sohne, and Wien: Universal Edition, 197$)® 6 8

occurs in Op.23/1, measure 2, again with E and D# (Example 6a), and in Op.21/6, measure 21 (Example 6b), where the fourth A to D is respelled G# to C# one beat later, and the remainder of the measure is notated in flats. These cases, although comprising only a % . ... % I

Usad by pamlssion of .vith oaralsalon of Edition iVllhalm Hanaan, Copenhagen, Denmark Balmont Munie Publiahere, Ex. 6. Two more examples of enharmonic spelling, (a) from Op.23/1, mm. 1-2, and (b) Op.21/6, m.21.

minute fraction of the music under consideration, raise doubt about the role that spelling can play in explain ing the music. Sharped tones do not necessarily pro ceed upwards in "leading tone" fashion. Conversely, flatted tones often ascend by half-step. Such anoma lies can, of course, also be found in tonal music, when a part changes direction after a note has been altered in the reverse direction. Atonal spelling, however, still lacks a regulating principle. A few general practices can be observed, but there are probably almost as many exceptions as there are confirmations. It is often the case that: (1) spelling maintains general in terval quality, e.g., series' of fourths or sixths of 69

different specific sizes; (2) motivic items are spelled con sistently» In Op.11/2} for example, the D in measure 2 is motivically related to the D in m.5 (top voice) and m.6 (top voice), but not to the C#'s in those two bars—so that spelling distinguishes motivic material (Example 7)5

______IXaaa by Permission of Palmont SJuaic Publishers, los Angeles, California 90049 7* Op.11/2; Consistent spellings of motivic D in measure 2 and C# in mm. $-6.

(3 ) items constructed from tonally reminiscent units, such as triads and seventh chords, tend to be spelled so that each constituent part is evident. In Op.21/5, m.11, for example, the spelling of the last six-note chord in the piano retains the identity of the two constituent parts, both being "seventh chords" without a "fifth" (Example 8),

Uaoa by Peraiaeion of Bslmont Uuaic Publishers, Los Angeles, California 90049

Ex. 8. Op.21/5: "Seventh chords" at the end of m.11, spelled to show their distinct make-up. 70

This may explain v b j the right hand was not spelled The top note Is not at all related to the notes of the left hand. This topic Is discussed at length In Chapter II In the section on vertical layer in g . A striking feature of the atonal period Is the frequency of dynamic, tempo, and textural changes. The opening of the Five Pieces for Orchestra, Op.16 Is an example. A t the outset, the three bassoons play an ostlnato-llke figure against a motive In clarinets and cello. This Is Interrupted by a tuttl eighth rest, after which a new texture of flute and clarinet trills Is Introduced. After another tuttl rest, a legato fragment enters In even eighth notes, followed by another rest and a new syncopated fragment In the oboes with the strings playing pizzicato. This sort of descriptive "analysis" Is merely an attempt to verbalize the aural experience; to this point. It has described only the first thirteen measures of the p ie c e . Because harmonic activity, and with It the harmonic cadence. Is apparently eliminated In the atonal Idiom, the mere Identification of phrase units may be difficult. The tuttl rest might serve to Indi cate phrase endings where the composer Is aware that 71 the vertical activity does not suffice. This Is one of many altered uses of artlculatlve devices that are dis cussed at length In Chapter IV below. The alterations In musical language that typify the atonal Idiom, such as enigmatic use of enharmonies or an extremely fragmentary surface, are summarized In the statement by Perle: "The atonal composer.•.can take nothing for granted except the existence of a given limiting sound world, the semitonal scale.T he oth er lim itations of conventional notation and Instrumentation may also be assumed. Within these assumed lim its, Schoenberg's atonal works reveal a broad range of proce dures, from conventional motivic applications to what Mosco Garner called a "fluid, amorphous, and Inverte brate atonal m ass...the liquidation of all previous means of formal and harmonic organization."^? The following chapters deal with the separate constituents of vertical construction, melody, and form In an attempt to create a standard for measuring the relative presence and absence of conventional proce dures In Schoenberg's atonal Instrumental works.

^^erle. Serial Composition, p.I. ^?Mosco Garner, "Music In the Mainland of Europe, 1918-1938." In The Modern Age, 1.890-Î-96Q. ed. Martin Cooper, v.TO of the New Oxford History of Music (London: Oxford University Press, 197^)j p.341. Chapter I I THE VERTICAL DIMENSION IN ATONAL MUSIC

In the preceding chapter it was shown how Schoenberg ondermlned numerous long-accepted musical notions. The essential details of atonality, free dissonance treatment, the permission of a ll vertical structures, and the elimination of harmony as a con sideration completely altered the vertical dimension. In this chapter, a method of chord categorization based on the conventional notion of chord quality w ill help reveal the entirely new character of the vertical dimension. For purposes of comparison in the count of sim ultaneities in piano works by Schoenberg, Brahms' Op,76 serves as a standard for fairly chromatic common-practice music. In order to measure Schoenberg's treatment of the vertical dimension in conventional terms, the notion of chord quality needs to be expanded to account for all possible simultaneities. Two other systems of vertical analysis w ill be examined. Forte's pitch-class sets and Maegaard's tonally-de rived symbols. Because p-c sets involve assumptions 72 73

about the equivalence of interval-class, they cannot accurately measure conventional vertical relations (see p. 84" below). Maegaard's symbols, lA ile having the advantage of showing the tonal derivation of simultaneities, cannot be used in a strict vertical count because they are not mutually exclusive (see p. 82 below). In spite of the known absence of harmony in the conventional sense, the attempt w ill be made to duplicate the process of harmonic analysis as closely as possible. Harmonic analysis consists of a number o f o p e ra tio n s, such as determ ining which simultaneities are prevalent, their composition or quality, and patterns of progression and cadence. As the notion of chord quality is examined, it w ill be seen that all possible "qualities" of simultane ity • for three or four notes are used by Schoenberg in the course of the atonal piano works. When the number o f d iffe r e n t s im u lta n e itie s in c r e a s e s , the number o f p o s s ib le p ro g ressio n s in c r e a se s exponen tially in comparison. The chord count gives numeri cal support to the apparent irregularity of the ver tical dimension, and demonstrates an alternative to pitch-class set analysis. 74

Regularity in harmonic activity can be re vealed by a count of all vertical structures in a tonal sample. Even in a tonal piece, non-harmonic tones pro duce many non-tertian simultaneities, which, in a thor ough count, must be categorized and counted along with more familiar chords. In the atonal music, no dis tinction is possible between harmonic and non-harmonic tones. This is yet another difference between tonal and atonal works that must be kept in mind in making a comparison.

The Verbal Categorization of Atonal Simultaneities

Because the conventional terminology for in tervals and chords is derived from tonal harmony, the use of such terms as "major third" or "diminished triad" may be thought to imply a tonal orientation. Nevertheless, the familiarity of these terms is often a practical reason for continuing to use them even in an atonal context. Here, they merely serve as conven ient labels for structures, without implying any par ticular orientation. Conventional names are, of course, lacking for most of the simultaneities found in Schoenberg's atonal music, and thus some sort of new nomenclature is required (see p. 88 below). We can be quite certain from Schoenberg's writings that 75 harmonic function is no longer a consideration in his atonal idiom, and that all vertical structures take on equivalent importance. Hence, frequently encountered terms like "sound," "sonority," "verticality," and "simultaneity" become almost interchangeable. The term "simultaneity" connotes the inadvertent sounding together of tones that might be progressing toward more significant sonorities. "Chord," on the other hand, implies an intrinsically significant vertical str u c tu r e . On a purely numerical basis, the count, of sim ultaneities discussed on p. 102 below shows that Schoenberg neither preferred nor avoided any particu lar class of vertical structures. Nevertheless, a superficial glance at a page of the music reveals a preponderance of sonorities containing the semitone and its derivatives. In the first forty measures of Op.16/ 1, for example, all six chords in Example 9 (a-f) appear as simultaneities. Here, these chords have been condensed to one staff from the wide spac ing that Schoenberg used for the large orchestra, in order to show their resemblance to the string of "chords" in a passage from 0p.2lA (Ex.9, g-m). 76

g h i j k 1 m p* «-Vu 4 * r

Ex. 9. Structures containing a major seventh in Op. 16/1 and Op.21 A*

Chord ( a ) , exclu d in g th e n ote A, is identical to (f) without the D, and to chords (j) and (k). Chord (b) without the D is identical to chord (g); chord (b) without the E is identical to chord (h)• All of these structures consist of the interval of a major seventh plus an intervening note, placed either a third, fourth, fifth or sixth above the lower note. That is, with D taken as a "root," six structures can be generated by shifting the inner note within the major seventh (Example 10). Each of these three-note "chords" is familiar as a simultaneity

1 2 3 4 5 6 I i Exi 10. Three-note structures containing a major seventh and some inner interval. with an expected resolution in tonal harmony. The first simultaneity occurs in a minor key if the leading tone is an appoggiatura (or retardation) 77 above the tonic triad. The second Is either a major seventh chord without the fifth , or a suspended seventh that normally resolves to a sixth. The third simultane ity could occur as two notes of a diminished triad in D major or minor, written over a tonic pedal, resolving to the notes D and F# (or F^). The fourth simultaneity in Example 10 could become an E-thirteenth chorù if the root ware added in the bass. (In Schoenberg's tonal theory, the notion of an omitted root was quite normal, so that he himself might have analyzed this chord in such terms if he encountered it in a tonal composition.^) The fifth simultaneity is similar to (T) and (2) and the sixth could occur as a double appoggiatura in B minor. There would be no purpose in elaborating upon the tonal possibilities of every chord used by Schoenberg in his atonal music. It must be stressed that it is not only the make-up of the individual sim ultaneities, but also their succession that produces an atonal effect. In this music, tonal references are, at best, of fleeting and incidental interest. One result of Schoenberg's equalization of the vertical dimension was the number of simultaneities

^cf. Schoenberg, Structural Functions of Har mony (New York: W.W. Norton and Co., 1969), P*35*In a tonal context, such typically atonal "chords" could take on a distinct function. 7 8

containing the semitone, or Its octave Inversion and com pound, the major seventh (M7) and minor ninth (m9), re spectively. Three-note simultaneities constructed In perfect fourths create a m? between the highest and low est notes, but If either fourth Is augmented, the seventh becomes major. Those chords that do not contain m2, M7, or m9 fall into three categories: tertian, i^ole-tone, or pandlatonic. Tertian chords, for pur poses of this discussion, are those three- and four- note chords that are spelled like root position triads or seventh chords. The latter may appear without the third or without the fifth . Whole-tone chords are self- explanatory, and may Include Items that could be ex plained as French sixths, dominant sevenths with altered fifths, and major triads with flatted fifths. A chord may be labelled "pandlatonic" If It Is not tertian but still contains notes of a hypothetical diatonic scale (i.e.. It could be transposed to the white keys on the piano). Chords built in perfect fourths thus turn out to be pandlatonlc up to seven notes. On the other hand, a pandlatonlc chord could contain two semitones, just as a major scale does. Tertian chords may contain one semitone, as In the major seventh chord. As a conse quence, the categories are not entirely mutually 79 exclusive» In Example 11, (a) represents tertian, (b) lAiole-tone, and (c) pandlatonlc chords.

a a b cc d e f g ’-^ =---- — Of? 2— —i"z.Qo—efi— jo-

Ex. 11. Three types of chords : (a) tertian, (b) whol e -to n e , and (c) p a n d la to n lc; (d-g) are Incomplete chords, with (f) and (g) Implying (h) and (1), respectively.

Because of the absence of any prevailing scale In atonality, there can be no Implied "harmony." Omitted tones cannot be supplied "by the ear" and every simultaneity must be considered literal and complete In I t s e l f . Aa a result, repeated Intervals like the major thirds In Op. 19/2 and the minor thirds In Op. 1,1/2 do not Imply triads; their ambiguity Is assured by the lack of a tonal context. In discussing atonal simultaneities. It Is useful to distinguish between harsh sonorities and com plex ones. Open fifths, a simple sound, can have a harsh effect when taken out of context, for example. In a Mozart sonata. Sometimes an additional note makes a sound less harsh. The trltone In Example 11 (d) Is made less harsh by the Inclusion of the note D, as In chord (e). Similarly In (e), the major second Is made -more consonant when tonally oriented by the trltone. 80

Consequently, %Aiile Schoenberg used many harsh sonori ties, some are mere complex than others. Another concept that is absent in Schoenberg's atonality is the chord root. Without scale degree or other tonal orientation, the analyzer is at a loss to identify the tone on which a chord is constructed. One could perform a Hindemithian analysis, deriving a series of roots, but for such a task to be fruitful it would be necessary to employ a theory of chord progression, qualities of prevalent simultaneities, resolution, and so on. The questionable appropriateness of this method may be partly measured by looking at Hindemith's analy sis of Schoenberg's Op.33a, a twelve-tone piano piece. Hindemith's difficulty with the analysis stems from an attempt to "group...as many chords as possible around one tonal center, so far as that is possible at all in t h is c a s e . "2 Hindemith said: "It w ill be objected that no analysis of the present sort was in the mind of the composer when he wrote this piece," but rationalized that "this objection applies to all music, since this type of analysis has never been in use before."3

2Paul Hindemith, The Craft of Musical Com p o s itio n , V . I (New York: Associated Music Publishers, 194$), p.219.

3 lÈ iâ . 8 1

The lack of identifiable tonal centers, which was the cause of Hindemith's difficulty, makes it impossible, in Example 11 above, to associate chords (f) and (g) with (h) and (i), respectively. In both cases, the har monic implications possible in a tonal context are lack ing in an atonal context. Chords that would be func tionally equivalent in tonal harmony (German sixths and Italian sixths, for example) must remain differentiated in atonal analysis.**"

New Symbol Systems for Categorizing Atona1 Sim ultaneities

Forte and Maegaard introduced new symbol sys tems for categorizing atonal sim ultaneities. Each sys tem reveals an analytic orientation, Maegaard's toward tonality. Forte's toward serialism. The two approaches are outlined briefly below. Because Forte's p-c sets can account for any simultaneity, this system is com pared in greater detail with the system of chord quali ty analysis to be adopted in this study. Maegaard categorized the sim ultaneities used by Schoenberg according to their relation to traditional

**■ As mentioned in Chapter I (note 13), this topic is dealt with in Robert Suderberg, "Tonal Cohe sion in Schoenberg's Twelve-tone Music." 82

chordal structures.^ The following list indicates the type of "chord" described and the symbol Maegaard pro posed for each: Three- to five-note tertian ...... Tn (Tonalklang) Minor third structures t (kleine Terz) VIhole-tone chords...... G (Ganzton) Fourth chords...... Qu (Quartern) Third-plus-seventh chords...... TS (Terz-Sept) Combinations of sevenths ...8 (Sept) These symbols are modified by some additional conventions. With regard to specific interval size, lower and upper case letters indicate minor and major, respectively. The addition of a digit (e.g., "t4") indicates the number of notes in the chord. The letter "a" indicates an altered chord. Tho arithmetic symbol for division, indi cates the omission of a chord member, so that Tn3f5 means a tertian seventh chord with the fifth omitted (th u s o n ly th ree members remain) and Qu4j2 means a hexa- chord in fourths minus two notes. In cases where the notion of a "third" or "fifth" of a chord does not apply, the sum of the two digits indicates the size of the complete chord. Maegaard observes that many symbols can, indeed, describe more than one type of item. Any major or minor triad, for example, being a "tonal triad," is labeled Tn3* Similarly, some chords may be correctly labeled by more than one symbol. A dominant

^Studlen. These symbols are used throughout V.2. 83

seventh with the fifth omitted could be either a Tn*-3 or a G3. The search for an accurate chord classifica tion system that also refers to possible derivations has not, in this case, produced a viable result. Forte, along with Perle, has approached the problem from another point of view. For both, the first step was to determine the limit of all possible vertical structures. Then this great number of "chords’* was re duced to a more manageable quantity by virtue of cer tain "equivalences," namely transposition to a single referential pitch.level and the elimination of octave (harmonic) and interval-class (mirror) inversions. In The Structure of Atonal Music. Forte reduced a ll possi ble pitch combinations to what he called "pitch-class" s e ts ." -Assuming octave eq u iv a len ce, he then matched each pitch-class with an integer, with C through B cor responding to 0 through 11. He then assumed interval- class equivalence, so that equivalent interval classes (i.e ., equal distances in semitones whether ascending or descending) are not duplicated. -As can be seen from Forte's -Appendix I, there are twelve three-note sets, twenty-nine four-note sets, and thirty-eight five-note sets.^ These represent the quantities of sets of n

^The Structure of Atonal Music, p.179. 8 4 pltch-clàssôs transposed to a single reference point, \iith the Inversions1 equivalence of both octaves and Interval-classes assumed.^ Richard Chrlsman, In Intro ducing his system of "successlve-lnterval arrays," pointed out certain advantages In Including both Inter- va1-class Inversions of a pair (I.e., ascending and de scending), although this does not Increase the quantity df basic "chords."^ He agreed that although It should be possible to observe the equivalence of 1-c related Items, the specific aspect In vdiich they appear should not be considered so trivial that It cannot be Indicated by the set label. Interval-class equivalence Is not a principle so universally accepted In analysis that It may be assumed as readily as octave equivalence. More over, unordered pitch-class sets are represented as an ordered sequence of pltch-classes, Including a "best normal order." Since the prime form of a set represents transposition to the arbitrary level of 0=0, the odds are only one In twelve that the specific pltch-classes

^■The derivation Is given In detail In Parle, Serial Composition, pp.106-110. %1chard Chrlsman, "Describing Structural As pects of Pitch-Sets Using Successive Interval Arrays," In Journal of Music Theory, v.21/1 (Spring, 1977)» P P .1-2U .According to Perle (Serial Composition, p.148), this notion originated In Eric Regener's article "On Allen Forte's Theory of Chords." Regener, however, cites Chrlsman's Ph.D. dissertation "A Theory of Axls-Tonallty for Twentieth-Century Music," (Yale University, 1969) as the origin of the successlve-lnterval array concept. 85

In the prime form w ill actually be those in a given spe cific instance. Thus, it hardly makes sense to talk about pitch-classes at all, vdien it is really the intervallic relationship between the pitches that distinguishes Q one set from another.^

The Application of Chord Quality Analysis to Schoenberg’s Atonal Works

It is next necessary to consider how traditional chord theory can be expanded to permit the analysis of a ll possible simultaneities derived from the twelve-tone ag gregate. In traditional chord theory, prevalent simul taneities are categorized by chord qualitv, according to the intervals they contain. Since tonal chords.are structured, as a rule, in thirds, the specific types of thirds (i.e ., major, minor, etc.) and the number of them are vrtiat account for the qualities of the typical tonal chords. For pedagogical purposes, triad quality is occa sionally expressed as a series of thirds, such as tfai (major-minor) for a major triad. Accordingly, a major seventh chord is MmM. Although Chrisman did not men tion the relationship of his "arrays" to chord qualities, they are similar in that any interval may be expressed

^The reader is again directed to Richmond Browne's review of the Forte book. 86 as a distance in semitones and any simultaneity as a se ries of such semltonal distances. In this way, the se ries MmM would be expressed 4-3-^. The fact that the se ries of thirds Is now expressed In digits does not alter the role of the Interval series as an extension of the conventional notion of chord quality. Since the concept "root" does not apply to atonal simultaneities^ there Is no referential pitch from which to calculate the series of Intervals. Therefore, an additional Interval idiich completes the octave must be Included In each Interval succession, thereby locating each unique Interval series within the octave. This added Interval Is always the complement of the interval between the highest and lowest notes of the actual simul taneity. Therefore, lAien all the digits are Included, the sum Is always twelve. For example. In the major seventh chord, the added Interval 1, Is the complement of the major seventh between the highest and lowest notes. The symbol ^-3^1 thus represents only the quali ty of the major seventh chord. In a similar way, digit sequences can be used to represent any group of notes of any size from two to eleven, reduced to a single oc tave. Rotation (i.e., placing the first digit last or last digit first) of the digits In sequence precisely duplicates the process of harmonic Inversion, by 87 automatically transposing each interval in the simulta neity the distance of its harmonic complement. According to traditional harmonic theory, a chord retains its quality in the course of harmonic inver sion. In other words, the simultaneity represented by the digit sequence ^-3*+1 retains its quality through rotation into 344^,4^43, and 1434, in the same manner that a major seventh chord is inverted into first, second or third in version. Traditionally, however, chord quality is not always maintained through interval-class inversion, in which the intervals change direction rather than occurring in complementation as in harmonic inversion. Since the intervals in a chord quality symbol are arbitrarily rep resented in ascending order, reversal of the order pro duces the descending i-c equivalent of each interval in the simultaneity. While tonal harmonies may be reduced to their simplest form (i.e ., within an octave) for analytical purposes and then given a normal order based on a re ferential pitch, atonal "chord qualities" (CQ's) require an arbitrarily stipulated referential pitch. Once this is stipulated, a CQ symbol gives just as much information about a vertical structure as traditional chord quality nomenclature. In other words, outside the tonal context, the description "major triad in first inversion" conveys 88 no more Information than the simple label **35^»" The labels merely permit the analyzer to give a distinct title to every possible vertical structure, as if each were as common as any other. A chord previously designated as an "augmented triad with a major seventh" is now simply labelled "1443," with the specific spelling, inversion, and possible derivation not requiring immediate interpre tation. Other simultaneities formerly requiring lengthy verbal descriptions are identified by their CQ symbols on p. 108 below. Schoenberg's Op. 19/5 can serve as an example of how CQ analysis is applied to atonal music. After the first’ note in this brief movement, each hand spells out a four-note item (Ex. 12).. In the R.H., it is C-A-ob-sb, or from lowest to highest within an octave, G^-A-sb-C. j r 1

' Usea by pernlsslon of p urt.iberToll Belmont Uuelc Publishers, Los Angeles, California 90049 LT t3 6.2. Ex. 12. Inversion-related CQ's in m.l of Op.19/5.

In the L.H., i t i s ob-B-D-F, or reduced, ob-D-F-B. In p-c set analysis, both items prove to be reducible to (0,2,3,6). This prime form is designated as the twelfth of the twenty-nine four-note sets in Forte's table, or 89 s e t 4-12. According to CQ analysis, the first item is 3126 and the second 1362. In this representation, an ordered rotation of the digits constitutes "harmonic inversion" of the simultaneity, since the total inter va llic distance is always the sum of twelve semitones. Thus, the four possible harmonic inversions of the first CQ are 3126, 1263, 2631, and 6312. The "normal order" is defined as the lowest possible integer repre sentation of the label, achieved by rotating the se quence until the smallest digit, or digits, is at the beginning. In this way, simultaneities related by "harmonic inversion" can easily be shown to be the same CQ. The particular format for normal order is chosen so that CQ's can be easily listed and referred to in numerical order.

Some General Characteristics of Chord Qualities

The two items from Example 12 may now be examined more closely. The normal order for cb-A-sb-C i s 1263, and fo r ob-D-F-B i t i s 1362. Since interval- class (i-c) inversion is achieved through reversal of interval direction, any CQ can be inverted to yield its i-c equivalent by simple reversal of the digits. The mirror form is then expressed as an ascending interval succession. Order is still maintained, merely reversed. ■ 9 0

By this procedure, 1362 becomes 2631.. Rotation into nor mal order yields 1263» Interval-class equivalence exists between 1362 and 1263; both are instances of p-c set 4 -1 2 . Some CQ's are self-invertible, that is, their i-c inversions are also harmonic inversions. This fea ture comes about when the Interval pattern of the CQ is symmetrical, and is readily apparent upon inspection of the CQ symbol. In the case of four-note chord qualities (abbreviated "CQ^."), symmetry occurs if the pattern of the intervals can be expressed according to the models aabb or abac. Examples of the former are 2244 and 1155;' of the latter, 1416 and 232$. It can be seen that re versals (retrogrades) of any of these can be rotated into orders identical to the original. Of course g, and b may stand for the same interval, so that 3333 (aabb) is symmetrical, as is 2226 (abac). Symmetrical CQ^'s occur in the form aab (a may equal b) » or the arrange ment abaj %rtiich is actually a different rotation of aab. Symmetrical CQ^'s take the form abbac or aabcb, where a may equal b or c, but not both. Invertible pairs, or pairs that are i-c equivalent, constitute only a single p-c set in Forte's table, because i-c equivalence is assumed. The two CQ's d isc u sse d above, 1362 and 1263, make up such a p a ir . 91

Other CQ's, since their i-c equivalent CQ's are also har monic inversions, make up a single p-c set by themselves. In other words, some p-c sets may break down into two distinct CQ's, whereas others consist of only a single CQ, regardless of the aspect in which they appear. Of the twelve three-note p-c sets, seven produce i-c equivalent pairs that constitute different CQ^'s. The remaining five are symmetrical, forming only a single CQg. The seven pairs plus the five single CQ^'s add up to 19 d is t in c t CQ^'s (sea Table 1).^ ^ The tw enty- nine distinct four-note p-c sets consist of fifteen self-invertible CQ^'s and fourteen i-c equivalent pairs, making a total of *+3 CQh's. Of the thirty-eight five- note p-c sets, only ten are symmetrical; the twenty- eight remaining pairs plus the ten make a total of 66 CQ^'s. In addition, there are 20+(2 x 30) CQ^'s, mak ing a total of eighty. These quantities are summarized in Table 1:

lOPerle, Serial Composition, p.109. 92 TABLE 1

The t o t a l number o f p -c s e ts and th e ir distribution into the total number of sym m etrical CQ's and p a irs o f i - c e q u i- valeht CQ's.

number number s iz e o f number of o f i c - t o t a l p c -s e t o f symmetri eq u iva- number o f or CQ DC-sets c a l CQ's le n t n a irs . CQ's

3 12 5 7 5H2 X 7)= 1-9 h 29 15 Xh 15+C2 X 14)= 43 5 38 1,0 28 10+(2 X 28)= 66 6 50 20 30 20+C2 X 30)= 80

As Schoenberg brought his twelvoytone theory to fruition, he became increasingly interested in interval- class equivalence (see p. 4 above). For this reason it might be useful to compare this type of inversions 1 equivalence with more traditionally accepted octave equivalence. The notion of "chord quality" is normally associated with a harmonic item that retains its identity despire the process of harmonic inversion. Pitch-class s e t s , vdien a ssig n ed to v e r t ic a l str u c tu r e s, presumably retain their identity in the course of i-c inversion as well as harmonic inversion. Thus, chord qualities tra ditionally considered to be distinct, such as major and minor, or dominant seventh and ha If-diminished seventh, turn out to be classifiable within a single p-c set. 93

Through CQ symbols, harmonically equivalent items can be immediately recognized (when put in normal order) and i-c équivalent items can be recognized if one member of the pair is read in reverse order. In this way, Schoen berg's developing interest in i-c equivalence can be measured free from the constraints of a system that assumes i-c equivalence. By the time of Opus 23, Schoen berg's use oi i-c inversion became so common that the two systems of analysis are almost equally applicable. However, one means of measuring the relative significance of i-c inversion in the pre-twelve-tone works is to de termine whether i-c equivalent CQ's are treated as such in the course of a composition; or, posed another way, to determine viiether there is evidence that Schoenberg recognized the i-c equivalence of the two chords from Op.19/5 (Ex. 12) and exploited this feature. Do such congruities appear regularly, or is this particular case anomalous? A numerical tabulation proves to be enlightening in this regard (see pp.102-124). For further comparisons with CQ theory, some details of Forte's p-c set theory w ill be reviewed. Forte used the term "vector" to refer to the interval- class content of a p-c set. Strictly speaking, a vec tor is a directed distance, such as "four semitones -higher" or "a perfect fourth lower." Interva1-classes 94 are not directed distances, insofar as they be direct ed either up or down. An inventory of the various in terva 1-classes present in a p-c set is certainly not a vector in the normal use of the term. Actually, the p-c set itself is closer to the concept of a vector than is the i-c content of a set. The content was represented by Forte as a six-digit figure, with each successive digit representing a distance in semitones from one to six. Thus, the string 111000 represents an i-c content of one m2, one M2, and one m3, or one each of interval-classes 1, 2, and 3* A CQ is something like a true vector, because it represents a series of directed intervals, not in terva 1-classes. Since a CQ symbol lists the actual intervals that make up an item (reduced to one octave), the i-c content can be quickly determined from the sym bol. For example, CQ 255 clearly contains a whole-step (two semitones) and two perfect fourths (five semi tones each). The i-c content reads 010020. In the case of a CQ^, the six intervals comprising the i-c content are, given the symbol abed: 95 That is, the i-c content of any C%, ahcd, is fe, c, Â» 8+b. and b+c. The calculation of the four first- order intervals (1, 2, 3» and h) and two second order intervals (5 and 6) can be shown to exhaust the i-c con tent. The second-order interval a+b is the complement of c+df since a+b+cfd=12. Hence, only the sum a+b or the sum c+d should be counted. Since b+c and a+d are also complementary, they represent the same interval- class and only one or the other need be counted. All other calculations repeat those already made. Given CQ 1272, for example, the i-c content consists of 1, 2, 7, 2, 1+2, and 2+7, or 1, 2, 2, 3, 7, and 9. This content is represented in the symbol 122010, where 7 becomes its complement, i-c5, and 9 its com plement, i-c3. The CQ 1272 corresponds to Forte's (0,2,3,5), set 4—10, idiich is shown to have the con tent 122010. The i-c content of any CQ^ abode is de termined as follows: a., h, A, d, a, a±h, h±A, A+d, d+e, and a+e. Thus the i-c content of CQ 12414, Forte's (0,1,3,7,8) or set 5-20, is 211231. (There is no danger of confusing lists of i-c content with the symbols for CQ&'s, because the digits of a CQ always add up to twelve, and the digits of the i-c content add up to 3, 6, 10 and 15 for CQ^'s, CQ^/s, CQ^'s and CQ^'s, r e s p e c tiv e ly .) 96

Forte's p-c sets may be quickly derived from a CQ if the latter is ordered with the largest possible digit at the end and, if possible, the smallest at the beginning. This procedure may require using the i-c inversion of the CQ to determine the prime form of the p-c set. As an example, 122^3 may be rotated into the form ^3122 and inverted (reversed) to 2213^. Since the last, and now largest, interval merely fills out the octave, it is not needed to generate the five pitch- classes of the set. Starting at zero, then, 2213 generates 0,2,4^5,8 (i.e ., C,D,E,F,Ab), idiich proves to be Forte's 5-26. The i-c content, determined as dis cussed above, is 122311. An additional advantage of CQ notation, be sides the fact that it does not presuppose "set- consciousness” (see p. 32 above), is the multiple func tion of the symbol. While Forte's table involves three designations; a set label, a list of pitch-classes, and a vector, CQ symbols act as/both a label and a list, and quickly yield the i-c content \dien it is needed. Since i-c equivalence of CQ's is revealed by simple reversal of the digitsr analysis using these symbols has several distinct advantages over the use of Forte's sets and la b e ls . 97

Thus far, p-c sets and CQ»s have been dis cussed only in connection with the vertical dimension. Lengthy themes, in which specific pitches, are placed in a specific order and note-value pattern, resulting in a specific contour, are not employed in Schoenberg's free atonality. A so-called "cell" is even more basic than a motive (see p. 16 above), because only the indi vidual pitches, or more precisely, the interva 1-classes, are significant, and not the order. In a p-c set, too, the specific pitches and intervals are no longer essen tial, only the interva1-classes. Pitch-class sets, then, are a way of categorizing "cells." Thus, "set- consciousness" (or "cell-consciousness") is really a matter of a composer systematically using specific in terva 1-classes at certain points in a composition, vertically, horizontally, or two-dimensionally, and at any pitch level. Because of this, a system of analysis emphasizing interval make-up, rather than pitch make-up, is preferable for atonal music, even where small in stances of "set-consciousness" can be demonstrated. It is not known precisely \ih en Schoenberg accepted the notion that inversionslly related inter vals (or mirrorings) make up interva 1-classes. The only way to prove "set-consciousness" in Schoenberg's atonal 98

music, works written before his disclosure of the twelve- tone method in 1921., is to compare the analytic results when i-c equivalence is alternately assumed and not assumed. Chord quality analysis is capable of represent ing i-c equivalence clearly, but does not assume it. It is important to point out that CQ analysis is also useful in categorizing melodic segments. As stated in the first chapter (p.26 above), the principle of verticalization may eliminate order from a horizon tal item. Thus, it permits the same type of analysis to be done on horizontal and vertical items alike. Con sequently, any melodic item may be categorized as if it were an arpeggiated CQ. Given a certain CQ, there are several re arrangements of the digits that represent neither har monic nor i-c inversions. Given the i-c equivalent CQ pair 1263 and 1362, each has three harmonic inversions. All eight are equivalent by i-c inversion. These inver sions are produced by rotating the digits of the CQ mak ing each digit first, in turn. For CQ 1263, this pro cess yields 2631, 6312, and 3126; for CQ 1362, this yields 3621, 6213, and 2136. All eight of these order ings are related either by harmonic or i-c inversion, or both. Other arrangements of the digits 1362, 95 > however, such as 1623, 1632, 1326 or 1236, are not In ver slona lly related to it, because the order is not main tained by strict rotation or reversal of the digits. The completely distinct qualities of these unrelated pairs may be shown if each is matched with its i-c content:

Î263J- 112101 13261-111111 12361-112011

Caution must be taken that similar looking anagrams of CQ's are not mistaken for related CQ's. It is only be- • cause of the numerical representation of these items that the confusion of anagrams and actual inversions is p o s s ib le . Before comparing the tabulations of chord qualities in selections by Brahms and Schoenberg, it w ill be useful to demonstrate how CQ analysis can give a complete numerical representation to both vertical and horizontal elements in these works. Opus 19/1 has been taken as an example, and the results are shown in Table 2. In each measure, the CQ's that occur verti cally, horizontally, or entirely within one hand are in dicated. Horizontal segments were based on rests or other clear punctuations in the parts. The brackets indicate congruities between CQ's. In order to give as accurate an impression as possible, temporally close congruities containing identical pitches were 100

considered mere repetitions rather than the emphasis of

a given CQ. The most striking feature of the work re

vealed by this analysis is the wide variety of CQ^'s and

CQg»s employed. Beyond this, the only repeated CQ

treatment appears to be that of CQ's 1335 and 1533»

appearing in measures 2 , 3» 4-, 6, 7, and 8. These repe

titions are not applied in any systematic way. The aurally unstructured effect of Op,19/1 is, indeed, cor roborated by the material in Table 2. 101

TABLE 2

Meas, Vert. Horiz. R.H. L.H. Meas. Vert. Horiz. R.H. L.H. 0 I- 1137 7 1623 [1533 2244 L1335 1 1164 1542 255 8 121314 165 1443 r156 [1335 Li 533 2 Li 56 r1533 1146 345 H533 237 9 14223 1434 1443 3 1137- 1119 1623 11253 10 1443 1146 1443 1236 11442 [1173 2343 13143 Li 173 r 1335 12243 336 13143 2235 11343 1236 11442 12243 4 12216 1722 237 12315 1119 11 11442 1623 1443 2325 13143 1722 ^ 1335 12 1353 11343 r129 13 12153 1128 336 228 13215 264 L-192 13224 12414 5 1137 r138 246 1362 r LI 38 336 14 1227 1362 336 1317 11163 ■ 444 [1443 1434 165 L1344 [2433 L- 183 2433 L2334 15 1425 1353 147 1335 11424 138 12243 11325 12333 14232 11442 12144 16 11424 1317 [ 147 11514 174 6 1335 - ' 14232 1245 1416 17 12225 1416 147 2226 -1533 11325 138 11244 ■ 147 11325 129 Note : Brackets indicate two identical CQ's containing different pitches and those that are sufficiently distant to indicate a congruity, rather than a repetition. 102

ATabulation of Chord 'Qualities In Schoenberg’s Atonal Plano Worka

This section gives the details and results of a count of all simultaneities in Schoenberg's atonal piano works (0pp.11.19 and 23), and a comparative count in Brahms' piano pieces, Op. 76. This count was con ducted without reference to non-harmonic tones, so that the issue of essential and non-essential harmonies in atonality could be avoided. The quality of every 3-, , 5“ > and 6-note simultaneity in these works has been determined and assigned a CQ. Even this straight forward approach was not without complications, such as how to deal with apparently ornamental tones. As far as possible, analogies have been drawn from common practice music, rather than from Schoenberg's twelve- tone music, in determining which notes to include. The following criteria have been applied: (1) In cases of alternating note figures (e.g.. Op..11/2, m.61), only one occurrence of each simultaneity has been counted. Recounting each repetition would produce an inaccurately unbalanced picture of the frequency of that particular simultaneity. 103 (2) Held notes have, In almost all cases, been observed for their notated duration, regard less of the effects of decay. In cases \diere several newly attacked tones would cover a faint sustained tone, the latter was not in cluded as part of the simultaneity. (3) Short grace notes, although usually integrated in strict serial practice, have been treated as in common-practice music, i.e ., as non- essential tones. They have been disregarded for purposes of this count, since they are clearly ornamental even in this context. (^•) The few brief passages involving the use of harmonics have been omitted from the count for reasons similar to those in criterion (2). (5) As in common practice music, trilled notes have been read as the notated pitch, rather than the upper neighbor, the latter being exclu d ed .

One purpose of such a count is to reveal whether any particular simultaneity is actually preva lent. The simultaneity sought might be a single CQ, or an inversionslly related CQ pair corresponding to a single p-c set. In the latter case, the relative totals of each specific CQ, each representing a dif ferent aspect (prime or inverted) of the p-c set, might reveal Schoenberg*s concern with chord quali- 11 ties in the traditional sense.

^^Although there are certainly a few cases in vrtiich the above criteria might be subject to differing interpretations, they represent only a very small pro portion of the more than 3,$00 chords counted. In any case, the comparative totals for the Brahms and Schoen berg samples can be considered quite reliable. 1 0 4

The fact that e v e ry single vertical structure was counted had to be taken into consideration, since the effect of such an unselective procedure was not known. To show the effect of including idiat might be "non-essen- / tial" structures in the CQ count, the same procedure was applied to Brahms' Op.76. In this case, the prevalent simultaneities could be predicted, and clearly pre dominated despite many unfamiliar CQ's resulting from the inclusion of nonharmonic tones. The results of these counts are displayed in a series of tables. In Table 3, the raw data from each movement by Schoenberg are shown. In Table 4, the data from the Schoenberg and Brahms sam ples are summarized. (N.B.: because of the brevity of the individual movements in Op.19, the entire work has been treated as a single movement for purposes of com p a r iso n .) The CQ's in Table 3 are not arranged in simple ascending numerical order. Instead, the symmetrical CQ's (i.e., those that are p-c sets in themselves) are listed at the beginning of the section for each size. Then each i-c equivalent pair is listed, with the first of each pair in ascending numerical order. This arrange ment immediately shows the relationship between the frequencies of i-c equivalent chord qualities. TABLE 3 - Raw data for the CQ count of Schoenberg's 0pp.11, 19, and 23

CCl^ 11/1 11 /2 11/3 19 23/1 23/2 23/3 23/4 23/5 11/1 11/2 11/) 19 23/1 23/2 23/3 23/4 .23Z5_ 1110 0 1 0 0 6 0 4 0" 5 2424 1 1 0 0 0 1 2 0 2 220 T k 0 2 " 6 0 5 3 14 3333 0 1 0 0 0 0 1 4 0 255 2 3 1 1 5 2 7 4 1 1128 2 3 0 0 2 4 1 0 5 336 8 6 2 1 5 • 1 7 6” 0 1182 0 0 3 0 0 1 2 0 3 r 6 2 3 3 3 10 12 1137 4 1 1 2 2 0 1 0 4 129 3 %" 1 1 - 4 0 2 4 ' 2 1173 3 0 ..... B ■" '2 0 0 0 1 4 192 3 2 2 1 5 4 3 1 2 1146 i 0 2 0 1 1 2 0 1 136 15 19 2 1 8 4 5 8 7 1164 0 4 4 1 0 0 3 0 4 183 11 1 3 1 4 6 8 7 7 1236 1 4 2 4 0 1 3 1 0 147 7 7 0 14 0 2 2 T 1632 • 1 10 2 C 0 0 3 0 0 174 4 7 2 1 14 1 10 3 2 1245 0 8 2 2 2 1 7 0 3 156 2 5 2 3 10 0 6 0 0 1542 0 2 0 0 0 0 2 2 1 165 0 4 6 0 7 1 3 1 0 1254 0 4 2 . 1 0 0 4 0 0 237 5 2 1 0 8 0 2 2 2 , 1452 2 0 0 2 0 2 1 3 4 273 5 3 0 È 8 2 "S' 2 -6' 1263 2 2 2 0 0 1 3 0 0 246 19 9 3 0 11 4 3 6 4 , 1362 3 5 0 1 1 3 6 4 : 0 264 Ô 6 3 1 9 3 T 13 -■ S 1 1227 0 0 0 1 1 0 1 1 7 3^5 10 7 0 1 9 2 7 11 3 : 1722 2 1 0 0 0 1 2 0 0 354 à 8 1 1 5 1 10 5 1 1 Ï326 2 4 1 0 0 0 1 1 4 1623 2 10 1 4 1 0 3 3 3 j .. ^ 1119 0 0 0 0 0 1 1 0 2 ! 1335 4 5 3 5 0 2 0 1 ri55 0 4 5 0 2 3 1 0 1 ' 1533 ■ r ' 6" 3 B 1 4 7 1 1 lâïï 1 5 1 0 1 3 3 1 2 , 3 344 5 13 5 3 3 2 5 8 3 13x7 3 7 4 4 3 1 1 11 2 , 1443 3 3 2 é 0 4 6 5 11 Ï4l6 2 6 2 3 3 2 2 2 0 1425 1 14 3 4 2 1 3 1 2 1515 1 0 1 0 1 1 2 0 0 1524 1 13 3 0 2 1 3 0 1 1272 0 1 1 0 0 0 2 0 1 2235 1 4 0 2 2 1 0 4 4 0 0 2 1353 0 4 2 1 1 0 3 5 1 2253 1 0 1 0 2 1 Ï5'34 1 2334 1 7 0 2 1 2 4 3 1 3 1 1 2 2 0 2 1 — 2j“ 2226 3 4 0 2 0 0 0 2 15 — 23_------2_ ------— ------——------— 2244 5 6 4 3 1 0 5 2 21 • H 2325 0 1 2 2 1 2 2 0 0 3 Ul 2343 0 2 1 2 0 3 0 ■4 "2 CQ, . .AJfi__ 0 0 0 0 0 0 0 0 0 l l / l 1 1 /2 1 1 /1 19 21 /1 2 1 /2 2 1 /1 2 1 /4 2 i/< 11118 CQ, 0 I 0 1 0 1 3 0 I 112A2.. 0 0 0 0 0 0 0 0 0 4 1 2126 0 2 0 1 0 0 3 0 0 iiaü, J 1 1 0 0 1 2 0 11424 0 2 0 12162 0 4 2 0 0 2 0 0 0 1 1 0 1 0 0 1 12116 0 0 0 1 0 0 0 1 0 12144 1 0 2 3 1 1 1 1 1 1216? 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2 2 12226 0 0 0 1 0 0 0 1 1 o: 3 3 0 3 1 0 16222 1 2 0 1 0 0 0 1 0 22224 1 0 c 1 0 0 2 0 0 12214 0 Ù 0 0 0 0 1 1 0 22231 1 0 0 3 0 3 0 0 0 14122 J 0 0 0 0 0 0 0 0 SSI22. 0 0 0 0 0 0 1 0 0 12262 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12622 0 1 0 4 0 0 1 2 0 a m . 0 0 0 3 c 0 0 0 0 12116 0 0 1 1 0 0 1 D 1 11136. 0 0 0 0 0 0 0 0 0 11216 0 4 0 1 0 0 0 0 3 0 0 1 0 0 0 0 0 0 12124 0 0 0 2 0 0 1 0 0 11145_ Û 0 1 0 0 0 0 0 0 14232 0 0 1 2 0 0 0 1 0 0 0 0 0 0 0 0 0 12414 2 2 2 0 0 0 0 0 0 U 2 1 Z . 0 Ü 0 0 2 0 1 0 0 14142 0 0 1) 2 0 0 j 2 c 1171?.. 0 0 0 0 c 0 3 1 0 12111 0 0 0 1 0 0 1 0 0 1 1 2 2 6 . 0 0 0 0 0 0 0 2 0 11112 0 0 0 1 0 0 1 0 0 11622 0 2 0 0 2 0 0 0 12142 0 1 0 1 0 0 1 0 0 11216 0 0 1 0 0 0 1 0 0 12412 0 2 0 1 0 0 1 0 1 11612 0 0 0 0 0 0 3 0 0 12421 0 0 0 1 0 0 1 3 11244 1 0 1 1 0 0 2 1 1 11242 0 1 2 J 0 0 1 0 0 1 1 4 4 2 . 1 2 1 3 0 1 0 0 0 12611 0 3 2 0 0 0 0 4 0 11261 0 1 1 0 0 0 0 0 0 11162 4 4 3 1 1 0 0 0 ^1362 0 0 1 0 0 0 1 c 0 11134 0 1 J 2 0 I 5 1 1 11316 1 0 2 0 0 0 1 0 0 11141 0 3 0 1 0 0 1 0 U & ll 1 0 2 0 0 0 1 1 0 11224 0 3 1 2 0 0 1 3 0 JLI3?S 0 2 0 2 1 . 0 0 0 1 14223 Û 0 1 0 0 0 1 0 1 1 2 U 0 0 0 0 0 Û 1 0 0 13211 0 1 1 0 0 0 1 3 0 0 0 1 2 0 0 1 0 0 13121 0 1 1 3 0 0 1 1 1 c 0 0 Û 0 0 1 c 0 12241 2 0 2 0 0 c 2 0 0 m i 5 . 1 1 1 1 1 0 0 0 0 13422 j 1151t. 0 c 3 0 1 0 0 0 0 107 More insight into the data w ill be gained by a closer look at CQ labelling. This aspect of CQ analysis sim plifies chord reference and avoids the issue of har monic function. Without the analysis of harmonic func tion, there can be no notion of incomplete chords (see p. 81 above)• Thus, chords that would be classi fied alike in tonal music are necessarily differentiated in a literal CQ count. One example is CQ 2^-6, which might be analyzed in tonal music as a dominant seventh with the fifth omitted (e.g., F-G-B) or an Italian s ix t h . In th e harmonic a n a ly s is o f a >k>zart so n a ta , such a chord would be analyzed as a Wiether the fifth wore present or not. In the same way, 237 would be a minor seventh with the fifth omitted (e.g., C-D-F). The notion of incomplete chords would permit us to equate CQ 246 with CQ 2433 (the tritone, 6, is broken into two minor thirds, 3 and 3), and CQ 237 with CQ 2343 (the fifth is broken into a major and minor third. The CQ count revealed that in the Brahms selections, incom plete seventh chords were actually more frequent than complete seventh chords. The dominant-related CQ 246 occurred a total of .108 times in the eight pieces, vdiile CQ 2433 occurred only 79 times. The incomplete CQ 237 occurred 96 times, but the fu ll minor seventh, CQ 2343, occurred only 18 times. In the Schoenberg selections, 108

where implied harmony could not be assumed, such connec tions were not drawn. Many other relationships between CQ's and triadic chords may be noted (other than the familiar triads CQ's 336, 444, 34$, and 354), such as:

CQ^ 147 - major seventh with fifth omitted: B-C-E 174 - major seventh with third omitted: B-C-G 273 - minor seventh with third omitted: C-D-A 264 - major triad with flatted fifth: C-E-GP CQ. 1353 - "major-minor” triad: B-C-E^-A^ ,1434 - major seventh chord: C-E-G-B

In the discussion of prevalent simultaneities (see p.65 above), the categories of pandiatonic and whole- tone chords were discussed. The CQ's that fall.into one of these two categories are:

CQ 228 - two consecutive vtio le ste p s : C-D-E ^ 255 - two P 4 's or P 5 's: C-F-G 156 - P4 and A4: C-F-B 165 - A4 and P4: F-B-E CQi^ 2226 - three consecutive whole steps : F-G-A-B 2325 - three P4's: D-G-C-F 1416 - P4, A4 and P4: C-F-B-E 1227 - two ^ ole steps and P$: C-D-E-B 1722 - P5 and two \rtiole step s : C-G-A-B 1425 - A4, P4 and P4: F-B-E-A 1524 - P4, P4 and A4: G-C-F-B 2235 - two \diole steps and m3 : C-D-E-G 2253 - two \diole ste p s and P4: C-D-E-A

It can be seen that the specific examples were all drawn from the C major scale. Many of the above CQ's can be generated by a series of fourths ; any one of them can 109

appear In a tonal piece as a result of diatonic suspen sions or other nonharmonic tones. Of course, any CQ con taining only digits that are multiples of 2 can be de rived from a whole-tone scale. The origins of these chords have been shown to help explain their frequency in the Brahms selections, as shown in Table h» Since many of them are "passing" sonorities, a total count can help determine the proportion of "passing" sonorities to essential harmonies. Because a ll vertical structures were counted, many CQ's counted in the Brahms selections were known to be nonharmonic structures. Even if the essential simul taneities in Schoenberg's atonal piano works were dis tinguishable from the non-essential ones, the ratio of essential to non-essential would still have to be much greater in the Brahms sample, because of the greater se lectivity exhibited. That is, on the basis of the tabu lation alone, the essential harmonies in the Brahms se lections can be identified because of their more fre quent occurrences. In the Schoenberg pieces, no CQ's or CQ stand out in a comparable way, as Table 5 shows. There are some cases in \diich the total of occurrences for an invertible pair is large enough that the p-c set in question might be said to dominate the vertical -organization. In Op. 11/1., for example, CQ's 138 and TABLE 4. Summary of results of the CQ tabulation in Schoenberg's 0p p .11, 19 , and 23, and Brahms' Op.76 piano pieces.

------Opp.ll, iiZ i 11/3 12 23/1 2 3 6 . 23/3 A. Of 19 CQ^'s, number tia ed .... 19 17 19 14 15 19 13 19 B. Of 43 CQ^'a, number u se d .... 43 28 36 28 26 23 28 .38 C. Of 6A CQ^'s. number u se d .... gB 12 26 27 34 5 5 32 D. Total 3-note chords counted.. 722 . 124 104 31 21 141 34 97 B. Total 4-note chords counted.* 752 61 176 65 63 37 53 114 P. Total 3-note chords counted.. 286 20 49 43 51 5 11 51 0. Most frequent CQ^....,...... 138 SÜ6 138 . 161 156 l&7alZ& 1S3 i7A.31& H. Most frequent CQ|^...... 2244.1344 2244.1344 m s 1155.13fâ 1443 (1) (2) 1533.1215 1. Most frequent CQ^..;...... 13134 Of (4) (5) 12311 ** 1314] J. Frequency of above dQ^..... 9.5* 15. 3* 18.3* 19.4* 14.3* 9.9* 17. 7* 10. 3* K. Frequency of above CQ^.. . . . 6.3* 8.2* 7.9* 7.7* 9 . 5* 8.1* 7 . 6* 6 . 1* L. Frequency of above CQ^«.*«. 5 . 6* 20.0* 8.2* 7.0* 7.8* 20.0* 18.2* 9.9* K. Total 3-4-5-6-note chords.. I851 209 332 173 145 183 104 284 N. Percent 3-,4-note chords.. 39.0, 59.3, 31, 3, 17,9, 14.5, 27.5, 32. 7, 34. 3 , 40.6 29.2 53.0 37.6 43.4 20.2 51.0 40.2 0. Avg. ST's per chord counted.. 0.97 0.78 0.92 1.45 1.20 0.73 1.12 1.01 P. * of chords with2or more ST'S 25.7 18.1 21.4 54.9 35.8 13.7 35.6 23.2

(1) 1344.1414.1317 (2) (3) 11343.13134 (4) I?135,12324.l3i2& (5) four used three times each * none more than twice O TABLE If, continued

i2ÙL 23ZS m P76/1 m u B76/3 P?6A B?6ZS B76/i B76/7 B76/B A. . • • 17 16 19 17 17 12 15 13 15 13' 16 B. . . . 24 33 31 19 20 15 9 7 15 12 13 c. . • • 23 11 12 4 4 2 0 6 1 0 2 De . . . 38 82 1383 209 245 51 191 220 165 99 203 E. . . . 75 112 347 41 55 63 31 22 50 29 56 P. . . . 37 12 35 4 6 4 0 7 1 -0 13 Q. . . . 3 ^ 228 m m m m I5Ü 2&Ï m H. ...1317 2244 m i (6) sail 2!kji»imm i a m 2433 2433.2334 m i I. . .m M • 2%233 •• * * # * * • J. . . . 14*7f 14.6% 19.7% 16.7% 23.3% 27.5% 20.9% 25.9% 22.4% 20.2% 24.6% K. . . . 14.6% 9.8% . 22.8% 9.8% 14.1% 14.3% 32.3% 54.5% 26.0% 17.2% 32.1% L. . . . 10.6% 16.7% 22.9% • * * * • • • * N. . . . 216 216 1765 254 306 118 222 249 216 128 272 H. . . . 40.B. 37.9, 78.8. 82.3. 80.1. 43.2. 85.8. 88,4. 76.4, 80.5, 74.6 34.7 53.7 19.7 16.1 17.8 53.4 14.2 8,8 23.1 19.5 20.6 0. . . . 0,83 0.84 0.15 0.27 0.24 0.33 0.18 0.08 0.13 0.12 O.lJ

(6) 1117.1261.2413 * non* nor* thantwlo*

H H H 1 1 2

TABLE 5

The ten most commonly appearing CQg's and CQ^/s in the Brahms and Schoenberg samples.

Brahms Schoenberg CQ-^ % CQ:t % T. 354 19.69 138 9-55 2. 345 19.26 246 8.1? 336 15.58 264 7.34 246 7.79 345 6.92 5 . 273 7.14 444 6.78 6. 237 6.92 183 6.64 7. 255 5.26 174 6.09 8. 264 4.11 354 5.54 9 . 174 2.23 228 5.54 10. 147 2.09 336 5.00 T otal % accounted for 9 0 .07 67.57

^ CQ4 ^ 1 . 2433 22.76 1344 6.25 2 . 3333 8 .6 4 2244 6.25 3 . 2334 7.78 1443 5.31 4 . 2325 6.34 1317 4.78 5. 2343 5.18 1425 4 .1 2 6 . 1434 5.18 1623 3.59 7 . 1254 4.61 2226 3.45 8 . 1533 4.32 1245 3.32 9 . 1236 4.32 1335 3.32 1 0. 2235 ^A 5 1533 3 .1 9 T otal ^ 1524 accounted for 72.58 4 6 .7 7 113

183 occurred a total of twenty-six times.. The fairly balanced distribution, fifteen and eleven, respectively, could be interpreted as evidence that the composer saw them as equivalent (see Table 3). In Op.23/1 as well, the sum of occurrences of CQ's 1^7 and 17^- is twenty- eight, i.e ., fourteen each. Here, the two criteria applied to discover possible "set consciousness" are sub stantial frequencies and fairly equal distribution be tween the two CQ's of the invertible pair. If the sub stantial data collected show little or no evidence of "set-consciousness," then its significance in these works must be doubted. More substantial frequencies might in dicate Schoenberg's interest in a given choice of inter val classes, and the balance between occurrences of the two CQ's might indicate equal interest in the two aspects of those interval classes. The results show, however, that even in the cases vdiere the distribution is balanced between two aspects, the sum of the two frequencies is still quite low. In fact, it is below the typical fre quency of the most frequent CQ^ in almost every one of the Brahms pieces. That is to say, the 28 combined occurrences of 1^7/17^ in Op.23/1 give that pair a fre quency o f 19 . 9^. There is only one Brahms selection, B76/I , idiere the most frequent single CQ had a frequency lower than the combined frequencies of CQ's 1^7 and 17^ 1 1 4

in Op.23/1* Interpreted in this way, the figures sup port "set-consciousness"in the Brahms sample more con clusively than in the Schoenberg. In th e ca se o f CQi^'s, th e equal d is tr ib u tio n gives a numerical explanation for the "harmonically" noncommita1 effect of much of Schoenberg's atonal piano music. As Table 5 shows,.the difference in frequency between the first and the tenth most common was, for Brahms, just over 19^, but for Schoenberg, slightly more than 3/2. Compared to the r e la t iv e fr e q u e n c ie s o f the ten most frequent CQ^'s and CQi,.'s found in the Brahms selections, those found in the Schoenberg showed an al most equal distribution. Another important comparison is the total percentage of chords accounted for by the ten most frequent. In the use of CQj^'s, for example, over 72^ of those used by Brahms were among the ten most frequent. For Schoenberg, less than half (46.77^) were among the ten most frequent. Four-note simultaneities made up a far greater proportion of the vertical dimension in the Schoenberg selections than in the Brahms (Table *+, lin e N ), in d ic a tin g more com plex, though not necessarily thicker vertical textures (be cause of the variety of doublings used by Brahms). Also, Schoenberg used more than twice as many differ ent CQi^'s as Brahms in an average p ie c e , as shown in 115 Table 6 . The figures reveal an indisputable effort on Schoenberg's part to avoid an emphasis on any sonority, v h e th e r it contains 3» or 5 notes, or \diether its

TABLE 6

The average number o f d iffe r e n t CQ's o f each s iz e appearing in a given movement in the sample.

Brahms Schoenberg CQb 1^.75 16.56 cqm. 12.25 29.33 CQ5 2.37 19.44

structure is tertian or otherwise. A notable feature of the vertical texture is the high "dissonance" level, in conventional terms. The item in line 0 of Table 4 is not a count o f the number o f sem itones p resen t a t any given time, because two-note combinations and combina tions of seven or more notes have not been included. As the item states, it provides only the average number of semi-tones per,chord counted. This sum is the total num ber of digit "1's" appearing in the CQ's counted, and therefore includes the derivatives of the semitone as w e ll. A lso n otab le i s the number o f s im u lta n e itie s occurring with at least two semitones. In the total 116

Schoenberg sample, 25*7^ of the sim ultaneities contained two or more semi-tones. Examples of such CQ's are 1164, 1128, 11235j e t c . The same c a lc u la tio n fo r th e Brahms sample yielded 0.5/^, I.e., only one out of every 200 si multaneities with two or more semitones.

The Case Against Interval-Class Equivalence as an Important Factor In Schoenberg's Atonal Procedures

To reiterate a point discussed In the first chapter (see p.43), one can make an Issue of vdiether Schoenberg's belief In the unifying potential of Inter- va 1-class equivalence Is demonstrated In the pre-twelve- tone works, or idiether that belief is. In Itself, sound. Obviously, Interval-class equivalence Is an Integral element In Schoenberg's twelve-tone serlallsm. The Issue at this point Is not whether Schoenberg eventually began to use Interval-class equivalence as a unifying device In the works Immediately preceding the twelve- tone period (i.e ., 0pp.23 and 24); nor Is the Issue vdiether these devices actually contributed to the unity of those works. The question"Is merely whether Interval- class equivalence Is an Important structural device in Schoenberg's atonal music. Evidence for real "set consciousness" In Schoenberg's atonal works would take the form of some systematic application of Inversion 117

relations. As evidence against Schoenberg's systematic use of interval-class equivalence, the argument w ill be offered that many clear-cut applications of i-c related CQ's can be viewed as mere accidents of tho constantly fluctuating vertical dimension in Schoenberg's atonal m usic. The musical connection between a vertical structure and its i-c inversion has been assumed by twelve-tone theorists and serially-oriented analyzers. In the horizontal dimension, the problem is somewhat com plicated by the use of melodic inversion in earlier music, although the two types of inversion are not thoroughly identical. All that can be proven about the two CQ's of an i-c equivalent pair is that they are arithmetically equal, not that they are musically akin to one another. An arithmetic connection also exists between anagram- related chords, although their musical equivalence can hardly be asserted. If anagram relations are comparable in frequency to inversion relations, the significance of the latter is reduced. No commentator has argued in favor of "anagram-consciousness" in Schoenberg's atonal works, although the numerical evidence supports it more strongly than "set-consciousness," as the tabulation below indicates (see Table 7, p.123 ). If a certain in vertible pair seems to accur with comparable frequency, 118 or to reappear at strategic points, this tendency should be compared to similar tendencies of anagram-related chords. One should recall, however, that the 1-c Inver sion of a CQ Is also one of Its anagrams. In this case the exact reversal of Interval direction. If 1-c Inver sions occur only In a moderate proportion of anagram cases and are viewed as accidents of anagram occurrence, their organizational significance must necessarily be brought Into doubt—a condition that bears on the evaluation of 1-c Inversion as a compositional device. The tabulation of occurrences of anagrams and 1-c Inversions (Table 7, p .123) offers another way to compare the merits of CQ and p -c s e t a n a ly s is . For CQ^'s a l l anagrams are a ls o Inversions. A shift In the order position of only one digit already yields the 1-c Inversion. Thus, no com parison can be made between CQ3 relations that are mere anagrams and those that are 1-c Inversions. The smallest CQ for Tdilch the comparison may be made Is CQi^. Even In chords of at least four notes, however, symmetrical chords cannot be used for this comparison, because they appear the same In prime and Inverted aspects. Some sym metrical chords can have anagrams, vdille others cannot, depending on the digit pattern. Any CQi,. of the pattern aaaa obviously can have no anagram or 1-c Inversion. The same holds true for aaab. Thus, the only chords 1 1 9

that have been taken Into consideration for this compari son are members o f CQ^. or CQ5 I n v e r tib le p a ir s . The greater the extent to which anagram relations outnumber 1-c Inversions, the more the latter may be viewed as mere accidents of Inevitable anagram relations. The evidence severely undermines the notion of ^set-consciousness," vdilch would be demonstrated In the Intentional and sys tematic application of Inversion relations. The original purpose of the CQ count was to see If Schoenberg's atonal works repeatedly demonstrated a preference for certain CQ's over their 1-c Inversions. Any marked preference for one aspect of a given CQ would show that the particular Intervals, rather than Interval- classes, continue to be significant. In actual fact, the CQ count In Table showed that despite an occasional em phasis he gave to a CQ^ or CQj^, Schoenberg did not show a preference for any CQ or p-c set In the vertical dimen sio n . Lines A, B, and C of Table Indicate the num ber of available CQ's of each size that actually appear at least once In a given movement. The lim its, as de rived earlier, are Included for each size In the Item description, so that the degree to idilch the vertical dimension Is saturated with different structures can be observed. In three of the selections, 0pp. 11/ 2, 2 3 /1 , 120 and 23/3? every one of the 19 possible CQ^'s appears at le a s t o n ce. The g r e a te s t number o f d iffe r e n t CQ^'s used by Brahms in the movements analyzed was 17, in B 76/I and B76/ 2 . So, with regard to CQ^'s, Schoenberg achieved total saturation of available CQ's in three of the movements and Brahms achieved nearly total saturation in two. In the case of CQj^'s,'Schoenberg used 38 o f th e possible 4^3 In Op.23/3» For Brahms, the greatest number of different CQi^'s appearing in a single piece (B 76/ 2) was only 20. The total number of structures analyzed of each size appears in lines D, E, and F. By comparison with lines A, B, and C, one can see that the two movements by Schoenberg w ith th e g r e a te s t number o f n ote sim ul taneities counted (0pp. 11/2 and 23/3) also had the greatest number of different GQi^'s. The underlined figures in items G, H and I are the labels for the most frequent CQ's in each piece. In cases where space did not permit the listing of multiple CQ's, they are indicated in a footnote. In several move ments \diere no CO^ occurred more than twice none could be designated as most frequent. The number of occurrences of the most frequent CQ was then divided by the total num ber of simultaneities of that size counted, as shown in line D, E or F. This ratio is expressed as a percentage in lines J, K and L. For example, in Op.19 , the most 121 frequent CQj^ was lV+3, which accounted for of all . in Op•19* Line M shows th e t o t a l number o f sim u l taneities analyzed in each piece. Some simultaneities of more than six notes occur in these works, but the quan tity is very small. The two percentages in line N repre sent the quotient of line M divided into lines D and E, respectively, showing the relative proportion of 3- and 4-note simultaneities in the sample. This figure gives a general indication of the complexity of texture in a given movement. The first column in Table 4, idiich contains the totals for all nine Schoenberg selections, shows that four-note simultaneities, slightly outnumbered three-note simultaneities. The sum of both percentages in line N, ■vdien subtracted from 100 to give the remaining percent age, also indicates the percentage of simultaneities of more than four notes. It can be surmised then, that the pieces with the most complex texture are those for vrtiich th e second number in lin e N i s much la r g er than th e f i r s t , but for which the total of both numbers in line N is low. The two selections fitting these criteria can quickly be identified as 0pp. 11/3 and 19 . The true importance of CQ distribution can be measured only after a complete analysis of horizontal as 122 welll as vertical structures. This analysis requires the categorization of every three-, four-, five-, and six-note setment in each voice. Just as the unfamiliarity of the idiom makes it impossible to distinguish essential from non-essential harmonies, it also hinders the analyzer from simplifying the melodic material by means of a break down into phrases, motives, etc. This approach was attempted, however, in Table 2 (p.ioi) above. The formal structure of much of this music is still so vague that key structural points cannot be conclusively identified. (This problem is discussed in Chapter IV under the topic of contextual emphasis.) The vertical count in Table ^ does, however conclusively demonstrate that the pitch or ganization in the purely vertical dimension is of a very low ord er. The complete CQ count of Opp.ll, 19 and 23 re vealed only a few cases of definite "set-consciousness." For the purpose of comparing inversion and anagram rela tions (see p. 98 above), three different items were sought in an additional count: contiguous inversions, alternate inversions, and aba inversions. The criteria are defined below, and the totals appear in Table ?• A "contiguous inversion" is an instance in \diich a CQ and its i-c inversion appear in two consecutive chords. An "alternate inversion" exists where a CQ and its i-c inversion occur 1 2 3 with a single chord intervening. An "aba.inversion" describes a CQ, its i-c inversion and the CQ again in direct succession (i.e., in the pattern a-b-a). An identical count was made for contiguous, alternate and aba anagrams. This was a possible way of judging in stances of i-c inversion as accidents of anagram rela tions. Several excerpts from Op.11/3, illustrated in

TABLE 7 A comparison of i-c inversion and anagram relations.

CQi, CQ6 T ot. contiguous inversions 12 3 1 16 contiguous anagrams 30 15 3 lf8 alternate inversions 6 0 0 6 alternate anagrams 26 8 1 35 aba inversions 4. 1 3 8 aba anagrams 0 1 0 1 total inversions total anagrams 2k it IS

Example 13, show how the count was made; contiguous in versions : measure 2 (CQ^); contiguous anagrams : measure 2 (CQ5), measure 3, (bwo CQ^*s), measure I 3 (CQ5 and CQg), and measure 18 (CQ^ and CQ^); alternate anagrams: mea sure 2 (CQ^), measure 8 (CQi^), measure 10 (CQi^), mea sure 18 (CQ^), and measure 20 (CQi^). To repeat : the great frequency of anagram relations is a blow against any case that one might make for "set consciousness" 124

m,|o rnmmer

i«* & ^ 1 T 5 1 I I I I L i I J I 3 J- } 5 JL 1 LA-* 6 A-J u

m.2o

I I 5 5 1 *# L A-»

Ex.13. Instances of anagram (A) and inversion (I) relations in Op.11/3.

The brackets indicate the related structures, shown by an arrow above the CQ designation. 125

In this music. Anagrams are not, as they might in itially appear, sets of unordered pitch-olasses. Because the di gits of the CQ represent ascending semitonal distances, anagrcus, being reorderings of these distances, are noth ing more than reordered interval sets. Since reordering a set of intervals entirely changes its characteristics, by changing the second-order interva Is, the occurrence of anagrams cannot support any particular analytic posi t io n . The total CQ count did reveal rare instances of the use of i-c inversions. The only substantial case of such usage occurs in Op.23/3» mm. 32-33» resulting from inverted "counterpoint" at the major ninth (Example Ih). 126

Mifîl .Vlth permisalon of Edition Wilhelm Hansen, Copenhagen, Denmark

Ex* 14. Inverted "counterpoint" in Op.23/3, creating a series of interval-class inversions.

The fact that this piece directly preceded the twelve-tone period may explain the use of this typical twelve-tone procedure. In the passage, if "A" represents a CQ and "A" represents its i-c inversion, the i-c inversions occur in retrograde with two intervening chords : [a BBCDCA^

Ea [b a CDCBB^, In this representation, simultan eity VE" is a CQ^. and a ll others are either a CQ^ or CQ^. 127

Layers of Vertical Activity

The problems encountered in compiling a CQ count for Schoenberg*3 piano works become virtually insurmoun table in the analysis of the more polyphonic works, such as 0pp. 16 and 21. Besides thicker texture and increased contrapuntal complexity, other conditions in these works frequently make CQ analysis impossible. In Op. 16/1, for example, a triple pedal point begins in measure 26 and continues to the end of the movement, some 102 measures in all. In a thorough CQ analysis, these three pitches would have to be included in the tabulation, combined with the sonorities in the higher voices. This type of compositional procedure often creates eight- or nine-note simultaneities that are merely composites of distinct smaller structures. In many movements from Op.21, ex tremely ornate configurations on the one hand and notes of long duration on the other hand create similar ana lytic problems. As a way of approaching the more thickly-tex- tured works, Maegaard introduced the notion of layers 12 (Schichten) of vertical activity. This notion rests on a new conception of counterpoint consisting not merely of multiple voices, but of multiple layers, each

12Maegaard, Studlen, v.2, p.^2. 128

of which is made up of multiple voices. The overall com positional procedure then entails a combination of two or more specific procedures. While pedal points and ostinati, as in Op. 16/1, also qualify as elements of lay ering, many cases involve entirely new compositional de v ic e s . A layer of activity may stand out clearly with in the total texture but may still be obscure in terms of its internal construction. In general, the separate lay ers of multiple layer passages display as much CQ variety as layers in simpler textures. These composite levels of wide CQ distribution result in even greater variety vhen layering is employed than vdien textures are simple. If, as with Schoenberg, a composer strictly avoids octave doubling, then thicker texture must always entail more complex vertical structures—that is, five independent voices always produce a five-note sonority. Viewed his torically, Schoenberg's atonal works represent the first idiom in \diich such an affinity exists between texture and the complexity of vertical structures. An additional characteristic, a constantly changing voice structure, is discussed in the detailed analyses in Chapter V (see p . 2 4 6 ) .

In layered passages, the tendency toward maxi mum pitch turnover can be observed as well as the tendency 1 2 9 toward maximum CQ variety. An excerpt from Op,21/5, mm. 15-18 (Ex. 15), shows how three factors combine to create this particular fabric. Three-note structures in each hand of the piano are "ornamented" by the flute and clarinet lines. (The brief canon in the woodwinds is not relevant at the moment.) The L.H. consists of various structures derived in fourths. The combination of the two hands, with no tones doubled, consistently produces six-note simultaneities.

• dor Luit. Ak.kor da ft5 - roa dor Vorxvoiflung

J - i ‘ Used by Fersisciion of Belmont Uuaic Publishers, Los Angeles, Califomia 90049 Ex. 15» Layered texture in Op.21/5, created by CQ's in each hand o f th e p ian o, beneath a canonic passage (*). The spelling is consistent within each hand, revealing two discrete layers. The construction of the resulting CQ^'s thus becomes much clearer. In fact, a scan of the CQ's in each hand shows that no pair of CQg's repeats. The additional pitches in the clarinet and flute produce 130 eight-note simultaneities, and, in cases like m,16, fill out the entire twelve-tone aggregate. (The text for this passage is, interestingly, "Chords of wild lust disturb icy dreams of despair...") More about maximum pitch turn over and chromatic saturation is said in the following chapter (p. I 38 b elo w ). The concentration of traditionally dissonant intervals varies from place to place in the atonal music. In some cases, a consistent "dissonance" level is main tained by activity in semitones against a sustained "chord" which itself may contain semitones. In rarer in stances, the semitonal activity may actually be a direct semitonal transposition of the sustained structure. In Op.19 / 3 , m.4- (Ex.16), the pitches of the L.H. all lie one semitone (plus an octave) below the pitches of the aug mented triad in the R.H., producing another "arpeggiated" augmented triad before the note 8 ^ is reached, vdiich lies a semitone above the A in the R.H. The final chord of the preceding movement consists of two augmented triads a semitone apart, although they are spelled a perfect fifth apart on and . Both entire movements are, in fact, good examples of the use of semitonal displace ment as a compositional procedure. 131

pp. | g

Usad by Panaission of Belnont Music Publishers, Los Angeles, California 90049

toe 16. Op.19/3: semitone displacement of each pitch in left hand from augmented triad in r ig h t .

In the absence of general regulating principles, the analyzer can do no more than describe a number of in dividual cases. The CQ count in Table 3 showed that any regulation of the vertical dimension in Schoenberg's atonal piano works was definitely oriented away from, rather than toward the emphasis of any simultaneity. A more qualified CQ count could aid in devising a hypothe sis about essential and non-essential structures in these works, although the results of the CQ count make it doubt ful lAiether such a distinction exists. One could, how ever, count only CQ's on "strong" beats (these, too, would be difficult to determine); or one could simply tabulate the first and last CQ of each movement. In addition, pro gressions of CQ's could be counted and tabulated to meas ure any recurrence. In Schoenberg's atonal music, the general char acteristics of constant variety and instability are 132 u nd en iab le. Chord q u a litie s th a t are t r a d it io n a lly con sidered dissonant, containing the semitone and its deri vatives, dominate the vertical dimension. It must be pointed out, however, that if Schoenberg's "vocabulary" consists of all possible simultaneities, those containing the semitone must prevail: 9 o f the I9 CQg's co n ta in a semitone, 33 of the 4-3 CQlf's at least one semitone, and 63 o f the 66 CQ^'s a t le a s t o n e. I t i s a ls o th e case that out of these 128 CQ's, 56 contain at least two semi tones. Hence, the presence of semitonal sonorities may be explained as a necessary mathematical result of the even distribution of chord qualities.

In this chapter, a general description of the vertical dimension in Schoenberg's atonal works has been followed by a survey of some existing vertical categori zation systems. A particular approach based on the tra ditional notion of chord qualities was adopted. These chord qualities (CQ's), based on ordered series of inter vals, rather than interva 1-classes or unordered pitch- classes, aided in reaching two conclusions : ( 1) th a t in terval-class equivalence plays only a small role in the vertical dimension of Schoenberg's atonal piano music; and ( 2) that the vertical dimension does not show a preponderance of any structure or structures. The 133 following chapter shows a slightly higher degree of selec tivity in Schoenberg’s construction of the horizontal or melodic dimension. Chapter III ATONAL MEIODY As with other aspects of Schoenberg’s atonality, the topic of melody raises immediate problems of termino logy. One might object that the term "melody" itself is too laden with associations to prior practice to be ap plicable to music as unconventional as Schoenberg's atonal works. Yet, if the minimal definition of melody proposed in the Introduction above (i.e ., a succession of single tones given prominence in the texture) is accepted, then this traditional term is still useful in reference to atonal music. It is also important to establish how much emphasis Schoenberg and his school placed on melodic activity (see p. 3^ above). Rufer stated that all

characteristics of the presentation, shaping and development of musical ideas out of the motivic substance apply both to tonal and to twelve-note music.^

It is reasonable to assume that the atonal period was not excepted from this view. The term "motive," then, may be used to refer to small melodic items that emerge as

^Rufer, Composition with Twelve Notes, n.116 134 135

formally significant through repetition in the course of a work. "Atonal melody," therefore, may or may not actually consist of motivic items. In this chapter, the means of analyzing melodic construction, even in the frequent absence of motivic items, are considered. While more specific applications of these means are not dis cussed until Chapter IV, the following general treatment should demonstrate that atonal melody can be meaningfully examined, and that it was, indeed, an important composi tional consideration for Schoenberg. Just as the notion of pitch-class excludes register as a consideration, the notion of interval-class excludes direction. Since the contour of a given melody is determined primarily by the direction of the intervals (and partly by their size and note-value patterns), Schoenberg's increased interest in interva 1-classes neces sarily meant less emphasis on melodjLc contour. This shift in emphasis leaves the meaning of the word "shape" open to some reinterprete tion. Schoenberg commonly referred to the twelve-tone series as the GrundgestaIt. Humphrey Searle, in his translation of Rufer's text, rendered this term as "basic shape," although "basic form" would have been equally plausible, and would have avoided the issue of contour or outline. The notion of shape implies a signi ficance in the outline or contour of the series. The 136 role of melodic contour was mentioned by Schoenberg in his own analysis of the Four Orchestral Songs, Op. 22.^ He stated that in this work he was no longer relying upon the "frequent repetition of motives" for continuity. His complex discussion of motivic relationships in these songs mentioned the use of basic melodic contours, some specific interval>classes, and the interpolation of tones within a m otive. As a possible excuse for any inconsistencies in his analysis, Schoenberg said: "All I know is that these songs do not dispense with logic, but I cannot prove it ."3 It is important to note that in reference to melodic organization the notions of contour and interval-class are diametrically opposite. An agreement or congruity of con tour between two melodic items is based on the general di rection of the melodic motion (which determines their "shape"), regardless of the exact distance. A congruity of interval-class rests on the equivalence of intervallic distances, regardless of direction. Thus, both princi ples can only apply simultaneously to a given relationship between melodic items if the two items are identical. This distinction is illustrated in Example 17, where there is a

2"Analysis of the Four Orchestral Songs, Op. 22," trans. Claudio Spies in accompanying booklet to Columbia recording M2S709, The Works o f Arnold Schoenberg, v.3« 3lb id , p .21. 137

congruity between (a) and (b) based on contour and between (c) and (d) based on Interval-class equivalence.

Uaad 'oy P a m ia a io n of with paraission of C.P. Patera Corporation, Naw York Balmont Uualc Publlshara, Loa Angalea, California 90049

Ex. ^7• Congruities of contour (a and b) from Op.16/5» and of i-c inversion (c .end d) from Op.19/1,

The "arhythmic" nature of the twelve-tone series further weakens its possible identity as a contour. As Rufer stated: "The series, as a de-rhythmised basic shape, presents the melodic substance of a work in, as it were, a 'musically neutralized' form.The notion of a string of pitches isolated from note-values is clearly applied in an atonal context in the Five Piano Pieces, Op.23 (discussed at length in Chapter V, p.279 below). In the purely horizontal dimension, the isolated pitch-string represents one way in which pitches may regulate melodic activity independently of note-value patterns. In the course of some analyses in this study, a specific set of pitches and note-values may be isolated as a possible

Rufer, Composition with Twelve Notes, p .137. 138

motive and referred to as a "pitch/rhythm item." For the purposes of this study, a pitch/rhythm item (P/R) is con sidered to retain its identity through transposition, but not through inversion. That is, congruent pitch/rhythm items must contain identical intervals and note-value patterns, but may be at different pitch levels. Hence, pitch-strings are not associated with a specific contour, but P/R*s always are. Both play a role in Schoenberg's atonal compositional procedures.

The Role of Chromatic Saturation in Melodic Organization

The avoidance of tonal implications and the re sulting equal emphasis (or de-emphasis) of a ll tones are fostered by the device of chromatic saturation. The principle involved in chromatic saturation is the exhaust ing of a ll chromatic pitches within a given range or seg ment of the chromatic scale. While "chromatic" music from as long ago as the Renaissance demonstrated this prin ciple by direct chromatic descent or ascent, Schoenberg's atonality rarely contains such direct motion. Instead, in a broken chromatic line, a note's upper and lower "chro matic neighbors" do not immediately precede and follow it, but appear in proximity. The effect is to lessen the po tential of any tone to sound like a tonic. 139

In Its most extreme form, chromatic saturation is equivalent to maximum pitch turnover. For both condi tions, the twelve-tone aggregate is the reference for com pleteness. In atonal music, saturation frequently occurs across spans smaller than the fu ll twelve-tone range. Rosen stressed the importance of the aggregate in atonal composition, referring to it as the "total chromatic space \diose saturation is the strong form of cadence and resolu tion. Use of the aggregate or chromatically saturated portions of it not only helps to avoid tonal implications, but also represents the "tendency to f ill out chromatic ' fi space as a kind of gravitational force.A twelve-tone melody or chord represents the most extreme possibility of chromatic saturation, namely maximum pitch turnover. It should be noted that in this context, "chromatic" re fers not to a tonally-derived operation (i.e ., non-diatonic), but to the individual members of the semitonal scale or aggregate. Simple semitonal ascent or descent can be made disjunct by the octave displacement of one or more tones, as Leichtentritt pointed out (see p. 25 above). In Op,23/1, measure 7, for example, each of the four chro matic tones from D to B appears in a different octave

-^Rosen, Arnold Schoenberg, p.60. &Ibid. p .59. 140

(Ex. I8a). Direct semitonal motion can be interrupted by •vdiole ste p s or la r g e r lea p s th a t are then f i l l e d in . In O p.19 / 1, measure 3, the right hand circumscribes the area from B down to D. All of the chromatic tones in the fifth

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Ex. 18 . Three examples of semitonal construction : (a) octave displacement in Op.23/1, (b) chromatic saturation in Op.ig/1, and (c) chromatic saturation in Op.16/2. from A to D are filled in, except the E^ and ok , which immediately follow the rest in measure 4 (Ex.l8b). In measure $, the span between E and A in the right hand is saturated, giving the effect of two voices in contrary motion. The secondary theme of Op,16/2, at measure 151 (Ex. I8c) contains saturation of the fourth from B to E, and in measure 15^, the fifth from bI? to E^ is treated s im ila r ly . As one way of dealing with the issue of octave displacement in semitonal motion, Maegaard categorized 1 4 1

Schoenberg's atonal voice-leading into "direct and indirect identities and neighbors."? Identities are common tones and neighbors are semitonal adjacencies. The indirect

0 dr cC

dràngend cresc..

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Ex. 19» Three examples of direct and indirect identities and neighbors from (a) Op,21/2, (b) Op.21/5, and (c) O p.ll/ 3 .

?Maegaard, Studien. V. 2, P .19 1 4 2 relation comes about through octave displacement, so that leaps of the octave, major ninth, or major seventh become incidental to the voice-leading. This approach permits the explanation of certain strings of simultaneities, such as those in Example 19. In (a) and (b), all of the verti cal structures are connected exclusively by direct and indirect identities or neighbors. In (c), each hand pro ceeds almost exclusively in the same manner. Only the circled note is not approached in one of the four ways. In thick textures, the pitch turnover can be come more rapid, as Example 19 shows. In a series of six- note structures, every pitch must be approached in one of the four ways described by Maegaard. If no identities occur, only neighbors, the complete aggregate obviously

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Ex. 20. Op.21/11, mm.23-24: The two hands exchange pitches in an application of indirect neighboring reminiscent of Stlmmtausch. 143

results. This situation is extremely rare, however, in Sohoenberg*s.atonal instrumental works. A more frequent occurrence is a spreading and contracting reminiscent of Sjblmmtausch, in which two tones are actually retained by "indirect neighboring." This procedure can be seen in Example 20.

Tyues of Melodic Interval Succession

Austin's "rules of harmony" (see p. 22 above) present the possibility of categorizing different types of melodic interval succession. In the music of the com mon practice period, two general categories are recognized, namely scalar and chordal (arpeggiated) motion. Neither of these categories applies in the atonal idiom, because there are neither scales nor prevalent chords. Since all possible vertical structures are typically used, any atonal

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Ex. 21. An arpeggiaticn of CQ 1425 in m.2 and its vertical representation in m.4, of Op,11,2, 1 4 4

segment is the arpeggiatlon of some atonal vertical struc ture. "Arpeggiation" thus only makes sense in instances where corresponding vertical and horizontal structures are expressed in proximity, as in Op.11/2, measures 2 and 4- (Ex. 21). The term "horizontalization" has been used to refer to the process of arpeggiation in atonality. André Hodeir noted this process in Schoenberg's last completely tonal work, the Chamber Symphony, Op,9, although it is difficult to see why he considered it so innovative :

. . . t h e Chamber Symphony did con tain one very important innovation: the linear expression of a harmonic figure (in this case it was a g chord of fourths that gave birth to a theme...

The truly new device that was introduced in this period was the reverse: the vertical expression of a melodic figure (see p.35 above). Since there are no referential scales in atonal ity, stepwise motion can only be divided into direct semi tonal or whole-tone motion, or motion within ë. hypothetical scale. This means that the pitches (possibly enharmoni es lly) of a melodic setment fit into a particular major or minor scale, although the implications are hardly evident in the atonal context. Thus, the scale exists only hypo thetically (see Ex.24- (c) below). A melodic line can actually consist only of a succession of steps and/or 14^

m t.

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Ex, 22. The piano part in Op.21/I3, m.13, showing a great deal of semitonal motion displaced by o c ta v e .

Ex. 23. An octave reduction of the left hand of Ex.22, showing tho degree o f in d ire c t semitonal motion.

leaps, and, of course, rests. Hypothetical scalar motion can be displaced by octave, giving it a disjunct charac ter. Thus, leaps of a seventh or ninth may be seen as "indirect neighbors" within a hypothetical scale. This kind of octave displacement is observable in the passage shown in Example 22. The removal of such octave 1 4 6

differences for analytical purposes represents the appli cation of the notion of pitch-class, whereby the specific octave in which a pitch is stated is disregarded. In some cases, the result is a simplified picture of melodic activity, as demonstrated in Example 23. While com pression into a single octave clarifies pitch-class con tent, it eliminates the contour of the melodic segment• Contours should always be noted, because they are often important in the atonal music. Schoenberg made c le a r h is e v e r -in c r e a sin g ob jection to the blatant repetition of any musical idea. In the essay "Brahms the Progressive,"^ he cited Strauss' "Blue Danube" and Verdi's "Di quella pira" as examples of excessive repetition. Melodic sequence, for example, was seen as an "inferior method of composing," consisting of "unvaried or slightly varied repetitions differing in nothing essential from first appearances, except that they are exactly transposed to other degrees."10 Sequence is another concept that becomes altered in the atonal context. In the tonal context, three sequential types are identified: real, tonal, and

^(19^7) in Style and Idea, pp.399-^00. lOgchoenberg, "Criteria for the Evaluation of Music" (1946), in Stvle and Idea, p.129. 147 quu?sl-sequentlal. The quasl-sequezice contains a clear and direct contour relation between the units, giving the effect of a real or tonal sequence, but lacking consistent intervallic transposition. Since the notion of a tonal sequence is based upon a referential scale and tonality, total sequences are not strictly identifiable as such in an atonal context. While sequences that are hypotheti cally tonal may be identified on the basis of spelling, such sequences are usually indistinguishable from quasi sequences in atonal music. One example is found in

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FI.

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Ex. 24. Examples of atonal quasi-sequences from (a) Op.11/2, mm.9-11, (b) Op.21/3, m.13, and (c) Op.21/5, mm.10-11. 1 4 8

Op,11/2, measures 9-11 (Ex.24a). Another example is in Op,21/3; measure 13 (Ex.24b), In Op,21/5, measures 10- 11, the flute plays vdiat would be a tonal sequence in the context of C minor. The result in all three cases is a quasi-sequence with a close sim ilarity of contour. In common-practice music, the device of imita tion was used in conjunction with "rules” for the combina tion of lines, or voice-leading, A discussion of imita tion may deal only with the points of imitation, or it may include consideration of the manner in which lines are com bined, Because the "rules" of combination in atonality (see p, 22 above) are so sketchy, imitation was not nearly as challenging a device for atonal composers as it was for tonal composers. On the subject of imitation in twelve- tone music, which in this case may have included atonal music, Schoenberg wrote:

I believe canonic or other imitation should serve only in order to base accompanying voices, which make the sonority fuller, on a more intimate rela tion to the main voice. Even the writing of whole fuguesjis a little too easy under these circum stances, Composing of these forms in which the highest achievement has already been reached by composers >Aiose form of expression was that of contrapuntal combinations—composing of these forms should only be undertaken for some special r e a s o n .11

^Schoenberg, "Composition with Twelve Tones ( 2 ) , " p . 2 4 8 . 14 9

According to this statement, Schoenberg felt that contra puntal combination was not his usual "form of expression." There are, nevertheless, some notable exceptions in his atonal output, possibly "undertaken for some special reason." Pierrot Lunaire contains three fully imitative movements, nos. 8, 17» and 18. Of these movements. Perle said: "No genera 1 vertical consideration seems to influence the progress of the individual voices...except that of avoid in g doublings.It is questionable whether a type of imitation in which the combination of tones is not regulated really falls under the category of counterpoint at a ll. In addition to the fully Imitative movements, sh ort im ita tiv e p assages are not uncommon, such as th e one shown in Example 2$.

m ^ iiiS l

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Ex. 2$. A brief imitative passage in Op.11/1, mm.25-27*

12Perle, Serial Composition, p.31. 150

Local Variation Procedures

Schoenberg overcame his aversion to repetition not only by the occasional use of imitation, but often by means of brief units of repetition within a voice or part. A given item may receive only a single repetition, or it may receive several, as in a brief ostinato. In the place of the immediate and exact repetition of items, Schoenberg often employed the technique of immediate variation. Here, the transformation of material is often readily discern ible. The means of transformation, which may be called Schoenberg's "local variation procedures," consist of four basic elements: metrical displacement, note-value altera tion, interval expansion or contraction, and pitch inter polation or elimination. Schoenberg produced metrical displacement in one of two ways. A melodic idea can be so constructed that agogic or other accents do not coincide with the normal metrical stress pattern, or it might be shifted so that the variations produce irregular stress. In general, the metrical patterns are complex and irregular, and show little relation to the meter signature. Very rarely does the effective stress of the music coincide with what might be considered the normal stress of the indicated meter. In such cases, it is usually the result of an ostinato, 151 e.g ., Op,16/2, measures 175-18$ and 207-213. More frequent are ostlnatl that are themselves cross-metrical. The osti nato in Op.11/2, present in 23 of 68 measures, actually 6 12 has the effect of a hemiola producing against the g meter, because of the two-note pattern F-D (Ex.26a). In Op.16/1, a three-note ostinato begins in measure 3^» nota ted in a Q meter that is already in a cross-metrical rela- -3 tion with the basic meter of g ; the result is the "cross- meter of a cross-meter" (Ex.26b). The ostinato in Op,21/2, measures 33-37? is also a hemiola, repeating at the half measure (i.e ., every 1^ beats) in ^ time (Ex.26C), Local (i.e ., non-recurrent) melodic items that are metrically displaced are less prominent than ostinato figures. Such an item, though repeated only once, often differs in metrical placement from original to repetition. Several specific examples may be observed. In Op.11/1, the three-note item at the end of measure l4 returns as the first three notes of measure 16 (Ex.27a). In both statements, the sforzando occurs on the second sixteenth note. Displacement also plays a role in Op.11/3, in.the repetition of the item in the right hand from measure 2 to 3 . 152

(a)

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( c ) ▼lei UnifHainfr I Jfct tool

▼id lani(sam'

** * .JIZT^^imTTTTTr.- i ppp viel langsamer fC. Used by permission of Belmont Uuoic Publishers, Los Angeles, California 90049 Ex. 26. Three examples of ostlnatl that create cross-metrical stress In (a) Op.11/2, (h) Op.16/1, and (c) Op.21/2. 153

(Ex«27b)• Three successive displacements of a three-note item make up m easures 32 and 33 o f the same p iece (E x .2 7 c ).

I m m

(c)>> k è

Ex. 27" Examples of metrically displaced melodic items in (a) On.11/ 1, mm. 1^-16, (b) Op.11/3, mm.2-3, and (c) Op.11/3, mm.32-33»

Another example may be found in Op.19/3» where tne note- value pattern beginning on the first beat of measure 2 in the right hand is shifted to the second beat in measure 3»

^ f i : A.i-ip

Used by permission of aalnont Uuaic Publishers, Los Angeles, California 90049

Ex. 28 . O p.19 / 3 : Displacement of a note-value pattern from m.2 to m.3 # 154

In the simplest situations, note-value alteration consists of strict diminution or augmentation. This device can be seen by comparing measures 26 and 27 of Op.21/2, where the violin's note-values become twice as short (Ex.29a). A similar operation takes place in Op.16/2, measures 177-78 in the bassoon (Ex.29b) and in Op.16/4, comparing measures 265 and 267 (Ex.29c). In the latter movement, the doubly fast version also begins simultane ously with the original in measures 286, 289, and 292.

Used by permission of Balmont Uusic Publishers, Loa Angeles, California 90049

m a

With permission of C.P. Peters Corporation, New York

Ex. 29 . Three examples of rhythmic dimunition in (a) Op.21/2, mm.26-27, (b) Op.1:6/2, mm. 277- 78 , and (c) Op,.16/4, mm. 265-67.

The determination of interva llic expansion and pitch interpolation or elimination require the establish ment of a referential pitch that defines the upper or 155 lower limit of the range of a given item. Even this pitch commonly changes in the course of variation. An example occurs in Op.11/1, measure 13, in the left hand (Ex.30). The referential pitch is Eb as the augmented fifth ex pands to a major sixth. The referential pitch then rises to E^j, creating an interval contraction.

Ex. 30. Interval expansion and contraction in O p.1 1 /1 , m.13 *

The interpolation or elimination of pitches re quires the establishment of one or more referential pitches to or from vAiich various intervening pitches may be added or deleted. Pierrot contains several examples, one of which is illustrated in Examp l a 31» The r e fe r e n t ia l

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Ex. 31. Pitch elimination in Op,21/2, mm.21-22: , the D# is eliminated beford the second AP 156

pitch is Ab, as the notes preceding it, D# and A, are varied to G, E and A. The latter three pitches then be come th e re feren ce as the top n ote expands to C. What ever coherence this passage may have is afforded by this rather complex melodic construction.

Idiosyncratic Features

The apparent lack of repetition characteristic of the athematic atonal works can be corroborated only by a complete count of a ll melodic items. A correspond ing count of vertical items (pp.102-'126.above) revealed a lack of concentration in that dimension. The vertical dimension is, however, clearly defined by simultaneity. In the horizontal dimension, the size of items is not de fined by such a clearly objective standard. In atonal music, the beginnings and ends of melodic phrases or smaller units are generally indeterminate and must be ar bitrarily stipulated. A complete count of all horizontal items might be tabulated with the comparable goal of nu merically demonstrating the lack of repetition in the melodic dimension. Even if horizontal items of only an arbitrarily specified length were counted, however, the count would involve far more items than a vertical count for the same piece or pieces. These factors make the 157

lack of repetition in the horizontal dimension more d iffi cult to confirm. Maegaard attempted the most detailed count of atonal melodic items to date in his analysis of Schoen berg's monodrama, Ervartune. Maegaard*s study revealed that, if transpositions are included and note-value pat terns disregarded, the recurrence of some three-note items can indeed be found in Erwartune. There is evidence that Schoenberg sometimes worked with ideas as small as three notes (see p .l 60 below).One example in Ervartune is the item D-F-C#. According to Maegaard's study, although certain three-note pitch-strings recur, Schoenberg suc ceeded in composing the measures of Erwartune without repeating a single item of three or more notes in pitch 1*+ and rhythm. Although standards for what constitutes musical recurrence may vary (see p. 184 below), it is dif ficult to imagine a lower degree of recurrence in a work employing discrete notation. The tabulations performed by Maegaard were di rected at the Hauntstimme and the voice part of Erwartune.

13see H.H. Buchanan, "A Key to Schoenberg's ErwartTong." in Journal, o f th e American M u sico lo g ica l S o c i e t y , V.20/3(1967) P:434 and Perle's analyses of Op. 11/I and 23/1 in this regard. ^^Maegaard, Studien. v.2, pp.312-438. 158

In order to work with some selectivity, Maegaard chose only to include the two most prominent melodic lines in his count. Each segment of the Haiiptatlmme set off by brackets in the score was included in the count and each separate entrance of the voice after a rest was consi dered a new melodic segment in that part. Within a given segment, a ll subsegments were also counted, so that a five-note segment consisted of itself, two four- note segments (notes 1 through 4 and 2 through 5), three three-note segments (notes 1 through 3, 2-^, and 3-5)» etc. The total numbers of four-note segments counted were 1,321 in the Hauptstlmme and 966 in the voice part. Since repeated notes were included in the count, it was possible for a four-note segment to involve only three different pitches. Because of Maegaard's elaborate, tonally derived chord categories, the results are difficult to assess. It appears, however, that in the Hauptstimme, the most frequently occurring segment, expressed as a CQ, was I 38 , or vrtiat Maegaard called a minor third/major seventh chord (see p.82 above). In the voice part, the most frequent segment was a four- pitch item vdiich can be expressed as CQ 1317» Each occurred as approximately 8 . 3# o f the t o t a l number o f segments of all lengths counted. The relationship be tween these two CQ's is illustrated by the fact that if 159

the pitch F# is added to the item D-F-C# (138), it pro duces CQ 1317. If Schoenberg was intentionally employing such items as primitive motives, he was certainly doing so in a less than overt fashion* There is little evidence to show that common mo tiv e s ever lin k movements or works in Schoenberg's atonal output. There are, however, at least two instances in which a substantial portion of one piece is quoted in another* H. H. Buchanan discovered in Erwartune a quota tio n of the song "Am Wegrand*"^^ In Opus 21, the quota tio n of Number 7 in Number 13 is a far more obvious in stance, since it occurs within a single work. While such applications may be viewed as quotations or reprises, they do not create the type of motivic unity that is so significant in a piece such as Schoenberg's Pelleas und Melisande* Op.5. The three-note item mentioned in connection with Erwartune may simply be considered one of Schoen berg's idiosyncrasies. Buchanan referred to this item as the "major-minor c e ll," e .g ., B-G#-G^. At the pitch le v e l D-F-C#, Maegaard found i t in seven places in Erwartune, and transposed in sixteen more places. Since one aspect actually makes up CQ I 83 and the other 138,

1^Buchanan, "A Key to Schoenberg's Erwartune. " 160

the "major-minor cell" and the one Maegaard found can only be considered equivalent if inversional equivalence is ac cepted. The 138 aspect is also found as the first three notes of Herzgew3chse. Op.20, and as the in itial items of Nos. 2, 7, and 9 of the Buch der haneenden Garten, Op,15. In the atonal instrumental works, CQ 138 may be found melodically in the first three notes of Op,11/1, Op,11/2, Op,16/^, Op,21/ 17, and Op,23/2. I t also co n sti tutes the first three notes of the right hand in Op.23/1, the Hauntatimme in Op.21/5, and the canon in Op,21/8. The same CQ occurs as the last three notes of Op.21/13 and Op.23/ 2, Although the strategic locations of this item might indicate motivic applications, the extremely diverse treatment it receives in these places minimizes any possible effect as a "reprise." One small item, shown in Example 32, recurs in two basic forms in the course of Pierrot Lunaire. This is the only case in Schoenberg's atonal instrumental works where even a small melodic item recurs in several movements of a multi-movement work. As the example shows, the first interval in the item is either a descending second or an ascending third. The pitch level and note- value pattern are not the same in all instances. In more or less the form shown, item (a) appears at eight 161

points in Op,21 : No.2, min.l^-, 18, and 19» No,6, mm,6 and 11; No,13» m,10; No,l$,m,9» and No.16, m,8 (three times). Item (b) appears seven times : in No.2, mm.6 and 18; No«5» mm,2 and 11; No,7» m,6; No.9» m,7» and No,13, m,27« The occurrences of item (b) in Nos. 7 and 13 retain the ori ginal note values. In No,13, m.27, the statement in the flute is closely imitated in the clarinet, further high lighting this exact, though transposed, recurrence. (E x.32c).

(a) (b) (c)

Ex. 32. Two small recurring items (a and b) from Op.21. Imitation (c) involving the second item in Op.21, m.27*

In Schoenberg's own judgement (see p. 16 above), three notes are the minimum that can constitute a recur ring item without an associated note-value pattern. Such units of three or more notes will be referred to as pitch- strines (see p. 189 below), representing formal applica tions of the isolated pitch series discussed earlier in 162

this chapter. Some other small items are noticeable as melodic traits, but cannot really be considered motivic. One of the most common of these i s shown in Example 33» This

Ex. 33. Two common melodic items as they appear in Op.21/10, m.l

item resembles chromatic saturation on a minute level. The directional changes and registral displacements tend to reduce the significance of the individual pitches. Thus, a homogeneous fabric of tones is created where spe cific pitch is subordinate to timbre, volume and duration. Although the specific choice of notated pitches creates a unique result, that choice is not as crucial as in tonal music, where the norms of melodic and harmonic progression are constantly taken into consideration by the composer. Because of this subordination of pitch to other consti tuents, Schoenberg's atonal music often consists of little more than a series of coloristic effects, rather than a .progression toward a specific goal, pitch-centered or otherwise. The most striking examples of this 163 subordination of pitch are fast, florid passages, such as those found in Op,21/2 and 21/1M- (Ex*3M-). The ear can . hardly be expected to register the individual pitches in turn.

Used by parmisalon of Baloont Music Publishers, Los Angelas, California 90049

Ex. 3^* Two florid passages from (a) Op.21/2, mm.30-31 and (b) Op,21/1^, where the individual pitches become subordinate to the coloristic effect.

Perpetual "Variation"

The fact that significant portions of the atonal works consist of non-motivic, non-recurrent material was acknowledged by Schoenberg. Athematicism was described by Schoenberg in terms of perpetual or developing varia tion,^^ or ;diat he also called "musical prose." To him,

I^Schoenberg, "Brahms the Progressive" (19^7), in Stvle and Idea, p.^11. 164

th is meant that

variation of the features of a basic unit produces a l l the thematic form ulations vdiich provide for fluency, contrasts, variety, logic and unity, on the one hand, and character, mood, expression, and every needed differentiation, on the other- hand—thus elaborating the idea of the piece.

Further insight into these processes can be gained from Schoenberg's own analysis of the Four Orchestral songs. Op.2 2 . This analysis, dating from 1932, begins with a discussion of the treatment of intervals in the first eighteen measures of the first song. The intervals of a minor second and a major third are shifted to various pitch levels, and the minor second then inverts to a major seventh. Schoenberg proceeded to describe approx imately thirty transformations of the "motive," the final group of which appears in Example 35* He then concluded:

One might be led to believe that this is a coincidence, especially since this motive is not in itself a striking one, and could therefore appear elsewhere without any parti cular significance—let alone the circumstance that changes do occur in the size and direction of its interva Is.19

1-7Schoenberg, "Bach" (1950), in S tyle and Idea, p .397. l8schoenberg's "Analysis of the Four Orchestral Songs, Op.22." 19lbid, p.26. 165

ÛL

Ex. 35. Nine motivic transformations according to Schoenberg's analysis of Op.22/1.

Music based on motivic relationships as tenuous as these identified by Schoenberg in his own works remains, for all practical purposes, athematic. Because of the slightness of such relationships. Perle objected to the term "varia tion" in these cases. In his words, the term

implies (1) the presence of some stable referen tia l patterns, however temporary, which is identi fiable as the subject and distinguishable from the modifications to which it is subjected, and (2) some delimitation of the range of variational possibili ties. Neither of these conditions is characteristic of the athematic style, a kind of musical stream of consciousness lAiereln the thread of continuity is generated by momentary a sso c ia tio n s. Microcosmic elements are transposed, internally reordered, temporally or spatially expanded or contracted and otherwise revised in a fluctuating context that constantly transforms the unifying motive itself.

20Perle, Serial Composition, p. 19* 166

Aa his comment Implies, the Issue of melodic construction Is closely tied to the Issue of the construction of larger forms from melodic units. Although the horizontal dimension Is not as well suited to a numerical tabulation as the vertical dimension, more melodic Idiosyncrasies are notable than vertical ones In Schoenberg's atonal Instrumental works. The local variation procedures mentioned In this chapter often fo l low Immediately after the presentation of a melodic Idea. Schoenberg's own an alysis showed that contour was often an Important consideration, but that Interval-class In version, with \dilch It Is not compatible, also operated from time to time. On the subject of Imitation, Schoen berg observed that without many "rules" for combination, contrapuntal procedures were not very challenging for atonal composers. Without regulation In the vertical dl- mentlon, it Is doubtful whether there can be counterpoint at a l l . N evertheless, f u lly Im itative movements and shorter passages w ithin movements from the period were pointed out. Deviation from normal metrical stress pat terns was found to be so widespread that the notated meters are commonly Irrelevant to the course of the music. 167

The following chapter deals with Schoenberg's wide range of formal melodic treatment in movements from the atonal instrumental works, from the literal repeti tion of motives to an athematicism based on non-repeti tio n . Chapter IV FORMAL RECURRENCE

Rather than attempt a general definition of form here, it is more to the point simply to consider those factors that determine the form of an atonal work. In 192 $, Schoenberg felt obliged to reiterate an idea from his Harmonielehre, "That the harmonic alone is form-deter mining is a widely spread delusion..."1 Part of what he was implying is that other important means of formal defi nition exist, principally melody. Many forms from pre vious periods, such as Bach's fugues or Mozart's sonatas, were, in fact, melodically as well as harmonically de fined. In a sonata form, the return of the home key is typically accompanied by the return of the principal sub je c t. Since, in Schoenberg's own judgment (see p .i4 above), harmony no longer operates in atonal music, its form can be defined only by melody or other articulative means. Because form has been bound up closely with melo dic recurrence in the past, this chapter focuses upon melodic recurrence, with only brief reference to other

^Schoenberg, "Tonality and Form" (1925) in Style and Idea, p.255.

168 169 types of repetition. It will be seen that the logical tendency for the elimination of melodic recurrence to have a loosening effect on form operated In Schoenberg's atonal music. For the sake of orderly classification, a hier archy of formal categories Is established In this chap ter. These categories reflect the extent to which moti vic Items play a role In determining the form of the In dividual atonal movements. Analyses of representative movements are then presented In Chapter V, The catego r ie s for movements In \dilch form Is determined or a r t i culated by motivic recurrence are placed higher In the hierarchy because of their closer relation to conven tio n a l, c la s s ic a l forms. Categories fo r movements In which motivic Items are less significant, or perhaps to tally absent, are placed lower In the hierarchy. These Include the most nearly amorphous cla ss of "forms" ( if they can be said to be forms at all) In the atonal In strumental works. Rosen expressed the aberrant nature of Schoenberg's "athematic" or "non-motlvlc" movements In saying that they do not "require recognizing the mo tifs from one part of the work to another as all music from Bach to Stravinsky demands."^ The e ffe c t of th is

^Rosen, Arnold Schoenberg, P.M-1. 170

deviation from motivic recurrence poses serious problems for the listener and the analyzer. In an atonal work, the reference to a given mo tive can be of varying degrees of clarity, depending upon the features of the motive itself, the contexts in which it is presented, and the degree of relatedness between the original and the restatement. Thus, although a mo tive may not be exactly repeated, some variation of it may appear. In the hierarchy to be presented (on p. 193 below ), movements containing varied r e p ititio n or no repetition at all are also given categories. The con clusion that a given movement contains no motivic re currence must be based on the analyzer's failure, after close examination, to find any motivic items. When the conclusion is reached that a particular movement is, in deed, athematic, alternate means of construction must be explored, often minute and momentary details of repeti tio n .

The Melodic Articulation of Form

In classical form, the primary melodic line is one of the main indicators of formal sections. Although sonata allegro form, for example, may be described princi pally in terms of key areas, commonly those areas are divided into sections by the melodic structure. The m

The secondary key area usually consists of two distinct melodic groups, the secondary theme and the concluding theme. In the typical recapitulation, the key is uni form for the most part, and primary and secondary areas can be distinguished only on the basis of thematic mate rial. (The case of a monothematic sonata form is one exception in which formal definition rests more heavily on key areas. Even then, the transitional material is usually distinct.) If form is to be motivically articulated in any work, primary, secondary, and transitional material must then be differentiated. With regard to this dif ferentiation in atonal music, Perle stated:

A central problem, that of defining the "thematic" material and differentiating it from secondary and transitional material without the benefit of the articulative procedures of tonality, is uniquely presented and solved in each atonal w o r k .3

If the melodic surface does not provide formal cues in the-form of motives, the aural experience can be ex pected to be quite different from that of listening to common-practice music, in vrtiich recurrence plays a major role. In some of Schoenberg's works, the surface con tains no melodic formal cues, and this melody, devoid of

^Perle, Serial Composition, p.9. 172

repetition, ceases to have a form-articulating function. Although it is sometimes possible to discern other types of formal definition in atonal works, the analyzer must be careful to make the distinction between the conven tional and the unconventional types. In common-practice music, the repetition of material is generally discernible through either exact repetition or a close connection between the restatement and the original. A classical development section, as the expression "working out" im plies, in volves not only changes of key, but also the systematic variation of melodic elements. In such cases, a firmly established theme is altered, but still retains a perceivable con nection to the original. Often, for example, the con cluding theme of a classical sonata form is derived from the main subject, relying on rhythmic shape for the connection. Some examples from the first movements of Mozart symphonies are shown in Example 36. This type of obvious reference to earlier material is just the sort that Schoenberg dispensed with in the atonal works.

Connections that are less direct than strict repetition rely on other constituents. The use of dif ferent aspects of a motive (e.g., retrograde or inver sion) is a less conventional and less direct connection, especially if the original note values are altered, and 173

jftW f^i^ni^rir'rÿCrif

Ex.36* Conventional connections between main and concluding themes in Mozart's (a) K. 385 , (b) K .550, and (c) K.551. the inversion is based on interval-class rather than to nal inversion. Even more remote types of connection may often be perceived only in the musical score, Schoen berg, for instance, reported how he sought a connection between the first and second themes of his Kammersvm- phonie, Op,9 (a tonal work), feating that the two were totally unrelated. The relationship he discovered (see Ex.37) was revealed as follows : The "true principal tones" of the first theme (actually the fourth, twelfth, thirteenth, and fourteenth notes), vdien inverted, pro duce the first four notes of the second theme. 174"

(b),

Ex. 37* Op*9: The "true principal tones" (marked S; of the f i r s t theme (a ), \dien inverted, produce the first four notes of the sec ond theme (b ), according to Schoenberg's a n a ly sis.

Schoenberg remarked: "I doubt whether any composer would have cared deliberately to construct a theme in this way..."^ A connection may exist, but it is certainly of a different order from the more conventional connection between the principal and concluding themes in Mozart symphonies. Whatever the d ecisiv e factors are in deter mining whether a given event constitutes a recurrence of an earlier one, there can be no doubt that a wide range of possibilities exists from distinct to very obscure

^Schoenberg, "Composition with Twelve Tones (1)," p .223. 175 connections* The most distinct repetition of an item is, of course, literal. Even transposition constitutes the variation of one constituent, namely, pitch level.

Contextual Emphasis

In the course of a work from the eighteenth or nineteenth centuries or earlier, certain melodic items stand out as formally significant. Such items, consist ing of an aurally identifiable relation of pitches and rhythms, can be highlighted at their initial statement, even before they are emphasized through repetition. Thus, in common-practice music, significant melodic or thematic items are not only recognized as such retro spectively upon their repetition, but are afforded a certain prominence simply by the time and nature of their initial presentation. The item itself may be more or less striking in character. Schoenberg's frequent removal of precisely the criteria by which primary melo dic material is normally identified was intended to pro vide subtlety for the formal construction in his atonal works. The use of such su b tle tie s had become more f r e quent in the nineteenth century, as extended symphonic forms were developed. However, removal of the criteria by which material can be recognized as formally signifi cant has the effect of making all melodic items appear 176

equally significant (or insignificant). Since signifi cance is only a relative quality, the result of such melo dic equalization is athematicism. One of the most important causes of athematicism in Schoenberg's atonal works is the uncommon treatment he gives to the role of musical context. The establishment of any musical context relies upon the conventions of musical syntax. Although Schoenberg sought to pronounce changes in the musical syntax, this may not be possible, because its conventions depend to a large extent upon the expectations of the audience, and their aural capabilities. Of course, given the proper context, any melodic item can be emphasized by the composer, regardless of its char acter. This effect can simply be called contextual emphasis. In Schoenberg's music, items so emphasized often prove, in the course of a work, to be no more important than other, less emphasized items. This often aurally confusing effect can frequently be noted in the atonal works (see pp.235-266 below). The formal sig n ifica n ce of a melodic item (or any other feature of a work) can only be measured by the extent to which it is present or prom inent, in a literal or varied form, in the course of the work. The momentary emphasis of a non-recurring item is one of the main factors in Schoenberg's athematicism. 177

Generally speaking, contextual emphasis results from any of the several factors enumerated in Table 8» Melodic material receiving such treatment is emphasized, implying that its formal significance w ill be confirmed by later repetition and/or development.

TABLE 8 Some factors that give contextual emphasis to melodic items.

(1) appearance at the beginning of a section or movement (2) association with an expressive marking (dolce, canta- bile, etc.) (3) ostinato treatment (m-) statement as an isolated, monodic or unison melody (5) a sso cia tio n with a marked dynamic change (6) association with a marked tempo change (7) association with a marked change in timbre or texture (8) association with rests or other extreme punctuation (9) association with a change of rhythmic configuration (10) immediate repetition.

The first movement of Beethoven's Sonata in F- sharp. Op. 78 provides some examples of the traditional use of contextual emphasis. The Allegro non troppo satisfies factors 1, 6, and 8, plainly presenting the main thematic material of the piece. Measure 5 satisfies factors 2, 4, 7; and 10. Even though the f ir s t two thematic items are presented only briefly, contextual emphasis creates the expectation of their return. (The listener's familiarity 178

with sonata form is responsible for similar expectations in th is ca se.) Later in the movement, the formal s ig n i ficance of these melodic ideas is confirmed through repe tition, showing that the contextual emphasis was, indeed, given to formally significant material. One of the problems in understanding Schoen berg's atonal idiom is that the elimination of recur rence does not necessarily carry with it the nullifica tion of the traditional means by which melodic items are given contextual emphasis. Often, items are varied which might not have been recognizable even if they were liter ally repeated (see pp.170-172. aboüe); or, a series of emphasized items occurs, none of which is confirmed by

later repetition. In Op.19/1, (see p.242 below), the opening figure receives emphasis by factor 1 ; at meas ure 4, factors 2, 7, and 8 apply; at m.7, factors 4, 7, 8, and 9 are in effect; at m.8, factor 3» at m. 13, fa c tors 2, 4, 7» and 8; and at m.l5, factor 7» Within seventeen measures, six items receive the kind of empha sis that was traditionally given to formally significant (i.e., recurrent) melodic items. Yet, none of the items given emphasis actually recurs. A melodic item can receive contextual emphasis in only a limited number of ways. Consequently, Schoen berg could not devise new ways of emphasizing certain 179

Items, but only new ways of using the traditional means of emphasis on recurrent and non-recurrent items alike. Hence, one of the most radical aspects of Schoenberg's atonal idiom is that the same type of treatment may in one place give emphasis to a truly significant item, and in another, to a thoroughly trivial one. No matter how thor oughly repetition may be avoided, the emphasizing effect of marked changes in expression, dynamics, tempo, timbre, and texture is part of basic musical syntax. When these changes occur, emphasis cannot be avoided. Musical context alone is the cause of much of the alien quality of Schoenberg's atonal music. By often disregarding the effect of musical context, Schoenberg seriously altered the entire notion of musical form. Re garding many of the atonal works, there is frequently doubt vAiether he has created any expectations for the l i s tener. There is no doubt, however, that he has used tra ditional notation, and that he has produced many situa tions that involve the traditional use of contextual em phasis. In some movements, such as the first two move ments of Op,11, contextual emphasis plays almost the same role it played in nineteenth-century music. In the analyses in the following chapter, nota ble cases are mentioned where the contextual emphasis of an item is not confirmed by later restatement, and 180 creates unfulfilled expectations. It is also important to note how, in the period immediately preceding the atonal works, Schoenberg observed the effects of contextual em phasis in nearly the traditional manner. In Frlede auf Erdeja, Op.13 ( 190 ? ), the t u t ti rest and abrupt dynamic change (factors 8 and 5» respectively) serve to mark for mal sections. One or the other of these devices oper ates at measures 11, 21, 75? 89? ICO, 122, and I 3I. Thematic material at mm.1, 11, and 21 returns at mm.100, 89 ? and 122, respectively. Thus, five of the eight points receiving contextual emphasis actually contain re curring items.

The Role of Contextual Emphasis in Aural Coherence

A brief analysis of the opening of Op.16 (see p .70 above) shows that the pace at which contrasting material is introduced makes the comprehension of its form quite difficult. Difficulty caused by such factors is prob ably most apparent in O p.ll/ 3, which poses many analytic problems as well. These problems result from the ex tremely complex texture, and widely differentiated note- value configurations, and the registral extremes. A pat tern can be seen in the atonal works, wherein movements that present one type of analytic difficulty, such as dealing with a complex texture or virtuosic flourishes. 181 are more likely to present others, such as coping with a dearth of m otives. Furthermore, i f these movements lack any material that sounds primary in nature, they are also likely to present performance problems and be more re sistant to formal elucidation. In Op.ll/3, the melodic material at the opening could have served as a thematic item if it had recurred in some recognizable form. Any material at the beginning of a movement has the potential to be primary in importance (see Table 8 , factor 1). Here, the opening idea continues only through measure 2, beat 5* A new idea lasts one bar, then a tutti rest precedes a one-bar item that is also of a potentially pri mary nature, as the interval of an augmented fourth appears sequentially (Ex. 38 ). In all, the 35 measures of this piece contain 18 newly emphasized items, 18 tempo

Uaod by permission of Belmont Uuaic Publishers, Loa Angeles, California 90049

Ex. 38 . A loud dynamic creating contextual emphasis of a non-recurring item in O p.ll/ 3. 182

changes, 9 sudden dynamic contrasts, and 21 tutti rests. After each change, contrast, or pause, Schoenberg elected to introduce new material, rather than to repeat former material. S till, this cannot be considered a general procedure of the period; the f i r s t two movements of the same work both contain well-defined thematic material. One device of formal subtlety used by earlier composers is after-the-fact contextual emphasis. Al though this procedure is not found in the atonal works, it may help to explain some of Schoenberg's formal inno vations. According to this device, an idea receives little or no emphasis in its first appearance(s), prov ing to be significant only in later, more prominent appearances. This procedure is common to Haydn finales, where the main theme i s o ften played piano before a transition to a forte version. Of course, the soft ver sion does receive some emphasis by being the opening mate rial, but the dynamic contrast counteracts this emphasis, even making the loud statement sound lik e the i n i t i a l one. In the nineteenth century, the intentional counteracting of contextual emphasis became more common. Examples reminiscent of Haydn's device can be noted in Dvorak's Eighth Symphony (second movement, measures 1 and 77) j and E lgar's Serenade in E minor (second movement, meas ures 17 and $1. 183

Schoenberg often reversed the emphatic process described above. Rather than suppressing material whose significance later emerges, he often produced a crescendo (emphasis factor 5) to an item being heard for the first and only time. Indeed, he may have been proceeding on the assumption that the rhetorical effect is the same, whether the material recurs or not. The clearest in stance of this sort of contextual emphasis lacking con firmation by recurrence is in Op.16/5, at measure 440 (Ex.39), where the crescendo to fff supports an entirely new melodic idea. The effect here of presenting the largest crescendo of the movement in conjunction with an entirely new idea must be quite different from that in Op.11/2, where, in measure ^5, the item returns for the fourth time.

With parmiaaion of C.P, Patera Corporation, Now York

Ex. 39* An item heard once at f f f near the end of Op.16/5. 1 8 4

Types of Relatedness

Schoenberg reported the evolution of certain sub stitutes for strict or even considerably varied formal re currence. In the essay "My Evolution," written in 1949, he said, in reference to the period around I908 :

. . . I myself and my pupils Anton von Webern and Alban Berg, and even A lois Héba b elieved that now music could renounce motivic features and remain coherent and comprehensible nevertheless, 5

In 1931 , Schoenberg made this general observation:

Music in i t s primal condition co n sists of most primitive repetitions; and the element which functions as a unifying factor in the higher forms to which it has developed, the element which guarantees that one may be able to relate all the sections to each other—the motive—can manifest its presence only through repetition. The more artistic forms do indeed obscure this fact in a great variety of ways; but since even today it is impossible to mold a form with p la s t ic it y , and in an e a s ily comprehensible way, unless one uses repetition...that is to say, since up to the present we have found no other basic principle for giving shape to music—it is a justifiable thesis that repetition is the initial stage in music's formal technique, and variation and development its higher developmen tal stages.®

c Schoenberg, "My Evolution," p.88. ^Schoenberg, "For a Treatise on Composition," ( 1931 ) j in Style and Idea, p .265. 185

Schoenberg's commentaries span two extremes on the issue of repetition and form. In his atonal compositions, the extremes of frequent repetition on the one hand, and non repetition on the other, are represented, along with various intermediate levels of repetition. Beginning with the atonal music, Schoenberg's standards for formal consistency became extremely vari able. Perle hinted at the frequently resulting problem of singling out any item as a significant element :

In the perpetually changing tone weft of the "athematic" style, any recognizably consistent feature, regardless of its brevity, becomes a structural element.?

Perle's description implies that minute features become "structural elements" by default, because no larger con sis te n t featu res are d iscern ib le. Do they become "structural elements" because they were so stipulated by the analyzer, or do they truly represent the composer's means of organization? In either case, such features do not become structural elements in the course of analysis; either they are part of the work's basic plan or they are not. According to Perle, \dien a composer has applied the "principle of non-repetition,"

^Perle, Serial Composition, p.21. 186

progression is achieved through Juxtaposition of minimal elements, with surface reiteration avoided except for isolated and temporary d e t a ils .°

If such a principle is actually in operation, the analyzer can expect great difficulties in disclosing repeated items. Perhaps such works even defy formal analysis; perhaps they were intentionally created to do so. As a way of exhibiting the formal range for tonal as well as atonal music, Maegaard enumerated 186 analytic categories. The last nineteen of these (nos.168 to 186 ) are analytic categories that Maegaard found applicable to Schoenberg's atonal works:9

168. Sonata form 269. Sonata with strophic addition 170. Two-part varied 171" Three-part, contrasting middle 172. Three-part, A-B-B' 173. Scherzo 174^ Theme and variations 175» Three-part, plus introduction and coda 176. Song cycle 177. Two-part, plus development and varied recapitu la tio n 178 . Three-part, plus development and varied recapi tu la tio n 179 . Exposition plus development 180 . Expanded two-part, plus coda 181. Three-part developmental form

Gib id . ^Maegaard, Studien, v .2 , p .463, my tran sla tio n . 187

1.82. Two-part sonata-like form 183 . Dramatic-literary I8^f. Extensively altered recapitulation 18$. Concentration of expression and phrasing 186 . Form not thematically articulated

From this list, it can be seen that Maegaard has gone to some lengths to view Schoenberg's atonal forms in terms of prior practice. Two works (opp.11 and 16) that are treated in the present study are also analyzed in Mae gaard' s study. He categorized Op. 11/1 as "two-part plus development and varied recapitulation" (1?7); Op.11/2 and Op.16/3 as "three-part plus development and varied recapitulation" (I 78 ) ; Op.16, nos.1 and 4 as "exposition plus development" (179)5 Op.16/2 as "ex panded two-part plus coda" (180); Op,16/5 as a "three- part developmental form" (181); and Op.11/3 as a "two- part sonata-like form" (182). In addition, he placed Op,16/ 3 , Op,16/5 and Op,11/3 in the category of "form not thematically articulated" (186), and said that Op,11/3 also had an "extensively altered recapitulation" ( 18^) and a "concentration of expression and phrasing" ( 185 ) . Thus, according to Maegaard, Op,16/3 is a three- part movement with a development and varied recapitula tion, but its form is not thematically articulated. If, indeed, such cases do exist, the form-articulating item, in Perle's words the "recognizably consistent feature," is not a motive, but something else—in this 188

case both the chord structure and the instrumentation.^®

Similarly, Maegaard divided Op,16/5 into three parts,

but indicated that the form is not thematically articu

lated. In his summary analysis, he called the form of

Op.16/5

unclear [with] presentation of a theme, contrast of dynamics and of compositional technique, and formal organization with structural grooves lack ing. Nevertheless, a three-part melodic arch form is d' cernible.^'

It remains unclear whether Maegaard considered the form

to be thematically articulated or not, or whether a

"melodic arch-form" could exist in a movement with no

themes. If no recurring motive is found, and, to my knowledge, none has been found in Op, 16/5, then such a

"melodic arch-form," if its presence is even demon

strable, must surely differ from melodic arch-forms that do contain motives or themes.

Although Schoenberg attempted to create non- thematic forms, as in Op,16/3, in many other atonal move ments, he did rely on motivic recurrence, usually at the original pitch level. The precise criteria for estab lishing the motivic status of a melodic item are

l®Maegaard discussed th is p o s s ib ility in Studien. v.2, p.251. See also p.213 below. lllbid. p.453, my translation. 189 difficult to formulate without a certain amount of arbi trariness. For present purposes, the following guide lines have been adhered to: (1) no two-note item can be a motive; (2) a three-note item must have a note-value pattern associated with it to be considered a motive;

(3) if an item of four or more pitches is repeated, but without an associated note-value pattern, it has been considered motivic and called a pitch-string. There are two borderline-caseS'involving guideline (2 ),-namely

Erwartung (pp.157-160 above) and Op. 16/5 (pp.235-241 below). Since these are generally considered to be the two most extended athematic works of the period, the re currence of three-note items, as horizontal instances of

CQ^'s, have been discussed to show the lack of recur rence even of such small items. In some recurrences at the original pitch level, the entire motive is repeated an octave higher or lower. Because the pitches remain in the identical intervallic relationship, these were not considered transpositions. Furthermore, although every movement with a pitch-string involves at least one horizontal restatement, some pitch-strings in the transitional Op.23 actually become: pitch-cl^,R-s^tr-lfigs. This takes place when the pitches do not remain in the same registral relation to one another. Also in this work, some strings; are used in tran sposition and 190

combined vertical and horizontal dimensions, just as in later full-blown serialism. The points of recurrence in the atonal instru mental works are lis te d in Table 9. Where there is at least one recurrence at the original pitch level (GPL), the measures have been indicated. In this tabulation, however, immediate repetition of a melodic item is not considered a recurrence, but rather a local event. That i s , the o r ig in a l and the restatement must be at a su f ficient temporal distance to constitute a formal recur rence. Here, the notion of recurrence applies only to melodic items that retain a strict identity, based on guidelines (1), (2), and (3) above, from one portion of a movement to another. Perle put forth the following generalization about thematic treatment in atonal compositions: In general, the atonal "theme" emerges only in the course of a composition and does not appear as a salient design at the outset of the work, as in tonal m u s i c . 12

Yet, of the fo rty movements lis te d in Table 9, twenty- six contain recurrence at GPL. Of these twenty-six, twenty initially present the recurring item in the first

^2perle, Serial Compcsltloa. p.9- 191

TABLE 9

Points of recurrence in 0pp. 11, 16, 19, 21, and 23

. O riginal Restatement Opus/movement in measure in measure (a) Pitch level 11/1 1 53 OPL 11/2 2 13, 55 OPL 11/3 no recurrence 16/1 1 36 P4 higher 16/2' 128 205 OPT. 16/3 240 260 OPL 265 286 OPL no recurrence 19/1 no recurrence (s ta tic ) no recurrence 19/4 10 OPL 19/5 no recurrence 19/6 (s ta tic ) 2 1 /1 1 25 OPL 2 1 /2 2 7 P12 lower 21/3 1 15 OPL 21/4 no recurrence 21/5 25 OPL 21/6 no recurrence , 1 m.23 of.Op.21/13 OPL 2 1 /8 4 11, 21 OPL 21/9 1 13 OPL 2 1 /1 0 no recurrence 2 1 /1 1 15 OPL 21/12 no recurrence , -p 1 OPL m 1 OPL 1 11 OPL ÎYAÎ 1 16 OPL 21/17 1 17 OPL 21/18 1 19 OPL 21/19 no recurrence 21/20 3 9 OPL 21/21 2 15 OPL 23/1 16, 23, 26 OPL 23/2 10, 14 OPL 23/3 9, 12, 14, 26 OPL 23/4 1, 23 OPL 23/5 100 OPL 192 m e a s u r e .O n e movement, Op.21/7, Is quoted at length at OPL in a la ter movement. Op,21/13» Two contain r e p e ti tion that is not at OPL, and two more have been classified as formally static, meaning that the pitch material is similar throughout. This leaves only ten displaying no motivic recurrence whatsoever, corresponding to Maegaard's category 186. Of these 10, Maegaard him self has placed only Op,11/3 and Op.16/5 in category 186. The other eight come from works not included in his categorization. These appear to be equally athematic.

The Categories of Formal Recurrence

On the most basic level, six categories dealing with the recurrence of items may be established, without establishing direct ties to specific classical forms, as Maegaard attempted. These six categories are shown in Table 10. To understand these categories, one should bear in mind that a "pitch/rhythm item" (see p.138 above) is identified through retention of intervallic

^^The Peters edition of the score to the Five Pieces for Orchestra (no.6061, 1973 edition) contains consecutive numbering of the measures throughout the work. For simpler reference, that numbering has been employed here. 193 TABLE 10 The six categories of formal recurrence, listed in order of the conventionality of their constructive procedures.

Movements Category Description included A. Polymotivic and sectionalized; Op. 11/2 more than one pitch/rhythm Op. 16/1, 16/2, ■ item repeated at original and 16/4 pitch level.

B. Im itative and "contrapuntal" ; Op.21/8, 21/17, at least one pitch/rhythm and 21/18 item repeated at original pitch level.

C. Monomotivic; Op. 11/1 lim ited to one recurrent Op. 16/3 pitch/rhythm item at Op.21/1, 21/5, original pitch level 21/7, 21/11, 21/13,21/15, 21/16,21/20, and 21/21 D. Monomotivic; Op.19/4 lim ited to one recurrent Op.21/2 and 21/3 pitch-string at OPL or Op.23/1, 23/2, one recurrent transposed 23/3, 23/4, pitch/rhythm item and 23/5

E. Athematic; Op. 11/3 containing an exploited Op.19/2 and 19/6 chord or interval Op.21/9 and 21/14

P. Athematic; Op. 16/5 containing no items of Op. 19/1, 19/3, motivic status or and 19/5 exploited chords or intervals. Op.21/4, 21/6, 21/ 10, 21/ 12, and 21/19 194

and note-value relationships. This means that a pitch/ rhythm item can retain its identity through transposi tion, or through strict augmentation or diminution, as long as the relative intervals or note values are re tained. As Table 10 suggests, this type of treatment has been considered conventional. A "pitch-string" retains only the intervallic, and not the note-value relation ships. The recurrences in Op,23 indicated in Table are those in vAiich the intervallic relationships are retained. Recurrences of "pitch-class-strings" are not shown. In category D movements, at least one consti tuent of the item fails to recur, either the note-value pattern or the original pitch level. The only examples in Schoenberg’s atonal instrumental works of a P/R item that recurs only at a transposed level can be found in Op.21, numbers 2 and 3» It may be in te r e stin g to note that all classical forms, exclusive of recitative, fall into either category A or B, The notion of a minute recurring item or none at all is thoroughly modern. Table 10 is arranged as a hierarchy of formal recurrence, ordered according to the degree of conven tionality of the formal procedures. Category A move ments are those in \diich more than one single motivic item is repeated. Within these movements, the distinct items delineate sections, making them polymotivic and 195 sectionalized# In category B movements, the repetition results from imitative procedures, so that the motivic recurrence usually takes place both at near and distant points. Often, those recurrences are closer together than in category A, C or D. This proximity does not in validate the recurrence as a mere local event, because the imitation, besides taking place in a different voice, is usually extensive enough to constitute unmistakably the constructive procedure of the movement. The m ajority of the movements lis t e d in Tables 9 and 10 present a single pitch-string at OPL as the re current item. When the pitches are also associated with a specific note-value pattern (i.e. constituting a P/R item), the movement falls into category G, If either the note-value pattern or the original pitch level fails to recur, the movement is in category D. A few move ments, assigned to category E, exploited chords or in tervals that may become the "recognizably con sistent feature" that Perle sought. Category F is for those movements th at, lik e Erwartung (see pp.157-160 above) continue to thwart attempts at "thematic" analysis, raising the question of vrtiether or not there can be form, in the conventional sense, without re p e titio n . Congru- ities of texture, timbre, and dynamics may provide the only formal d e fin itio n in a category F movement. 196 The hierarchy does not account for every possible means of recurrence, only those relevant to Schoenberg's formal procedures in the atonal instrumental works. For example, melodic repetition by i-c inversion is not in cluded as a formal category, because those movements in \diich it occurs also contain the more conventional re currence of intervallic relationships. This is not to say that repetition by i-c inversion and retrograde are not interesting and significant to the development of the twelve-tone method. Several instances of i-c inver sion are, in fact, mentioned in the analyses in Chapter V. The point is not that they are foreign to the atonal period, but that they are not essential to the atonal idiom. I f , in those movements believed to contain no m otivic recurrence, someone were to discover re p e titio n by i-c inversion or by retrograde, those categories would then be shown to be essential formal procedures in Schoenberg's atonal works. Besides the basic formal categories, there are several temporary organizational procedures for short sections of movements. These procedures, called "local and low-grade congruities" are discussed on p. 213 below, as categories G-P. A formal device that is entirely absent from the atonal works is the repeat of an entire section. 197

Beginning with the Serenade, Op.24-, Schoenberg once again used this procedure. For 0pp. 11 to 23, however, there is hardly any purpose in assigning letter names to whole sec tions, as in "ABA" form, even 'vriiere motivic material re curs. Indeed, it is difficult to relate any movement in these works to classical forms at all. Since, in the atonal style, the development of items immediately fo l lows their presentation ("developing variation"), the id e n tific a tio n of a separate "working out" sectio n , as in sonata form, is senseless.

Category A: Polymotivic and Sectionalized Movements

The category A movements in the atonal in stru mental works are Op, 11/2, and Op. 16, numbers 1, 2 and The second movement of Op.11 contains the most clearly differentiated material of any movement in the period, with three motives that recur at OPL and an ostinato figure that is present for approximately one-third of the piece's duration. A lower-level type of congruity exists between the first four notes of motives A and C (Ex.40), both proving to constitute CQ 1*+25. This is considered a lower level congruity because of the many more readily apparent congruities that can and do exist in this work. 1 9 8

"ff/f kp

ij‘r^

Ex.40« Three motives from Op.11/2, showing the congruity of CQ lM-25 between A and C.

The other three movements in category A are from Op.16. The second of these, "Vergangenes," receives a detailed analysis in Chapter V. The other two, numbers 1 and h, have statements of the motive at the outset, as well as recurrent secondary material. Because the move ments in this category readily admit to similar analyses, it is only necessary to discuss one in detail.

Category B; Imitative "Contrapuntal" Movements

Because of contrapuntal factors, category B requires deeper investigation into melodic procedures and 199

pitch combinations than A., An analysis of a Baroque fugue may indicate the entry points, episodes, bridge passages, stretto devices, etc., without saying anything significant about the actual working out of the lines. Yet, the "rules" for vertical combination were a significant part of the challenge of writing in an imitative or otherwise contrapuntal manner. Because such "rules" do not exist for atonal music, the analysis of imitative atonal move ments can consist-only of the horizontal treatment of the subject (see pp.22 and 148-14-9 above). The works in th is category are the im ita tiv e movements from P ierrot Lunaire. Op.21/8, 21/17, and 21/18. Number 8 receives a detailed analysis in Chapter V (see p.257 below). Number 17, "Parodie," contains a canon by in version between the clarinet and viola through measure 20. The flute then answers the viola from measure 22 to 26. The clarinet and viola then resume the imitation in measure 26, and the piccolo imitates the piano for one measure, in 28. In no.18, "Der Mondfleck," two crab canons are played simultaneously, so that in the last ten-and-a-half measures each of the four upper parts plays the retrograde of its first ten-and-a-half meas ures. The piano part consists of a number of short mo tives that are freely transposed. The clear motivic identity in each of these movements, coupled with the 200

"contrapuntal" imitative procedure, creates three of the most structurally straightforward movements from the period.

Cateeorv C: Monomotivic Movements

The function of the hierarchy in categorizing formal procedures becomes even more evident in category C movements. The large number of movements containing mo tivic recurrence at OPL indicates that, although tonality was no longer a concern of Schoenberg's, pitch level (or tonal level) was. The number of movements falling into categories A, B and C (18 of kO) shows that the idea of a motive, in the traditional sense, was still signifi cant. Nevertheless, vrtien only one untransposed pitch/ rhythm item can be id e n tifie d , and perhaps even only one recurrence of a brief item, extensive portions of a work must be accounted for by other means. It i s not merely the fact that a motive returns, but also its relative significance to the piece as a vrtiole, that contributes to its categorization as a more conventional form. In Op.11, for example, a rather lengthy motive (seven notes) returns in several transpositions, and in m.53, at OPL (an octave higher). By contrast, the recurring P/R item in Op.16/3 is only three notes long, and the 201

remaining portion of the work contains only a very slowly changing vertical structure. A ll of the remaining category C movements are from Pierrot. Although they are relatively short, they display considerable diversity in the role played by the untransposed P/R items. The first movement contains an ostinato figure that lasts the first four measures, then returns in mm. 11, 1$, 17, 25, 29, 35, and 39» It is absent at the most for the eight measures from 17 to 25- On the other hand, in Op.21/5, the Hauptstimme at meas ures 2 and 23 contains one recurring three-note P/R item , and no other motivic recurrences can be found. The remainder of the movement belongs, in effect, to cate gory P (athematic), showing how just one brief recurring item can separate a category C movement from a category F type.

Category D: Untransposed Pitch-strings or Transposed P/R Items

Movements containing untransposed pitch- strings or transposed P/R items fall into category D. Here, the line is drawn between items that retain at le a st a sp e c ific p itch o% rhythm id en tity and items that do not. In the case of Op.23, untransposed pitch strings are the primary organizing element. This means that the 202

original note-values are no longer considered an essential motivic feature. This concept had been used in earlier periods, but only after a given note-value pattern had been firmly established (Ex.^-1 ).

AlUw Wolio Poto II 111' u 'I

Ex.^1. An example of a recurrence with a change of note values from Beethoven's Third Symphony, fourth movement.

A ll f iv e movements from Op.23, one of the f in a l works before Schoenberg's twelve-tone period, are in category D, indicating how closely this procedure pre saged la te r ones. There are also two movements (op.21/2 and 21/3) in which a transposed P/R item is the only means of recurrence. One could consider this symptomatic of Schoenberg's renunciation of a tonal center, except that movements containing recurrence at OPL are far more numerous. Although Op.21/3 does contain the recurrence of a three-note P/R item at the original pitch level, the opening motive that is restated in m.30 appears at a transposed level. This situation requires some interpre tation. The opening P/R item appears three more times 203

in m.30: in the clarinet a major thirteenth and then a major third lower than the original, and in the piccolo a minor ninth higher than the original. The original is

stated ££., although the three restatements are all d d p . The untransposed P/R item that occurs at the end of the first measure and in m.15 in the clarinet is stated p p p in both places. Thus, in spite of a minute P/R item at OPL, this movement is placed in category D. This case i s unique, because in a l l other movements with an un transposed P/R item, it is also the most prominent re curring item. Op.23 provides the most representative category D movements. In all five movements, the notion of an untransposed pitch-string is supplemented by transposi tion and inversion. Obviously, however, these other treatments are of secondary importance if, as in Op.23/1, a pitch-string returns five times at the original pitch level, uninverted (at mm,17, 23, 26, 28, and 32) in a total of 35 measures. Applications of other procedures besides à pitch-string are apparent at other points in Op.23/1, The imitation of some fragments occurs at the beginning and end and in mm.23, 26, and 29» In the f in a l measure, the descending minor third of the opening motive is imi tated in the left hand, resulting in what appears to be 204 a small case of retrograde inversion (Ex.42). Since this motive consists of a series of minor thirds, this stretto treatment of a fragment is indistinguishable from a brief instance of retrograde inversion. The only instance where the first four pitches of the motive actually appear in inversion is in measure 7: B-D-E&-C (Ex.43), transposed down a fifth from the original. Perle

A \j

Ex. 42. An apparent instance of retrograde inversion in the final measure of Op.23/ 1.

.Vlth parmisaion of Edition Vilhelm Honaan, Copenhagen, Denmark

Ex. 43. Op.23/1; The first four pitches of the motive in inversion, m.7« 205

succeeded in isolating one true case of retrograde in Op.23/1:

The ordered linear formations of Op,23, no.l with the exception of a single retrograde state ment in the left hand of bars 30-31, are given exclusively In their prime aspect and at a single pitch level.

"ordered linear formations'* are, of course, pitch-strings, although he does not define the term as such. Although the untransposed pitch-string is still of primary importance. Perle noted that, in contrast to the first movement of Op.23, the next three movements display more treatment of the pitch-string in inverted and verticalized form. Here, not only are the original pitches of the string free from any associated note-value pattern, but other serial devices take on increased im portance. In P e r le 's words, in Ho.4:

the multifarious associations that each note acquires tend to negate the integrative pos sib ilities that presumably motivate the em ployment of serial procedures in the first p la c e .^

Or, one might say that the ornate character of the open ing material tends to make the pitch-string difficult to

^^erle. Serial Composition. p.k-$. ^^IMd, p.4? 206

discern. Again, the arhythmiccharacter of the pitch- string contributes to the decrease in significance of pitch-rhythm identity. Instead, the recurrent item is merely a succession of pitches (or occasionally pitch- classes, a far less pronounced type of identity). The original pitch level of a string nevertheless remains significant in the typical formal applications. The use of transposition, inversion and retrograde does not undermine the formal prominence given to the prime as pect of the pitch-string at its original pitch level. The preceding cursory analyses of movements from categories A, B, C, and D suggest the large role played by contextual emphasis and original pitch level. In Op.23, the recurring pitch-strings are consistently stated horizontally at the outset of each movement- Although in numbers k and 5j the string is often partly verticalized, there is one horizontal restatement at OPL. In Op.23/3, the pitch-string returns at the ori ginal pitch level in mm.9? 1^, and 26. The nature of the intervening material in number 3 reveals, however, a much stricter adherence to serial principles than in numbers 1 and 2. Permutations of the motive now take the place of fr e e ly composed episodic m aterial. 207

As a general rule, the item that is subject to recurrence in the atonal-works is stated in the first measure (see Table 9, p.191 above)., In this music, there is ho analog to an introduction that might precede the initial statement of motives. Of the twenty-seven move ments with recurring motives, twenty-two actually com mence with a statement of that motive. I The Concept of Musical Prose

The discussion of the last two formal categor ies in the hierarchy (E and F) requires the examination of Schoenberg's concept "musical prose," vAiich he used in connection with athematic compositions both instrumen tal and vocal. Schoenberg defined musical prose as "a direct and straightforward presentation of ideas, without any patchwork, without mere padding and empty repeti tions."^^ To Maegaard, th is concept im plied a

rhythmic freedom and independence from symmetry of form, differentiation of structural elements with regard to size and content. He called for renunciation of what he considered the primi tiv e aids to memory, lik e rhythm and rhyme.17

^^Schoenberg, "Brahms the Progressive," p.4C0. ^^Maegaard, Studien, v .2 , p .287, my trans la tio n . 208

There is an evolutionary dichotomy between Schoenberg's move toward freedom of construction, represented by musical prose, and the increased extramusical controls of the twelve-tone method. He sought freedom from for mal symmetry, yet delighted in sm all-scale symmetry of p itch combinations, ty p ifie d in the symmetry of the twelve-tone set complex. The above statements about mu sical prose attest to Schoenberg's fear that excessively obvious organization might make music blatant, simple, or primitive. Schoenberg did not abandon organization altogether, but sought to avoid intuitively obvious or ganization. Schoenberg apparently came upon the notion of musical prose in relation to opera. His description of Mozart's operatic technique is remarkably suited to his own athematic style:

Accommodation of the music to every change of mood and action, materially or psychologically, is the most essential problem an opera composer has to master. Inability in this respect might produce incoherence—or worse, boredom. The technique of the recitative escapes this danger by avoiding motiva 1 and harmonic obligations and their consequences. The 'Arioso' liquidates rapidly and ruthlessly that minimum of obligations in which it might have engaged. But the 'Finales' and many 'Ensembles' and even 'Arias' contain heterogeneous elements to which the technique of lyric condensation is not applicable. In 209

pieces of this type a composer must be capable of turning within the smallest space.

Like many of Schoenberg’s writings, this passage contains a few terms whose meaning is in doubt. What, for exam ple, is meant by "the technique of lyric condensation?" Perhaps this is merely a reference to Mozart's avoid ance of strophic construction. The overall bent of this quote seems to be that "obligations" are to be avoided, and "liquidations" and "heterogeneous elements" are assets. Also, incoherence is apparently preferable to boredom. This, of course, was not the first time in musical history that prose was a guiding factor in composition. According to Grout, in earlier operas,

...the prevailing impression in the solo portions is one of almost rhapsodic freedom, as though the melodic line existed solely to add the ultimate fulfillment of song to a poetic language already itself more than half music.

He was referring to the operas entitled Euridice of both Peri and Caccini. In Claude P a lisc a 's opinion,

18 Schoenberg, "Brahms the Progressive," p .^11.

1 9 ^Donald Jay Grout, A Short History of Opera. 2nd ed. (New York: Columbia University Press, 1965), p.45. 210

Peri vras the one #10 realized a solution that answered the needs of the stage...His solution was to free the voice from the accompaniment both rhythmically and harmonically and yetpderive musical coherence from its support... ^

The mention of these examples is not intended to imply that the situations are entirely analogous. To begin with, the age immediately before Schoenberg's was one in which opera composers had slowly attempted to phase out recitative entirely. In addition, symphonic struc tures. were becoming more thematically unified in the nineteenth century, in instrumental and vocal music. Yet, in spite of these differences, certain parallels between Schoenberg's musical prose and the early reci tative style remain. Both were claimed to promote the expression of the text. Both contained only sparse repetition of melodic items and frequent clashing of the melody with the "harmonic".background. Thus, if one; accepts Schoenberg's modern concept of musical prose, it makes no more sense to seek motivic unity in Erwartung than to seek m otivic unity in the lengthy recitatives of early opera. Further confusion arises from the fact that pieces such as Op.16/5 or 19/1 are examples of "musical prose" without text. Here, the

r — : r ' 20 Claude V. P a lisca , Baroque Music (Englewood Cliffs, N.J.I Prentice Hall, 1968), p.30. 211 aesthetic justification is not as clear, because the text, which might have lent the final vestige of continuity, has been removed. On the other hand, the analysis of the music is made no easier by the presence of a text in a piece like Erwartung. In fact, the basic analytic ques tions have proven to be as problematical for the works with text as for those without. Minute elements of repetition may be found even in "musical prose." One such element is the exploited vertical structure, or, as Maegaard called them, "fixed chords" (fixierte Alckorde) This refers to a CQ that is associated with an original pitch level and a speci fic registral configuration. In Op.11/3, the three- note "chord" A-D#-G# occurs in mm.1, 2, 3, 12 and 13 (see p.268 below), rîümerous transpositions and arpeg- giations also occur. Certainly, in the complex texture and vertical activity of this movement, these vertical structures are not especially prominent, and may not even be audibly discernible as such. Nevertheless, the CQ described in Op.11/3 actually receives clear contextual emphasis as a significant item in measures 3^ and 35? at two different transpositions. This

^^Maegaard, Studien, v.2, p.133» 212 congrulty from one point of the movement to another has as its referent neither an untransposed pitch-string nor a P/R item, and thus is. considered a low-grade congruity. Because the referent is not a motivic item, Op.11/3 i s placed in category E, Such movements lack not only substantial themes, but even so much as a small motive. Although they are, in effect, "amotiv- ic," the more common term from the literature, "athe matic," refers equally well to this property. Other movements in the atonal works contain exploited "chords" that pervade the music more thor oughly than the one in Op.ll/3. If a simultaneity or series of simultaneities is repeated, the congruities may become just as sig n ific a n t or even more so than untransposad pitch-strings or P/R items. This is the case with Op.16/3, Op.19/2 and Op,19/6, three of the more au rally a cc essib le movements from the period. The simultaneity in each case returns so frequently that no associated note-value pattern is required to identify it. Hence, along with a stasis in the vertical dimen sion, there tends to be a rhythmic stasis. Both Op. 19/2 and 19/6 were indicated as "static" in Table 9, but Op.16/3 was classified as containing a recurring item. Actually, for Op.16/3 more than one organizational scheme can be c ite d . Not only does the b rie f P/R item 213 recur at OPL, but the slow-moving chords actually recur in a slow-moving canon disclosed by Charles Burkhart. Burkhart's article also represents an attempt to dis- 22 cover a form-defining role for orchestral color. In this case, the return at OPL in measure 260 qualifies this movement for category C. The exploited chord is, nevertheless, an interesting and noteworthy feature of Op.16/3. The hierarchy in Table 10 represents different degrees of conventional formal coherence, which, means that the feature most aurally prominent determines the category. The fact that another interpretation might place a movement in a different category is less impor tant than the fa ct that the categories accommodate every atonal formal procedure. Often in "musical prose," the nature of the expository material provides an indication of the de gree of r e p e titio n to be expected. Several movements of Op,21 contain material that cannot even create the expectation of development or continuation. For example, in number 10, the actual pitches appear to be less important than the sixteenth-note groupings; num ber 12 r e lie s on an accelerando and an in creasing

Zacharies Burkhart, "Schoenberg's Farben," P ersp ectiv es of New Music, Autumn 1973~Summer 197^» pp.1 4 1 -1 7 2 . ~ 214

amount of sixteenth-note motion (see p. 261 below) for momentum. In other cases, like Op.21/6 and 21/19» a non-recurrent item "masquerades" as a significant item, demonstrating contextual emphasis in its most aurally misleading guise. Examples of extended opening melody (Table 8, factor 1) abound in P ierro t, numbers 6 and 19 being those in which such emphasis is not confirmed. In number 6, Schoenberg used a bracket to indicate the Hauptstimme. This indication, however, does not neces sarily imply an analytic statement that the designated part contains formally significant material. Converse ly , primary m aterial in movements containing recurrent motives often appears without the Hauptstimme brackets. This divergence between momentary prominence and formal significance is another aspect of Schoenberg's incon sistent regard for contextual emphasis. For example, in the category C movement. Op.21/11, the ostinato mo tive returns in m.1$, but brackets do not appear until m.l8, in conjunction with non-recurrent material. The Hauptstimme marking must be seen as the expression of Schoenberg's desire to emphasize certain ideas that might not achieve enough prominence of their own, either through repetition or contextual emphasis. 215

Local and Low-Grade Congruities

In many of Schoenberg’s atonal movements, par ticularly those in category C, the recurrent items of the sort mentioned above account for only a small pro portion of the total composition. Although parts of the remainder of many movements display no p itch or rhythm patterns, other temporary organizational factors are often d iscern ib le over b rief spans. Such fa c to r s, which can obtain for as little as.a single measure, cre ate what might be called "local congruities." Although local congruities afford some degree of continuity, they do not relate more distant events, as do motivic recurrences. In other cases, items that are not related as motives may exhibit more tenuous connections that might be called "low-grade congruities." In the case of local congruities, local variation procedures (see p. 150 above) frequently account for small areas of or ganization as new material is introduced, varied and re linquished. These various factors are shown below, and serve as additions to the categories in the hierarchy of Table 10. Significant portions of every atonal move ment are governed by one or more of these procedures. 216

II. local Congruities

G. Direct Repetition (including ostinato) H. Imitation I. Sequence or quasi-sequence J. Local Variation Procedures

III. Low-grade Congruities

K. CQ congruity L. Horizontal/vertical congruity M. Textural congruity N, Contour congruity 0. Note-value pattern congruity P. D elineation by punctuation

Local congruities are usually very evident, but quite brief. A typical example occurs in Op.2l/5, mra.3A-35 (Ex.A4), where three instruments repeat their parts note-for-note. In mm.40-42, literal repetition occurs, with only the bass clarinet changing its pitch. 217

«ia wm.fmm filatil

Usaa by paralaaion of Belmont iluaic Publishera, Loa Angelas, California 90049

Ex.M+. The local congruity of direct repitition, in Op.21/5, mm.3^-35.

, ______

_ _ — 9

Used by parmioBion of Balnont IJuaio Publiahara, Lob Angelas, California 90049

Ex.^5. A highly varied canonic passage from Op.21/8. 218

This device of direct repetition is represented by cate gory G. Local congruities may also result from imita

tion, as in Op,21/5, mm.16-18 or Op,21/8, mm. 19 ~2*+ (Ex.U-5) « In the latter example, the canon is contained in the two hands of the piano, with the left hand an swering at a fifth below, one sextuplet later. In m,20, the interval of imitation varies, and in m.21, the dux shifts to the left hand, with the comes a major ninth higher, three sextuplets later. Such examples are indi cative of the high rate of variation, even within local congruities. Category H represents local imitative pro cedures like those just described. Other types of local congruities are less clear-cut, like some quasi-sequences (category I). The opening of Op.21/6 contains a f a irly long example of quasi-sequence. The cello plays three consecutive, pizzicato, scalar runs, from E up a ninth to F and back down (Ex.46). Only the accidental associated with each pitch name is subject to change, altering the specific step pattern of each run. A diagram of the changes shows no particular regularity to the pattern of the accidentals. Even if some stepwise pattern could be discerned, the congruity would rely more on the nota tion than on the aural perception of a literal sequence. 219

ascending descending e p g a b ç d e £ED0BASE f i r s t run second run third run

Ex. k-6. Op.21/6: The contour congruity in the opening cello part.

The aural congruity actually results from the repeated melodic contour and pizzicato timbre. In this case, the contour coincides with the normal metrical stress, a rare occurrence in the atonal works. The sequence or qua si-sequence makes up category I. The local variation procedures discussed in Chapter III comprise another category of local congrui ties, category J : metrical displacement, note-value alteration, interval expansion or contraction, and pitch interpolation or elimination. When subject to procedures of this kind, the varied item generally re tains a distinct identity. While "local congruity" refers to a procedure applied briefly in the course of a movement, "low-grade 220 congruity” refers to a particular type of connection be tween either local or distant events. As the examples below will show, the vagueness of these connections accounts for the qualification "low-grade.” Because they are so weak, they need only be sought in the absence of more substantial features. In most of Schoenberg's atonal movements, p a r ti cular CQ's appear at more than one point. Category K consists of low-grade congruities in CQ make-up between vertical or horizontal structures. Of course, every re petition of a CQ will not stand out unless some other low- grade congruity is retained, like the original timbre or texture (category M). Category K represents an isolated instance of the kind of congruity that becomes the main formal ch a ra cte ristic in category E movements. In Op,

21/ 13, a category C movement, the CQ 1^-7 repeats in exactly the same instrumentation (clarinet, viola and cello) in mm.5, 8, and 21. In the case of horizon- talized CQ's, CQ^'s that lack an associated note-value pattern become low-grade CQ congruities rather than mo tivic recurrences. A CQ congruity between horizontal and vertical items (or possibly combinations of both) falls into category L. The fact that vertical and horizontal items 221

may be related implies the notion of a third category combining horizontal and v e rtic a l elements. Only in serially-oriented analysis, however, has it become plausible to seek the notes of a recurrent item partly in the vertical and partly in the horizontal dimension. Two examples may be drawn from Op.19A« In mm.5-6 (Ex.^7), the R.H. plays the pitches B-C-F#-G (excluding the grace note D). These pitches spell CQ 1^-16. The

Usad by Ppr^iasion of Balnont Uualc Publishers, Los Angeles, California 90049

Ex. *+7* A CQ congruity in Op. 19 /^, CQ 1416.

last note of m .9 and the first four of m. 10, E-tF-A-B^, also , spell CQ lM-16. The significance of this congruity is severely lessened by the presence of other pitches

in m.6 , and the rest in m.9» which separates the E from the pitches in m.lO. For this reason, some type of supporting congruity is needed to make a low-grade con gruity notable. For example, the congruity between m.2 and m.8 is fa r more d istin c t, because the same CQ, 156, appears in a similar note-value configuration (Ex.^8). 222

i É

Usad by Pemiisaioii of Bolmonli Muaio Publishero, Los Azigalas, California 9004-9

Ex. *+8. 0p.19/M-: a congruity of CQ supported by a congruity of note-value pattern.

Congruity of texture, category M, may be eith e r partial or complete. It is clearest when •'specific instru ments repeat specific types of configurations. The mere fact that the same instruments are playing is usually not enough to estab lish a tex tu ral congruity between two par ticular passages. On the other hand, slight changes in texture or timbre might not undermine a congruity. In Op.16/5, the very drastic texture change at m.395 un mistakably marks the end of the f i r s t section, although several less prominent changes have taken place before

i t . A good example of tex tu ral congruity may be found in Op.21/^. The chordal texture at the opening becomes more florid by m.9, but returns to the opening texture in m.13, with new pitch material. Since low-grade con gruities never involve precise pitch/rhythm recurrences, they are far more convincing in compound instances. 223

Categories N and 0 involve contour congruities. The notion of contour congruity may-be traced back to the Grundeestalt (basic shape, see pp .135-138 above), which, according to Rufer, was also Schoenberg's term for the twelve-tone series. In Schoenberg's analysis of his own Op.22, he also appealed to the notion of shape:

It can be pronounced a law of music that it is possible to recognize (i.e., to perceive) not only the regular rearrangements of musical shapes, but, given favorable conditions, irreg u lar ones as well, provided only that enough will remain constant, once the intervals have been exchanged.23

Not only are these "favorable conditions" an important consideration, but also the consistency of the relation between the shape and its "rearrangement." Because the basic outline appears to be the feature that is retained in these instances, the word "contour" will be used to relate two items with a similar basic outline. Contours, as some examples will show, are not defined here in terms of specific pitch/rhythm char acteristics, although the recognition of such outlines was certainly a concern of Schoenberg's. Contour . .

Z^Sohoenberg, "Analysis of the Four Orchestral Songs, Op.22." 224

recognition, in fact, is often difficult in Schoenberg's music, where, in the words of Erwin Stein,

the motif in question does not change by gradual development, but immediately (or very soon) submits to far-reaching transformations.2*

Stein, furthermore, takes the unusual position that such immediate changes actually strengthen the connection. For further clarification, a few examples of contour congruity will be discussed. Although these congruities constitute weak recurrences %Aen they occur at a wide enough separation, many good examples between closer items may be found. At the very opening of Op. 11/1, the first melodic phrase bears an antecedent- consequent relationship with the phrase beginning in m.9

(Ex .4 9 ).

$ « g

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Ex. 4 9 . A contour congruity and an antecedent------consequent relationship in Op.11/1,

^^Erwin Stein, Oruheus in New Guises (London: 225

This is an unusual case, because the two phrases are not juxtaposed, but are separated by a second idea in mm.^-8. The relation of the melody at the beginning of each phrase can be seen in the identical note-value pattern and semi-tonal ending (though in reverse directions). The important feature is that none of the corresponding intervals is the same in the two phrases. Only the con tour : descending-descending-ascending-descending-same has remained constant. Each pitch also remains in the same general re la tio n ( i .e ., simply above or below) to the other pitches in the phrase. In (a), however, the first note is the highest, and in (b), the fourth note, G#, is the highest. This asymmetry makes it unlikely that the congruity would be heard as a literal transpo sition of the original. The retention of rhythm and basic shape creates the congruity of contour. A contour congruity constitutes a weak type of recurrence if it relates distinctly separate points in the movement (see p.l90 above). This type of low- grade recurrence appears in Op.16/5, a movement lacking the recurrence of an actual motive. The prose-like quality of this movement is notable in Schoenberg's title, "The Obligatory Recitative'' (see p.207 above). In one instance, five pitches, though only three 226

ijya «I ------. ^

Va. ’ ' T M : . 138

w ith perraisai^ of G.P. Patera Corporation, Mew York

Ex. 50. A repeated CQ in Op,16/5.

different pitches, are repeated, but not in the Hanntstimme (Ex.50). Indeed, the majority of contour congruities in Op.16/5 do not occur between Hauntstimmen. Two -of these congruities are discussed in Chapter V (see

pp. 235- 2^1 below). The rest of Op.16/5 seems to be "variations" on g meter. Maegaard iso lated the entire Hauptstimme of this piece, hoping to reveal any unity contained in it.%5 His reduction makes it. easier to ob serve the variety of note-value patterns that the com poser has f i t into a single m etrical scheme. Hence, in spite of a great variety of material. Op.16/5 contains only a few contour congruities.

^^Maegaard, Studien. v .3 . 227

Schoenberg's concept of basic shape is so broad that it might refer to a set of pitches or pitch- classes as specific as a twelve-tone series or as general as a melodic or rhythmic contour. Since Schoenberg used shape as an element of unity, melodic contours and note- value patterns are placed within the low-grade congrui ties, categories N and 0 , respectively. There are three punctuating devices that, in spite of the absence of any congruities, are salient enough to delineate sections by themselves. These three devices involve an abrupt change in texture, dynamics, or tempo. Although these changes may serve to give con textual emphasis to the material immediately following, they have at least a mild sectionalizing effect under any circumstances. If a particular texture, dynamic, or tempo is maintained, this constitutes some sort of low-grade congruity, if juxtaposed with a contrasting condition. Numerous examples exist, because abrupt changes are one of the essential features of Schoenberg's atonal idiom. Occasionally, more than one element will change at a tim e, as in Op.21/2, where a new tempo and texture occur in m.33, marking the fin a l sectio n of the movement. Category P, then represents Schoenberg's means of sectionalizing a movement regardless of the 228 m aterial in the movement. This chapter has dealt with the variety of ways in which material may recur in Schoenberg's atonal works, ranging from substantial melodic recurrence to a lack of recurring material that is compensated for only by a rough punctuation into sections. The formal categories in-the order of a hierarchy, A through F (Table 10, p.1^3 ) represent procedures that govern entire movements. Categories G through P (see p. 2l6 above) apply to sec tions and subsections of movements. The more detailed analyses in the following chapter w ill help demonstrate how local and low-grade congruities contribute to the or ganization of athematic movements. The congruities also appear abundantly in the more formally conventional move ments, but are superseded by more substantial elements of repetition. The numerous categories and divisions in Tables 9 and 10 are necessitated by the wide variety of formal procedures employed by Schoenberg in his atonal works. These tables represent a means of confronting the inconsistency of the types and degrees of recurrence displayed in these works. Since many of these congrui ties are also found in common-practice music, conven tional analytic methods can reveal a substantial amount of the organization present in Schoenberg's atonal instrumental works. Chapter V USE OF THE ANALYTIC CATEGORIES IN ANALYZING REPRESENTATIVE MOVEMENTS

The formal hierarchy and the list of congruities introduced in Chapter IV (pp .193 and 2 l6 ,‘resp ectiv ely ) consist of categories representing Schoenberg's principal compositional procedures in the atonal instrumental works. Procedures described by a ll the categories are demon strated in the analyses in this chapter. In addition, some passages are simply considered "free," because no generalizable procedures appear to be operating. Using common-practice music as the standard, the categories in the formal hierarchy progress from the most conventional to the least conventional. After the appro priate formal category has been found to describe the basic procedure of a movement, the other categories are used for describing local and low-grade congruities. There is a trial-and-error aspect to the application of these categories. First, since the basic formal cate gories are defined in terms of recurrent items, each movement must be scrutinized for v^at recurrence, if any, takes place. The condition of a movement containing no

229 230

motivic recurrence is, of course, the most difficult to corroborate: the entire piece constitutes the evidence. Another trial-and-error aspect of these analyses pertains to local and low-grade congruities. Small elements of repetition can be sought on a local scale in the same manner that they are sought through an en tire movement. Congruities of CQ, vertically, horizontally, or in com bination (categories L and M), are probably the most minutely precise types of congruity in the list, and are only mentioned if some other type of prominence is afforded them. Finding all CQ congruities requires not only a complete v e r tic a l tabulation of a movement, but a consistent system for counting all two-dimensional com binations. The criterion of a second confirming con gruity diminishes the number of CQ congruities worth noting to a more manageable and meaningful quantity. Because many movements are similar in their for mal procedures, a good understanding of the idiom can be obtained without giving a complete formal analysis of every instrumental work from Schoenberg’s atonal period. They have, however, all been classified in Table 10 (p.193). Those movements that most closely resemble classical forms admit more readily to conventional types of analysis. They require less detailed elucidation here 231

than the more unconventional movements, which better test the particular applicability of the categories to Schoen berg's atonal works. In the less conventional movements, i^ich are placed in lower formal categories, local and low-grade congruities make a more significant contribu tion to the often loose formal construction. When the basic formal procedure is more clearly defined by mul tiple motivic recurrences, as in categories A and B, local and low-grade congruities play a less significant form-defining role. Those movements that rely more h eavily on local and low-grade congruities are treated first in this chapter. This approach has been taken because the more conventional movements from Schoenberg's atonal output have tended to receive more extensive treatment in the literature.^ Accordingly, the formal categories are discussed in the reverse order of their appearance in the hierarchy (i.e., F through A). Each lo c a l and low-grade category id e n tifie s a specific and explicit procedure. These categories

^The only two notable exceptions are Maegaard's analyses of Op.16/5 and Erwartung. which consist mainly of isolating the Hauotstimmen (shown in V.3 of Studien) and examining them for recurrence. Rheinhold Brinkmann's study, Schoenberg: Drei Klavierstiicke, Op.11 gives far more attention to the first two movements of Op.11. Perle's most extensive analysis deals with Op.11/1. 232 are; designed to permit a great number of concrete obser vations to be made about conventional procedures in a given movement. Where the forward-looking s e r ia l tech niques are clearly employed, these, too, are noted, al though they only become a major factor in Op. 23. Since the athematic categories (E and F) are especially problematic, every movement placed in either of these categories is given a detailed analysis below. Then, in order that the reader may see the essential features of the other categories, representative move ments from categories A through D are treated. The move ments to be analyzed in detail in this chapter are, from category F: Op.16/5» Op.19 , numbers 1, 3, and 5» Op.21, numbers )+, 6, 10, 12, and 19» from category E; O p .ll/ 3, Op.19 , numbers 2 and 6; Op.21, numbers 9 and Ik-; from category D: Op.21/2 and Op.23/2; from category C: Op.21, numbers I3 and 21; from category B: Op.21/8; and from category A: Op.16/2. The i n i t i a l formal categorization of each move ment was indicated in Table 10. This step required a thorough formal analysis, even more so Wien the claim was made that a movement shows no motivic recurrence whatso ever. The particular criteria for making this claim were apparently slightly more selective than Schoenberg's own (c f. p p .l6 and 189 above), and there are certainly 233 borderline cases, such as Op,21/ 2. For the most part, however, the differences between the conventional and un conventional formal procedures are quite distinct. Two tendencies may be noted in the formal categorization of the atonal movements. On the one hand, there are a wide variety of formal types from movement to movement within each work. On the other hand, certain categories are represented almost ex clu siv ely by movements from a sin g le work (see p.l$3 above). For example, fifteen of the twenty-two movements in Pierrot Lunaire f a l l under eith er category C or E (i.e., 9 and 6 respectively). Within a category, further differentiation is possible on the ba sis of three criteria: the extent or duration of the recurrent item, the actual degree of similarity between the original and the restatement, and the temporal separation between the original and the restatement. Short items, besides simply having less duration, are also likely to be apprehended as significant. Also, an item that is repeated by the same instrument at the ori ginal pitch level creates a more striking congruity than one repeated by a different instrument at a different pitch level. Other constituents, such as phrasing and dynamics, also play obvious roles in the clarity of recurrence. With regard to temporal separation, if an 234 item is repeated only once, and at the extremes of a movement*s duration, as in Op.23/5, that repetition is obviously less forceful than closer,, more frequent re turns. All of these considerations have to do with the certainty with which the ear is likely to single out a certain item as motivically important; they determine the conventional aural coherence of a movement. Con textual emphasis always plays a large role in this de termination. It is important to remember that local and low- grade congruities are necessarily contained within a category higher on the list. If a motive returns, for example, thereby qualifying a movement for category A, B, C, or D, then the melodic contour and note-value pat tern also return, although these latter categorizations become superfluous. Hence, assignment of an entire movement or a single congruity to a category necessarily implies assignment to other categories lower on the l i s t . The present purpose is to show how conven tionally classifiable features are a significant fac tor in the generally unconventional movements that comprise Schoenberg*s atonal works. Investigation of local procedures in every category A and B movement 235 would no doubt be worthwhile, but it more closely re sembles the analysis of common practice music, and thus exhibits less fully the particular applications of the present approach. In most category E and F movements, every congruity makes a more notable contribution to the limited formal organization. For this reason, the treatment of category E and F movements i s , as might be expected, longer and more detailed than that of cate gories A through D. The analysis of each category F movement consists of a verbal summary of formal events, followed by a list of the apparent local and low-grade congruities. In addition, a diagram showing the gen eral location of these congruities within the movement is supplied. The lists and diagrams will demonstrate the systematic application of categories G through P in making substantive observations about athematic com p o sitio n s.

Analyses of Athematic Movements (Category F)

Op.16/9: Das obligate Rezitativ.

Except for Erwartune. the fifth movement from the Five Pieces for Orchestra, Op.16 is probably the most extended example of "musical prose" (see p.207) that Schoenberg ever composed. It poses far 236 fewer analytic problems than the monodrama, however, be cause of certain stabilizing factors. The ^ meter is constant throughout; the effects of delineation by punc tuating devices are not nearly as complicated as in Erwartung or O p .ll/ 3 , the latter of which will be dis cussed under category E. Nevertheless, the problem of basic form remains, because of the absence of motives in Op.16/$. In spite of some apparent sectionalization, the sections do not contain distinct melodic material. The opening section ends with a unison forte in the winds at m.3 7 8 . The next major point of punctuation is m.39$, where the strings are played sul ponticello. Pianissimo, At m.k02, a texture like that of the open ing is resumed, and at iu.^50, the crescendo to fff sub sides, signaling a closing section. In Op.16/5, the elements of repetition are so brief and rhythmically variegated that the effect is en tirely athematic. In particular, pitch/rhythm items are never repeated without some detail being altered. With in the constant g meter, two specific note-value pat terns attain some prominence; these are illustrated in Table 11. The first of these, labelled (a), demon strates an additional congruity of melodic contour. The second, (b), is solely an example of a note-value pattern congruity. The d etailed breakdown of each item 237 TABIE 11 Two low-grade congruities in Op.16/5

(a) ascending scalar contour with note-values: JT3 i' Me as. In str . Step prog. Beat Pitches 332 c e llo II S S S S 1 P#-G-ül>-A-B^-B 334 c e llo I T T T 5 3 B-G#-D#-E#^P#-G 350 c e l l i S S T S 3 A#-B-0-D-E>-P 361 c e l l i T S S S 1 G-A-BV-B-C* 393 v io la TM3 S S 1 Gj^—A— B—Dj^—E

(b) note-value pattern;

Meas, P itches _C&. 346 G#-C-G-P#-A^ 11136 359 p-E^-C-Ab-Bv 22323 360 Bb-C-Bï-C#-A 11118 361 AP-B-Gb-AÇ -G 1137 361 G-EP-BD-Db-C# 11433 362 D#-D#-D-B-C# 1182 371 D—G—B—Aj^—B 1128 372 G—BP —AP — G 11226 373 D#-E-D#-P-E 11- 10 . 374 P —E v —D —G—P 1227 378 E-D-E-G#-A# 1263 379 A— Gf^— E—A—D 1524 388 D#-P#-D-G#-E 11127 392 A-D#-E-A#-A 1515 424 jBV 1515 429 B-D#-E-G-A 13224 430 Gj^—B—Gj^—A—G 11226 432 Eb-P-Eb-G#-A 1623 451 G-E-P#-G#-G 11442

* Last note missing. 238

serves to substantiate how strict repetition is carefully eschewed. The data in Table 11 reveal only a few rather remote relationships. Item (b) is twice the horizontalization of CQ's 11226 and 1515> and once of each CQ of the i-c related pair CQ 1182 and 1128. In all three cases, octave displacement and reordering eliminate strict repe tition. Other shorter note-value patterns recur, as shown in Example 52. In these, strict pitch/rhythm repetition is avoided in a similar manner. Although the above patterns take on some aural prominence, there is a repeated CQ^ that, in spite of its recurrence, remains unsupported by other congrui ties. Because there is no note-value pattern associated with it, it cannot be considered a motive. Remarkably, though, it is the arpeggiation of the same CQ (I 38 ) that was found throughout Erwartung and other works of the period (see pp.159-160 above). In fact, as this three-note pattern appears in m.3V+ of Op.16/5, it is quite sim ilar to the opening of Op.11/1 ( c f . Examples and 50, pp.224-226). Here, although the CQ has no associated note-value pattern, it does have an original pitch level, F#-D#-D. At this and other pitch levels, in either the Hauptstimme or some secondary voice, it appears melodically twenty-two times in the course of 239

135 measures (see Ex.52). At the pitch level of F#-D#-D, including the occurrence at m.44-2, it appears in mm. 3^ , 352, 366, 395, and M+2.

Although this single qua si-motive, CQ 138 , does not assume the status of a truly motivic item, especially in a movement of the dimensions of this one (135 mm.), it still represents one of the more substantial features of the movement’s construction. It should be noted that the pitches of CQ 138 appear in a different order in several places other than those listed above. These varied versions of the CQ are heard at mm.331, 337, 355, 357-58, 359, 378, 381 , 389, 390, and 420. Contextual emphasis plays a role in obscuring the form of this and other movements. For example, the Hauptstimme at the beginning, consisting of a descent by minor second followed by a minor ninth, recurs at m.M+7, but at a different pitch level and with an entire ly new note-value patterns (Ex.51)- Once again, the relationship is too vague to constitute a motivic recur rence. The striking scalar fragment at the "climax" in m.442 (Ex.39, p.157) does not originate earlier in the movement, although i t receives contextual emphasis from the loud dynamic le v e l. In general, the b revity and temporal separation of the minute elements of repetition 2 4 0

With permission of C.P. Peters Corporation, New York

Ex. $1. Op.16/$: The return of the first three pitches of the Hauptstimme at

in Op.26/5 prevent them from counteracting the impression of athematicism. Although the relations discussed above are the most prominent features of the work, they are of such in s u ffic ie n t scope that Samson remarked that

Op.16/5 "avoids any thorough-going motivic organization "2 of its pitch content.

Local Congruities G. Repetition in Hauptatimme. mm.392-393: C-E-D#. H. Imitation in strings, mm.396-397: G-E-P-Bk at the octave. I . Sequence in strings, mm.396-397 , J. Displacement and interval expansion in BPclarinet, mm.332- 335. Interval expansion in bass clarinet, bassoon, trombone, harp, and low strings, mm.433-435.

Ex. 52. Congruity list and diagram for Op.16/5.

■Samson, Music in Transition, p .18y. Low-Grade Congruities X K. CQ 138 (h o riz.): mm.331.337,344,352,355,357,359. 366,369, 372 Ul 374,378,381,389,390,393,395,396-97,420, 425, 427-28,442-44. CQ 174 (horiz.); mm.340,379,380,380-81,407-09,429. o CQ 183 (horiz.): mm.333,349-50,356-57,362,376,448. § L. no'horiz^/vez't* congruities supported by other congruities, ^ M. Pour major texture changes, mm.378,395,402, and 450. 3 N. One prominent contour shown in Table 11. ® 0. I tems J' and (b) fi j j j from Table 11; also ^ JD at mm.333,356,363,377,380,389.405,411,428,431,433, ŒQ 434,435,436,437, and 448; *7/TO at mm.336,337,349, and 442. P. Punctuation through texture changes, category M.

K K K K K K KKK K K K K K / ** .00 I______iQ 0^1 lO Q lOOO 0 I jO & 0 0

4 a J M ^ K . iP OQ?t I fi-g i - Q — - j ------1------@_ j _ ------jfij------_J_ ------rsb m l m W É2 K K K K K m 1 6 . 0 00,0 0 00(000___ IÙ I 0 ,0 I______1______m m m ' ^ H 242 Op.19/1: Lelcht. zart

One of six miniatures for piano, Op,19/1 i s an example of a movement where material is sharply contrasted and minute details assume increased formal significance. In th is movement, even lo c a l and low-grade con gru ities become scarce. Melodic contours and note-value patterns display little repetition. The opening contour in the L.H., for example, returns in m.8 (Ex.53)« The interval

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Ex. 53* 4 contour congruity in Op. 19 / 1. of the perfect fifth is maintained in both instances, G-G and D-A, preceded by a minor third in m.O and a major third in m.8 . In m.3j the L.H. plays B-D-A#, which is transposed to D-F-C# in m.15, a congruity of CQ 138 . The correspondence of m.3 with m.14 was dis cussed in the first chapter (p . 67 above), in particular, the possible congruity between the tied enharmonic notes, A# to nb in m.3, and G# to A^ in m.l4. Points of imitation are found in m.2 and mm.5-6 (Ex.54). In m.2. 2^3

the notes of the R*H*, constitute an augmen tation of the L.H. ^ F-E-D^-sb, transposed up a PM-. The three notes in the "alto" of m.5, Ab-G-B, are repeated

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Ex. 5^. Two points of imitation in Op.19 / 1. in the "soprano" directly afterwards, then in the alto in m.6, a major third lower. The C#-D-F# in the lowest voice in m.5 are repeated in the tenor of m.6, an octave and a fifth higher. The material in measures 8 through 11 co n sists of two flo u rish es in the R.H. over the tremolo CQ IV+3 in the L.H. The procedure in m. I3 (Ex-55) seems to be semitonal voice-leading of the type described by Maegaard (see p. 1^1 above). No more can be said about conventional types of coherence in Op.19 / 1, where hypotheses about spe cific compositional choices, devices or procedures become d if f ic u lt to make. This an alytic dearth i s not 244" as confounding as it might seem vrtien one realizes the dichotomy in Schoenberg’s work between apparently strict construction and apparently free spontaneity. The former eventually led to twelve-tone serialism; the latter cor responds to "musical prose," as in th is movement, where no theory of pitch generation appears to be operating.

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Ex. 55» Semitonal voice-leading in Op.19 / 1, m.13* 245

Local Congruitiea G. Repetition in L.H. tremolo, mm.8-10; in R.H., m.17: E-G#-D# repeats. H. Imitation in R.H., m.2: augmentation of L.H. P4 higher; top voice in m.5: Ab-G-B an octave higher than "alto," again "alto" m.6: E-D#-G, a minor sixth higher than in m.5. I. Quasi—sequence in "alto" m.4 of last 3 notes in top, m.3. J . (No item long enough to he varied.)

Low-Grade Congruities K. CQ 1533 (h o r iz .): m.2; CQ 1335 (v e r t.): mm.3 and 5; CQ 1173 (h o r iz .): m.10. Lo CQ 1137 (horiz./vert.): mm.O and 3. See also Table 2,p.101 M. Texture is extremely fragmented. N. Contour in L.H., m.2 and R.H., m.8; in L.H., m.3 and R.H.. m.17. 0. mm.0 ,2 ,8 , and 10.

H T HH K K K V. H W M N P—P—I-----1-----1— 4-----1----F—I------—I------1----- 1-----1---- 1-----1-----f— J 5 10 15 17

Ex. 56. Congruity, list and diagram for Op.ig/1. Zli-ô

Op.19/1: Sehr lanesame Vlertel

The essence of "musical prose" is also demon

strated in the nine measures that comprise Op. 19/3

(Ex.58 ). Initially, the right hand material has the appearance of an ordinary four-part "harmonization." The vertical construction, however, obscures any poten tial motive, vAiile the left hand, though more linear, is indicated at a very soft dynamic level. These opening measures typify Schoenberg's manner of frequently chang ing the number of individual "voices," particularly in the solo piano music, without providing any further clues to the part-writing. A four-voice arrangement of only the right hand in the first four measures is shown in Example 57» None of these lines appears to

m I f W j ¥ g

Ex. 57* A four-voice reduction of the rig h t hand in mm.1-M- of Op. 19/3, showing melodic organization. 24-7

Sehr langsame J i I I Y Phi

In den eriten 4 Tokten loU die rechte Hand durchaui die linke durthaut pp ipielen.

pp.

m I? r m

Usau by Parrùaaion of Balmont auaic Publiahars, Loa Angelaa, California 90049 Ex, 58. Op.19/3 reproduced in its entirety to show CQ congruities. 2 4 8

have the character of a motive, although the pattern of a ha If-step followed by a minor or major third, or the reverse, occurs four times. The pitches in the top-voice in m.2 are related to the pitches in m.6, A-G-Eb-D, by a note-value pattern congruity, probably more prominent than the minute melodic organization of mm.1-4. It would be worthwhile to point out an instance of iî-c inversion in th is movement where confirmation by other factors makes it appear that it may be significant from a compositional standpoint. In this case, the same

CQ 1452, appears as both the first and last simultaneity of the piece. The i-c inversion, CQ 1254, occurs in m.1, as the simultaneity F-G-C-E. I ts anagram, 1425, appears twice in m.3, as E-fib-D-A and fib-A-D-G. The anagram also appears as the melody in m.6, A-G-fib-D, and its inver sion, 1524, is the four-note group in the rig h t hand of m.5, E-A-D#-fi. Without a rule for grouping notes in analysis, any note in reasonable proximity to the others may arbitrarily be included if it completes the simultan eity or p-c set the analyzer seeks in order to satisfy his hypothesis. Without a notion of implied harmony, there is no conventional concept to vrtiich the grouping of partially horizontal and vertical items can corres pond. In the analysis of this movement, the complexity 249

of the analytic hypothesis should be commensurate with the complexity of the music. For a nine-bar piece, one should avoid positing a complex structure the implica tions of which could easily have produced a much longer piece. Besides the congruity of the first and last simultaneities, this movement contains a few congruities

Local Congruitiea G. No repetition. H. No imitation. I. No imitation. J, (No item long enough to be varied.)

Low-Grade Congruities K. CQ 1452 (v e rt.): mm.1 and 9; CQ 1425 ( v e r t.) ztwice in m ^ L. CQ 1425 (vert.) in m.3, (horiz.) in m.6. M. Texture of L.H. in octaves, mm.1-4. N. Contour of top voice, mm.2,3, and 6; first 2 notes of L.H. in mm.1 and 5. 0. n d in mm.2,3 and 6. P. Punctuation by one-beat rest in m.5.

KM- S J 3 4------1------1------f -----*—

Ex.59. Congruity list and diagram for Op.19/3* 250 of melodic contour; the. top voice in mm.2-3 contains a repeated contour; and the first two note attacks in the left hand in m.1 have the same contour as those in the left hand of m.5« The note-value pattern of the top voice in m.3 is heard at twice the speed in the first three notes of the top voice in m.7« These minimal con nections constitute the elements of aural coherence in

Op. 19 / 3 .

Op.19/5: Btwas rasch

As was shown in the case of Op.16/5, considerable divergence in the amount of discernible formal defini tion is possible, even among movements that are unques tionably athematic. Intricate relationships emerge in

Op. 19/5 that do not actually qualify as motivic. The movement contains no repeated pitch/rhythm item or pitch-string, but shows some melodic consistency. For example, all the pitches of the R.H. in mm.2-6 come from either CQ I 92 or 129. Starting in m.2, the pitches may be grouped; A-G#-F# ( 192 ); F#-D#-E (129);

F-E^-F# (192 ); G-F#-A (129 ) as shown in Example 60. The notes of the L.H, in m.2 also comprise 129. The procedure of alternating aspects of the CQ continues in mm.7-8, lAere the L.H. pitches make up CQ 192. A new unit in the R.H. of mm.8-9 consists of A-A#-B-F, 251 or CQ 1164. In m.10, F#-C-C#-D make up CQ 1146. Even this apparent case of i-c inversion is represented graphically by CQ analysis (see Ex.60). The remainder of the movement is held together mostly by major and minor thirds occurring vertically. Identical note-value patterns involving both hands appear in mm.12 and 13, constituting a low-grade congruity. The final two meas ures show no relation to preceding material, other than the simultaneities containing thirds. 252 V

Etwas rasch (J))

u_ 1 'kr======-—

o "c [rrp . .. --..^.J- ..... - ... ) ------^ —::: "nri. - ■ —■ . y ...

C^~bT&i i

PP - I. U. stacc. LHstacc.

n«co a noro rit.. _ inolto rit._ . . " " r\

I —

// " - : u!:»' i' h—-, Usaa by pamiaalon of aelnont liuaic Publishers, Loa Angelas, California 90049

Ex.60. Op,19/5 In its entirety, showing several congruities of CQ and a contour congruity. 253

Local Congruitiea G. No repetition. H. Imitation in mm,7-8; "mirroring" of R.H. with L.H. I. Sequence in L.H., mm.9-10; quasi-sequence in top voice, mm.4-5 and in L.H. in mm. 12-13. J. (No item long enough to be varied.)

Low-Grade Congruities K. CQ 129 (horiz.): mm.2,3,5-6, and 8; CQ 192 (horiz.): mm,2 ,4 , and 4-5. L. No vert./horiz. congruities. M. No texture congruities. N. No contour con gru ities. 0. jrf3 in mm.1 (twice) and m.10. P. Punctuation used throughout.

X H K K KKK K 1 » » 1 *- lo II a IS H *

Ex. 61. Congruity list and diagram of Op.19/5.

Category F Movements from Pierrot Lunaire

Pierrot Lunaire. Op.21, provides a wide variety of movements representing almost every formal category. Included within the athematic category F are numbers 6, 10, 12, and 19. Thus, in movements h through 12, every other movement except no.8 belongs in this category. 254 suggesting that this alternation of formal procedures is part of the design of the work as a vAiole. The cate gories of the twenty-one movements of P ierrot are given in Table 12 with the movement numbers and Schoenberg’s tripartite grouping to show this pattern. The succession of movements w ithin each of the three parts also displays a semblance of symmetry with regard to ca teg o ries.o f r e currence.

TABLE 12 The formal categorization of each movement in Pierrot Lunaire. Op.21

Part I Part II Part III No. 1 - C No. 8 - B No.15 - C No. 2 - D No. 9 - E No. 16 - B No. 3 - D No. 10 - F No.17 - B No. 4 - F No.11. - C No. 18 - B No. 5 - G No.12 - F No.19 - F No. 6 - F No.13 - C No.20 - C No. 7 - C N o . 1 4 - E No.21 - C

A detailed study of the relation of the text in Pierrot to the formal structure has yet to appear in the literature. It is clear, however, that the strict scheme of repetition in the poetry is not paralleled in the settings. In each of the thirteen-line poems, lines 1 and 2 are repeated as lin e s 7 and 8, and lin e 13 i s the same as line 1 and line 7» Noidiere is this poetical 255

refrain accompanied by a musical refrain. Furthermore, there is no evidence of inter-movement unity, beyond the very brief motives discussed in Chapter III (p.15^ -163) and the obvious repeat of almost all of no. 7 in n o .13.

Op.21 A ; Eine blasse Wascherin

The fourth movement of Op.21 maintains as little overall continuity as any movement in this study; thus, only a few substantive remarks can be made. In this and a few other movements, local congruity is often limited to single measures, as can be observed in the repetition and sequences in mm.10, 11, A , and, at the end, 16-18. No Hauptstimme is indicated, and.frequent crossing of instruments creates an athematic texture without potential motives. As a result, even the effects of contextual emphasis are slight. One feature that can be observed is the textural congruity (category M). Because only three instruments are used, contrast of texture and timbre are somevdiat limited. Within these lim itations, the opening "homophony" gives way to more independent lines in mm.8-11, followed by a return to note-against-note texture. The pitch mate rial does not repeat, but the resumption of "homophony" 256

in m,12 does vaguely produce the effect of a formal return. In the case of more distinctive textural congruities, such returns can be considerably more vivid, as in Op.21/8, at m.24-.

Local Congruities G. Repetition in all instruments, mm,16-18. H. No imitation. I. Sequence in flute, m.10; quasi-sequence in violin, m.10. J. Displacement in violin, m.10: E-P#-Di{^; and in clarinet, m.11: C#-D-C#.

Low-Grade Congruities K. CQ 336 (vert.): mm.1-3, all instruments. L. No horiz./vert. congruities. M. Texture congruities, mm.6-8 and mm.13-15, a ll instruments, N. No contour congruities. 0. 7 JT3 in mm.6 ,7 ,1 2 , and 15. P. Punctuation by tutti rests in mm.5,8, and 12.

X 7 J M- M p 0 o p 9 O 4 ^ ------1------1------P------1------{------1------f ------f------f------1------\r ------1------A S 10 IS

Ex. 62. Congruity list and diagram for Op.21/4. 257

Op.21/6: Madonna

The quasi-sequence in the opening cello part of Op,21/6 was discussed in Chapter IV (p.219). The effect is that of an atonal "walking bass." After this quasi sequence ends in m.7, the interval of a descending minor ninth appears in the flu te and c e llo , and then in a l l three instruments in m.9« An unusual skipping passage follows in mm.1$-16, at a point of contextual emphasis. Following the fermata that distinctly marks the end of a section is a group of large leaps downward: two octaves plus a major seventh (D# to E) in the bass c la r in e t, and two octaves plus a minor ninth (A to G#) in the cello. This material receives contextual empha sis after the fermata, but is much too fragmentary to be m otivic. In movements or passages lik e th ese, l i t t l e of substance can be reported, except detailed observa tions of "free" atonal procedures. For example, the use of chromatic saturation is evident in an octave re duction of the cello part in m.20, shown in Example 63. The sudden entrance of the piano in m.21 marks a final section in which some local congruities are displayed. Three instruments repeat their parts in mm.22-23. 258

Usad by permission of Qalmont Uusic Publishers, Loa Angeles, California 90049

Ex. 63. Op.21/6, in.20, cello part, shown in (a), and an octave reduction, showing chromatic saturation, in (b).

local Congruities G. Repetition in violin, cello and piano, mm.22-23. H. No imitation. I. Quasi-sequences: cello in mm.1-5; bass-clarinet and cello in m.20, violin in m.21. J. No local variation.

Low-Grade Congruities K. CQ 255 (vert.) and CQ 165 (vert.); piano in m.21. 1. No vert./horiz. congruities. M. Texture in mm.1-12 of three instruments plus speaker, N. Contours repeated in quasi-sequences. 0. J* J73 in flute, mm.1-2. P. Punctuation in m.14, fermata; in m,20, tempo and texture ; in m.21, entrance of piano.

Ex. 64. Congruity list and diagram for Op.21/6. 259 Ex. 64. continued.

&- IX K P—4______f_P_ 10 w io at

Op.21/10: Raub

The tenth movement of Pierrot demonstrates how a series of locally congruent measures can be strung to gether into an athematic whole. Different items of local repetition are introduced in mm.2-3, 7, 9-10, 11- 12, 14, 15, 16, 16-17, and 19-20. Although there are several note-value congruities, long-range repetitions are never of motivic status because of minute changes in pitch. The first three notes of the clarinet part appear again in ra.7, transposed down a fifth . This three-note figure is idiosyncratic to Schoenberg (see \<,h p. above). Here, it occurs in a different form in the flute in mm.1, 7, and 16, as well as the three notes (in concert pitch) played in the clarinet in mm.1, 7, and 16 (Ex. 65). The note-value pattern of four six teenths occurs in mm.2, 3, 7, 8, 12, l4, 15, 16, 17, 18, 19 , and 20. The four sixteenths repeat on a single pitch in mm.2, 3, 1^, 15, 16, 17, and 19. With a rest 260 in place of the first sixteenth, this pattern can be found in mm.l, 7, 8, 16, and 20. Although no motive can be identified, these congruities afford this movement an un mistakable continuity.

^ iji' '.1 -.7 A K- Used by permission of Belmont Music Publishers, Los Angeles, California 90049

Ex. 65. Idiosyncratic figures as they appear in Op.21/10.

Local Congruities G. Repetition in clarinet, m.1; in all instruments, mm.2-3; in flute and violin, m.7; in violin, mm.9-10; in all instruments, mm. 14-17. H. No imitation. I. Quasi-sequence in flute, m.18. . J. Pitch interpolation in clarinet in m.7: Av-A becomes AJ^-BP-A; elimination in cello in mm.9-10: G~D removed.

Low-Grade Congruities K. No CQ congruities. L. No vert./horiz. congruitieso M. No texture congruities. N. Contour in clarinet in m.1 repeated in m.7. 0. ? clarinet in mm.2-3;yj^ in violin and flute, m.7 and m.16. P. Punctuation by rest in m.12, parallel motion in m.15, and £2. dynamic in m.13.

Ex. 6 6 . Congruity list and diagram for 0p.2l/l0. 261 Ex; 6 6 . continued.

e, g K ^ ^ 0 0 p p P 0 h4--h-i—'t—I—I—I -I I -I -f - i S \0 » ï x o

Op.21/12: Galgenlied

Probably the shortest movement (about ten sec onds) in Schoenberg's entire output, Op.21/12 is essen tially one brief accelerando. The pace of Pierrot’s march to the gallows increases as punctuated sixteenth- note figures evolve into runs of thirty-second notes by m.12. Any possible motivic structure passes far too quickly to be heard or exploited (Ex.68).

Local Congruities G. Repetition in viola, mm.11-12. H. No imitation. j ! Displacement in viola, mm«8-9: E-A-D-C-B-C (fin a l A interpolated in m.9).

Ex. 6 7 . Congruity list and diagram for 0p.2l/l2. 262 Ex, 6 7 . continued.

Low-Grade Congruities K. No CQ congruities. L. No vert./horiz. congruities. M. No texture congruities. No Contour in cello, mm.7 &nd 9, viola mm.5 and o and cello , m.10. 0. ^ 739 in viola, mm.10-11. p. No punctuation.

M M N \ 1 1 1 V—iS 1 1 1 1 I» 11 —I

Op.21/19: Serenade Like the "Minuet" from the Suite for Piano, Op.2$, the highly stylized slow waltz, Op.21/19, is sub ject to definite metrical irregularities. The text opens "With a grotesque, giant bow, Pierrot scratches on his viola." The movement is, however, a cadenza-like fan tasia for the cello. The appearance of an ostinato accompaniment figure in mm. 30-3^ presents an item suitable for later repetition. This sextuplet figure is hinted at in sixteenth notes in m.40, and does, indeed, return in varied form in m.*+1 (Ex.69). 263 12. Galgenlied.

Picrolo.

r - _ j# F = r = t . u , -----i=T= BraUelis. ?. . . : p. : G Vp . ------t ------k_------L Vloloaecll. "-nv.'h ■-----\------, ; r J \ S e h r p aseh (J.oalao) Rflcitation. ( ------1-., J\ t, _ ----

Die dOr . re Dir . ne mit Ian. . gem H al. ae wird aai.ne lets . te Qs. .

® aeeel.

v«i.

a c e e l.

In seinem ,n e «tflckt wia ein Na . gel dis dUrjro Dir . ne imt

Vcl.

accei. bis 2um S c b lu B

Ûal.ae. BcblankwiadiePi . nie, am Hala einZSpfchen, wol . lil.atigwird aie den

ilamlich lange Pauaa, (im Takt) dann folgtt E nthauptung, KlavUr. OAi'KlarüivtU. 0nlM h«. ViolooMll.

Schelmuin - bal - aru die dur - re Dlr - ne! Used by permission of aelmont Music Publishers, Los Angeles, Califorriia 90049

Ex. 68. The brief "Galgenlied", Op.21/12, consisting of one continuous accelerando. 264

Uoad by permission of Balmont Musie Publishers, Los Angolas, California 90049

Ex. 69 . A contour congruity in the piano part, Op.21/ 19 .

The "accompaniment” also shows some lo c a l congruities earlier in mm.8-9, 13-1^, and 26-27, and later in MM.38-39 and 44-4$. Close scrutiny of the apparently ornamental configurations reveals that they are just that, rather than points of repetition or development. In this and similar movements, the wide variety of note-value patterns offers strong evidence that specific pitch/rhythm items are not playing a formal role. This leaves only occa sional congruities of contour, like that between mm.37 and 43, serving as long-range congruities. (Ex.70). 265

Used by permission of Belmont Uusic Publishers, Los Angeles, California 90049

Ex, 70, A contour congruity in the cello part. Op,21/19,

Local Congruities G, Repetition in piano, mm,13,15» and 16; in cello, mm,26-27, in piano mm,30-34; in piano mm,38-39. H, No im itation , I, Quasi-sequences in cello m,25 and m,29., J, Pitch elimination in piano, mm.8-9: AP; and D; interpola tion in cello, mm,38-39: D# added; note-value alteration in cello, mm,46-47: eigths into triplets, Low-Grada Congruities K, CQ 13143 (vert,); piano, mm,25,26,27. L, No vert./horiz, congruities, M, No texture congruities. N. Contour in piano, mm.30 and 41; in cello, mm.37 and 43. 0. in mm,26,27,28,35,36,38,46, and 52, P, Punctuation; piano tacet, m,25; three instruments enter, m.46, G Q & G—• €»■C»— — • G-G—• X I KKK „000 ^

10 IS 2 0 ■ t HO HS So

Ex. 71. Congruity list and diagram for Op.2l/l9. 266

The Analysis of Athematic Movements (Category E)

Op.11/1: Bewegte Achtel

The identification of a specific exploited chord or interval does not necessarily elevate a movement to a high status of formal coherence. The formal procedures in

Op. 11/3 remain, for the most part, complex and obscure, when they can be detected at a l l. Rheinhold Brinkman presented one view of the difficulties of Op.ll/ 3 :

Wherever v e rtic a l as well as horizontal re la tio n ships are composed freely and unsystematically, the analyzer finds himself in a precarious situa tion. For, even in the preceding works, it was still a matter of traditional elements in some sort of mixture. An observation that emphasizes any of these connections has a tendency to carry too much weight. Now, categories derived from other composition al levels step into the picture. In other cir cumstances, these categories would be considered • incidental: dynamics, tempo, reg ister, tone color. The fact that these considerations have even entered the picture is certainly an indication of the analyzer's perplexity with regard to 267

musical freedom. Yet this reveals the very essence of expressive necessity for this art: these cate gories are the easiest to represent and are (even aurally) the most a p p a r e n t, 3

Brinkraann confirms that the analyzer's role is to find order even in the most loosely constructed compositions. While he is correct in saying that certain types of ana ly tic observations would otherwise be considered inciden tal, it is also true that the constituents of dynamics, tempo, etc., are of unusually great significance in

Op. 11/ 3 . Brinkmann also mentioned the importance of an eight-measure deletion in the original manuscript.^ One can see that this crossed-out excerpt does not con tain material from other portions of the movement, as might be expected. The passage shows much more coher ence than the rest of the movement; perhaps this was the reason for its eventual rejection. One of the most d iffic u lt questions relatin g to Op.11/3 is how it logically follows the first two move ments. They represent two of the more formally conven tional movements from the atonal period. Op.11/3

^Brinkmann, Arnold Schoenberg: Drei Klavier- stücke. Op.11, supplement to Archiv fÛr Musikwissen- echaft, V.7 (Wiesbaden, F, Steiner, 1969), p .110, my translation. ^Reproduced on p.111 of the Brinkmann study. 268 follows only a faintly discernible pattern of local varia tion and low-grade congruity. The exploited chord, CQ 165, was-discussed earlier in the description of category.E

(p . 211 above). Somewhat; broader connections exist between mm.1 and 19» The note-value pattern in the R.H. of m.19 is that of the L.H. in m.1 (Ex. 72). The R.H. figure at the beginning of m .21 has a contour sim ilar to the one on beats 4 and 5 of m.1, in the R.H. These tenuous re la tionships represent the total extent of the "recapitula tion" in m.19 (Ex. 72).

Uaed by panaiasion of 3alaont Music Publlshera, Loa Angelas, California 90049

Ex. 72. Contour congruities between mm.1 and 19 and 1 and 21 in O p .ll/ 3 . Also shown are the CQ^'s in the L.H. of m.19. 2 6 9

Although the bar line no longer serves as an indicator of rhythmic or metrical organization (in this sense it is purely vestigal), it gives an orderly im pression. In spite of cross-meters and accents off the beat, the bar line often helps in the grouping of local congruities. For example, of the seventeen internal tempo changes in the movement, twelve come at the down beat or the first note attack of a measure. Instances where tempo and phrase changes do not coincide with bar lines are found at measures 5? 11, 17, 21, and 26. Em phatic downbeats occasionally occur, as in mm. 19 , 21, and 30. Certain local congruities span a bar line, as in mm.2-3, 3-^, 10-11, 12-13, and 32-33* Notes are fre quently tied across (in 12 of the 35 measures in the movement), while the local procedure is in the process of changing. The result is a dovetailing of local con gruities, making the perception of these already vague details all the more difficult. The extent of the apparent measure-by-measure organization is shown in Table 13* Because of extensive vertical layering, the CQ vocabulary of Op,11/3 appears more extensive than it actually is. A few different CQ*s are combined in ways that avoid doubled tones, consistently producing new 270

TABLE 13 Local congruities in Op.ll /3

Starting measure ______Congruity 8 parallel augmented triads (CQ in top staff 3 direct repetition in top and bottom staves 4 tritone sequence down a m3» Repeated chord in R.H. 5 series of transposed M3 's in different octabes 6 triplet-sixteenths note-value pattern 7 sequence in R.H, 10 quasi-sequence in both hands 11 qua si-sequence in L.H., note-value pattern in R.H. 28 quasi-sequence in R.H., interval expans ion in L.H. 29 metrical displacement,repetition pitch interpolation 30 contour congruities in. both hands 31 repeated in te rv a l, F to E in R.H. 32 CQ congruity, 165

simultaneities. The best examples of this procedure occur in mm. 19 (Ex.72) and 27 (Ex.73)» The la tte r h alf of m.19 consists of three six-note, and four five-note simultan eities. Viewing the L.H. for the last three counts, one can observe CQ»s I83 , 17^, 1^7, 17^, 183, and I 38 . The right hand shows 165, 156, 165, 264, and three two-note items. The only pitch doubled in any of these six-note simultaneities is the high E, in both hands on the sec ond h alf of beat four. Schoenberg*s emphasis on the avoidance of oc tave doubling in atonal composition, expressed in his essays on twelve-tone composition, also evolved into a tendency toward maximum pitch turnover (see p.139 above).

» 271

The principle of maximum pitch turnover becomes important

in the complex texture of O p .ll/ 3 . As a principle, it was at least as important to the development of the twelve-tone method as the avoidance of octave doubling, because its necessary result is the twelve-tone aggre gate. One result of either principle is that the nurüber of voices present tends to equal the CQ size of any ver tical structure. Thicker texture thus means more com plex simultaneities. Although m.27 contains two dou bled E's, doubling is avoided for the remainder of the measure (Ex.73)» In m.27, the thirteen CQ^*s occurring in each hand are eith er 165, 156, 17^, or 1^+7» The CQ's in the R.H. are 17^, 165, 165, and 17^, and in the

L.H., 165, 17^, 156, 165, 156, 156, 147, 165, and 165. Again, the specific inversions revealed by CQ labelling are of interest, revealing a mirroring in their order. Congruities in the passage from mm.12-27 are almost completely obscured by the abundant hand cross ings and texture changes. Many instances of small- scale chromatic saturation are observable in the rela tions of the thick chords. An extended melodic item appears in ra.2^, constituting nothing more than a point of unconfirmed contextual emphasis. The lack of sub stantial connection between ideas in Op.ll /3 produces 272

m cresc..

' 2 '

• ■ m i I s Used by penaisaion of Balaont Uusic Publishers, Los Angeles, California 900^9

Ex. 73* Op. 11/ 3, mo27: avoidance of octave doubling using only four different CQ^'s,

what Perle called a "stream of consciousness" effect (see p. 165 above). To emphasize everything is to em phasize nothing at all; total variety eventually be comes tantamount to homogeneity.

Op.19/2: Langsam

In comparison to the exploited CQ 165 of Op.11/3, the exploited interval, G-B, of Op.19/2 is extremely obvious. In this nine-measure movement, it appears in every measure except m.6. Less obvious is Schoenberg’s prevention of a G major effect stemming from this repeated third. In mm.3, 7, and 8, this 273

effect is offset by alien v^ole-tone collections. In mm.3 and 5» additional tones are displaced by semitone from G and B (A^-C and F#-A#, respectively). Measure 6 contains two parallel lines of chromatic saturation (Ex.7^)» The only sonority not related by semitone or whole tone to the pitches of the exploited interval is

UsQd by Parniaaion of flalaont Music Publishers, Los Angolas, California 90049

Ex. Chromatic saturation in Op.19/2, mm.6-75 only B1? and E are absent. the one tied from m.6 to m.7« This is a layered simul taneity, consisting of two diminished triads a major seventh apart. It also contains two thirds previously heard, B-D and C-sb (respelled B#-D#). The difference between this category E movement and Op,11/3 is demon strated by the fact that here the interval G-B is re peated 27 times in 9 measures. In neither of the two movements is there a significant pitch/rhythm item; thus, both are placed low in the formal hierarchy. 274

Op.19/6: Sehr langsam

Op.19/6 lies somewhere between Op.ll/3 and Op.

19/2 in its relative degree of repetition and variety.

The exploited chords in this movement are CQ 2/3 and three

transpositions of the chord in fourths, CQ 255 (see

Ex.75). The interval of the semitone, as in ram.3-4, pro

duces a sort of chromatic neighbor figure, which becomes

displaced by octave in m.7* The motion from E to Eb in

•m.8 is merely a respelling of E-D# from m.4. The first

left hand structure in m .8 is also 255, and when the F# ascents to G, this supplies the pitch needed for a

CQ 255 in the right hand, D-G-C, The descending vdiole step G# to F# in mm.5-6 is also displaced by octave in the final measure. The continuity in the movement is supplied not by these minute melodic ideas, but by the repeated simultaneities. .Given these "chords" as the essential material, however, it appears impossible to establish Schoenberg's procedure for generating the additional pitches. The contextual emphasis of m.7 , marked "with extremely tender expression," directly af ter a fermata, gives the false impression that the item may be the recurrence of an earlier event. It is also possible that the movement would be more musically 275 VI

Si'lir lanîrsain(J)

:cT- IM> 7

f h r \ -àz. PPP

PPP

mit sehr zartein Ausdruck

wie ein

Uaed by Panaiaaion of 3elmotit ùluaic Publishers, Los Angeles, California 90049

Ex. 75. Op.19/6 reproduced in it s entirety to show the use of exploited chord CQ 273 and CQ 255. 2 7 6 effective if the item were a reprise of some sort, rather than still another new melodic figure only two measures before the end. This comment could, of course, be made about the fin a l movements of Opp.11 and 16 as well.

Op.21/9: Gebet an P ierro t

The recurring item in Op.21/9 is actually a progression of two vertical structures. As in most move ments where any recurrence can be noted, the item appears at the very beginning. Two three-note structures, Db-F-C and A-C#-G, appear in the left hand, along with the major th ird G-B and the three-note structure E-F#~C in the right hand (Ex.76).

K). J w Uaed by Parmiaaioa of 3almoac Muaio Publishars, Loa Angelaa, California 90049

Ex. 76. The opening of Op.21/9, which recurs in m.13. 277

This progression recurs in m.I 3 , without the intervening obin the right hand. This small event constitutes the only recurrence either at original pitch level or other wise, in this movement of twenty measures. The clarinet part can easily he seen to contain no pitch-strings or recurrent pitch/rhythm item. The more complex piano part also proves to he free from repetition. A congruity of CQ Ik-7 can he noted as part of layering in mm.4-6 and

13-16 (Ex.77)) hut never with the.same additional pitches as in mm.1 and I3 .

(^,accel. p o co rit.

ere»

Uoea by pamiaaioti of Balnorit iluaic Publiahera, Loa Angelea, California 90049

Ex. 77. Op.21/9, mm.4-6 and I 3-I 6 , showing multiple appearances of CQ 147. 278

Op.21/14^ Die Kreuze

The only recurrence at original pitch level in Op.21/14 involves the very opening and closing chordal attacks of the movement (Ex,78). The textural complexity of the keyboard writing is comparable to that of Op,11/3, particularly in the first nine measures of this movement.

Internal contour congruities can be found in mm.5, 6 , and

9 , along with some literal repetitions and sequences (categories G and I, respectively). The opening structure

Used by penaisaion of aelnont lluaio Publiahera, Loa Angelas, California 90049

Ex, 78 , The exploited chords of Op,21/14, vrtiich begin and end the movement, in fourths in the right hand reappears in m ,3 (beats 2 and 4 ), m.8 (beat 1), and sequentially in m .9 (see Ex.79), The other instruments enter in m.lO with a series of coloristic sustained tones (category P), The remaining measures show a large number of purely local 279

congruities, with a sequence in mm.15-16, ostinato in

mm.17- 19 j and the return of the opening pitches in the final two measures.

acool.

martiUnto

mnrUUato^^^f martciiafoA 4 ^ ^ ^ % \ S.^ km . 11 I II —m*— ^ #T»—b^wv*— ^ ' »• ♦-*A •— *• • S3!5 S î ^^2| •• “* 1 a zzdAiJz:. I BkZu !fcSITli'iS ik« ' :-f i - : : : * f ! , “iiV Uaoa by Parniasioa of Balmont Muaio Publiahera, Loa Angelas, California 90049

Ex. 79. Op.21/1^,m.9: sequence of fourth chords, CQ 255.

Analysis of Two Representative Monomotivic Movements (Category D)

Schoenberg's use of an untransposed pitch-string was a significant step toward serial techniques. Of the eight movements assigned to this category (see Table 10, p. 193 )> five comprise the five pieces of Op.23- In these, the use of pitch-strings of less than twelve pitches appears to presage use of the twelve-tone series. A major difference is that in four of these transitional works, the string occurs only as an intermittent motive. 280

In Op.23/ 5, because the entire pitch structure is deter mined by the strin g , and the string a ctu a lly is a tw elve- tone series, the result is the first entirely twelve-tone piece. Another important serial technique that is evi dent in Op,23 is the use of the twelve-tone relations of pitch-class and interval-class. That is, besides being sta ed as a horizontal entity with a fixed interva H ic content, the string can appear with one or more pitches transposed to a different octave; or, it may appear entirely in mirror form, with each interval being the i-c inversion of the original intervals. In an approach based on conventional analysis, like the present approach, a careful distinction must be made between statements of a pitch-string that entirely match the original intervals and those that involve octave displacement and i-c inver sion. Although tonal inversion was well-known as a con trapuntal technique in the past, the formal use of i-c inversion, particularly without the congruity of note- value patterns, is an entirely twentieth-century device. Verticalization, the third of the so-called "twelve-tone relations" (see pp. 28- 30 above), also becomes more significant in Op.23. The other three movements in category D are Op,19/^, and Op,21, numbers 2 and 3» All three involve 2 8 1

only single restatements of motivic items. In Op.19/4, the string of five pitches in m.0-1 is repeated an octave lower, with a new note-value pattern in m.10 (Ex.80).

/ innrtellato

Uaed by pemiaaion of Ualmont iluaio Publiahera, Loa Angelas, California 90049

Ex. So. The pitch-string in Op. 19/4, recurring in m.10.

In Op,21, numbers 2 and 3, a transposed pitch/rhythm item constitutes the motivic recurrence. It is interesting that the only two movements with th is ch a ra c te ristic are consecutive movements of the same work.

O n . 21/2; Columbine

"Columbine" has been selected as a representa tive category D movement because, although the recurring item is brief, local and low-grade congruities are quite 282 diverse. It contains one recurrence of a transposed pitch/rhytlim item. The three eighth-notes, C#-E-D in the violin part in m.2 are transposed down an octave plus a f i f t h to F#-A-G in the L.H. of the piano in m.7 (Ex.81). Because the item recurs only five measures later (the movement is 4l measures long) and is actually shifted to the main part of the beat, it can barely be considered motivic. On the other hand, the preceding and succeeding notes of the restatement maintain a very close contour

VI. m " ** * * Pi'ono

Uaed by Pem iaaion o f Palnont iiluaic Publiahera, Loa Angeles, C aliforn ia 90049

Ex. 81. The very brief motive in Op. 2 1 /2 , m .2, and i t s recurrence in m.7. relation with the original. For the remaining 33 meas ures, only local and low-grade congruities occur. In m.8, the violin plays a brief P/R item that is metri cally displaced in the L.H. in m.10 (see Ex.82). Two different ostinato figures produce local congruities, one in mm.2^-28 and one in mm.33-38» 283

V(. Used by Pemiaaion of Belaont Muaio Publiahera, laa Angeles, California 90049

Ex. 82. A local pitch/rhythm item in m.8, transposed in m.10 of Op.21/1.

The violin part contains some contour congrui ties of the type seen in Op.19/3. The four figures in Example 83 can be found by combining the la s t beats of mm.2, 3, and 8 with the first beat of each follow ing measure (all in the Hauntstlmme). The interval of

I , 11,^11

Used by Pemission of Belnont Music Publishers, Los Angeles, California 90049

Ex. 83 . Contour congruities in the Hauptstimme violin part of Op,21/2. 284 the descending minor seventh appears in both instruments in m.9, and in the piano L.H, in ram.9 and 10. In the absence of larger units, these "motives" are the only regulating melodic features. A single transposed pitch- string of four notes may be observed, comparing D-C-B-C# in the v io lin at mm.2-3 with Db-ct^-sb-C at mm.8-9 (Ex.84), The first of these two strings is marked subito DP and phrased in two separate segments, making the lin e understated and fragmentary. Once again, continuous d iv ersity creates the e ffe c t of a r e la tiv e ly homogeneous fabric that begins and ends unpredictably.

U30a by psraiaaion of 3elmont rJusio Publishers, Ion Angeles, California 90049

Ex. 84. A transposed pitch-string in the violin Hauptstimme of On.21/2^ mm.2-3 and 8-9.

Op.23/2r Sehr rasch

The pitch-string in Op.23/2 appears in the first measure in the right hand: D-F-Ab-F#-G-A-cb-Bb-Db

(see Ex.85). The only horizontal restatement of the 285 string at OPL that does not alter these intervals in any way occurs in m.20, where the entire string is transposed down two octaves (see Ex.86). All other versions of the string are subject to octave displacement, i-c inversion, or p a rtia l v e r tic a liz a tio n . In ra.7, the string appears horizontally at OPL, but the second and sixth notes are displaced an octave higher from the original (see Ex.87). In m.10, the string appears an octave lower than the ori ginal, with every two pitches combined vertically, and without the final d1? (Ex. 88).

Sehr rasch (J )

.Vith penaission of Edition //ilhaln Hansen, Copenhagen, Canmar.t

Ex. 85 . The pitch-string of Op.23/2, appearing in the first measure. 286

(d«i Itltttn Ttkiei)

Ex. 86. The only horizontal restatement of the string of Op,23/2 thast does not include octave displacement of any pitches.

•I’ith of Edition iVilhelta Hansen, Copenhagen, Denisarc

Ex, 87» -A horizontal statement of the string in Op.23/2, with the F and A displaced an octave higher. 287

J J î ^ (dti GrundmtOoi^ ——

iVlth parnlssion of Bdltlon iVllhelo Hanson, Copenhagen, Dennarlc

Ex. 88. A verticalized, statement of the string in Op,23/2.

Jetwas laagsamer

iVith pomtsaion of Edition .Vilhaln Hansen, Copenhagen, Dennarlc

Ex. 89 . Another partly verticalized statement of the string in Op.23/2.

In m.14, two extraneous pitches, and G# appear in the partly verticalized restatement (Ex. 89 ). Although this restatement is at OPL, all but four of the pitches are displaced by octave, with the final C# (enharmonically ob) 288

displaced three octaves lower. The string appears in stretto and inversion, transposed down a perfect fifth and up a minor ninth in m .l8, and up a major th ird , down a minor ninth and down a perfect fourth in mm.19-20

(Ex.90).

dim;

iVlth perniaalon of Edition /.'ilhalm Hansen, Copenhagen, Dennarlc

Ex. 90. The stretto treatment of three inversions of the pitch-string of Op.23/2.

The final appearance of the string is in the last two measures, where only the first and fourth notes appear in the original octave.^ The identification of a pitch-string and its numerous applications is only part of the analytic

^This analysis duplicates much of Perle‘s analysis in Serial Composition, pp.48-51. There, he also mentions the formal role of the three notes in the le f t hand of m.1. 289

challenge posed by a movement like Op.23/ 2. The problem of accounting for all other notes remains. This especially involves passages from which the string is entirely absent, such as mm.8-9 and 11-13. In Op.23/2, however, a second, local pitch-string can be identified in mm.5-6, where the L.H. p itches are exactly those of the R.H. in mm.8-9 (Ex.91). S ■J.J

I #

et was ruhiçer im Ausdnick

] .ïith poroiaaion of Edition .ïilhsia nanaon, Copenhagen, Dennark

Ex. 91. A local pitch-string in Op.23/2, with corresponding groups labelled (a), (b)* ( c ) , and (d ). 2 9 0

Starting with the D in the R.H, of m.5j the pitches are identical to those in the L.H, of m.8. The pitches of the L.H, in m,4 are the same as those of the R.H. in m.17- No such connection appears to exist for m.12, from vrtiich the primary string is also absent. This movement is the most elaborate example of untransposed pitch-string applications in this study. The transpositions of the primary string, mentioned above, weakly establish other secondary sections. Hence, the movement remains monomotivic. The pitch-strings of the other non-twelve-tone movements from Op.23, numbers 1, 3 , and do not pervade those works nearly as thoroughly as that of Op.23/2.

Analyses of Two Representative Monomotivic Movements (Category C)

Category C, which involves pitch/rhythm items, differs from E and D mainly in the stronger identity of the recurring item. Before it can achieve the status of a motive, a simultaneity or pair of simultaneities re quires considerably more confirmation from other factors than a pitch/rhythm item. Furthermore, the recurrence of pitch/rhythm items permits the possibility of contour congruities, which an isolated vertical structure, as in category E, does not. There is also an aural distinc tion between vertical and horizontal events, probably 291 even greater than that observed by Schoenberg (see pp. 30 -31 above). Since the use of a pitch-string, as in category D, is often combined with s e r ia l techniques, additional statements of pitch-strings are often verti cal or two-dimensional. This type of serial treatment and the lack of rhythmic identity also eliminate con tour congruities. Serial music requires an auditory reorientation of the listener because contour becomes subordinate to pitch-class as an element of repetition. Free octave displacement also destroys contour. In cate gory C movements, contour remains a factor because the identity of pitch/rhythm items, always horizontal enti ties, is maintained. The two movements that have been selected as representative of category C are numbers 13 and 21 of Op,21. Both contain interesting local and low-grade congruities in addition to the brief recurring pitch/rhythm items.

Op.21/11: Enthauptung

In Op.21/ 13, the pitch/rhythm item marked Hauptstimme in m.1 (see Ex.92) recurs in mm.8-9 and m.17 without the initial sb. In m.17, the piano, marked hervor (prominent), states the motive in the top voice. The note values are slightly contracted, but the descending sevenths, B-C and D^-E remain in .1 292 sixteenth notes. A constant sixteenth-note motion from m.10 to m.16 creates a middle section where no local repe tition, only local variation, is used. Following the re statement in the piano in m.17, the other three instru ments take up the descending sevenths in sixteenth n otes. A t ms22, a reprise of an entire section of num ber 7 begins5 the flute part is identical to the first seven measures of number 7 » although the accompanying parts are new (number 7 i s a flute solo). After these seven measures, the original is abbreviated and altered. Seven measures of number 7 are skipped, so that m.29 of number 13 corresponds to m.15 of number 7« The m aterial in m.30 and the first half of m.31 does not originate in number 7, but then mm.31- 3^ correspond to ram.20-2*+ of number 7* The la st two measures of number I3 are loosely derived from the preceding material and from m.26 of number 7» The la st two notes of number 7 appear tvro octaves lower in the cello at the end of number 13» The added parts in this "coda" of Op.21/13 are marked beeleitend (accompanying). The bass clarinet and viola (and the cello for four notes) begin imitatively, but continue so for only one measure. The clarinet line beginning in m.33 undergoes rhythmic dimunition in m.3$, 293

Pifl-KUri»tl« inB.

BrilNrha

Vliitunerll.

ZlemllchbBwefftoJ(e« m) Raiitation. Ziemllch bawegto J (o> ia«)

Klavier.

iIIkIi gro$— d riu i er hfa.ab durch •«m«*

. U C. M14. «Ml.

•t.

[MCora t t m j M j i m dl«K a U ,

Used by parmiiiBion of Balnont Music Publishers, Los Angeles, California 90049

Ex. 92. The motive of Op.21/13, stated in m.^ and restated in mm.8-9 and m .1/. 294 while the flute undergoes augmentation, with each retain ing the same pitches in a sort of local, untransposed pitch-string (Ex.9 3 ).

Uaad by permission of Beimont Uusic Publishers, los Angelas, California 90049

Ex. 93» Op.21/ 13, mm.33-35* combined diminu tion in the clarinet and augmentation in the flute.

Op.21/21: 0 alter Duft

A straightforw ard example of a category C movement is Op.21/21. In this movement, the recurring pitch/rhythm at m.l4 appears an octave higher than the original, but lasts almost three full measures (ex.94). The piano is the only instrument playing this complete motive. The left hand also anticipates the first three notes of the motive in m. 13, in a "mi-re-do" pattern that also appears in m.9 and in the viola and cello in m.26, the latter at OPL for three notes. 295

'c m z - f r oco ri(.

It Uaad by peralasion of Balnont Uusic Publishers, Los Angeles, Caiifomia 90049

Ex. 9^« The lengthy recurrence in Op,21/21 in mm.Ik—16, appearing an octave higher at OPL,

The movement also has some prominent chords and intervals, a category E characteristic. Major and minor triads and thirds make up several of the vertical struc tures. Isolated triads occur in mm.3, 6, 16, and 18, As part of chord layers, they occur in mm.2k and 28. Parallel thirds occur in mm.1, 2, 3, 9» 11, 12, 13, Ik, 15, 19, 20, 26, and 27, or 13 of 30 measures in the piece. A contour congruity exists between mm.9 and 19 in the piano (Ex.95), both being series of three-note structures. In m,9, the CQ^'s played by the piano are CQ's 1?k, 26k, 26k, and 273. In m.19, the CQ's are 237, lk7, 1k7 and Ik7 . In m.9, the CQ^ in the upper parts is CQ 1331k 296

(B-G-sb-C-G); in m.19j two CQ^'s appear in the upper parts, CQ 2343 (sb-D-G-F) and CQ 1236 (üb-D-G-E), and one CQ^, 12^23 (üb-D-fib-Ab-E), Thus, the clear contour congruity is not supported by CQ congruities.

poco rll. . Tempo

poco rit

T em po ■rt dioioioli.teLufl.

iT ~ R Allmeiiien ppp ^ ^

\ W i

Uaed by permission of Belmont Uusic Publishers, Los Angeles, California 90049

Ex. 95. Op.21/21; a contour congruity in the piano between mm.9 and 19 that is not supported by CQ con gru ities. 297

Analysis of a Representative Imitative "Contrapuntal" Movement (Category B)

Of the three imitative "contrapuntal" movements, Op.21, numbers 8 , 17, and 18, number 8 , "Nacht," demon strates the widest -variety of imitative procedures. The other two (see p.199 above) are dense but quite strict in their imitation.

Op.21/ 8 : Nacht (Passacaelia)

In Op.21/8, subtitled "Passacaglia," local variation procedures are employed in the treatment of the principle motive, shown in Example 96. The character of a passacaglia is achieved through frequent return to the motive at OPL, but often in rhythmic diminution.

j|j~

Mt m

Uaad by parmisaion of aelmont Uuaic Publlahara, Loa Artgalaa, California 90049

Ex. 96. The motive of the "passacaglia" in Op.21/8. 2 9 8

The movement begins with an imitative passage in the piano, followed by an elongated version of the motive, overlapping between the cello and bass clarinet. Starting in measure 4, each successive measure has an entrance of the motive, first in the bass clarinet, then cello, then piano L.H,, and last, the piano R.H., in m.?. The bass clarinet then begins a series of three diminutions of the motive in eighth notes. Because of the pitch levels of these diminutions, the first note of each results in the motive in its original duration (Ex.97)* This technique is also employed in the L.H, in m.12. The motive also appears in strict diminution in a canonic passage in the piano from m.19 to m.23 (see Ex.4$, p.217).

Used by perniaaion of Balmont ttuaic Publlahara, ]>Jb Angelaa, California 90049

Exr 97* The motive of Op,21/8 in rhythmic diminu tion, also spelled out in the original by the first note of each group of eighths. 299

The countermotives to the principal motive con sist mainly of direct semitonal ascent and descent, em ployed in mm.5-10, 12-18, and 20-24. In contrast to most of the atonal movements, this movement displays a great economy of musical ideas, developed in an unusually clear and systematic fashion. The pitch material of the Sprechstimme even becomes important in this movement. In spite of its notation, the Sprechstimme does not generally contain musical pitches. There are, however, three p itches to be sung in m.10 of th is movement.

P P P P P p

J L J L. ' I I l_u_ ' I L /O »5 Z.O 2 S

Clarinet - 0 literal motive at OPL - C ello - V varied motive at OPL ïz z n Piano - P varied motive at other pitch levels Voice - S

Ex. 98. A diagram of the distribution of the motive in Op.21/8. 3 0 0

(S ix other movements have one or tvro sung notes in them.) These sung pitches are also the notes of the motive at OPL. The distribution of the motive throughout the movement i s diagrammed in Example 98.

Analysis of a Representative Polvmotivic. Sectionslized Movement (Category A)

Category A movements contain the clear exposi tion of primary motivic material and differentiated secondary material. Movements-in other categories, such as Op.11/1 (category C) or Op.21/8 (category B) might contain equally explicit motives. They lack, however, the sectionslization based on secondary material that makes category A movements most clo sely resemble c la s s i cal forms. Op.16/2 is perhaps the most interesting of these, because the use of orchestral color even more dis tinctly divides the movement (see Exs. 99? 100, and 101);

Op.16/2; Vergangenes

The only case in Op.16/2 where contextual em phasis is not confirmed by later recurrence is the melo dic item in the woodwinds at m.132. Aside from this, the motives are clearly identifiable. The first section is framed by motive (a), shown in Example 99, which recurs in the flute, English horn and trumpet at m.1^8, in a 3 0 1 slightly elongated version. A middle section is based on motive (b), shown in Example 100. This motive, initially stated by a solo viola in m.1$1, is fragmented and rhythmically altered in some twelve repetitions during the next 24 measures. At m.175» a third section, con sisting of a threefold ostinato, begins. The three ele ments of the ostinato are initially stated in the flute, bassoon and c e le s te , as shown in Example 100. The celeste part happens to be canonic in itself, that is, the ostinato figure is continuously in stretto. In m.l85, the (b) motive returns, followed by a return of the opening motive (a) at m.20$. The ostinato is heard again, and motive (b) is finally used as closing material. Rhythmic diminution is employed in the tr e a t ment of motive (b) and the bassoon portion of the o stin a to . Other woodwinds join the bassoon in mm.182-183 in the stretto treatment of a doubly fast version in six teenth notes; from m-l85 to m.204, the clarinet and bassoon continuously trade off the sixteenth-note version. The first three notes of the celeste ostinato appear in the cla rin et and horn Hauptstimme at m.30 (Ex. 102).

'•/Ith peralasion of C.P.,Patera Corporation, New York

Ex. 99. Op,16/2: motives (a) and (b). 302

R. “5 ——i

Bn- T

01.

with parmisaion of G.P. Patera Corporation, Now York

Ex. 100. Op.16/2; Threefold ostinato in celeste, flute and bassoon.

X j/y///y////y//7:^//WZ/zz7/z^ ///^

X 1 I..U.I III! .1.1.,I-I \ 1,1 1 M i l LLLL.IJLX n i l 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 I i r i | L )5 1 I L l l A l l l l 1 I h III II II IHC n r ^ n s* l i s M7

X: L i n

-A05 207 2*4 rfE) ii T 1 1 i 1 2 7 ' 1 i J 117, A e x 1 11M 1 1 U 11.J-l-T [

1 2 bassoon only. flute and celeste only

Ex. 101. A diagram of the six sections of Op.16/2, delineated by the presence or development of (a), (b), or (c). 303

w ith permission of G.P. Peters Corporation, New fork

Ex. 102. Op.16/2: the Hauptstimme at m.130, ivhose first three notes also appear in the celeste ostinato, a major tenth higher.

While this movement is certainly as "atonal" as any from the period, it demonstrates the possibilities for formal coherence, if atonal music is not also athe matic. Clear sectionalization and confirmed contextual emphasis combine to produce one of the most straightfor ward movements from the period, from both an an alytic and an aural point of view. The same will, of course, hold true for any category A movement. A graph of the formal plan of Op.16/2 appears in Example 101.

The other movements in categories A through D admit to conventional ar lysis in much the same way as those discussed above. The fragmentary effect of move ments in categories E and F comes from fragmentary 30^ construction based on local and low-grade congruities. In categories E and F we are no longer dealing with explicit motivic material. Nevertheless, it is undeniable that the characteristic of one category can contribute to a movement in a different category. In his analysis of Op.22 (see p. 163 above), Schoenberg showed how quickly m aterial can be altered beyond recognition even when a consistent procedure is used. If no motive can be identified, then no develop mental procedures can be traced. What separates a motive from its transformations is the relative formal signifi cance of each. The former is essential, the latter are supplementary. Complete equality for melodic items re sults in athematicism, just as the fundamental equality of tones results in atonality. 'Chapter VI SUMMARY AND CONCLUSIONS

The works of Arnold Schoenberg are divided into three distinct periods : tonal, "free" atonal, and twelve- tone serial. Schoenberg indicated the crucial transi tion s as the abandonment of to n a lity in 1908 and the formulation of the twelve-tone method in 1921. The works of the intervening period, that of "free" atonality, lack an organizing principle of the scope of either tonality or twelve-tone serialism. Although Schoenberg wrote a number of theoretical works on tonal harmony (most nota bly the Harmonielehre) , and lectured extensively on twelve-tone serial practice, he said little about specific compositional procedures in the period from I90 G to 1921. The befy of works selected for analysis consisted of: the Three Piano Pieces, Op.11, The Five Pieces for Orchestra, p .16, the Six Little Piano Pieces, Op.19 , Pierrot Li: e., Op,21, and the Five Piano Pieces, Op.2 3 . The last of these was transitional in nature, actually completed in 1923 » and has as i t s la st movement a b asic, but thoroughly twelve-tone piece. Because of the period

305 306 that followed "free" atonality, attempts have been made, notably by Perle and Forte, to explain the atonal works in terms of certain twelve-tone relations : pitch-class, interval-class, and verticalization. Because Schoenberg valued the classical tradition as he did, it is also important to view the atonal wcirks in terms of conven tional practice. This means attempting to apply the pro cess of conventional analysis as closely as possible to Schoenberg's atonal works. The individual constituents of vertical, melodic, and formal construction have been examined from this viewpoint. The result has been an analytic approach that is far more .systematic than a search for twelve-tone relations. Even for atonal works where the conventional approach yielded little, the re sult has been to show their unconventionality against a quantifiable standard. Before the chapters dealing with individual constituents, the first chapter dealt with the theoreti cal implications of atonality. According to the accounts of Schoenberg and other theorists, atonality can bo cor rectly viewed as an extreme extension of chromatic tonal ity. It has been observed by other writers, however, that chromaticism can exist only in a tonal context, i.e ., in contract to diatonicisra. When the chromatic tones be come equally significant, the result is panchromaticism 307 (see p. 5^ above). Although so-called ’’vagrant" chords (diminished seventh, augmented sixth, etc.) may weaken the effect of a tonal center, they cannot by themselves undermine the effect of tonality in general. In atonal ity, because function and progression are no longer a consideration (p. 13 above), chords create not multiple expectations, but rather no expectations at all. In spite of the efforts to trace a historical continuum, tonal and atonal music must be seen as intrinsically dif ferent. Although Schoenberg claimed that in the atonal idiom all prior means of cohesion remained except a tonal center, in his works all constituents of atonal composition received some new kind of treatment. In Chapter II, conventional methods of vertical analysis were adapted for use in atonal.music. This involved the expansion of the notion of chord quality to account for all possible simultaneities. The chord quality notion stresses the unique first- and second- order interval makeup of a vertical structure. Therefore, the specific twelve-tone relation of interval-class inver sion was excluded, while the conventional notion of the harmonic inversion of chords could be retained. A count of all simultaneities in the atonal piano works (0pp.11, 19 and the transitional Op.23) showed that Schoenberg carefully avoided giving emphasis to one or a small number 308 of v e r tic a l stru ctu res. This count was compared to a sim i la r count for Brahms' Piano P ieces, Op.7 6 . Even i^en nonharmonic structures were included in the count, the Brahms sample showed a much higher degree of s e le c t iv it y in the v e r tic a l dimension. The count also showed stronger e v i dence for the vertical use of interval-class inversions in the Brahms sample. The Schoenberg sample was far more "dissonant" in conventional terms, containing a much greater proportion of semitones, major sevenths, and their compounds. The almost to ta l lack of regu lation in the vertical dimension could not be explained or reduced by the twelve-tone relations of pitch-class or interval- c la s s . The horizontal dimension was found to contain many items that could be considered %eIodic in the conven tional sense. Categories of melodic succession were iden tified: by semitone, by whole-tone, scalar, and arpeggiated. Because all vertical structures are equally plau sible in atonality, any atonal melodic segment may be re garded as an "arpeggio" as well. This affinity eventu ally led to a greater unity in Schoenberg's twelve-tone music between the vertical and horizontal dimensions, a unity that Schoenberg called the two-dimensional "space" 309 in vAiich musical ideas are presented.^ A vertical/hori zontal count of Op.19/1 (p .101 above) showed that th is unity did not play a major role. As an apparent pre saging of twelve-tone procedures, however, the chromatic saturation of smaller-than-octave ranges was noted (p. 138 above). Certain melodic idiosyncrasies of Schoenberg's idiom were observed, in particular, the horizontaliza- tid n of CQ's 138 and I 83 ( e .g ., C-C#-E and C-C#-A), and small semitonal items that appeared to be brief instances of chromatic saturation (see p. 162 above). Local varia tion procedures were identified, and were often found to be used as part of the process of "perpetual variation." It remained questionable whether the identy of an ori ginal motive could be successfully maintained in the course of Schoenberg's typically far-reaching transforma tions (see p. 163 above). The broad question of motivic identity through out an atonal work was dealt with in Chapter IV. Because the formal support previously afforded by harmony is ab sent in atonality, other means of formal definition were sought as the substitutes Schoenberg may have applied. A formal hierarchy was established based upon the con ventionality of the means by which form in the atonal

^Schoenberg, "Composition with Twelve Tones (1)," p.220. 3 1 0

works is delineated. An example of a conventional type of motivic connection was the relationship between princi pal, and closin g themes in some symphonies by Mozart (see p. 172 above). I t was found that in the m ajority of move ments from Schoenberg’s atonal instrumental works, at least one motivic item, though usually quite brief, re curs at the original pitch level (GPL). Only ten of the fo rty movements under consideration display no m otivic recurrence whatsoever (p.193 above). In these, local congruities and less conventional low-grade congruities supply the only formal coherence present. Another topic related to form,concerned the means or emphasizing principal material. It was observed that significant (i.e., recurring and/or developed) items may be made prominent at their points of introduction and restatement by various means called "factors of contextual emphasis" (p.177 above). It was observed that in the course of the atonal works, Schoenberg frequently treated a momentary item in a manner that, in previous periods, would have caused i t to be apprehendeC as sig n ific a n t, on the basis of context alone. It was concluded that the giving of contextual emphasis to non-recurrent mate rial was often an obstacle to the apprehension of a dis tinct form in the atonal works* 311 In the analyses of representative movements, in Chapter V, more details of the various levels of recur rence were demonstrated. Although many local and low- grade congruities may be found in movements that f a l l into motivically articulated forms (categories A, B, C, and D). such congruities do not play as significant a role as the p rin cip al recurring item s. In athematic movements (ca te gories E and F ), and in some movements categorized in A through D, large portions are controlled only by local and low-grade co n g ru ities, whose role becomes compara tively greater. The analytic methods used in examining these movements were derived from the conventional techniques of harmonic, m elodic, and formal a n a ly sis. Through these means, the analyzer can find whatever formal coher ence (in the conventional sense) happens to be present, whether it be much or little . Because the commoh-practice period notions of harmonic selectivity, octave inversion of chords, scalar and arpeggiated melodic successions, recurring items, and development or variation techniques are taken into consideration, the approach adopted in this study could also be appropriately applied to coramon- practice music. Many results would duplicate those of more familiar approaches, because the present approach 312 is based on them. Certain additional areas might be ex plored, however, such as: (1) using the CQ system to analyze nonharmonic structures in common-practice music; (2) cataloging a CQ tabulation for music of any period by taking specific inversions into account (not possible in p-c set analysis); (3) using the hierarchy of formal recurrence to gauge the significance of transitional items in common-practice music; and ()+) using the CQ sys tem to catalog melodic items in common-practice music. In conclusion, it is important to stress the transitional nature of Schoenberg's atonal period. Although Schoenberg continued to use the terra "atone 1'' in reference to the twelve-tone idiom, he also distinguished explicitly between serially and non-serially organized music (see pp. 4 and 33 above). The links between tonality and atonality on the one hand, and atonality and twelve-tone serialism on the other were discussed in Chapter I . Certain conclusions were drawn about the th e o retic a l im plications of the abandonment of a tonal center, the indiscriminate treatment of consonance and dissonance, and the adoption of twelve-tone relations. A number of necessary consequences of the aban donment of tonality were noted. Schoenberg observed that modulation is necessarily excluded from atonality 313 (see p. 52 above). Also necessarily excluded are the dis tinction between real and tonal sequences (see p. 146 above), between various forms of harmonic cadence (see p. 79 above), and between incorrect and correct "coun terpoint" (see pp. 148 and 199 above). Enharmonies must also be treated as identical, because tonal reference is no longer a factor. Besides these inevitable results of the renouncement of a tonal center, Schoenberg's- atonal ity displays many other features that are not direct re sults of this one fundamental change. First, as he noted, "dissonances" are to be treated like consonances, thus preparation and resolution are eliminated. Second, the field of available vertical structures is opened. Unre lated to these alterations, however, are the lack or re petition of melodic items and the frequently fragmentary and irregular melodic surface. Although the equalization eliminates the traditional notions of scale and arpeggio, many other means of melodic construction remain. Schoenberg's atons 1 procedures, therefore, con sist of a number of elements that are not directly en tailed in the elimination of a tonic. The remaining means of unification, specified by Schoenberg as "rhythms, motives, phrsses," (see p. 34 above), are often employed in a less than unified manner. Schoenberg even 314 acknowledged this inherent self-contradiction (see pp. 46 - 47 above). Yet, in spite of the many departures from conventional means of coherence, Schoenberg still paid remarkable heed to the original pitch level at which items were introduced, and to the significance of intro ducing them at the beginning of a work (see p. 190 above). The relationship of atonality to twelve-tono serialism was also considered. Certain characteristics are shared by "free" atonal compositions and twelve-tone works: (1) the absence of a tonal center;^ (2) the equal treatment of consonance and dissonance; and (3) the sub sequent opening of the vertical dimension to all struc tures. The use of twelve-tone relations was by no means a necessary part of free atonality; but with the number of procedures being consciously avoided (e.g., Austin's "rules," p. 22 above), some framework for selecting pitch material became necessary. The transitional phase, dubbed "working with tones" by Schoenberg, represented a partial infusion of twelve-tone relations into "free" atonality. One must not overlook the fact that four of

^As Perle points out, this is not a necessary, but an incidental fact of twelve-tone serialism: "...the assumption of a twelve-tone complex does not preclude the existence of tone centers." (Serial Composition, p .8 ). 315 the works in th is study, 0pp.. 11, 16, 19 , and 21, were written between I908 and 1912. Only towgrd the end of the atonal period did twelve-tone relations begin to govern substantial portions of the musical structure. The por tions mentioned in Chapter V were exceptional cases in the pretransitional works. Although Schoenberg went to great lengths to p ub licize h is tw elve-tone method, he o ften warned against overestimating the potential of the method. Since he stressed other compositional considerations (see pp.34 - 45 above), the analytic approach presented in this study can also be of value in examining the features of Schoen berg’s twelve-tone compositions that are not directly related to row applications. In terms of basic form, the twelve-tone period seems to have been a conservative reaction by Schoenberg to the extreme modernism of the atonal phase. As Rosen stated:

There is no question that the conservative tendencies in Schoenberg's style increased and even hypertrophied with the appearance of serialism. The forms are often simpler and more symmetrical...3

3Rosen, Arnold Schoenberg, pp.72-73* 316 Table 1^ has been assembled to show the points of recur rence in the instrumental works from 1923 to 1936, all of them s e r ia l except fo r several movements of the Serenade, Op.2^. As can be seen,a small proportion of the move ments do not display recurrence at original pitch level; on the vAiole, however, the increased sig n ifica n ce of fo r mal recurrence in this period is apparent. In 0p.2>+, one movement is in a variation form, which would not be ex pected to contain literal repetition. The first and f if t h movements contain the notation of a f u l l sectio n a l repeat, a clear recollection of classical procedures. The fourth movement, with a vocal part, is the only strictly serial movement of Op.2^. The Suite, Op.25 con tains two da capo movements; a l l five movements are se ria l. Apparently, unity in the atonal (and twelve- tone serial) works is achieved by exactly the same means as in preceding periods; motivic identity, pitch level, and contextual emphasis. It is the new proportion of unity and variety, and sometimes the lack of any unify ing element, that constitute the radical differences between Schoenberg's post tonal works and even his own tonal compositions. The deliberately avante-garde 317

TABLE 14 Peints of recurrence in Schoenberg’s instrumental works, 1923-1936

Original Restatement Pitch Opus/movement in measure in measure level Serenade, Op.24/1 9 80 * OPL 24/2 1 37* OPL (1) 24/3 (variations) 24/4 (vocal) (sectional repeat) - î Y â 1 23* OPL 24/7 (no recurrence) S u ite, Op. 25/1 1 16 OPL 25/2 capo) - — 25/3 0 30* OPL 25/4 1 37 OPL 25/5 1 64 OPL Q uintet, Op.26/1 1 128* OPL 26/2 1 62* OPL 26/3 1 104* OPL 26/4 1 218* OPL Quartet, Op.30/1 5 295 trans] 30/2 recurrence) — — 30/3 1 40*,168* OPL 30/4 1 112,163* OPL Quartet, Op.37/1 1 239 * OPL 37/2 285 592 * OPL 37/3 recurrence) — — 37/4 704 889 * OPL

* - indicates an associated note-value pattern (1) also a minuet-trio (2 ) also a da capo 318 attitude that produced the new style was described by Schoenberg in one place as follows:

There should be avoided: chromaticism, expressive melodies, Wagnerian harmonies, romanticism, private biographical h in ts , su b jectiv ity , fu n ction al harmo nic progressions, illustrations, leitmotivs, concur rence with the mood or action of the scene and characteristic déclamation..of the text in opera, songs and choruses. In other words, all that was ^ good in the preceding period should not occur now.

The apparent negativism of Schoenberg's atonal compositional approach has probably not been mitigated by the close scrutiny the music has received in this or other writings. In some of the works, there exists . little of substance for the listener or the analyzer to grasp. Close examination merely permits us to be in creasin gly secure in the conclusion that such movements do not contain some latent organization yet to be dis covered. ^ In light of the musical world's continued difficulty with these works, it is somewhat ironic to read what Schoenberg wrote in 19 ^8 :

Atonality or dissonance are no yardsticks for evaluation. Superficiality might base its judgements on such qualities. True love and understanding of music w ill wonder: What has

k Schoenberg, "New Music, Outmoded Music, Style and Idea," p.120. 3 1 9 been said? How was it expressed? Was there a new message delivered in music? Has a new personality been discovered? Was the tech nical presentation adequate? Of course, to identify the style is easier and procures for one the glory of a connois seur. But the love of the friend of art does not derive so indirectly—it is appreciation that it aims for

Analysis and appreciation are two separate things, having different motivations. Of the two, Schoenberg's atonal music has received far more analysis than appreciation in the past, and w ill probably continue to do so in the future.

^Schoenberg, "A Self-Analysis," p.77* BIBLIOGRAPHY

Adorno, Theodor. Philosophy of Modem Music, trans. A.G. M itchell and W.V. Blomster. New York: Seabury Press, 1973. Austin, William. Music in the Twentieth Century. Nev/ York: W.W. Norton and Co., 1966. Berg, Alban. "What is Atonality?" interview, trajis. M.D. Herder Norton in Nicholas Slonimsky, Music Since 1900. New York: W.W. Norton and Co., 1937» p .1311, ’Why is Schoenberg's Music So Hard to Under stand?" Music Review. v.l3 (1952), pp.187-196. Brinkmann, Rheinhold. Schoenberg: Drei K lavierstücke. . . Op.11. supplement to Archiv fdr Musikwissenschaft, y.7« Wiesbaden: P. Steiner, I969 . Browne, Richmond. Review o f The Structure o f Atonal Music. Journal of Music Theory, v.10/2 (Fall. 19741. pp.390-415. Buchanan, H.H. "A Key to Schoenberg's Erwartung. " Journal of the American Musicological Soci ety, y.20/3 (1967), pp. 434- 449 , : ' Chrisman, Richard. "Describing Structural Aspects of Pitch- Sets Using Successive-Interval Arrays." Journal of Music Theory. v.2l/l (Spring, 1977), pp.1-28. Dean, Jerry M. "Evolution and Unity in Schoenberg's George Songs." Ph.D. dissertation. University of Michigan, 1971. Deutsch, Diana. "Memory and Attention in Music," in Music and the Brain, ed. MacDonald Critchley and P.A. Henson. London: William Heinemann Medical Books, 1977 Forte, Allen. "Schoenberg's Creative Evolution." Musical Quarterly (April, 1978), pp.133-176. The Structure of Atonal Music. New Haven: Yale University Press, 1973. 320 321 Priedheim, Philip. "Rhythmic Structure in Schoenberg's Atonal Compositions." Journal of the American Musicological Society, v,20 (Spring. 1966). pp.59-72. . "Tonality and Structure in the Early Works of Schoenberg." Ph.D. dissertation. New York Iftiiver- s i t y , 1963 . Gerhard, Roberto. "Tonality in Twelve-tone Music." Score (1952 ), pp.23- 35. H ill, Richard. "Schoenberg's Tone Rows." Musical Quarterly V.22 (1936 ), pp.14-37. Hoffmann, Richard. "Concerning Row Deviations in the Music of Schoenberg." Bericht ûber den 1. Kongress der Internationalen Schoenberg-Gesellschaft. Wien: Elisabeth Lafite, 1974. Krenek, Ernst. "Extents and Limits of Serial Techniques." Musical Quarterly, v.46 (i 9 6 0 ), pp.210-232. Krieger, Georg. Schoenberg's Werke fu^ Klavier. Gottingen: Vandenhoek und Ruprecht, I 96 Ô. Largent, Edward James, Jr. "An Investigation into the Perceptibility of Twelve-tone Rows." Ph.D. disser tation, The Ohio State University, 1972. L e ich ten tr itt, Hugo. Musical Form. Cambridge : Harvard Uni versity Press, 1951 . MacDonald, Malcom. Schoenberg. London: J.M. Dent and Sons, 1976 . Maegaard, Jan, "Some Formal Devices in E xp ression istic Works," Dansk Aarbog fo r Musik-Forskning, I (1961 ), pp.69 - 75. Studien zur Entwicklung des dodekanhonen Satzes bei Arnold Schoenberg. Copenhagen: William Hansen, 1972 . Mitchell, Donald. "The Emancipation of the Dissonance.’ Hinrichsen's, v.7, p.l4l. Neighbour, O.W. "The Evolution of Twelve-Note Music." Royal Musical Association Proceedings. v.8l (1954 - 3 5 ), pp.49 - 61. 322 Neighbour, O.W. "In Defence of Schoenberg." Music and L etters. V .33/I» pp.10-27. Perle, George. Serial Composition and Atonality. 4th ed. Berkeley: University of California Press, 1977. ______. Twelve-tone Tonality. Berkeley: University of California Press, 1977» P illin, Boris William. Some Aspects of Counterpoint in Selected Works of Arnold Schoenberg. Los Angeles : Western International Music, 1971 . Regener, Eric. "On Allen Forte's Theory of Chords," Perspectives of New Music, v.13/1 (1974), pp.191- 2 1 2 . Rogge, Wolfgang. Das Klavierwerk Arnold Schoenbergs. Regensburg:'Bosse, 19^4. Rosen, Charles. Arnold Schoenberg. New York: Viking Press, 1975 . Rufer, Josef. Composition with Twelve Notes Related Only One to Another, trans. Humphrey S earle. London: Barrie and Rockliff, 1970. ______. The Works of Arnold Schoenberg, trans. Dika Newlin. London: Faber and"Faber, 1962, Samson, Jim. Music in T ransition. London: J.M. Dent and Sons, 1977 . ______. "Schoenberg's 'Atonal' Music." Tempo. v.l09 (June, 1974), pp.16-25. Schoenberg. Berg. Webern: The String Quartets; A Documentary Study, ed. Ursala von Rauchhaupt. Hamburg: Deutsche Grammophon Gesellschaft, 1971. Schoenberg, Arnold. "Analysis of the Four Orchestral Songs, Op.22," tran s. Claudi Spies. Accompanying booklet to Columbia recording M2S709» The Works of Arnold Schoenberg, v.3. Also appears in Perspectives of New Music, v.3 /2 (Spring/Summer, 1965), pp.1-21. Harmonielehre, 3rd,ed. Wien: Universal Edition, 1922 . . Letters, ed, Erwin Stein, trans, Eithne Wilkins 323 and Ernst K aiser. New York: S t. M artins's, I 965 . ______. "The Orchestra Vaxiations, Op.31." Score. • V.I7 ( i 9 6 0 ), p .2 7 . ______. Structural Functions of Harmony. New York: W.W. Norton and Co., I969 . ______. Sty le and Idea, ed. Leonard S tein . Nev/ York: S t. Btertin's Press, 1975» ______. Theory of Harmony, trans. Roy E. Carter. Berkeley: Ikiiversil^ of California Press, 1978. S te in , Erwin. Ornheus in New G uises. London: R o ck liff, 1953 . Stuckenschmidt, H.H. Schoenberg, transH* Searle-and E. Temple-Roberts. London: Calder, 1959. Twentieth-Century Music, trans. Richard Deyeson. New York: McGraw H ill, 19^9. Suderberg, Robert. "Tonal Cohesion in Schoenberg's Tv/elye-tone Music." Ph.D. dissertation, Univer sity of Pennsylvania, 1966 . Thrall, Bruce E. "The Audibility of Twelve-tone Serial Structures." Master"a thesis. The Ohio State University, i 960 . Weber, Anton. The Baths to the New Music. New York: Presser, 1963.

Bibliographic note: The above list represents a select bibliography of the major works dealing specifically with Schoenberg's compositional procedures and related topics. Also included are important sources since 1972 . For 8 cur ces before 1972, Jan Mae,f;aard's Studien zur Entwicklung des dodekanhonen Satzes bei Arnold Schoenberg contains an extensive bibliograpl^ of biographical, theoretical, and historical works on Schoenberg in several languages. See v.2, pp.589-617»