Alban Berg (1885-1935)
Analysis of Piano Sonata, Op. 1 (1907-8)
by Andrew Kuster
Alban Berg's Piano Sonata, Op. 1 is a fascinating work which employs, within a tonal framework, many of the techniques Berg would use in his mature style. The Sonata is a one-movement work in the traditional sonata form, including an exposition (which repeats), a development, and a varied recapitulation with coda. Each main theme (first, second, and closing themes) is stated in the Exposition in a different tempo. These themes, which are motivically linked, are all developed from the opening theme. The work's tonal center and key signature is b-minor, and the key areas utilized in the course of the movement are historically logical, but its complex chromaticism has led Carner to call Berg's Sonata "a study in the use of chromatically 'altered' suspensions and passing-note chords." (Carner: 1975, 101) Typical to his style, Berg uses many cyclic tonal patterns in the Sonata. Especially prominent are chromatic (1-cycle) progressions and "wedges", whole-tone (2-cycle) chords and progressions, augmented progressions (4-cycle), and quartal chords and progressions (5-cycle).
Berg's Sonata, (1907-8), was first performed at a recital of compositions by students of Schoenberg on 24 April 1911. Berg composed the Sonata during the first year of his apprenticeship "for himself," not to be examined by Schoenberg. (Leibowitz: 1949, 140) Nevertheless, the work was composed in reaction to Berg's teacher's ideas, and is influenced by another work employing sonata form and using 5-cycle progressions, Schoenberg's Chamber Symphony, Op. 9. Samson claims that "to the extent that the work approaches total thematicism as a unifying method which might replace tonality, it reflects the influence of Schoenberg..." (Samson: 1977, 121) Many analysts comment on the Tristanesque quality of the Sonata, but I sense a connection (perhaps because of the form or the medium) with the sonata movements of Scriabin and their chromaticism, and cyclic progressions and chords.
The Sonata opens with two motives which are used and developed throughout the entire composition. (a Grundgestalt, Hedlam: 1996, 23) The first motive begins immediately in the right hand: G-C-F#, [0,1,6]. The second motive, heard in the second and third measures in the upper voice, is a descending 4-cycle followed by chromatic falling motion G-Eb-B-D-C#, which makes up a whole-tone group with one added note [0,1,2,4,8]. (Samson divides motive 2 into two motives: motive (b) is B-Eb-B, motive (c) is D-C#) The opening phrase of the Sonata lands solidly on the b-minor tonic chord, approached by a 5-cycle bass note progression, C#-F#-B, and can be analyzed traditionally as ii/°-V-i, but the harmonic progression is not by traditional voice leading. Rather, "the harmony is 'filled in' with characteristic passages in major thirds moving chromatically or by whole-tone steps to create whole-tone harmonic areas." (Samson: 1977, 118) Played simultaneously with the second motive are two descending chromatic lines (1-cycles), one in the right hand B-Bb-A-etc., the other in the bass C#-C-B-etc. which continue (inverted) into the fifth measure. The conjunction of the 1- and 4-cycles in the first measure creates harmonies based on the 3-cycle (beat 1: C#-G <6>, beat 2: C-Eb <3>, and beat 3 B-B <0>). Berg uses patterns of this sort in the course of the Sonata, and more extensively in his later works.
The first theme area in the exposition (ms. 1-28) is tripartite, the third part being a varied repeat of the first part and the transition to the second theme area at the same time. Within the first part of the first theme, the motives first heard in the opening measures are developed in measures 3-7. Motive 1 is played in the bass part of measure 3 and motive 2 is sounded in the right hand wedging out to a whole-tone (2-cycle) based measure (ms. 7) and a repeat of motive 2 in measure 8. The second part of the first theme area begins in measure 11. This second part, which implies D-major, the relative major of b-minor, uses motive 1 and upward moving chromatics (1-cycles). Motive 1 combines with itself (in measures 11-12) to form whole-tone collections with one added note (similar to the collection formed in motive 2). A 5-cycle bass progression (ms. 13 E, ms. 14 A, ms. 16 D) leads back to the return of the first part of the first theme area in measure 16. Instead of the resolution to tonic as in measure 3, now there is a deceptive progression in measure 19 leading to a sequence of motive 2 to measure 23.
The material in measures 23-28 leads to the second theme area. This new material, played in the right hand is motive 3 which is used in transitional passages elsewhere in the Sonata. Motive 1 is heard in inverted form in the left hand of measure 25. Measure 26 contains chromatically descending 5-cycle chords in the left hand. A 5-cycle bass progression (B in ms. 25, E in ms. 27, A in ms. 29) delivers us to the second theme.
The second theme area (ms. 29-48) is in two parts. The first part of the second theme is in D-major (over an A pedal), the relative major of b-minor, although no solid cadence to D is heard. The second theme uses the dotted rhythm and pitches of motive 1 with an added half-step forming a [0,1,6,7]. Motive 2 is played in measure 30, beat 3 right hand. A cadence to E is reached in measure 33, followed by a sequential pattern using [0,1,6,7] until the second part of the second theme area beginning in measure 38. Here, motive 1 alternates with scales based on whole-tones with added notes. A sequence which repeats for three measures begins in measure 40. Motive 3 returns in measure 43 forming a link to the closing theme area at measure 49.
The short closing theme area (ms. 49-55) which begins with a prominent F# in the bass (the dominant of b) uses chromatically descending whole-tone based chords in the left hand over which is a melody based on motive 1 from measures 45-47. Both the closing theme and the second parts of the first (without F) and second theme areas have the pitches E-F-F#-A-C in common. A sequence in measures 52-53 proceeds without a solid cadence to the exact repeat of the exposition.
The development section (ms. 56-110) is highly sequential and homophonic, simpler than the exposition which is highly developed in itself. It is divided in three parts, each of which develops a different part of the exposition. The first part of the development (ms. 56-70) develops motive 1 and uses overall descending chromatic progressions. Motive 1 is used in 3-cycle, in measure 56 (on Ab), in 58 (on D), in 61 (on Bb), and in 63 (on E). A 4-cycle progression (or [0,1,4,8]) in measures 66-67 leads to a whole-tone measure (ms. 69) and the second, and longest, part of the development section (ms. 70-99). The second part of the development uses motive 1 and motive 2. Beginning in measure 73 both motives are tossed back and forth between hands. Motive 3 is developed from 81 to the climax halfway through the development in 84. Beginning in 84 a 5-cycle bass progression (G in 84, C in 88, and F in 89) moves to a chromatic descent starting at the loudest part of the work in measure 91. The development calms before the third section (ms. 100-110) which is based on the second theme. Motive 2 is heard in measure 109, like the false entrance of the horn just before the recapitulation in Eroica.
The recapitulation sneaks back in measure 111 at the same pitch level as the Sonata's opening material. Berg's recapitulation is varied and developed, not simply the exposition material repeated in new keys. While composing the recapitulation, Berg must have taken the message of Schoenberg to heart: "Never do what a copyist can do." (Carner: 1975, 102) The initial phrase of the recapitulation does not offer a solid cadence as in the exposition, but instead leads to an extensive development of motives 1 and 2. A whole-tone area (ms. 127) moves to the second part of the first theme area beginning in measure 131. The second part of the first theme begins solidly on F# (V/V in E or the dominant of B). A colorful "white" arrival in measure 134 moves to the second theme area. The return of the first part of the first theme area (the transition of the exposition) is truncated from the recapitulation. The first theme area ends with an important harmonic move to V at the end of measure 164.
When the second theme area returns (ms. 137), the subdominant E is reached (as opposed to B as in traditional sonata form). The second theme sounds over a pedal B, now serving as the dominant of E. In measure 153 to 160 motive 3 is expanded upon sequentially, landing on E (subdominant) in measure 163.
The ending coda (ms. 167-179) is based on the closing theme (using descending whole-tone based chords). As with the closing theme in the exposition, it begins prominently on F# (dominant) in the bass. The closing theme melody is played again in the left hand of measures 169-170, and then is inverted and used in sequence for the next four measures. A half-step motion from C-B in the top voice reinforces the tonic B (like a bII) at the same time as whole-tone collections on F# (the dominant of B) are played. A solid V-i cadence on B occurs in measure 175 and is repeated three times, the last of which is delayed during which motive 1 is sounded.
The Sonata is formally complete in itself. The work is roughly symmetrical. Its exposition is 55 bars long (110 including the repeat), its development is 55 bars long, and its recapitulation is 69 bars long. At one time Berg had intended to compose additional movements for the Sonata, but he later changed his mind. After Berg told his teacher that he could not think of musical ideas for other movements, Schoenberg replied that, for this Sonata at least, "he had said all there was to say." (Carner: 1975, 99)
Many of the techniques that Berg would come to use in his later works are explored in this early Piano Sonata. A thorough analysis of the work offers insight to the logic and coherence of Berg's compositional method, and at the same time causes awareness of the intense emotion and passion which are the core of his musical language. Certainly Op. 1 is an important stepping stone in the understanding of early 20th Century extended tonality.
Carner, Mosco. Alban Berg: the Man and His Work. London: Duckworth, 1975. 99-102.
Gable, David and Robert Morgan. Alban Berg: Historical and Analytical Perspectives. Oxford: Clarendon Press, 1991. 64-69.
Hedlam, David. The Music of Alban Berg. New Haven & Yale: Yale University Press, 1996. 22-33.
Jarman, Douglas. The Music of Alban Berg. Berkeley & Los Angeles: University of California Press, 1979. 30-33.
Leibowitz, René. Schoenberg and His School. Translated by Dika Newlin. New York: Da Capo, 1949. 140-144.
Samson, Jim. Music in Transition. New York: Norton, 1977. 116-121.
"In Memoriam Alban Berg?": An Analysis of René Leibowitz's Five Pieces for Clarinet and Piano, Op. 29 (1952)
Timothy J. Bowlby
Very little suggests any connection whatsoever between Alban Berg's Op. 5 Four Pieces for Clarinet and Piano and René Leibowitz's Five Pieces for Clarinet and Piano, Op. 29. The quickest glance at the first pages of the two scores (examples 1a-b) reveals some of the many vast dissimilarities that exist between them. For example, Berg's piece begins with a solo for the clarinet, in the middle of the instrument's register. Leibowitz's begins with the piano in low range. Berg's phrases are far longer than Leibowitz's. Melodic and harmonic thirds, while present in both works, are more obvious in Berg. Textures are thinner in Leibowitz's piece. About all the Opp. 5 and 29 seem to have in common is the ensemble of a clarinet, one pitched in B-flat (Berg) and one in A (Leibowitz), paired with a piano; even that is not exactly the same.
Appearances, however, can be deceptive. In reality, there are very subtle connections between these two works. Presenting an analysis of the Leibowitz and a detailed discussion of the links between the two composer's clarinet and piano works are the principal purposes of this paper. To accomplish the second, we must consider sources of information other than the manuscripts themselves. We will, however, come away with a much fuller appreciation of the way in which Leibowitz went about writing music in general, and his Op. 29 in particular. We will also discover how perceptions of Berg, his music, and Berg's place in history influenced the composition of the Frenchman's Op. 29.
The twelve-note row Leibowitz based his Op. 29 on is as follows:
D, E b, B b, B, F#, C, D b, F, A, E, G, A b (1)
This is an I3 semi-combinatorial row, but never in the course of the work is P0 paired with I3. (Example 2a shows the matrix for Leibowitz's Op. 29; P0's combinatorial relationship to I3 is shown in Example 2b.) It is nevertheless important to note the combinatorial nature of the row for two reasons: 1. combinatorially related hexachords are used to control the flow of aggregates in the second movement; and 2. inversions and inverting as a process are important throughout the work as a whole.
Example 1a: Alban Berg, Four Pieces for Clarinet and Piano, Op. 5, no. 1, mm. 1-5.Permission of European American Music
Alban Berg 4 Stücke fur Klarinette und Klavier, op.5. Copyright 1924 by Universal Edition.
Copyright renewed. All Rights Reserved. Used by
Distributors Corporation, sole U.S. and Canadian agent for Universal Edition.
Example 1b: René Leibowitz, Five Pieces for Clarinet and Piano, Op. 29, no. 1, mm. 1-8.
Reprinted by permission.
Example 2a: Row Matrix of René Leibowitz's Five Pieces for Clarinet and Piano, Op. 29.
Example 2b: The Combinatorial Relationship between the P0 and I3 Forms of Leibowitz's Row.
Five Pieces for Clarinet and Piano, Op. 29, no. 1.
The importance of inverting and inversions is stressed throughout the first movement (Example 3). In each half of the movement's sixteen measures, an inverted form (either straightforward or retrograded) of the row is paired with an analogous "original" form: P0 and RI6 (i.e., the retrograde inversion starting on A, which is six semitones away from D, the first note of P0) appear in mm. 1-8, followed by R6 and I0 in mm. 9-14, with RI6 returning in mm. 15-16. The return of RI6 at the end of the piece with material derived from the piano's introductory phrase places emphasis upon an inversion rather than an original form of the row, thus cleverly stressing the importance of inversions and inverting.
Leibowitz constructed the first movement of his Op. 29 in an arch or bow form, which is articulated in several ways. In terms of row deployment, the first half of the movement is built in two unequal phrases, the first one (based on P0) being five measures long and the second one (derived from RI6) only three measures in length. The second half of the movement is begun with a three-measure phrase (R6) and concludes with a five-measure phrase (I0 and RI6). Thus we have a symmetrical (5 + 3) + (3 + 5) phrase construction in the first movement. The two five-measure groups are further
broken down, by tempo changes, into (2 + 3) and (3 + 2). So too are the three-measure phrases subdivided into groups of (1 + 2) and (2 + 1). The resulting phrase construction is, therefore, symmetrical on more than one level:
5 3 3 5
(2 + 3) + (1 + 2) // (2 + 1) + (3 + 2)
The instrumentation of the piece (i.e., solo piano, clarinet and piano, solo piano) also creates an arching effect. Bow formations are stressed at the metrical level as well. The metre signatures mirror one another around mm. 8 and 9:
4/4 3/4 4/4 3/4 2/4 4/4 // 4/4 2/4 3/4 4/4 3/4 4/4
Tetrachordal rotation is, in terms of pitch, the prevalent compositional method in the first movement. A look at mm. 3-5 reveals that the clarinet presents the row in a straightforward manner. (The starting note, D, is found in the last half of the last beat of m. 2). Between mm. 3-5 the right hand of the piano part presents, at the rate of one tetrachord per measure, the second tetrachord of P0: first, the third one second, and finally the first. Tetrachord three of P0 is presented in m. 3 in the left hand of the piano, followed by tetrachord one and then tetrachord two in mm. 4-5 respectively. This procedure is used, with the exceptions of mm. 1-2 and 15-16, throughout the movement; it creates a slow harmonic rhythm and a kind of ostinato effect. The special cases of mm. 1-2 and 15-16, which also break the row into tetrachords, will be considered later in this paper.
Not much in the way of motivic repetition/variation is apparent in the first movement. The rhythmic similarities of mm. 3 and 12 of the piano (right hand) is especially noteworthy because it stresses inversionally-related forms of the row at a point in the piece where a return to the opening material takes place. This dearth of motivic repetition/variation might be a manifestation of the "athematic" movement in composition prevalent in the late 1940's and early 1950's and of which Leibowitz was for a time a member. (2) Since the row, according to the athematicists, was omni- present (like an ostinato) there was no need to repeat rhythmic patterns and motifs. Indeed it was incumbent upon the composer to perpetually vary the rhythmic motives and patterns in order to maintain interest. (3)
Example 3: René Leibowitz, Five Pieces for Clarinet and Piano, Op. 29, Movement 1.
Reprinted by permission.
Five Pieces for Clarinet and Piano, Op. 29, no. 2.
As was mentioned earlier, the simultaneous appearance of the two types of inverted row forms (i.e., an I with RI) at the end of the first movement stresses the importance of inversions and inversions as a compositional device for Leibowitz. They are also an important factor in the second movement, where no complete statements of the row appear.
(Example 4). Instead, combinatorially-related hexachords from R0, RI3, I9, and P6 are woven together to create its fabric. (4) There is one exception: mm. 20-21 in the piano, where the first seven notes of I9 are used. The pitch structure of the second movement was derived from the process of pairing hexachords from inverted forms of the row with hexachords and from straightforward forms, similar to the pairing of straightforward and inverted rows in the first movement; Leibowitz therewith strengthens further the link between the first two movements of his Op. 29.
The second movement is cast in a ternary (three-period) form. The first period, mm. 1-8 inclusive, is further broken into two halves by virtue of the fact that in the first half thereof only the first hexachords of the four row forms mentioned above are found. The second halves of these four rows are deployed in the second part. There are two parts to each of the first part's two phrases as well, since the rate at which hexachords are introduced is, basically, one per measure. The rate at which twelve-tone aggregates are completed, one every two measures, creates a nearly constant "harmonic rhythm." That these aggregates are frequently distributed between the two instruments of the ensemble creates another close link to the first movement, wherein a similar procedure (i.e., tetrachordal rotation) was used.
In period two, mm. 9-16, the harmonic rhythm is accelerated slightly to an aggregate every one and a half measures. This acceleration of aggregate flow starts at the "negative" Fibonacci division (or Golden mean) of the movement. (5) The original harmonic rhythm returns slightly after the "positive" Golden mean has been reached. Dynamics also help to further articulate the "Golden sections" of this piece; the longest stretch (four measures) of quiet dynamics begins at the "negative" Golden section and ends exactly at the "positive" Golden section.
Period three starts out like a varied restatement (or recapitulation?) of the preceding two periods. Its opening two measures, with a sweeping ascent in the clarinet, are very similar to the opening bars of the work. The triplet chords in the piano are closely related to those found in mm. 4-5. All this material, however, is constructed out of the exact "opposite" hexachords. That is to say, the row materials first given to the clarinet now shows up in the piano, and that first found in the piano is now played by the clarinet in a kind of stimmtausch--rather like the idea of invertible counterpoint.
But period three is no mere restatement of previously heard materials. In mm. 20-22 an ascending "sequence" of trilled minor sixths appears in the clarinet while the piano accompanies with mostly triplet rhythms. Identifying the hexachords used in the piano part is easy: I9 and R0. The clarinet part, on the other hand, does not fit into any hexachordal pattern. There are actually three tetrachords deployed in the clarinet line of mm. 20-22. These three tetrachords (the first four pitches of P6, P3, plus, apparently, the last four notes of RI3) do not combine to create a chromatic aggregate as the two hexachords found in the piano part. But they do serve as a reminder of the tetrachordally-based first movement. It should be noted that the last tetrachord of RI3 contains the exact same pitches as the first tetrachord of P0. The first tetrachords of P3 and P6 are very similar, off by one note each (C and G), to the second and third tetrachords of P0. This could, perhaps, be a subtle reminder of P0 here at the end of the second movement that also hints at the departures from "traditional" row techniques we have found in this movement, and that will be even more apparent in the next. (More evidence for this will arise and be discussed at the appropriate point in this paper.)
Hexachordal organization is apparent in both instruments in the last two measures of the second movement with P6 and I9's second hexachords found in the clarinet and piano parts respectively. Once again the emphasis is placed upon inversional relations between "row forms" at the end of the piece. The first, third, fourth, and sixth notes of the clarinet part (fluttertongue) in the last two measures of the work form two compound descending minor sixths; this inverts the direction of the intervals found in the previous three-measure sequence.
Example 4: René Leibowitz, Five Pieces for Clarinet and Piano, Op. 29, Movement 2.
Reprinted by permission.
Example 5: René Leibowitz, Five Pieces for Clarinet and Piano, Op. 29, Movement 3.
Reprinted by permission.
Five Pieces for Clarinet and Piano, Op. 29, no. 3.
Nowhere is inversion as a process more important than in the central movement (Example 5 above). My attempts to analyse of the first two measures of the movement in terms of rows met with very little success until I noted that the clarinet's melodic line is comprised of an alternating intervallic progression of an ascending minor second, descending minor sixth, and then two falling minor seconds coupled with, appropriately enough, its inversion.
This process can be seen more clearly in the piano part: a rising minor second, rising minor sixth, ascending perfect fifth, and then a tritone (a non-inverting interval) appears in the left hand; the right hand has a descending minor second followed by a rising major tenth--which is equivalent to a falling minor sixth and, most likely, is used in order to avoid the inconvenience of crossing hands--a descending perfect fifth, and then a non-invertible tritone. Thus the right hand has the same interval progression
(second to third/sixth to fifth to tritone) as the left hand, but the intervals ascend in the right and descend in the left. In mm. 1-2 the clarinet part "fuses" two such intervallic importance of inversions and inversion as a compositional device for Leibowitz. They are also an important factor in the second movement, where no complete statements of the row appear progressions together. The clarinet part in mm. 5-6 is constructed in the same manner as that found in mm. 1-2; alternating ascending/descending minor seconds are followed by perfect fourths.
Leibowitz does not use the row in this movement at all. Rather, he relies upon the fusion of a sequence of intervals and its "reflection" for his pitch materials. Since the row displays inversional (I3) semi-combinatoriality, to abandon the row in the third movement and adopt the technique described above is merely an extension of the possibilities that were inherent in the work's basic materials.
Measure 3 is constructed in a similar fashion. The clarinet line is composed of two ascending intervals: a minor third followed by a minor second, and various types of "inversions" of this motive appear in the piano part. A falling major sixth followed by a descending enharmonic major seventh (A - A is equivalent to G - A) appears in the right hand of the piano on beat one. On the second beat, the intervals are a falling minor third preceded by what is in effect a falling minor second. The piano's left hand-part presents two ascending intervals (major sixth and major seventh) which are the same intervals as that found on the beat one of the right hand, but with "inversions" of their direction. Each of the four three-note groups in m. 4 is a collection of two thirds, one major and one minor. The clarinet, for example, has a minor third (G-B) and then a minor second (B-B). All the other trichords in m. 3 are similarly built.
Besides such inversionally-based passages as this there are measures in this movement, specifically, mm. 3, 5, 7, 8-9, and 11, wherein the twelve notes of the chromatic scale are partitioned into four augmented triads. Measure 3 is the first and most obvious instance of this, and it functions as a cadence. In m. 5, two augmented triads are embedded within the piano part. All four augmented triads are found in the clarinet part of m. 7-8, and in "all instruments" in mm. 9 and 11. The process of partitioning the total chromatic into augmented triads is combined with the intervallic inversion technique described above in the m. 8 clarinet part; Leibowitz develops these procedures by fusing them together at the "positive" Fibonacci division of the movement. This strengthens the connection between the third movement and the second, wherein important structural events also appeared at Golden means. The perfect fourth/tritone triads get fused with the intervallic inversion technique at the "negative" Fibonacci division of the piece.
A couple of other aspects of this third movement should be noted here before we press on to movement four. First of all, the sonorities heard in mm. 6, 12 (piano), and 10 (clarinet and piano), triads made up of a perfect fourth and a tritone, are, along with augmented triads, very important as references to the Op. 5 Four Pieces for Clarinet and Piano by Alban Berg. (I am getting ahead of myself; a full discussion of the
relationship of Leibowitz's Op. 29 to Berg's Op. 5 will be presented later.) But the augmented triads and the perfect/tritone chords are by no means merely non-structural references to Berg's Op. 5 in Leibowitz's Op. 29. Within Leibowitz's row (see Example 1a) an augmented chord is found between pitches seven, eight, and nine. Also, the chord composed of a tritone and perfect fourth is formed between pitches four, five, and six. Leibowitz thus constructed his row in such a way that other compositions can be "referenced" within a work based on it. Organic unity is nevertheless retained since the materials used to make these references are also part of the row.
Secondly, the third movement is in effect an oscillation between augmented triads and the "fourth chords" described immediately above. Augmented triads are used primarily as cadential devices in the first half. "Fourth chords" are generated melodically by the "oscillating intervallic progression technique" in the first half of the piece (mm. 5-6, clarinet part) and then used cadentially in mm. 10 and 12-14. Augmented triads are then subjected to intervallic oscillation at the outset (m. 8) of the second half of the piece. This produces a "triadic/procedural bow" form in this movement. If we compare the outer ends of the third movement, we see that they are either preceded or followed by a partitioning of the chromatic scale into augmented chords. Shortly after or before this, depending on what half of the movement is being looked at, the "fourth chords" we noted appear. This is again broken up by the appearance of augmented triads. The major third/minor third trichords, first found in m. 3, also participate in a bowing of procedures. This "triadic/procedural bow form" is illustrated in Example 6.
Example 6: The "Triadic/Procedural Bow" of Leibowitz's Op. 29 no. 3.
Five Pieces for Clarinet and Piano, Op. 29, no.'s 4 and 5.
Leibowitz's pitch derivation techniques are much less difficult to understand in the fourth movement than in the third (Example 7); it may be that this is an attempt to compensate for the complexity of "row" manipulations in the third movement, if one can indeed speak of rows in connection with the third movement at all.
The following forms of the row are used: I8/RI2 and P9/R3. In fact, the only part of the fourth movement that was at all puzzling in terms of rows used was the very first measure, where the piano presents what is in effect two augmented triads a perfect fifth apart. The first appearance of P9 is likewise interesting because only the first five notes thereof are presented in the clarinet part in m. 4. Only gradually does P9/R3 appear in its entirety. A five-note succession from R3, the reverse of the five-note succession from P9, is disclosed in mm. 6-7 of the clarinet part. P9 does not reappear until the piano plays its first hexachord in m. 9. Its second hexachord does not appear until mm. 11-12. It starts out in the piano and is then concluded in the clarinet part. Similarly, R3 is first stated in the clarinet in m. 10-11 and is then finished in the piano in mm. 11- 12.
All this is worth mentioning because of the way in which it implies a kind of arching of row forms. As we have seen, bow or arch form is used in the first movement. We also noted a "procedural arch" in movement three. The arching of rows here within movement four itself is most in evidence in the presentation of pitches 1-5 of P9 that then become pitches 8-12 of R3. The procession of 3/2, 4/4, and 3/2 meter signatures in mm. 5-6 further underscores the idea of arching. The distribution of notes in mm. 2-3 also produces a mirroring effect between the two bars.
Mirrors are at work in mm. 8-12 as well. If we compare the way in which RI2 is deployed in mm. 8-9 to the distribution of I8 in mm. 8-10, we see that they are the exact opposites of each other and registrally "frozen," as it were. A similar though elongated example of this comes in the last four bars of the piece, where the first hexachord of P9 (starting in the piano part in m. 9) becomes the last hexachord of R3 in mm. 11-12, and the first half of R3 (starting on the second third of beat two, m. 10, in the piano) becomes the last half of P9 in m. 11 (piano) and m. 12 (clarinet). The effect of this movement is that of a series of longer and shorter "mirrored" phrases.
Overall there are mirrorings between the second and fourth movements as well. Texturally they are quite similar. Only four rows are used in the fourth movement; four hexachords are used in the second. The more structured second and fourth movements serve as a kind of frame for the loosely knit third movement, wherein the treatment of the row is free at best.
But there is at least one commonality between the three inner movements of Leibowitz's Op. 29, namely the augmented triad. There is one in the fluttertongued clarinet line of m. 23 of the third movement. Augmented sonorities are nearly, as we have seen already, omnipresent in movement three. Another pair of augmented triads are superimposed in the piano part at the start of the fourth movement. The stress placed on augmented triadic sonorities within the three inner movements of Leibowitz's clarinet and piano pieces bind them together, and at the same time emphasizes bow-type constructional principles.
Connections exist between the outermost movements of Leibowitz's Op. 29 as well. The obvious use of complete rows occurs in movements one and five only (compare Examples 1 and 8). Furthermore, the end movements are the only ones in which P0, I0, and R6 appear. (RI6, which appeared in mm. 6-8 and 15-16 of the first movement, does not resurface in the last.) I do not believe, however, that the return of P0, I0, and R6 in the last movement serves to establish the functional supremacy or "tonicity" of the rows that were used to construct the first movement. If that had been the composer's aim, I suspect he would have kept using P0 until the end of the piece. Instead of doing this he introduces P6 in m. 19 and preserves it until the end of the movement. The fifth movement is thus linked to the second through the use of P6 (mm. 8-9, right hand piano, and again, both instruments, in mm. 19-21), as well as R0 in mm. 1-4.
But the last movement (Example 8) certainly has its own individual properties as well. For example, I6, unique to this movement, appears in mm. 6-7. The most striking thing, though, is mm. 15-17, where the piano part does not fit into a row. P0 is very plainly presented in the clarinet, but the piano part does not fit into any row sequence at all. This creates an effective link between the central third movement and the fifth.
Right at the end of the second movement, an incomplete and highly disguised reference to P0 was made in the clarinet part (mm. 20-22) before stating the last half of P6. Here, at the end of the entire composition, both the clarinet and piano participate in presenting a comparatively obvious P0 followed by three statements of P6. We should likewise note that C and G, the two pitches from the second and third tetrachords of P0 that were not, in movement two, shared by the first tetrachords of P3 and P6 respectively, are brought out in the left-hand piano part in mm. 18, 20-21 of the fifth movement. The "tonicity" of P0 is not brought out, but a kind of tritonal "root motion" at the end of both movements two and five link them together, implying a larger scale structure than might first be perceived in Leibowitz's Op. 29.
In fact, the entire fifth movement deals with tritones in one way or another. In the first seven measures, R0 gets paired with its retrograde I6. The "0-6" pairing implies tritonal relationships. In mm. 8-9, RI0 and P6 are paired together in the piano. Moving rhythmically parallel to each other and with lots of crossing of the two voices, they begin and end on the interval of a tritone. R6 and I0 are deployed, in the piano and clarinet respectively, in mm. 10-14. Thus the final tritonal relationships at the end of this movement are prepared for not only at the end of the movement but throughout the fifth movement as well. We should also note that the interval formed between the first and last notes of Leibowitz's row, D and A, forms a tritone.
Example 7: René Leibowitz, Five Pieces for Clarinet and Piano, Op. 29, Movement 4.
Reproduced with permission.
Example 8: René Leibowitz, Five Pieces for Clarinet and Piano, Op. 29, Movement 5.
Reproduced with permission.
Musical Links Between Alban Berg's Op. 5 and René Leibowitz's Op. 29.
Connections within individual movements and between the different movements of the Op. 29 are not the only kinds of linkages in which Leibowitz was interested, though. I believe that mm. 15- 16 of movement five are intended to allude to Alban Berg's Op. 5 Four Pieces for Clarinet and Piano. The piano part in m. 15 of the Leibowitz bears a striking resemblance to mm. 10-12 in the first movement of Berg's Op. 5, where the clarinet plays G in a rhythmic pedal point underneath static chords cast in a quintuplet gruppetto in the upper range of the piano (Example 9). Measures 15-16 of the Leibowitz are in 5/8--this is the only time this meter signature appears in the entire work--making the link between the two passages even stronger.
Example 9: Alban Berg, Four Pieces for Clarinet and Piano, Op. 5, Movement 1, mm.10-12.
ücke fur Klarinette und Klavier, op.5. Copyright 1924 by Universal Edition. Copyright renewed.
Alban Berg 4St
All Rights Reserved. Used by Permission of European American Music Distributors Corporation, sole U.S.
and Canadian agent for Universal Edition.
It should be noted as well that Berg's chords here are made up of interlocking tritones and perfect fourths. This same chord type was discovered in the third movement (mm. 6, 10, and 12) of Leibowitz's Op. 29. Augmented triads are very conspicuous in the middle three movements of the Leibowitz, particularly in the third. Augmented chords also appear in the Berg. For example, an augmented triad appears in the last two measures of the Op. 5 second movement in the right hand of the piano, functioning cadentially just as it did in the second and third movements of the Leibowitz. Another augmented triad is arpeggiated in the left hand at the outset of the Op. 5 third movement. The initial sonority of Berg's last movement contains an augmented triad. (Examples 10a-c) Two augmented chords a perfect fifth apart are made by the B of the clarinet in m. 2 of the Berg's fourth movement; we have heard this sonority in the Leibowitz, i.e., at the outset of the fourth movement. (6)
Example 10a: Alban Berg, Four Pieces for Clarinet and Piano, Op. 5, Movement 2, mm. 7-9.
Example 10b: Alban Berg, Four Pieces for Clarinet and Piano, Op. 5, Movement 3, mm. 1-2.
Example 10c: Alban Berg, Four Pieces for Clarinet and Piano, Op. 5, Movement 4, mm. 1-2.
Example 11: Alban Berg, Four Pieces for Clarinet and Piano, Op. 5, Movement 1, mm. 6-7.
Example 12: Alban Berg, Four Pieces for Clarinet and Piano, Op. 5, Movement 3, mm. 15-18.
Three other references to Berg's Op. 5 in the Leibowitz should be noted here as well. The arpeggiation of all four augmented triads that occurs in the seventh measure of the clarinet part in Leibowitz's third movement is highly reminiscent of the clarinet's arpeggiation in m. 7 of Berg's first movement (Example 11 above). The final measure of the second movement of the Leibowitz should be compared to the last four measures of Berg's third movement (Example 12 above). The rapid descents of the clarinet lines (using fluttertongues) are similar to one another. The leaping piano parts also bear a close kinship to one other. Finally, the ends of both compositions need to be compared. If we look at the piano parts of both works we will note the appearance of what are in essence "major-major seventh" chords. Berg (Example 13 below) asks the pianist to silently depress the keys necessary for a C major-major seventh chord to resonate. Leibowitz, in his last system constantly bangs out thirdless major-major seventh chords in his piano part. The first of these takes C as a "root," as does the last one. Note should also be taken of the fact that Leibowitz's two C major-major seventh "chords" are octave transpositions of one another. (7)
Example 13: Alban Berg, Four Pieces for Clarinet and Piano, Op. 5, Movement 4, mm.17-20.
A subtler link between Berg and Leibowitz's compositions for clarinet and piano is the use of bows and arches as a formal device. As we have seen, Leibowitz is very overt in his use of arching structures in the Op. 29. Berg frequently used bow form in his later works. Douglas Jarman claims that the Op. 5 was the last of Berg's "major" works to avoid the use of a large-scale structural retrograde; (8) I take issue with that. A case can be made for the presence of an at least incipient bow form in Berg's Op. 5. (9)
Berg's first movement begins with a clarinet solo that contains within it a disguised chromatic circling about the tone G. The fourth movement ends with a slightly accompanied version of the same kind of clarinet line (compare Examples 13 and 14). Thus the outer ends of the cycle are similar. Furthermore, octave transpositions of the same note, A, begin and end the piece. Comparing bar five of the first piece with the fifteenth and sixteenth measures of the final one reveals several motivic shapes common to these measures, particularly the chromatic grace-note apoggiatura figures that appear first in the left hand of the piano part in m. 5 of the first movement, and then in the seventeenth measure of the clarinet part in the fourth movement. The sextuplet figure that appeared on the last beat of the clarinet part in the first movement's fifth measure reappears in the left hand of the piano in both mm. 15-16 of the fourth movement. The dotted eighth-note and sixteenth note figures stay in the left hand in both movements. The clarinet tremolo of m. 6 in the first movement reappears in the right and left hands of the piano in mm. 15-16 of the fourth movement (Examples 15a-b). After this, stretches of musical material in which major thirds and augmented triads are prominent. On the one "side" of the center of the work--which is the first measure at the top of p. 7 (i.e., m. 9 of the third movement) in the printed score--this occurs five measures away from the center. On the "other side" it occurs nine measures away from the center (Examples 16a-b). Movement 2 begins with major thirds in the piano; the 6/8 measure (m. 35) of the third seems to me like a conscious recall of movement 2. An augmented triad ends movement 2; another one starts the third. An augmented triad with an added major seventh built on a G "root" appears in the right hand of the piano in mm. 5-6.
Example 14: Alban Berg, Four Pieces for Clarinet and Piano, Op. 5, Movement 1, mm. 1-2.
Example 15a: Alban Berg, Four Pieces for Clarinet and Piano, Op. 5, Movement 1, m. 5.
Example 15b: Alban Berg, Four Pieces for Clarinet and Piano, Op. 5, Movement 4, mm. 15-16.
Example 16a: Alban Berg, Four Pieces for Clarinet and Piano, Op. 5, Movement 2.
Example 16b: Alban Berg, Four Pieces for Clarinet and Piano, Op. 5, Movement 3, mm. 9 -14.
The resulting structure reveals a subtle retrograding of materials in Berg's Op. 5 (Example 17). Berg, I believe, consciously used retrograding in his Op. 5, but went to extraordinary lengths to disguise it, to create the feeling of these pieces being short, seemingly unrelated aphorisms. Use of large-scale structural devices such as retrograding in what were supposed to be small-scale musical expressions might well have been what Schoenberg objected to in Berg's Op. 5. (10)
III. Other Evidence.
All of Leibowitz's possible references and allusions to Berg's Op. 5 that have herein been discussed are, admittedly, very highly developed and may even seem fortuitous. Three pieces of evidence should, however, be considered carefully before we make up our minds all together as to whether or not these supposed links between the Berg and Leibowitz clarinet and piano pieces were part of Leibowitz's original intentions or not.
Example 17: The Implied Bow Form in Berg's Op. 5.
First of all, at least one other scholar has commented on the highly referential nature of Leibowitz's compositions. Jan Maguire, in the second of a two-part article published in Tempo, notes that "Leibowitz's op.8 was inspired by Schoenberg's op. 25, although [the Leibowitz] more resembles [Schoenberg's] op. 33b in style." (11) In the opera Todos Caeran, Maguire sees Leibowitz reaching the very essence of Schoenberg and Webern's "technique of permanent [or perpetual] variation with the most economical means." (12) Maguire also identifies several "situational" references to operas by Puccini, Donizetti, and Wagner in Todos Caeran. The characters of the three counter-revolutionaries are, according to Maguire, "derived from the three mandarins Ping, Pang, and Pong in Puccini's Turandot, and they have similar names, Pico, Poco, and Pongo." (13)
The second act of Leibowitz's Todos Caeran:
opens much like the third act of Don Carlos, with the dictator alone in his study, at dawn, singing in a moving bass aria, of how his mistress never really loved him. He continues with the same words sung by Hans Sachs in Die Meistersinger, "All is folly." The two women [i.e., a revolutionary and the dictator's girlfriend] enter and argue, providing a contrast which negates his mood. [Two] captured revolutionaries are brought in, and the dictator pardons them. However, just after an extremely cleverly written sextet, along the lines of the one in Lucia di Lammermoor, in which each character expresses a different thought underlined by a different melodic line, one of them grabs a revolver and kills the dictator. (14)
In the dictator's funeral scene, the chorus of mourners and ringing church bells are, according to Maguire, reminiscent of Il Trovatore. (15)Die Meistersinger is referred to once more "at the end of the scene of confusion at the end of the first act, when the crowd leaves little by little, the orchestra dwindles, the three enigmatic characters cross the stage in silence, and the curtain closes on one loud [fortissimo] chord." (16) Maguire then explains that Leibowitz's allusions to the standard operatic repertoire are:
[parodies], but they are also intended in a broader sense to imply all opera itself, not only its passions but also its structure, its very existence, and to stand it up against the absurdity of the contemporary political situation, and the pathos of the humanity involved. (17)
The second piece of evidence we must weigh is that there was at least one time when Leibowitz and Jacques-Louis Monod, one his composition students in the 1950's, were involved with Berg's clarinet and piano pieces. In 1951, Dial released a recording of music by Berg, including Irene Joachim's rendition of an orchestration of Berg's Op. 2 songs. Leibowitz orchestrated the original piano part for this recording and conducted the ensemble. Also included on the "old Dial 15" are Berg's Op. 5, performed by clarinetist Earl Thomas and Monod at the piano. It is likely that Monod consulted with Leibowitz during his preparations to record Berg's Op. 5; Leibowitz might even have attended rehearsals and coached the ensemble. If so, he would certainly have had an opportunity to familiarize himself with Berg's score at that time.
Leibowitz, furthermore, had other "irons in the Bergian fire" as well. He conducted the recording of Berg's Op. 13 Kammerkonzert that was released on Dial, album 9. He also published an important analytical paper on Berg's then unpublished Op. 4 Altenberg Lieder in 1948. (18) The Dial projects are important for setting a precedent for Leibowitz's revising music originally composed by Berg. Orchestration of this type is very much a kind of revisional work. This might well have been part of his motivations to model another one of his works, i.e. his Op. 29, on the music of Berg.
The timeline unfolds nicely: first comes a paper on Berg's Op. 4; then the "orchestrational revision" of Berg's Op. 2 is made; the revised Op.2 and Berg's Op. 5 are then rehearsed, recorded, and released on Dial 15; Berg's Kammerkonzert is also recorded by Leibowitz for Dial. Shortly thereafter (1952) Leibowitz composes his own Op. 29 Five Pieces for Clarinet and Piano.
The "revisions" of Berg's music are symptomatic of a general way of proceeding in Leibowitz's compositional activities. During a telephone conversation (22 June, 1994), Prof. Monod himself told me that Leibowitz very often used music by the second Viennese school, Webern and Schoenberg especially, as models for his own works. (19) Frequently the result bore a striking resemblance to the original, too. For example, Leibowitz's Flute Sonata contains, according to Prof. Monod, references to the second movement of Webern's Op. 27 Piano Variations. Webern's Opp. 16 and 24 are alluded to in Leibowitz's Opp. 2 and 12 respectively. Prof. Monod also suggested that I compare the opening measures of Leibowitz's Op. 29 to the second of Schoenberg's Op. 48 songs.
Sure enough, there is a close kinship between the two works (compare Example 18 and 1b). The rhythms used in the first measure of Leibowitz's piano part match Schoenberg's exactly. Both Leibowitz and Schoenberg's piano parts, furthermore, begin in the lower parts of the instrument's range. The first two pitches played by the clarinetist in Leibowitz's Op. 29, no. 1, are the same as the first two sung by the voice in Schoenberg's song. The last few measures of Leibowitz's Op. 29, no. 1, are also very similar to the beginning of Schoenberg's Op. 48, no. 2.
Third, we know from passages in his theoretical prose that Leibowitz, at least two years before the project for Dial records had been completed, considered Berg's Op. 5 to be a highly significant work. In the tenth chapter of Leibowitz's Introduction a la Musique de Douze Sons (published in 1949), he lists a number of works from the Second Viennese School that were important as precedents to the new "athematic" generation of twelve-tone composers:
[...] We find a number of their pre-dodecaphonic works that we can call athematic. Of Schoenberg's works: [opp. 11, 16, 17, 19, and 22]; Webern's: [opp. 10 and 11]; and of Berg's: some of the Songs on Picture Postcard Texts by Peter Altenberg for Voice and Orchestra op. 4, and the Clarinet and Piano Pieces, op. 5.
All of these display - to a very subtle degree - certain athematic characteristics. (20)
Thus Berg's pieces were seminal works for the athematic movement of which Leibowitz was at that time a staunch member. Leibowitz could very easily and naturally have used Berg's Op. 5 as a creative basis and point of departure for a work of his own scored for clarinet and piano. It is also interesting to see that the other influential work on Leibowitz were Berg's Op. 4 songs for voice and orchestra. another work which Leibowitz revised.
The most compelling link to Berg is made by the very complex, even abstruse, way Leibowitz treats the row in his Op. 29, if a passage from Leibowitz's still unpublished "Treatise on Twelve-Tone Composition" is taken into account. Justifying his not including examples from Berg's works in his Treatise, Leibowitz explains:
the omission is due to historical circumstances: the awareness of the functional structures of twelve-tone music is a comparatively new acquisition. It will be noticed that the vast majority of the examples are taken from works later than 1930 (or even 1935). Berg died in 1935 and he composed comparatively few twelve-tone works. He was still at the first--we might call it the empiric stage of twelve-tone composition and he did not have time, alas, to participate in the awareness of which we are speaking. (21)
Leibowitz's use of the word "empiric," which is defined in The American College Dictionary as "depending upon experience or observation alone, without using science or theory," (22) reveals that the compositional procedure in the Five Pieces was influenced by the perception of Berg's historical position (i.e., being stuck in the "unsystematic" stage of composition with the twelve tone series). For Leibowitz, Berg's use of the row was, due to his early and tragic death, to remain forever empiric. The singular manner in which the row is used in Leibowitz's Op. 29 is thus an "artist's conception," or portraiture, of Berg's "methods" of writing twelve-tone music.
The reason for the allusion to Schoenberg's Op. 48 no. 2 is also revealed in the above passage from Leibowitz's Treatise on Twelve-Tone Composition as well. Berg was dead before the "systematic" compositions of Schoenberg and Webern were written. The title of the poem set in Schoenberg's Op. 48 no. 2 is "Tot," or Death. Since the third of Schoenberg's Op. 48 songs is analyzed in Leibowitz's chapter on small song forms in his Treatise on Twelve-Tone Composition, (23) it is reasonable for us to conjecture that in 1950, when Leibowitz was writing the Treatise on Twelve-Tone Composition, and two years before he composed his Op. 29, Leibowitz had some opportunities to become familiar with the other songs contained in Schoenberg's Op. 48.
Example 18: Arnold Schoenberg, "Tot," Op. 48, no. 2, mm. 1-8.
Reproduced with permission.
Leibowitz has an expressive reason for alluding to Schoenberg's songs in his Op. 29--to lament the premature demise of Alban Berg. Leibowitz's Op. 29 can be thought of as a prelude followed by four highly "Bergian" pieces. The prelude, movement 1, frames a very "systematic" use of the row (mm. 3-14) between passages alluding to death, creating a kind of cradle for the middle measures of the first movement. The next four movements of his Op. 29 contain references to Berg's Op. 5 within a portraiture of Berg's "empiric" ways of composing twelve-tone music. In his Op. 29 Leibowitz presents a vision of Berg, who, imprisoned in death, remained forever untouched by the then new "athematic" movement of twelve-tone composition that began in the middle of the 20th century.
To end, I will repeat the truism stated at the outset of this paper: appearances are frequently misleading. Leibowitz certainly "covered his tracks" very well by composing his Op. 29 in the way that he did. However, with a little luck and a lot of diligent digging in the right places, we have unearthed substantial links between Berg's and Leibowitz's pieces for clarinet and piano. This does not, by any means, lessen the impact of Leibowitz's composition. Rather it shows the remarkable subtleties that Leibowitz imagined and employed in his homage to Berg. It also demonstrates how influential Berg's music was on Leibowitz and the rest of the "athematic generation" of dodecaphonic composers coming of age in the late forties and early fifties.
1. A perusal of mm. 1-2, however, does not reveal a straightforward statement of the row (see Example 3). A precedes G in the right hand of the piano in the first half of m. 2; in the second half G and A are played simultaneously. It is only after the clarinet begins that the true P0 form of the row is played. This was done, I believe, to underline the introductory nature of mm. 1-2.
2. In Chapter 13 of his Introduction à la Musique de Douze Sons Leibowitz presents a discussion of the "New Generation of Twelve-Tone Composers." In it he names the principal personalities involved in the "athematic" movement, including himself. He also presents analyses of several works representative of the new dodecaphonic generation (not all of them "athematicists") and gives a list of compositions by the Second Viennese School that served as precedents for the athematic idiom. Introduction à la Musique de Douze Sons (Paris: L'Archive, 1949): 250-270.
3. For Leibowitz and his fellow "athematicists," incidentally, redundancy was to be avoided in not only the rhythmic domains of music; melodic processes, such as canon and fugue, as well as variations, were also banned. In the tenth chapter of his as yet unpublished "Treatise on Twelve Tone Composition," which treats of canon, fugato, and variations, Leibowitz states that the use of such processes in twelve-tone music is redundant because "by definition, every twelve-tone piece [...] is, in the last analysis, simply a succession of variations on a basic series," and "since the functional unity of a twelve-tone work is conditioned by the use of a series of intervals, to use a type of writing like the canon, for example, now seems something of a tautology to us." "Treatise on Twelve-Tone Composition:" 82-83.
4. The first hexachord of R0 is the retrograde of the last hexachord of P6. Similar relationships exist between the first hexachords of I9 and RI3. The dashed lines in the first period of Example 4 show these connections.
5. The Fibonacci division, "Golden mean," or "Golden section" of any piece of music can be determined by multiplying the total number of measures by 0.618. For example, the "Golden mean" of a composition that shapes 250 measures would be approximately at m. 155 or 156 (250 x 0.6182=154.6). The "negative Golden mean" can be derived by multiplying the total number of measures by 0.382 (1-0.618=0.382). Thus the "negative Golden mean" of our hypothetical 250 measure composition would therefore be at m. 95 or 96, since 250 x 0.382=95.5.
The "Golden Section" has been demonstrated to be an important factor in the creative methods of such 20th-century composers as Claude Debussy and Bela Bartók. While I have not found any evidence to support the notion that fibonacci ratios were used by Leibowitz, neither have I discovered any that leads to the opposite conclusion.
6. For a fuller explanation of the importance of the augmented triad in the development of the music of Arnold Schoenberg and Alban Berg see my "Contextual Analysis of Arnold Schoenberg's Quintet for Woodwinds and Horn, Op. 26," (Master's thesis, University of Illinois at Urbana-Champaign, 1991): 83-90.
7. It is interesting to note the very close kinship of Berg's chords (that comprised of two augmented triads a perfect fifth apart, and the silent major seventh) to two chords found in Schoenberg's Op. 19 piano pieces. Several instances of Berg referring to Schoenberg's "aphoristic" music around the Op. 19 have been identified by various writers. This could well be another instance of Berg lifting material out of the works of his teacher/mentor, and placing them into his own music. Leibowitz either inadvertently, or consciously refers to Schoenberg's music, as well as Berg's, in his Op. 29.
8. Jarman adopts the term "major work" in order to exclude the song "Schließe mir dei Augen beide" and the Canon Berg composed for the Frankfurt Opera from the list. Douglas Jarman, The Music of Alban Berg (Berkeley, Calif.: University of California Press, 1985): 42, 185.
9. I first discovered this subtle arching of structural elements in 1989, while writing a paper on the Berg Op.5 for professor Paul Martin Zonn's graduate theory seminar at the University of Illinois.
10. Together with the Op.4 Songs on Picture Postcard Texts by Peter Altenberg, Berg's Vier Stücke für Klarinette und Klavier was the cause of the first major disagreement between Schoenberg and the younger composers.
11. Jan Maguire, "René Leibowitz (II): the Music," Tempo 132 (March 1980): 2-10; the passage cited appears on p. 3. The first part of Maguire's article, "René Leibowitz (I): the Man," appeared in Tempo 131 (February, 1980): 6-10.
12. Ibid., 7.
13. Ibid., 8.
15. Ibid., 10.
18. "Alban Berg's Five Orchestra Songs, Op.4," The Musical Quarterly 34(1948) no.4:487-511.
19. Webern's Strongest Readers, my soon-to-be-completed doctoral thesis, explores the relationship of Leibowitz's 1939 Ten Canons for Woodwind Trio, Op.2, and Webern's Latin Canons, Op.16, no.'s 1 and 3, as well as other selected works by Ernst Krenek, Henri Pousseur, and Franco Donatoni modeled after compositions by Webern (especially his Opp. 1, 9 no.1, 24, and 27).
20. [...] Nous trouvons en effet parmi leurs uvres prédodécaphoniques un certain nombre de partitions que nous avons le droit taxer d'athématiques. Ainsi de Schoenberg: [opp. 11, 16, 17 19, et 22]; de Webern: [opp. 10 et 11]; de Berg: certaines deMélodies avec orchestre, op. 4, et les Pièces pour clarinette et piano, op. 5. Toutes ces témoignent--à un degré tres poussé--de certaines caracteristiques athematiques. Leibowitz, Introduction à la Musique de Douze Sons (Paris: L'Archive, 1949):266.
22. The American College Dictionary, C.L. Barnhart, ed (New York: Random House, 1967):394.
23. Leibowitz, ibid., 91-92.