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Schoenberg Piano Piece op. 33b

In the context of cultural and social chaos in European history that had resulted from the WWI, Schoenberg developed the twelve-tone method and composed almost exclusively with it from 1923 until his death in 1950. (Schoenberg struggled with the pre-conceptions of the method even before the war, but the active formalization and adoption of the method took place after the war.) The method’s rejection of the tonality and traditional forms established before along with its invention of new sound and form is presumably Schoenberg’s own artistic reaction to the tumultuous and cynical social and cultural mayhem of the time.1

Written in 1931 during a stay in Barcelona, Schoenberg’s Piano Piece op.33b is considered as a mature, -yet still developmental- work of the 12-tone method until its full fruition in 1936, and along with the Piano Piece op. 33a, written two years earlier, demonstrates how far Schoenberg had developed his serial twelve tone system by the 1930s.2 It is the last piano serial piece the composer had written which shows a subtle mastery of the method.3 However, it is ignored in concert halls and music theory literature, receiving only a partial attention compared to surrounding works such as 33a, Suite, Variations for Orchestra, Violin Concerto, and third and fourth Quartets, and it had been criticized by theorists who found the deviations from the strict presentation of the 12 tones inconsistent and self-refuting of the method, with remarks such as the following statement, “…the row usage reveals Schoenberg’s inability to accept the limitations imposed by an ordered system.”4 However, as the following analysis will show, such deviations are not due to such flaws in the system, but are likely intentional as a part of strategic design that is consistent with Schoenberg’s style.

The Piano Piece op.33b utilizes only four different row forms -PE, I4, RI4, and RE, derived from two distinct rows ordered forward and backward,- but achieves much complexity and many dimensions of structure and sonority in various combinations of the hexachord collections. In this analysis, the design and characteristics of the piece will be examined on two levels: 1) On macro level, the form of the piece and the rows used will be illustrated along with the relationship between chosen row forms and formal structure, and 2) on micro level, how partitioned sets of pitch groupings of two/four and three, along with stylistic traits of different articulations, dynamics, and moods support the formal scheme will be analyzed. In conclusion, the analysis of the form and features will reveal Schoenberg’s intended compositional style of comprehensive and multi-dimensional aspects of the piece, which are achieved by the organizations of aggregates that encompass varying fragmentation of the rows in different sections.

The form of the piece can be interpreted as two parts with a coda or three parts consisting two main bodies and a third minor body. Adopting the two-part with a coda interpretation for simplification sake, the following is the summary of the general form:


Pt1: Pt2:























Pt1: Pt2: Coda:





















The rows used to generate the form above are PE, I4, RE, and RI4, which can be summarized in the following way:

PE: (HexAp/r)E15398 (HexBp/r)6T7402 : RE

Vertical ics: 5 1 5 3 3 1 3 5 1 5 3 1

I4: (HexBi/ri)42T067 (HexAi/ri)958E31 : RI4

The two rows, related at T3I (adding the vertical dyads produce 3 in mod12) as visible in the alignment above, produce aggregates with the vertical collections of the two hexachord combinations. This feature of the formation of the aggregates is the main unifying factor in the structure of the piece, as it is ubiquitous throughout the work in the organization of the rows.

The two sections, I and II are defined by the emphasized combinations of row forms that are particular to the larger divisions. Section I is marked with the usage of PE and I4 in the beginnings of each parts (m1-4 of Part 1 and m21 of Part 2,) whereas Section II starts with RE and RI4 combinations in the beginnings of both Part 1 and Part2 (m32-36 of Part 1 and m52 of Part 2, although not as straightforwardly.) Furthermore, such combinations within each section are more frequent than any other combinations (Section I’s PE/I4 combinations: m1-4, m10-11, m21, m25-29, and Section II’s RE/RI4 combinations: m32-41, m49-53, m55-56,) giving each section a distinctive harmonic character different from each other. The different harmonic language resulting from the different combinations of the row forms are inevitable and can be seen more clearly from the earlier alignment of the two rows that generate the four row forms used. The vertical intervals resulting from the alignments are of ic 5,1,5,3,3,1,3,5,1,5,3,1, reading from left to right for PE and I4 combination, which when read from right to left for RE and RI4 combination, will produce a very different order and intervallic quality, resulting in a distinctive harmonic character.

The Coda resembles Section I’s Part 1 greatly and thus can be interpreted as a truncated recap of Section I, in that it uses the same row combination of Section I, PE and I4, and because the A theme melody is stately almost verbatim over m57-60 (right hand in m57-58 and the bass line in the left hand in m59-60,) but its brevity and lead to the closure of the piece, along with the different metrical marking of 4/8, a hybrid of the two other meters previously used (combining the denominators of 2/4 and 6/8,) and rhythmic similarity to Section II’s Part 1, distinguishes this segment from the other two sections, suggesting a comprehensive and concise closing characters of an appendix to the two preceding main sections. Thus in summary of the form and the rows used, there are two large main harmonic areas, labeled Section I and II, that are distinguished by the different emphasis of two main combinations of row forms, PE/I4 and RE/RI4.

The delineation of the sub-sections within these larger sections I and II is clarified by the different tempi markings and the time signatures, 2/4 for Part 1 and 6/8 for Part 2 of both I and II. As the meters precursor, the sub-sections are further clarified by the dyadic/tetrachordal grouping and partitioning of pitches in Part 1, and triadic divisions in Part 2. The structural importance of dyadic grouping can be first seen m.1-3, the beginning dyad [E1] outlines ip10 as does the ending dyad [02] of the row in the bass, and these bracketing gestures are also seen in m3-5 in I4’s beginning of the melody, [T0] and the cadential [31] in the accompaniment. In fact, ip 10 delineates all the beginnings and ends of phrases in Part1 of both Section I and II, either as +10 or as -10.

The dyadic groupings are further grouped into tetrachord groupings in Part 1, and resulting tetrachord sets further distinguishes Part 1 from Part 2. In the opening measures, PE starts with the falling motives of [E1] and [6T], forming (0237) when combined as [6TE1] along with the accompanying tetrachords, broken into two falling dyads, [53 & 98] and [74 & 02] which form (0146) and (0247) respectively. The opening accompaniment set (0146) in m1 returns in the tetrachordal partitioning of the melody in m.17 and 18, as [02 & 89] and [67 & 31], closing the Part 1 of Section 1. It is also interesting to note that the melodic sets in m17-18, [8902] and [1367] are T3I related, which is the relationship of the two rows PE & I4 (or RE & RI4.) Further cohesiveness of Part1 can be seen in the T10 relationship of opening [3589] in m1 accompaniment and [1367] in m18 melody, echoing the ip10 emphasis of beginning and end of Part1.

The set (0146) in fact plays a dominating role in defining Part I of Section II, in that the partitioned melody of m32-35 and m39-40, [20 & 89], and of m37-38, [13 & 76] all form (0146.) Furthermore, in the Coda, which is the area that summons the recap of A from Section of I and rhythmic similarity of a of Section II, (0146) is ubiquitous as [9802] –right hand- and [3176] –left hand- in the outer voices of m61-63, and as the half notes in m64-68, spelling [9802] and ending the piece. The opening melody set (0237) in m1, comes back verbatim in the beginning measure 57 of Coda, with only a slight alteration in the beginning rhythm and is followed in m59’s bass by [T0 & 89] which is the latter melodic part of A theme from Part 1 of Section I. The set recalled is (0124), which is another defining tetrachord of Part 1, along with (0146), (0135) and (0248).

The tetrachords (0124), (0135), and (0248) are first partitioned in m3-5 as [T0 & 8E] in the melody, and as [42 & 67] and [59 & 31] in the accompaniment. Besides the reappearance in Coda mentioned earlier, (0124) returns within Part 1 of Section I, in m12-16, in the melody, as [53 & 74] and [E8 & 0T], where [3457] is related to the original set [8TE0] at T3I. (0135) reappears in transformed sets of [91 & E8] in m12 and as [26 & 47], where the latter represents a different ordering of the original [2467] in m3 and is related to [89E1] at T3I. [1359] or (0248) returns in m15 with the same pitches but shuffled as [53 & 91], further drawing coordination of the A theme in m1-5 and A’ in m11-16. (0135) and (0248) further reappear in Part 1 of Section II, in m32-34 accompaniment, where from the hexachord sets [1E8359] in m32-33 and [20476T] in m33-34 can give both (0135) and (0248) when partitioned in different ways; [1E98] and [2746] for (0135) and [1359] and [206T] for (0248). Lastly, consistent with the reappearance of other tetrachords such as (0146), (0124), (0237) in Coda, (0135) and (0248) also appear in Coda, in m57 accompaniment, as [1530] taking the upper notes and the [0] for (0135) and as [42T0] taking the outer notes and the [0] for (0248). Thus, as demonstrated by these examples, the dyadic groupings that are further grouped into tetrachordal sets of (0146), (0135), (0248), (0237), and (0124) reappear in Part 1 areas of Section I and II and in Coda which resembles parts of Part 1 of both Section I and II.

Along with the observations of the dyadic/tetrachordal groupings of Part I areas of the composition, the rhythmic similarity in the accompaniment and the lyrical trait in the melody of Part I areas further strengthen the correspondence of the areas in different sections. The distinctiveness in dynamic schemes also help to separate the these areas of Part 1 from Part 2, in that Part 1 is generally characterized by soft dynamics and lyrical themes, and contrary to that, Part 2 areas feature jagged, masculine lines and louder dynamics overall.

Before Part 2 is introduced for the first time in Section I, m19-20 function as a pivot area, that may be viewed both as part of Part 1 and Part 2. It can be argued to be an end of Part 1, as it is still in the meter, but it is also introductory to Part 2 in character, especially by the triplet grouping which is prevalent in the opening of Part 2. It is a special area that spells out not only all the rows used in the most clear, concise forms, but that also presents the two and three groupings of structural dyads, triads, and tetrachords, viewed horizontally, vertically, and in combination of the two dimensions, crisscrossing across the rows. For example, the dyad [E1] presented vertically in m19, show ip10 emphasis discussed earlier, along with all the dyads on the beats of m19-20, and the tetrachords formed by the combination of vertical and horizontal dimensions also recount the important tetrachords discussed earlier. For example, in m19, combining dyads [E1] and [89] horizontally gives (0135) and combining dyads [35] and [89] vertically gives (0146). The triadic groupings of four horizontal lines spell out all the relevant trichords, both discrete -(026)(016)(014) and (024)- and remaining -(013)(036)(037) and two more (024) and one more (026)- from the row, and makes a cohesive segue into Part 2 that emphasizes partitioning of three pitches for a phrase and accompaniment gestures.

The triadic grouping appears not only in one dimension but in versatile combinations, as different trichord groupings of beginnings and endings of phrases in Part 2 of section I produce discrete trichord collections of two rows at the same time; in m21, one grouping [E13][589] –(024) and (014)- yield Hex Ar, whereas another grouping can be seen as [E15][398] –(026) and (015)-, which spell Hex Ap. Similar gestures are seen at beginnings of m25, m27 (a bit after beginning of the bar), and in m28 beginning of I4/PE. Such ambivalent feature of the trichord partitioning result from the invariant property of the (026) and (024), which Schoenberg made use of in his choices of notes in constructing Part 2 phrases and characterization of this area. As briefly mentioned earlier, the discrete and the remaining trichords of the rows contain three (024)s and two (026)s, allowing invariants to occur in different row forms and such feature is exploited in Part 2 of both Sections I and II.

The (024)s appear ubiquitously in various pitch class sets in Part 2 areas, most distinctively in the eighth triplet grouping of the main themes of the areas, giving the sub-sections a prevalent whole-tone sonorities. For instance, in m21-22, the melody grouped in triple notes spell (024) by [E13] [642] and [1E9]. In fact, whenever there is a distinctive triplet grouping of the melody, it outlines (024), as also evident in the bass melody in m23-24 as [E13][642][024][135] –where the two latter sets are accentuated with tenuto/staccato articulations,- in the right hand triple figures in m25-26 as [T02][E13][246], and in outer voices of m28-29 as [426][9E1][135] in the right hand and as [E19][642][246] in the left hand. The accompaniment is also saturated with (024) both in direct and indirect ways in this area; in m21, the outer triple grouping of pitches in the left hand give [240] and [9E1], where as in m22 [246] and [351] are in the inner triplet grouping of the accompaniment, and similar partitioning can be seen throughout the area. The prevalent (024) sonority is evident also in Part 2 of Section II area, (although not as emphatically since the corresponding segment is truncated and has less ubiquitous triplet grouping compared to Part 2 of Section 1,) as seen in the bass melodic lines of m52-53 as [E13][642][20T], in m54 right hand triple figures as [E13][642], in m55 as [135][1E9] and in m56 as extractable subsets of [0T24] in the accompaniment that has reverted to duple/quadruple grouping to segue into the Coda.

The formation of (024), clearly a structural characteristic unique to Part 2 areas, is a major reason for the seemingly unordered usage of the rows or discrepancies in sequences of the rows. In Part 2 areas especially, the row forms are not presented straightforwardly but rather appear to be grouped in aggregates in fragmented forms. For example, in m22-24, tracing the 12 notes in the orders dictated by different row forms are not sequential either horizontally or vertically, but rather bits of the rows are fragmented or looped around in various direction. In m22 left hand, for example, the RE row starts out with 2047, but to trace the rest of the sequence, jumps to the end of the bar to T, loops back to 6 and follows the rest of 89351E. Similar tangling of the lines are seen in m23, 24, 52, 53 and 54, where the aggregates of two hexachords are always preserved to indicate rows used, even though the strict orderings of the rows are not observed, in the process of trichordal fragmentations of (024)s and others.

Delving further into the aspect of aggregate formation in the piece leads to the discussion of the hexachords which illustrates the importance of (024) sonority. The hexachords are all set class (013579) with the interval vector <142422>. The vector reveals that the set has intervallic emphasis of ic2,4,6, corresponds to the prevalent formation of (024) sonority, as seen in the previous analysis of Part 2 areas. Such sound of whole tone or (02) is also clarified in the observation of the adjacent intervallic series of the row, or in the horizontal dyadic division of the row, which reveals that the dominating dyadic intervals are ic2 and 4. It is interesting to note, however, that the vertical dyads resulting from the alignment of the two rows, will provide intervals of ic 1,3,5, only, which are complement ics of the horizontal dyads. Such observation is not accidental, but carefully designed and intended property of the hexachords in creating the row and picking the particular rows, and such intervallic class complementary and comprehensive characteristic is shown most directly in Part 2 areas as horizontal sonorities are dominated by (024)s and the vertical alignment give many ic1,3,5 intervals.

So far, overall form of the piece, rows used, and the distinctive compositional features of different Sections were examined. As discussed, the structure of the piece is intertwined with the combinations of different row forms used which give different harmonic schemes for the two main Sections. Each Section contains two parts, Part 1 and 2, which differ from each other by general grouping of the pitches (duple/ quadruple vs. triple,) meter markings (2/4 vs. 6/8,) articulations (lyrical vs. jagged,) and dynamics (piano vs. forte,) and result in overall contrast in atmospheres and sound.

The consistent feature of aggregate formations in both Parts of both Sections unify the piece, and debunks the criticism of inconsistency or flaw in the 12 tone method, as the deviations from the sequence are intentional to form necessary partitioning of dyadic/tetrachordal and trichordal sets to distinguish sub-sections and are always within the boundaries of the aggregate formations. Such fragmentations of rows within the aggregate formation rather than the strict orderings of the rows, are stylistic characteristics in Schoenberg’s composition, that tends to result in comprehensive and multi-dimensional or layers of structure and sound, and suggest a different interpretation against some of the previous theorists who could not legitimatize the inconsistencies of Schoenberg’s 12 tone method.

1 Dodecaphony: Schoenberg, by Martha Hyde, Models of Musical Analysis © 1993 Basil Blackwell Ltd (p.56)

2 http://www.schoenberg.at/6_archiv/music/works/op/compositions_op33a_notes_e.htm

3 http://query.nytimes.com/gst/fullpage.html?res=9C01E6DA1339F932A25752C1A9679C8B63&sec=&spon=&pagewanted=print

4 Unveiling Schoenberg's op. 33b, by Brian Alegant, Music Theory Spectrum © 1996 University of California Press (p.143-144)