Since the later chapters of this study expand on the substantial body of literature devoted to analysis of Stravinsky's twelve-tone works, this chapter will present an overview of pertinent existing Stravinsky analyses and will describe some general characteristics typical of Stravinsky's twelve-tone compositions. In order that Stravinsky's unique twelve-tone method will come into stronger focus in the remaining chapters, this investigation will analyze Schoenberg's De profundis (1950) and compare it to Stravinsky's technique.
Analytical approaches to Stravinsky's twelve-tone music generally can be divided into four categories. The first category involves the description and explanation of the twelve-tone rows, hexachords, and verticals in Stravinsky's late works. The second category focuses on harmonic aspects of Stravinsky's row simultaneities and the implied tonality of the rows. The third category looks at large-scale structure in the twelve-tone works. The final category involves the application of poetic analysis to Stravinsky's music.
Most detailed analyses of Stravinsky's late works, since the music is twelve-tone, involve the identification of the rows and their manipulations. However, several analysts focus on the structure of Stravinsky's rows, their implications for subsets, their pitch class content, and symmetry. Robert Gauldin and Warren Benson explore the numerological implications of sets already evident in Stravinsky's pre-twelve-tone serial composition In Memoriam Dylan Thomas (Robert Gauldin and Warren Benson, "Structure and Numerology in Stravinsky's In Memoriam Dylan Thomas," Perspectives of New Music 23:2 (Spring/Summer 1985): 166-185.). Claudio Spies examines Stravinsky's row structure in detail, and explains Stravinsky's set rotation and verticals in several articles (Claudio Spies, "Notes on Stravinsky's Abraham and Isaac," "Notes on Stravinsky's Variations," and "Some Notes on Stravinsky's Requiem Settings," Perspectives on Schoenberg and Stravinsky, 2nd edition, (Princeton: 1972): 186-249). Joseph Straus examines verticals and Stravinsky's subsets in detail (Joseph N. Straus, "Stravinsky's `Construction of Twelve Verticals': An Aspect of Harmony in the Serial Music," Music Theory Spectrum, 21:1 (Spring 1999): 43-73.). Straus and David H. Smyth point out several inconsistencies between Stravinsky's pre-compositional rows and sets (obtained from manuscript sketches), and his implementation of those rows and sets in several of his works (Joseph N. Straus, "Two `Mistakes' in Stravinsky's Introitus," Mitteilungen der Paul Sacher Siftung, 4 (Jan. 1991): 34-36. David H. Smyth, "Stravinsky at the Threshold: A Sketch Leaf for Canticum Sacrum," Mitteilungen der Paul Sacher Siftung, 10 (Mar 1997): 21-26.).
Some authors take set analysis one step further and describe the harmonic and tonal implications of the rows in Stravinsky's twelve-tone works.
Roberto Gerhard discusses "poles of attraction" or harmonic centers in the serial sections of Canticum sacrum (Roberto Gerhard, "Twelve-Note Technique in Stravinsky," The Score 20 (June 1957): 38-43.). David H. Smyth explores Stravinsky's manuscripts for Canticum sacrum and finds a regularity in vertical dyads in a sketch that demonstrate both a pre-serial construction and a harmonic basis for the work's outer movements (David H. Smyth, "Stravinsky at the Threshold: A Sketch Leaf for Canticum sacrum," Mitteilungen der Paul Sacher Siftung 10 (March 1997): 21-26.). Jerome Kohl discovers pitch centers in Stravinsky's hexachordal rotations in Variations (Jerome Kohl, "Exposition in Stravinsky's Orchestral Variations," Perspectives of New Music (Fall/Winter 1979 and Spring/Summer 1980): 391-405.). Anthony Payne and Spies examine melodic segments to find key centers in Requiem Canticles (Anthony Payne, "Requiem Canticles," Tempo 81 (Summer 1967): 10-19. Claudio Spies, "Some Notes on Stravinsky's Requiem Settings," in Perspectives on Schoenberg and Stravinsky, 223-249.). Lynne Rogers looks to vertical simultaneities to highlight pitch centers in The Flood and The Owl and the Pussy-cat (Lynne Rogers, "Stravinsky's Serial Counterpoint and the Voice of God." Unpublished paper presented at the 1999 Society of Music Theory national conference, Atlanta.). Pieter van den Toorn looks for octatonic collections within Stravinsky's twelve-tone compositions (Pieter Van den Toorn, The Music of Igor Stravinsky, (New Haven, Connecticut: Yale, 1983): 427-455.).
Some analysts of Stravinsky's twelve-tone music focus on the large-scale formal structure of his works. Thomas Clifton constructs a large-scale formal symmetrical structure of Stravinsky's A Sermon, A Narrative, and A Prayer based on the focal symmetry that he finds in Stravinsky's rotated rows (Thomas Clifton, "Types of Symmetrical Relations in Stravinsky's A Sermon, A Narrative, and A Prayer," Perspectives of New Music (Fall/Winter 1970): 96-112.). Spies provides formal outlines for many of Stravinsky's late twelve-tone works (Claudio Spies, Perspectives on Schoenberg and Stravinsky, 186-249.). Straus examines the large-scale tonal, motivic, and harmonic structures in Stravinsky's late works (Joseph N. Straus, "A Strategy of Large-Scale Organization in Stravinsky's Late Music," Integral 11 (1997): 1-36.).
Several analyses present relationships between the poetic texts of Stravinsky's twelve-tone works and his music. Gauldin and Benson analyze the poetry and music of the serial, pre-twelve-tone work In Memoriam Dylan Thomas in great detail (Robert Gauldin and Warren Benson, "Structure and Numerology in Stravinsky's In Memoriam Dylan Thomas," Perspectives of New Music 23:2 (Spring/Summer 1985): 166-185.). Spies also incorporates analyses of poetry in his articles (Claudio Spies, Perspectives on Schoenberg and Stravinsky, 186-249.).
Stravinsky's row construction and his melodic and harmonic manipulation of these rows distinguish his twelve-tone music from that of other serialist composers.
Stravinsky revealed his characteristic serial manipulation of pitch collections in Cantata (1952) and In Memoriam Dylan Thomas (1954). These two works precede his first twelve-tone composition, Canticum sacrum (1955). In the "To-morrow shall be my dancing day" movement of Cantata, Stravinsky employs serial procedures (Inversion, Retrograde, Retrograde Inversion, Transposition) on a an eleven-note collection that includes repeating pitches. In the "Dirge-Canons" of In Memoriam Dylan Thomas he treats a collection of five pitches with serial procedures.
Stravinsky's rows can most easily be traced in the music written for one or a few polyphonic lines. In such instances, he typically employs rows melodically, in simple, horizontal order. In multi-voiced homophonic chords, rows are often more difficult to trace. In homophony, Stravinsky often creates chords based on half of a row, an entire row, or portions of rows that are rotated or (in his late music) employed as verticals.
Like many other twelve-tone composers, Stravinsky often repeats notes or small groups of notes in the course of his set use.
Stravinsky also employs notes from rows out of order, including such procedures as row element rotation, skips in row ordering, as well as palindrome- or arch-shaped row deployment. Set rotation in Stravinsky ranges from simple reordering in the works of the 1950's to his frequent use of more complicated rotation and verticals in the works of the 1960's.
Stravinsky only occasionally employs combinatoriality, i.e. when aggregates are formed from simultaneous statements of two or more rows. Often found in Schoenberg's music, combinatoriality appears most frequently in Stravinsky's early twelve-tone works, in which he employed the technique in an experimental manner. In Stravinsky's later works, when he used verticals made up of six-note sections of the rows, he was less concerned with the formation of aggregates than with other consequences of row employment, such as the transposition of verticals by half-step. Similarly, in most of his twelve-tone compositions, Stravinsky does not commonly highlight row subset invariance, i.e. when the same groups of notes occur adjacently in different rows. However, Stravinsky often employs rows that are invariant by one note (the first or last in a row).
Stravinsky was less concerned with the compositional exploitation of internal row patterning than the classical serialist composers. Although some analysts point out the pitch-class set types in segments of Stravinsky's rows, Stravinsky seldom takes full and exclusive advantage of common tri-, tetra-, penta- or hexachords in most of his twelve-tone music. Additionally, Stravinsky does not frequently use certain portions of the row as recurring formal motives, as Schoenberg or Webern. Rather, Stravinsky's motivic row use is on a much smaller formal scale, although he often uses entire rows as subjects in fugal expositions.
Stravinsky almost exclusively confined himself to employing rows related to each other by their first and last pitches. In additions, in his more complicated works Stravinsky chose rows related to or transposed from, in turn, the first and last notes of the principle rows. This row relationship often occurs on the surface of a piece as a pivot, or an overlapping principle, where the last member of a stated row becomes the first member of the next row. (For example, often Stravinsky follows a row statement with its Retrograde.) But this row relationship also occurs in deeper structural levels of Stravinsky's music, as will be discussed in the course of this paper. The row succession in Stravinsky's music will be considered in detail in the next section.
Joseph Straus points out that in some of Schoenberg's works, the composer employs regions or areas in which a few related rows are used for formal effect (Joseph Straus, Introduction to Post-Tonal Theory (Prentice Hall, Englewood Cliffs, NJ: 1990), 169-79.). In Piano Piece, Op. 33a, Schoenberg begins and ends with rows related to each other by combinatoriality. In the middle of the piece, other rows with similar relationships to each other are employed to formally move away from the principle row area. A formal return of the beginning of the piece is indicated by a return of the principle rows.
George Perle analyzes Schoenberg's Op. 33a as well as works by Webern and Babbitt, and concludes that row areas at times are used as formal and structural building blocks in twelve-tone music (George Perle, Serial Composition and Atonality, 6th ed. (University of California, Berkeley: 1991), 111-145.). In addition, Perle has written extensively on large-scale and musical-poetical serial employment in Berg's music.
A brief examination Schoenberg's De profundis will aid in the presentation of an Object-Oriented study of Stravinsky's twelve-tone works. Schoenberg's last completed composition, De profundis, exemplifies his characteristic compositional devices, such as combinatoriality and set succession.
Schoenberg composed De profundis, Op. 50b, in 1950, five years before Stravinsky's first work using twelve-tone technique, Canticum sacrum. Schoenberg dedicated De profundis to the newly formed state of Israel. The work calls for a six-part unaccompanied chorus (SSATBB) and soloists (SATBB). The Hebrew words are taken from Psalm 130. Following traditional Jewish practice for the musical presentation of Hebrew words, Schoenberg's setting replaces the Psalmist's tetragrammaton (YHWH) with "adonay" in every occurrence of the word. The English translation offers "LORD" for the tetragrammaton and "Lord" for "adonay." Table 2 shows the Hebrew words and English translation of De profundis.
(YHWH changed to adonay)
(King James Version)
mimaamaqim qeratiha adonay
|A Song of degrees.
1. Out of the depths have I cried unto thee, O LORD.
|7-12||adonay simah veqoli tihyeynah ozneyha qasuvot leqol tahanunay||2. Lord, hear my voice: let thy ears be attentive to the voice of my supplications.|
|13-17||im awonot tismor yah adonay mi yaamod||3. If thou, LORD, shouldst mark iniquities, O Lord, who shall stand?|
|18-22||ki imha haslihah lemaan tiware||4. For with thee there is forgiveness, that thou mayst be feared.|
|23-28||qiwiti adonay qiwtah nafsi welidvaro hohalti||5. I wait for the LORD, my soul doth wait, and in his word do I hope.|
|29-33||nafsi ladonay misomrim laboqer somrim laboqer||6. My soul waiteth for the Lord from one morning watch unto the other.|
|34-41||yahel yisrael el adonay ki im adonay hahesed weharbeh imo fedut||7. Let Israel hope in the LORD: for with the LORD there is mercy, and with him is plentious redemption.|
|42-55||wehu yifdeh et yisrael mikol awonotayw||8. And he shall redeem Israel from all his iniquities.|
The Prime row is taken from the first aggregate heard in the chorus (MM. 1-6). Table 3 shows the standard twelve-tone matrix for De profundis.
int: -6 -1 -4 -2 -4 -3 +4 +1 +6 -1 -4 I-0 I-6 I-5 I-1 I-11 I-7 I-4 I-8 I-9 I-3 I-2 I-10 P-0 Eb A Ab E D Bb G B C F# F C# P-6 A Eb D Bb Ab E C# F F# C B G P-7 Bb E Eb B A F D F# G C# C Ab P-11 D Ab G Eb C# A F# Bb B F E C P-1 E Bb A F Eb B Ab C C# G F# D P-5 Ab D C# A G Eb C E F B Bb F# P-8 B F E C Bb F# Eb G Ab D C# A P-4 G C# C Ab F# D B Eb E Bb A F P-3 F# C B G F C# Bb D Eb A Ab E P-9 C F# F C# B G E Ab A Eb D Bb P-10 C# G F# D C Ab F A Bb E Eb B P-2 F B Bb F# E C A C# D Ab G Eb
In De profundis Schoenberg employs only two rows, and their retrogrades: P-0, R-0, I-3, and RI-3. These rows have a combinatorial relationship so that the first half of P-0 (1-6) and the first half of I-3 (1-6) form and aggregate, as do the second half of P-0 (7-12) and the second half of I-3 (7-12). Schoenberg exploits this combinatoriality in the course of the composition.
Table 4 shows all of the rows used in De profundis. Hexachords are split up so often that the first six notes in each row will be designated the "a" hexachord, and the last six notes in each row will be the "b" hexachord. P-0a contains the same six notes, in reverse order as R-0b; likewise I-3b contains the same six notes, in reverse order, as RI-3a; etc.
|17||RI-3a & R-0a||R-0a & RI-3a|
|18-19||4||R-0b & RI-3a||RI-3b & R-0a||Speaking|
|23-26||5||P-0 w/ Tenor||I-3b w/Alto||I-3a w/Bas
|P-0 w/Sop||I-3a w/Alto|
|26-28||RI-3b w/Tenor||P-0b w/Bar & Bass||RI-3b w/Sop||P-0b w/Mezz & Alto|
|29-30||6||R-0b w/Tenor||P-0b||R-0b w/Sop||R-0a|
|31-33||RI-3 [including error]
|34-36||7||P-0 w/Bass||Speaking||P-0 w/M & A|
|36-37||I-3a w/Bass||P-0a||I-3a w/Soprano|
|44-45||I-3a & RI-3b||I-3|
In the mezzo-soprano part in M. 32, two pitches, d" and eb' are out of order. Most analysts agree that Schoenberg mistook the soprano clef (C1) for a treble clef (G3) when he wrote these notes. The corrected pitches, transposed up a third (to f" and gb') maintain Schoenberg's formal construction with his row choices.
As this investigation will later show, the rows that Schoenberg chooses are not related in the way that Stravinsky commonly chooses his rows. Whereas Stravinsky chooses rows related to the first and last notes of the Prime row, in De profundis the rows that Schoenberg uses do not share any beginning or ending pitches. In this work, Schoenberg is concerned with the economy of combinatoriality and a few rows. The next section of this paper will show how Stravinsky's row choices are different.
A common feature of all of Stravinsky's twelve-tone works is their row succession, i.e. which rows he employs and when. Stravinsky relies on the same type of row succession (albeit to varying degrees) in all of his serial works. In Stravinsky's row succession, the most important aspects of a row are its first and last (twelfth) notes. These pitches provide a pivot, hinge, or nexus that relate rows to each other.
Stravinsky's typical row manipulation includes four forms: the Prime form (or Original form), the Retrograde form, the row in Inversion, and the row in Inverted Retrograde (as opposed to Retrograde Inversion). (The term Inverted Retrograde comes from Claudio Spies: "it is preferable to make a distinction between [IR and RI] for the cogent enough reason that Stravinsky's 'untransposed' set forms have consistently included the inverted retrograde in preference to the retrograde inversion. [Spies' italics]" See Claudio Spies, "Notes on Stravinsky's Abraham and Isaac," in Perspectives on Schoenberg and Stravinsky, (Princeton, 1972): 200.) The Inverted Retrograde, in Stravinsky's standard usage, is not simply the reverse form of the row's Inversion, but is more precisely the Retrograde Inversion beginning not with the final note of the Inversion form, but with the final note of the Prime form.
A typical example of Stravinsky's row manipulation is found in Epitaphium. Table 5 shows the forms used in Epitaphium. The Prime row of Epitaphium begins on C# and ends on A. The Retrograde form uses the same pitches as the Prime form, but in reverse order, from A to C#. The Inversion begins on the same pitch as the Prime form, but the intervals between the pitches are reversed: it begins on C# and ends on F. The table shows that Stravinsky's Inverted Retrograde is the same as RI-4: it begins on the last pitch of the Prime form and proceeds backwards (like the Retrograde) with reversed intervals (like the Inversion), from A to F. These four are the only rows that Stravinsky employs in Epitaphium. For illustration, the traditional serial Retrograde Inversion row (RI-0) is listed in the table below along with the forms just described.
|Prime Form (P-0)||C# Bb Eb E C B F# F D G Ab A|
|Retrograde (R-0)||A Ab G D F F# B C E Eb Bb C#|
|Inversion (I-0)||C# E B Bb D Eb Ab A C G F# F|
|Inverted Retrograde (IR)||A Bb B E C# C G F# D Eb Ab F|
|Retrograde Inversion (RI-0)||F F# G C A Ab Eb D Bb B E C#|
|Retrograde Inversion (RI-4)||A Bb B E C# C G F# D Eb Ab F|
Within most of his twelve-tone works, Stravinsky consistently employs rows obtained from these four forms (Prime, Retrograde, Inversion, Inverted Retrograde), to the exclusion of any other rows. (In the course of analyses below, the phrase "Retrograde Inversion beginning with the last note of the Prime form" (RI-4 in the case of Epitaphium) will be used in preference to "Inverted Retrograde" (IR) to facilitate analysis. When Stravinsky does employ the actual un-transposed Retrograde Inversion (RI-0), this paper makes clear the relationship of the rows.) Further, when he does employ other rows, he often does so according to a system generated from similarly related rows. This system will be illustrated later in this paper with Object-Oriented analysis.
Of great interest to the conductor is that Stravinsky often employs a specific row for a structural event or to musically underscore the poetry. For example, Stravinsky often uses the Inverted Retrograde form of the row to highlight a particularly poignant musical or poetic-textual moment in a piece. On other occasions, Stravinsky uses specific foundational rows in certain sections of a work, then moves away from these forms and returns again at significant formal instances.
Stravinsky's Topology. Doctoral Dissertation. Boulder, CO: University of Colordao, 2000. www.lulu.com/akuster
(C) Copyright 2000 Andrew Kuster. All Rights Reserved.