Ashton Allan MU 228 Tonality within Aaron Copland s Piano Variations The closest Aaron Copland ever got to atonal music was his 1930 composition, Piano Variations. This work, constructed from twenty independently composed variations on a theme with a coda, is now considered my many as a masterwork of the great American composer. Perhaps the most exciting aspect of this piece is its projection of tonality- specifically, one founded on the germ of the melodic theme material. Copland, speaking about the Piano Variations in a conversation with Leo Smit in 1977, gives some important insight to keep in mind while listening and analyzing this piece: The Variations took a long time to write. I didn t write the variations consecutively. In other words, I got ideas for the variations and worked on them without having too clear a notion as to exactly where they were going to fit in the finished piece. And then one fine day every variation seemed to run to its right place. That was, of course, a fine day. (Butterworth, 203) Copland s Piano Variations of 1930 projects a tonality based on composing out the primary theme tetrachord, beginning in E and ending structurally in C#. Copland s use of Schoenberg s 12 tone technique is mostly restricted to the manipulation of the piece s primary tetrachord. Stated as the first notes of the composition, E, C, D#, and C# (pitch classes 4,0,3,1) is the primary theme of the composition. The theme is an octatonic configuration which in unordered form, also coincidentally feeds Bach s C# minor fugue in his Well-Tempered Clavier Book 1. The piece travels through 20 variations on this theme before arriving at the closing coda. Copland s use of the 12 tone manipulations (see Figure 1) comes to fruition by the sixth theme, where he transposes the theme up a minor third (three half-steps) to G, Eb, F#, E (7, 3, 6, 4). In the eighth variation, the theme is further transposed up a perfect fifth (7 half-steps) to B, G, Bb, Ab (11, 7, 10, 8). These first three variations of the tetrachord arpeggiate a minor chord. The ninth variation presents the theme at its original pitch 1
level with the right hand, while the left hand plays the theme transposed up a major third (4 half steps) to G#, E, G, F (8,4,7,5). Copland transposes the tenth variation up a half step, the eleventh up a whole step, the fourteenth back to pitch, the nineteenth up a perfect fifth, and again returns to the original pitch level for the coda. Copland harmonizes this theme with 10 of the 12 tones that form the aggregate. These 10 tones belong to the E-major and E-minor scales (see Figure 2). The remaining tones, pitch class 10 (Bb) and pitch class 5 (F) are reserved for later entry into the variations. The addition of these pitches can be explained by the addition of the C# major scale, a matter soon to be discussed in greater detail. The listener first hears pitch class 10 in the second variation. Although Copland plays the pitch class five times. In four of those times, the pitch class is the lowest sounding pitch of a chord. The pitch confronts the listener at the beginning of the third variation, where it sounds in octaves at extreme registers. Pitch class 5 remains missing until the seventh variation. Here (m. 72), it rings strongly in the bass of an F major chord, completing the aggregate. After the aggregate is complete, the piece gives no indication of 12-tone importance (other than the theme transpositions of course); the structure in no way expresses row variations, or even a complete 12-tone row. In fact, the presentation of the theme in the melody of variations rarely breaks away from the initial ordering. Much of the energy of this piece is derived from rhythmic and dynamic variation. The thematic opening of the piece begins with strong articulations and a slow motion. In the first few variations, the pace hardly moves faster than one or two notes at a time on one beat. In the third variation at measure 34, a rhythmic motif announces itself, propelling the listener into the reoccurring rhythmic motif of the fourth variation. The intensity and dynamics continue to build up to the end of the seventh variation culminating in a grand E major chord. The tension relaxes by variation 8, then grows for the rest of the piece into the final climax in the coda. This second build-up includes references to previous variations, staccato pulses, arpeggiating runs, meter changes, arching melodic articulations of the theme, ostinati and fast exchanges. Although these 2
surface elements provide a strong motion and sense of unity, an even greater beauty may lie at a slightly deeper level. At more of a middle-ground level of analysis of the Piano Variations, local projections of tonality appear. The first tonal elements of the work seem to bear reference to a Russian style of mixing the major and minor within one chord (referred hereafter as a major/minor chord). This practice, a notable favorite of Stravinsky, appears to have had an important impact on the piece s construction. Another notable Eastern European style Copland references is Bartók s use of both the perfect fifth and the tritone to assert a tonic. Copland s use of this technique will prove quite important in the second half of the work. The projection of local tonality begins within the theme itself. This theme makes apparent several possibilities (See Figure 4, middle-ground graph). By pure structure, C# may have the most convincing case for a projected tonality; however, the register in which Copland places the first C# is so separated from the rest of the melody that the surprise seems to make a case for the theme being in E at this point. Also, the first E of the next thematic iteration resolves the D# perfectly, making the first phrase a half instead of deceptive cadence. At the end of the first phrase, the piece already confronts the listener with an ambiguous chord; the A6-major/minor in measure 3. This chord also brings the listener toward an understanding of the theme in E, because both A- major and A-minor have a place within the E tonal center (IV of I and iv of i), whereas in C#, A can only exist as a major chord (VI of i) because vi of I has A# as a root. The second phrase of the theme also emphasizes E as a tonal center by moving 4,0,4,3,1. The punctuation here (m. 6) also implies an E major/minor tonality. The sounding C# represents the major scale degree 6 (hereafter ˆ6) while the D sounds as minor ˆ7. The fourth phrase begins arpeggiating a C# minor, but seems to correct itself midway, and shifts to an arpeggiation of E major with octave doubling. This passage has the same harmonic interpretation as the C# interpretation of the theme (I6-V-I). At this moment of E assertion, an acute ear may also hear the completion of an upper register 3
arpeggiation of C# minor (C# of m. 3&5, E of m. 4, G# of m. 8). Although to my ear, the E-major clearly wins out, the C# articulation here will play an interesting role in the background analysis. Also, this misleading moment continues to foreshadow a possible descent below E when the upper voice continues to drop to D# and then to B#. The fourth phrase is punctuated by a C (B#) major/minor chord. Oddly, this chord can only be interpreted as a major chord within E (VI of i). Also, spelling begins to play a role in pitch importance. Here, B# can be interpreted within C# as the leading tone (perhaps resolving at the beginning of the first variation). Another important local element of the theme is the low bass motion. As shown in the sketch, these pitches exhaustively express the unordered motif. The thematic material of the Piano Variations have clear tonal elements and implications, even though the meanings of these tonal elements are not as clear. The variations tend also to project local tonalities. In the first variation, the extreme registers can be isolated to reveal that the low C# in measure 12 and D-4 in measure 16 have the same relationship as in measure 6. In measure 12, the D ascends to E by the next measure. At the end of this variation, Copland writes a B# in the same low register as the C#, implying C# as tonal center again; however, this is not resolved until variation 10 s misspelled Db, or until the end of the coda with an actual C#. In the fourth variation, the listener is again challenged by tonal implications. With the new rhythmic motif, Copland stretches his soundscape. This section seems to elaborate on the C and A major/minor sonorities. The reiteration of these chords serves as a reference to the theme section s use of these chords as articulation to the tetrachord. While doing this, Copland also manages to express E major in the upper register as he did C# during the theme (G# of m. 45&47, E and B of m.47). At the same time, the lower voices spell out a C dominant 7 chord; the dominant of pitch class 5, which has not thus far occurred in the piece This C dominant sonority happens again in the fifth variation, measure 53, expressed this time as a C ninth chord. The seventh variation also presents important local tonal implications. Here, the 4
low bass opens with G, implying E minor. The next important moment is when Copland first introduces pitch class 5 with the F major chord in measure 72. Despite the distance between this chord and the dominant-type C chords in measures 45 and 53, it may be possible to link them from an aural standpoint since both are accented tonal chords especially since there are no other accented tonal chords. After the F, the bass returns with another low G, followed by an A, B and D, outlining a minor B4/2 chord, dominant of E, which in measures 74 through 77 is clearly articulated in a grand major chord. With this in mind, it seems appropriate to analyze some of the earlier tonal implications within E. In this regard, The C7 could be regarded as V/Neapolitan, F major as Neapolitan and the B4/2 as a minor dominant. Likewise, the eighth variation gives tonal implications. The right hand centers around E in octaves until the B in measure 81, and after that, continues reenforcing a tonal E through the end of the variation. Meanwhile, the left hand is articulating the theme as transposed up a perfect fifth. The tenth variation has a strong focus on Db in the bass, often supporting a Bb major/minor chord. This chord can only be easily interpreted within C# tonal center (vi of I). This moment is analogous to the C major/minor chord at the end of the theme (the only possible function VI of i). Also, the D/Db relation within the chord is linked to the pitch class 2&3 clash of measure 6. The relation is also articulated in the extreme registers in measure 108. This brings a connection between the end of the theme and the variation half-way point. Another possible connection resides in the variation s closing: a statement of the fourth variation transposed up a half-step. These two measures can also be linked to the end of the theme like variation four. However, this argument is greatly diminished by the transposition level change. The eleventh variation has a slight tonal implication not previously encountered in the piece. The very end of the variation seems to hold an A major chord, then adds a D to the hold, essentially adding a tonic resolution to a dominant. The dynamics play an important role (ppp) because by the time the D sounds, the A major has almost totally dissipated. The twelfth variation seems to imply an Eb focus because the latter 5
continually sounds alone in the bass. The Eb center is then carried into the next variation an octave down. The fourteenth variation seems to move into an area of C through articulation similar to the previous variation. This variation also brings the theme back to its original pitch level. Variation sixteen heavily implies C. The opening melodic figure, E-C-E-Eb-D, implies a major/minor contrast within C. Yet, as measure 202 shows with its right hand F# and G# minor chords, the section alludes to C# minor as well. This implication is picked up again in 208 with a D#, C# descent in the upper register. Copland also uses the low bass register again to compose out the original theme. The C#, D# descent appears again, but this time in the bass, in variation seventeen. Although this variation is primarily composing out the tetrachord theme, measures 236-239 present a solid, closed position E major chord prepared by a D# (m. 234) and high B (m. 235). Variation eighteen presents instances of local tonality reinforced with Bartókian tritone bass motion. In measure 255 & 257 the bass reaches a low Bb, then at the end of the variation, Copland calls for an E at extreme registers (m. 267). Then, the voices close down and the bass progresses E, G#, E, Bb, E, C. The end of the nineteenth variation explores the Bartókian tritone, perfect fifth relation. Starting in measure 277, Copland begins articulating high C#s in the right hand, followed closely by a drop in the bass, reenforced by tritones, down to the G tritone. Right after this articulation, a slowly descending treble line hits the perfect fifth, G#. The juxtaposition of these pitches begins to adjust the acute ear toward a C# overall tonality. The final variation also reveals many local instances of tonality. These begin within the domain of the theme, in its transposition up a fifth. The composing out of the theme naturally juxtaposes G and G#, indicating the major and minor third of E or the V and tritone of C#, while B and Bb work out the tritone and V of E. The highpoint of this section at measure 293 reveals C#, bringing, in light of the previous section, another reference to Bartókian relationships (of course, taking the G and G# into consideration). The second chord, if the Ab is respelled G#, is a V6 of E. This 6
expectation is fulfilled in measure 290 and again in 303 with clear, staccato E major chords in the right hand; however, these expectations are also not entirely satisfying, due to the low Eb s in the bass, arpeggiating to G, implying, with the aid of frequent Bb s in the variation, a tonal center around Eb. The end of this section also articulates D in the low bass, the leading tone of the sounding bass tonal center. The coda also projects certain local tonalities. It begins with the rhythmic motif of variation 4 transposed an octave down, connecting it with the end of the theme section through A and C major/minor chords. Starting in measure 341, the right hand articulates E major, but the rest of the sounding chord implies an A major/minor 9. This sonority may work to bring the listener s ear away from E, much like the Eb in the final variation. Also, Copland uses rhythmic references to the sixth variation, the first to transpose the theme. At measure 349, the listener encounters an F# major/minor chord with an A# in the bass. The section at 351 continues with pitch class 10 in the bass, but spelled Bb. The piece again refers to the fourth variation in measure 359 before moving into what sounds like a cadence in C#. This motion begins when the voices move back to where they started in the bass clef (This moment will be discussed in greater detail in the background). Finally, the last few measures of the work bring a jazz-esque plagal cadence between articulations of the theme at its original transposition level. Over a C# pedal, measure 367 brings an F# 9 chord with A# in the bass. This moves through a G, C, E and A by half-step into a full C# major 7 diminished 5. The strong local tonal implication of a plagal cadence over a pedal tonic merits the possibility of lower-level tonal structure. Through further reduction, one can find a coherent background tonal structure to Copland s Piano Variations. Figure 5 shows a bass line sketch for the entire piece. The low bass in this piece provides a clear articulation of the thematic material in an exhaustive manner. For example, the low bass of the theme itself spells out C, C#, E, Eb, and the first seven variations articulate a bass motion, an octave lower, of C#, C, Eb, E, as a response to the theme. Variations eight, nine and ten give an interesting insight 7
into the overall structure as well. This section begins with G in the bass for the first variation; then in nine, the G becomes G# at the beginning, and E appears in the low bass. The tenth variation, with its Bb6 major/minor chords, articulates Db, a misspelled C#, in the bass with pitch class 5 sounding above it (as E#). A few measures later, the pitch class 2 appears in the same register as the G and E from the previous variations. This bass motion addresses the E major/minor condition in the first two variations, and finally shows the E surrendering to the lower C#, thus finishing out the arpeggiation. Another interpretation of the arpeggiation spells out a diminished chord, leading to a D tonality. There is evidence for this at the end of the eleventh and twentieth variations. This interpretation however, lacks evidence that stretches beyond a local level of tonality. According to the composer, the piece has a structural break after the tenth variation. This break makes sense within the interpretation of this entire piece as composing out a motif. In this regard, the theme and first seven variations can be interpreted within the context of E; the eighth through thirteenth variation can be understood as transitional material mirrored around the division; variations fourteen through nineteen can be understood in C, the last variation in Eb, and the coda finally resting on C#. This progression utilizes the local tonalities to compose out the theme of the piece on a grand scale. The main arguments against this theory remain the questions: Why would the harmonic pacing increase so rapidly, and why would Copland use transitional material through the middle of the piece? The first criticism can be overturned by a dramatic interpretation: the second half of the piece is building in intensity up into the coda; therefore, an increase in harmonic tempo is entirely appropriate for the effect. The second criticism proves to be a greater problem, because these sections do project local tonalities that operate within the tetrachord. One may interpret variation eleven as a continuation of the pitch class 2 tonality established in the previous variation. Variations twelve and thirteen use low Eb, and variation fourteen seems to be a simple bass transposition of thirteen. Another possibility remains: perhaps variations twelve and thirteen do represent a structural pitch class 3. If this is 8
true, the overall structural bass composition of the melodic theme would be out of order, and perhaps have pitch class 3 emphasized again in variation twenty. Although there can be no doubt of a structural bass expression of the motif, the exact implications of this expression raise questions as to whether the piece was assembled with the ordered tetrachord in mind. More compelling evidence toward the existence of a background tonal structure resides in the projection of an Urlinie (figure 6 for overall background projection of Urzats). The first evidence of such a line appears in the theme section. The highest sounding note in the opening of the piece is G# in measure 8. This pitch makes a particularly good candidate for a head tone because it works within both the initial E key tonality as ˆ3, and in the final C# tonality as ˆ5. This head tone makes its next appearance after an octave transfer in the fourth variation. In measure 45, the G# takes part in the right-hand arpeggiation of E major, discussed as a local tonality. In the sixth variation, the head tone is transposed into E minor mode as G. This transposition is coherent because at this moment, the listener experiences a modulation as the theme is transposed for the first time (here, appropriately, up a minor third). This minor head tone is carried into the seventh variation, where, starting in measure 73, it begins a descent, through F#, to E. Here, Copland uses traditional tonality again to reassert the head tone with a Schenkerian overlap; at the moment of cadence to an E major chord, he restates G# as the highest pitch, negating the descent into E and preparing the head tone for another journey. The head tone next appears in variation sixteen, this time, however, supported in the bass by C#, implying G# as the head of a five line. In the seventeenth variation, during the E major chords after measure 236, G# appears in its original register and supported again by E, however, the B sounding above the head tone greatly diminishes its power to assert itself as structural. In the nineteenth variation, however, pitch class 8, misspelled Ab, sounds strongly in the upper register. This tone is carried through the beginning of the final variation. At the beginning of the coda, a low, structural C sounds, anticipating the B# in measure 366 as a structural 9
leading tone for the piece. From here until the final cadence and descent of the urlinie, the affect of structural dominant provides much of the anticipation and motion through to the end of the piece. Soon after, in measure 341, the G# is again articulated in the high register, but, as in measure 236, it is somewhat obscured by a B sounding higher. This chord, however, if the lowest sounding C is read as a B# (leading tone anticipation), over it sounds a C# minor chord with both a major and minor seventh. A descent to ˆ4 is anticipated in measure 349 over F# major/minor. This chord, prolonged through the bass Bb, rearticulates F# as ˆ4 in measures 356 and 357. Then in the subsequent measure, one might interpret an urlinie drop through ˆ3, ˆ2 and ˆ1, but with the final C# supported by its leading tone, the descent is deceptive and fails to hold structurally. Nevertheless, in measure 364, the listener experiences a slight retrograde when the head tone drops down to bass clef, spelled Ab, and descends through an implied ˆ4 over the A (which connects to the previous ˆ4 from measure 356), ˆ3, ˆ2 supported by the B# leading tone, and ˆ1 over the pedal C#, now sounding as structural tonic of the piece. This compelling transition from a three line to a five line works in perfect conjunction with the piece s means of composing out the thematic motif, starting in an E tonality and finishing with C#. Copland s Piano Variations projects a tonality based around an octatonic motif handled melodically as a post-tonal tetrachord, beginning by asserting an E major/minor tonality with a three line, moving through assertions of C and Eb toward the final C# tonality using the previous ˆ3 as a five line, and asserting the final tonality as an overall structural tonality for the work. Copland s Piano Variations of 1930 projects a tonality based on composing out the primary theme tetrachord, beginning in E and ending structurally in C#. The way Copland composed this piece, and how it fell into a tonal structure despite its atonal foreground, is testimony for both his strong roots in tonality and the strength of tonal implications. To Copland, this piece was especially important because he felt any other composer would have handled the same thematic material in a different way. While 10
this is certainly true on a foreground level, it may be the case, with Bach s C# minor fugue as evidence, that the implicit tonalities of this melody express a more fundamental tonality which would in any case find its way into a piece s structure. Works Consulted Aaron Copland Collection, the. Online, available at 11
http://memory.loc.gov/ammem/achtml/achome.htm (has many of Coplands sketches available). *Butterworth, Neil. The Music of Aaron Copland. Toccata Press, Wellingborough, 1985. Copland, Aaron. Copland 1900-1942. St. Martin s/marek, New York, 1984. Copland, Aaron. Piano Variations. Boosey & Hawkes, USA, 1959. Smith, Julia. Aaron Copland: His work and contribution to Amerian Music. E.P. Dutton & Co, New York, 1955. * cited Figure 1: Theme transpositions Theme: 4, 0, 3, 1; T= 0 Variation 6: 7, 3, 6, 4; T= 3 minor 3rd Variation 8: 11, 7, 10, 8; T= 7 perfect 5th Variation 9: Right Hand: 4, 0, 3, 1; T= 0 Left Hand: 8, 4, 7, 5; T= 4 major 3rd Variation 10: 5, 1, 4, 2; T= 1 minor 2nd Variation 11: 6, 2, 5, 3; T= 2 major 2nd Variation 14: 1, 0, 3, 4; T= 0 Variation 15: 4, 0, 3, 1; T= 0 Variation 19: 11, 7, 10, 8; T= 7 perfect 5th 12
Coda: 4, 0, 3, 1; T= 0 Figure 2: Scale elements E major/ C# minor:e F# G# A B C# D# 4 6 8 9 11 1 3 E minor: E F# G A B C D 4 6 7 9 11 0 2 C# major: E# F# G# A# B# C# D# 5 6 8 10 0 1 3 Figure 3: Theme Interpretations C#: E: C: 13