Play and Ambiguity in Reich’s Variations for Winds, Strings, and Keyboards



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When Steve Reich composed Variations for Winds, Strings, and Keyboards for the San Francisco Symphony, Edo de Waart premiered the work the following year in 1980.  The minimalist sound that characterizes the piece developed through the experimentation of American composers such as Reich, Philip Glass, Terry Riley, and later John Adams.  Reich, like the other composers in the group, was not satisfied with the label used to describe the sounds he was creating.[1]  However, the term continues to be applied to their work, as it serves some usefulness in describing the aural effect their music produces.  The term “minimalism” came from the art world:


[T]he leading art movement of the 1960s, Minimalist art focused directly on the object itself.  It experimented with the limits of art by asking how many of the elements traditionally associated with it could be taken away to leave something which could still be considered art.[2] 


Likewise, minimalism in music focuses on the gradual, nearly imperceptible change: this work, though over 20 minutes long, presents merely three variations of the theme[3] (over six minutes per statement is a lengthy amount of time in which to vary a theme). 


In addition to employing the sparse-sounding elements of minimalism, Reich also drew on aspects of non-Western music.[4]  Indeed, he mixes Eastern and Western ideas and sounds together in order to produce an interesting example of narrative openness, of progression without finality, all the while underwritten by an ambiguity between and within the two spheres (East and West) themselves.  As will be examined later, the three statements of the theme are arranged according to rhythmic acceleration and complexity.[5]  A narrative, a forward progression, develops.  Yet the piece will conclude on an ambiguous thirteenth chord, fading out with no real commitment to any of the tones included in its chordal structure (since a thirteenth chord uses all the notes in the scale, the root can be any one of those notes).  Though a journey begins, it never really ends (at least, not in a conclusive way).

The harmonic language of the piece is tonal in that the motivic fragments that form the building block of Variations centre on a primary tone.  As the motivic fragments morph throughout the course of the piece, the emphasized tone shifts to create a new centre, in a manner somewhat similar to a chord progression in the traditional harmonic sense.  However, unlike in traditional tonal harmony, the emphasis is horizontal rather than vertical. The various instrumental lines each have their own independently forward-moving plan; they certainly overlap and produce simultaneous sounds, but triadic chord progression is not a priority.  Furthermore, intervals of open fourths (and, later in the piece, open fifths) emphasize a tonal centre (one note is primary), but not a mode (a specific major or minor colouring is absent).  Or rather, the Western diatonic scale will be pitted against the Eastern pentatonic scale in order to develop an ambiguous interaction between two opposing sides.  A Derridean différance[6] plays between various binaries (West/East, tonal/pentatonic, linear/cyclical) that create several ambiguities in the sounds that meet our ears.[7]   




This ambiguity is first noticeable in the motivic fragment that relentlessly repeats itself in the winds and strings sections. The motive that comprises the basic material for the winds and strings sections is based on a scale that sounds pentatonic, but on the other hand looks like c minor (Ex. 1).


Ex. 1: Variations for Wind, Strings, and Keyboards, Flutes 1,[8] m. 1-2.


The pentatonic sound comes from the open hollowness of the descending fourths in the first two beats of measure one. Indeed, until the D of beat five, the notes all fit into a perfect pentatonic scale based on E-flat.  The upper notes of m. 1 in fact outline such a descending scale (Ex. 2).


Ex. 2: Variations for Winds, Strings, and Keyboards, Reduction of Flutes 1, m. 1.


The pesky D and the range of the motive (a descent from C to C), though, provide evidence for the case for c minor.  In addition, where the different voices do in fact create a triad (on beat six in the first measure and beat one of the second measure, for example), the chord that is formed is c minor (Ex. 3).  Thus, we hear a c minor tonality repeated at intervals.  Even if the harmony is not functioning in such a way as to pull the ear to c minor, familiarity often produces privileging of its own (i.e., since we become used to hearing c minor, we consider it to be the most important).


Ex. 3: Variations for Winds, Strings, and Keyboards, Flutes 1-3, m. 1-2.


Yet, on the other hand, c minor is not the only chord formed.  Several B-flat major triads are also present.  Because the A-flat from the key signature is consistently avoided in the two-measure motive, the tone centre could arguably emphasize B-flat (which as the closest related note to E-flat, favors an E-flat interpretation; once again, the Western circle of fifths is mingling with the Eastern pentatonic scale).  However, the fact that the c minor chords fall on the beats whereas the B-flat major triads fall in between the beats favors the c minor interpretation.  Nevertheless, the pentatonic elements and the absence of a leading tone pull the scale away from the minor sound and keep it in the Aeolian mode.  To further counteract a clear c minor sound, the electric organ and the violin play an E-flat and B-flat open fifth.  The tonal centre, while present, nevertheless vacillates between dual options, related by key signature.


The ambiguity of tonal centre is played out in the interaction of the winds and keyboards with the strings, most notably the cello in the latter group (Table 1).  The tones vacillate between emphasizing the minor mode and emphasizing the major mode associated with each key signature.  Thus, not only do we have ambiguities between pentatonic and Western scales, we have ambiguity even within the Western scale, for a key signature can refer to either a major or a minor mode (as indicated in first column of Table 1).


Table 1: Key Signatures/Emphasized Tones (Winds, Cello), Variation 1, m. 1-144.


Key Signatures

Upper voices

String motive (cello)

3 flats (E-flat or c)

C octave


(5 flats)

5 sharps (B or g-sharp)


A-sharp (enharmonic)


B natural (enharmonic)

6 sharps (F-sharp or d-sharp)



5 sharps (B or g-sharp)

B natural


3 sharps (A or f-sharp)

B natural


1 sharp (G or e)



No sharps or flats (C or a)



1 flat (F or d)



2 flats (B-flat or g)



3 flats (E-flat or c)




Yet so far we have just been examining the motive of descending fourths and thirds (later to become descending fourths and fifths in subsequent statements of the theme) that occurs in the winds and keyboards. While the upper voices have been relentlessly reiterating the two-measure motive (Ex. 1), the strings, most notably the cello, have been providing an expansive counter-motive in tied half and whole notes. 

Why does the cello contain the counter-motive rather than the bass (an instrument with a lower range)?  The bass makes occasional appearances as if to remind one of its potentially supportive foundational role in the textural ensemble, but it soon disappears without completely fulfilling that expectation.  The rumble of its low notes roll in and out of the music, unstable, and thus unsuitable for harmonic architectural projects.  Instead of supporting the progressing tonal centres, the bass strings act as a disruptive force, entering with opposing dissonance and leaving once resolution hints at subordinating these notes to a functional purpose.  Thus, the bass strings provide colour rather than structure, washing over the textural palette while the cello provides the actual counter-motive to the upper voices. 

Compared to the quickly moving eighth notes, this counter-motive sounds expansive and anchors the variation, resembling the cantus firmus of medieval chant.  However, as mentioned before, harmony in this piece is not so much vertical as linear; the upper voice motive presents a progression of tone centres much as if someone had unraveled a string of chords and stretched them across a room. This produces a feeling of progression despite the lack of traditional “movement by fifths” triads.  Indeed, in the progression of key signatures, while the first five tonal changes wander away from the home centre, the final five rigidly traverse the circle of fifths and thus emphatically reinforce a traditional return to home.

The cello motive also reinforces this return to home.  After it, too, wanders rather far from the home tonal centre, it settles down on an A before concluding with F-G-C, or in other words, the skeletal outline of a VI-VI-V-I progression (although, one which plays with minor/major distinctions again).  Of course, the length of time required to spin out this progression diminishes its power on the ears, but the movement is there, nonetheless.


Micro-level Variation Techniques


The lengthy Variations for Winds, Strings, and Keyboards only presents three statements of the theme. With such great spans of time devoted to each variation, the ear and memory begin to lose track of the original theme, and thus the need for micro-level variations arises. By accomplishing variations on the micro-level (varying the basic material within the theme itself), Reich keeps the ear interested in tracing the progression of the theme (which will be examined later in this paper).


How does Reich maximize his material within the theme?  His task is not so different from that of previous composers, who also faced the challenge of creating a work based on a repetitious or cyclical format that yet avoids monotony.  A careful and detailed composer,[9] Reich begins with a basic unit of motivic material and gradually, almost imperceptibly, morphs the variation before our ears.  Even the basic motive itself can be broken down into two sub-units that are simply variations of the same descending fourths and thirds, octave span scheme (Ex. 1 again).  Both measures trace the descent of a scale, but the second descent is rhythmically offset in order that the notes that fell on weak beats the first time through now fall on the strong beats. However, the tied note still occurs in the same place, thus preserving the overall rhythmic shape of the motive.  Over the course of the first variation, this motive wanders through several tonal centres, tracing octave descents through the following progression: C, B-flat/A-sharp, B natural, D, C (Ex. 4).  Such a progression corresponds roughly to the same movement away from centre and a conventional return to home that occurred in the progression of key signatures.


Ex. 4: Variations for Winds, Strings, and Keyboards, Reduction of Emphasized Tones, Var. 1, m. 1-144.



Another technique that varies the monotony of the persistent motive is the use of phasing.[10]  Phasing, which occurs in various other works by Steve Reich such as Piano Phase or Violin Phase, also involves the gradual change characteristic of minimalism, but this time in the rhythmic synchronization of two parts.  Typically, two instruments begin by playing the same part simultaneously.  Gradually, one instrument starts to accelerate while the other remains steady.  Eventually, the synchronization between the two parts becomes more and more distant, until at last the wandering instrument overtakes the steady instrument, and the two are once more playing together.  In the case of Variations for Winds, Strings, and Keyboards, the two parts are identical, but start out rhythmically offset.  The second voice in the winds and keyboards echoes the two-measure motive an eighth beat behind the first voice (Ex. 3 again).  This distance gradually increases with each variation, reaching a maximum lag time of three beats (six times the original distance).  Unlike other versions of his phasing technique, the motives in Variations for Winds, Strings, and Keyboards never complete the full cycle of unison, disunison, unison.  Instead, Reich transforms the cyclical aspect of phasing into a linear one.


Advancing Rhythmic Complexity


Another way that Reich achieves variation is through an increase in rhythmic complexity: as the variations progress, the syncopation occurs more frequently.  In addition, the value of the notes decreases slightly, producing rhythmic crescendo.  Yet the developing complexity of the syncopation works against the decreasing note values: because the syncopated notes are held longer, the motive slows down even as it appears to speed up.  


The wind and keyboard motive contains only eighth notes (Ex. 1 again) in the first variation.  Yet in the second variation, the descending fourth figure is inverted to a descending fifth and filled in with sixteenth note passing tones, sending the motive into a fast start (Ex. 5).  Yet by the end of the first measure, three syncopated notes are each extended a full one and a half beats, slowing the motive back up.  The final three beats are steady eighth notes, as if to provide some balance to the fitful starts and stops of the beginning of the motive.  In addition to viewing the sixteenth notes as passing tones between a descending fifth, one can also see the first two and a half beats of the first measure as a compression and overlap of the final three beats of the second measure.  Thus, once again Reich maximizes a minimal amount of motivic material.


Ex. 5: Variations for Winds, Strings, and Keyboards, Flutes 1, m. 145-146.


The final variation uses the sixteenth notes to ornament the upper note of the descending fourth figure (Ex. 6).  At the same time, this ornament, an upper neighbor, reminds one of the descending-fifth figure that opened the second variation.  Hence another example of ambiguity arises: is the figure outlined the original falling fourth or its related inversion, the fifth?  Once again, the sixteenth notes promise rhythmic acceleration, and indeed propel the motive forward for an entire measure, but by measure two, the lengthened syncopations (four, each a beat and a half long) once again slow the progression down.  What in the second variation took a half measure to accomplish has been extended to a full measure, enhancing the start-stop opposition.  Further emphasizing the opposition is the fact that it is repeated in truncated form, making the final variation six beats longer than the other two statements (if one counted by measures, the final variation, at four measures, is twice as long as the other two variations).  The syncopated notes vary the pattern of descending fourths and thirds by using ascending seconds.


Ex. 6: Variations for Winds, Strings, and Keyboards, Flute 1, m. 313-314.


Increasing rhythmic complexity also characterizes the cello motive as well.  Whereas in the first variation, the cello advanced ponderously by whole or tied notes, in the second variation, movement picks up to include half notes much more frequently.  Yet in the case of the cello motive, the rhythmic acceleration occurs in an arch form: the motive returns to tied whole notes in the third variation. 

Correlating with this arch progression in rhythm is the variation in texture.  The first variation opens with the relentlessly present winds and keyboards and supplements those sections with the expansive string section.  In the second variation, however, the texture thins as the winds and keyboards drop out on occasion, giving our ear the opportunity to attend to the cello more closely.  Freed from the distracting chatter of the upper voices, the cello finds room to speak.  When, in the third variation, the winds and keyboards return to centre stage, the cello once again recedes to its subsidiary position.   

In addition to rhythmic variation, the cello motive also undergoes a morphing of a different kind.  Just as the descent of fourths (and the inversion of fifths) and thirds play a major role in the upper voice motive, so the play of fourths and seconds affect the structure of the cello motive.  The first variation proceeds (as the key signature changes did) far away from home centre in the first half and then returns by conventional routes during the second half (Ex. 7):  

Ex. 7: Variations for Winds, Strings, and Keyboards, Reduction of Cello Line, Variation 1.


This basic outline shape is preserved through the second variation, as the half notes in Ex. 8 demonstrate.  The first three notes of the motive and the last three notes form groups of intervals consisting of fourths and seconds.  In the second variation, not only is the basic outline of the original motive preserved, but it is expanded through the use of inversions and retrogressions of the second-fourth combination.  Not every note can be grouped into one of these second-fourth pitch collections, but several variations of collection can be found.

Ex. 8: Variations for Winds, Strings, and Keyboards, Reduction of Cello Line, Var. 2.


Again, the basic motive is preserved in the third variation (see the half notes in Ex. 9).  However, the variations on second-fourth patterns have been exchanged for a pattern of movement by step followed by movement by wide leaps.  Perhaps this movement is the idea of seconds (movement by step) and fourths (movement by leaps) expanded even further (stretching the motive out).  In any case, each variation is slightly longer than the previous, thus progressing by length as well as by rhythmic complexity.


Ex. 9: Variations for Winds, Strings, and Keyboards, Reduction of Cello Line, Var. 3.


The Theme: Where Is It?


If the upper voices, whose repetitiveness gives the ear something to follow, are mostly undergoing microlevel changes, where do we find the macrolevel theme or statement?  Is the theme in fact in the cello counter-motive?  The cello counter-motive certainly works closely with the theme. However, the theme itself is found in the progression of tonal centres that are indicated by changing key signatures.  Departing from a common practice, the theme is not presented initially in its simplest version prior to the variations.  Rather, we encounter the theme in media res.  Thus the first appearance of the theme is in fact its first variation.  Yet since the theme itself changes little, one might compare the form of Reich’s piece to a passacaglia in which the progression of key signatures fulfills the same function as the ground bass.


The key signatures can be arranged according to the pattern found in Ex. 10-12.  The pattern is preserved in the second and third statements (with the exchange of the initial 5 sharps for 4 flats which, as it results in one enharmonic equivalent of tonal centres, is really a minor modification).  After repeating the pattern precisely in the third statement, the key signature changes one last time to reverse the order, as if in the coda the piece seeks to double back upon itself.  The ambiguity which characterized the opening motive is echoed in the piece’s refusal to come to rest in a final tonal centre.  We are left unsure of whether the piece actually ended, or whether it is merely taking a rest.  The order of the key signatures’ tonics produces a major triad in first inversion, and then a scale-wise descent before ascending by fifths to arrive back home at the initial tone centre (and despite whether you want to argue that the tonal centre is c or E-flat, the movement away and return to home happen in the same way).


Ex. 10: Variations for Winds, Strings, and Keyboards, Key Progressions, Var. 1.


Ex. 11: Variations for Winds, Strings, and Keyboards, Key Progressions, Va. 2.


Ex. 12: Variations for Winds, Strings, and Keyboards, Key Progressions, Var. 3.


The shape of the overall piece is an arch form, with a progression toward the end.  The building rhythmic complexity of each statement means the piece does not return fully to the original structure, but advances forward.  The return to the original texture (relentless winds/keyboards with supporting cello line), however, hints at a cyclical construction that opposes a straightforward linearity.  A play of oppositions and delight in ambiguity once again comes forth.  This play is illustrated in Fig. 1 by an arc that never fully returns to the starting level of intensity, but rather finishes at a higher level. 

Fig. 1: Variations for Winds, Strings, and Keyboards, Diagram of Arch Form.

Nowhere is this ambiguity more forcefully stated than in the coda (so named because this final section acts as a tag or a tail coming after the completion of the third variation).  After the theme has finally reached the home key of three flats for the last time, then it reverses direction, turning upon itself to retrace its steps (refer back to Table 2).  Codas normally fulfill a formal function of extension: a coda will extend a piece of music past the point where its formal structure ends before finally wrapping up (thus further emphasizing closure in the tonic by extending the tonic key just a little further). Here, however, the coda does not emphasize closure, but pulls away from the home tonal centre; thus, though it serves a traditional function of extension, it disrupts rather than confirms the sense of return to a home key.  If the listeners had been hoping for a concluding sonority that indicated which tone had truly been the dominant one (one that had merely been lurking in obscurity during the piece and was now ready to emerge triumphant), they are unfortunately to be disappointed.  Indeed, the piece ends even more ambiguously than it began.  For whereas the beginning vacillated between two choices, the end offers many choices: all the tones are stacked on top of each other into one giant thirteenth chord.  The thirteenth chord has no root. One can begin with any of the tones and stack upwards by thirds until all available tones have been used.  Thus, the thirteenth chord most strikingly symbolizes the ambiguity that has marked the piece.  The presence of all the tones indicates the importance of all, dissolving tonal hierarchy at the end and fading away.  Indeed, the expanse of the piece also lends itself to the feeling of timelessness.  The sparseness of the open fifths and fourths and the pentatonic scale flavor the harmony with sounds that, in the Western canon, appear to be exotic. 


Throughout the Variations for Winds, Strings, and Keyboards, Reich relies on a very compact supply of basic motivic material in order to build his piece.  He draws both upon the tradition of the West (the key signatures of Western modes as well as the skeletal outline of progression by fifths) and the East (pentatonic scales) in order to create a blend of sounds.  He also mixes the Western idea of narrative growth, progression, and arrival with an Eastern nonlinear alternative, not only through juxtaposing the two alternatives against each other, but also through the exploration of ambiguity within the Western system itself.  The play of sounds evokes a Derridean sense of différance, as even the end (the traditional place of finality) eludes the resolution of ambiguity; we are left suspended with our expectations unfulfilled.  Perhaps we are meant to reexamine those expectations.  Regardless, Variations for Winds, Strings, and Keyboards performs a fascinating interplay of style and sound that does cause us to reexamine our understanding of finality and end.























Potter, Keith.  Four Musical Minimalists; La Monte Young, Terry Riley, Steve Reich, Philip Glass.  Cambridge: Cambridge University Press, 2000.

Reich, Steve. Variations for Winds, Strings, and Keyboards. London: Hendon Music, 1981.

Steinberg, Michael.  Variations for Strings, Winds, and Keyboard.  West Germany: Philips), 1984, linear notes.




[1] Michael Steinberg, Variations for Strings, Winds, and Keyboard (West Germany: Philips), 1984, linear notes.

[2] Keith Potter, Four Musical Minimalists; La Monte Young, Terry Riley, Steve Reich, Philip Glass (Cambridge: Cambridge University Press, 2000), 8.

[3] Michael Steinberg, liner notes.

[4] Michael Steinberg, liner notes.

[5] Ibid.

[6] The form of variation itself emphasizes opposition, since variation arises from the play between same/different.

[7] One might argue that the binaries never really play, since the composer’s perspective governs the production of sounds and the listener’s perspective governs reception. Our perspective might hear and understand the tonal/pentatonic sounds as West/East, when in reality these notes don’t represent anything in particular. Yet since we can’t approach a piece of music from outside our perspective, I will use the binaries I have outlined above.

[8] For reasons of space, I refer to this and ensuing examples as the Flute 1 part. However, the piano and electric organ double the flutes in all the examples used in this paper.

[9] Keith Potter, 151.

[10] Since the phasing that occurs in Variations for Winds, Strings, and Keyboards is written out rather than improvised, it is technically a variation on the phasing technique rather than true phasing.