Copland Piano Variations
Encyclopedia
The Piano Variations of American
composer
Aaron Copland
were written for piano solo from January to October 1930. They were dedicated to American writer Gerald Sykes and were originally published by Cos Cob Press in 1932, which merged with Arrow Music Press in 1938 and was taken over by Boosey & Hawkes
in 1956. The approximate performance time is 11 minutes.
. The influence of composition pedagogue Nadia Boulanger
, with whom Copland studied in Paris at the Fontainebleau School of Music for Americans, is prevalent in the formal style, logic, patterns, and attention to detail in the Piano Variations and other works in this period.
Copland stated that he worked on the variations
individually without an agenda for fitting them together or sequencing them, which seems to contradict the piece's highly ordered construction and seemingly inevitable development. Copland acknowledged this contradiction but maintained that, in fact, "One fine day when the time was right, the order of the variations fell into place." Copland had ambitious plans for this "serious piano piece" — the first of three including the Piano Variations (1930), the Piano Sonata (1939-41), and the Piano Fantasy (1957); he worked painstakingly and thought at epic proportions, saying he "should like to call them like Bach
did the Goldberg Variations
— but thus far haven't been able to think up a good one."
The Orchestral Variations are scored for the following instrumentation.
Woodwinds:
Brass
:
Harp
Strings
Percussion:
very highly for his refined tone and subtle coloration, especially in the performance of Debussy, and insisted that no one else could give a satisfactory premiere of his masterpiece. Unfortunately, Gieseking turned down Copland's request for a premiere due to the piece's "crude dissonances" and "severity of style." Copland thus premiered the piece himself at a League of Composers
Concert in New York on January 4, 1931.
The Piano Variations were praised in some esoteric circles, but the public was generally courteous but lukewarm in its reception. The work was variously described as new, strange, dissonant, stark, bare, and disconcerting. Critic Paul Rosenfeld
contemplated its "flinty, metallic sonorities." American composer Marc Blitzstein
called it "Lithic." The cold, hard tone of Copland's playing at the premiere, far from that of a concert pianist, lended a sharper edge to an already austere work. Leonard Bernstein
later reported that he adored the piece, which was "hard as nails," and also used it at parties to "empty the room, guaranteed, in two minutes." It was to him a "synonym for modern music — so prophetic, harsh and wonderful, and so full of modern feeling and thinking."
Despite the wide spectrum of opinion, the Piano Variations were immediately recognized for their originality and made a lasting impression. The New York Herald Tribune reported that in the piece, Copland "sardonically thumbed his nose at all those esthetic attributes which have hitherto been considered essential to the creation of music." The work is now regarded as one of the most significant in contemporary piano literature.
Dancer-choreographer Martha Graham
requested permission to choreograph a solo piece on the Piano Variations. At Copland's consent, she produced Dithyrambic, an evocation of Dionysus
that was received with the highest enthusiasm. Copland admitted to being "utterly astonished that anyone could consider this kind of music suitable for dance... although her choreography was considered as complex and abstruse as my music."
techniques of Schoenberg
. The concision, rigor, and lack of ornamentation have been compared to that of the style of Anton Webern
(as in his Variations for piano). The dissonance
s (ubiquitous minor seconds, major sevenths and ninths) are precisely chosen for their degree of "shock value". While working on the Piano Variations, Copland cultivated a tautness and clarity of form and texture that became a precursor to the style of his other works.
Copland does not actually follow the precepts of the Second Viennese School
exactly, although he considers them. Aside from the fact that the four-note "row" is eight tones short of being a 12-tone
row, Copland frequently uses repetition in a declamatory style, as well as modifies and inserts new ideas into his motifs. This is another, smaller-scale form of "variation" that pervades the whole piece. This additional degree of freedom for the composer's imagination permits a gradual metamorphosis of the theme, and in a short period of time he explores many different moods, textures, tonal centers, harmonies, tempi, and rhythms, with a powerful cumulative effect. Copland describes the result as manifesting a "very dry and bare grandiosity."
Copland also experimented with the potential of the physical instrument, as he did with microtones on the stringed instruments in Vitebsk
. In the Piano Variations, some notes are held down silently while pitches selected from their overtone series are struck, which produces an effect of ringing resonances without hammering the tones directly.
Another prominent characteristic is the piece's rhythmic irregularity. The meters change constantly within an essentially 4/4 framework.
Copland instructs the performer to "strike each note sharply" in the opening motif, as each is highly significant. The first four notes, E – C – D# – C#, a view of the octatonic scale, "seed" the whole work by determining the language of its harmonies and pitches. Some scholars believe that the presence of the major
and minor third
in the motif are due to Copland's previous experimentation with jazz and the blues. Whether or not this is true, there is certainly an element of polytonality
immediately apparent in the third measure, which has an accented chord in both A major and minor.
Alternatively, the theme can be conceived of as part of a C-sharp minor scale; scale degrees ^3, ^7, ^2 and then ^1. This rather diatonic sequence is obscured by Copland's crunchy harmonies throughout the rest of the piece, but despite dissonances going on around it, whenever this theme arises again its pull engenders a sense of tonic in the listener, which makes the otherwise chaotic sounds comprehensible.
The organization of the piece partitions the variations into halves; variations 1-10 can be considered a unit with two large sections of five variations each. In this entire first half, the quarter note functions as the basic rhythmic unit. What differs between the two five-variation sets is the tonal center of the four-note motif; in variations 1-5 it is as stated in the theme, and in variations 6-10 it is permitted to be transposed.
This variation is a simple canon at the unison.
The theme expands into registers in a sort of dialogue in the first phrase, and is harmonized in the second phrase.
There is dialogue of the theme against itself as in variation 2, but Copland adds dotted rhythms and pointillist effects that further broaden the range.
(mm. 34-37)
The theme harmonized in three voices, over which a fourth melodic line wanders lyrically.
The chords thicken and become accented, increasing drama and intensity.
This variation marks the end of first harmonic section.
In the second half of the first unit (variations 6-10), the four-note motif is transposed. For this particular variation, it is transposed up a minor third, now reading G — Eb — F# — E. From here on, the placement of the theme is sometimes less apparent amidst the increasing complexity of surrounding elements, so Copland indicates to "mark the melody."
The mood becomes bolder as the theme sweeps in spaced-out quarter notes up the keyboard, settling on E-major triads (and one in F major) at the end of each gesture. This is an example of Copland's ability to weave consonance seamlessly with dissonance.
(mm. 68-72)
Copland marks the section to be played "blurred," as if a murk of brewing musical ideas. The four notes transpose up another third to B — G — Bb — Ab and appear in the inner voice of the left hand.
This warm and singing variation brings back the original theme's transposition in the right hand. The left hand uses a different transposition: G# — E — G — F.
The four-motif, F — Db — E — D, is now marked fortissimo and spans three octaves. Material from variation 4 is repeated before transitioning into the second half of the variations. This cyclic
technique unifies and concludes the first half of the variations.
The second half starts in a quiet, improvisational interlude over F# — D — F — Eb (up a half step).
This timid scherzo is the beginning of a slow building of intensity to the climax of the entire piece.
Another scherzo in the manner of variation 12.
The original four notes come back with a new orthography of E — C — Eb — Db. This transposition is maintained for next five variations, which are more concerned about rhythmic development.
The theme appears in augmentation amidst a circling pattern of eighth notes.
(mm.169-172)
Chords interrupt the line, with frequent changes of meter.
Runs and leaping octaves are tempered by a single consonant, static phrase in the middle of the variation comprising repeated E-major chords in the right hand and a left hand oscillating irregularly between C and E.
Another scherzo reminds the listener of variations 12 and 13, placing this variation in the second half and putting the imminent climax in perspective.
This variation starts calmly with quiet, sustained chords over B—G—Bb—Ab before launching the ascent to the climax.
Variation 20 is considerably longer than all the others. The motive moves forward and in retrograde simultaneously in a nervous, excited rhythm characterized by 32nd notes. The brilliant climax brings the performer to the extremes of the instrument's range.
The coda synthesizes material from many of the variations in a slow, stately, almost orchestral manner. The original relationship of the four-note motif returns.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
composer
Composer
A composer is a person who creates music, either by musical notation or oral tradition, for interpretation and performance, or through direct manipulation of sonic material through electronic media...
Aaron Copland
Aaron Copland
Aaron Copland was an American composer, composition teacher, writer, and later in his career a conductor of his own and other American music. He was instrumental in forging a distinctly American style of composition, and is often referred to as "the Dean of American Composers"...
were written for piano solo from January to October 1930. They were dedicated to American writer Gerald Sykes and were originally published by Cos Cob Press in 1932, which merged with Arrow Music Press in 1938 and was taken over by Boosey & Hawkes
Boosey & Hawkes
Boosey & Hawkes is a British music publisher purported to be the largest specialist classical music publisher in the world. Until 2003, it was also a major manufacturer of brass, string and wind musical instruments....
in 1956. The approximate performance time is 11 minutes.
Background
The Piano Variations were a product of Copland's second-style period, also called the abstract period, which comprised only instrumental (non-vocal) compositions. During this time, the composer moved away from the jazzy idioms he experimented with in the 1920s and started working more in the direction of absolute musicAbsolute music
Absolute music is a concept in music that describes music as an art form separated from formalisms or other considerations; it is not explicitly about anything; it is non-representational. In contrast to program music, absolute music makes sense without accompanying words, images, drama, or...
. The influence of composition pedagogue Nadia Boulanger
Nadia Boulanger
Nadia Boulanger was a French composer, conductor and teacher who taught many composers and performers of the 20th century.From a musical family, she achieved early honours as a student at the Paris Conservatoire, but believing that her talent as a composer was inferior to that of her younger...
, with whom Copland studied in Paris at the Fontainebleau School of Music for Americans, is prevalent in the formal style, logic, patterns, and attention to detail in the Piano Variations and other works in this period.
Copland stated that he worked on the variations
Variation (music)
In music, variation is a formal technique where material is repeated in an altered form. The changes may involve harmony, melody, counterpoint, rhythm, timbre, orchestration or any combination of these.-Variation form:...
individually without an agenda for fitting them together or sequencing them, which seems to contradict the piece's highly ordered construction and seemingly inevitable development. Copland acknowledged this contradiction but maintained that, in fact, "One fine day when the time was right, the order of the variations fell into place." Copland had ambitious plans for this "serious piano piece" — the first of three including the Piano Variations (1930), the Piano Sonata (1939-41), and the Piano Fantasy (1957); he worked painstakingly and thought at epic proportions, saying he "should like to call them like Bach
Bạch
Bạch is a Vietnamese surname. The name is transliterated as Bai in Chinese and Baek, in Korean.Bach is the anglicized variation of the surname Bạch.-Notable people with the surname Bạch:* Bạch Liêu...
did the Goldberg Variations
Goldberg Variations
The Goldberg Variations, BWV 988, is a work for harpsichord by Johann Sebastian Bach, consisting of an aria and a set of 30 variations. First published in 1741, the work is considered to be one of the most important examples of variation form...
— but thus far haven't been able to think up a good one."
Transcription as Orchestral Variations (1957)
Copland transcribed the Piano Variations for orchestra in 1957 after a commission from the Louisville Symphony Orchestra. These Orchestral Variations were premiered the following year under conductor Robert Whitney. Copland regarded the "lean, percussive and rather harmonically severe" quality of the piano as essential to the Piano Variations in 1930, but after 27 years, reinvented the work to take advantage of a full orchestral palette. The Orchestral Variations offer a new perspective on the work, focusing instead on the contrasts of its multifarious moods and colors.The Orchestral Variations are scored for the following instrumentation.
Woodwinds:
- 2 fluteWestern concert fluteThe Western concert flute is a transverse woodwind instrument made of metal or wood. It is the most common variant of the flute. A musician who plays the flute is called a flautist, flutist, or flute player....
s (both doubling piccoloPiccoloThe piccolo is a half-size flute, and a member of the woodwind family of musical instruments. The piccolo has the same fingerings as its larger sibling, the standard transverse flute, but the sound it produces is an octave higher than written...
) - OboeOboeThe oboe is a double reed musical instrument of the woodwind family. In English, prior to 1770, the instrument was called "hautbois" , "hoboy", or "French hoboy". The spelling "oboe" was adopted into English ca...
- English horn
- 2 B-flat clarinetClarinetThe clarinet is a musical instrument of woodwind type. The name derives from adding the suffix -et to the Italian word clarino , as the first clarinets had a strident tone similar to that of a trumpet. The instrument has an approximately cylindrical bore, and uses a single reed...
s (2nd doubling bass clarinetBass clarinetThe bass clarinet is a musical instrument of the clarinet family. Like the more common soprano B clarinet, it is usually pitched in B , but it plays notes an octave below the soprano B clarinet...
) - 2 bassoonBassoonThe bassoon is a woodwind instrument in the double reed family that typically plays music written in the bass and tenor registers, and occasionally higher. Appearing in its modern form in the 19th century, the bassoon figures prominently in orchestral, concert band and chamber music literature...
s
Brass
Brass instrument
A brass instrument is a musical instrument whose sound is produced by sympathetic vibration of air in a tubular resonator in sympathy with the vibration of the player's lips...
:
- 4 hornHorn (instrument)The horn is a brass instrument consisting of about of tubing wrapped into a coil with a flared bell. A musician who plays the horn is called a horn player ....
s in F - 2 trumpetTrumpetThe trumpet is the musical instrument with the highest register in the brass family. Trumpets are among the oldest musical instruments, dating back to at least 1500 BCE. They are played by blowing air through closed lips, producing a "buzzing" sound which starts a standing wave vibration in the air...
s in B-flat - 3 tromboneTromboneThe trombone is a musical instrument in the brass family. Like all brass instruments, sound is produced when the player’s vibrating lips cause the air column inside the instrument to vibrate...
s - TubaTubaThe tuba is the largest and lowest-pitched brass instrument. Sound is produced by vibrating or "buzzing" the lips into a large cupped mouthpiece. It is one of the most recent additions to the modern symphony orchestra, first appearing in the mid-19th century, when it largely replaced the...
Harp
Harp
The harp is a multi-stringed instrument which has the plane of its strings positioned perpendicularly to the soundboard. Organologically, it is in the general category of chordophones and has its own sub category . All harps have a neck, resonator and strings...
Strings
String section
The string section is the largest body of the standard orchestra and consists of bowed string instruments of the violin family.It normally comprises five sections: the first violins, the second violins, the violas, the cellos, and the double basses...
Percussion:
- TimpaniTimpaniTimpani, or kettledrums, are musical instruments in the percussion family. A type of drum, they consist of a skin called a head stretched over a large bowl traditionally made of copper. They are played by striking the head with a specialized drum stick called a timpani stick or timpani mallet...
- 2 Percussionists playing:
- Snare drumSnare drumThe snare drum or side drum is a melodic percussion instrument with strands of snares made of curled metal wire, metal cable, plastic cable, or gut cords stretched across the drumhead, typically the bottom. Pipe and tabor and some military snare drums often have a second set of snares on the bottom...
- Tenor drumTenor drumA tenor drum is a cylindrical drum that is higher pitched than a bass drum.In a symphony orchestra's percussion section, a tenor drum is a low-pitched drum, similar in size to a field snare, but without snares and played with soft mallets or hard sticks. Under various names, the drum has been used...
- Bass drumBass drumBass drums are percussion instruments that can vary in size and are used in several musical genres. Three major types of bass drums can be distinguished. The type usually seen or heard in orchestral, ensemble or concert band music is the orchestral, or concert bass drum . It is the largest drum of...
- Bongo drums
- Conga drum
- CymbalCymbalCymbals are a common percussion instrument. Cymbals consist of thin, normally round plates of various alloys; see cymbal making for a discussion of their manufacture. The greater majority of cymbals are of indefinite pitch, although small disc-shaped cymbals based on ancient designs sound a...
s - Tam-tam
- Wood blockWood blockA woodblock is essentially a small piece of slit drum made from a single piece of wood and used as a percussion instrument. It is struck with a stick, making a characteristically percussive sound....
- GlockenspielGlockenspielA glockenspiel is a percussion instrument composed of a set of tuned keys arranged in the fashion of the keyboard of a piano. In this way, it is similar to the xylophone; however, the xylophone's bars are made of wood, while the glockenspiel's are metal plates or tubes, and making it a metallophone...
- XylophoneXylophoneThe xylophone is a musical instrument in the percussion family that consists of wooden bars struck by mallets...
- Tubular bellTubular bellTubular bells are musical instruments in the percussion family. Each bell is a metal tube, 30–38 mm in diameter, tuned by altering its length. Its standard range is from C4-F5, though many professional instruments reach G5 . Tubular bells are often replaced by studio chimes, which are a smaller...
s - Antique cymbals
- Cow bellCow bellA cowbell or cow bell is a bell worn by freely roaming livestock, so that they do not run away or wander off without being heard. While bells were used on various types of animals, they are typically referred to as "cowbells" due to their extensive use with cattle.A trychel is a large cow bell...
- Snare drum
Reception
Copland regarded pianist Walter GiesekingWalter Gieseking
Walter Wilhelm Gieseking was a French-born German pianist and composer.-Biography:Born in Lyon, France, the son of a German doctor and lepidopterist, Gieseking first started playing the piano at the age of four, but without formal instruction...
very highly for his refined tone and subtle coloration, especially in the performance of Debussy, and insisted that no one else could give a satisfactory premiere of his masterpiece. Unfortunately, Gieseking turned down Copland's request for a premiere due to the piece's "crude dissonances" and "severity of style." Copland thus premiered the piece himself at a League of Composers
League of Composers
The League of Composers/International Society for Contemporary Music is a society whose stated mission is "to produce the highest quality performances of new music, to champion American composers in the United States and abroad, and to introduce American audiences to the best new music from around...
Concert in New York on January 4, 1931.
The Piano Variations were praised in some esoteric circles, but the public was generally courteous but lukewarm in its reception. The work was variously described as new, strange, dissonant, stark, bare, and disconcerting. Critic Paul Rosenfeld
Paul Rosenfeld
Paul Leopold Rosenfeld was an American journalist, best known as a music critic.He was born in New York City into a German-Jewish family...
contemplated its "flinty, metallic sonorities." American composer Marc Blitzstein
Marc Blitzstein
Marcus Samuel Blitzstein, better known as Marc Blitzstein , was an American composer. He won national attention in 1937 when his pro-union musical The Cradle Will Rock, directed by Orson Welles, was shut down by the Works Progress Administration...
called it "Lithic." The cold, hard tone of Copland's playing at the premiere, far from that of a concert pianist, lended a sharper edge to an already austere work. Leonard Bernstein
Leonard Bernstein
Leonard Bernstein August 25, 1918 – October 14, 1990) was an American conductor, composer, author, music lecturer and pianist. He was among the first conductors born and educated in the United States of America to receive worldwide acclaim...
later reported that he adored the piece, which was "hard as nails," and also used it at parties to "empty the room, guaranteed, in two minutes." It was to him a "synonym for modern music — so prophetic, harsh and wonderful, and so full of modern feeling and thinking."
Despite the wide spectrum of opinion, the Piano Variations were immediately recognized for their originality and made a lasting impression. The New York Herald Tribune reported that in the piece, Copland "sardonically thumbed his nose at all those esthetic attributes which have hitherto been considered essential to the creation of music." The work is now regarded as one of the most significant in contemporary piano literature.
Dancer-choreographer Martha Graham
Martha Graham
Martha Graham was an American modern dancer and choreographer whose influence on dance has been compared with the influence Picasso had on modern visual arts, Stravinsky had on music, or Frank Lloyd Wright had on architecture.She danced and choreographed for over seventy years...
requested permission to choreograph a solo piece on the Piano Variations. At Copland's consent, she produced Dithyrambic, an evocation of Dionysus
Dionysus
Dionysus was the god of the grape harvest, winemaking and wine, of ritual madness and ecstasy in Greek mythology. His name in Linear B tablets shows he was worshipped from c. 1500—1100 BC by Mycenean Greeks: other traces of Dionysian-type cult have been found in ancient Minoan Crete...
that was received with the highest enthusiasm. Copland admitted to being "utterly astonished that anyone could consider this kind of music suitable for dance... although her choreography was considered as complex and abstruse as my music."
Overview
Unlike a traditional theme and variations, Copland's Piano Variations are not episodic. They are continuously played through, in an undisrupted development of the four-note "row" in the theme from which Copland builds the rest of the piece. All of the content can be traced back to this or transpositions of this four-note otif (music)|motif, suggesting the serialistSerialism
In music, serialism is a method or technique of composition that uses a series of values to manipulate different musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, though his contemporaries were also working to establish serialism as one example of...
techniques of Schoenberg
Schoenberg
Schoenberg is the surname of several persons:* Arnold Schoenberg , Austrian-American composer* Claude-Michel Schoenberg , French record producer, actor, singer, popular songwriter, and musical theatre composer...
. The concision, rigor, and lack of ornamentation have been compared to that of the style of Anton Webern
Anton Webern
Anton Webern was an Austrian composer and conductor. He was a member of the Second Viennese School. As a student and significant follower of Arnold Schoenberg, he became one of the best-known exponents of the twelve-tone technique; in addition, his innovations regarding schematic organization of...
(as in his Variations for piano). The dissonance
Dissonance
Dissonance has several meanings, all related to conflict or incongruity:*Consonance and dissonance in music are properties of an interval or chord*Cognitive dissonance is a state of mental conflict...
s (ubiquitous minor seconds, major sevenths and ninths) are precisely chosen for their degree of "shock value". While working on the Piano Variations, Copland cultivated a tautness and clarity of form and texture that became a precursor to the style of his other works.
Copland does not actually follow the precepts of the Second Viennese School
Second Viennese School
The Second Viennese School is the group of composers that comprised Arnold Schoenberg and his pupils and close associates in early 20th century Vienna, where he lived and taught, sporadically, between 1903 and 1925...
exactly, although he considers them. Aside from the fact that the four-note "row" is eight tones short of being a 12-tone
Twelve-tone technique
Twelve-tone technique is a method of musical composition devised by Arnold Schoenberg...
row, Copland frequently uses repetition in a declamatory style, as well as modifies and inserts new ideas into his motifs. This is another, smaller-scale form of "variation" that pervades the whole piece. This additional degree of freedom for the composer's imagination permits a gradual metamorphosis of the theme, and in a short period of time he explores many different moods, textures, tonal centers, harmonies, tempi, and rhythms, with a powerful cumulative effect. Copland describes the result as manifesting a "very dry and bare grandiosity."
Copland also experimented with the potential of the physical instrument, as he did with microtones on the stringed instruments in Vitebsk
Vitebsk
Vitebsk, also known as Viciebsk or Vitsyebsk , is a city in Belarus, near the border with Russia. The capital of the Vitebsk Oblast, in 2004 it had 342,381 inhabitants, making it the country's fourth largest city...
. In the Piano Variations, some notes are held down silently while pitches selected from their overtone series are struck, which produces an effect of ringing resonances without hammering the tones directly.
Another prominent characteristic is the piece's rhythmic irregularity. The meters change constantly within an essentially 4/4 framework.
Analysis
- Theme
Copland instructs the performer to "strike each note sharply" in the opening motif, as each is highly significant. The first four notes, E – C – D# – C#, a view of the octatonic scale, "seed" the whole work by determining the language of its harmonies and pitches. Some scholars believe that the presence of the major
Major third
In classical music from Western culture, a third is a musical interval encompassing three staff positions , and the major third is one of two commonly occurring thirds. It is qualified as major because it is the largest of the two: the major third spans four semitones, the minor third three...
and minor third
Minor third
In classical music from Western culture, a third is a musical interval encompassing three staff positions , and the minor third is one of two commonly occurring thirds. The minor quality specification identifies it as being the smallest of the two: the minor third spans three semitones, the major...
in the motif are due to Copland's previous experimentation with jazz and the blues. Whether or not this is true, there is certainly an element of polytonality
Polytonality
The musical use of more than one key simultaneously is polytonality . Bitonality is the use of only two different keys at the same time...
immediately apparent in the third measure, which has an accented chord in both A major and minor.
Alternatively, the theme can be conceived of as part of a C-sharp minor scale; scale degrees ^3, ^7, ^2 and then ^1. This rather diatonic sequence is obscured by Copland's crunchy harmonies throughout the rest of the piece, but despite dissonances going on around it, whenever this theme arises again its pull engenders a sense of tonic in the listener, which makes the otherwise chaotic sounds comprehensible.
- Var. 1 (m. 12)
The organization of the piece partitions the variations into halves; variations 1-10 can be considered a unit with two large sections of five variations each. In this entire first half, the quarter note functions as the basic rhythmic unit. What differs between the two five-variation sets is the tonal center of the four-note motif; in variations 1-5 it is as stated in the theme, and in variations 6-10 it is permitted to be transposed.
This variation is a simple canon at the unison.
- Var. 2 (m. 21)
The theme expands into registers in a sort of dialogue in the first phrase, and is harmonized in the second phrase.
- Var. 3 (m. 32)
There is dialogue of the theme against itself as in variation 2, but Copland adds dotted rhythms and pointillist effects that further broaden the range.
(mm. 34-37)
- Var. 4 (m. 42)
The theme harmonized in three voices, over which a fourth melodic line wanders lyrically.
- Var. 5 (m. 49)
The chords thicken and become accented, increasing drama and intensity.
This variation marks the end of first harmonic section.
- Var. 6 (m. 57)
In the second half of the first unit (variations 6-10), the four-note motif is transposed. For this particular variation, it is transposed up a minor third, now reading G — Eb — F# — E. From here on, the placement of the theme is sometimes less apparent amidst the increasing complexity of surrounding elements, so Copland indicates to "mark the melody."
- Var. 7 (m. 67)
The mood becomes bolder as the theme sweeps in spaced-out quarter notes up the keyboard, settling on E-major triads (and one in F major) at the end of each gesture. This is an example of Copland's ability to weave consonance seamlessly with dissonance.
(mm. 68-72)
- Var. 8 (m. 78)
Copland marks the section to be played "blurred," as if a murk of brewing musical ideas. The four notes transpose up another third to B — G — Bb — Ab and appear in the inner voice of the left hand.
- Var. 9 (m. 91)
This warm and singing variation brings back the original theme's transposition in the right hand. The left hand uses a different transposition: G# — E — G — F.
- Var. 10 (m. 104)
The four-motif, F — Db — E — D, is now marked fortissimo and spans three octaves. Material from variation 4 is repeated before transitioning into the second half of the variations. This cyclic
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
technique unifies and concludes the first half of the variations.
- Var. 11 (m. 113)
The second half starts in a quiet, improvisational interlude over F# — D — F — Eb (up a half step).
- Var. 12 (m. 125)
This timid scherzo is the beginning of a slow building of intensity to the climax of the entire piece.
- Var. 13 (m. 134)
Another scherzo in the manner of variation 12.
- Var. 14 (m. 142)
The original four notes come back with a new orthography of E — C — Eb — Db. This transposition is maintained for next five variations, which are more concerned about rhythmic development.
- Var. 15 (m. 168)
The theme appears in augmentation amidst a circling pattern of eighth notes.
(mm.169-172)
- Var. 16 (m. 201)
Chords interrupt the line, with frequent changes of meter.
- Var. 17 (m. 225)
Runs and leaping octaves are tempered by a single consonant, static phrase in the middle of the variation comprising repeated E-major chords in the right hand and a left hand oscillating irregularly between C and E.
- Var. 18 (m. 247)
Another scherzo reminds the listener of variations 12 and 13, placing this variation in the second half and putting the imminent climax in perspective.
- Var. 19 (m. 271)
This variation starts calmly with quiet, sustained chords over B—G—Bb—Ab before launching the ascent to the climax.
- Var. 20 (m. 286)
Variation 20 is considerably longer than all the others. The motive moves forward and in retrograde simultaneously in a nervous, excited rhythm characterized by 32nd notes. The brilliant climax brings the performer to the extremes of the instrument's range.
- Coda (m. 339)
The coda synthesizes material from many of the variations in a slow, stately, almost orchestral manner. The original relationship of the four-note motif returns.