Double variation
Encyclopedia
The double variation is a musical form used in classical music. It is a type of theme and variations
that employs two themes. In a double variation set, a first theme (to be called A here) is followed by a second theme (B), followed by a variation on A, then a variation on B, and so on with alternating A and B variations. Often there is a coda
at the end.
The double variation is strongly associated with the composer Joseph Haydn
, who wrote many such movements during his career.
, the sixth of that composer's Sonatas with Varied Reprises, (W. 50/6, H. 140), in C minor (1760). Elaine Sisman
, an authority on variations, notes "This set of sonatas was advertised in Vienna several times in the period in which Haydn wrote his first [double] variations."
While Haydn's double variations show considerable diversity, there are some general patterns.
As Haydn's career proceeded, he moved toward a very particular type of double variations, having the following additional specific characteristics.
also emerges as a major composer of double variations. With the partial exception of the Piano Trio in E flat major
, Op. 70 No. 2, which Sisman sees as an homage to Haydn, Beethoven's double variations have a rather different character. For instance, sometimes only the A theme is strongly varied, with B remaining relatively constant. Beethoven also likes to interrupt or truncate one or both themes, producing a less regular structure than Haydn's, seen in the often-complex structural formulae given below.
Thus flexibly construed, the double variation emerges as the musical form for some of the most famous of Beethoven's works. Here is a list of movements for which Sisman argues that a double-variation structure is present.
As Sisman notes, Beethoven placed his double variations in the same genres as Haydn: the piano trio, the string quartet, and the symphony.
' String Quintet No. 1
(1882) is described by Joanna Wyld as a set of double variations.
's Seventh Symphony
(1883/1885) is described by A. Peter Brown as a set of double variations.
's String Quintet Op. 97 (1893)
is described by Colin Lawson as a set of double variations.
, bassoon
and orchestral wind ensemble by Edward Harper
was premiered in 1989; see program notes.
Alternatively, some of the variations can be single (AxAxBxBx) and others double.
An example of this usage is found in Cedric T. Davie's discussion of the last movement of Beethoven's Piano Sonata Opus 109
, in which some but not all of the variations are double in the intended sense. The full formula for this movement (adapting Davie's verbal description) is:
The two kinds of "double variation" are not mutually exclusive. In Haydn's Piano Trio H:13, the first movement is a double variations in the first sense given in this article (that is, it takes the form ABA1B1A2B2), and the last variation of the B theme (B2) is a double variation in the second sense, with different treatment of the repeats in each half of the theme. There appears to be no standard nomenclature for keeping the two senses distinct.
dance suite, a dance movement was sometimes immediately followed by a single variation, which was called the "double".
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:...
that employs two themes. In a double variation set, a first theme (to be called A here) is followed by a second theme (B), followed by a variation on A, then a variation on B, and so on with alternating A and B variations. Often there is a coda
Coda (music)
Coda is a term used in music in a number of different senses, primarily to designate a passage that brings a piece to an end. Technically, it is an expanded cadence...
at the end.
The double variation is strongly associated with the composer Joseph Haydn
Joseph Haydn
Franz Joseph Haydn , known as Joseph Haydn , was an Austrian composer, one of the most prolific and prominent composers of the Classical period. He is often called the "Father of the Symphony" and "Father of the String Quartet" because of his important contributions to these forms...
, who wrote many such movements during his career.
The double variation in Haydn
The double variation first appears Haydn's work of the 1770s. Haydn may have been inspired by an earlier example of Carl Philipp Emanuel BachCarl Philipp Emanuel Bach
right|250pxCarl Philipp Emanuel Bach was a German Classical period musician and composer, the fifth child and second son of Johann Sebastian Bach and Maria Barbara Bach...
, the sixth of that composer's Sonatas with Varied Reprises, (W. 50/6, H. 140), in C minor (1760). Elaine Sisman
Elaine Sisman
Elaine Rochelle Sisman is the Anne Parsons Bender Professor of Music at Columbia University, where she has taught since 1982...
, an authority on variations, notes "This set of sonatas was advertised in Vienna several times in the period in which Haydn wrote his first [double] variations."
While Haydn's double variations show considerable diversity, there are some general patterns.
- Both themes have the same tonic, but in opposite modes, so that if A is major, B is minor, and vice versa.
- The second theme is usually thematically reminiscent of the first, though not so close as to be an actual variation of it.
- The total number of variations is small, often just one or two for each theme.
- The number of variations is (with just one exception) arranged to place the major theme last. Thus, if the first theme is major, Haydn generally uses ABABA form, but if the first theme is minor, Haydn uses ABABAB.
As Haydn's career proceeded, he moved toward a very particular type of double variations, having the following additional specific characteristics.
- The tempo is moderate, typically andante.
- The minor theme is placed first.
- Each theme is divided into two sections, and each section is repeated.
- The internal arrangement of both themes is often that of sonata formSonata formSonata form is a large-scale musical structure used widely since the middle of the 18th century . While it is typically used in the first movement of multi-movement pieces, it is sometimes used in subsequent movements as well—particularly the final movement...
, with the music moving to the dominant or relative major key in the first part, to remote keys in the first half of the second part, and then to a recapitulation of the opening material in the tonic key. This observation is made by Charles RosenCharles RosenCharles Rosen is an American pianist and author on music.-Life and career:In his youth he studied piano with Moriz Rosenthal. Rosenthal, born in 1862, had been a student of Franz Liszt...
(in The Classical Style) concerning the double variations in the Drumroll SymphonySymphony No. 103 (Haydn)The Symphony No. 103 in E-flat major, Hoboken 1/103, is the eleventh of the twelve so-called London Symphonies written by Joseph Haydn.This symphony is nicknamed "The Drumroll", after the long roll on the timpani with which it begins....
; it holds true in several other cases as well. - While assessments of emotional content are necessarily subjective, it is reasonable to claim that the minor themes sound tense and the major themes blissful. Jean-Yves Bras, writing in program notes for a performance of the Piano Trio H:23 (Harmonia Mundi 901400), describes the minor and major themes "somber" and "radiant", respectively. Charles Rosen, writing of the major theme from the Piano Trio H. 13, says that in it Haydn created "an emotion that was completely his own and that no other composer, not even Mozart, could duplicate - a feeling of ecstasy that is completely unsensual, almost amiable." Rosen's remark could be applied to several of the other major double variation themes.
List of works by Haydn written in double variation form
According to Sisman, Haydn wrote 21 double variation movements. Sisman's list is restated below in chronological order. Where different authorities provide different dates, both are given; NG = the New Grove (used by Sisman), MH = Maurice Hinson's edition of the piano sonatas. For the keys of the A and B sections, lower case designates minor; upper case major. The structural synopses are taken from Sisman with minor corrections; in Sisman's notation an asterisk means "altered".Year | Work | Form | A | B |
1770-75? (ES); before 1780 (MH) | Piano sonata H. XVI:36. 2: Scherzando | ABA1B1A2coda | A | a |
1771-3 (ES); ca. 1768-1770? (MH) | Piano sonata H. XVI:44. 2: Allegretto | ABA1B1; a minuet | g | G |
before 1778 (ES); 1771-1773? (MH) | Piano sonata H. XVI:33. Finale: Tempo di Minuet | ABA1B1A2; a minuet | D | d |
before 1778 (ES); 1773 (MH) | Piano sonata H. XVI:22. Finale: Tempo di Minuet | ABA1B1A2; a minuet | E | e |
1778/79 | Symphony No. 53 Symphony No. 53 (Haydn) The Symphony No. 53 in D major, Hoboken I/53, is a symphony by Joseph Haydn. It is often referred to by the subtitle "L'Impériale". The symphony was composed by 1774. It is scored for flute, two oboes, bassoon, two horns and strings.... , "L'Impériale". 2: Andante | ABA1B1A2A3 | A | a |
1778/79 | Symphony No. 70 Symphony No. 70 (Haydn) The Symphony No. 70 in D major, Hoboken 1/70, was written by Joseph Haydn to mark the start of construction of a new opera house on the Eszterháza estate... , 2: Specie d'un canone in contrapunto doppio: Andante | ABA1B1A2. | d | D |
1779 | Symphony No. 63 Symphony No. 63 (Haydn) The Symphony No. 63 in C major, Hoboken I/63, is a symphony by Joseph Haydn written sometime between 1779 and 1781. It is often known by the title of the second movement, La Roxelane, named for Roxelana, the influential wife of Suleiman the Magnificent of the Ottoman Empire... , "La Roxelane". 2: Allegretto (O piu tosto allegro) | ABA1B1A2*B2* | c | C |
1781 | String quartet Op. 33, No. 6 String Quartets, Op. 33 (Haydn) The Op. 33 String Quartets were written by Joseph Haydn in the summer and Autumn of 1781 for the Viennese publisher Artaria. This set of quartets has several nicknames, the most common of which is the "Russian" quartets, because Haydn dedicated the quartets to the Grand Duke Paul of Russia and... . 4: Allegretto | ABA1B1A2 | D | d |
before 1784 | Piano sonata H. XVI:34. 3: Vivace molto | ABA1*B1A2. First variation in A is lengthened by a reprise of the initial section. | e | E |
1784 | Piano sonata H. XVI:40. 1: Allegro innocente | ABA1B1A2. In the following movement, in ternary (ABA) form, the A sections form yet two more variations of the A theme of the opening movement. | G | g |
1789 | Piano sonata H. XVI:48. 1: Andante con espressione | ABA1B1A2 | C | c |
1786 | Symphony No. 82 Symphony No. 82 (Haydn) The Symphony No. 82 in C major, Hoboken 1/82, is the first of the so-called six Paris Symphonies written by Joseph Haydn. It is popularly known as the Bear Symphony .-Background:... . 2: Allegretto | ABA1B1A2coda | F | f |
1787 | String quartet Op. 50, No. 4. 2: Andante | ABA1B1A2 | A | a |
1788 | Symphony No. 90 Symphony No. 90 (Haydn) The Symphony No. 90 in C major, Hoboken 1/90, was written by Joseph Haydn in 1788 as part of a three-symphony commission by Comte d'Ogny for the Concerts de la Loge Olympique... . 2: Andante | ABA1B1A2coda | F | f |
1788 | String quartet Op. 55, No. 2, "The Razor". 1: Andante più tosto Allegretto | ABA1B1A2B2 | f | F |
1789 | Piano trio H. XV:13. 1: Andante | ABA1B1A2B2 | c | C |
1793 | Variations for solo piano in F minor Variations in F minor The Andante with variations in F minor , also known as Un piccolo divertimento, was composed for piano by Joseph Haydn in 1793, and is among his most popular piano works. The variations here are a set of double variations, the first theme is in F minor and the second theme in F major... , H. XVII:6. Andante | ABA1B1A2B2A* with extensive coda. This work is widely admired by commentators; Sisman calls it the "most profound" of all of Haydn's alternating variations. | f | F |
1793 | String quartet Op. 71, No. 3. 2: Andante con moto | ABAA1B1A2coda | B♭ | b♭ |
1794 | Piano trio H. XV:19 in G minor. 1: Andante | ABA1B1 followed by a second quasi-variation on B in Presto tempo, expanded to full sonata form. For discussion of this expansion, see Charles Rosen Charles Rosen Charles Rosen is an American pianist and author on music.-Life and career:In his youth he studied piano with Moriz Rosenthal. Rosenthal, born in 1862, had been a student of Franz Liszt... , The Classical Style, pp. 83-88. | g | G |
1795 | Piano trio H. XV:23 in D minor. 1: Andante molto | ABA1B1A2B2 with coda | d | D |
1795 | Symphony No. 103, "The Drumroll" Symphony No. 103 (Haydn) The Symphony No. 103 in E-flat major, Hoboken 1/103, is the eleventh of the twelve so-called London Symphonies written by Joseph Haydn.This symphony is nicknamed "The Drumroll", after the long roll on the timpani with which it begins.... . 2: Andante più tosto Allegretto | ABA1B1A2B2 form, with a long coda based on B. The themes are said to be based on Croatian folk tunes Haydn and folk music This article discusses the influence of folk music on the work of the composer Joseph Haydn .-Background:Haydn was of humble family, perhaps unusually so for a famous composer. His parents were working people . They dwelt in an obscure rural village, and had no musical training... . | c | C |
The double variation in Beethoven
Although the double variation is associated strongly with Haydn, Elaine Sisman has pointed out that, provided we adopt a somewhat looser definition of the form, Ludwig van BeethovenLudwig van Beethoven
Ludwig van Beethoven was a German composer and pianist. A crucial figure in the transition between the Classical and Romantic eras in Western art music, he remains one of the most famous and influential composers of all time.Born in Bonn, then the capital of the Electorate of Cologne and part of...
also emerges as a major composer of double variations. With the partial exception of the Piano Trio in E flat major
Piano Trios Nos. 5 - 6, Opus 70 (Beethoven)
Opus 70 is a set of two Piano Trios by Ludwig van Beethoven, written for piano, violin, and cello. They were published in 1809.The first, in D major, known as the Ghost, is one of his best known works in the genre . The D major trio features themes found in the second movement of Beethoven's...
, Op. 70 No. 2, which Sisman sees as an homage to Haydn, Beethoven's double variations have a rather different character. For instance, sometimes only the A theme is strongly varied, with B remaining relatively constant. Beethoven also likes to interrupt or truncate one or both themes, producing a less regular structure than Haydn's, seen in the often-complex structural formulae given below.
Thus flexibly construed, the double variation emerges as the musical form for some of the most famous of Beethoven's works. Here is a list of movements for which Sisman argues that a double-variation structure is present.
Year | Work | Form | A | B |
1802 | Third Symphony Symphony No. 3 (Beethoven) Ludwig van Beethoven's Symphony No. 3 in E flat major , also known as the Eroica , is a landmark musical work marking the full arrival of the composer's "middle-period," a series of unprecedented large scale works of emotional depth and structural rigor.The symphony is widely regarded as a mature... . 4: Allegro molto | AA1A2BAxB1A3B2Ax1B3B4coda | various, centered on E♭ | various, centered on E♭ |
1808 | Fifth Symphony Symphony No. 5 (Beethoven) The Symphony No. 5 in C minor, Op. 67, was written by Ludwig van Beethoven in 1804–08. This symphony is one of the most popular and best-known compositions in all of classical music, and one of the most often played symphonies. It comprises four movements: an opening sonata, an andante, and a fast... . 2: Andante con moto | ABA1B1A2, cadenza on A, B2 A3, coda based on A | A♭/once in A♭ minor | A♭-C, A♭-C, C |
1808 | Piano Trio Op. 70, No. 2 Piano Trios Nos. 5 - 6, Opus 70 (Beethoven) Opus 70 is a set of two Piano Trios by Ludwig van Beethoven, written for piano, violin, and cello. They were published in 1809.The first, in D major, known as the Ghost, is one of his best known works in the genre . The D major trio features themes found in the second movement of Beethoven's... . 2: Allegretto | AA1BA2B1 with coda | C | c |
1812 | Seventh Symphony Symphony No. 7 (Beethoven) Ludwig van Beethoven's Symphony No. 7 in A major, Op. 92, in 1811, was the seventh of his nine symphonies. He worked on it while staying in the Bohemian spa town of Teplice in the hope of improving his health. It was completed in 1812, and was dedicated to Count Moritz von Fries.At its debut,... . 2: Allegretto | AA1A2A3BA4, fugato on A, B1, coda based on A | a | A to C, A |
1824 | Ninth Symphony Symphony No. 9 (Beethoven) The Symphony No. 9 in D minor, Op. 125, is the final complete symphony of Ludwig van Beethoven. Completed in 1824, the symphony is one of the best known works of the Western classical repertoire, and has been adapted for use as the European Anthem... . 3: Adagio molto e cantabile | ABA1B1, episode on A, A2, episode1 on A, A3, episode2 on A, A3, coda | B♭ | D, then G |
1825 | String Quartet No. 15, Op. 132 String Quartet No. 15 (Beethoven) The Quartet in A minor, Op. 132, by Ludwig van Beethoven, was written in 1825, given its public premiere on November 6 of that year by the Schuppanzigh Quartet and was dedicated to Count Nicolai Galitzin, as were Opp. 127 and 130... . 3: Molto Adagio — Andante ("Heiliger Dankgesang") | ABA1B1A2 | F Lydian, notated C | D |
As Sisman notes, Beethoven placed his double variations in the same genres as Haydn: the piano trio, the string quartet, and the symphony.
Later double variations
After Beethoven, the double variation appears to have been only seldom employed. The following list is ordered chronologically.Brahms
The second movement of Johannes BrahmsJohannes Brahms
Johannes Brahms was a German composer and pianist, and one of the leading musicians of the Romantic period. Born in Hamburg, Brahms spent much of his professional life in Vienna, Austria, where he was a leader of the musical scene...
' String Quintet No. 1
String Quintet No. 1 (Brahms)
Johannes Brahms' String Quintet No. 1 in F major, Opus 88 was composed in 1882 in the spa town of Bad Ischl, Upper Austria, and published by the firm of Fritz Simrock. It was first performed at a chamber music evening in Frankfurt-on-Main on 29 December 1882....
(1882) is described by Joanna Wyld as a set of double variations.
Bruckner
The second movement of Anton BrucknerAnton Bruckner
Anton Bruckner was an Austrian composer known for his symphonies, masses, and motets. The first are considered emblematic of the final stage of Austro-German Romanticism because of their rich harmonic language, complex polyphony, and considerable length...
's Seventh Symphony
Symphony No. 7 (Bruckner)
Anton Bruckner's Symphony No. 7 in E major is one of his best-known symphonies. It was written between 1881 and 1883 and was revised in 1885. It is dedicated to Ludwig II of Bavaria. The premiere, given under Arthur Nikisch and the Gewandhaus Orchestra in the opera house at Leipzig on 30...
(1883/1885) is described by A. Peter Brown as a set of double variations.
Dvořák
The Larghetto movement of Antonín DvořákAntonín Dvorák
Antonín Leopold Dvořák was a Czech composer of late Romantic music, who employed the idioms of the folk music of Moravia and his native Bohemia. Dvořák’s own style is sometimes called "romantic-classicist synthesis". His works include symphonic, choral and chamber music, concerti, operas and many...
's String Quintet Op. 97 (1893)
String Quintet No. 3 (Dvorák)
The String Quintet in E-flat major, Op. 97, B. 180, was composed by Antonín Dvořák during the summer he spent in Spillville, Iowa in 1893. It is a "Viola Quintet" in that it is scored for string quartet with an extra viola. It was completed in just over a month, immediately after he wrote his...
is described by Colin Lawson as a set of double variations.
Harper
A set of double variations for oboeOboe
The 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...
, bassoon
Bassoon
The 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...
and orchestral wind ensemble by Edward Harper
Edward Harper
Edward Harper was an engineer who travelled to Colombo in 1921 to work in the Ceylon Telegraph Department. Harper was appointed Chief Engineer. He had an innovative mind and his passion was broadcasting...
was premiered in 1989; see program notes.
Distinct variations for repeated sections
Occasionally, authors on music use the term "double variation" in a quite different sense. This definition presupposes that the theme consists of two parts, each one repeated (that is, AABB). In a double variations of this kind, each repeat gets its own variation, as shown below:- AABB A1A2B1B2 A3A4B3B4 ...
Alternatively, some of the variations can be single (AxAxBxBx) and others double.
An example of this usage is found in Cedric T. Davie's discussion of the last movement of Beethoven's Piano Sonata Opus 109
Piano Sonata No. 30 (Beethoven)
Ludwig van Beethoven's Piano Sonata No. 30 in E major, Op. 109, composed in 1820, is the antepenultimate of his piano sonatas. In it, after the huge Hammerklavier sonata, Op. 106, Beethoven returns to a smaller scale and a more intimate character...
, in which some but not all of the variations are double in the intended sense. The full formula for this movement (adapting Davie's verbal description) is:
- Theme: AABB
- I. A1A1B1B1
- II. A2A3B2B3
- III. A3A4B3B4
- IV. A5A5B5B5
- V. A6A7B6B7
- VI. A8A9B8B9
- Coda, incorporating the original AABB
The two kinds of "double variation" are not mutually exclusive. In Haydn's Piano Trio H:13, the first movement is a double variations in the first sense given in this article (that is, it takes the form ABA1B1A2B2), and the last variation of the B theme (B2) is a double variation in the second sense, with different treatment of the repeats in each half of the theme. There appears to be no standard nomenclature for keeping the two senses distinct.
"Double" as designating a single variation
In the BaroqueBaroque music
Baroque music describes a style of Western Classical music approximately extending from 1600 to 1760. This era follows the Renaissance and was followed in turn by the Classical era...
dance suite, a dance movement was sometimes immediately followed by a single variation, which was called the "double".