The double variation (also known as alternating variations) 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 double variation first appears in Haydn's work of the 1770s. Haydn may have been inspired by an earlier example of Carl Philipp Emanuel Bach, 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." [1]
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.
According to Sisman, [1] 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. [3] 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, "L'Impériale". 2: Andante | ABA1B1A2A3 | A | a |
1778/79 | Symphony No. 70, 2: Specie d'un canone in contrapunto doppio: Andante | ABA1B1A2. | d | D |
1779 | Symphony No. 63, "La Roxelane". 2: Allegretto (O piu tosto allegro) | ABA1B1A2*B2* | c | C |
1781 | String quartet Op. 33, No. 6. 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. 2: Allegretto | ABA1B1A2coda | F | f |
1787 | String quartet Op. 50, No. 4. 2: Andante | ABA1B1A2 | A | a |
1788 | Symphony No. 90. 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 in C minor. 1: Andante | ABA1B1A2B2 | c | C |
1793 | Variations for solo piano in F minor, 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 Rosen (1997:83–88). | 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". 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. | c | C |
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 Beethoven also emerges as a major composer of double variations. [1] 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.
Year | Work | Form | A | B |
---|---|---|---|---|
1802 | Third Symphony. 4: Allegro molto | Intro-A-A1-A2-B-Ax-B1-A3-B2-Ax1-B3-B4-coda | various, centered on E♭ | various, centered on E♭ |
1808 | Fifth Symphony. 2: Andante con moto | A-B-A1-B1-A2-cadenza on A-B2-A3-A4-coda based on A | A♭/once in A♭ minor | A♭-C, A♭-C, C |
1808 | Piano Trio Op. 70, No. 2. 2: Allegretto | A-A1-B-A2-B1 with coda | C | c |
1812 | Seventh Symphony. 2: Allegretto | Intro(1 chord)-A-A1-A2-A3-B-A4-A5-B1-coda | a | A to C, A |
1824 | Ninth Symphony. 3: Adagio molto e cantabile | A-B-A1-B1-A2-A3-coda | B♭/once in E♭ | D, then G |
1825 | String Quartet No. 15, Op. 132. 3: Molto Adagio — Andante ("Heiliger Dankgesang") | A-B-A1B1A2 | 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.
After Beethoven, the double variation appears to have been only seldom employed. The following list is ordered chronologically.
The second movement of Johannes Brahms' String Quintet No. 1 (1882) is described by Joanna Wyld [4] as a set of double variations.
The second movement of Anton Bruckner's Seventh Symphony (1883/1885) is described by A. Peter Brown [5] as a set of double variations.
The Larghetto movement of Antonín Dvořák's String Quintet Op. 97 (1893) is described by Colin Lawson [6] as a set of double variations.
Occasionally, authors on music use the term "double variation" with a different meaning. 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:
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 [7] 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.
In the Baroque dance suite, a dance movement was sometimes immediately followed by a single variation, which was called the "double". [8] A widely known example is the first partita from Johann Sebastian Bach's sonatas and partitas for solo violin where each of the four dance movements is followed by a double that elaborates on the bass-line of the previous piece.
Johannes Brahms was a German composer, pianist, and conductor of the mid-Romantic period. Born in Hamburg into a Lutheran family, he spent much of his professional life in Vienna. He is sometimes grouped with Johann Sebastian Bach and Ludwig van Beethoven as one of the "Three Bs" of music, a comment originally made by the nineteenth-century conductor Hans von Bülow.
Sonata, in music, literally means a piece played as opposed to a cantata, a piece sung. The term evolved through the history of music, designating a variety of forms until the Classical era, when it took on increasing importance. Sonata is a vague term, with varying meanings depending on the context and time period. By the early 19th century, it came to represent a principle of composing large-scale works. It was applied to most instrumental genres and regarded—alongside the fugue—as one of two fundamental methods of organizing, interpreting and analyzing concert music. Though the musical style of sonatas has changed since the Classical era, most 20th- and 21st-century sonatas still maintain the same structure.
Chamber music is a form of classical music that is composed for a small group of instruments—traditionally a group that could fit in a palace chamber or a large room. Most broadly, it includes any art music that is performed by a small number of performers, with one performer to a part. However, by convention, it usually does not include solo instrument performances.
Sonata form is a musical structure generally consisting of three main sections: an exposition, a development, and a recapitulation. It has been used widely since the middle of the 18th century.
A piano trio is a group of piano and two other instruments, usually a violin and a cello, or a piece of music written for such a group. It is one of the most common forms found in classical chamber music. The term can also refer to a group of musicians who regularly play this repertoire together; for a number of well-known piano trios, see below.
The Trout Quintet (Forellenquintett) is the popular name for the Piano Quintet in A major, D. 667, by Franz Schubert. The piano quintet was composed in 1819, when he was 22 years old; it was not published, however, until 1829, a year after his death.
In music, variation is a formal technique where material is repeated in an altered form. The changes may involve melody, rhythm, harmony, counterpoint, timbre, orchestration or any combination of these.
Sonata rondo form is a musical form often used during the Classical and Romantic music eras. As the name implies, it is a blend of sonata and rondo forms.
Symphony No. 103 in E♭ major is the eleventh of the twelve London symphonies written by Joseph Haydn. This symphony is nicknamed The Drumroll after the long roll on the timpani with which it begins. It is from 1795, and his second-to-last symphony.
Cyclic form is a technique of musical construction, involving multiple sections or movements, in which a theme, melody, or thematic material occurs in more than one movement as a unifying device. Sometimes a theme may occur at the beginning and end ; other times a theme occurs in a different guise in every part.
Ludwig van Beethoven is one of the most influential figures in the history of classical music. Since his lifetime, when he was "universally accepted as the greatest living composer", Beethoven's music has remained among the most performed, discussed and reviewed in the Western world. Scholarly journals are devoted to analysis of his life and work. He has been the subject of numerous biographies and monographs, and his music was the driving force behind the development of Schenkerian analysis. He is widely considered among the most important composers, and along with Bach and Mozart, his music is the most frequently recorded.
D major is a major scale based on D, consisting of the pitches D, E, F♯, G, A, B, and C♯. Its key signature has two sharps. Its relative minor is B minor and its parallel minor is D minor.
B-flat major is a major scale based on B♭, with pitches B♭, C, D, E♭, F, G, and A. Its key signature has two flats. Its relative minor is G minor and its parallel minor is B-flat minor.
E-flat major is a major scale based on E♭, consisting of the pitches E♭, F, G, A♭, B♭, C, and D. Its key signature has three flats. Its relative minor is C minor, and its parallel minor is E♭ minor,.
D minor is a minor scale based on D, consisting of the pitches D, E, F, G, A, B♭, and C. Its key signature has one flat. Its relative major is F major and its parallel major is D major.
F-sharp minor is a minor scale based on F♯, consisting of the pitches F♯, G♯, A, B, C♯, D, and E. Its key signature has three sharps. Its relative major is A major and its parallel major is F-sharp major.
Elaine Rochelle Sisman is an American musicologist. The Anne Parsons Bender Professor of Music at Columbia University, Sisman specializes in music, rhetoric, and aesthetics of the 18th and 19th centuries, and has written on such topics as memory and invention in late Beethoven, ideas of pathétique and fantasia around 1800, Haydn's theater symphonies, the sublime in Mozart's music, and Brahms's slow movements. She is the author of Haydn and the Classical Variation and Mozart: The 'Jupiter' Symphony and editor of Haydn and His World. Her monograph-length article on "variations" appears in the revised New Grove Dictionary of Music and Musicians, and she is at work on studies of music and melancholy, of Don Giovanni, and of the opus-concept in the eighteenth century.
The Symphony No. 75 in D major is a symphony composed by Joseph Haydn between 1779 and 1781.
Homotonal (same-tonality) is a technical musical term that describes the tonal structure of multi-movement compositions. It was introduced into musicology by Hans Keller. According to Keller's definition and usage, a multi-movement composition is 'homotonal' if all of its movements have the same tonic (keynote).
Johannes Brahms composed his Piano Trio No. 2 in C Major, Op. 87, between 1880 and 1882. It is scored for piano, violin and cello. He wrote this piece at the age of 49.