Kaii Lee had combined several piano/keyboard method books and her life long music learning books to create this sequential music theory study for this website. This page is about the understanding of the Theme & Variations. By clicking on the other colored links at the bottom of this page, the other music theory topics can be found easily.

For more information, please contact Kaii directly: info@kafm.net

 

Bach | Mozart | Paganini | Rachmaninoff

The composition form, Theme & Variations, was developed well from the Baroque Period, through the Classical Time Period, and beyond the Romantic Period. It holds a very prominent position in music composition history. All Theme & Variations music has the same format: a Theme that is presented at the beginning of the music, and several or many Variations follow that Theme one at a time.

The most famous Theme & Variations composition from the Baroque Period was composed by Johann Sebastien Bach. It is called the "Goldberg Variations" and first published in 1741. It is named after Johann Gottlieb Goldberg, who might have been the first performer of this work. There is a Theme at the top. Bach had chosen an Aria in this case. Following the Theme, Bach created 30 variations, by using different articulations, dynamics, harmony, melody, meters, moods, rhythm, and tempo. Three of the Variations were written in G Minor, #15, 21 and 25. Specific compositional forms were used as well, such as Canon and Fugue.

Johann Sebastien Bach's "Goldberg Variations" Theme, BWV 988

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Variation 1 changes to a speedy scale and arpeggio runs throughout the piece. Like the Theme, it has two sections and both are repeated, while the first section lands on a Dominant chord and the ending stands on a Tonic chord.

Johann Sebastien Bach's "Goldberg Variations" Variation 1, BWV 988

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Look at the Canon in the treble staff in Variation 3. It is a Canon in the Unison (same pitch) between the two voices.

Johann Sebastien Bach's "Goldberg Variations" Variation 3, BWV 988

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The "Little Fugue" in Variation 10 has all the elements of a 4-voices authentic Fugue.

Johann Sebastien Bach's "Goldberg Variations" Variation 10, BWV 988

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Variation 15 was the first of the three variations that were written in G Minor and Canone alla quinta. It was a Canon to the (interval of a) Fifth.

Johann Sebastien Bach's "Goldberg Variations" Variation 15, BWV 988

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Variation 20 requires keyboard players to cross their hands. However, with two keyboards, like a harpsichord, players would have an easier time playing this variation.

Johann Sebastien Bach's "Goldberg Variations" Variation 20, BWV 988

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Variation 21 was another variation that was written in G Minor and this time, Canone alla settima. It was a Canon to the (interval of a) Seventh.

Johann Sebastien Bach's "Goldberg Variations" Variation 21, BWV 988

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Variation 28 was probably what inspired Franz Liszt to write his fancy music. This variation would play better with two keyboards.

Johann Sebastien Bach's "Goldberg Variations" Variation 28, BWV 988

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The final Variation, no.30, was labeled "Quodlibet." A Quodlibet is a musical composition that combines several different melodies—usually popular tunes—in counterpoint, and often in a light-hearted, humorous manner. Then, at the end of this piece, Bach wrote, "Aria da capo e Fine" for players to know to return back to the Theme (Aria) as the final section of this huge piece of music called "Goldberg Variations."

Johann Sebastien Bach's "Goldberg Variations" Variation 30, BWV 988

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A very famous Theme & Variations by Wolfgang Amadeus Mozart called "12 Variations on the Theme of 'Ah, vous dirai-je maman'" is the next music example. When Mozart was in Paris as a young child, he heard the French folk song, 'Ah, vous dirai-je maman' (Ah, I’ll tell you mom), and wanted to write a song about it. Since the Theme was rather short, Mozart decided to write 12 variations of it.

From a simple "Twinkle, Twinkle, Little Star" melody, Mozart used different music elements, such as articulations, dynamics, harmony, meters, moods, rhythm, and tempo, to create the twelve variations. While Variation 8 is the only Variation that was written in the key of C Minor, Variation 12 was the only Variation in 3/4 Time Signature. Starting in Variation 1, Mozart kept the integrity of the melody and harmony throughout the Variations.

Wolfgang Amadeus Mozart's 12 Variations on the Theme of 'Ah, vous dirai-je maman', K.265, Theme & Variation 1

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Mozart had switched the rhythm from 16th notes to eighth-note triplets easily between Variations 2 and 3. In the meantime, he kept the harmonic structure in place.

Wolfgang Amadeus Mozart's 12 Variations on the Theme of 'Ah, vous dirai-je maman', K.265, Variations 2 & 3

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To add a little twist to this music, Mozart used C Minor as the tonality for Variation 8. There was no visible speed change in this variation.

Wolfgang Amadeus Mozart's 12 Variations on the Theme of 'Ah, vous dirai-je maman', K.265, Variation 8

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When Mozart was back in a playful mood, he designed this variation for players to cross their hands to play. The melodic line of "Twinkle, Twinkle, Little Star" would be played by the left hand over the right-hand harmony in 16th notes.

Wolfgang Amadeus Mozart's 12 Variations on the Theme of 'Ah, vous dirai-je maman', K.265, Variation 10

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After a little chasing around on the keyboard, Mozart put down an "Adagio" Variation for players to catch a breath. Unlike the other Variations, this one has a gentle melody that utilizes the Dotted Rhythm in both hands. The uses of 32nd-notes, Aberti Bass, and Appoggiatura can be found here too.

Wolfgang Amadeus Mozart's 12 Variations on the Theme of 'Ah, vous dirai-je maman', K.265, Variation 11

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When Mozart switched to the 3/4 Time Signature for the final Variation, he allowed more notes to be written and played. The melodic line can be heard easily in the treble staff and the harmonic structure cemented in the bass staff. The final four measures work like a little Coda for this glorious piece of music.

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Many composers have written music with the Theme & Variations form over the centuries. Niccolo Paganini's "24 Caprices for Solo Violin" was written in the Theme & Variations form. The last Caprice was the most famous one and has been adapted by many other composers for their own Theme & Variations compositions.

Niccolo Paganini's Theme here is a simple A Minor melody, with mostly intervals of half and whole steps and occasional intervals of thirds and octave endings.

Niccolo Paganini's "24 Caprices for Solo Violin", Op.1 No.24, in A Minor, Theme

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All solo violin players would understand the difficulties in playing octaves, which are double-stops, meaning playing on two different strings at the same time. Variation 3 here is pure octaves for the whole Variation.

Niccolo Paganini's "24 Caprices for Solo Violin", Op.1 No.24, in A Minor, Variation 3

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Variation 6 involves more double-stops in the intervals of thirds and tenths, including harmonics, meaning light touches on the strings without pressing down onto the finger board.

Niccolo Paganini's "24 Caprices for Solo Violin", Op.1 No.24, in A Minor, Variation 6

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Variation 9 requires players to take turns to play with the bow 9arco) and to pluck (pizzicato) the strings.

Niccolo Paganini's "24 Caprices for Solo Violin", Op.1 No.24, in A Minor, Variation 9

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When an octave sign is used above multiple high ledger lines, like in Variation 10 here, the music has very high pitches. The perfect pitches could only be created by moving the fingers ever so slightly.

Niccolo Paganini's "24 Caprices for Solo Violin", Op.1 No.24, in A Minor, Variation 10

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When this Caprice starts with a tempo mark of "Quasi Presto", players understand that it is a very fast moving music. However, there are 32nd notes in Variation 11 and shifting double-stops in between. Finally, the Finale section culminates with more arpeggios and double-stops before the music modulates to A Major for the last seven measures, including a low trill. Wow!

Niccolo Paganini's "24 Caprices for Solo Violin", Op.1 No.24, in A Minor, Variation 11 & Finale

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Many composers have written music with the Theme & Variations form by using the Paganini's Theme above. Sergei Rachmaninoff took that melody from Niccolo Paganini's Violin Caprice as the Theme and wrote "Rhapsody on a Theme of Paganini" with 24 Variations. Many different tempos can be found in this composition, such as Allegro Vivace, Più vivo, Meno mosso, a tempo moderato, Moderato, a capriccio, Tempo di Minuetto, Scherzando, Allegretto, Andante cantabile, and more. Rachmaninoff used different Time Signatures as well, from the original 2/4, 3/4, to 12/8.

The following examples are taken from a two-piano score and a reduction of the orchestral score.

Sergei Rachmaninoff's "Rhapsody on a Theme of Paganini", Op. 43, Introduction

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The Paganini melody was introduced in the orchestra while the piano solo is only playing the simple chord progression. Unlike the Paganini violin music, there are no repeat signs here.

Sergei Rachmaninoff's "Rhapsody on a Theme of Paganini", Op. 43, Theme

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In Variation 2, the piano solo and orchestra traded roles. The piano music begins to fly.

Sergei Rachmaninoff's "Rhapsody on a Theme of Paganini", Op. 43, Variation 2

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A chordal structure in the solo piano part gives the player a little rest from a very busy and fancy Variation 6.

Sergei Rachmaninoff's "Rhapsody on a Theme of Paganini", Op. 43, Variation 7

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A different chordal approach in Variation 8, Rachmaninoff created a dynamic contrast here.

Sergei Rachmaninoff's "Rhapsody on a Theme of Paganini", Op. 43, Variation 8

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For the first time in this composition, "Rhapsody on a Theme of Paganini", Rachmaninoff had changed the Time Signature to 4/4, and alternated between 4/4 and 3/4 in Variation 10.

Sergei Rachmaninoff's "Rhapsody on a Theme of Paganini", Op. 43, Variation 10

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With a key change and a Meter change, Variation 12 was labeled "Tempo di Minuetto" and written in the key of D Minor.

Sergei Rachmaninoff's "Rhapsody on a Theme of Paganini", Op. 43, Variation 12

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Variation starts with a piano solo in the style of legato, while the subdued orchestra plays the accompaniment role later in this Variation. It was labeled "Più vivo and Scherzando" for a fast finger work of scales and arpeggios.

Sergei Rachmaninoff's "Rhapsody on a Theme of Paganini", Op. 43, Variation 15

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While the music marches on, Rachmaninoff miraculously modulated to B-Flat Minor and back to the 2/4 Time Signature.

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Variation 17 continues with the dark and moody characters, but a new Time Signature, "C" for Common Time and (12/8) as an alternate when the subdivision of the beats are changed.

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Maybe the most famous variation of them all, Variation 18 has been used in numerous movies and been edited and published as a separate and individual song by others as well. Two smart moves that Rachmaninoff inverted the Paganini melody and wrote it in the key of D-Flat Major.

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Going into Variation 19, Rachmaninoff wanted the solo piano part sounded like a violin and labeled "quasi pizzicato" for the players to play like a violin's pizzicato (pluck of the strings).

Sergei Rachmaninoff's "Rhapsody on a Theme of Paganini", Op. 43, Variation 19

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With many modulations, meter changes, and mood changes, and "a capriccio" (on a whim), from Variation 20 through 23, Rachmaninoff managed to keep the Paganini melody clearly in its five initial tones (four 16th notes and on eighth note) pattern.

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After all the non-stop and glorious music, Rachmaninoff gave a simple and quiet ending with 2/4 Time Signature and in the original A Minor. How fun!

Sergei Rachmaninoff's "Rhapsody on a Theme of Paganini", Op. 43, Ending

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The next topic in this Music Theory site is all about "12-Tone Music." Thank you for reading!

 

Music Theory that every musician could use and should know
The Basics	Math in Music	More Math and Signs	Music Forms
Time Signatures	Intervals	Modulations	Homophonic Style
			Polyphonic Style
	Diatonic & Chromatic Steps	Transposition	Contrapuntal Techniques
Key Signatures	Triads & Inversions		Binary Form
	Primary Triads	Augmented Sixth Chords	Ternary Form
	Secondary Triads	Traditional Compositional Tools	Dance Suites
Scales	Seventh Chords	Contemporary Compositional Tools	Prelude & Fugue
	Secondary Dominant	Musical Signs	Sonata Form
	Cadences		Rondo Form
Modes	Chord Progressions	Musical Terms	Theme & Variations
	Figured Bass & Basso Continuo		Serialism

 

For more information, please contact Ms. Lee at: info@kafm.net

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