The Mathematical Compositions of Arvo Pärt

Jon Milet
3 min readFeb 17, 2017

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Arvo Pärt is an Estonian minimalist classical composer and creator of the Tintinnabuli compositional technique. He was born in Estonia in 1935, and graduated from Tallinn Conservatory in 1963. Pärt has had a long career spanning three major periods of output and as we will see below, it is clear why he has been described as a minimalist and mathematical composer.

His pre 1960s work was very much of the Soviet style, taking inspiration from composers such as Dmitri Shostakovich and Sergei Prokofiev.

Then in 1960 he began a phase of experimentation that put him in conflict with his Soviet contemporaries. Pärt explored Serialism (a rigorous form associated with Arnold Schönberg), Aleatory (music of chance, where anything can happen) and Collage (cutting and pasting disperate elements and putting different techniques next to one another) which also involved combining ideas from Baroque and the 20th century next to one another.

Collage over B-A-C-H

One example of his experimental compositions was Collage over B-A-C-H. The idea was based on a theme, also explored by Schumann and Liszt, taking the four letters of J.S. Bach’s surname and using them as notes: B flat, A, C & B Natural (H in Germany).

In Pärt’s composition, the violas play B flat, the cellos A, 1st violins C, 2nd violins play B Natural. The combination of these notes played together gives a dissonant sound. Additionally within the 1st violins, sub sections play the notes Bb, A, C as a chord.

For the melody, the same motif is played by each section with the 1st violins playing the standard melody, violas playing an inversion, the cellos augmenting and the 2nd Violins playing a semitone up.

In 1968 Pärt entered a phase of creative silence. He emerged from this in 1977 with a piece composed in response to the death of Benjamin Britten in late 1976.

Cantas

Arvo honoured the complex simplicity of Brittains writing with Cantas. Using a single bell tuned to A with a string orchestra. Cantas is made up of one long sequence of decending A minor scales against an A minor triad chord (made of three notes: A, C, E). Each orchestral section split in two playing the melody and A minor chord and taking twice as long the lower they are, i.e. basses playing notes twice as long as cellos, playing notes twice as long as the violas, etc. Arvo called this Tintinnabulation.

I have discovered that it is enough when a single note is beautifully played. This one note, or a silent beat, or a moment of silence, comforts me.

The rhythm of the piece slackens as it nears it’s end, a metaphor for the pulse nearing death.

Silouan’s Song

Silouan’s Song was inspired by Silouan the Athonite, a Russian Orthodox monk that wrote extrodanary works born out of solitude expressed through prayer. Arvo Pärt created Silouan’s song using his Tintinnabulie method of minimal notes with different sections playing simple phrases that overlap and build chords. Here different sections play the same line but move in opposite directions.

Arvo Pärt’s work and method is truely inspirational and I for one will add elements of his method to my future compositions.

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Jon Milet

Software engineer by day, composer by night. Loves art, design, technology, history & philosophy.