86 Permutations of Melancholia

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My good friend and student Roberta shares with me a certain fascination with numerology – an occult study of number patterns (limited to their applicability in music, in my case). There is even a reproduction of a magic square (an arrangement of numbers where rows, columns and diagonals add up to the same sum – the “magic number”) on one of the walls in her house – the square that appears in Melancholia, an engraving by Albrecht Dürer.

86 Permutations of Melancholia performed by Matthew Strover and Alex Nikiporenko
My good friend and student Roberta shares with me a certain fascination with numerology – an occult study of number patterns (limited to their applicability in music, in my case). There is even a reproduction of a magic square (an arrangement of numbers where rows, columns and diagonals add up to the same sum – the “magic number”) on one of the walls in her house – the square that appears in Melancholia, an engraving by Albrecht Dürer.


The magic square – its magic number is 34


When tasked with writing a piece for Roberta’s 50th birthday, I decided to base it on the Melancholia square. I enjoy using number-based processes to write music and this particular magic square had a clear connection to Robbie, so it felt like a perfect match.

 The piece is scored for cello (Roberta’s and mine favourite instrument) and piano (the instrument that I play). 

The Process


The cello part goes through the rows and then columns of the square, each time starting in the top left corner. The numbers are mapped onto a chromatic scale starting at C2 – the lowest note on the cello.




The piano part goes through the square’s 86 possible solutions – 4-number combinations that sum to the square’s magic number, 34. This time, I have mapped the magic square numbers onto the major scales starting on the notes played by the cello, which are played simultaneously with the beginning of each solution. The rhythms in the piano part are determined by the numbers’ position in the square – the numbers in the first column are played on the first quaver of the bar, second column on the second quaver, etc.

Here is the annotated score of the first 4 bars of the piece:



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