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Magic Numbers

There is another thread weaving its way through this season, though less obvious, and possibly less audible. Composers have long been fascinated by the interplay of music and numbers, and many of them have used them, as structural devices and musical signatures, similar to the b,a,c, b-flat (h in German) employed by Bach and D e-flat (Es in German) c b-flat (h in German) used by Shostakovich.

Bach’s Goldberg Variations Sep) use many different number patterns. Every third variation is a canon, followed by a genre piece and an ‘arabesque’. This ternary pattern is repeated nine times, before being broken by the infamous quodlibet, using a theme previously employed by Buxtehude in a 32-part partita.

Then there was the discovery of 14 additional canons in Bach’s personal copy of the Variations; musicologists speculate that the number 14 refers to the ordinal values of the letters in his name: B(2)+A(1)+C(3)+H(8) = 14. It is even argued that Bach delayed joining the society of musical sciences to ensure he could be the 14th member.

As this example points out, the connection between music and numbers can take on almost mythical or even superstitious dimensions.
Contrary to Bach, Olivier Messiaen, in his Quartet for the End of Time, uses patterns based on prime numbers, especially 5, 7, 11 and 13, to counter Western Music’s tendency to employ regular rhythms, and thereby creates a sense of tension and never-ending time (19 Jan).

Haydn, in his ‘Palindrome’ Symphony (26 Jan), takes the use of patterns to a different level, writing a Minuet where the second part is exactly the same as the first, but backwards. He then proceeds to do the same in the trio, yet both still make musical sense.

Whole theses have been written about Mozart’s Masonic number codes in The Magic Flute, and the series of numbers in the opening scenes of The Marriage of Figaro (the measuring of the room…) and Don Giovanni (Leporello’s catalogue aria). More intriguingly, an American mathematician has argued that Mozart used the Golden Ratio in a number of piano sonatas (he analysed Sonata No.1 K279), suggesting it is no wonder that his music sounds simply perfect: it is mathematically (25 Feb).

Finally, there is the power of the number 9 when it comes to symphonies. Following Beethoven’s example, composers became wary when they approached that number. Schubert did not write another after his Great C Major Feb) – although the numbering is now disputed, maybe itself proof of the power of this myth? Dvořák’s last is his New World (16 Sep). Bruckner died before completing his 9th. Mahler was so terrified that a 9th symphony would be his last, he decided to write Das Lied von der Erde instead (24 May). Convinced he had now beaten fate, he wrote his Symphony No.9 – and sadly passed away having completed just a movement of its successor. While the ‘curse of the Ninth’ seems to have been broken with Shostakovich, whose own 9th (17 Nov) was followed by 6 more, music’s connection with numbers continues to flourish. I hope you will enjoy discovering these and more this season.

© Thorben Dittes