The Mathematical Genius of Bach

Spitalfields Festival
The Mathematical Genius of Bach
Goldberg Variations

James Sparks, City of London Sinfonia, Alexandra Wood 
Christ Church Spitalfields, 30 June 2022

The opening concert of the Spitalfields Music Festival referred back to The Spitalfields Mathematical Society, a club that met from 1717 in taverns around Christ Church Spitalfields. Its aim was to give “the public at large an opportunity of increasing their knowledge, on terms so easy, as to be within the reach of every individual, who has a taste to cultivate, or curiosity to gratify.” It educated the working-class men of the district, who included “weavers, brewers, braziers, bakers, bricklayers”. It merged into the Royal Astronomical Society in the 1840s. The Festival continued the Society’s role of educating with a talk by James Sparks (University of Oxford) on the mathematical genius of Bach, illustrated with a performance of the Goldberg Variations, while the audience had access to interactive maths puzzles.

Before the event started, a series of what I would call numerical logic rather than mathematical questions appeared on a central screen just above an ominous-looking drum kit where a church altar might have stood. This generated a ripple of mansplaining amongst the audience.

The first third of James Sparks’ talk was on the history of the Spitalfields Mathematical Society. The first constitution dictated that membership would be limited to 8 squared, a figure later increased to 9 squared. Apparently, this mathematical figure was based on the seating arrangements in the local pub in which they gathered. By about 1800, the working-class weavers, brewers, braziers, bakers, and bricklayers had long gone, and the membership consisted of lawyers, doctors and other professional people. That gentrification is very much in evidence in today’s Spitalfields with its trendy coffee bars and hang-outs for wealthy youth.

Most of the rest of the talk was on the mathematical links to Bach’s music, using not the Goldberg Variations, but the Musical Offering, with its Crab Canon played as an example. The structure of the canons in the Goldberg Variations was briefly explained, with this rather complicated slide to accompany it.

Unfortunately, when the Goldberg Variations were actually played, there were no further visual aids or any indications of where we were at, and what bit of Bach’s mathematical genius was being demonstrated. A rolling score would have been a minimum aid to understanding. But what was more concerning to me was the performance itself, given by a modern-instrument string orchestra – the City of London Sinfonia. Although all of Bach’s notes were played, they were not in the way that Bach intended, with many additional ones added in this (un-named) arrangement. Why they didn’t use a harpsichord player is beyond me. As it was, the structure of Bach’s musical lines was lost in the complex use of several instruments to play a single line of music, for example, in the two-part Variation 5, where there were five instruments playing. THe were also frequent obtrusive musical additions, notably from a double bass player, giving rhythmic accents to Bach’s already rhythmic music.

Many of the variations are in the form of a two-part canon over a bass line but, rather than treating the two canonic voices as equal, the first violinist frequently dominated the sound, often making the second line (usually played on 2nd violin or viola) more-or-less inaudible. When the 2nd violin took over that solo line, the aural balance was much better. Added confusion came when other instruments took over a solo line mid-stream.

Such confusion continued throughout. Another oddity was the frequent moments when what Bach very clearly indicated as two separate lines of music (to be played on the two keyboards of a harpsichord) were played by a single instrument, making nonsense of, for example, Variations 14 and 29. The lack of historically informed performance was also evident in the interpretations of individual variations, which ranged dramatically in style and timbre. Variation 10, for example, was clod-hoppingly agricultural while an inconsistent approach to Bach’s repeats marking gave an unbalanced feel to the whole set.

No description or explanation for the arrangement was given, so many in the audience would have gone away thinking they had heard the Bach Goldberg Variations in the way that Bach might have intended – but they hadn’t. At the very least, I hope the Festival arranges for a much more authentic performance on a harpsichord in the next Festival and invites the same audience back to hear Bach the way Bach wanted.

What is particularly sad for me is that, for many years, the Spitalfields Festival was known for its top-notch performances of early music as well as music of the present day. In recent years the focus has moved away from the early repertoire, toward a much wider range of music and community events. That is a loss to the world of early music.

PS. The only mathematical question I didn’t get was the first one pictured above.
In case you are still struggling with it, the answer is
888+88+8+8+8 = 1000