Maths and Arts: The Drum Set and The Golden Ratio.

I have been involved with several collaborations through the University of Leicester, working alongside various mathematicians and creative arts practitioners there since 2019. One recent endeavour has been responding to Liam Taylor-West’s ‘The Golden Ratio’ (a solo for 2 high pitched drums) from his ‘Irrational Drumming Patterns’ composition. This particular partnership came about through UoL’s Maths/Arts Tiger Team – coordinated by Dr. Katrin Leschke – where we had been invited to present at the London Mathematical Society and Institute of Mathematics and its Applications joint conference in September 2021, with the theme ‘Maths in Human Society’.

Recording The Golden Ratio Drum Solo.

Liam had already written a collection of short percussion studies based around irrational number pattern sequences and I proposed the idea of investigating performance possibilities around these for our conference presentation. Liam explains the maths:

“The Golden Ratio drumming pattern is a musical representation of the first 34 steps of the infinite, never-repeating sequence that can be found using the golden ratio. Imagine you are moving diagonally across a chess board, and playing two different beats whenever you cross a horizonal or vertical line. If for every square you travel sideways, you travel up one golden-ratio-amount of squares (1.618… squares) the sequence of beats you will play will be the Golden Ratio drumming pattern. This pattern has lots of interesting fractal qualities to it and works well musically, as the beats can be gathered into groups of 2 and 3 (as well as into groups of larger Fibonacci numbers).” Liam Taylor-West

Notation for Three Irrational Drumming Patterns, Liam Taylor-West (2021).

I chose to respond to Liam’s ‘The Golden Ratio’ item for this initial experiment, but I also hope to develop ideas for the other two items in the future. The simple melodic figures created by varying rhythmic groups of twos and threes inspired this solo’s approach. I wanted to set the composition’s mix of 8/8 and 5/8 bars against an accessible rhythmic constant – and a samba setting felt ideal for this, with the tom-tom melodies representing a Brazilian bell pattern over the top of a samba pedal rhythm. I used the South Indian ‘Carnatic’ counting system of ‘Konnakol’ (vocalising percussion rhythms – in this case “Tha-Ka” = division of 2; “Tha-Ki-Ta” = division of 3) to help internalise the irregular 34 step rhythm. In keeping with the samba’s straighter, simple/duple time feel and 4/4 bar structure, I extended the ‘a tempo’ portion to a 5-bar phrase (40 1/8 notes total), which also left a little natural space to respond more loosely to the written part. The rest of the solo is developed through open improvisation around these bases. Here it is:

For more information on my various Maths/Arts exploits:

Minimal Surfaces: https://le.ac.uk/miv/minimal-surfaces-artists-views

Accounts of 2019 projects: https://le.ac.uk/miv/minimal-surfaces-artists-views/blog

LMS/IMA Conference: https://ima.org.uk/17272/lms-ima-joint-meeting-2021-maths-in-human-society/