Orchestral Geometries


Composer Emily Howard is Director of PRiSM. Her music is known for its inventive connections with mathematical shapes and processes. The development of a series of geometry-inspired orchestral works has been central to Howard’s work over the past five years. In this post, she shares some thoughts about the creative process behind this series.

This is followed by performances of three Orchestral Geometries – Torus (2016), sphere (2017) and Antisphere (2019). PRiSM is delighted to share recordings of these works, and grateful to the London Symphony Orchestra and Sir Simon Rattle, the BBC National Orchestra of Wales and Mark Wigglesworth, the BBC Symphony Orchestra and Martyn Brabbins, and Edition Peters for making this possible.

Creating Orchestral Geometries

by Emily Howard

Mathematicians tell me they often make progress by seeking to translate one area of mathematics into another. In this way they can open up new lines of enquiry with questions like ‘does this still make sense?’, ‘How has this changed things?’. Perhaps my early training in mathematics shaped the way I create as it feels deeply rooted in an analogous method of translation. Transforming mathematical notions into musical ideas has become an important part of what I do. It never can be a direct translation, but it is precisely by attempting to carry out this impossible task that something is gained. I find this approach often reveals new questions from unusual vantage points that result in unexpected ways to organise sound.

I have a deep love of writing for orchestra. There is something uniquely thrilling about bringing together so many people and working with such a vast collective timbral palette. And there is something infinitely meaningful about orchestral togetherness, loud or soft or otherwise, as well as the shared concentration that arises between so many players and an audience in live performance.

Over the past five years, my musical exploration of mathematical shape has led to a series of geometry-inspired orchestral works. For each of these Orchestral Geometries, an abstract mathematical shape was the imaginative cornerstone of the creative process. There are three so far: Torus (2016), sphere (2017) and Antisphere (2019). Each work is titled with the shape in question and it’s as though this shape was a filter through which myriad decisions about the piece were made. These rational decisions affect the proportions of the work and its soundworld. Should this section be long or short? Loud or soft? How many instruments are playing? How many independent musical layers are there at any given time, and how do they interact? Should I use this exponential function to transform pitch? Perhaps I should shrink and stretch the proportions of this harmony in response to notions of negative curvature?

In the early stages of writing each work, it has felt as though my mind’s eye has conjured up some kind of protean shape-energy, somewhere between several senses, in part a response to the foregrounded shape and various mathematical properties associated with it that I am also engaging with. But never this in isolation: it’s also a response to everything else. The commissioning details. Conversations with mathematicians, musicians, students. My mood. The thousands of hours of experience I have gained from writing previously. What I’ve been listening to. All of the live music I have experienced ever. My worries. Interactions with my cat. The list goes on.

To begin with, it’s hazy. I experience this internalised shape-energy as frequently changing but perhaps it’s just that I don’t know it well enough yet. I take time to explore it. I wander around on its surface. I zoom out so that I’m able to view the whole entity from a distance, and then return to examine the surface in microscopic detail. I think about it as often as possible and in as many different ways, from as many different angles as I can. I try to capture it with a vague sketch and pin it to my wall. I redraft it more precisely and pin it to my wall. I redraft it less precisely and pin it to my wall. I give this internalised platonic ideal intense focus. Slowly, over a period of time, and many iterations of this ritual, it begins to reveal more of itself to me. I hear more of it. I begin to know it intimately. It matters to me.

There is a complex relationship between my knowing this internalised shape-energy, and the piece of musical notation that materialises. And it’s different for each work. The musical score often emerges through the consideration of multiple journeys around the imagined entity, from multiple viewpoints. I’m always aware of the further layer of interpretation that the performers will add as they realise the score, and I’m excited to experience it. I find that there is something infinitely rewarding about listening to a new piece of music with no expectations, and I usually find it is in live performances of works new to me that I discover something new myself.

Emily Howard, September 2020

Antisphere (2019)

Commissioned by the Barbican Centre for Sir Simon Rattle and the London Symphony Orchestra, Antisphere opened the London Symphony Orchestra’s 19-20 Season in September 2019. Watch the world premiere performance.

sphere (2017)

sphere was commissioned by Stiftung Bamberger Symphoniker for the Bamberg Symphony Orchestra conducted by Alondra de la Parra and received its premiere in Schweinfurt, Germany in March 2017. The recording below is of the UK premiere given by BBC National Orchestral of Wales conducted by Mark Wigglesworth at 2018 Aldeburgh Festival.


Torus (2016)

Commissioned by BBC Radio 3 and the Royal Liverpool Philharmonic Society, Torus was first performed by Royal Liverpool Philharmonic Orchestra (to celebrate its 175th Anniversary) conducted by Vasily Petrenko at the BBC Proms in 2016. More recently, it was broadcast as part of the BBC Archive Proms 2020. Torus won a British Composer Award (Orchestral Category) in 2017. The recording below is of the Barbican Life Rewired performance given by the BBC Symphony Orchestra conducted by Martyn Brabbins in November 2019.



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