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Harmonic Ratios: An Introduction

'Music and crystals' as a topic in and of itself has been largely unexplored. However, musicians and crystallographers have respectively referenced the other’s subject of study as having a key presence in their own. Aesthetically the two are compatible in that they are simultaneously complex and simple; multiple and one. There is, at the heart of the aesthetic, a mathematical structural link between the two that relies on fundamental ratios between tones, “Harmonic Ratios”, and those between the angles of crystals faces. In 1818, Christian Samuel Weiss, early founder of the dynamist tradition of crystallography, introduced the study of crystal structures in a public talk and made a point of explicitly demonstrating a musical analogy in crystallographic systems. He proved that the relationship between ratios among segments formed by faces of crystals of the cubic systems are identical to those between musical tones. Musicians have also noted this link, using the form of crystals as inspiration for and a means by which to describe their musical compositions.

French composer and inventor of the definition of music as ‘organised sound’, Edgard Varese, wrote of the relationship between his music and crystals: “…I was struck by what seemed to me an analogy between the formation of my compositions and the phenomenon of crystallization…There is an idea, the basis of an internal structure, expanded and split into different shapes or groups of sound constantly changing in shape, direction, and speed, attracted and repulsed by various forces. The form of the work is the consequence of this interaction. Possible musical forms are as limitless as the exterior forms of crystals.” More recently, mega-star, Bjork, dedicated a track of her 2012 album, Biophillia, to crystals, using their formation as a basis for the song’s aesthetic and structure. In an interview with David Attenborough on the subject, Bjork said: “it has an inner logic to it…it seems a very natural fit”.

Pythagorean harmonic music interval diagram showing perfect numerical ratios appearing  through music

Pythagorean harmonic music interval diagram showing perfect numerical ratios appearing

through music

The underlying similarity between music and crystals has resulted in there being a pattern in the way that they are used by the human species. Both crystals and music are often ascribed magical powers - the ability to heal, to retrieve lost memories, to produce love - and whilst I myself am not a believer in magic, I do understand the temptation to turn to these highly logical and yet wonderfully varied structures as the source of something beyond that which we know and comprehend. In fact, I have often, in arguments concerning the validity of organized religion, referenced music as a justification for the existence of personal faith outside of the pre-existing religious structures, understanding that I use music as a means by which to have a 'spiritual' experience. Our comprehension of both music and crystals in this way is sourced in what is highlighted above: in their ability to introduce the fundamental logic of nature and the universe whilst remaining unpredictable and new.

In Harmonic Ratios: Music and Crystals, 5 artists and 4 experts explore the wonderful world of music and crystals, looking at the mathematical links, the aesthetic relationship, and the sonic implications between the two. Each work and intellectual contribution in the show gives an insight into a different angle of the topic, allowing a near-full sensory as well as cerebral experience. Music and crystals will be entwined together to create one sensational, unified presence.


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