The Music of Spheres

Making-music-with-a-mobius-strip_1We’ve talked in the past about
the interaction between music and science (see Mozart, Bird Song and IQ) but this has largely centred on the psychological effects of
music. What about the mathematical dimension to sound and the interrelationship
between musical, chemical and physical structures? 

For maths geeks, a recent video
from the magazines Quanta and Scientific
may prove interesting. Many of us are aware that the differential
equations of vibrating strings and surfaces help us understand harmonics and
tuning systems; rhythm analysis informs us of the ways a measure can be divided
into beats; and the study of symmetry relates to the translations in time and
pitch that occur in a fugue or canon.


However, the video explores a less well-known connection: musical chords naturally inhabit
various topological spaces
, which show all the possible paths
that a composer can use to move between chords. The space of two-note
chords is a Möbius strip, while the space for a three-note chords is a
kind of twisted triangular torus. 

In a less formal but much more
wide-ranging project, Icelandic pop and avant-garde musician Björk famously
undertook her own exploration of the relationship between music and science, for
which she enlisted the help of renowned naturalist David Attenborough and
numerous musical and scientific experts. 

Her Biophilia project involves
not only a studio album which was ‘partly recorded’ on an iPad and released as a series of apps, but is a major multimedia project “encompassing
music, apps, Internet, installations, and live shows”. Exploring ideas from
physics, chemistry and biology, it featured specially developed instruments
based around a range of scientific principles



Classic Tesla Transformer

The song ‘Thunderbolt’ presents a
Tesla Coil as
a musical instrument, while a so-called ‘gameleste’ – a hybrid between a gamelan and a celesta – was
programmed to be played remotely by a tablet computer: this features in both
the tracks ‘Crystalline’ and ‘Virus’. Meanwhile, the song ‘Solstice’ brings a
whole new meaning to the phrase ‘music of the spheres”: in a tribute to the
concept of Foucault’s pendulum,


Foucault Pendulum

it was partly created with a group
of swinging pendulums which were used to subtly transmit the movements of the
earth by plucking a harp.


The crossover between science and
music has recently been explored in-depth in a series of programmes on BBC
Radio 4. ‘The Science of Music’ touches on everything from the origin of
music (are we really descended from singing cavemen?) to the logic,
engineering and physics underlying the musical sounds we hear and what goes on in our head
when we listen to music.


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