Long Division with Remainders
by Michael Southorn
Original drawing for the series ‘14 Versions of the Same EP’ by Chris Baldwin
Mankind began communicating through music long before the evolution of speech made verbal communication a possibility. Evidence of this is provided by the numerous achaeological digs that have uncovered crude musical instruments interred with the bones of prehistoric homo sapiens. Perhaps the most famous example is the 'Oradea flute', excavated from a burial site in Romania. To the casual obsever, this artefact is little more than a hollow stick with rough holes gouged through its outer shell. Leading anthropologists, however, have come to recognise it as a staggering example of pre-civilised human ingenuity. In skilful hands, the Oradea flute was capable of producing sophisticated melodies that would have entertained listeners too primitive to express the equivalent emotions in words. For the curious, a modern reconstruction of this remarkable instrument can be heard on many of the most successful works of the popular recording artist Chris Rea.
Though music has undoubtedly been central to societal development across the ages, it is placed in context by an underlying framework even more fundamentally important. The theory of mathematics has existed independent of all physical phenomena since the dawn of time, and perhaps long before. Indeed, there is a case for claiming that mathematics gave birth to the universe; that all we see around us is no more than the whim of a magnificently powerful, unswervingly logical force that painstakingly shades the tiniest minutiae of our lives with elegant fractal detail. In the view of the renowned Greek scholar and philosopher Plato, mathematics provides the solitary arena in which we may be certain of possessing knowledge, free from the vague relativism of the 'real' objects we hold so dear. If I ask a group of moderately experienced and intelligent people, "What is the sum of two and two?" they will all concur on the answer: "Four". If, on the other hand, I ask the same group, "How hard is that plank of wood?" they will insist upon drawing comparisons with other objects possessing the quality of hardness; for instance a nearby wall, or one another's skulls. Mathematics, in short, is incontrovertibly 'right', and as such has precedence over the ambiguous matters of taste, morality and mortality that occupy a disproportionately large sector of contemporary debate.
We have, then, identified two vital, but seemingly unrelated discplines: those of music and mathematics. For the elegant blending of these fields, we owe a debt of gratitude to Pythagoras, another eminent polymath of the ancient Greek era. Whilst plucking his lyre, he noted that stopping the strings at particular points along their lengths could be relied upon to produce particular musical intervals. From there, Pythagoras deduced the relationship between ratio and tone that still provides a challenge to piano-tuners to this day. So momentus was this intellectual discovery that it is tempting – but ultimately impossible – to forgive him for his subsequent foray into mystical numerology. ("Numbers are... the cause of gods and daemons," he once remarked, without offering a shred of rigorous analytical proof to support his conjecture. A sad decline for a mind that was once so potent, and an inexcusable betrayal of his mathematical brethren.)
With the foundation stones of a unifying theory in place, the burgeoning friendship between mathematics and music quickly blossomed into an intimate romance. Civilisations have risen from dust and crumbled back to the same, but these unlikely inter-disciplinary bedfellows have remained entwined until the present day. (Witness, for example, Bartok's deployment of Fibonacci numbers in many of his early-twentieth-century compositions.) An afficionado of music is unlikely to remark upon the differential equations governing the inharmonic overtones that lend his favoured instrument its unique timbre, just as no credible mathematician would claim to enjoy the grandiose sweep of a symphony on anything other than a theoretical level. This is not to say that there is no common ground between the two camps. Mathematicians are the Dr Jekyll to the music-lover's Mr Hyde – they are simply two manifestations of the same undiscriminating, passionless phenomenon. The appreciator of music may be viewed with pity as the deranged dark side of the mathematician's well balanced psyche, driven mad by delusions of artistic sensitivity and so-called 'higher meaning'.
All of which brings us to the purpose of this history: the collection of musical recordings you currently have in your possession under the banner of 'Long Division with Remainders'. Originally little more than a psychological experiment intended to further pacify musical 'artists' between their regular doses of sedative medication, the project has surprised its supervisors by yielding fourteen fascinatingly geometrical soundscapes based around a single Riemannian audio-manifold. Some mention should also be made of the hundreds of other musicians who submitted unacceptable EP 'Versions', and have since been sent to the glue factory. Many thanks to all those who took part.
In conclusion, these recordings are designed to appeal to soberly analytical and haphazardly creative minds alike. Whatever your inclination, it is our sincere hope that you will find much to enjoy in the mathematical elegance – and perhaps even the subjective musicalilty – contained within them.
This essay originally appeared in the box set collection of the project ‘14 Versions of the Same' EP’ - you can still download all the audio from the project (including an EP by Leyland Kirby) from ldwr.net
