Reinventing Pythagoras

Reinventing Pythagoras by Bazyli Brzóska

After developing a theory based on the teachings of ancient Babylonians and Egyptians, Pythagoreans, followers of the Pythagorean Brotherhood, investigated different possibilities of uniting different sciences with music and spirituality.1 This great philosopher of the Greeks defined a new way of thinking - using mathematics, mainly numbers, to represent each and every aspect of natural reality.2 Following Pythagoras' own hypothesis, he tried to find patterns and regularities in music and tried to apply those theories to cosmology and other sciences, in order to link them together. He succeeded, as his findings had undergone further research in modern times, and most of them, after some reinterpretations, are now regarded as mainstream knowledge. Many scientists have tried to construe thoughts and findings of Pythagoras. His so called "Music of the Spheres" doctrine was just a conjecture, but with the advent of quantum physics and other theories in modern science, it is now regarded as being true.3 New, updated and expanded ideas emerged from his studies of ratios between lengths, weights, volumes of air and the original concept of order and harmony. Some tried to elucidate that concept literally, while others thought it was purely a conceptual or metaphoric idea. Even people like Isaac Newton acknowledged to have exercised the Pythagorean notion of musical ratios in their own research.2 Johannes Kepler, a German mathematician and astronomer, tried to expand on this concept, creating a masterpiece 'harmonus munide'. Gibson and Johnston explain his work in the article entitled 'New Themes And Audiences For the Physics of Music': "(...) he presented the orbital angular velocity for each planet on a musical staff (...) The ratios of these angular-velocity pairs are very close to those defining musical intervals, and their corresponding notes could be arranged into four harmonious chords".4 Another example, a composition by Gustav Holst, called 'The Planets' was an artistic representation of the same idea. 'AtlasEclipticalis' was one of John Cage's experiments, that was also inspired by the work of Pythagoras. Cage tried superposing the notes on star charts. There are many more examples of artistic works done in afflatus caused by this 'Master Philosopher'.1 Except being a great inspiration to contemporary musicians, his findings are continuously being re-evaluated and expanded upon to date. The concept of overtones caused considerable changes in 1

CURTIS, D. 2005. Music and Music of the Spheres. [PDF] http://www.sacredresonance.com.au/articlessr/MusicandMusicoftheSpheres.pdf (8 October 2009). 2 CALEON, I. and RAMANATHAN, S. 2007 From Music to Physics: The Undervalued Legacy of Pythagoras. Science & Education [Online journal] Available from Springerlink at http://www.springerlink.com/content/44wt849t2v317265 (8 October 2009). 3 NE'EMAN, Y. Wigner Centennial Conference. Pécs, Hungary, 8-12 July, 2002. 2002. Symmetry and "Magic" Numbers or From the Pythagoreans to Eugene Wigner. Tel-Aviv University and University of Texas, Austin 4 GIBSON, G. and JOHNSTON, I. 2002. New Themes And Audiences For The Physics Of Music. Physics Today. 55 (1), pp. 42 - 49.

musical composition. Their usage was slowly adapted by artists. Around 600 A.D. the only acceptable intervals were unisons and octaves. A couple years later, fifths and fourths were added. The major third had to wait even longer to be used regularly, let alone other dissonant sonorities, some of which were not commonly recognised until very recent times - the 20th century. Even now there are still elements to expand in this area. We can calculate harmonics to a point where we divide the semitone, after which microtonality emerges.5 The fact that human brain is sensitive to inherent mathematical relationships, which Pythagoras was fond of, can also help with understanding of the combination of harmony and melody. Very recent mathematics have defined "quotient spaces" or "orbifolds", which are spaces that contain singularities, similar to black holes, in accordance with Einstein's general relativity. Dmitri Tymoczko of Florida State University writes in his article titled "The Shape of Music": "Western music can ultimately be represented as a series of points and line segments on abstract shapes in higher dimensions. If we can understand their structure, then the deep principles underlying Western music will finally be revealed." He later on explains how to literally turn music into math using his theory.6 Ideas of Pythagoreans have a major impact on our understanding of music today. Their research is the root of the Western music genealogy. It is the modern temperaments - equal and circular temperament, Western musical scales and intervals - they all were able to grow on the fundamental ଵ ଵ ଵ ଵ

musical concept of harmonic series - ଶ, ଷ, ସ, ହ etc. that Pythagoras found.7 The universal application of his theory proved to be relevant, being the inception or at least a contribution to many, relatively new fields of science, like: sympathetic vibratory physics8, quantum physics6, nano-biotechnology, astronomy and, naturally, musical harmony. As I pointed out in numerous examples, people like us, students and scientists, can still greatly benefit from the works of Pythagoras and his disciples. Not only will it enhance our understanding of music, but also it can be an inspiration to both our spiritual, artistic souls and scientific, analytical minds.

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COWEL, H. 1996. New Musical Resources. Cambridge: Cambridge University Press. TYMOCZKO, D. 2008. The Shape of Music. Seed Magazine [Online magazine] http://seedmagazine.com/content/article/the_shape_of_music/ (8 October 2009) 7 ROSENTHAL, J. 2005. On Mathematics and Music: The Wave Structure of Matter (WSM) in Space. [WWW] http://www.spaceandmotion.com/mathematical-physics/mathematics-music-waves-vibrating-space.htm (8 October 2009). 8 POND, D. 2000. It Really is a Musical Universe!. University of Science and Philosophy: The Cosmic Light. [Online magazine] http://www.svpvril.com/musicuni.html 6