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Euclidean Algorithm for Sound Generation

Semen Gorokhovskyi,

Abstract: Euclidean algorithm is known by humanity for more than two thousand years. During this period many applications for it were found, covering different disciplines and music is one of those. Such algorithm application in music first appeared in 2005 when researchers found a correlation between world music rhythm and the Euclidean algorithm result, defining Euclidean rhythms as the concept.In the modern world, music could be created using many approaches. The first one being the simple analogue, the analogue signal is just a sound wave that emitted due to vibration of a certain medium, the one that is being recorded onto a computer hard drive or other digital storage called digital and has methods of digital signal processing applied. Having the ability to convert the analogue signal or create and modulate digital sounds creates a lot of possibilities for sound design and production, where sonic characteristics were never accessible because of limitations in sound development by the analogue devices or instruments, nowadays become true. Sound generation process, which usually consists of modulating waveform and frequency and can be influenced by many factors like oscillation, FX pipeline and so on. The programs that influence synthesised or recorded signal called VST plugins and they are utilising the concepts of digital signal processing.This paper aims to research the possible application of Euclidean rhythms and integrate those in the sound generation process by creating a VST plugin that oscillates incoming signal with one of the four basic wave shapes in order to achieve unique sonic qualities. The varying function allows modulation with one out of four basic wave shapes such as sine, triangle, square and sawtooth, depending on the value received from the Euclidean rhythm generator, switching modulating functions introduces subharmonics, with the resulting richer and tighter sound which could be seen on the spectrograms provided in the publication.
Keywords: Sound generation / Euclidean rhythms / music / algorithm / digital signal / functions

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