NEIMOG 2022 Organizing Just Intonation Pitches through Xenakis' Sieves and Prime Decomposition

Описание: Xenakis 22: Centenary International Symposium - Presentation!

Article: http://gg.gg/11k4ww

OM-Patches and Libraries: https://github.com/charlesneimog

Abstract: In this article, we will present how we can create, organize and understand pitches of Just Intonation using 1) the theory of sieves (XENAKIS, 1992) to filter the numbers of the harmonic series, 2) the decomposition by prime-numbers (EXARCHOS et al., 2011) applied to the numbers resulted from the sieve, 3) the concept of harmonic identities by Johnston (2006), and finally, 4) the Combinations-Product Set (CPS) by Erv Wilson (NARUSHIMA, 2018), that allows us to see the relationships between harmonic identities. When we understand that only prime numbers generate new harmonic identities in the interval sense (JOHNSTON, 2006), and odd-numbers create just a new pitch-class from staking prime numbers, we can apply the prime-decomposition for all the numbers of one sieve and claim that: all the non-prime numbers can be understood how intersections between distinct harmonics series. Based on Exarchos' (2011) analysis of sieves, this idea can help us find a way to use the sieves of Xenakis in the Just Intonation context. Complementary with this compositional idea, we will present two OpenMusic libraries developed to help the compositional process.