Pitch Multiplication (2017)

Summary

In this post I’m going to talk about pitch multiplication - a topic related to pitch organization that for a very long time I found to be equally fascinating and perplexing. I first came across the term around 2011 or 12 when I first started studying Pierre Boulez’s music intensely, but I never took much time to really research the topic to understand it. To be fair, I was more concerned with Boulez’s use of instrument color, orchestration, gestural language and his writings on music. Though pitch structure was (arguably) a primary compositional element of Boulez’s music (and overall philosophical approach), I was never really interested in the theoretical underpinnings of how he created pitch structures. As a result, I never fully understood how pitch was organized in some of my favorite works (Eclat, Pli Selon Pli, Third Piano Sonata).This isn’t to say I wasn’t interested in integral serialism or systematic ordering of pitches, it’s actually quite the opposite. I was just more interested in approaches by Xenakis, Berio, Robert Morris, and (my own teacher) Mikel Kuehn. Around 2014, my focus and interests in Boulez’s music started to shift and I refocused my attention on understanding his methods of inventing and working within rigorous mathematical pitch structures, but this was still mostly related to his method of integral serialism.However, it wasn’t until late 2016 that I really began looking into pitch multiplication, as previous attempts were always unfruitful. I guess my background in math just wasn’t what it needed to be, or maybe I was just having issues wrapping my brain about the concept, because what I ultimately discovered is that the math is quite simple, I was just making it harder than it needed to be.All of that aside, this leads to the main question at hand - what is pitch multiplication? Not only that, but how can it be used in a meaningful way that doesn’t render it an academic or theoretical exercise? The simplest explanation is that pitch mult...