November 26, 2025
From vibes to times tables
Pitch Multiplication (2017)
Math vs melody: Boulez’s number tricks split the crowd
TLDR: A composer breaks down Boulez’s pitch multiplication in plain language, showing the math is simple and musically useful. The comments explode into math-nerds vs. vibe-purists, trading jokes and jabs over whether multiplying note sets makes art or just extra homework.
The post dives into Pierre Boulez’s mysterious “pitch multiplication,” and the community instantly turned it into a battle of brain vs. ears. In simple terms, it’s like taking two sets of notes and combining them with a math-y recipe. The author admits he once struggled with it, then came back with a clearer, simpler breakdown, linking to sources and explaining how this method expands musical possibilities without turning it into a dry theory drill. Read the full explainer here: Pitch Multiplication.
But the comments? Pure theater. One camp is cheering, “finally someone demystified Boulez,” while the other fires back, “this sounds like homework.” The hot take wars include Xenakis stans insisting “chaos did it better,” Berio lovers demanding more “color and vibe,” and Boulez fans flexing their set-theory muscles. Memes rolled in fast: “Boulez invented times tables,” “OIS stands for ‘Oh I Sigh,’” and the savage “multiply pitches, divide audiences.” One commenter joked this is “Le Marteau sans MasterCard,” another called integral serialism “crypto-calc.” The thread climax: a surprisingly wholesome truce where someone says, “use it if it helps you make music—then ditch it when it doesn’t.” Still, the math vs. music tension is the real symphony here.
Key Points
- •Pitch multiplication multiplies one pitch-class set by another to create a superset of pitch classes.
- •The article focuses on simple multiplication and notes that complex multiplication is covered in external references.
- •Key terminology is defined, including multiplicand, multiplier, product, normal form, IP set, initial pitch class, and OIS.
- •OIS is illustrated with the example set (5,9,0), yielding an interval structure of (047).
- •Pitch multiplication is attributed to Pierre Boulez as a method to vary pitch content beyond integral serialism.