February 4, 2026
Tune wars: bring the popcorn
The Mathematics of Tuning Systems
Pianos, “devils” and a nerd brawl over how music should be tuned
TLDR: Baez breaks down how music tuning evolved from ancient ratios to today’s equal temperament, complete with slides and a draft book. Comments lit up over a “devil in music” line, while others debated 12-tone tuning, real‑world instrument quirks, and even shared coding tools—proof that tuning still sparks strong feelings.
John Baez’s friendly tour of tuning—from ancient ratios to today’s equal temperament—hit all the right notes, and then dropped bonus slides and even a draft book. The crowd cheered the buffet of links, with one reader laughing that just when you think it’s over, boom, more to binge. But the comments didn’t stay mellow for long.
The spark? A dramatic line about chasing the Pythagorean ideal “unleashing the devil in music.” That set off a vibe shift. One reader bristled, asking who exactly this “devil” is and why music needs to be “Christian” to sound good—calling out the metaphor as loaded. Others sidestepped the culture-war energy and dove into the nerdery: how 12-tone equal temperament (aka 12tet), the modern system of evenly spaced notes, “includes” close-enough versions of old-school intervals, and what that does to how players choose notes and how transcribers write them down. Cue deep breaths—and deeper theory.
Then the physics squad pulled up: a pianist reminded everyone that real strings don’t behave perfectly, so higher notes go a bit sharp, twisting the tidy math. Meanwhile, coders rolled in with toolkits—Xenharmlib for C++ and PyTuning for Python—turning theory into code. Verdict: fascinating talk, surprisingly spicy comments, and a thread tuned to 11.
Key Points
- •John Baez’s talk examines Western tuning systems from Pythagorean tuning to equal temperament.
- •The piano keyboard’s pattern of 7 white and 5 black keys repeats every 12 notes, forming a 12-tone scale.
- •Ascending 12 semitones reaches a pitch with nearly double the starting frequency; intervals correspond to frequency ratios.
- •Note names A–G trace back to Boethius; starting on A yields the minor scale, starting on C yields the major scale.
- •Historically, pitches outside the 7-tone system were called “musica ficta”; accidentals became accepted, with flats and sharps denoting them.