Benedetti's Puzzle (mathematically impossible music)

Summary by Krater

This video explores Giovanni Battista Benedetti's musical puzzle from 1585, which demonstrates that tuning a melody purely using frequency ratios causes the pitch to rise as the music repeats due to the comma pump. It concludes that mathematically pure music and stable pitch are incompatible when using Western harmony in five-limit tuning, leading modern music to settle on twelve-tone equal temperament.

From the video

Answers: Why does Giovanni Battista Benedetti's 1585 musical puzzle make pitch rise?

• musical puzzle
• comma pump
• tuning theory
• five-limit tuning
• just intonation
• pitch drift
• syntonic comma
• twelve-tone equal temperament

What it concludes

• Musical harmony can never be completely and consistently mathematically perfectly in tune using Western harmony in five-limit just intonation.
• A choir singing purely in tune will experience pitch drift because natural semitones differ in size from tempered semitones.
• The 12-tone equal temperament system solves the issue of pitch drift by tempering commas out of the system, keeping pitch stable across keys at the cost of perfect tuning intervals.