More or Less: Behind the Stats Ed Sheeran and the mathematics of musical coincidences
Jun 25, 2022
Eugenia Cheng, a mathematician and concert pianist, dives into the fascinating world where music meets mathematics. She explains how with only 12 notes, musicians like Ed Sheeran can still create an abundance of unique melodies. Cheng illustrates the exponential growth of possible combinations through playful examples, revealing that even a few notes can yield thousands of variations. The conversation also touches on how historical composers like Bach and Handel navigated originality amidst similar melodies, blending creativity with numerical possibilities.
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Bach and Handel
- Bach's 18th-century piece has a theme that appears in Handel's Messiah.
- This demonstrates that musical similarities have existed for centuries.
Exponentials in Music
- Eugenia Cheng points out that exponentials explain the vast number of musical possibilities.
- Multiplying choices for each note quickly leads to enormous numbers of potential melodies.
Scales and Melodies
- Most melodies use major or minor scales (8 notes), not all 12 chromatic notes.
- Even with 8 notes, four-note melodies have over 4,000 combinations (8^4).
