People I (Mostly) Admire 49. Mathematician Sarah Hart on Why Numbers are Music to Our Ears
Oct 30, 2021
Sarah Hart, a professor at Birkbeck College and Gresham Professor of Geometry, shares her passion for the intersection of mathematics and music. She demonstrates how whole numbers resonate with pleasing sounds and reveals the fascinating imperfections of octaves. The conversation touches on the gender gap in mathematics and the importance of creative teaching in making math accessible. Hart also discusses overcoming creative slumps, emphasizing adaptability and inspiration as keys to success in both math and the arts.
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Octaves and Ratios
- Notes an octave apart have a simple mathematical ratio of 2:1 in their frequencies.
- This ratio, combined with overtones, explains why they sound harmonious when played together.
Harmony and Ratios
- Pythagoras discovered the relationship between string lengths and musical intervals.
- Simple fractional ratios between frequencies create pleasing harmonies, a principle known since ancient Greece.
The Twelve-Semitone System
- An octave is divided into 12 semitones due to the relationship between octaves and perfect fifths.
- Twelve fifths approximate seven octaves, a compromise based on the inherent incompatibility of these intervals.
