How Pythagoras Broke Music (and how we kind of fixed it)
Oliver Lugg・15 minutes read
Pythagoras and his followers, the Pythagoreans, made significant advancements in mathematics, focusing on the connection between numbers, geometry, and the universe. Despite their contributions to the Pythagorean theorem and the creation of a musical tuning system, challenges led to the development of new tuning systems like equal temperament, resulting in the modern musical scales we use today.
Insights
- The Pythagoreans, followers of the possibly mythical Pythagoras, advanced mathematics by exploring the relationship between numbers, geometry, and the universe, culminating in the Pythagorean theorem.
- The evolution from the Pythagorean tuning system to equal temperament revolutionized music by creating consistent intervals across all octaves, shaping modern musical scales and leading to widespread adoption through inventions like Stefan's equal temperament piano.
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Recent questions
Who was Pythagoras?
A philosopher from ancient Greece with a devoted following.
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Summary
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Pythagoras and the Musical Mathematics Evolution
- Pythagoras, a legendary figure from ancient Greece, was a philosopher who may or may not have existed around 2500 years ago.
- He had a devoted following known as the Pythagoreans, who were known for their eccentricities.
- Despite Pythagoras not being the original discoverer, the Pythagoreans made significant advancements in mathematics, believing numbers and geometry held the key to understanding the universe.
- The Pythagorean theorem, a fundamental discovery, states that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
- Pythagoras and his followers delved into the connection between mathematics and music, leading to the creation of a musical tuning system.
- Pythagoras observed that different-sized hammers striking anvils produced different notes, inspiring him to explore the relationship between vibrations and musical tones.
- The Pythagorean tuning system, based on fifths, aimed to create a set of notes within an octave using simple mathematical ratios.
- However, the Pythagorean tuning system faced challenges due to the discrepancy between perfect fifths and octaves, resulting in dissonances like the Wolf interval.
- Over time, musicians and mathematicians developed new tuning systems like equal temperament, which focused on creating equal intervals between notes within an octave.
- Equal temperament, utilizing irrational numbers like the 12th root of 2, allowed for a consistent tuning system where intervals remained the same across all octaves, leading to the modern musical scales we use today.
16:25
Stefan's invention revolutionizes piano tuning.
- Stefan's invention integrated equal temperament into the piano, leading to its widespread adoption and the prevalence of equal tempered music in the Western world, conditioning listeners to perceive it as in tune despite Pythagorean ratios sounding out of tune.
