Pythagorean whole-number ratios led to the doctrine of the music of the spheres

Evidence

Scientific and engineering knowledge of communication processes has developed over the last hundreds, even thousands, of years. First there were beliefs that sounded rational, but a closer investigation found them to be false or only partially true. Some early thinkers and experimenters, such as Pythagoras, turned out to be very successful and influential (Hunt, 1992). Pythagoras studied the behavior of strings and understood the inverse relation between pitch and string length in ancient Greece during the sixth century B.C. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 96 (#expands, via linked claim)

To conceive of the earth, not as the centre of the universe, but as one among the planets, not as eternally fixed, but as wandering through space, showed an extraordinary emancipation from anthropocentric thinking. When once this jolt had been given to men’s natural picture of the universe, it was not so very difficult to be led by scientific arguments to a more accurate theory. — Bertrand Russell, History of Western Philosophy, 900 (#expands, via linked claim)

Categorization

• XREF: connects to: Pythagoras established the inverse relation between pitch and string length — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 96; Pythagorean scales are constructed by stacking perfect fifths; Designing scales from upper harmonics yields ratios no Pythagorean scheme can reach (+2 more)

Related

• Designing scales from upper harmonics yields ratios no Pythagorean scheme can reach (similarity 0.92)
• Pythagoras established the inverse relation between pitch and string length (similarity 0.87)
• String length ratios explain musical intervals since Pythagoras (similarity 0.87)
• Simple whole-number ratios that rule musical intervals were extended into a cosmic harmony doctrine (similarity 0.83)
• Pythagoras linked musical consonance to small-number string ratios by 600 BCE. (similarity 0.83)
• Pythagorean cosmology provided the conceptual leap toward the Copernican hypothesis. (similarity 0.82)
• Pythagoras’ simple-ratio tuning system proved ultimately unsatisfactory. (similarity 0.80)
• Pythagorean scales are constructed by stacking perfect fifths (similarity 0.78)

Broader Connections

• Pythagoras established the inverse relation between pitch and string length #expands (0.80) — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 96
• Designing scales from upper harmonics yields ratios no Pythagorean scheme can reach #complicates (0.75)
• Pythagorean scales are constructed by stacking perfect fifths #expands (0.70)
• Demonstrative deductive mathematics originated with Pythagoras and mysticism #expands (0.70) — Bertrand Russell, History of Western Philosophy, 177
• Pythagorean cosmology provided the conceptual leap toward the Copernican hypothesis. #expands (0.70) — Bertrand Russell, History of Western Philosophy, 900