String length ratios explain musical intervals since Pythagoras

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 (#corroborates, 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; Musical scales universally favor intervals with small integer frequency ratios; Musical intervals trace directly to harmonic-series frequency ratios (+6 more)

Related

• Designing scales from upper harmonics yields ratios no Pythagorean scheme can reach (similarity 0.94)
• Pythagoras established the inverse relation between pitch and string length (similarity 0.92)
• Pythagorean whole-number ratios led to the doctrine of the music of the spheres (similarity 0.87)
• Pythagoras linked musical consonance to small-number string ratios by 600 BCE. (similarity 0.85)
• A string’s harmonic frequencies encode the Pythagorean length rule (similarity 0.85)
• Simple whole-number ratios that rule musical intervals were extended into a cosmic harmony doctrine (similarity 0.81)
• Musical scales universally favor intervals with small integer frequency ratios (similarity 0.80)
• Pythagoras’ simple-ratio tuning system proved ultimately unsatisfactory. (similarity 0.78)
• Body size relative to open-string pitch shapes each string instrument’s distinctive timbre. (similarity 0.78)
• No pure integer-ratio system can tune musical intervals without compromise. (similarity 0.78)
• Small-integer ratios cannot govern all musical intervals consistently (similarity 0.78)
• When a string’s linear density is fixed, pitch is varied by tension and length (similarity 0.78)

Broader Connections

• Pythagoras established the inverse relation between pitch and string length #corroborates (0.95) — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 96
• Musical intervals trace directly to harmonic-series frequency ratios #expands (0.80)
• Musical scales universally favor intervals with small integer frequency ratios #expands (0.75)
• Musical intervals between adjacent harmonics shrink as harmonic number rises #exemplifies (0.75)
• Twelve stacked fifths slightly overshoot seven octaves by the Pythagorean comma #qualifies (0.72)
• String pitch depends on mass per unit length, length, and tension #qualifies (0.72)
• Pythagorean scales are constructed by stacking perfect fifths #expands (0.72)
• Demonstrative deductive mathematics originated with Pythagoras and mysticism #responds-to (0.72) — Bertrand Russell, History of Western Philosophy, 177