Legacy of Pythagoras: Exploring the Mathematics and Music of the Spheres


Embark on the mysterious legacy of Pythagoras and discover the relationship between numbers and music in the cosmos.

Pythagoras, a  genius figure from 570 to 490 BCE, captivates us with his enigmatic persona and numerous accomplishments. Although no surviving written works directly attributed to Pythagoras exist, we have gleaned insights into his life and achievements through the writings of historians and his devoted followers. Iamblichus, a prominent disciple of Pythagoras from 224 to 325 BCE, extensively documented his teachings and philosophies. However, the true extent of Pythagoras’ contributions remains a subject of debate, as it is unclear whether his achievements were solely his own or the collective work of many individuals spanning several generations. Some theorists propose the possibility that Pythagoras could have been a culmination, an amalgamation of multiple individuals, but conclusive evidence to support this hypothesis remains elusive.

Pythagoras: The First Mathematical Physicist

Mathematics and Music of the Spheres, Pythagoras
Pythagoras, source: Wikimedia Commons

Regarded as the first mathematical physicist or theoretical physicist of his time, Pythagoras sought to unravel the mysteries of the cosmos through his groundbreaking wave theory, now commonly known as “string theory” or the Music of the Spheres. Departing from the prevailing reliance on supernatural causes, Pythagoras endeavored to explain the workings of the universe using his wave theory. This revolutionary concept posed the central question of why Pythagoras chose to emerge as a cult figure in an era abundant with diverse cults. During the 6th century BCE, cults flourished, encompassing various forms of worship, ranging from bronze pets to abstract concepts of the ethereal.

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The Philosophy of Pythagoras: Change, Number, and the Universe

Pythagoras, fueled by his passion for mathematics, embraced the concept of duality, emphasizing that “change is the only constant” and that “all is number.” He restricted his definition of number to positive integers, excluding zero and negative numbers. For all other entities that did not fit this numerical category, Pythagoras posited that the universe comprised of “the limiting and the unlimited.” An ardent cosmopolitan, Pythagoras excelled not only in mathematics but also as a skilled lyre player. He studied under Thales and delved into the mysteries of Egyptian religions. Founding a cult during a time when such practices were prevalent, Pythagoras established rigorous initiation rituals, requiring long periods of apprenticeship, adherence to specific dietary restrictions such as vegetarianism (excluding beans), and abstinence from all forms of animal flesh. Additionally, silence, personal cleanliness, unwavering loyalty, and attire made of pure linen were considered virtuous within his sect.

The Downfall of Pythagoras: The Decline of an Academy

The annals of Pythagoras’ life reveal limited facts, with one notable account recounting the uprising of local residents in Croton, Italy, where he established his academy. It is widely believed that Pythagoras managed to escape, but the precise reasons for the local population turning against him and destroying his academy remain subject to speculation. Many historians assert that Pythagoras became entangled in local politics, thereby alienating the residents. However, no definitive records exist to corroborate this theory. Alternatively, some propose that the locals perceived him as a demonic figure, ascribed with magical powers—an explanation that may serve as a convenient scapegoat. Considering the Mediterranean’s historical tolerance for mystery cults, it is plausible that Pythagoras’ disciples, disillusioned by perceived flaws in his reasoning and claims, joined forces with the disgruntled locals, leading to his downfall.

Pythagoras and the Harmonic Explorations

Pythagoras and the Harmonic Explorations

Pythagoras’s fascination with the harmonics of strings potentially played a significant role in the development of Greek musical scales, including the foundational five modes: tonic, dorian, phrygian, lydian, and mixolydian. According to his followers, Pythagoras also proposed an early wave theory to explain the observed phenomena. However, due to the fragmented nature of the historical and archaeological records, reaching a definitive conclusion about the full extent of his contributions remains challenging. Renowned for his musical prowess, Pythagoras, being well-versed in the harmonics of open strings, understood that when a string was touched at its midpoint, the subdivided intervals created a note one octave higher than the fundamental frequency, with a precise ratio of 1:1. Similarly, a stopped string produced a note one octave higher than the open string, with a wavelength ratio of 1:2. This doubling of frequency occurred as the string’s length halved when stopped at the midpoint.

Pythagoras’s experiments extended beyond strings to include bells and tuning forks of varying weights. Through these investigations, he made an intriguing discovery: a bell with twice the weight of another would produce a note one octave lower, establishing a direct correlation between weight and pitch. These explorations into harmonics and tones unveiled new realms of understanding.

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The Pythagorean Belief System: A Harmonious Numerical Path

The Pythagoreans attributed great significance to numbers, with their mystical pursuits ultimately challenging the notion that numbers inherently possessed harmony or served as the foundation for all knowledge. The precise reasons for this philosophical shift remain obscured by the passage of time and the blending of myth and reality. However, it is clear that the intervals within musical scales provided precise solutions to the wave equation governing vibrating strings. As waves interacted with strings, only specific ratios—such as 1:2, 2:3, and 3:4—could form nodes that satisfied the wave equation. Hence, within the octave, this ordering of intervals proved accurate. Pythagoras’s wave theory demonstrated validity to a certain degree. However, the music of his time encompassed a broader dynamic range than a single octave. Pythagoras asserted that by cycling through the scale, emphasizing perfect fifth intervals, one could map out seven octaves of the pitch.

The Celestial Harmony: Pythagoras’s “Music of the Spheres”

Pythagoras fervently believed in the concept of the “music of the spheres,” which postulated that the celestial bodies—the planets and stars—created an inaudible symphony as they traversed the heavens. Each sphere emitted a distinct musical note corresponding to its movement, and the collective resonance formed a flawless harmony. Pythagoras contended that this celestial music was a reflection of the mathematical and harmonic principles governing the universe. Moreover, he proposed that the human soul, attuned to this celestial symphony, could gain profound insight into the cosmos by studying music and mathematics. This profound concept exerted a lasting influence on Western music and philosophy, permeating the works of later luminaries such as Plato and Johannes Kepler, who frequently referenced the music of the spheres in their own intellectual pursuits.


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