Extraordinary Hertz

Can there be an inherent unity between music and philosophy? Can philosophy be articulated through music? Questions of this nature are increasingly finding their place within contemporary debates. So much so that courses entitled "Philosophy of Music" are being integrated into university curriculums. But can philosophy truly have a relationship with music? You might think that they are completely separate fields, or even that it is near impossible to convey the depth and complexity of philosophical thought through sound; you wouldn't be entirely wrong. Yet, even if it seems unlikely, prominent philosophers throughout history have never hesitated to emphasise the vital significance of music in human life. One of the most striking figures among them was the ancient Greek philosopher, Pythagoras. In this piece, we will look at Pythagoras’s discoveries, his relationship with music, his life, and delve slightly into ancient Greece.

Pythagoras lived between 570 BC and 493 BC. It is highly probable that he was the very first philosopher to develop theories regarding music. Hearing the high and low pitches produced by hammers in a blacksmith's shop, an intense curiosity awoke within his sensitive heart. He didn't merely hear the music; he envisioned the significance it could bring to the universe and humanity. Using the monochord—a single-stringed instrument utilized in the Middle Ages to measure sound—he examined the relationship between varying string lengths and musical pitch. Following this, he analyzed mathematical ratios and studied their impact on musical harmony. In this manner, he discovered theories linking the mathematics of music to the mathematics of astronomy. Not content with this alone, he searched for other relationships involving whole-number ratios across the world, finding these exact proportions in geometry, astronomy, and medicine. It is said that following Pythagoras’s discoveries, science as we know it began to exist.

The most distinct interval observed by Pythagoras highlights the universality of his findings. The 2:1 ratio is known as an octave (an eight-tone interval in a musical scale). When the frequency of one tone is double the speed of another, the first tone is said to be an octave higher than the second, yet curiously, the pitches are generally perceived as almost identical. For instance, while a woman’s voice might fluctuate around 220 Hertz, a man’s voice may sit around 110 Hertz—roughly half the frequency of the woman's. Yet, if they sing together, even though they are an octave apart, it sounds as if they are delivering the exact same melody in unison. This extraordinary physical phenomenon is so fundamental that even monkeys and cats are capable of perceiving it.

Subsequently, gaining fame as a thinker through these discoveries and theories, he left his birthplace on the island of Samos, and it is said that he travelled the world. Regrettably, although it is claimed he "travelled extensively", his exact destinations remain unknown, for Pythagoras never penned a single book regarding his life or discoveries; the knowledge available to us has survived strictly through the accounts of his students. Ultimately, after settling in the city of Croton in Southern Italy, he began to offer instruction in mathematics tied to philosophy, gathering students around him. Following this formation, his students became his devoted followers, conducting studies that concluded the entire universe was bound to "harmonious numbers"; beyond merely analyzing figures, they revered them. In addition, Pythagoras stood as the central figure of the Orphic cult, which asserted that music embodied divine mysteries.

The Pythagoreans believed that specific numbers held a sacred significance. The number one represented the pure, undivided unity from which all existence takes its form. The number two (the dyad) signified opposing pairs and the concept of division. They introduced a set of ten such dualities to categorise everything in existence: finite / infinite, rest / motion, odd / even, straight / curved, one / many, light / darkness, right / left, good / evil, male / female, square / oblong.

Let us carry on... the number three (the "divine triad") represented completed existence, unifying creative unity with the duality that organises matter into categories. The triad also encompasses the beginning, the middle, and the end.

As I mentioned above, Pythagoras discovered a theorem regarding right-angled triangles; and although his school was esoteric and spiritual, he became one of the founders of modern science. His concepts of numbers and harmony fueled the imagination of generations to come. At the same time, he was a mystic who believed in reincarnation, and his followers established a society dedicated to the veneration of mathematics. Though one might call it a sect or a cult, realising that a brotherhood founded centuries ago was so deeply on the side of existence makes it utterly impossible to comprehend the dozens of modern cults that know nothing but destruction. In this context, when trying to understand Pythagoras, one must comprehend the era he lived in. For it is glaringly obvious that much has changed between that time and this.

Pythagoras holds his place within the most ancient currents of history. "He is so rooted in antiquity that he is the very first individual mentioned after the Milesian school in any textbook on the history of mathematics, philosophy, or science." In this period, Greek cosmology held that the universe was comprised of a series of concentric spheres with the Earth at its centre; a sphere each for the Moon, the Sun, all the planets, and the fixed stars. Within this framework, it was believed that mathematical relationships existed between these celestial spheres, and that these proportions corresponded to musical harmony. Pythagoras conceived the idea of the unheard celestial "music of the spheres," generated by the movement of planets around the Earth. Although he believed the human ear was incapable of perceiving this music, he was convinced it pointed to the holistic harmony of the cosmos. These theories ought to be taught as a mandatory lesson to those in our current era who fail to see the significance of the "unity of the universe" and live solely for consumption, if we are to prevent our world from facing the peril of destruction once more.

Let us return to our subject... If we look back to ancient Greece, Greek musicians were the creators of the music they performed. They were "makers of song" or melopoioi—producing melos, compositions consisting of lyrics, melody, and rhythm. Unquestionably, music carried immense weight in ancient Greece. To the extent that Plato recorded that the very first schools dedicated to musical education were established by the Cretans. However, the period when music truly flourished in the classroom was during the sixth and fifth centuries BC, when music schools were founded in Athens, instructing students between the ages of thirteen and sixteen on how to play the lyre and the kithara, and how to sing.

The inherent qualities that physics and mathematics identified in music long ago may help explain why so many physicists and mathematicians are also musicians. This intersection is perfectly illustrated by a quote from Einstein: "The theory of relativity occurred to me by intuition, and music was the driving force behind that intuition... My new discovery was the result of musical perception."

We might not—in all likelihood—be able to fully articulate philosophy through music alone. Rather than the analytical debates generated by philosophy, we can only create artistic ideas. In a digital era, it remains unknown whether philosophy and art (music) can carry on sustaining themselves. Even if individuals dedicate their entire lives to the knowledge contained within thousands of volumes, they can never succeed in reading them all. Such mathematics and time simply do not exist. Nevertheless, I invite you all to keep these fields alive—disciplines that have survived for centuries, creating boundless wisdom out of nothing. In defiance of those who ban music and smash musical instruments! Furthermore, when we bring these fields down to the people, perhaps we will capture the "unity of the universe," just as Pythagoras suggested. Who can say?