The Mathematics of Sound
In the tradition of western philosophy, there has long existed theoretical interest in relationships between mathematics and music. The idea that music is the aural result or manifestation of a mathematically structured, metaphysical reality reaches back to the presocratic philosophers of ancient Greece. Even before Plato and Aristotle, in the 6th century B.C. E., the mystic genius, Pythagoras, and his privileged students debated notions concerning the relationships between forms of thought and the various entities that make up the material world, the things that the ideas are believed to reference through language and other physical interpretative mechanisms.
It is argued that such references appear within an expansive spectrum where everything that exists in the material world can be logically placed. Every thing falls somewhere -- from pure mathematical spectacle, such as the calculus involved in the architectural blue prints for building the Acropolis or the U. S. Capitol, or even a Steinway piano, to the much more subtle 'asymmetric symmetry' of fractals in ice and other crystals, or a Ligeti symphony, even toward some completely enigmatic incongruity, like metallic fluids and decay or insanity.
The Piano as Idea
Pianos, too, can be found somewhere within this vast mathematical spectrum. In fact, although the 'eternal idea' or 'form' of a piano hadn't yet been 'discovered' or dreamt of during the hay day of ancient Greek Philosophy, the piano serves as an excellent 'ontic' example of what the Greek philosophers were attempting to describe and define. That is, the piano serves as a good example of how mathematics relates to the construction and resulting manifestation of a mathematically determined material object, in this case, the piano itself.
It's true, the wood of the pin block, the steel of the plate and strings, the angled intricacies of this incredible music box are all held together and kept in working suspense by planning, testing and putting into material form, an intricate and detailed mathematical plan. The materials of the natural world seem to defy strict mathematical exactitude, yet they do conform.What intrigued the old philosophers was the crossover from the conceptual to the material.
Imagine these original thinkers of the West could time travel and they found themselves in some soft, mysterious music room of a modern DC townhouse or condo. Beyond their complete surprise at the amazing musical instrument in the room, a bright student of Pythagoras might explain to the participants that it doesn't really matter if there's an actual piano in the room, there would still be a piano, and even a piano player in the universe of numbers. Another might object that the piano and piano player would then only 'exist' 'on paper' or in thought. Some would insist, no doubt, that the nonexistent piano and its nonexistent player are perhaps more real than the real piano and real piano player, if they existed. Of course, someone might wonder out loud about what it might sound like for music to be played on a nonexistent piano by a nonexistent piano player... At that point, surely, more drinks would be served.
All absurdity aside, within and arising out of this ancient debate, a notion eventually concretized suggesting that the harmony of the universe is governed by numbers and that the entire Being of the world is in reality, number, and in fact, music. Some still believe that every single thing that exists emerges into the cosmos as a particular note in an unfolding, unfathomably immense cosmic symphony, or in the vernacular of this material season, one giant itune.
Beyond any conclusions that would have been drawn at this imaginary piano party in downtown Washington, DC, it is true that with the very real, existing pianos we repair, rebuild and restore, we do in fact often follow mathematical formulas on pretty much every aspect of piano repair. Maybe Pythagoras was right. Too bad he never set eyes on a piano.