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FrameBenignly comments on Programming-like activities? - Less Wrong
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Music is like the art of math. The playing of musical instruments is art, but the writing of it and the instrument design and the understanding of how those instruments operate is all math. Music can be created without art, but music cannot be created without math; not even in the slightest aspect of it. It is the only major form of classical arts to which that claim can be prescribed. A drum requires a calculation to generate reverberation to make itself heard. A scale must be calculated from its underlying frequencies. Strings must be measured in length, thickness, and tension to determine their resonance. The hole spacing and size of wind instruments must be calculated. Even something as simple as humming while alternating between high and low is a binary expression of either volume or frequency. It is only over the course of several millennia that we have developed the ability to teach an artistically gifted person to generate music without learning a bit of math. But that person still owes their artistic creations to the mathematicians of history. The connection is not at all tenuous. It is a very clear case of cause and effect.
By tenuous I mean that many great musicians and singers never learned much math and never needed to. Not sure how much math Stradivari knew, either. But I guess it all depends on how we define "math".
ADBOC
"Music cannot be created without math" is true only in the same grossly misleading sense as "you can't catch a ball without finding an approximate solution to a differential equation".
That is not the same. A complex set of equations are not required to calculate how to make an object to throw at people, nor is it required to make a glove or to figure out where to place your hands to catch the ball, but generating resonance at a given volume and frequency is a very hard thing to do. Stradivari may not have been a great mathematician, but he still had to carefully measure, and set to very exacting specifications each one of his instruments. He had to follow the calculations even if he did not know those calculations. In the time of ancient Greece, before those calculations were completed, it did require a mathematician to devise a musical instrument more complex than a drum. This is why many cultures never got past the stage of drums and horns before the more complex instruments were imported from Europe. These equations can be used by those unfamiliar with them, but they can't be created without someone learning those equations in the first place in the same sense that computer software cannot be created without engineering.
What? This doesn't sound like you're describing folk music at all.
Folk music is a very wide-open term. The origins of it are mostly unknown in most parts of the world, but traditional folk music was usually quite simple. There were only very simple changes in pitch; often binary or ternary or none at all. These are simple enough to where a person could intuitively grasp the calculations in their head (by counting the tempo and arrangement of percussive hits); even if they could not express them in written form. Later forms of folk music were derived from western classical music which definitely did require a lot of complex calculation.