A Treatise on Music
Music, an art form consisting of sounds, is a crucial step in the communication of people. It bridges all the things in Man's life. Speech, mathematics, science, and art all factor into this witch's brew, and like ingredients, lack something when put in alone.
Speech
Speech, in fact, of itself, is a style of music. The cadence of speech, the speed of speech, the dips and spikes in pitch, the pauses, and the timbre all affect how we feel. Speech is music, and music enhances speech.
Mathematics
Music is, and always will be, based on numbers. Fractions are its philosophy, while trigonometry is its practice. This combination, while abstract and insufficient on its own, can produce the most fascinating of pieces. Additive rhythms, time signature changes, pulse patterns from interweaving sine curves, playing in between standardized notes, and similar techniques have been used to spice music. Math permeates music from its core.
Science
With math comes science always, but here the science is mainly experiment-based. Musicians are scientists -- they test, they try, they try to grow collective knowledge. Sometimes, they fail -- their experiment runs into the wilderness, the experiment is a stillborn -- but nevertheless, they go back, trying to find a "theory of everything."
Additionally, they record, even purely mentally, how each song makes the audience feel: were they pleased? were they tense? did that note make them feel physically uncomfortable? is this what the author wanted to happen? Each song brings the composer to another bit of knowledge. And what is science if not the strive to gain knowledge.
Art
Finally, art rounds out the ingredients. There is a set of personal and communal pleasure in music; the music must have geist in order to be music. Without soul, feeling, a drive to succeed, a drive to move people, the "music" is simply an mathematical science experiment to see what would happen. This is not to say that experiments are bad, for they acheive a drive towards knowledge; merely that an experiment is generally not perceived as music as an art form. However, if an artist wishes to proclaim that their art is music, whether being "full of ingredients" or a seemingly incoherent experiment, they may do so, and it is up to the listeners to decide and form an opinion.
To sketch a tree to work on sketching foliage would most likely be considered art, though one might say it is a much simpler form of the medium, and therefore "just homework"; to sketch a tree with the knowledge clear that you will always have a sketch of a tree is art, to sketch a tree with the thought of evoking an emotion or statement is art, to sketch a tree with any purpose beyond simply trying to is also art.
The Witch's Brew
There are some who claim that only their mother's recipe for soup is legitimate and right, and that all other soups are lacking something crucial. There is no fault or arrogance in thinking that they are wrong. Soup is soup.
Similarly, music is music. Whether a Bach chorale, a Bartok quartet, a Johnson blues, a DMX rhyme, or a Spector Wall of Sound, it has a higher cause than simply mathematical manipulation. Theory lawyers are into theory because they find order graceful and beautiful. Metal heads feel the blunt mood of Metal, and revel in it. All music is created equal.
Moving Beyond Definition
With all these strict and hard rules and definitions, it seems that it sucks the soul from music. However, music has one thing that transcends words, and that is how it touches the listener. It truly escapes the realm of words when a song is heard. Inactive listeners are touched as much as Active ones, just differently - mood vs. emotion, sound vs. notes - on second glance, is it not the same thing? We are all, unquestionably touched by this speech-making, mathematical, scientific art of Music.
