A musical tone is the ear's response to a vibration that repeats at a fast, regular rate. Noise comes from vibration with no repeating pattern. So the first and most basic split among sounds comes from the shape of the motion in time, not from loudness or source.
Painting and poetry point to things beyond themselves. Musical tones represent nothing, and they act on us directly. So the science of how the ear senses sound matters far more to music theory than the science of light or perspective matters to painting.
Melody is the true foundation of music. Harmony is a recent Western way of strengthening melodic relations, and highly developed music has existed for thousands of years without it. A theory claiming that every rule of modern harmony is a law of nature has proved too much, so it must be wrong.
Every musical note carries a series of fainter, higher tones inside it. These overtones were long treated as minor curiosities. In fact the mix of them is what makes one instrument sound different from another playing the same note, and it shapes the tones most useful for music.