I've been trying to find the "true and correct" visualization of music that would reflect its "inner symmetry". I started with an assumption that music is a much simpler entity than drawings, simply because it's one-dimensional. Now I think it's actually more complex because it represents an abstract entity that has no shape, yet has symmetry and for this reason it's so difficult to "draw music". Schopenhauer apparently knew this well:

"Absolutely direct experience of the will is impossible, because it will always be mediated by time, but in first-personal experience of volition and the experience of music the thing in itself is no longer veiled by our other forms of cognitive conditioning."

Music has many different concepts at play, some of which are easier to conceptualize geometrically than others. Waveforms are one, but another visualization that resonated (pun semi-intended) with me was to visualize triads in three dimensions by plotting the pure sine wave of each note of the triad on its own axis as a function of time.

When you plot triads like this, you immediately see that the more harmonic a chord is, the visually simpler its graph is. This is unsurprising to anyone who knows the basics of the math behind music (simple ratios = harmonic, complex ratios = dissonant), but it's striking to actually see it drawn out like that.

I definitely would not say music is one-dimensional. Whether you're considering the interplay between intervals, the movement and manipulation of various emotions and motifs in a piece, or whatever, maybe the thing that strikes me most about music relative to other media is its arbitrary dimensionality.

Not sure I get the idea about triads. Say the three notes are just sine waves with frequencies 200Hz, 300Hz and 500Hz. What will the graph look like?

Music is a graph.

Everything is a graph

Nothing is a graph

Everything is a node

All

Music is everything?

Drawing music makes as much sense as singing a painting or dancing architecture.