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> That problem is that sheet music is terrible.

Something that people with casual exposure to musical notation probably don't know is that before the standard 5-staff notation became ubiquitus there were quite a few alternatives, maybe the most interesting from a mathematical perspective being the Byzantine notation

Broadly speaking, while the modern system focuses on pitch values and an elaborate (modulated) map from frequency space to physical space (paper), older systems used in the Byzantium used "deltas" or the first differences of pitch values.

So you start with a base note (lets say C) and then you go +1, +1, -2 to indicate pitch changes (in semitones). This is quite well adapted to monophonic chant. This notation was never developed to cope with the complexity of modern music but its not immediately obvious that it can't be done

There is no easily accessible exposition of this musical notatin style, this cheatsheet gives a flavor http://www.byzantinechant.org/notation/Table%20of%20Byzantin...