There are many books exploring musical theory with maths. However, so far I have only seen discussions about the consonance/dissonance of two notes played simultaneously (intervals) -- this is the theory of "the vertical" on the score. Such theories only consider the sound of the frequency domain at a time, but in reality, music keeps on changing its frequency. None of the books I have read address the issue of "horizontal" movements where the music moves from one note to another, changing the spectrum of frequencies of sounds.
Examples of "horizontal movement":
- Why some dissonant chords tend to resolve into consonant chords (usually by step)? Theories I have seen do a good job at explaining why something is dissonant, but none of them explain why I need to resolve it.
- Why melodies tend to move mostly by steps?
Are there any books that discuss those issues?