Section 32.1 Introduction
In music, Ramsey Theory can help to recognize or ensure the presence of certain themes, harmonies, or rhythms in large sections of music. This may mean that no matter how complex a piece of music is, repetitions or patterns will inevitably occur, just as a monochromatic subset will inevitably be found in sufficiently large set.
Our methodology involves mapping integers to musical notes, with Schur's Theorem guiding the creation of harmonic Schur triples and melodic lines. The theorem asserts that any sufficient large partition of integers will contain a set of numbers that form a monochromatic Schur triple, i.e.,a monochromatics set of the form \(\{a,b,a+b\}\text{.}\)
Drawing inspiration from Schu's Theorem, our project aims to translate this mathematical concept into an engaging piano work.