The Mathematics Behind The Music Volume 2 : Mathematical Foundation In Music

The relation to music and Mathematics is quite a thick topic to discuss because, in a very general sense, music is mathematics. It is a difference and consistency of changes in melody and rhythm that generates sound in a way that we enjoy and appreciate it. Many different applications have been used to describe these changes from logarithmic fluctuation in sound wave frequency to the difference and scale relations of transposed music. This topic interests me in particular because I have always loved composing music and the differences in melodies via Music theory. Being both a mathematician and a musician Ive never been terribly impressed with, and consequently interested in, attempts to combine the two.It is perhaps even more surprising that music, with all its passion and emotion, is also based upon mathematical relationships. Such musical notions as octaves, chords, scales, and keys can all be demystified and understood logically using simple mathematics.Mathematical models can be found from theoretical analysis to actual composition or sound production. Increasingly in the last few decades, musical scholarship has incorporated modern mathematical content. One example is the application of methods from Algebraic Combinatorics, or Topology and Graph Theory, to the classification of different musical objects. However, these applications of mathematics in the understanding of music have also led to interesting open problems in mathematics itself.