I have heard that, in recent years, many mathematicians as well as music theorists have applied different branches of mathematics to music.
I would like to know about some books/resources relating to this topic.
[Math] Mathematics and Music
book-recommendationmusic-theoryreference-requestsoft-question
Related Solutions
It sounds like you really want to read Benson's Music: a Mathematical Offering (freely available at the link). I'm not completely sure what you're asking, but if it's anything like "why is it natural to think about music in terms of sine waves," this question is addressed right in the introduction:
...what's so special about sine waves anyway, that we consider them to be the "pure" sound of a given frequency? Could we take some other periodically varying wave and define it to be the pure sound of this frequency?
The answer to this has to do with the way the human ear works. First, the mathematical property of a pure sine wave that's relevant is that it is the general solution to the second order differential equation for simple harmonic motion. Any object that is subject to a returning force proportional to its displacement from a given location vibrates as a sine wave. The frequency is determined by the constant of proportionality. The basilar membrane inside the cochlea in the ear is elastic, so any given point can be described by this second order differential equation, with a constant of proportionality that depends on the location along the membrane.
The result is that the ear acts as a harmonic analyser [emphasis added]. If an incoming sound can be represented as a sum of certain sine waves, then the corresponding points on the basilar membrane will vibrate, and that will be translated into a stimulus sent to the brain.
The paragraph you refer to is about probably 50th and 60th, and I am not well aware of the book from that period. However, I would like to point out that starting from 1980 and till 1992 a series of math and physics books was published under the title "Библиотечка Кванта" (Kvant's library). Some of these books are translations of very insightful books, but most are written by big names such as Kolmogorov, Pontryagin, etc. You can find all the issues here. If someone is at school, likes physics and math, and reads Russian, this is a great read.
I would also recommend to check out the magazine Kvant. It has tons of wonderful problems with solutions.
About other books: Probably the series by I.M.Gelfand and co-authors is worth mentioning. These books were initiated and planned by Izrael Moiseevich, but written mostly by the co-authors. You can find some of them in English just going through the books by Gelfand.
Best Answer
You may want to take a look at the book Music: a Mathematical Offering by David J. Benson. It can be downloaded for free in PDF format from this page of author's homepage.