A classical book in this direction is "Gödel, Escher, Bach" of Douglas Hofstadter from 1979.

Dear Armin,

thank you,

but not that!

It is a very bad book,

from the point of view

of the scientific content.

I see. Maybe you like this more: http://tones.wolfram.com/generate/

Here are some explanations how it works: http://tones.wolfram.com/about/faqs/howitworks.html

Also this page provides some information, and further references to the literature: https://ccrma.stanford.edu/~blackrse/algorithm.html

You may have a look the french institute of research in music and acoustic IRCAM.

You can find there books and scientific paper notably on math / music.

http://www.ircam.fr/?&L=1

Possibly the two attached papers might interest you. They deal amongst other things with how perception of music can be expressed verbally and how these verbal utterings are related to features of the music. Both resulting data sets are analysed with three-mode principal component analysis.

Music and mathematics are both vast fields, and much has been written about their relationship.  Here, for starters, are some of my favorites.

    Pythagorean Plato by Ernest G. McClain

    Genesis Of A Music by Harry Partch

    Musimathics by Gareth Loy

    Music, Language, and the Brain by Aniruddh D. Patel

If your interest encompasses computer music, you might find my book interesting:

    Elements of Computer Music by F Richard Moore

http://www.amazon.com/Musimathics-Mathematical-Foundations-Music-Volume/dp/0262516551/ref=pd_bxgy_b_img_y

http://www.amazon.com/Genesis-Of-Music-Creative-Fulfillments/dp/030680106X/ref=pd_rhf_dp_s_cp_3_Z71X?ie=UTF8&refRID=1ZNNH7Z9ZX28EKC5ZWBQ

http://www.amazon.com/Pythagorean-Plato-Prelude-Song-Itself/dp/0892540109/ref=asap_bc?ie=UTF8

http://www.amazon.com/Music-Language-Brain-Aniruddh-Patel/dp/0199755302/ref=sr_1_fkmr2_1?s=books&ie=UTF8&qid=1421945860&sr=1-1-fkmr2&keywords=music+mind++brain+patel

http://www.amazon.com/Elements-Computer-Music-Richard-Moore/dp/0132525526/ref=sr_1_sc_1?s=books&ie=UTF8&qid=1421945926&sr=1-1-spell&keywords=elementes+of+computer+music

Another already referenced musimaths, so I can but second this. I might add, though, the following:

Beran, J. (2004). Statistics in musicology. CRC Press.

Chew, E., Childs, A., & Chuan, C-H. (Eds.) (2009). Mathematics and Computation in Music (Communications in Computer and Information Science 38). Springer.

Yust, J., Wild, J, & Burgoyne, J. A. (Eds.) (2013). Mathematics and Computation in Music (Lecture Notes in Computer Science 7937). Springer.

Haas, R., & Brandes, V. (2009). Music that works: Contributions of biology, neurophysiology, psychology, sociology, medicine and musicology. Springer.

I don't know whether it can be considered appropriate, but there is a very nice book by Andrea Frova "La Fisica nella Musica" (physics of music)... Unfortunately I don't think there is an english version, but I guess for Giancarlo that should not be a problem!!

In my previous response, I inadvertently omitted this remarkable (and difficult) book on mathematical aspects of stochastic musical composition:

Formalized Music, by Iannis Xenakis

http://www.amazon.com/Formalized-Music-Mathematics-Composition-Harmonologia/dp/1576470792/ref=sr_1_2?ie=UTF8&qid=1422129281&sr=8-2&keywords=xenakis

• Music: A Mathematical Offering, David Benson
• The Physics and Psychophysics of Music, Juan Roederer
• Music and Mathematics, From Pythagoras to Fractals - Editors: Fauvel, Flood & Wilson
• Mathematics and Music, David Wright
• The Physics of Music and musical instruments, David Lapp

You find some of them in the WWW-World by "googling". 

Would like to recommend a book:

Emblems of mind:the inner life of music and mathematics

By Edward Rothstein

Seemingly two worlds apart: math and music were connected and linked so effectively by the author that it made me fall deeper in love with mathematics while deepening my passion for music even further.

http://press.uchicago.edu/ucp/books/book/chicago/E/bo3771161.html

@Shian_Loong_Lew

Thank you very much indeed.

@Ulrich_Groh

Thank you very much indeed