Musimathics, Volume 2: The Mathematical Foundations of Music (The MIT Press) 59507th Edition

The sad thing about this series is that the keywords that invite readers to stop by, hide the fact that these texts go far beyond music, to USE music as a gentle introduction to extremely complex, relevant and timely math concepts. The best teachers use four paths to explain a math concept: verbal, formulaic, algorithmic and pictographic. These help the brain comprehend the topic regardless of our learning modality. The authors here are simply MASTERFUL math teachers, and clarify everything from Eulers Law (relation of e, the base of the natural logarithms to pi, the base of the trig functions) to Fourier Transforms, in a way that a bright High School student will get. If you've been out of math (any math) for a long time, and want a masterful review of math concepts and techniques, this series is THE place to start. You can then extend that foundation to many other applied areas, from signal processing to physics, voice recognition, etc. Fourier transforms (and their more recent spin off in Cepstrums) are being used in too many fields to list today, from radar and electronic engineering, to whale songs.In every section, the author's excitement is contagious. Rather than give a bunch of dry proofs that reek of hubris and disregard for the reader, Gareth uses a "curious mind" tone, as if he were just learning and discovering this too, like a kind of puzzle or murder mystery. Loy is Monk, Holmes and Columbo combined. For example, he gives a few expansion series for e, then says: "Wow, there seems to be a striking and beautiful pattern here, doesn't there? Wonder what it can be?" Leave it to a guy into both math and music to see the wonder in a time series!One more example. Any texts on waveforms have to involve deep calculus, especially PDE's. Unfortunately, deep PDE's don't happen until grad school. But, rather than assume the reader uses calculus all day long, Loy starts with the basics at "now let's see how the first derivative is actually slope finding and integration is the area covered by the moving curve..." including those perhaps more musically inclined who have forgotten what a derivative is. Astonishingly, Loy sneaks around the dry topic of limits to use MUSIC as a great practical refesher on calculus (p. 263 of the second volume, in the section that is the hottest topic in Physics today, from Astronomy to Medical Imaging to of course music: Resonance).Gareth is one of the few mathematicians around who can relate math to the astonishment of life around us. After all, our brain is doing advanced Fourier Transforms every time we cross a street in traffic, and when we get an MRI, the Fourier Transforms that convert magnetic alignment to pictures are assuming that the atoms in our body are a song, which when pulsed with a radio wave, will sing the positions of their water molecules back to us in harmonics that can be seen as well as heard.Highly recommend this series, not only for everyone interested in math and music, but math and life!

Incredible. Just incredible.The heart and dedication put into these 2 volumes... just unimaginable.

This is a review of the second volume which assumes you have read the first volume. Each chapter starts off with a summary of the topic which would be useful for someone with little knowledge of college level math. It then proceeds with more detailed description of the concept which definitely requires a good understanding of college level mathematics and ends with a much more detailed description which would best be understood if one had a math degree. Even though I have a good understanding of college math: Calculus, Deferential Equations, Matrix Algebra, Topology, etc., I still found it necessary to read the chapters more than once. But I do have to say that reading the book greatly increased my knowledge of both Math and Music.

This second volume is very much a detailed lesson in spectral analysis. The examples and graphics are very good. You will need a very solid background in college math to follow everything presented. If you have never heard the words, 'Fourier transform', it will be over your head.

I bought this book for someone close to me and they absolutely love it! They talk about it all the time and they keep mentioning how so many things in music makes sense. I've read a bit of the book myself and there's a lot of really interesting and cool information in this book. You don't have to be a total expert to understand the content in this book. In conclusion, this is a really neat book with a LOT of interesting information!

The first volume is mind-blowing enough, but this one is more math-heavy and super-cool -- a gripping thriller! Before this book reached my hands, I had no idea such a clear view of mathematics + music was available, and now that this book has turned my world upside-down I find myself studying complex numbers and calculus with renewed fervor. If you know someone even vaguely into music and computers, let 'em know that this book exists.

As an aerospace engineer who plays guitar, I always wondered EXACTLY what was at the basis of why the instrument worked.I always got close but never sat down and put it all in one place. This pair of books does.Wholeheartedly recommended.

This is the Math - if you're a musician with a technical bent. There's two books in the series and I recommend both.

The book covers much well-known material, but in a subtly nonstandard notation. For example, it uses the convention that omega = 2*pi, not omega = 2*pi*f. Such things mean that one has to go through all the elementary stuff to get used to the notation, before learning anything new is possible.Furthermore, factual correctness is sometimes sacrificed for easy readability. The DA converter in Figure 1.18, for instance, would be very nonlinear in practice.A disappointment.

This is a wonderful series. This has very specific info to fill some holes in my knowledge to better understand audio dsp functions etc. I was hoping the first book would be more like this one. But together they make a great reference for people interested in this sort of audio stuff.

to Digital TechniquesIn audio Signal processing.It`s a good Starting point and Prerequisite for more Mathematical Treatments of this Topic,like those of J.O.Smith,Dafx etc.

Dieses Buch veranschaulicht bildhaft einfache und komplexere Vorgänge der Mathematik. Auch Erfahrene können diesem Werk noch die ein oder andere Information entlocken.