Music, Math, and Mind: The Physics and Neuroscience of Music

by David Sulzer

Why does a clarinet play at lower pitches than a flute? What does it mean for sounds to be in or out of tune? How are emotions carried by music? Do other animals perceive sound like we do? How might a musician use math to come up with new ideas?

This book offers a lively exploration of the mathematics, physics, and neuroscience that underlie music in a way that readers without scientific background can follow. David Sulzer, also known in the musical world as Dave Soldier, explains why the perception of music encompasses the physics of sound, the functions of the ear and deep-brain auditory pathways, and the physiology of emotion. He delves into topics such as the math by which musical scales, rhythms, tuning, and harmonies are derived, from the days of Pythagoras to technological manipulation of sound waves. Sulzer ranges from styles from around the world to canonical composers to hip-hop, the history of experimental music, and animal sound by songbirds, cetaceans, bats, and insects. He makes accessible a vast range of material, helping readers discover the universal principles behind the music they find meaningful.

Written for musicians and music lovers with any level of science and math proficiency, including none, Music, Math, and Mind demystifies how music works while testifying to its beauty and wonder.

Genres: Music, Science, Nonfiction, Neuroscience, Psychology, Physics, Mathematics

304 pages, Hardcover

First published April 27, 2021

Reviews

[Claudia · Rating 4 out of 5]

David Sulzer, the neuroscientist, 'meets' Dave Soldier, the musician, to create one of the most interesting science books I've read so far.

However, as the author states, "this is not a 'pop science' book to be absorbed in a single reading", and he is right. It's very dense, with a lot of technical details, and those chapters are indeed to be reread if your interest is beyond than simple curiosity. It isn't my case, because I don't try to make or even understand music (I can't even sing a single note); I just enjoy hearing it, no matter the structure behind it.

But all the other facts related to sound, how it is perceived, what are the differences between humans and animals hearing, the path music took throughout history, its etimology, and many more, I have found to be extremely appealing.

There is a variety of topics from different fields which are related to sound and interconnected, such as physics, maths, biology, even astronomy, and the connection between them is fascinating.

It is not a light reading, but it compensates in being a very rewarding one for those who are avid for information.

I extracted some quotes from the book, but they may be subject to chnage, since this is an uncorrected ARC.



"The approach to contemporary musical education is rooted in a system developed to train orphans and abandoned children in Renaissance Naples. The word 'conservatory' meant "places to save children", and mysic provided a way for those who did not inherit a family trade to learn to compose, play instruments, and sing to make a living."

"In contrast, the creation of music in some other styles requires no theory classes - or even instrument or singing lessons - but simply talent, opportunity, and work. A pioneer of this approach was the French radio engineer Pierre Schaeffer, who in the 1940s composed exciting music by splicing together recording tape. Fifty years later, this approach was updated by the hip-hop group Public Enemy, who created instrumental tracks entirely by juxtaposing previously recorded sounds."

"Young people, like the Bronx DJs Kool Herc and Afrika Bambaataa, adapted the sparse instrumental resources available to them - drum machines and turn tables from stereo supply stores - and used them to create a style that Bambaataa named hip-hop, presently the most popular musical style in the world."

"At the high end of our hearing, teenagers extend up to about 20,000 Hz, above which we humans do not perceive sounds. This means that with good hearing, we cand hear across a ten-octave range. Dogs hear as high as 45,000 Hz, cats to about 80,000 Hz, mice to about 100,000 Hz, and some bats and whales to a ridiculous 200,000 Hz, more than three octaves higher than we can."

"The early physicists who wanted to understand sound waves had a challenge: how do we study invisible waves in the air? An important development was the siren, as in a police car, which was invented by the Scottish physicist John Robinson (1739-1805) as a musical instrument. The siren was improved by Charles de la Tour in 1819, who named it after the mythological singing legends of ancient Greece."

"The word music is derived from the Greek goddesses the Muses, and the word lyrics comes from instrument, the lyre"

"Some gravitational wave frequencies reached 80 Hz and higher, and in case of a collision between black holes of unequel size, they noted the presence of the third harmonic (SOL), in a way confirming the presence of intergalactic music."

"Cricket stridulation is faster when the air is watmer, and the pulse speed of the cricket songs cand be used to estimate the temperature."



One more thing: there are a lot of recommendations of songs and musical pieces as diverse as possible, from classical music to experimental ones, animal sounds and many, many others, and the ones I have looked up for so far are available on YouTube and Spotify. Quite an experience to read about some musical tehnique and then listen to its exemplification.

Enjoy!

>>> ARC received thanks to  Columbia University Press  via NetGalley <<<

[Ricardo · Rating 5 out of 5]

This is a fascinating, mind-opening dive at a very concrete intersection of art and science. I suspect this will be a read that will come to mind often, many years hence. It's an especially rare piece of work because the author clearly knows about every field he brings to the table and, pricelessly, knows how to convey the weaving of such wide-ranging content in an engaging way. Do not misunderstand me: this is not light reading. It is dense with information, standing maybe midway between popular science and college textbooks. It begins with a caffeinated refresher on your high school Physics: waveforms, cancellation and thereabouts. Biology comes along, making us glimpse not only the structure of our hearing equipment (from the ear to what's currently known about the brain) but also how the external waves travel and convert and eventually lead us to perceive where the sound is coming from... how loud it is... how rich and embellished we sense them to be. That we can possibly recognize and respond to rhythm, tuning and other elements, deriving sensations such as joy and building the capacity to follow along and add to what's being heard is nothing short of astonishing -- although usually taken for granted. You'll never take your ability to sing along for granted after this. Plus, the presentation extends to what's known about other animal species and their relationship to organized sounds, including what many of those species can do. A wide-world tapestry of music and music history envelops everything, and each chapter reveals many listening suggestions one can hunt on music services, YouTube and publicly-accessible recordings -- to further one's understanding of how deeply human and universal the language of music really is.

I rarely reread books these days, but will certainly circle back to this later on in my life. I wish to thank NetGalley for allowing me free access to the book in exchange for this review -- I could not possibly envision the journey I'd begin then!

[Paul · Rating 4 out of 5]

As the title suggests, this includes a lot of math. But it is accessible/understandable math. It is also highly academic (it is a university publisher, after all). But again, the info is written in an accessible and sometimes entertaining way. Nice use of images and illustrations, too. Highly recommended for those interested in music from a somewhat scientific standpoint. Interesting stuff.

I really appreciate the ARC for review!!

[Maggie]

Dense, fascinating, erudite, and even funny.

Also - impossible to summarize, and probably not for everyone.

[Vitória Fernandes · Rating 4 out of 5]

Thanks to NetGalley and Columbia University Press for the digital copy of the book in exchange for an honest review.

I am not a musician in any way shape or form, but I'm interest in music and specially how we perceive it. The first few chapters have a focus on music, how it works and some math involved (the math is pretty ok to follow). Then it talks about how we hear and what happens in our brain when we hear. At last it brings a bit about how other animals listen and their relation to music.

As the author states at the beginning, this is not exactly the kind of book you are going to fly through, you may want to read it slowly and even reread some parts. It is a well researched book and the author did a good job passing a lot of relevant and interesting information in the field to the reader.

What I really enjoyed was that the author at the end of each chapter suggests songs for us to listen that are related to the topics mentioned in that chapter.

If you are interested in music, give this one a try!

[GONZA · Rating 4 out of 5]

A rare book that puts together all the things that I love (with the exception of some math ;).
An Handbook which should be a recommended reading for every musician and an interesting reading for neuroscientist also. Brilliant.

Uno di quei rari libri, che mette insieme gli argomenti che piú mi appassionano (senza esagerare con la matematica comunque). Un manuale che dovrebbe essere consigliato ad ogni musicista e un interessante lettura per gli amanti delle neuroscienze. Brillante.

THANKS EDELWEISS FOR THE PREVIEW!

[J. · Rating 3 out of 5]

Thank you to both NetGalley and Columbia University Press for providing me with an advance copy of David Sulzer's nonfiction work, Music, Math, and Mind, in exchange for an honest review.

As a lover of all things music, I find it difficult to shy away from titles that mention the subject. My focus becomes so narrow the second that music enters the picture, that I completely glazed over the word in the title that describes my least favorite subject: math.

Overall, however, the author does a great job explaining difficult concepts in a way that is accessible to readers. He even mentions in the intro that readers should use the table of contents as a guide to skip to chapters that discuss topics they are interested in and not to read the work as if it were a standard fiction novel.

Although anyone can read this book, it definitely leans toward the heavier and drier end of the bookcase. I highly recommend it for musicians and math enthusiasts, but stay clear if you are not interested in any of the topics mentioned in the title.

[Khanh · Rating 5 out of 5]

Music, Math, and Mind was for me, a dense but rewarding exploration of the deep connections between music, physics, mathematics, and neuroscience. David Sulzer (who is both a neuroscientist and a musician) draws on his extensive expertise in each field to illuminate the underlying structures of sound, perception, and musical expression. From tuning systems and harmonics to auditory processing and cognition, the book offers a multidisciplinary lens through which to understand not just how music works, but why it affects us so profoundly.

This was not an easy read for me, but it was an immensely rich one. Life’s chaos often pulled me away from the book, and I found myself rereading many sections to take as much as I could in—not out of confusion, but because each chapter is so layered, so dense with insight, that I don't feel a single reading can do it justice. This is a book I would like to reread so that I can take more in. I feel I have barely scratched the surface. I will return and revise/add more thoughts when I revisit this wonderful book.

[Josh Coe · Rating 4 out of 5]

This was a rewarding book about physics, acoustics, and the history of sound and music. As a music composition professor, I found this book engaging and creatively stimulating. I’m not sure that a reader with an average knowledge of music and acoustics would find it accessible, though. To get the most out of the book (for professionals and amateurs alike), queue up each chapter’s listening list before you begin to read, then stop and listen as you learn each new concept. The listening lists are a great idea, and listening to the examples while reading really enriches the experience!

I was impressed with the diversity of musical examples (from prehistoric flutes all the way to Jacob Collier!), the confidence with mathematical equations, and the clarity of the writing and format. This book was both humbling and thoroughly informative. Strongly recommended.

Thank you to NetGalley and to Columbia University Press for the advance copy!

[Paul Perrone · Rating 3 out of 5]

Good read - but not the answers expecting

I read the book and generally liked and appreciated it. I didn’t really learn the neuroscience of music as I thought I might. I have a basic knowledge of neuroscience and was hoping to make a better connection to what constitutes a good melody according to the brain. There is plenty of good introductory info here and info on frequencies and their path through the brain. The beginning chapters on math were a little outside of what I was expecting but I read through them. The last chapter on animal music I could’ve avoided and I skimmed through it. It reads more like a bunch of individual papers and the author is a good writer and keeps it light. So recommend as a read. But not if want to understand the real neuroscience of music. Which, maybe simply isn’t known yet.

[Andrea Dr. Strádi · Rating 4 out of 5]

Ez a könyv valóban zenészeknek és természettudomány-kedvelőknek az igazi! Nem egy könnyed regény. Az eleje főként a hangok és hangszerek fizikájával foglalkozik, személy szerint nekem ez tetszett a legjobban. A záró fejezetben leírt nem-ember állatok zenei szokásai is nagyon érdekes voltak. Furcsa módon éppen a szerző szakterületéhez tartozó neurobiológiai rész volt kevésbé élvezetes.

[pianogal · Rating 3 out of 5]

This one was ok, but it got a little boggy in the math for me. I really liked the beginning - some of the sidebars were excellent, but then it settled it to a lot of science speak and kind of lost me. Also, I think some of the recordings would be amazing to here, but I wasn't sure how to find them. A playlist somewhere (spotify, amazon, etc) would be super helpful.

[Rock · Rating 3 out of 5]

To a large degree, this book is just a collection of things the author thinks is interesting. Luckily, the author is fantastically well-informed about these things. I found the first half, on the physics of sound and music, more readable than the second half, which was mostly the neuroscience stuff.

[Stuart Barrow · Rating 4 out of 5]

Enjoyed this one quite a bit - although I found the back half (about the neuroscience aspects of hearing) more accessible that the front half (the maths and music theory), which is probably a reflection of my pop-science reading habits.

Still: will come back to this one with notebook and headphones.

[NessinMorse · Rating 4 out of 5]

Book is exactly as the title says, I probably have missed things and had to reread at least as much, yet the book itself feels like a complete compendium of great and interesting ideas deeply rooted in Alpha, Beta & Gamma studies. It combines music in very unique ways and sheds light on subjects that are not often discussed.

[Yannis Vasilakis · Rating 4 out of 5]

As a PhD student in Artificial Intelligence and Music, I try to find ways of communicating my research to untrained individuals and this book provides a good way of simplifying the science of sound, although I found specific notions that implied some knowledge.

[Jason Mill · Rating 3 out of 5]

I think I wanted less neuroscience and more of an anthropology look at this topic tbh, got very neurosciencey at times, and I think the last chapter about animals and music could easily be its own book, I’d read it.

[Joe Isler · Rating 5 out of 5]

Very accessible survey of the neuroscience of sound and music, from the basic physics of sound to the emotions evoked by music. Lavishly illustrated. An added benefit is exposure to the highly eclectic musical taste of the author.

[Josh · Rating 2 out of 5]

Well I guess it turns out I don’t really like math. Liked the idea of this book but it was too math-y for my blood. At least he was kind of funny.

[Thomas Fratkin · Rating 3 out of 5]

Unless you have a deep background in music theory and mathematics or physics or neuroscience... this is not for you.

[Batisse · Rating 5 out of 5]

A comprehensive textbook for either ambitious students or fanatics, really.

[Ivan · Rating 3 out of 5]

audio processing intro

[Amelia Johnson · Rating 4 out of 5]

This book was chock-full of very interesting information. As a musician, I was fascinated by learning more about the math and science behind my craft. The book was dense because of all of the information housed in it, so it is best read in multiple sittings. Sulzer makes the information pretty accessible and understandable. I especially loved the listening suggestions at the end of each chapter. They were very diverse and gave a great opportunity to hear the information from the chapter exemplified. I found this book to be absolutely fascinating!

[Kunal Sen · Rating 4 out of 5]

During my high school and early college days a question started bugging me -- why do we find some sequence of sound musical and melodious. I could not find any books that could answer my question, and sitting in Calcutta I had no other access to such information. Therefore, I used by interest in electronics and built a very simple electronic synthesizer where I could tune each individual note and also play with the shapes of the waves and their envelope. A very poor man's analog synthesizer where strips on tin from a can served as the keyboard. Using this, and my home made frequency meter, I tried to figure out the mystery of the musical scales and also tried to generate some algorithmic music to figure out what constitutes a melody. It was a lot of fun. If I had access to this book then, I would have been deprived of the joy of discovering something using really primitive tools.

This is a great book to learn about these and many other things about music and hearing in terms of physics, mathematics, and neurology. In fact I have not come across any other book that takes this approach. Most books about music theory are written for musicians and not for the scientifically curious.

The sad thing is while it confirmed many of those things that I had discovered on my own in my younger days, it also busted many of my theories that I cherished for the last 40 years as truth. You win some, and you loose some...