The Cognitive Neuroscience of Music

Book Description

Music offers a unique opportunity to better understand the organization of the human brain. Like language, music exists in all human societies. Like language, music is a complex, rule-governed activity that seems specific to humans, and associated with a specific brain architecture. Yet unlike most other high-level functions of the human brain - and unlike language - music is a skill at which only a minority of people become proficient. The study of music as a major brain function has for some time been relatively neglected. Just recently, however, we have witnessed an explosion in research activities on music perception and performance and their correlates in the human brain. This volume brings together an outstanding collection of international authorities - from the fields of music, neuroscience, psychology, and neurology - to describe the amazing advances being made in understanding the complex relationship between music and the brain. Aimed at psychologists and neuroscientists, this is a book that will lay the foundations for a cognitive neuroscience of music.

Customer Reviews:

Very interesting overview of current research in the subject.......2005-02-11

The collection of articles in this book gives a fascinating overview of human musical cognition and how it is modeled computationally. It also addresses the effect of brain lesions or abnormalities on musical competence and abilities, and thus gives the reader a taste of the kind of research that is being done in current research circles in the cognitive neuroscience of music. It is readily apparent after reading the articles that much is known about musical cognition, but there are many questions yet to answer. Because of space constraints, only a few of the articles will be reviewed here.

When considering human musical ability and competence it is natural to ask whether it is the result of evolutionary adaptations or whether it is "accidental" or "evolutionary vestige." The article by David Huron discusses these questions in some detail, with emphasis on the ability of evolution to shape not only physiological attributes and functions, but also human attitudes, emotions, cognitive abilities, and so on. The author gives an overview of the `nonadaptive pleasure seeking' (NAPS) view of music, and also the view that music is indeed an evolutionary vestige. He concludes, interestingly, that the truth of NAPS would place music lovers at an evolutionary disadvantage. If music is an evolutionary vestige, it still is important to ask, says the author, what value it had in the past for human survival. He discusses various types of evidence for supporting an evolutionary origin for music, such as genetic, neurological, ethological, and archaeological. Noting that no genes have been discovered which are correlated with musical ability, the other types of evidence do add plausibility to his evolutionary hypothesis, he argues at length in the article. The ability of music to form social bonds he believes shows the greatest promise as a plausible evolutionary origin for music. Most interesting is his discussion of how music brings about social bonding, with the hormone oxytocin playing a major role in this regard.

The article by Stephen McAdams and Daniel Matzkin on the perception of musical similarity is interesting for its own sake but also from the standpoint of artificial intelligence. Measures of similarity and to what extent a given concept can be changed and still be judged or perceived to be in the same category are of great interest in artificial intelligence. The authors of this article argue that the empirical evidence in similarity perception limits the `transformation space' for given music material. In other words, one can only go so far in the transformation of the original musical material before it is judged as completely new. The authors discuss in detail the factors that contribute to these limitations. In this context, the authors discuss a very interesting experiment to test among other things whether professional musicians are able to hear similarity to a greater degree of transformation if the transformations respect certain syntactical rules. The authors conclude, and their conclusions adhere to what is expected based on listening experiences, that the space of possible variations of musical material that is perpetually similar to an original piece of music is very limited.

Neural networks naturally enter into any discussion on human cognition, and they do so here in the article by Barbara Tillman, Jamshed Bharucha, and Emmanuel Bigand, who use them to model music cognition. Simulation of mental processes is of immense importance in brain research and allows one to study the effect of various anatomical and physiological abnormalities on cognition. The authors mention these capabilities in their article, but their emphasis is on explaining how neural networks coupled with unsupervised learning, can be used to model music cognition. They also mention, but do not discuss in any detail, the use of self-organizing maps to simulate the neural plasticity that allows the capacity to extract regularities and to then become sensitive to musical structures and regularities.

The article by John Brust discusses the effect of neurological disorders on musical function. The author discusses `musicogenic seizures', which are triggered by the hearing of music. Interestingly, these seizures can be triggered in some people by merely listening to their own voice. In some individuals, sound can also produce the perception of colors. This is called `synesthesia' by the author, but he does not discuss it in any great length. Apparently synesthesia is poorly understood, but has been noted to happen very frequently in individuals using hallucinogenic drugs. Also discussed is `amusia" which is an acquired impairments of musical processing.

The next article by Isabelle Peretz continues the discussion on amusia, but the emphasis is on what it reveals about brain specialization for music. The author holds that music has neuroanatomical specialization, in that there is a collection of neural networks that are dedicated to the processing of music. The author discusses various patients who had accidents causing brain damage in certain areas of the brain but were still able to retain musical skill. This occurred even when the damage occurred in the part of the brain responsible for language abilities. Even more surprising is that the auditory recognition of music is supported by cognitive processes that are not used at all in speech recognition or in environmental sound recognition. The author also discusses musical savants and the phenomenon of tone deafness. In terms of neural networks, the author asserts that brain specialization for music involves the encoding of pitch along musical scales and the ability to impute a regular beat to incoming events. She believes though that further research is needed to show that neural networks that are domain specific for music are the result of evolutionary adaptation.

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Even better than Drums, Girls and Dangerous Pie
You'll Laugh, You'll cry...
Music, old people and decapitated gnomes make for a good read
A must read!
Notes From the Midnight Driver

Notes From The Midnight Driver
Jordan Sonnenblick
Manufacturer: Scholastic Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0439757797

Book Description

16-year-old Alex decides to get even. His parents are separated, his father is dating his former third-grade teacher, and being 16 isn't easy, especially when it comes to girls. Instead of revenge though, Alex ends up in trouble with the law and is ordered to do community service at a senior center where he is assigned to Solomon Lewis, a "difficult" senior with a lot of gusto, advice for Alex, and a puzzling (yet colorful) Yiddish vocabulary. Eventually, the pair learn to deal with their past and each other in ways that are humorous, entertaining, and life changing.

Customer Reviews:

Even better than Drums, Girls and Dangerous Pie.......2007-05-03

Jordan Sonnenblick keeps getting better. NOTES is the story of an angry adolescent - even angrier than most! Alex's parents have gotten divorced and after drinking an excessive amount of vodka, he's going to just drive over and tell his dad how angry he is. Luckily, he doesn't hurt anyone when he crashes the car, but now he is even angrier, because he has to spend time at an old folks' home talking to possibly the crankiest man in the whole place - Sol. Sol's tough love is hilarious, poignant, and ultimately effective. Great book, great read, great for kids just starting to drive or even just thinking about starting to drive. I'm using it with my ninth graders right now, and they love it!

You'll Laugh, You'll cry..........2007-02-12

Not exactly a sequel to Drums, Girls & Dangerous Pie but you will see some of the same characters and be back in the same high school. Notes from the Midnight Driver also deals with a serious topic but lets you laugh your way through it. The main character begins the book by seriously messing up; he gets drunk and into a car. Fortunately only a lawn gnome was injured and the stupid kid gets a chance to straighted out his life. He ends up with community service with a cranky old man who never gives him a break but teaches him about life and death.

Music, old people and decapitated gnomes make for a good read.......2007-01-02

After Sonnenblick's incredibly touching first book, Drums, Girls and Dangerous Pie, I was wondering if his second book would make me feel as much as his first book did. I am happy to report, I gained even more from this book.

Alex is your average high school junior--anticipating getting his driver's license, worring about the SATs, dealing with family and girl issues. That is until he decapitates his neighbor's lawn gnome after getting drunk on his absentee father's vodka and sealing his mother's car for a joyride. But he's the only one who doesn't feel lucky when the judge sentences him to 100 hours of community service at the local nursing home.

There he meets Sol, a crotchety old man who's determined to take Alex down a notch or two and help him see he's destined for more than a drunk driving conviction at sixteen. Sol also wants to help Alex become a better guitar player, learn some dirty Yiddish phrases and kindle a romance with his best gal pal Laurie.

The book has the classic elements of a good read with some great jazz history, a good plot-twist or two and a little romance. Alex's biweekly letters updating the judge on his "progress" also help to show Alex's development from a troubled teen to a young man willing to take responsibility for his mistakes.

With great dialogue and a smart plot, Sonnenblick puts heart and humor into a sad tale of learning to be accountable for your mistakes. Fan's of Drums, Girls and Dangerous Pie will be excited by the cameo appearances of Steve and Annette, but new readers will fall hard for Alex's quick whit and development. This is a great read, and the lively characters keep the book light even when the harsh realities of the plot threaten to give the book too dark a tone.

A great read for middle/high school students dealing with divorce, death of a grandparent, minor legal infractions or just life.

A must read!.......2006-10-21

And you think your life is tough. Sixteen-year-old Alex Gregory miscalculated the consequences of his anger when he decided to teach his father a lesson. Nothing good can come of a poorly thought out plan, especially when it entails stealing your mother's car, driving drunk and obliterating a poor unsuspecting lawn gnome.

Alex thought it was a great idea at the time. The police and the judge, well, not so much. He was sentenced to hundreds of community service hours in a nursing home, catering to Sol, a cantankerous old curmudgeon who's writing the last chapter of his life.

While Alex is doing 'hard time' in a nursing home, his parents are separated, and dad's dating his third grade teacher, he's discovered his childhood friend, Laurie, is pretty 'hot' and the judge isn't buying his written declarations that he's not qualified to help with Sol's problems. It's enough to send a guy to his room to play the blues (or maybe jazz) on his guitar.

Never underestimate the power of tough love. Alex and Sol navigate the generation gap and forge the relationship of a lifetime. Personal responsibility and giving people (especially parents, because they really are trying) a second chance is the lesson of the day. And you'll never see the twist coming, and it'll warm your heart.

Sonnenblick delivers a great story with snappy patter wrapped up nicely in a life lesson.

I laughed and I shed some tears. And I decided Notes From the Midnight Driver is a must read.

Armchair Interviews says: Nice to have more quality books for young adults.

Notes From the Midnight Driver.......2006-10-13

Home alone, 16-year-old Alex Gregory, enraged over his parent's separation and fuming about his dad's involvement with Alex's former 3rd grade teacher, gets drunk and sets off in his mom's car to confront his father and "that woman." He doesn't get far, but he's lucky. The only victims of the resultant accident are a decapitated French lawn gnome and the cop he barfs on when he's arrested.

To Alex's dismay, a judge sentences him to 100 hours of public service, assigning him to visit some cantankerous old guy at the home for the aged where Alex's mother coincidentally works. Obligatory progress notes to the judge punctuate the action and raise interesting speculations as Alex gets to learn something about, and from, old Solomon Lewis. Sol's severe emphysema and apparent abandonment by his only daughter, have not suppressed his chutzpah, Yiddishisms, or zest for pulling "Gotcha" surprises on everyone. Without preachiness and with much humor, the story will appeal to middle schoolers as Alex is transformed, accepting responsibility and change while learning - and teaching -- forgiveness.

As for Jewish content: Alex, his best gal pal Laurie, and their families are not Jewish, but both old Sol and the judge are. The most overtly Jewish aspect of this book springs from Sol's frequent use of Yiddish, the wisdom underlying his wisecracks, and the basic Jewish values such as family, community and accountability, which shape the story.
Alex's initial behavior and some minor scenes might make this problematic for some very traditional schools. For ages 12-14. Reviewed by Rita Berman Frischer

Listening: An Introduction to the Perception of Auditory Events (Bradford Books)

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Listening: An Introduction to the Perception of Auditory Events (Bradford Books)
Stephen Handel
Manufacturer: The MIT Press
ProductGroup: Book
Binding: Paperback

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The Psychology of Music, Second Edition (Cognition and Perception)

ASIN: 0262581272

Book Description

Listening combines broad coverage of acoustics, speech and music perception, psychophysics, and auditory physiology with a coherent theoretical orientation in a lively and accessible introduction to the perception of music and speech events.

Stephen Handel is Professor of Psychology at the University of Tennessee.

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Shows the link between musical style, perception, and probability

Music and Probability
David Temperley
Manufacturer: The MIT Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0262201666

Book Description

In Music and Probability, David Temperley explores issues in music perception and cognition from a probabilistic perspective. The application of probabilistic ideas to music has been pursued only sporadically over the past four decades, but the time is ripe, Temperley argues, for a reconsideration of how probabilities shape music perception and even music itself. Recent advances in the application of probability theory to other domains of cognitive modeling, coupled with new evidence and theoretical insights about the working of the musical mind, have laid the groundwork for more fruitful investigations. Temperley proposes computational models for two basic cognitive processes, the perception of key and the perception of meter, using techniques of Bayesian probabilistic modeling. Drawing on his own research and surveying recent work by others, Temperley explores a range of further issues in music and probability, including transcription, phrase perception, pattern perception, harmony, improvisation, and musical styles.

Music and Probability--the first full-length book to explore the application of probabilistic techniques to musical issues--includes a concise survey of probability theory, with simple examples and a discussion of its application in other domains. Temperley relies most heavily on a Bayesian approach, which not only allows him to model the perception of meter and tonality but also sheds light on such perceptual processes as error detection, expectation, and pitch identification. Bayesian techniques also provide insights into such subtle and advanced issues as musical ambiguity, tension, and "grammaticality," and lead to interesting and novel predictions about compositional practice and differences between musical styles.

Customer Reviews:

Shows the link between musical style, perception, and probability.......2007-06-11

If music perception is largely probabilistic in nature this should not be surprising since probability pervades almost every aspect of mental life. Thus the author invokes a number of concepts from probability theory and probabilistic modeling, relying most heavily on Bayes Rule, an axiom of probability. In music perception, one is often confronted with a pattern of notes and wishes to know the underlying structure that gave rise to it. Bayes' Rule allows us to identify that underlying structure. The author also makes use of concepts from information theory such as the idea of cross-entropy. Cross-entropy shows in a quantitative way how well a model predicts a body of data. In chapter 2 the author surveys all the probability theory needed for the following chapters. He also shows a few simple examples, and discusses the applications of probability theory to other areas of study. In chapter three the author addresses a basic problem of music perception - the identification meter - and proposes a probabilistic model of this process.

Chapters 4 and 6 examine the problem of key perception from a probabilistic standpoint. The author first proposes a model of key perception in monophonic music (melodies). This model is then expanded to accommodate polyphonic music. With regard to both meter and key, the models proposed are not merely models of information retrieval, but also shed light on other aspects of perception. In particular they lead very naturally to ways of identifying the probability of actual note patterns. This in turn provides a way of modeling cognitive processes such as error detection, expectation, and pitch identification, as well as more subtle musical phenomena such as musical ambiguity, tension, and "tonalness". These issues are explored in chapter 5 with regard to monophonic music and chapter 7 with regard to polyphonic music. The final three chapters of the book explore a range of further issues in music and probability. Chapter eight surveys some recent work by other authors in which probabilistic methods are applied to a variety of problems in music perception and cognition: transcription, phrase perception, pattern perception, harmony, and improvisation. Chapter nine considers the idea of construing probabilistic models as descriptions of musical styles and thus as hypotheses about cognitive processes involved in composition.

In summary, this book is a good one in demonstrating that a probabilistic perspective opens the door to a new and powerful approach to the study of music creation. Highly recommended for all who have an interest in algorithmic composition. The following is the table of contents:

1. Introduction 1

2.Probabilistic Foundations and Background 7
2.1 Elementary Probability 7
2.2 Conditional Probability and Bayes' Rule 8
2.3 Other Probabilistic Concepts 14
2.4 Early Work on Music and Probability 19

3. Melody I: The Rhythm Model 23
3.1 Rhythm and Meter 23
3.2 Previous Models of Meter Perception 26
3.3 A Probabilistic Rhythm Model 30
3.4 The Generative Process 31
3.5 The Meter-Finding Process 36
3.6 Testing the Model on Meter-Finding 41
3.7 Problems and Possible Improvements 43

4. Melody II: The Pitch Model 49
4.1 Previous Models of Key-Finding 50
4.2 The Pitch Model 56
4.3 Testing the Model on Key-Finding 62

5. Melody III: Expectation and Error Detection 65
5.1 Calculating the Probability of a Melodic Surface 65
5.2 Pitch Expectation 66
5.3 Rhythmic Expectation 71
5.4 Error Detection 74
5.5 Further Issues 76

6. A Polyphonic Key-Finding Model 79
6.1 A Pitch-Class-Set Approach to Key-Finding 79
6.2 The Generative Process 83
6.3 The Key-Finding Process 85
6.4 Comparing Distributional Models of Key-Finding 89
6.5 Further Issues in Key-Finding 92

7. Applications of the Polyphonic Key-Finding Model 99
7.1 Key Relations 99
7.2 Tonalness 108
7.3 Tonal Ambiguity and Clarity 116
7.4 Another Look at Major and Minor 121
7.5 Ambiguous Pitch-Collections in Common-Practice Music 125
7.6 Explaining Common Strategies of Tonal Harmony 131

8. Bayesian Models of Other Aspects of Music 139
8.1 Probabilistic Transcription Models 139
8.2 Bod: The Perception of Phrase Structure 143
8.3 Raphael and Stoddard: Harmonic Analysis 147
8.4 Mavromatis: Modeling Greek Chant Improvisation 151
8.5 Saffran et al.: Statistical Learning of Melodic Patterns 156

9. Style and Composition 159
9.1 Some Simple Cross-Entropy Experiments 161
9.2 Modeling Stylistic Differences 166
9.3 Testing Schenkerian Theory 172

10. Communicative Pressure 181
10.1 Communicative Pressure in Rules of Voice-Leading 182
10.2 The Syncopation-Rubato Trade-Off 184
10.3 Other Examples of Communicative Pressure in Rhythm 191
10.4 "Trading Relationships" 197
10.5 Low-Probability Events in Constrained Contexts 202
10.6 Conclusions 205

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Musical Form and Analysis
Glenn Spring , and Jere Hutcheson
Manufacturer: McGraw-Hill Humanities/Social Sciences/Languages
ProductGroup: Book
Binding: Spiral-bound

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ASIN: 0697153673

Book Description

Musical Form & Analysis provides a balanced theoretical and philosophical approach that helps junior and senior music majors understand the structures and constructions of major musical forms.

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Good for Beginners
a wealth of ideas
Moving and effective
A Life-changing Experience
Fantastic!

Art Is a Way of Knowing
Pat Allen
Manufacturer: Shambhala
ProductGroup: Book
Binding: Paperback

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ASIN: 1570620784
Release Date: 1995-04-11

Book Description

Making art—giving form to the images that arise in our mind's eye, our dreams, and our everyday lives—is a form of spiritual practice through which knowledge of ourselves can ripen into wisdom. This book offers encouragement for everyone to explore art making in this spirit of self-discovery—plus practical instructions on material, methods, and activities such as ways to: Discover a personal myth or story Recognize patterns and themes in one's life Identify and release painful memories Combine journaling and image making Practice the ancient skill of active imagination Connect with others through sharing one's art works Interwoven with this guidance is the intimate story of the author's own journey as a student, art therapist, teacher, wife, mother, and artist—and, most of all, as a woman who discovered a profound and healing connection with her soul through making art.

Customer Reviews:

Good for Beginners.......2003-03-09

Pat Allen gives an informed and moving account of her personal experiences and how art used therapeutically has helped her work through different life challenges. However, being an artist and pursuing the field of art therapy I found her approaches and explanations a bit simplistic and not challenging for those already initiated in the use of art materials and techniques. A section for those with art backgrounds, or a follow-up book, might be helpful in this regard. A good pick for beginners, but not for those already conversant and comfortable with techniques and materials. Her resourse lists are helpful and informative. I would have liked to see works by patients of Ms. Allen's also included, with comments. This might have made the reading more challenging and interesting.

a wealth of ideas.......2001-12-21

The author reveals much of her own journey through painfull life experiences and how art expressions helped her to heal.
The book is filled with her own original artwork,and it is a very open,brave art indeed.
Her suggestions for the reader are very stimulating,and make one eager to begin to make art.She offers many examples of art activities and materials.,and even has an appendix for a music catalogue(she suggests listening to music while artmaking)and an adress for art supply catalogue...Everyone will feel like an artist,as well as getting to know oneself at a deep level through doing this book.

Moving and effective.......2000-11-08

A very moving and effective book with seamless ties between art therapy and personal experiences - this book easily reaches out to anybody, artist or not, therapist or not. It's for the common man and its honesty and fluent accounts make it extremely accessible.

A Life-changing Experience.......2000-08-21

Pat Allen is a truly gifted individual who describes activities to help us connect with our deepest questions and our answers. For many years she has studied and refined ways to make this connection with herself and the others she has worked with. After just participating in a workshop with her where we did many of the activities included in Art is a Way of Knowing, I know for myself that she has clearly laid out ways of learning important truths about ourselves and healing from the pains of life. I look forward to using them so I can live a more centered life and be more effective in my work with others.

Fantastic!.......2000-05-04

The author's own very personal story of healing & growth through imagery and the art process, combined with a very clear, present-moment style of writing was absolutely riveting to me! This is a living, pulsing and highly moving, inspired and inspiring work. I couldn't put it down.

Speech and Audio Signal Processing: Processing and Perception of Speech and Music

Average customer rating:

Much breadth but little depth
Great, but don't buy it here....
Hitch Hiker's Guide to Speech & Audio Processing :-)
Speech and Audio Signal Processing: Processing and Perceptio

Speech and Audio Signal Processing: Processing and Perception of Speech and Music
Ben Gold , and Nelson Morgan
Manufacturer: Wiley
ProductGroup: Book
Binding: Hardcover

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ASIN: 0471351547

Book Description

Speech and music are the most basic means of adult human communication. As technology advances and increasingly sophisticated tools become available to use with speech and music signals, scientists can study these sounds more effectively, and invent new ways of applying them for the benefit of humankind. This book includes coverage of the physiology and psychoacoustics of hearing as well as the results from research on pitch and speech perception, vocoding methods and information on many aspects of automatic speech recognition (ASR) systems. The authors have made use of their own research in these fields, as well as the methods and results of many other contributors.

Customer Reviews:

Much breadth but little depth.......2002-12-21

There are many good books on speech processing, but not too many also cover music processing. In that sense, this book is good. However, the major shortcoming of this book is that in its attempt to cover many topics, it doesn't really cover any topics in great detail. The material in this book is merely a good introduction, but one is forced to go to the cited references to find more detail on specific subjects. My overall feeling on this book is rather neutral. If you are just interested in speech processing, there are other books out there which have better coverage. But I am still look for a good book that covers the signal processing of music.

Great, but don't buy it here...........2001-09-29

The basic purpose of this book is to understand sound well enough to be able to perform speech recognition, but it also contains a lot of material relevant to music recognition and synthesis. By some quirk of international pricing, the price of this book in the UK is about half what it is in the USA, so it may be worth your while checking out UK online bookstores such as amazon.co.uk or the UK branch of bol.com for this one.

Hitch Hiker's Guide to Speech & Audio Processing :-).......2001-05-20

OK, maybe the title of my review's a little misleading, in the sense that this book doesn't match the inimitable Douglas Adam's masterpiece in humour.I meant it in a more literal sense, that is,this book is an excellent guide to the field of Speech & Audio Processing, with a 'holistic' approach to the subject that is refreshing indeed.It can be approached by newcomers with little difficulty - it isn't 'overly mathematical', though all the essential maths is definitely there.The experts, too, shall find new insights from two leading experts in the field.

What i like best about the book is that the chapters are short - average chapter size is only about 15 pages.Thus material is presented in 'bite-sized' chunks, making it much easier to digest.Also, since the authors opt to focus on breadth more than on depth, the book isn't imposingly thick.The layout is also very nice,making it even more of a pleasure to read.

The clarity of writing is another strong point of the book, as are the illustrations.The authors go to the heart of the matter, successfully imparting the flavour of the topic, be it the basics, or the current state-of-the-art.An excellent chapterwise bibliography makes it easy to trace further details on any topic.

All in all, it's a great book, one which stands out for the originality of its approach and the expertise of its authors. In my opinion, anyone working in the area of Speech/Audio processing should have a copy of this most accessible guide.

Speech and Audio Signal Processing: Processing and Perceptio.......2000-03-08

This is a book much needed in the speech and audio community because of its unique perspective on these topics. By their very nature, speech, music and other audio signals are only fully understood if one takes into account their perception, production, and the context within whcih they exist (language, symphony). To appreciate what to process about such signals, the scientist must have a broad appreciation of linguistics, hearing, vocal tract models, and the brain in general, in addition to the standard engineering tools and approaches. This is why this book is valuable. It indeed attempts to reach out to all these fields with just enough details to inspire the reader, and to provide links to existing more detailed literature. The book is well written, full of excellent illustrations, and it was the perfect choice for a class to graduate students in the Electrical Engineering Department where I teach at the University of Maryland. I highly recommend it.

Average customer rating:

Excellent for the right reader
Great explanation of the math behind the music

Music: A Mathematical Offering
Dave Benson
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521619998

Book Description

Since the time of the Ancient Greeks, much has been written about the relation between mathematics and music: from harmony and number theory, to musical patterns and group theory. Benson provides a wealth of information here to enable the teacher, the student, or the interested amateur to understand, at varying levels of technicality, the real interplay between these two ancient disciplines. The story is long as well as broad and involves physics, biology, psychoacoustics, the history of science, and digital technology as well as, of course, mathematics and music. Starting with the structure of the human ear and its relationship with Fourier analysis, the story proceeds via the mathematics of musical instruments to the ideas of consonance and dissonance, and then to scales and temperaments. This is a must-have book if you want to know about the music of the spheres, digital music, and many things in between.

Customer Reviews:

Excellent for the right reader.......2007-02-20

This is an important book. Although very technical, and intended for musicians with a strong mathematical background, others can learn a great deal by neglecting the more technical parts. It is probably the most complete treatment of its various topics so far. It is interestingly and well written by a strong mathematician who has researched the musical aspects well.

Despite all this, I do propose that there needs to be a more elementary treatment of much of this material for those who have not taken major coursework in college-level mathematics. Thus, Benson has left a niche for others, less gifted, to fill.

Great explanation of the math behind the music.......2007-01-07

This book is the result of material that the author compiled while teaching an undergraduate course on the subject of sound and music and their relationship with mathematics. The mathematical level of different parts of the book varies tremendously from algebra to partial differential equations. Chapter 1 begins with the fundamental question "What is special about sine waves that we consider them to be the pure sound of a given frequency?" Chapter 2 deals with the mathematical subject that answers the question "To what extent can sound be broken into sine waves?". The answer is, of course, Fourier analysis. The mathematics of Bessel functions is also developed in Chapter 2. Chapter 3 goes on to describe the mathematics associated with musical instruments, which are divided into five categories depending upon the mathematical description of the sound they produce . This is done in terms of the Fourier theory developed in chapter 2, but it is really only necessary to have a vague understanding of Fourier theory for this purpose.

Chapter 4 is where the theory of consonance and dissonance is discussed along with the simple integer ratios of frequencies. Consonance and dissonance are musical terms describing whether combinations of notes sound good together or not. This is a preparation for the discussion of scales and temperaments in Chapters 5 and 6. The emphasis in these two chapters is on the relationship between rational numbers and musical intervals. The fundamental question here is "Why does the modern western scale consist of 12 equally spaced notes to an octave?" Has it always been this way? Are there other possibilities? After the discussion of scales, the book breaks off of its main thread to consider a couple of other subjects where mathematics is involved in music, the first being computers and digital music. Chapter 7 discusses how to represent sound and music as a sequence of zeroes and ones, and again Fourier theory is used to understand the result. Also described is the closely related Z-transform for representing digital sounds, and this is then used to discuss signal processing, both as a method of manipulating sounds and producing them. This leads to a discussion of digital synthesizers in Chapter 8, where we are again confronted with the questionof what it is that makes musical instruments sound the way that they do. The discussion is based around FM synthesis. Although this is an old-fashioned method of sound synthesis, it is simple enough to understand many of the salient features before taking on more complex synthesis methods.

Chapter 9 changes the subject completely and examines the role of symmetry in music. The area of mathematics concerned with symmetry is group theory, and the reader is introduced to some of the elementary ideas from group theory that can be applied to music. The book contains numerous exercises, and the answers to almost all of them are included in the book. It should be noted that the author assumes the reader can read music, as this subject is not approached with the exception of a few entries in the appendices. Thus this book is more of mathematics for musicians rather than vice versa. There is an online version of the book available if you want to browse it before deciding to buy. To me, this is one of the clearest books on the relationship of mathematics to music I have read. The text is accessible and clear, there is a good use of graphics, and the exercises emphasize the understanding of the mathematics presented. I highly recommend it.

Conceptualizing Music: Cognitive Structure, Theory, and Analysis (Ams Studies in Music Series)

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Conceptualizing Music: Cognitive Structure, Theory, and Analysis (Ams Studies in Music Series)
Lawrence M. Zbikowski
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

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ASIN: 0195140230

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This book shows how recent work in cognitive science, especially that developed by cognitive linguists and cognitive psychologists, can be used to explain how we understand music. The book focuses on three cognitive processes--categorization, cross-domain mapping, and the use of conceptual models--and explores the part these play in theories of musical organization. The first part of the book provides a detailed overview of the relevant work in cognitive science, framed around specific musical examples. The second part brings this perspective to bear on a number of issues with which music scholarship has often been occupied, including the emergence of musical syntax and its relationship to musical semiosis, the problem of musical ontology, the relationship between words and music in songs, and conceptions of musical form and musical hierarchy. The book will be of interest to music theorists, musicologists, and ethnomusicologists, as well as those with a professional or avocational interest in the application of work in cognitive science to humanistic principles.

Rhythm Games for Perception and Cognition (Revised Edition)

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Rhythm Games for Perception and Cognition (Revised Edition)
Robert M. Abramson
Manufacturer: Alfred Publishing Company
ProductGroup: Book
Binding: Paperback

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