Musimathics, Volume 1: The Mathematical Foundations of Music (Mit Press)

After about a ten year hiatus on books of this type being published, this is one of several new books combining mathematics, music, and programming aimed at musicians who want to know more about the math behind their musical compositions and are not content to just know what drop-down windows to click on using the latest musical software. The book starts with the basics of music and sound and works up to basic music theory, physics and sound, and acoustics and psychoacoustics. The final chapter of the book is the most interesting, since it concerns mathematics and composition techniques using the author's C++ based library "Musimat". Both this book and Musimat have companion websites, although the Musimat site is the most interesting with plenty of downloads in case you are interested in how to use this compositional library. There is a volume two scheduled for release in Spring 2007 that gets into signal processing, the role of digital signals, and the wave equation, so together they are a very complete treatise on math, music, and programming aimed at the musical composer. I highly recommend it. Of course, if you want to dig deep into individual subjects such as acoustics and psychoacoustics, you are going to need additional references. But this text is clear enough to get you started. The following is the table of contents:1 Music and Sound 11.1 Basic Properties of Sound 11.2 Waves 31.3 Summary 92 Representing Music 112.1 Notation 112.2 Tones, Notes, and Scores 122.3 Pitch 132.4 Scales 162.5 Interval Sonorities 182.6 Onset and Duration 262.7 Musical Loudness 272.8 Timbre 282.9 Summary 373 Musical Scales, Tuning, and Intonation 393.1 Equal-Tempered Intervals 393.2 Equal-Tempered Scale 403.3 Just Intervals and Scales 433.4 The Cent Scale 453.5 A Taxonomy of Scales 463.6 Do Scales Come from Timbre or Proportion? 473.7 Harmonic Proportion 483.8 Pythagorean Diatonic Scale 493.9 The Problem of Transposing Just Scales 513.10 Consonance of Intervals 563.11 The Powers of the Fifth and the Octave Do Not Form a Closed System 663.12 Designing Useful Scales Requires Compromise 673.13 Tempered Tuning Systems 683.14 Microtonality 723.15 Rule of 18 823.16 Deconstructing Tonal Harmony 853.17 Deconstructing the Octave 863.18 The Prospects for Alternative Tunings 933.19 Summary 933.20 Suggested Reading 954 Physical Basis of Sound 974.1 Distance 974.2 Dimension 974.3 Time 984.4 Mass 994.5 Density 1004.6 Displacement 1004.7 Speed 1014.8 Velocity 1024.9 Instantaneous Velocity 1024.10 Acceleration 1044.11 Relating Displacement,Velocity, Acceleration, and Time 1064.12 Newton's Laws of Motion 1084.13 Types of Force 1094.14 Work and Energy 1104.15 Internal and External Forces 1124.16 The Work-Energy Theorem 1124.17 Conservative and Nonconservative Forces 1134.18 Power 1144.19 Power of Vibrating Systems 1144.20 Wave Propagation 1164.21 Amplitude and Pressure 1174.22 Intensity 1184.23 Inverse Square Law 1184.24 Measuring Sound Intensity 1194.25 Summary 1255 Geometrical Basis of Sound 1295.1 Circular Motion and Simple Harmonic Motion 1295.2 Rotational Motion 1295.3 Projection of Circular Motion 1365.4 Constructing a Sinusoid 1395.5 Energy of Waveforms 1435.6 Summary 1476 Psychophysical Basis of Sound 1496.1 Signaling Systems 1496.2 The Ear 1506.3 Psychoacoustics and Psychophysics 1546.4 Pitch 1566.5 Loudness 1666.6 Frequency Domain Masking 1716.7 Beats 1736.8 Combination Tones 1756.9 Critical Bands 1766.10 Duration 1826.11 Consonance and Dissonance 1846.12 Localization 1876.13 Externalization 1916.14 Timbre 1956.15 Summary 1986.16 Suggested Reading 1987 Introduction to Acoustics 1997.1 Sound and Signal 1997.2 A Simple Transmission Model 1997.3 How Vibrations Travel in Air 2007.4 Speed of Sound 2027.5 Pressure Waves 2077.6 Sound Radiation Models 2087.7 Superposition and Interference 2107.8 Reflection 2107.9 Refraction 2187.10 Absorption 2217.11 Diffraction 2227.12 Doppler Effect 2287.13 Room Acoustics 2337.14 Summary 2387.15 Suggested Reading 2388 Vibrating Systems 2398.1 Simple Harmonic Motion Revisited 2398.2 Frequency of Vibrating Systems 2418.3 Some Simple Vibrating Systems 2438.4 The Harmonic Oscillator 2478.5 Modes of Vibration 2498.6 A Taxonomy of Vibrating Systems 2518.7 One-Dimensional Vibrating Systems 2528.8 Two-Dimensional Vibrating Elements 2668.9 Resonance (Continued) 2708.10 Transiently Driven Vibrating Systems 2788.11 Summary 2828.12 Suggested Reading 2839 Composition and Methodology 2859.1 Guido's Method 2859.2 Methodology and Composition 2889.3 Musimat: A Simple Programming Language for Music 2909.4 Program for Guido's Method 2919.5 Other Music Representation Systems 2929.6 Delegating Choice 2939.7 Randomness 2999.8 Chaos and Determinism 3049.9 Combinatorics 3069.10 Atonality 3119.11 Composing Functions 3179.12 Traversing and Manipulating Musical Materials 3199.13 Stochastic Techniques 3329.14 Probability 3339.15 Information Theory and the Mathematics of Expectation 3439.16 Music, Information, and Expectation 3479.17 Form in Unpredictability 3509.18 Monte Carlo Methods 3609.19 Markov Chains 3639.20 Causality and Composition 3719.21 Learning 3729.22 Music and Connectionism 3769.23 Representing Musical Knowledge 3909.24 Next-Generation Musikalische Würfelspiel 4009.25 Calculating Beauty 406Appendix A 409A.1 Exponents 409A.2 Logarithms 409A.3 Series and Summations 410A.4 About Trigonometry 411A.5 Xeno's Paradox 414A.6 Modulo Arithmetic and Congruence 414A.7 Whence 0.161 in Sabine's Equation? 416A.8 Excerpts from Pope John XXII's Bull Regarding Church Music 418A.9 Greek Alphabet 419Appendix B 421B.1 Musimat 421B.2 Music Datatypes in Musimat 439B.3 Unicode (ASCII) Character Codes 450B.4 Operator Associativity and Precedence in Musimat 450

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!

I can see why there are many who love these books. . .unfortunately, they're over my head for the most part. (ESPECIALLY VOL 2). I've been a professional musician and composer for 30+ years, but having flunked mathematics at GCSE Level, (i.e. at 15-16 years old), I am having a GREAT deal of trouble comprehending much of this material. The books were recommended to me by a lecturer at Goldsmiths Uni, London; not his fault at all for not knowing that I didn't have a solid mathematical skillset. . .but I read about the books before purchasing, including the rear cover notes from Volume 1, and thought, "these are for me!".This endorsement on back cover of Vol 1 from Stephen Travis, CREATE Lab, Dept of Music, University of California, Santa Barbara : "Musimathics is destined to be required reading and a valued reference for every composer, music researcher, multimedia engineer, and anyone else interested in the inter play between acoustics and music theory"And this from the rear cover description of Vol 1: "It is designed for musicians who find their art increasingly mediated by technology, and for anyone who is interested in the intersection of art and science."I feel that the cover notes are misleading; but, perhaps most music composers DO have the mustard to understand the contents of these books. . .poor fool me!In conclusion, I would love to have known that a specific (GCSE/A Level) level of mathematical ability is advisable. At the very least, the book’s description could include a note detailing the level and particular fields within mathematics that one would do well to get familiar with, so as to truly engage with this incredible material; resulting in an enjoyable, thought-provoking and ultimately inspiring read.With a sufficient level of mathematical prowess, and an understanding of the basics of music theory, this would probably be a real page turner. . .but for me. . .I've begun doing some veeery basic and rudimentary revision of early GCSE mathematics, with a view to, one day, actually reading and digesting what is written in Musimathics Vol I and Vol II.

This is a serious book on the mathematical foundation of music, but despite almost 500 pages, it is actually written in an easy style. I have only just recently got this book, and have not quite read it through yet, but I find it pleasant reading. It covers broad grounds, explains topics in clear and straight-forward terms, and is sufficiently grounded in maths that is comprehensible to most school leavers. It is a great reference book to keep, especially to lovers of music and its relationship to maths.

I already know the book, but I needed to have a paper copy. The copy I received is in good condition...

Questo testo è meraviglioso e dovrebbe essere letto da tutti i docenti di tecnologie musicali del liceo musicale PRIMA di mettere piede in classe. Per gli alunni sarebbe un notevole beneficio!

I love this book for not messing around. Using mathematics allows Loy to formulate music theory and acoustics in a very concise way. As a student of mathematics I can't judge the difficulty, but it should be understandable for almost everybody (lots fractions, solving simple equations and a bit of differentiation is almost all that's needed). The range of topics covered in the two books together is breath taking. I'm currently half way through the first book and read it whenever I have a free minute, it's a great read!