- Gebundene Ausgabe: 562 Seiten
- Verlag: Mit Pr (30. Juni 2007)
- Sprache: Englisch
- ISBN-10: 0262122855
- ISBN-13: 978-0262122856
- Größe und/oder Gewicht: 17,8 x 2,4 x 22,9 cm
- Durchschnittliche Kundenbewertung: 4 Kundenrezensionen
- Amazon Bestseller-Rang: Nr. 1.130.254 in Fremdsprachige Bücher (Siehe Top 100 in Fremdsprachige Bücher)
Musimathics, Volume 2: The Mathematical Foundations of Music (Englisch) Gebundene Ausgabe – 30. Juni 2007
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"It will be obvious by now that this is a book wholeheartedly to be recommended for a wide readership. As definitive as is possible, certainly the leading resource in the field, it will meet many needs. Those with school algebra and physics who are performers, engineers, composers, listeners will almost inevitably get much from Musimathics...The two volumes of this book, then, must be considered as the place to start any exploration of this field. Entertaining, secure, comprehensive, clear, authoritative, timely, up-to-date, well wrought in every way, these are for every music lover's shelves." -- Mark Sealey, Classical Net: The Internet's Premier Classical Music Source "Music and mathematics enjoy many points of intersection. Just think of musical scales and number theory, or the impact of computers--both analog and digital--on the composition and creation of musical sounds. The second volume of Musimathics ably covers these and many other instances of this happy union: Fourier and wavelet transforms, natural and artificial reverberation, and much more." --Manfred Schroeder, Professor of Physics, University of Goettingen, Germany "Musimathics is destined to be required reading and a valued reference for every composer, music researcher, multimedia engineer, and anyone else interested in the interplay between acoustics and music theory. This is truly a landmark work of scholarship and pedagogy, and Gareth Loy presents it with quite remarkable rigor and humor." --Stephen Travis Pope, CREATE Lab, Department of Music, University of California, Santa Barbara "From his long and successful experience as a composer and computer-music researcher, Gareth Loy knows what is challenging and what is important. That comprehensiveness makes Musimathics both exciting and enlightening. The book is crystal clear, so that even advanced issues appear simple. Musimathics will be essential for those who want to understand the scientific foundations of music, and for anyone wishing to create or process musical sounds with computers." --Jean-Claude Risset, Laboratoire de Mecanique et d'Acoustique, CNRS, France
This is the second volume of a commonsense, self-contained introduction to the mathematics and physics of music, focusing on the digital and computational domain; essential reading for musicians, music engineers, and anyone interested in the intersection of art and science. Volume 2 of "Musimathics" continues the story of music engineering begun in volume 1, focusing on the digital and computational domain. Loy goes deeper into the mathematics of music and sound, beginning with digital audio, sampling, and binary numbers, as well as complex numbers and how they simplify representation of musical signals. Chapters cover the Fourier transform, convolution, filtering, resonance, the wave equation, acoustical systems, sound synthesis, the short time Fourier transform, and the wavelet transform. These subjects provide the theoretical underpinnings of today's music technology. The material in volume 1 is all preparatory to the subjects presented in this volume, although either volume can be read independently. Cross-references to volume 1 are provided for concepts introduced in the earlier volume, and additional mathematical orientation is offered where necessary.The topics are all subjects that contemporary composers, musicians, and music engineers have found to be important. The examples given are all practical problems in music and audio. The level of scholarship and the pedagogical approach also make Musimathics ideal for classroom use. Alle Produktbeschreibungen
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You have to have of course some knowledge of mathematics but you should be able to understand everything if you know a little bit about trigonometry, algebra and complex numbers. No need for differential equations or higher mathematics.
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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!