Musimathics: The Mathematical Foundations of Music, Volume 1"In this volume, Gareth Loy presents the materials of music (notes, intervals, and scales); the physical properties of music (frequency, amplitude, duration, and timbre); the perception of music and sound (how we hear); and music composition. Musimathics is carefully structured so that new topics depend strictly on topics already presented, carrying the reader progressively from basic subjects to more advanced ones. Cross-references point to related topics and an extensive glossary defines commonly-used terms. The book explains the mathematics and physics of music for the reader whose mathematics may not have gone beyond the early undergraduate level. Calling himself "a composer seduced into mathematics," Loy provides answers to foundational questions about the mathematics of music accessibly yet rigorously. The topics are all subjects that contemporary composers, musicians, and musical 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. Additional material can be found at http://www.musimathics.com [Publisher description of vol. 1]. |
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Page 83
... string from the bridge to the first fret must be 17/18 of the length of the entire string xo . The distance from the bridge to the second fret , x2 , is calculated from the “ remaining distance , " which is x1 . So we subtract 1/18 of ...
... string from the bridge to the first fret must be 17/18 of the length of the entire string xo . The distance from the bridge to the second fret , x2 , is calculated from the “ remaining distance , " which is x1 . So we subtract 1/18 of ...
Page 110
... string vibrates under the influence of a bow . If the bow is stationary , a powerful static frictional force sticks the bow and string together . As the bow moves , it drags the string with it until the elastic force of the string ...
... string vibrates under the influence of a bow . If the bow is stationary , a powerful static frictional force sticks the bow and string together . As the bow moves , it drags the string with it until the elastic force of the string ...
Page 262
... strings and consider the effects of stiffness on nonideal strings . While the ideal string vibrates in a series of modes that are perfectly harmonic , actual strings have some internal stiffness , so they are not perfectly elastic ...
... strings and consider the effects of stiffness on nonideal strings . While the ideal string vibrates in a series of modes that are perfectly harmonic , actual strings have some internal stiffness , so they are not perfectly elastic ...
Contents
Representing Music | 11 |
Musical Scales Tuning and Intonation | 39 |
Physical Basis of Sound | 97 |
Copyright | |
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Common terms and phrases
acceleration acoustical amplitude angle angular bandwidth basilar membrane Bohlen-Pierce Bohlen-Pierce scale called chromatic scale composer composition consonance constant corresponding critical bands defined degrees diatonic scale diffraction displacement dissonant distance duration elastic equal equal-tempered equal-tempered scale equation example fifth force frequency function hearing hidden units increases input instruments Integer IntegerList interval order length linear loudness major third Markov mass mathematics measure melody membrane method microtonal minor scale modes MUSIMAT object octave Oh Susanna output Petri nets phon piano pitch classes play position pressure Print Pythagorean random range Real RealList reflected resonant reverberation Rhythm rotation semitone sequence shown in figure shows signal simple harmonic motion sinusoid sound intensity sound source spectral spectrum speed of sound string tempered theory timbre tonal tone transpose tuning variable velocity vibrating system wave waveform zero