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Download e-book for iPad: Analysis, Synthesis, and Perception of Musical Sounds: The by James Beauchamp

By James Beauchamp

This booklet encompasses a entire and actual mathematical therapy of the sounds of tune with an emphasis on musical timbre. The booklet spans the variety from instructional creation to complex learn and alertness to speculative evaluate of its a variety of strategies. the entire individuals use a generalized additive sine wave version for describing musical timbre which provides a conceptual solidarity, yet is of enough application to be tailored to many various tasks.

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Extra info for Analysis, Synthesis, and Perception of Musical Sounds: The Sound of Music

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5/ f a , the slope of the phase with respect to time, which gives the frequency deviation of harmonic k, becomes θk (H i) fa , π and the total estimated frequency of harmonic k is given by f k (H i) = f k (H i) = k f a + Finally, given θ k (H i) and can be recovered using f k (H i) = 1 + θk (H i) k fa . 20g) f k (H i) for frame i, the phase for the next frame i + 1 θk (H (i + 1)) = θk (H i) + θk (H i) = θk (H i) + π f k (H i) . 20h) In this way, except for roundoff error, the initial phases {θ k (0)} and frequency deviations { f k (H i)} of the harmonics at each frame are sufficient to recover the phases {θ k (H i)} of all of the harmonics at each frame.

3 33 Fundamental Frequency (Pitch) Detection There is some controversy about the use of the term pitch to mean fundamental frequency (or f 0 ). , Hess (1983) and Schroeder (1999)] use the two terms interchangeably, whereas most auditory science researchers insist on a clear distinction between them. According to the latter, pitch is strictly a percept and should not be confused with frequency. However, the pitch of a sound corresponds to the frequency of a sine tone that is judged to have the same pitch.

For comparison, Fig. 11b shows the corresponding musical score. 36 James W. 11. , 1993, Fig. 9, reproduced by permission of the Audio Engineering Society); (b) equivalent musical score. 1. an,” used for the phase vocoder. an” formats is that with the latter the amplitude and associated deviation from fixed harmonic frequency are stored for each harmonic at each frame, whereas with the “mq” format a set of amplitudes and corresponding absolute frequencies are given for each frame. an” format assumes that the same number of spectral components are used throughout the sound, whereas with the “mq” format the number of components varies with time.

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