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Bright chords and the centroid of the spectra,明亮的和弦和光谱的质心,

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Bright chords and the centroid of the spectra,明亮的和弦和光谱的质心,Bright chords and the centroid of the spectra,明亮的和弦和光谱的质心, The specter at the centre of the spectral centroid: an exploration of the psychophysical and mathematical relationships between timbre in multiple, complex signals and the frequency spectrum. Submitt...

Bright chords and the centroid of the spectra,明亮的和弦和光谱的质心,
Bright chords and the centroid of the spectra,明亮的和弦和光谱的质心, The specter at the centre of the spectral centroid: an exploration of the psychophysical and mathematical relationships between timbre in multiple, complex signals and the frequency spectrum. Submitted to CIM04, 30 October 2003 Emery Schubert School of Music and Music Education, University of New South Wales, Australia E.Schubert@unsw.edu.au Joe Wolfe School of Physics, University of New South Wales, Australia J.Wolfe@unsw.edu.au Desired mode of presentation talk Background in music perception Many researchers argue that the perception of the timbral brightness of a sound is a function of the physically determined spectrum centroid. High spectral centroid is thought to evoke the perception of a brighter sound than a lower centroid. In recent years, some research has suggested that the simple use of the spectral centroid confounds the effects of pitch and brightness, and that the centroid should therefore be normalised by dividing by the fundamental or pitch frequency (Kendall & Carterette, 1996; Kendall, 2002). Background in acoustics Whether or not the perception of brightness corresponds more closely with the centroid or the pitch-normalised centroid, the use of the latter poses problems whenever there is more than one fundamental or pitch frequency, or none. What is the pitch-normalised centroid for an orchestral chord? For a cymbal crash? Consideration of how the pitches and timbres of different instruments contribute to the spectrum and its centroid is necessary in any attempt to answer this question, and is an interesting question in itself because of the light it throws on aspects of orchestration. Aims This paper describes possible methods of pitch-weighting the spectral centroid for (pitched) orchestral chords, and compares calculations with the results of experiments to determine the perceived brightness. Main contribution This paper shows some of the difficulties of pitch normalisation in musically interesting examples. It also proposes several conceivable methods, and illustrates their weaknesses. Finally, the results of an experiment in progress will show the relation (if any) between these methods and perceived brightness. When the notes of a chord are known, the arithmetic (,f/n) mean pitch may i in principle be used to normalise the centroid. However, Weber's law nsuggests that the geometic(,f ) mean would be more appropriate. Further, i consideration of the case of a chord with one arbitrarily soft note suggests that the averages should be weighted. This raises the problem of the appropriate weighting parameter: although the amplitude of the fundamental may seem an obvious choice, examples of missing or almost missing fundamentals (common in some bass instruments) raise questions about this choice. In many chords, the fundamentals of higher notes may coincide with harmonics of the lower notes. This is particularly true in tall orchestral chords. Under which conditions should such fundamentals be included in the calculation? When does a high flute, for example, simply augment an overtone of a lower instrument (like an organ voicing) and when does it count as a separate note? These questions motivated the choice of stimuli used in the experiments. They also raise doubts about the possibility of defining or implementing a simple weighting algorithm for pitch-normalised brightness. Implications In the future, algorithms might be fast and sophisticated enough to automate such algorithms, but at the moment, there is no software capable of abstracting individual instrument spectra from a mixed, multi-timbral, orchestra-texture signal. Further, the meaning of a centroid thus weighted would be subtle, and would depend on the parameters of the algorithm, some of which would probably be chosen subjectively. References Kendall, R. A., & Carterette, E. C. (1996). Difference thresholds for timbre related to spectral centroid. Proceedings of the 4th International Conference of Music Perception and Cognition. Montreal, Canada, 91-95. Kendall, R. A., & Carterette, E. C. (1996). Musical timbre beyond a single note, ii: interactions of pitch chroma and spectral centroid. Proceedings of the 7th International Conference of Music Perception and Cognition. Sydney, Australia, 596-699. Biographies Emery Schubert name current position Postdoctoral fellow, University of New South Wales main fields of music psychology research main research Emotion in music, music perception areas relevant PhD (Music), BA (Music, Psychology), BE qualification (Electrical Engineering), Dip Ed. name Joe Wolfe current position Associate Professor, acoustics, University of New South Wales main field of Acoustics (physics) research main research areas Acoustics of musical instruments and the vocal tract relevant PhD qualifications
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