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Consonance of Complex Tones with Harmonics of Different Intensity

DOI: 10.4236/oja.2014.42008, PP. 78-89

Keywords: Consonance, Complex Tones, Scale, Critical Bandwidth, Intensity of Harmonics, Loudness

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Abstract:

The starting point of this study is the theory of tonal consonance by Plomp and Levelt. The major reference point is the theory of Critical Band and its use for evaluating consonance of simple tones. On the basis of such empirical criterion, our aim consists in providing a method of estimating the value of consonance of complex tones, by taking account not only of the number of harmonics, but also of the intensity of the partials which contribute to forming the tone. By introducing a specific algorithm, the level of consonance of a chord of complex tones is expressed in terms both of frequency differences and sound intensity of the partials. The results give rise to a series of considerations and applications, ranging from displaying the order of consonance of all intervals within the octave up to evaluating the hierarchy of chords in the frame of a musical scale.

References

[1]  von Helmholtz, H. (1863) Die Lehre von der Tonempfindungen als Physiologische Grundlage fur die Theorie der Musik. Verlag F. Vieweg & Sohn, Braunschweig.
[2]  Plomp, R. and Levelt, W.J.M. (1965) Tonal Consonance and Critical Bandwith. The Journal of the Acoustical Society of America, 38, 548-560. http://dx.doi.org/10.1121/1.1909741
[3]  Zwicker, E., Flottorp, G. and Stevens, S.S. (1957) Critical Bandwidth in Loudness Summation. The Journal of the Acoustical Society of America, 29, 548-557. http://dx.doi.org/10.1121/1.1908963
[4]  Sethares, W.A. (1993) Local Consonance and the Relationship Timbre and Scale. The Journal of the Acoustical Society of America, 94, 1218-1228. http://dx.doi.org/10.1121/1.408175
[5]  Kameoka, A. and Kuriyagawa, M. (1969) Consonance Theory Part I: Consonance of Dyads. The Journal of the Acoustical Society of America, 45, 1451-1459. http://dx.doi.org/10.1121/1.1911623
[6]  Frova, A. (1999) Fisica nella musica (Physics in Music). Zanichelli, Bologna (Italy).
[7]  Jeans, J. (1973) Science & Music. Cambridge University Press, Cambridge.
[8]  Rossing, T.B. (1990) The Science of Sound. 2nd Edition, Addison-Wesley Publishing Co., Reading.
[9]  Hall, D.E. (1990) Musical Acoustics. 2nd Edition, Wadsworth Publishing Co., Belmont.
[10]  Terhardt, E. (1984) The Concept of Musical Consonance: A Link between Music and Psychoacoustics. Music Perception, 1, 276-295. http://dx.doi.org/10.2307/40285261
[11]  Rameau, J.P. (1772) Traité de l’Harmonie. Dover Publications, New York. Reprint Edition (June 1, 1971).

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