Consonance of Complex Tones with Harmonics of Different Intensity

Antonio Bernini, Federico Talamucci

Dipartimento di Matematica e Informatica “U. Dini” (DIMAI), Universita di Firezne, Firenze, Italy.

DOI: 10.4236/oja.2014.42008                

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

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