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Two experiments were carried out to determine the dependence of perceived roughness on the frequency ratio of two simultaneous harmonic complex tones. In the first experiment, the frequency ratios of the tone pairs corresponded to 35 within-octave intervals of various musical tuning systems. In the second experiment 12 intervals were used; six of them ranged from 10 cents below to 10 cents above an equally-tempered fourth and the other six encompassed a similar range centred around the equally-tempered fifth. In both experiments the amount of roughness was assessed by absolute magnitude estimation. Results show that roughness considerably varies with the frequency ratio of a pair of harmonic complex tones, which is a well-known phenomenon. A new finding, that is in contrast to published theories of roughness, is that equally-tempered intervals produce less roughness than their counterparts based on integer frequency ratios. This effect is attributed to slow beats that arise between the harmonics of two complex tones when the frequency ratio of an equally-tempered interval slightly departs from integer ratio. Such beats, heard as fluctuations, impart a smooth character to the sound.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
737--748
Opis fizyczny
Bibliogr. 11 poz., rys., tab.
Twórcy
autor
- The Fryderyk Chopin Academy of Music Department of Sound Engineering Musical Acoustics Laboratory Okólnik 2, 00-368 Warszawa, Poland
autor
- The Fryderyk Chopin Academy of Music Department of Sound Engineering Musical Acoustics Laboratory Okólnik 2, 00-368 Warszawa, Poland
autor
- The Fryderyk Chopin Academy of Music Department of Sound Engineering Musical Acoustics Laboratory Okólnik 2, 00-368 Warszawa, Poland
Bibliografia
- [1] GUTHRIE E. R., MORRILL H., The fusion of non-musical intervals, American Journal of Psychology, 40, 624–625 (1926).
- [2] HELMHOLTZ H. VON, Die Lehre von den Tonempfindungen als psychologische Grundlage für die Theorie der Musik, F. Vieweg und Sohn, Braunschweig, 1863, English translation: A. Ellis, On the Sensations of Tone, Dover, New York 1954.
- [3] KAMEOKA A., KURIYAGAWA M., Consonance theory part II: Consonance of complex tones and its calculation method, Journal of the Acoustical Society of America, 45, 1460–1469 (1969).
- [4] INTERNATIONAL ORGANISATION FOR STANDARDISATION, Method for calculating loudness level, R-532B, ISO, Geneva 1966.
- [5] MIŚKIEWICZ A., RAKOWSKI A., RO´SCISZEWSKA T., Perceived roughness of two simultaneous pure tones, Acta Acustica united with Acustica, 92, 331–336 (2006).
- [6] PLOMP R., Timbre as a multidimensional attribute of sound, [in:] Frequency Analysis and Periodicity Detection in Hearing, R. Plomp, G. F. Smoorenburg [Eds.], Sijthoff, Leiden, 397–414, 1970.
- [7] PLOMP R., LEVELT W. J. M., Tonal consonance and critical bandwidth, Journal of the Acoustical Society of America, 38, 548–560 (1965).
- [8] PLOMP R., STEENEKEN H., Interference between two simple tones, Journal of the Acoustical Society of America, 43, 883–884 (1968).
- [9] TERHARDT E., Ein psychoakustisch begründetes Konzept der Musikalischen Konsonanz, Acustica, 36, 121–137 (1976).
- [10] TUFTS J. B., MOLIS M. R., LEEK M. R., Perception of dissonance by people with normal hearing and sensorineural hearing loss, Journal of the Acoustical Society of America, 118, 955–967 (2005).
- [11] ZWISLOCKI J. J., GOODMAN D. A., Absolute scaling and sensory magnitudes: A validation, Perception and Psychophysics, 28, 28–38 (1980).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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