Consonance and dissonance: Difference between revisions

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== Musical vs. sensory dissonance ==

Musical dissonance is a complex phenomenon depending on not only the fundamental frequency ratio but also the register, timbres, volume, spatialization, and the listener's conditioning and cultural background. '''Sensory dissonance''', '''discordance''', or '''roughness''', however, is a psychoacoustic effect that is much more consistent among most human listeners except for those with conditions like congenital amusia (tone deafness). In its most basic form, sensory dissonance occurs when two sine wave tones in the audible frequency range are played simultaneously, within about a critical band of each other but far apart enough that beating is not audible.

Musical dissonance is a complex phenomenon depending on not only the fundamental frequency ratio but also the register, timbres, volume, spatialization, and the listener's conditioning and cultural background. '''Sensory dissonance''', '''discordance''', '''discord''', or '''roughness''', however, is a psychoacoustic effect that is much more consistent among most human listeners except for those with conditions like congenital amusia (tone deafness). In its most basic form, sensory dissonance occurs when two sine wave tones in the audible frequency range are played simultaneously, within about a critical band of each other but far apart enough that beating is not audible.

A study by Kameoka & Kuriyagawa in 1969 had listeners grade the roughness of two sine waves played simultaneously at equal intensity. They computed that if the lower sine wave has frequency ''f''<sub>1</sub> Hz, then the upper frequency that maximizes roughness is about <math>f_2 = f_1 + 2.27 f_1^{0.477}\ \text{Hz}</math> (we will call this the ''maximal roughness formula''). This assumes that each sine wave has intensity 57 dB SPL; the formula changes slightly depending on volume. The interval <math>f_2/f_1</math> is about 1.56 semitones at 440 Hz, and narrows as frequency increases.

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 == Musical vs. sensory dissonance ==
-Musical dissonance is a complex phenomenon depending on not only the fundamental frequency ratio but also the register, timbres, volume, spatialization, and the listener's conditioning and cultural background. '''Sensory dissonance''', '''discordance''', or '''roughness''', however, is a psychoacoustic effect that is much more consistent among most human listeners except for those with conditions like congenital amusia (tone deafness). In its most basic form, sensory dissonance occurs when two sine wave tones in the audible frequency range are played simultaneously, within about a critical band of each other but far apart enough that beating is not audible.
+Musical dissonance is a complex phenomenon depending on not only the fundamental frequency ratio but also the register, timbres, volume, spatialization, and the listener's conditioning and cultural background. '''Sensory dissonance''', '''discordance''', '''discord''', or '''roughness''', however, is a psychoacoustic effect that is much more consistent among most human listeners except for those with conditions like congenital amusia (tone deafness). In its most basic form, sensory dissonance occurs when two sine wave tones in the audible frequency range are played simultaneously, within about a critical band of each other but far apart enough that beating is not audible.
 A study by Kameoka & Kuriyagawa in 1969 had listeners grade the roughness of two sine waves played simultaneously at equal intensity. They computed that if the lower sine wave has frequency ''f''<sub>1</sub> Hz, then the upper frequency that maximizes roughness is about <math>f_2 = f_1 + 2.27 f_1^{0.477}\ \text{Hz}</math> (we will call this the ''maximal roughness formula''). This assumes that each sine wave has intensity 57 dB SPL; the formula changes slightly depending on volume. The interval <math>f_2/f_1</math> is about 1.56 semitones at 440 Hz, and narrows as frequency increases.