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Acoustic explanations for consonance and dissonance
The article on consonance in the New Grove Dictionary of Music and Musicians discusses two explanations of why simple ratios may be considered more pleasing than complex ones. The first is concerned with how two frequencies coincide on a purely acoustic level, while the second is more biological - how the ear's responses to two different frequencies coincide more when the interval between them has a simpler ratio:
The first is connected with the fact that when two sinusoids (pure tones) with similar frequencies are presented together, the total sound fluctuates in amplitude, an effect called 'beats'. ... When two complex tones have fundamental frequencies in a simple ratio, such as 2:1, the harmonics of the upper tone always coincide in frequency with harmonics of the lower tone. Hence, no beats are audible. The more the fundamental frequencies depart from a simple ratio, the greater will be the tendency for beats between the harmonics.
The second explanation is connected with the fact that action potentials (nerve impulses, 'firings' or 'spikes') in the auditory nerve tend to be synchronized to a particular phase of the stimulating wave in the cochlea or inner ear (see Hearing and psychoacoustics); for example, the impulses may occur close to the peaks of the wave. As a result, the time intervals between successive nerve impulses are close to integer multiples of the period of the stimulus (the time taken for one complete cycle). Thus, if the stimulus is a sinusoidal tone with a frequency of 500 Hz, then the intervals between successive nerve impulses cluster around values of 2 milliseconds, 4 milliseconds, 6 milliseconds and so on. Pairs of tones presented together may sound consonant when the intervals between nerve impulses share common values for the two tones.
[these quotations are taken from the online version of New Grove. Your library probably subscribes to this but if it does not, demand to know why!]

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