gradually diminishes until it disappears (≈≥75–150 fluctuations per second, depending on the frequency of the interfering tones). Assuming the ear performs a frequency analysis on incoming signals, as indicated by Ohm's acoustic law, the above perceptual categories can be related directly to the bandwidth of the hypothetical analysis filters, For example, in the simplest case of amplitude fluctuations resulting from the addition of two sine signals with frequencies f1 and f2, the fluctuation rate is equal to the frequency difference between the two sines |f1-f2|, and the following statements represent the general consensus: If the fluctuation rate is smaller than the filter bandwidth, then a single tone is perceived either with fluctuating loudness (beating) or with roughness. If the fluctuation rate is larger than the filter bandwidth, then a complex tone is perceived, to which one or more pitches can be assigned but which, in general, exhibits no beating or roughness. Along with amplitude fluctuation rate, the second most important signal parameter related to the perceptions of beating and roughness is the degree of a signal's amplitude fluctuation, that is, the level difference between peaks and valleys in a signal. The degree of amplitude fluctuation depends on the relative amplitudes of the components in the signal's spectrum, with interfering tones of equal amplitudes resulting in the highest fluctuation degree and therefore in the highest beating or roughness degree. For fluctuation rates comparable to the auditory filter bandwidth, the degree, rate, and shape of a complex signal's amplitude fluctuations are variables that are manipulated by musicians of various cultures to exploit the beating and roughness sensations, making amplitude fluctuation a significant expressive tool in the production of musical sound. Otherwise, when there is no pronounced beating or roughness, the degree, rate, and shape of a complex signal's amplitude fluctuations remain important, through their interaction with the signal's spectral components. This interaction is manifested perceptually in terms of pitch or timbre variations, linked to the introduction of combination tones. "The beating and roughness sensations associated with certain complex signals are therefore usually understood in terms of sine-component interaction within the same frequency band of the hypothesized auditory filter, called critical band." Frequency ratios: When harmonic timbres are played in a Just intonation (or a sufficiently close approximation thereof), ratios of higher simple numbers are more dissonant than lower ones. However, the farther the timbre departs from the harmonic series, and/or the farther