Perceived dissonance resists full quantification because it is a human impression

Evidence

There will never be a way to fully quantify dissonance, since it is a human impression of sound, differing from one listener to the next, differing by experience and training, and differing by musical context. However, one can make rough and qualitative estimates of dissonance. The key idea for estimating the perceived dissonance of two complex tones is to search for any pairs of partials falling within a minor third interval. We assign a penalty to each pair (or group) we find. The penalty must also be weighted in some reasonable way by the amplitudes in each of the two offending partials, since the unpleasantness certainly depends on the power present in the partials. The precise nature of the result will depend on the form of the weighting, but the qualitative nature of the result will not. Since the degree of unpleasantness of two complex tones is itself only qualitatively measurable, these details may not matter much. All the penalties are added up for a pair of complex tones, leading to a single number measuring roughness. — Eric J. Heller, Why You Hear What You Hear- An…, 2338

Categorization

• DEFINE: Defines the roughness model of dissonance: sum of penalties for partial pairs within a minor third, weighted by amplitude.
• XREF: Connects to Helmholtz’s pioneering dissonance model and to modern roughness algorithms used in music information retrieval. — connects to: When quantification destroys qualitative perception, bare sensation replaces experience. — Theodor W. Adorno, Minima Moralia: Reflections from…, 257