Harmonic entropy: Difference between revisions

For dyads, the basic harmonic entropy model is fairly simple: it places the dyad we are trying to measure amidst a backdrop of JI candidates. Then, it uses a point-spread function to determine the relative strengths of the match to each, which are then normalized and treated as probabilities. The "entropy" of the resulting probability distribution is a way to measure how closely this distribution tends to focus on one possibility, rather than being spread out among a set of equally-likely possibilities. If there is only one clear choice of dyad which far exceeds all others in probability, the entropy will be lower. If, on the other hand, there are many equally-likely probabilities, the entropy will be higher. The basic harmonic entropy model can also be extended to modeling triads, tetrads, and so on; the standard way to do so is to simply look at the incoming triad's match to a set of candidate JI triads, and likewise with tetrads, and etc.

In recent years, it has become clearer that the model can also be very useful in modeling other types of concordance as well, particularly for dyads, where the same model does a very good job in also predicting beatlessness, periodicity buzz, and so on. In particular, Erlich has often suggested the same model, perhaps with slightly different parameters, can also be useful to measure how easy it is to tune a dyad by ear on an instrument such as a guitar, or how much of a sense of being "locked-in" the dyad gives as it is tuned more closely to JI. This may be less related to the perception of virtual fundamentals than it is to beatlessness and so on.

However, it should be noted that the various aspects of psychoacoustic concordance tend to diverge quite strongly in their behavior for larger chords, and thus, when modeling different aspects of psychoacoustic concordance, different ways of generalizing the dyadic model to higher-cardinality chords may be appropriate. In particular, when modeling beatlessness, Erlich has suggested instead looking only at the entropies of the pairwise dyadic subsets of the chord, so that the major and minor chords would be ranked equal in beatlessness, whereas they would not be ranked equal in their ability to produce a clear virtual fundamental (the major chord would be much stronger and lower in entropy).

Concordance has often been confused with actual musical consonance, an unfortunate fact made more common by the psychoacoustics literature under the unfortunate name '''sensory consonance''', most often used to refer to phenomena related to roughness and beatlessness specifically. This is not to be confused with the more familiar construct of tonal stability, typically just called "consonance" in Western common practice music theory and sometimes clarified as "musical consonance" in the music cognition literature. To make matters worse, the literature has also at times referred to concordance -- and not tonal stability -- as '''tonal consonance''', often referring to phenomena related to virtual pitch integration, creating a complete terminological mess. As a result, the term "consonance" has been completely avoided in this article