# Paul Erlich

(Redirected from Harmonic entropy)
His definition of harmonic entropy influenced by Ernst Terhardt[4] has received attention from music theorists such as William Sethares. It is intended to model one of the components of dissonance as a measure of the uncertainty of the virtual pitch ("missing fundamental") evoked by a set of two or more pitches. This measures how easy or difficult it is to fit the pitches into a single harmonic series. For example, most listeners rank a ${\displaystyle {\tfrac {4/5/6/7}{1}}}$ harmonic seventh chord as far more consonant than a ${\displaystyle {\tfrac {1}{7/6/5/4}}}$ chord. Both have exactly the same set of intervals between the notes, under inversion, but the first one is easy to fit into a single harmonic series (overtones rather than undertones). Due to the least common multiple, the integers are much lower for the major chord, ${\displaystyle {\tfrac {4/5/6/7}{4}}}$, versus its inverse, ${\displaystyle {\tfrac {105/120/140/168/210}{105}}}$. Components of dissonance not modeled by this theory include critical band roughness as well as tonal context (e.g. an augmented second is more dissonant than a minor third even though both can be tuned to the same size, as in 12-ET).