Paul Erlich

For the German physiologist, see Paul Ehrlich. For the American population biologist, see Paul R. Ehrlich.

Error creating thumbnail: File with dimensions greater than 25 MP

Harmonic entropy for triads with lower interval and upper interval each ranging from 200 to 500 cents. See full resolution for locations of the triads on the plot

Paul Erlich (born 1972) is a guitarist and music theorist living near Boston, Massachusetts. He is known for his seminal role in developing the theory of regular temperaments, including being the first to discover pajara temperament and its decatonic scales in 22-ET. He holds a Bachelor of Science degree in physics from Yale University.

His invention of harmonic entropy has received significant 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 4:5:6:7 chord as far more consonant than 1/7:1/6:1/5:1/4. Both have exactly the same set of intervals between the notes but the first one is easy to fit into a single harmonic series. (The other 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 although the interval, 300 cents, is the same for both).)

Further reading

• Erlich, Paul. "Tuning, Tonality and 22-Tone Temperament." Xenharmonicon 17, 1998.

External links

• "Some music theory from Paul Erlich", Lumma.org.
• "A Middle Path: Between Just Intonation and the Equal Temperaments", DKeenan.com.