About: Paul Erlich

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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 define pajara temperament and its decatonic scales in 22-ET. He holds a Bachelor of Science degree in physics from Yale University. For the th iteration of the Farey diagram, the mediant between the th element, , and the next highest element: is subtracted by the mediant between the element and the next lowest element:

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rdfs:label	Paul Erlich (en)
rdfs:comment	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 define pajara temperament and its decatonic scales in 22-ET. He holds a Bachelor of Science degree in physics from Yale University. For the th iteration of the Farey diagram, the mediant between the th element, , and the next highest element: is subtracted by the mediant between the element and the next lowest element: (en)
foaf:depiction
dcterms:subject	21st-century American male musicians American male guitarists Living people 21st-century guitarists American music theorists 1972 births
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Wikipage revision ID	1043002819 (xsd:integer)
Link from a Wikipage to another Wikipage	Boston 21st-century American male musicians American male guitarists Living people Consonance and dissonance Equal temperament Critical band Harmonic series (music) Harmonic seventh chord Physics Bachelor of Science 21st-century guitarists American music theorists William Sethares 22 equal temperament 1972 births Ernst Terhardt Guitarist Chord (music) Minor third Regular temperament Augmented second Yale Mediant (mathematics) Undertone series Overtone Virtual pitch Inversional equivalency Music theorist Farey diagram
Link from a Wikipage to an external page	https://en.xen.wiki/w/Harmonic_Entropy http://dkeenan.com/Music/MiddlePath.pdf http://lumma.org/tuning/erlich
sameAs	Paul Erlich Paul Erlich Paul Erlich Paul Erlich
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has abstract	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 define pajara temperament and its decatonic scales in 22-ET. He holds a Bachelor of Science degree in physics from Yale University. His definition of harmonic entropy, a refinement of a model by van Eck influenced by Ernst Terhardt 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 harmonic seventh chord as far more consonant than a 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). In the harmonic series, the integers are much lower for the harmonic seventh chord, , versus its inverse, . 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). For the th iteration of the Farey diagram, the mediant between the th element, , and the next highest element: is subtracted by the mediant between the element and the next lowest element: From here, the process to compute harmonic entropy is as follows:(a) compute the areas defined by the normal (Gaussian) bell curve on top, and the mediants on the sides(b) normalize the sum of the areas to add to 1, such that each represents a probability(c) calculate the entropy of that set of probabilitiesSee external links for a detailed description of the model of harmonic entropy. (en)
prov:wasDerivedFrom	wikipedia-en:Paul_Erlich?oldid=1043002819&ns=0
page length (characters) of wiki page	5598 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Paul_Erlich
is Link from a Wikipage to another Wikipage of	Limit (music) Fred Keeley Bohlen–Pierce scale Paul Ehrlich (disambiguation) 22 equal temperament Erlich, Paul Partita (Widmann) Joel Elkes Ehrlich Septimal comma Xenharmonic music Pajara temperament Harmonic entropy Relative harmonic entropy
is Wikipage redirect of	Erlich, Paul Pajara temperament Harmonic entropy Relative harmonic entropy
is foaf:primaryTopic of	wikipedia-en:Paul_Erlich

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