Paul Erlich: Difference between revisions
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:''For the German physiologist, see [[Paul Ehrlich]]. For the American population biologist, see [[Paul R. Ehrlich]].'' |
:''For the German physiologist, see [[Paul Ehrlich]]. For the American population biologist, see [[Paul R. Ehrlich]].'' |
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[[Image:Triadic harmonic entropy.png|thumb|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]] |
[[Image:Triadic harmonic entropy.png|thumb|Harmonic entropy for triads with lower interval and upper interval each ranging from 200 to 500 cents. Compare {{audio|Just major triad on C.mid|4:5:6}} and {{audio|Just minor triad on C.mid|10:12:15}}. See full resolution for locations of the triads on the plot]] |
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[[File:Harmonic entropy Farey sequence.png|thumb|Harmonic entropy: Dissonance may be explained as the uncertainty in determining a pitch caused by the relative closeness of complex ratios and distance around simple ratios. The space around intervals is shown above for the Farey sequence, order 50.]] |
[[File:Harmonic entropy Farey sequence.png|thumb|Harmonic entropy: Dissonance may be explained as the uncertainty in determining a pitch caused by the relative closeness of complex ratios and distance around simple ratios. The space around intervals is shown above for the Farey sequence, order 50.]] |
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Revision as of 23:24, 25 June 2018
- For the German physiologist, see Paul Ehrlich. For the American population biologist, see Paul R. Ehrlich.
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[1][2] and its decatonic scales in 22-ET.[3] He holds a Bachelor of Science degree in physics from Yale University.
His definition of harmonic entropy[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 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. 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).
References
- ^ "Pajara", on Xenharmonic Wiki. Accessed 2013-10-29.
- ^ "Alternate Tunings Mailing List". Yahoo! Groups. Launch.groups.yahoo.com. Retrieved 2013-10-29.
- ^ Erlich, Paul (1998). "Tuning, Tonality, and Twenty-Two-Tone Temperament" (PDF). Xenharmonikôn. 17.
- ^ Sethares, William A. (2004). Tuning, Timbre, Spectrum, Scale (PDF). pp. 355–357.
External links
- "Some music theory from Paul Erlich", Lumma.org.
- "A Middle Path: Between Just Intonation and the Equal Temperaments", DKeenan.com.