Henry Klumpenhouwer is a Canadian musicologist and former professor at the University of Alberta. He currently teaches at the Eastman School of Music. A former PhD student of David Lewin and the inventor of Klumpenhouwer networks, which are named after him, he is the former editor of Music Theory Spectrum .
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James Joseph Sylvester FRS HFRSE was an English mathematician. He made fundamental contributions to matrix theory, invariant theory, number theory, partition theory, and combinatorics. He played a leadership role in American mathematics in the later half of the 19th century as a professor at the Johns Hopkins University and as founder of the American Journal of Mathematics. At his death, he was a professor at Oxford.
Polykarp Kusch was a German-born American physicist. In 1955, the Nobel Committee gave a divided Nobel Prize for Physics, with one half to going to Kusch for his accurate determination that the magnetic moment of the electron was greater than its theoretical value, thus leading to reconsideration of—and innovations in—quantum electrodynamics.
The Eastman School of Music is the professional school of music of the University of Rochester in Rochester, New York. It was established in 1921 by industrialist and philanthropist George Eastman.
In post-tonal music theory, identity is similar to identity in universal algebra. An identity function is a permutation or transformation which transforms a pitch or pitch class set into itself. Generally this requires symmetry. For instance, inverting an augmented triad or C4 interval cycle, 048, produces itself. Performing a retrograde operation upon the tone row 01210 produces 01210. Doubling the length of a rhythm while doubling the tempo produces a rhythm of the same durations as the original.
Robert Daniel Morris is an American composer and music theorist.
Barry Martin Simon is an American mathematical physicist and the IBM Professor of Mathematics and Theoretical Physics at Caltech, known for his prolific contributions in spectral theory, functional analysis, and nonrelativistic quantum mechanics, including the connections to atomic and molecular physics. He has authored more than 400 publications on mathematics and physics.
David Benjamin Lewin was an American music theorist, music critic and composer. Called "the most original and far-ranging theorist of his generation", he did his most influential theoretical work on the development of transformational theory, which involves the application of mathematical group theory to music.
Sechs kleine Klavierstücke, Op. 19 is a set of pieces for solo piano written by the Austrian composer Arnold Schoenberg, published in 1913.
Robert Cogan is an American music theorist, composer and teacher.
Music Theory Spectrum is a peer-reviewed, academic journal specializing in music theory and analysis. It is the official journal of the Society for Music Theory, and is published by Oxford University Press. The journal was first published in 1979 as the official organ of the Society for Music Theory, which had been founded in 1977 and had its first conference in 1978. Unlike many other journals, Music Theory Spectrum was initially published in an oblong (landscape) page format, to better accommodate such musical graphics as Schenkerian graphs.
Don Freund is an American composer, pianist, and Professor of Composition at the Indiana University Jacobs School of Music. His over 100 performed works, include solo, chamber, and orchestral music, live performance with electronic instruments, large theatre works.
Neo-Riemannian theory is a loose collection of ideas present in the writings of music theorists such as David Lewin, Brian Hyer, Richard Cohn, and Henry Klumpenhouwer. What binds these ideas is a central commitment to relating harmonies directly to each other, without necessary reference to a tonic. Initially, those harmonies were major and minor triads; subsequently, neo-Riemannian theory was extended to standard dissonant sonorities as well. Harmonic proximity is characteristically gauged by efficiency of voice leading. Thus, C major and E minor triads are close by virtue of requiring only a single semitonal shift to move from one to the other. Motion between proximate harmonies is described by simple transformations. For example, motion between a C major and E minor triad, in either direction, is executed by an "L" transformation. Extended progressions of harmonies are characteristically displayed on a geometric plane, or map, which portrays the entire system of harmonic relations. Where consensus is lacking is on the question of what is most central to the theory: smooth voice leading, transformations, or the system of relations that is mapped by the geometries. The theory is often invoked when analyzing harmonic practices within the Late Romantic period characterized by a high degree of chromaticism, including work of Schubert, Liszt, Wagner and Bruckner.
A Klumpenhouwer Network, named after its inventor, Canadian music theorist and former doctoral student of David Lewin's at Harvard, Henry Klumpenhouwer, is "any network that uses T and/or I operations to interpret interrelations among pcs". According to George Perle, "a Klumpenhouwer network is a chord analyzed in terms of its dyadic sums and differences," and "this kind of analysis of triadic combinations was implicit in," his "concept of the cyclic set from the beginning", cyclic sets being those "sets whose alternate elements unfold complementary cycles of a single interval."
Arnold Schoenberg's Suite for Piano, Op. 25, is a 12-tone piece for piano composed between 1921 and 1923. The work is the earliest in which Schoenberg employs a row of "12 tones related only to one another" in every movement: the earlier 5 Stücke, Op. 23 (1920–23) employs a 12-tone row only in the final waltz movement, and the Serenade, Op. 24 uses a single row in its central Sonnet. The basic tone row of the suite consists of the following pitches: E–F–G–D♭–G♭–E♭–A♭–D–B–C–A–B♭.
In music, a cyclic set is a set, "whose alternate elements unfold complementary cycles of a single interval." Those cycles are ascending and descending, being related by inversion since complementary:
In music, klang is a term sometimes used to translate the German Klang, a highly polysemic word. Technically, the term denotes any periodic sound, especially as opposed to simple periodic sounds. In the German lay usage, it may mean "sound" or "tone", "musical tone", "note", or "timbre"; a chord of three notes is called a Dreiklang, etc.
Daniel Harrison is a music theorist, author, and former Chairman of the Department of Music at Yale University. Most interested in tonal theory, Harrison wrote his dissertation on the music of Max Reger at Yale, which eventually became Harmonic Function in Chromatic Music: A Renewed Dualist Theory and an Account of Its Precedents (1994). Also interested in pop music, particularly The Beach Boys, he appeared in the Don Was documentary Brian Wilson: I Just Wasn't Made for These Times (1995). During his tenure at Yale, he was named the Allen Forte Professor of Music Theory in 2006 and Chairman in 2007. From 2001 to 2003 he was editor-in-chief of Music Theory Spectrum.
"Riemannian theory" in general refers to the musical theories of German theorist Hugo Riemann (1849–1919). His theoretical writings cover many topics, including musical logic, notation, harmony, melody, phraseology, the history of music theory, etc. More particularly, the term Riemannian theory often refers to his theory of harmony, characterized mainly by its dualism and by a concept of harmonic functions.
Theophil Henry Hildebrandt was an American mathematician who did research on functional analysis and integration theory.
John Rahn is a music theorist, composer, bassoonist, and Professor of Music at the University of Washington School of Music, Seattle. A former student of Milton Babbitt and Benjamin Boretz, he was editor of Perspectives of New Music from 1983 to 1993 and since 2001 has been co-editor with Benjamin Boretz and Robert Morris.