Near it are all the most familiar chords of Western music. The red ball at the top of the pyramid is the diminished seventh chord, a popular 19th-century chord. In the blue spheres, the notes are clustered, in the warmer colors, they are farther apart. April 2009 Spring 2009 62 1 205 222 Generalized Musical Intervals and Transformations." Journal of the American Musicological Society 62.1 (2009).The figure shows how geometrical music theory represents four-note chord-types - the collections of notes form a tetrahedron, with the colors indicating the spacing between the individual notes in a sequence. ![]() She is on the editorial boards of Music Theory Spectrum, Journal of Mathematics and Music, and Journal of Mathematics and the Arts and is writing a book entitled The Sound of Numbers: A Tour of Mathematical Music Theory. Her research interests include mathematical music theory and ethnomathematics. "Review Rachel Wells Hall RACHEL WELLS HALL is Associate Professor of Mathematics at Saint Joseph's University. Journal of the American Musicological Society, 62(1), April 2009 Spring 2009 62 1 205 222 Generalized Musical Intervals and Transformations. Review Rachel Wells Hall RACHEL WELLS HALL is Associate Professor of Mathematics at Saint Joseph's University. Journal of the American Musicological SocietyĪPA Hall, R., &, (2009). Journal of the American Musicological Society University of California Press We are to imagine that s and t are musical structures belonging to the some "family" (for example, two pitches, two pitch classes, two 1) symbolizing the aim of the first four chapters: to draw an analogy between the historical concept of "interval" and the "characteristic gestures" one hears in actual music. Generalized interval systems and transformation groups GMIT opens with a picture (Fig. Likewise, I would encourage new readers of Lewin-especially those without a mathematical background- to begin by reading his musical analyses and then make inroads into the mathematical discussion. 212) and return to the beginning as needed. ![]() The nonmathematical reader may wish to skip to the second section ("Transformational analysis," p. ![]() I summarize some of the key mathematical concepts of GMIT in the first part of this review and discuss their implementation in the second and third parts. As my own background is in mathematics, this review engages Lewin's mathematics rather more than others have done. Musical structures in a sufficient number of situations? (3) Are Lewin's musical analyses persuasive? (4) Setting aside musical considerations, how does GMIT hold up as a math book? Both books are well known and have been reviewed many times. April 2009 Spring 2009 62 1 205 222 Generalized Musical Intervals and Transformations Review Rachel Wells Hall RACHEL WELLS HALL is Associate Professor of Mathematics at Saint.
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