## Reviews of Lewin's

*Generalized Musical Intervals and Transformations*

[1] Published in late 1987, Lewin's book generated a number of reviews which were quite positive in their reception. Perhaps the most thorough review was prepared by John Rahn for the *Journal of Music Theory* (Fall 1987) who states that Lewin "sets the standards for formal musical-theoretical discourse which match those of other disciplines, and which all of us should welcome." Rahn gives an interesting summary of some of the main aspects of Lewin's work, a discussion that would aid those who feel themselves to be numerically challenged, before attempting to place the book in a larger context of music theory. He points out that it is common for theorists to become "beguiled ... by the glamour of another discipline such as mathematics," resulting in trivial findings and a lot of graphs. Lewin's achievement, according to Rahn, is "posing significant musical questions in an interesting way" supported by a rigorous mathematical system.

[2] An equally enthusiastic review appears in *Music Perception* (Winter 1988). I found this review of particular interest because of the mandate of the publication: how do we hear music? Wayne Slawson writes that "the mathematics is not overwhelmingly difficult and it is used with marvelous effect to advance some profound new music-theoretical ideas that are amply illustrated in highly insightful musical analyses." Slawson is aiming his comments at the psychologist of music, and he does caution that "the experimental instruments we know about at present are simply not up to dealing with the aspects of music that Lewin and his music-theoretical colleagues find interesting." However, he suggests that Lewin could form the basis for new ways of examining music perception, and highly recommends the book to his readership.

[3] James Hearne's review in the *Computer Music Journal* (Spring 1988) also follows the mold of initial resistance to the mathematics before concluding that "it is a relief to discover that (the book) is not only really about music, but also embodies, in places, analyses of extraordinary depth." Despite a positive discussion of Lewin's methodology, the reviewer feels that the book has not addressed the needs of computer composers. However, Lewin's (condescending?) description of "readers who like to fool around with computers" seems to hit a nerve and may have influenced his final word on the book.

(4) J. Robin Hughes dissuasion of the book (*Music Analysis*, 8:3, 1989) although still very positive, points out a number of problems with Lewin's work. At this point I must confess that I am still getting through the mathematics of Hughes arguments and in some ways I feel that this may be the most insightful review of the four I discuss here - it is certainly the most detailed.

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