s been used since the time of Pythagoras. By the inner minds of the two disciplines, Rothstein means the way in which each relies on metaphor, abstraction, and comparison. Rothstein begins by examining the styles of thought that are characteristic and common to both disciplines and then considers more complex questions about what music does and why it is important. Teachout says that Rothstein's vision may seem chilly in the way it analyzes musical forms and relates them to mathematical precision, but this vision is warmed by the fact that Rothstein always sees music as tending toward one thing--beauty, which he finds as directly analogous to beauty in mathematics (Teachout 55-56).
Walton notes the duality of music as being the most sensual art on the one hand and mathematical on the other. Critics have called it the most ethereal, intellectual, and abstract of the arts. He points to critics as different as Eduard Hanslick (1825-1904) and Heinrich Schenker (1868-1935) who consider music to be pure structure:
Yet many--including even Hanslick and Schenker, implicitly or in unguarded moments--emphasize its emotional expressiveness. By distinguishing between the abstract world of music and its power to effect listeners, Mr. Rothstein has it both ways. But he exaggerates the extent to which the two functions are served by different kinds of music. . . (Walton 11).
Rothstein first indicates reasons why music and mathematics might seem very different. He notes that music is amorphous in that it shifts its texture and character from place to place and time to time: "It can be crystalline or cloudy, sentimental or bombastic. It is transitory: when played it dissolves into memory" (Rothstein 5).
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