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Marx framed this, interestingly, in terms akin to a biological imperative: 28 Chapter 2 Indeed, it appears that we must welcome this alteration, this variability of forms. The world hungers for the new or, at least, for change in its pleasures. Genius must stride forward, talent strives after it; that which is inwardly unﬁnished struggles despairingly in the feeling of its emptiness and impotence for some refashioned or even misshapen form, the “circulation of matter” from the inorganic through the organism back to the inorganic belongs every bit as much to the latter days of music as to the younger (and older) discipline of physiology.
Marx’s system of musical form was idealist both philosophically and programmatically. Its pedagogical elements applied to the individual composition student and the German people. Form as developmental, bound to audiences, fulﬁlls a classical, idealist social program. 29 The trick, then, was to cultivate an audience in which the purifying, spiritual side prevailed. This required listening in the proper way. 30 Chapter 2 A formalist approach to analyzing music required a formalist approach to listening to music.
The solution had been to choose certain intervals—the most commonly played ones—to be pure and to sacriﬁce others. The Pythagorean tuning system, used through the Renaissance, prioritized fourths and ﬁfths as pure. To do so, the Pythagorean “comma,” or the microtonal discrepancy between twelve perfect ﬁfth ratios and seven octaves, had to be distributed among the thirds and sixths so that they were slightly larger than pure. Compared to pure thirds or sixths, these Pythagorean-tuned intervals would have sounded quite jarring and out of tune.