In the previous chapter, we saw how Schenker's concern for accuracy motivated him to refine the traditional laws of strict counterpoint and functional harmony; he did so by constraining the laws of counterpoint harmonically and by grounding the laws of harmony contrapuntally. If Schenker's only contribution to music theory had been to devise more accurate laws of tonal voice leading and harmony, then his place in music history would have been assured. After all, these new laws overcome technical problems that had perplexed theorists for several centuries. But Schenker took another crucial step: he reformulated his new laws in a procedural form as a system of prototypes (Ursätze), transformations (Verwandlungen), and levels (Verwandlungs-Schichten, Stimmführungs-Schichten, or Schichten). This system allowed him to reach two important conclusions: 1) all functional monotonal pieces can be derived from a single prototype; and 2) there are only three possible prototypes for all functional monotonal compositions.

There are several reasons why these conclusions are so important. On the one hand, they allowed Schenker to achieve the sort of theoretic unification described in the Introduction. Indeed, whereas music theorists had traditionally treated counterpoint and harmony as largely separate phenomena, Schenkerian theory insists that they are irrevocably intertwined. This synthesis is undoubtedly a major step forward in our understanding of tonal relationships. On the other hand, these results allowed Schenker to widen the explanatory scope of tonal theory; instead of simply explaining tonal motion across an individual phrase, he could now explain tonal motion across an entire monotonal composition. Schenker achieved this goal by showing that the same laws of functional voice leading and harmony operate both in the small and in the large. This radical insight is encapsulated in his famous motto semper idem sed non eodem modo or “always the same but not in the same way.”

Remarkable though it may be, Schenker's system of prototypes, transformations, and levels does raise a number of interesting questions. How, in fact, are the individual components of the system related to the general laws of functional voice leading and harmony outlined in chapter 1? Why did Schenker insist that his prototypes, transformations, and levels have some forms but not others?