Of all epistemic values, none is more important to the music theorist than the quest for accuracy. Whether formulating concepts, developing explanatory laws, or devising effective procedures, music theorists always try to provide accurate accounts of the music they are analyzing. If their methods fall short, then they will try to devise new concepts, laws, and procedures that fulfill these expectations. And so it was for Heinrich Schenker. He began from the simple observation that the laws of strict counterpoint (or Der strenge Satz) are not accurate enough to explain the richness of functional tonality (or Der freie Satz). To account for these anomalies, he transformed the laws of strict counterpoint through the addition of functional harmonies, or Stufen. To quote from the Harmonielehre: “[Tonal] composition, then, appears as an extension of strict [counterpoint]: an extension with regard to both the quantity of [tonal] material and the principle of its motion. What is responsible for all these extensions is the concept of the Stufe.” Later, in Kontrapunkt I–II, he reiterated this view, claiming that functional relationships must be understood only as transformations or “prolongations” of strict counterpoint.

As it stands, Schenker's claim can be interpreted in two quite different ways. It could mean that the laws of strict counterpoint still operate in tonal contexts but, through the intervention of Stufen, they operate more freely. This interpretation is the one endorsed by most music theorists. The disadvantage with this view, however, is that functional tonality extends or transforms strict counterpoint is some ways, but not in others. If we generalize about when or why these extensions occur, then we inevitably end up proposing a new set of covering laws. This latter option is precisely the one shown in figure 1.1 (From strict counterpoint to functional tonality). Quite simply, it takes certain basic principles of voice leading and interprets them in three different contexts; interpreting them within a world of intervals allows us to explain the behavior of strict two-voice counterpoint; interpreting them within a world of simple triads allows us to explain the behavior of strict three- and four-voice counterpoint; and interpreting them within a world of Stufen allows us to explain the behavior of functional tonality.