Schenker's Ausfaltung unfolded: Notation, terminology, and practice

The process the Ausfaltung (unfolding) symbol represents is a central component of Heinrich Schenker's theory. Like the Zug and Urlinie symbols, the Ausfaltung symbol fundamentally represents the prolongation of a harmony. Despite its similarity to the Zug and the Urlinie, one needs to look no farther than Schenkerian analysis textbooks by Forte and Gilbert and Cadwallader and Gagne for disparate explanations of how to use the Ausfaltung symbol. Until this study, no prescribed use of the unfolding symbol has considered the unfolding's history. Schenker's ideas of musical "unfolding" first appear in Harmonielehre of 1906, and they are consistently present in his subsequent writings through Der freie Satz of 1935. Indeed, ideas of "unfolding" predate the first use of the word "Ausfaltung" in Der Tonwille 8/9 of 1924 and the first use of the Ausfaltung symbol in Das Meisterwerk in der Musik 3 of 1930. English-speaking theorists only describe an "unfolding" using the words "unfolding" or "to unfold," and they primarily or only associate "unfolding" with the German words "Ausfaltung" and "ausfalten." Schenker, however, uses many words that are equivalent to "unfolding" and "to unfold.";In this study, every textual "unfolding" in German and its English translation is accounted for, and progressions of trends are traced. The additional study of all graphs associated with textual "unfoldings" has revealed several graphic strategies predating the Ausfaltung symbol. In total, Schenker explains seven types of "melodic unfoldings" that describe the unfolding of one voice and two types of "harmonic unfoldings" that describe the unfolding of two voices, resulting in contrapuntal harmonic change. The melodic unfolding types are ranked from general to specific, and, collectively, the examples of the most specific melodic unfolding type provide the best explanation of how to use the Ausfaltung symbol. There is supporting evidence that this suggested usage of the Ausfaltung symbol participates in both the hierarchical and recursive processes of the theory in conjunction with the Zug and the Urlinie.;The first type of "harmonic unfolding," the rare and artful unfolding, is the predecessor to the second type, the nested unfolding. "Rare and artful unfoldings" are found from Der Tonwille 6 of 1923 until Das Meisterwerk in der Musik 2 of 1926, and "nested unfoldings" are found in Das Meisterwerk in der Musik 3 and Der freie Satz. There are design differences between the two, but the largest visual difference is the use of a fairly consistent second "unfolding" symbol to indicate all "nested unfoldings." The first use of the Ausfaltung symbol and the nested unfolding symbol occur in close proximity in Das Meisterwerk in der Musik 3. Ultimately, the design and use of the harmonic unfoldings prove to be inefficient and harmonically inconsistent, despite the unique symbol created for the nested unfolding. There is also insufficient evidence showing the participation of "harmonic unfoldings" in both the hierarchical and recursive processes of Schenkerian theory. Accordingly, the use of the nested unfolding symbol is discouraged.