... ideas of key. Starting with Edward Gollin's recent generalization of Moritz Hauptmann's key representations as “multiaggregate cycles”—which he also uncovers on the surface of and in the relations between harmonies in Bartók's music—the article briefly reconsiders Hauptmann's theories and depictions...

... “Ueber Tonalität” and the dissertation. These three works, which overlap in their content and genesis, form a larger debut that high- lights Riemann’s effort to get beyond Hauptmann’s highly influential Die Natur der Harmonik und der Metrik of 1853. To a considerable ex- tent this meant getting beyond...

... Hauptmann’s harmonic theory, which stands alone in developing its material from a sound principle, I shall attempt to continue where Hauptmann left off: namely, with applied harmony and meter.2 [3] What his work contains on these subjects is unfortunately nei- ther complete nor wholly agreeable...

... the writings of ninety-five theorists of vari- ous national backgrounds, ranging from works by well-known authors such as Jean-Philippe Rameau, Johann Kirnberger, Simon Sechter, Georg Joseph Vogler, Gottfried Weber, and Moritz Hauptmann, to works of forty authors...

... find implicit alge- braic groups in the theories of Moritz Hauptmann and Arthur von Oet- tingen, both of whom sought to model diatonic tonal concepts, and the latter of whom worked explicitly from an acoustic perspective (Engebret­ sen 2002, 101–17, 168–81). By contrast, Engebretsen shows...

... thought, Carl Dahlhaus once mused that the “sole historicist among nineteenth-century music theorists” was, ironically, neither a Goethean humanist like Moritz Hauptmann nor an erudite Musikwissenschaftler like Hugo Riemann, but rather the “distinguished physicist and physiologist...

... . 2003 . “ Toward a History of Attention in Culture and Science .” MLN 118 / 3 : 670 – 87 . Hauptmann Moritz . 1853 . Die Natur der Harmonik und Metrik . Leipzig . Holden John . 1766 . A Collection of Church-Music Consisting of New Setts of the Common Psalm-Tunes...

... International Conference, MCM 2007 , ed. Klouche Timour Noll Thomas , 406 – 11 . Berlin : Springer . Harrison Daniel . 2002 . “ Nonconformist Notions of Nineteenth-Century Enharmonicism .” Music Analysis 21/2 : 115 – 60 . Hauptmann Moritz . 1853 . Die Natur der Harmonik...

... Louis and Ludwig Thuille, to which it is especially close; Schoenberg’s Harmonielehre (1911), with which it shares some features; and the later writings of Riemann, at least some of which Schenker knew.5 Schenker refers specifically (English, p. 86n.; German, p. 109n.) to Hauptmann and Riemann...

...), and Moritz Hauptmann (1792–1868)—continued to seek “symmetrical structure in all sorts of musical phenomena” (Bernstein 1993, 379). Weber declared that “[music’s] essential nature, accordingly, consists in a perfect sym- metry, as it respects the duration and the accent of the tones. This sym- metry...

... rhythmic theories of Moritz Hauptmann to set a dramatic text by Arrigo Boito). Serious students of lyric drama in the nineteenth century will be well rewarded if they work their way through the three chapters on “Lessons in Dramatic Composition...

.... De Ghizé, Susan. 2006. “The Positives and Negatives of Hauptmann’s Theory of Meter: A Look at Mozart’s Piano Sonata in F major, K. 332.” Dutch Journal of Music Theory 11/3: 203–16. Gloede, Wilhelm. 2012. “Schlusshemiolen und...

... Korsyn, “Schenker and Kant- ian Epistemology,” Theoria 3 (1988): 1–58; Kevin Korsyn, “Schenker’s Organi- cism Reexamined,” Integral 7 (1993): 82–188; Michael Cherlin, “Hauptmann and Schenker: Two Adaptations of Hegelian Dialectics,” Theory and Practice 13 (1988): 115–131; Robert...

... ii Figure 9. A seventh-chord transformation: Childs’s S3(2), Gollin’s Iiii, or the UTT 1,11〉 = W1 inspired by the triadic theories of Moritz Hauptmann (1853), labels the elements of a seventh chord i, ii, iii, and iv, upward from the root of a major-minor seventh...

.../groupings are Moritz Hauptmann ([1853] 1888, 189–92) understands triple perhaps not opposites in the same manner as the opposites meter to be in opposition to duple meter, forming a thesis– that Lewin’s binary-code...

....” Perspectives of New Music 30 ( 1 ): 82 -131. Hauptmann, Moritz. 1853 . Die Natur der Harmonik und Metrik. Leipzig: Breitkopf und Härtel. English trans. by W. E. Heathcote, The Nature of Harmony and Metre (London: Swan Sonnenschein, 1888). Hyer, Brian. 1995 . “Reimag(in)ing Riemann.” Journal...

... and Beyond. Rochester, NY: University of Rochester Press. Brown, Matthew, and Douglas Dempster. 1989. “The Scientific Image of Music Theory.” Jour- nal of Music Theory 33/1: 65–106. Cherlin, Michael. 1988. “Hauptmann...

...; Hauptmann s triad of keys construction; Riemann s func- tional categories, which tend to group third-related chords together; and the common phenomenon in Schenkerian theory of a mediant or submediant harmony serving to pro- long a tonic. Third-substitution is discussed in Tymoczko 2011: 242 45...

... or mony was posited as early as the mid-nineteenth century by states not easily conveyed in tonal music through harmonic Hauptmann, Riemann, and Oettingen. The tension between means: otherworldliness, distance, timelessness, possibly these systems has increasingly drawn the attention of schol- even...