...Jason Yust This article introduces a type of harmonic geometry, Fourier phase space, and uses it to advance the understanding of Schubert’s tonal language and comment upon current topics in Schubert analysis. The space derives from the discrete Fourier transform on pitch-class sets developed...

... proposes the use of phase spaces and Quinn's harmonic qualities in analysis of a wide variety of twentieth-century styles. The main focus is on how these ideas relate to scale-theoretic concepts and the repertoires to which they are applied, such as the music of Debussy, Satie, Stravinsky, Ravel...

...Figure 12. (a) The spectrum of the basic rhythm of Phase Patterns (see Figure 10). (b) The phase space for coefficient 3 and different rotations of the rhythm in this space. ...

... tetrachordal activity via affinity-space rela- tions. Figure 15.2 shows that pairs of stacked gamma chords (adjacently located and related by p in cocycle 0) move by p2 (major third bass ascent) to exhaust the entire cocycle in phase 1. Figure 15.3 models the whole-tone...

... zero phase the is underlying associated with periodicities the positive ofin Quinn a set 2007. are explicitly represented. It is in the interval-class domain that the infinitely many sets in continuous pitch or pitch-class space can be analyzed, compared, and transformed on equal footing. First, we...

... more clearly within the phased melodic unit. Consider the fully phased occurrence of M 5 at rehearsal 215, shown in Example 8 . Strategic rests and static notes during attacks 8–13 open space for the contours of moving lines to emerge, resulting in the long string of crisp values in positions 8–13...

... function, likewise often take on such characteristics. In Example 3d, dominant emulation may occur if chromatic C≥ substi- tutes for diatonic C during the 6 phase. Example 4 shows several alternative chords that might occupy that space, including one in which the 6 phase’s eponymous 6...

... Discrimination of Isochronous Tone Sequences.” Human Perception and Performance 24 ( 6 ): 1 -15. Tass, P.A. 1999 . Phase Resetting in Medicine and Biology . Heidelberg and New York: Springer Verlag. Zaslaw, N. 1989 . Mozart's Symphonies: Context, Performance Practice, Reception. New York: Oxford...

... poems in Machaut's motet oeuvre due to musical factors, such as when absence of a rest at the end of a final tenor talea shortens the space for text delivery or the terminus prevents what has been regular phase overlap. Tenor factors explain, for instance, why in the triplum text of Machaut's M7...

... precludes the judgment that one parameter is nevertheless much more important than the other. To this end, the geometric space known as the ternary plot is introduced, within which all coherent claims about the interaction of two parameters in a repertoire can be represented; the ternary plot also serves...

... ground has heard it said: to paraphrase Pierre Boulez, Schenker est mort. Those inclined to believe 204 this rumor might be surprised to see the amount of space devoted to Schenker and his ideas in The New Grove 2. As a not entirely unbiased observer, I am happy to report that Schenker is well...

... of melody and harmony and define the field of possibilities in which each melodic/harmonic change takes place—a “space” in which the changes can be heard as meaningful in relation both to themselves and to the text. Overall, these results suggest how the ostensibly mechanical melodic and harmonic processes...

... dancers might refer to as “working in 2s against 3s,” or metrical crossing. Another kind of metric conflict, a displacement or syncopation, arises when there is a shift of phase, involving an exchange between beats and offbeats. From the standpoint of a military marcher, this might involve shifting...

..., the recitative also places us in a space apart from the once attractive plenitude of the happy ending: the irony of irony is that it can sen- timentalize the past. Given the historical position of Chopin’s nocturne, we might read its strange ending...

...—both in space and in time—is particularly important in a group dance like the contredanse. The location at which a figure ends will be the location from which the next figure begins, so mistakes in ending can affect more than one figure. Depending on tempo and overall length, dances could last anywhere...

...Leah Frederick This article constructs generic voice-leading spaces by combining geometric approaches to voice leading with diatonic set theory. Unlike the continuous mod-12 spaces developed by Callender, Quinn, and Tymoczko, these mod-7 spaces are fundamentally discrete. The mathematical...

... Schlummerlosen” derived from Williamson’s own three individual graphs but designed to bring out a composite tonal plan.6 The song has three formal sections that, though flowing in and out of one another, mirror the three phases of the prolon- gational structure.7 Each begins with the same D≥ half-diminished...

... with respect to both period and phase. The downbeats of these heard measures are the hyperbeats that relate to one another by means of the hypermetrical schemas. Metrical orientation is top-down and schema driven; it thus complements low-level, bottom-up cognitive accounts of meter. The hypermetrical schemas...

... . “Transpositional Combination of Beat-Class Sets in Steve Reich's Phase-Shifting Music.” Perspectives of New Music 30 : 146 -77. ———. 1996 . “Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late-Romantic Triadic Progressions.” Music Analysis 15 : 9 -40. ———. 2001 . “Complex Hemiolas...