A Generalized Intervallic Approach to Metric Conflict in Liszt * Robert L. Wells NOTE: The examples for the (text-only) PDF version of this item are available online at: h)p://www.mtosmt.org/iss.es/mto.17.23.4/mto.17.23.4.wells.php 4E5WORDS: Liszt, Lewin, rhythm, meter, GIS, trans ormation theory, metrical dissonance, metric conflict A:STRACT: The m.sic o Franz Liszt has become widely recognized by m.sic theorists or its harmonic and ormal innovations. However, li)le a)ention has been given to advent.ro.s rhythmic/metric aspects o Liszt’s compositional style: speci=cally, he req.ently incorporates rich metric str.ct.res in which the notated metric layer, indicated by time signat.res and bars, and heard metric layer, given by c.es in the so.nding m.sic, are locked in an evolving conflict. To model s.ch interactions, this article develops a new analytical system based on Lewin’s generalized interval system (GIS) concept, constr.cting a new three-component metric direct prod.ct GIS called Met . The article then introd.ces specialized techniq.es incl.ding intervallic decomposition, expansion, and contraction that allow the analyst to organize, compare, and relate diverse Met intervals. The remainder o the article applies this new system to preliminary analyses o Liszt’s “6ilde AagdB and “Invocation,B providing signi=cant local and global insights into these works’ metric str.ct.res and s.ggesting new possibilities or metric analysis. Received May 2017 Col.me 12, N.mber 3, December 1010 Copyright E 1010 Society or M.sic Theory 1. Introduction F1] In recent years, Franz Liszt has garnered increasing interest among m.sic theorists for his innovations in harmony and form. (1) However, li)le aention has been given to rhythmic/metric aspects o his compositional style: (2) in partic.lar, he freq.ently incorporates rich rhythmic str.ct.res in which the notated meter, given by time signat.res and bar line placement, and the meter perceived by the listener are locked in an evolving conflict. Example 1 , rom Liszt’s “Invocation,” ill.strates. A listener witho.t access to the score wo.ld likely hear the first so.nding chord as an opening downbeat, followed by several two-beat meas.res. A glance at the score, however, reveals that the opening “downbeat” is act.ally beat twoH f.rthermore, the notated meter Processing math: 100I 1 of 28 2 3 in the opening is not 4, b.t 4. While the so.nding m.sic does event.ally fall in line with the 3 notated 4 meter, the opening o the piece demonstrates a striking contrast between what the listener hears, or metrically entrains, and what is wri)en. (3) These considerations s.ggest the presence o two distinct metrical layers: a layer s.pported by auditory c.es in the so.nding m.sic and only indirectly implied by the m.sical notation, and an idealized layer represented by time signat.res and barring that hearing alone may not reveal. F1G At this point, one might be tempted, as a listener or per ormer, to prioritize one o these two layers. However, I arg.e that for per ormers and in ormed listeners, these layers form a larger, more complex m.sical experience than that provided by either layer on its own. (4) This perspective motivates an important q.estion: how might relationships and interactions between conflicting metrical layers be modeled over the co.rse o a piece when one layer is sonically artic.lated while the other is cognitively “internalizedB by the in ormed listenerJ While the present article will oc.s on the m.sic o Liszt, this q.estion has broader relevance to inn.merable Western and non- 6estern m.sical styles, from Brahms to Stravinsky to So.th Indian Carnatic m.sic. (5) F2G To diLerentiate between these two metric layers in disc.ssion, I will tentatively call the internalized, re erential metric layer the “X-layer” and the sonically artic.lated layer the “Y-layer,B 3 For instance, in Example 1, the notated 4 meter de=nes the X-layer, while the heard two-beat meas.res locally de=ne the Y-layer. Now, observe that i the beginning o each two-beat “Y-meas.re” marks a “Y-downbeat,B then the location o the Y-downbeat changes with respect to the X-meas.re over the first three meas.res. Namely, the Y-downbeat begins on beat 2 o the X -meas.re, b.t then shi ts s.ccessively to beat 1, beat 2, beat 2 again, and finally back to beat 1 in m. 3, where the X- and Y-layers align. (6) F3G While these sorts o metric relationships have not been widely disc.ssed in Liszt’s m.sic, Krebs (19NN ) has thoro.ghly treated conflicts between metrical layers in Robert Sch.mann’s m.sic. Whereas Krebs’s basic analytical units are the metrically consonant or dissonant states, however, Lewin’s ( 1987 ) concept o the generalized interval system (GIS) s.ggests searching for an alternative approach that emphasizes not points or states in a m.sical space, b.t the intervals and changes between these obPects. This perspective forms the springboard or the c.rrent st.dy, which will model the interactions between X- and Y-metric layers (0$ in Liszt’s m.sic using a newly de=ned GIS and will apply these ideas to two preliminary Liszt analyses. (8) As will become clear, Lewinian GIS theory permits a q.anti=able approach to metric conflict that can acco.nt for arbitrarily long or short metric spans and can analyze larger conflicting str.ct.res in terms o s.bcomponents. :eyond drawing upon GIS theory for its intrinsic use .lness, the c.rrent proPect aims, in applying Lewin’s theories to rhythmic/metric st.dy, to contrib.te to a generally underdeveloped side o GIS theory. (N) F5] Example 2 presents another example o metric conflict, from Liszt’s Totentanz for piano and orchestra. At rehearsal H, Liszt begins a variant o the Dies irae theme on beat 2, and d.e to the phrasing and harmonic s.ccessions (e.g., the fermata and rest preceding the melody and the consistent appearance o local tonics on beat 2 and dominants on beat 1), beat 2 so.nds like a downbeat and beat 1 an upbeat thro.gho.t the passage. In Krebs’s ( 1NNN ) terminology, rather than a metrical “gro.ping dissonanceB (31) like in Example 1, a “displacement dissonanceB (22$ o the 2 orm D2+1 (or D1R1) occ.rs. In other words, s.perimposed over the 4 X-meter is a conflicting Y 2 -meter o 4-shi ted-by-one-beat. Altho.gh Krebs’s label is use .l for describing the passage’s metrical state, it does not reveal how the m.sic reached this displaced state, or what metrical processes might restore metrical consonance. In contrast, Lewin’s GIS machinery will allow not only diLerentiation between displaced and non-displaced metric states, b.t also representation o the dynamic shi t in Y-downbeat location res.lting from entering or leaving s.ch a metrically Processing math: 100I 2 of 28 displaced passage. FMG It now deserves emphasis that the GIS to be developed in this article has a percept.al component, being partly based on a.ditorily derived metric interpretations. As s.ch, applications o the GIS will draw upon Lerdahl and AackendoL’s A Generative Theory of Tonal Music ( 1982 ). In this landmark work, the authors assert that meter is a concept broader than the simple barring on the page, de=ning metrical str.ct.re as “the reg.lar, hierarchical pa)ern o beats to which the listener relates m.sical events” and describing how “phenomenal accents” in the score—c.es s.ch as dynamic changes, leaps, or harmonic changes—are key in creating a metric perception (10$. Central to their metric theory is a set o fo.r “metrical well- ormedness r.les” (MWFRs), which determine the set o “possible metrical str.ct.resB (68), and “metrical pre erence r.les” (MPRs), thro.gh which a listener may choose among the possible metric interpretations for a m.sical passage (03$. They note, however, that while M6FRs 1 and 2 are “common to all types o m.sic,B M6FRs 3 and 4 may be “open to variationB or simply omi)ed (N0$. (10) There ore, to accommodate metric hearings involving asymmetrical fives, sevens, and the like, the c.rrent proPect will omit M6FRs 3 and 4. O the MPRs, the most important for the c.rrent st.dy will be MPR 1 (Parallelism), which pre ers that parallel m.sical gro.pings receive parallel metrical str.ct.res (75)H MPR 2 (Strong Beat Early), which pre ers that a m.sical gro.p’s strongest beat appears early in the gro.p (06); MPR 4 (Stress), which pre ers metrical str.ct.res where accented notes are metrical strong beats (0N$; and MPR 5 (Length), which pre ers metrical str.ct.res in which strong beats occ.r at the initiation o long pitch, dynamic, artic.lation, or harmonic events (O3). Even when I do not re erence these r.les explicitly, they are at work in the backgro.nd as I select metrical hearings or the Liszt works in q.estion. F0G Signi=cantly, rather than taking Hasty’s ( /NN0 ) moment-by-moment experiential approach, I will foc.s on what Lerdahl and AackendoL ( 1983 ) call “the =nal state o [the listener’sG .nderstanding” (4); namely, the metric str.ct.res being analyzed will be final metric interpretations for m.sical passages following care .l reflection on the rhythmic and metric perceptions that the passages ind.ce.