by Jonathan Liang
Prior to the 20th century, music of the Western classical tradition tended to maintain a single meter in each piece. However, in the late 19th and early 20th centuries, composers began to create music that juxtaposed different meters, sometimes placing widely-used simple and compound meters alongside asymmetrical meters such as 7/8. My final project will examine potential hearings of mixed meter music and the attentional tools that listeners may use to generate those hearings. Specifically, I will focus on pieces by Olivier Messiaen, who is well-known for writing pieces in free time, along with Modest Mussorgsky and Andrew Lloyd Weber. This topic is particularly interesting in the context of the neurological underpinnings of meter. Large and Jones present one prevailing model, in which linked oscillators maintain a regular sequence of attentional pulses. However, mixed meter music often lacks the nearly-isochronous onsets of sounds that are present in earlier Western music. Therefore, part of the project will explore potential interactions of mixed meter music with oscillators, with the goal of assessing whether mixed meter music can maintain attentional pulses on important beats. Furthermore, I plan to assess mixed meter music for the presence of hypermeter. A literature search revealed articles that invoke hypermeter as an organizing force in metrically-weak metal music; I am interested to see whether a similar organization could be present in classical pieces of the 20th century.
The methodology and background for this project is highly dependent on the need to complete both metrical and hypermetrical analyses of mixed meter music. I will apply an oscillator model to the onsets of sound found in mixed meter pieces. For a second perspective on meter, I will draw on the work of Christopher Hasty, whose model of “projection” has been used in previous analyses of 20th-century music. To examine hypermeter, I will adapt Lerdahl and Jackendoff’s grouping analysis. I may also use Maury Yeston’s attack-point analysis to clarify hypermetrical grouping structures. By combining and comparing these methods of analysis, I hope to identify the aspects of mixed meter music that are most relevant to listeners’ metric perceptions.
A two-pronged experimental study investigating the attentional demand of mixed meter music would complement the musical analysis. One prong of the experiment would separate subjects into two groups , both of which would complete a visual attention task. One group would listen to synthesized constant-meter music and the other would listen to mixed meter music, allowing a statistical comparison of performance on between the groups. The second prong of this experiment would extract ERPs from EEG monitoring of subjects exposed to both constant- and mixed-meter music. By combining experimental and music analysis results, it may be possible to progress towards a model for neural processing of that music. Such a model would be a significant advance, since cognition of metrically weak rhythms has so far received less attention in the literature than cognition of isochronous and metrically-strong rhythms.
Butler, Mark J. 2006. Unlocking the groove: Rhythm, meter, and musical design in electronic dance music. Bloomington, IN: Indiana University Press.
Though Butler focuses on electronic dance music, which tends to have a very regular bass beat, he develops concepts that are equally applicable to the analysis of music with uneven or undetermined meter. Critically, Butler discusses metric ambiguity, in which there is insufficient information to determine the placement of beats in one or more metric levels, and metric dissonance, in which different factors in the music suggest different beat placements for a level of the metric hierarchy. Given the very free nature of much of Messiaen’s music, it is possible that either or both of these phenomena will be important in passages with both even and uneven levels of meter. In that case, Butler’s observations about the consequences of metric ambiguity and dissonance for listeners will also be important background for this project. Furthermore, Butler introduces Hasty’s model of expectation. Though it may be impractical for analytical use, that model could have great value in explaining the cognitive effects of certain passages.
Pieslak, Jonathan. 2007. Re-casting metal: Rhythm and meter in the music of Meshuggah. Music Theory Spectrum 29, (2) (10/01): 219-45.
Pieslak analyzes the music of Swedish metal band Meshuggah, which makes use of uneven measures and even something akin to Messiaen’s “free time” in the piece “I.” “I” is also similar to segments of Messiaen’s works because it generally lacks patterns that can be used to define measures (at the time-scales in which measures are conventionally notated). In his analysis, Pieslak primarily relies on an “attack-point analysis” method to identify sections of the piece that are similar in the pattern of inter-onset intervals. Strikingly, he is able to infer isochronous hypermeasures that are governed by the recurrence of long rhythmic phrases or motives. Given Pieslak’s success in this analysis, it seems worthwhile to apply an attack-point analysis to selected excerpts of Messiaen’s music, using this article as a guide.
Repp, Bruno H., Justin London, and Peter E. Keller. 2005. Production and synchronization of uneven rhythms at fast tempi. Music Perception 23, (1): 61-78.
Repp, London, and Keller examine accuracy of synchronization to and continuation of uneven rhythmic patterns with 2 or 3 sound onsets per cycle, that span 5, 7, or 8 isochronous subdivisions. These sound onsets are rapid, with the subdivision being between 170 and 100 ms. One important finding that they make is that notes in 3:2 ratios tend to be tapped in ratios above 1.5:1, even when listeners are directly synchronizing to sound onsets. This trend indicates a significant preference for 2:1 note ratios, which may have consequences for the perception of Messiaen’s music, which contains a number of non-binary note length ratios. Unexpectedly, they also find that metric interpretation (the position of the downbeat relative to the start of a grouping of notes) has no consistent effect on either the ratio of produced notes or on the asynchrony of those notes, implying that “downbeats” are less important than once thought. However, they did find that downbeat position affects the difficulty of synchronization; downbeat-medial patterns yield greater interval variability (through not ratio variability) than other patterns.