Poster Session 3: Computer-Aided Analysis / Interrogating Riemann

Olivier Messiaen was famously active as a composer, a music theorist, and an ornithologist interested in birdsong. His unconventional music-theoretical interests are evident in the first volume of his Traité de Rythme, de Couleur, et d’Ornithologie (1994), as well as in his 1944 work Technique de mon langage musical, both of which extensively treat Greek metrics alongside ancient Carnatic rhythms. Birdsong, on the other hand, is the subject of the fifth volume of his Traité de Rythme, de Couleur, et d’Ornithologie (1999/2000), which features hundreds of the composer's transcriptions of birdsong from around the globe. Here I disentangle the reciprocal and often covert interactions between the composer’s activities in these three domains, and show how his purportedly naturalistic birdsong transcriptions in fact reflect his compositional habits and his theoretical ideas and influences. 

Presenting new computational tools and a novel algorithm for rhythmic search and alignment, I demonstrate the remarkable concordance (99.31%) between the algorithm’s findings and compositional analyses by the composer and by Messiaen scholars (Griffiths 1985, Cheong 2008, Kraft 2013). These new computational methods confirm the pervasiveness of Greek prosodic feet in the New Caledonian birdsong transcriptions (n=103), while also revealing the hitherto unsuspected presence of Carnatic fragments more familiar from his compositions, including 33-Turangalila and 54-Nandana. Moreover, analysis of the transcription’s pitch space demonstrates frequent conformity to the Modes of Limited Transposition (1944) both within and across avian species, further demonstrating that the composer’s langage musical permeated his naturalistic transcriptions. 

• Handout

Spectral music (in the broadest sense) foregrounds timbre and fluid processes in shaping compositions and most existing analytical approaches are not well suited to this repertoire. This poster presents research developing new interactive aural software to ameliorate this situation. 

We take as a case study An elemental thing by the Australian composer Liza Lim, a 15-minute work for solo woodblock. Software is used to enable the analyst and readers to relate analytical ideas directly to aural experience. Interactive taxonomies and dynamic structural charts can be ‘played’; the software includes a video recording of the work, facilitating integration of visual aspects of a performance, including physical gesture, into the analytical discussion. An interactive sonogram allows users to select segments in the graphic display, or scrub (with the mouse) in both time and frequency, hearing the results instantly. Visualisations of data from audio descriptors can be heard interactively. Our software encourages ‘readers’ to experiment with analytical materials for themselves, with findings presented, not simply as abstract ideas about an unfamiliar sonic environment, but in sound.

This interactive analysis demonstrates how the work is shaped and structured through transformations of timbres and textures generated using a range of implements and materials, and employing a variety of physical gestures to excite the woodblock and modify its resonance. More generally, it shows how software can enhance research into spectral music, linking data, graphic presentations and verbal descriptions to aural experience, facilitating interactive engagement with an analysis and incorporation of visual/gestural aspects into the research.

• Handout

Music-theory scholarship and pedagogy generally assume Hugo Riemann’s (1891; 1893), three functions: tonic, subdominant, and dominant. Some twenty-first-century theorists, such as Lerdahl (2001) and White and Quinn (2018), have suggested various additional functions. Already in the twentieth-century however, Prague was home to a school of Czech music theorists who developed expanded theories of harmonic function. The most famous of these theorists was Karel Janeček (1903–1974), who in his Základy moderní harmonie (Foundations of Modern Harmony, 1965) adds Lydian and Phrygian functions to Riemann’s original three.

This poster presents Janeček’s theory and compares it to Riemann’s. This juxtaposition clarifies three open questions concerning Riemann’s function theory. First, is the Schritt und Wechsel system vital to Riemann’s approach? Second, is Riemann’s function theory so diatonic that it limits musical possibilities, as Rehding (2003) suggests, or does Riemann allow for analyzing virtually any chord into any one of the three functions, as Harrison suggests (1994)? Lastly—a concern raised by Dahlhaus (1975)—why do triads related to the tonic by fifth receive the privileged status of dominant and subdominant functions? The goal of this study is to show that examining Riemann’s reception in Prague can elucidate Riemann’s function theory, and by extension, the theories of harmonic function that scholars continue to use and develop today.

Riemann’s theory of harmonic dualism occupies a unique place in the history of music theory: while widely considered to be of enduring heuristic value, its central empirical premise is universally acknowledged to be false. That premise, of course, is that subharmonics (undertones) are acoustically real, and hence audible when music is played and heard. The entire conceptual system of harmonic dualism derives ontologically from this premise. And this new system, because it places the minor system on equal footing with the major system (the former now derivable from the subharmonic series just as the latter derives from the harmonic series), incited a revolution in musical thinking that is still playing out today. However, subharmonics are objectively not present in musical sounds. When Riemann ultimately conceded this fact, the ontological basis of the dualist system crumbled. But what if Riemann wasn’t wrong? Or, more accurately, what if his error was a far less significant one—concerning not whether to look for subharmonic relationships, but where. As revealed in a recent monograph from the field of auditory neurophysiology, Gerald Langner’s The Neural Code of Pitch and Harmony (2015), the logic of subharmonic relationship is literally embodied throughout the entire computational structure of the auditory brainstem and midbrain, in those neural circuits that not only afford basic pitch processing, but are the first stages in higher-level conceptions of harmony, melody, and even rhythm and meter. These ideas suggest fruitful new avenues for exploration within dualist theory, as informed by auditory neuroscience.