Click the icons below to access author handouts.

Salons 1 & 2 • Thursday afternoon, 3:30–5:00

Instruments and Transformations

Mark Janello (Peabody Conservatory), Chair

Jonathan De Souza (University of Western Ontario) 

Instrumental Transformations in Heinrich Biber's Mystery Sonatas

Toru Momii (Columbia University) 

Sounds of the Cosmos: A Transformational Approach to Gesture in Shō Performance

Abstracts

Instrumental Transformations in Heinrich Biber's Mystery Sonatas

Jonathan De Souza (University of Western Ontario)

“Suppose you want to retune your violin,” writes David Lewin, “so that all its open strings sound notes of the F major harmony.” As Lewin demonstrates, the most efficient solutions involve a total shift of 5 semitones. But when Heinrich Biber retunes his violin to an F major harmony, the violinist-composer chooses a relatively inefficient solution. In his seventh Mystery Sonata, Biber raises the G string a perfect fourth and the D string a minor third, while lowering the E string a major third—a total shift of 12 semitones. Biber’s hand-grip notation, indicating finger positions rather than sounding results, can also unsettle the player. The Mystery Sonatas thus prompt two related questions, which connect transformational voice leading to the phenomenology of performance: How do alternate tunings relate to standard tuning? And how might they affect players?

Analyzing Biber’s alternate tunings according to two metrics of transformational voice leading—consistency and displacement—reveals overlapping categories. “Quintal scordatura,” which preserve adjacent-string fifths, tend to be more uniform, and they include zones where notated and sounding intervals match. “Chordal scordatura,” in which the open strings realize a single harmony, generally involve more displacement. Yet psychological research on altered pitch feedback suggests that a mix of consistency and displacement is most unsettling for players. It implies that scordatura are disruptive when they preserve aspects of standard tuning, creating both expected and surprising notes. Analyzing scordatura, then, ultimately shows how instruments function as tonal spaces and spaces for musical action.

Sounds of the Cosmos: A Transformational Approach to Gesture in Shō Performance

Toru Momii (Columbia University)

This paper incorporates the physical gestures of performing the shō—a free-reed mouth organ—into an analysis of its aitakē—five- to six-note pitch clusters played by the shō—to explore the relationship between performance practice and modal theory in gagaku. I demonstrate that the idiosyncratic arrangement of the pipes on the shō is closely related to the pitch structure and tonal function of the aitakē.

My analysis synthesizes two approaches. First, I adopt David Lewin’s transformational attitude (1987) to focus on the processes of motion enacted by the tē-utsuri— standardized finger movements for shifting between two aitakē—rather than conceptualize the aitakē as static harmonic entities. Second, I treat the aitakē as sonic byproducts of a performer’s instrumental gestures to examine how each of the aitakē are related to one another kinesthetically, and whether these relationships correlate with the pitch structures of the aitakē.

Relatedness between aitakē is determined by the parsimony of the tē-utsuri. I demonstrate that the most parsimonious movements can be enacted between four aitakē: , kotsu, ichi and otsu. These aitakē are identical to the clusters that accompany the fundamental tones of five of the six modes: Ichikotsu-chō, Hyōjō, Taishiki-chō, Ōshiki-chō and Banshiki-chō. These findings demonstrate that the pipes of the shō, while seemingly arranged in no discernable order, prioritize parsimonious tē-utsuri between each of the aitakē accompanying the fundamental modal degrees. An analysis of the pitch structure of aitakē through tē-utsuri reveals a striking correlation between gestural parsimony and tonal function.