The Tonnetz at First Sight: Cognitive Issues of HCI with Pitch Spaces

Summary

Empirical study investigating how people interact cognitively with Tonnetz-based computational platforms involving multimodal stimuli. 88 participants with varying backgrounds in music and mathematics interacted with a Tonnetz interface without prior knowledge of the pitch space.

Key Contributions

• First empirical study of how users cognitively interact with Tonnetz interfaces at first sight
• Strong music theory skills are needed to partially grasp the Tonnetz structure — specifically triad quality recognition and detection of shared pitch classes in harmonic motions
• The particular geometry of the Tonnetz can bias understanding when non-functional harmonic sequences are displayed
• Bridges neo-Riemannian music theory with cognitive science and HCI

Methods

• 88 participants, varied musical/mathematical backgrounds
• Interaction with a Tonnetz computational interface
• Measured recognition of triads, harmonic motion, and structural comprehension
• Connects to Krumhansl’s model of perceived triadic distance

Connections to Active Projects

AutoTonnetz: Directly relevant — this paper studies the cognitive challenges users face with Tonnetz interfaces, which is exactly what AutoTonnetz aims to address by making the Tonnetz accessible through audio-visual feedback. The finding that non-functional sequences bias understanding suggests AutoTonnetz’s cellular automata approach (which generates sequences based on rules rather than functional harmony) should include visual cues that help users track harmonic relationships.

Organised Sound: Relevant to the perception constructs being measured in the rater survey — particularly coherence and agency. If users struggle to perceive structure in Tonnetz representations, this affects how they rate the coherence of audio-visual outputs.

Suggested Reading

• Krumhansl (1998) — perceived triadic distance model
• Brower (2008) — psychological approaches to neo-Riemannian theory
• Moss (2020) — computational models of tonal pitch spaces