The <i>Tonnetz</i> at First Sight: Cognitive Issues of Human–Computer Interaction with Pitch Spaces
Bibliographic record
Abstract
Pitch spaces allow pitch relations to be expressed through geometrical representations for many different purposes. The Tonnetz is a well-known pitch space in the field of music theory; equivalent representations have been described in the field of cognitive science, especially Krumhansl's model of perceived triadic distance. Despite her empirical approach, we know very little about the way people interact, cognitively speaking, with Tonnetz-based computational platforms involving multimodal stimuli. Our study has approached this issue by means of empirical experimentation for the first time. A total of 88 participants, with varying backgrounds in music and mathematics, were asked to interact with a Tonnetz interface; they did not have prior knowledge of this pitch space. Results of our experiment confirmed our main hypotheses. On the one hand, strong skills in music theory are needed to partially grasp the overall structure of the Tonnetz at first sight; this aspect is mainly related to the quality recognition of triads and the detection of shared pitch classes in harmonic motions. On the other hand, the particular geometry of the Tonnetz may bias this understanding when non-functional harmonic sequences are displayed on it.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.010 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.010 |
| Scholarly communication | 0.005 | 0.012 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".