THE TONAL-METRIC HIERARCHY: A CORPUS ANALYSIS
Bibliographic record
Abstract
Despite the plethora of research on the role of tonality and meter in music perception, there is little work on how these fundamental properties function together. The most basic question is whether the two hierarchical structures are correlated – that is, do metrically stable positions in the measure preferentially feature tonally stable pitches, and do tonally stable pitches occur more often than not at metrically stable locations? To answer this question, we analyzed a corpus of compositions by Bach, Mozart, Beethoven, and Chopin, tabulating the frequency of occurrence of each of the 12 pitch classes at all possible temporal positions in the bar. There was a reliable relation between the tonal and metric hierarchies, such that tonally stable pitch classes and metrically stable temporal positions co-occurred beyond their simple joint probability. Further, the pitch class distribution at stable metric temporal positions agreed more with the tonal hierarchy than at less metrically stable locations. This tonal-metric hierarchy was largely consistent across composers, time signatures, and modes. The existence, profile, and constancy of the tonal-metric hierarchy is relevant to several areas of music cognition research, including pitch-time integration, statistical learning, and global effects of tonality.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.007 |
| Science and technology studies | 0.003 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".