A Flexible Approach to Automated Harmonic Analysis: Multiple Annotations of Chorales by Bach and Prætorius
Bibliographic record
Abstract
Despite being a core component of Western music theory, harmonic analysis remains a subjective endeavor, resistant automation. This subjectivity arises from disagreements regarding, among other things, the interpretation of contrapuntal figures, the set of "legal" harmonies, and how harmony relates to more abstract features like tonal function. In this paper, we provide a formal specification of harmonic analysis. We then present a novel approach to computational harmonic analysis: rather than computing harmonic analyses based on one specific set of rules, we compute all possible analyses which satisfy only basic, uncontroversial constraints. These myriad interpretations can later be filtered to extract preferred analyses; for instance, to forbid 7th chords or to prefer analyses with fewer non-chord tones. We apply this approach to two concrete musical datasets: existing encodings of 371 chorales by J.S. Bach and new encodings of 200 chorales by M. Prætorius. Through an online API users can filter and download numerous harmonic interpretations of these 571 chorales. This dataset will serve as a useful resource in the study of harmonic/functional progression, voice-leading, and the relationship between melody and harmony, and as a stepping stone towards automated harmonic analysis of more complex music.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.006 | 0.004 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.009 | 0.004 |
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".