Harmonic Syntax in Time: Rhythm Improves Grammatical Models of Harmony
Bibliographic record
Abstract
Music is hierarchically structured, both in how it is perceived by listeners and how it is composed. Such structure can be captured elegantly using probabilistic grammatical models similar to those used to study natural language. They address the complexity of the structure using abstract categories in a recursive formalism. Most existing grammatical models of musical structure focus on one single dimension of music--such as melody, harmony, or rhythm. While these grammar models often work well on short musical excerpts, accurate analysis of longer pieces requires taking into account the constraints from multiple domains of structure. The present paper proposes abstract product grammars--a formalism which integrates multiple dimensions of musical structure into a single grammatical model--along with efficient parsing and inference algorithms for this formalism. We use this model to study the combination of hierarchically-structured harmonic syntax and hierarchically-structured rhythmic information. The latter is modeled by a novel grammar of rhythm that is capable of expressing temporal regularities in musical phrases. It integrates grouping structure and meter. The combined model of harmony and rhythm outperforms both single-dimension models in computational experiments. All models are trained and evaluated on a treebank of hand-annotated Jazz standards.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".