Identifying Metrical and Temporal Structure With an Autocorrelation Phase Matrix
Bibliographic record
Abstract
This article introduces a new method for detecting long-timescale structure in music. We describe a way to compute autocorrelation such that the distribution of energy in phase space is preserved in a matrix. The resulting Autocorrelation Phase Matrix (APM) is useful for several tasks involving metrical structure. In this article we describe the details of calculating the APM. We then show how phase-related regularities from music are stored in the APM and present two ways to recover these regularities. The simpler approach uses variance or entropy calculated on the distribution of information in the APM. The more complex approach explicitly searches through the phase and lag space of the APM to predict meter and tempo in parallel. We compare these approaches against standard autocorrelation for the task of tempo prediction on a relatively large database of annotated digital audio files. We demonstrate that better tempo prediction is achieved by exploiting the phase-related information in the APM.We argue that the APM is an effective data structure for tempo prediction and related applications, such as real-time beat induction and music analysis.
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".