Figure 1
(a) First bars of lead sheet (from the iRealPro forum2) and (b) syntax tree representing the harmony of ‘Take the “A” train' by Billy Strayhorn. Image based on Harasim (2020). Dm7 is a terminal chord symbol, V/V is a preterminal since it is an abstract symbol representing a single terminal chord, and the highest occurring V is a nonterminal since it represents multiple lower‑level symbols. The turnaround has been omitted.
Figure 2
Graphical diagram of the neural PCFG, after Kim et al. (2019). is the start symbol; , are nonterminal; , , preterminal; and , , chord symbols. are rule probabilities, computed from embeddings by neural networks . Full lines between circles are PCFG rule applications, dotted lines indicate probabilistic dependencies, and full lines between rectangles indicate computations by neural networks.
Table 2
Validation F1 on JHT for progression losses when training on . I/M distinguishes between inside scores and marginals.
| Spans | I/M | F1 | |
|---|---|---|---|
| No loss | .453 | ||
| Rule | I | .466 | .013 |
| M | .484 | .03 | |
| Statistical | I | .438 | .015 |
| M | .465 | .012 |
Figure 3
Validation F1 for (a) the number of nonterminal (NT) and preterminal (P) symbols and (b) the hidden dimension of the MLPs used in the N‑PCFG. Shaded region represents standard deviation.
Table 3
Test F1 and recall (Re) of our models and baselines. Unsupervised models are on top, supervised models are in the middle, and trivial baselines are below. Best results per category in bold.
| Model | Train data | F1 | Re |
|---|---|---|---|
| N‑PCFG | JHT | .384 | .391 |
| N‑PCFG | iRealPro | .450 | .462 |
| Prog. loss | .461 | .476 | |
| N‑PCFG | ChoCo | .474 | .482 |
| Prog. loss | .487 | .495 | |
| SupCon | JHT | .640 | .643 |
| MuDeP | JHT | .607 | .606 |
| Random | .178 | .200 | |
| Left‑branching | .134 | .142 | |
| Right‑branching | .176 | .211 |
Figure 4
‘Blue Bossa’ by Kenny Dorham: (a) prediction and (b) annotation. Lead sheet in Suppl. Figure 9a.
Figure 5
‘Sunny’ by Bobby Hebb: (a, left) prediction and (b, right) annotation. Lead sheet in Suppl. Figure 9b.
Figure 6
NT precision versus a sample of (a) span ending chords sorted by frequency and (b) spans of chords. ‘o' indicates a diminished chord, ‘%' a half‑diminished chord, ‘m' a minor chord, ‘7’ a major seventh, ‘7’ a minor seventh, and ‘6' a major sixth. Some nonterminals are not used in this plot, which can be explained by the plot not showing all possible spans.
Figure 7
Induced rules with probability for N‑PCFG without progression loss. For every symbol on the left of , starting from the start symbol , the two rules with highest estimated probability are printed, and this is repeated for nonterminal symbols that occur on the right of the in one of the already printed rules (but the set of printed nonterminal symbols is only expanded 3). are nonterminal and preterminal symbols. This is only a fraction of all the rules.