Table 1
Dataset. All pieces are piano sonata movements by W.A. Mozart.
| PIECE | KEY | QUARTER NOTES | METER | MEASURES | |
|---|---|---|---|---|---|
| 0 | K279 i | C major | 546 | 4/4 | 136 |
| 1 | K279 ii | F major | 306 | 3/4 | 102 |
| 2 | K279 iii | C major | 426 | 2/4 | 213 |
| 3 | K280 i | F major | 593 | 3/4 | 198 |
| 4 | K282 i | E♭ major | 276 | 4/4 | 69 |
| 5 | K283 i | G major | 356 | 3/4 | 119 |
| 6 | K284 i | D major | 1010 | 4/4 | 252 |
| 7 | K309 i | C major | 1174 | 4/4 | 294 |
| 8 | K311 i | D major | 584 | 3/4 | 195 |
| 9 | K330 i | C major | 719 | 2/4 | 360 |
| 10 | K330 iii | C major | 703 | 2/4 | 352 |
| 11 | K332 i | F major | 665 | 3/4 | 222 |
| 12 | K332 ii | B♭ major | 160 | 4/4 | 40 |
| 13 | K333 i | B♭ major | 658 | 4/4 | 164 |
| 14 | K545 i | C major | 267 | 4/4 | 67 |
| 15 | K570 i | B♭ major | 600 | 3/4 | 200 |
| 16 | K576 ii | A major | 200 | 3/4 | 67 |
Figure 1
Reduction and clustering procedure illustrated on mm. 1–2 of K.279.
Figure 2
Centroids of the twenty clusters resulting from applying k-means with a Manhattan (a) and Euclidean (b) metric.
Figure 3
Spectra of the centroids of the 20 clusters, grouped according to whether |â3| (a–b), |â4| (c–d), or |â1| (e–f) is larger, for the k-means solutions by Manhattan (a, c, e) and Euclidean (b, d, f) metrics.
Figure 4
Phase space plot for centroids of (a) triadic, (b) tetradic, and (c) scalar clusters from the Manhattan k-means solutions. The vertical axis is the phase of â5, in all cases, while the horizontal axis is the phase of â3, â4, and â1 respectively. Ranges show the circular variance for each cluster: .
Figure 5
Dendogram showing hierarchical clustering solution.
Figure 6
Probability of each cluster appearing in each of five parts of a sonata form, split into three groups.
Figure 7
The twenty cluster centroids in the phase space for â5 and â3, with regions grouping clusters that have a similar frequency profile over the five main sections of a sonata form.
Figure 8
Sum and difference matrices for subordinate key and home key clusters in percentages over just the transitions involving these clusters and excluding trivial transitions. Values exceeding 1 standard deviation are highlighted. Redundant values (given by symmetry and antisymmetry) are excluded (in difference matrices we retain just the positive values).
Figure 9
Transition data for subordinate key and home key groups, plotted in φ4/φ5 space. Large arrows show high values in both the difference and sum matrices, small arrows in the sum or difference matrices only (double-headed for sum).
Figure 10
Sum and difference matrices for cluster groups. Values exceeding 1.5 standard deviations are highlighted. Redundant values (given by symmetry and antisymmetry) are excluded (in difference matrices we retain just the positive values).
Figure 11
Transition data for the cluster groups plotted in φ4/φ5 space. Group labels are positioned roughly in between their members, which are connected by dotted lines (with the exception of clusters 8 and 15 for clarity). Heavy arrows show high values in both the difference and sum matrices, lighter arrows in the sum or difference matrices only (double-headed for sum).