Figure 1
Segment-based recognition (top) vs. event-based recognition (bottom) on measures 11 and 12 from Beethoven WoO68, using note onsets and offsets to create event boundaries.
Table 1
Input representation for measure 12 from Beethoven WoO68, showing the pitches and duration for each event, as well as the corresponding segment and label, where G7 stands for G:maj:add7, and C stands for C:maj.
| Seg. | Label | Event | Pitches | Len. |
|---|---|---|---|---|
| s1 | G7 | e1 | G3, B3, D4, G5 | 1/8 |
| G7 | e2 | G3, B3, D4, F5 | 1/8 | |
| G7 | e3 | B4, D5 | 3/16 | |
| G7 | e4 | B4, D5 | 1/16 | |
| s2 | C | e5 | C4, C5, E5 | 1/8 |
| C | e6 | G3, C5, E5 | 1/8 | |
| C | e7 | E3, G4, C5, E5 | 1/8 | |
| C | e8 | C3, G4, C5, E5 | 1/8 |
Figure 2
Segment and labels (top) vs. events (bottom) for measure 12 from Beethoven WoO68.
Figure 3
Factor graph representation of the semi-CRF.
Table 2
Dataset statistics and summary of results (event-level accuracy AccE and segment-level F-measure FS).
| Dataset | Statistics | Full chord evaluation | Root-level evaluation | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| semi-CRF | HMPerceptron | semi-CRF | HMPerceptron | Melisma | |||||||||
| Events | Seg.’s | Labels | AccE | FS | AccE | FS | AccE | FS | AccE | FS | AccE | FS | |
| BaCh | 5,664 | 3,090 | 90 | 83.2 | 77.5 | 77.2 | 69.9 | 88.9 | 84.2 | 84.8 | 77.0 | 84.3 | 74.7 |
| TAVERN | 63,876 | 12,802 | 69 | 78.0 | 64.0 | 57.0 | 22.5 | 86.0 | 71.4 | 69.2 | 33.2 | 76.7 | 41.5 |
| KPCorpus | 3,888 | 911 | 76 | 73.0 | 53.0 | 72.9 | 45.4 | 79.3 | 59.0 | 79.0 | 51.9 | 81.9 | 62.2 |
| Rock | 25,621 | 4,221 | 48 | 70.1 | 55.9 | 61.3 | 34.6 | 86.1 | 65.1 | 80.7 | 42.9 | 77.9 | 36.3 |
Table 3
Comparative results (%) and standard deviations on the BaCh dataset, using Event-level accuracy (AccE) and Segment-level precision (PS), recall (RS), and F-measure (FS).
| BaCh: Full chord evaluation | ||||
|---|---|---|---|---|
| System | AccE | PS | RS | FS |
| semi-CRF | 83.2 0.2 | 79.4 0.2 | 75.8 0.2 | 77.5 0.2 |
| HMPerceptron1 | 77.2 2.1 | 71.2 2.0 | 68.8 2.2 | 69.9 1.8 |
| HMPerceptron2 | 77.0 2.1 | 71.0 2.0 | 68.5 2.3 | 69.7 1.8 |
Table 4
Root only results (%) on the BaCh dataset, using Event-level accuracy (AccE) and Segment-level precision (PS), recall (RS), and F-measure (FS).
| BaCh: Root only evaluation | ||||
|---|---|---|---|---|
| System | AccE | PS | RS | FS |
| semi-CRF | 88.9 | 85.4 | 83.0 | 84.2 |
| HMPerceptron | 84.8 | 78.0 | 76.2 | 77.0 |
| Melisma | 84.3 | 73.2 | 76.3 | 74.7 |
Table 5
Full chord Event (AccE) and Segment-level (PS, RS, FS) results (%) on the BaCh dataset, with and without metrical accent features.
| BaCh: Metrical accent evaluation of semi-CRF | ||||
|---|---|---|---|---|
| System | AccE | PS | RS | FS |
| With accent | 83.6 | 79.6 | 75.9 | 77.6 |
| Without accent | 77.7 | 74.8 | 68.0 | 71.2 |
Table 6
Event (AccE) and Segment-level (PS, RS, FS) results (%) on the TAVERN dataset.
| TAVERN: Full chord evaluation | ||||
|---|---|---|---|---|
| System | AccE | PS | RS | FS |
| semi-CRF | 78.0 | 67.3 | 60.9 | 64.0 |
| HMPerceptron | 57.0 | 24.5 | 20.8 | 22.5 |
Table 7
Event (AccE) and Segment-level (PS, RS, FS) results (%) on the TAVERN dataset.
| TAVERN: Root only evaluation | ||||
|---|---|---|---|---|
| System | AccE | PS | RS | FS |
| semi-CRF | 86.0 | 74.6 | 68.4 | 71.4 |
| HMPerceptron | 69.2 | 38.2 | 29.4 | 33.2 |
| Melisma | 76.7 | 42.3 | 40.7 | 41.5 |
Figure 4
Semi-CRF correctly predicts A:maj7 (top) for the first beat of measure 55 from Mozart K025, while HMPerceptron predicts C#:dim (bottom).
Figure 5
Semi-CRF correctly predicts C:maj (top) for all of measure 280 from Mozart K179, while HMPerceptron predicts E:min (bottom) for the first beat and C:maj for the other two beats (bottom).
Table 8
Event (AccE) and Segment-level (PS, RS, FS) results (%) on the KP Corpus dataset.
| KP Corpus 46 excerpts: Full chord evaluation | |||||
|---|---|---|---|---|---|
| System | AccE | PS | RS | FS | |
| semi-CRF1 | 72.0 | 59.0 | 49.2 | 53.5 | |
| semi-CRF2 | 73.4 | 59.6 | 50.1 | 54.3 | |
Table 9
Event (AccE) and Segment-level (PS, RS, FS) results (%) on the KP Corpus dataset.
| KP Corpus 46 excerpts: Root only evaluation | ||||
|---|---|---|---|---|
| System | AccE | PS | RS | FS |
| semi-CRF | 80.7 | 66.3 | 56.2 | 60.8 |
| Melisma | 80.9 | 60.6 | 63.3 | 61.9 |
Table 10
Event (AccE) and Segment-level (PS, RS, FS) results (%) on the KP Corpus dataset.
| KP Corpus 36 excerpts: Full chord evaluation | ||||
|---|---|---|---|---|
| System | AccE | PS | RS | FS |
| semi-CRF | 73.0 | 55.6 | 50.7 | 53.0 |
| HMPerceptron | 72.9 | 48.2 | 43.6 | 45.4 |
Table 11
Event (AccE) and Segment-level (PS, RS, FS) results (%) on the KP Corpus dataset.
| KP Corpus 36 excerpts: Root only evaluation | ||||
|---|---|---|---|---|
| System | AccE | PS | RS | FS |
| semi-CRF | 79.3 | 61.8 | 56.4 | 59.0 |
| HMPerceptron | 79.0 | 54.7 | 49.9 | 51.9 |
| Melisma | 81.9 | 60.7 | 63.7 | 62.2 |
Table 12
Event (AccE) and Segment-level (PS, RS, FS) results (%) on the Rock dataset.
| Rock 59 songs: Full chord evaluation | ||||
|---|---|---|---|---|
| System | AccE | PS | RS | FS |
| semi-CRF1 | 66.0 | 49.8 | 47.3 | 48.5 |
| semi-CRF3 | 69.4 | 62.0 | 54.9 | 58.3 |
Table 13
Event (AccE) and Segment-level (PS, RS, FS) results (%) on the Rock dataset.
| Rock 59 songs: Root only evaluation | ||||
|---|---|---|---|---|
| System | AccE | PS | RS | FS |
| semi-CRF | 85.8 | 70.9 | 63.2 | 66.8 |
| Melisma | 77.4 | 29.5 | 44.0 | 35.3 |
Table 14
Event (AccE) and Segment-level (PS, RS, FS) results (%) on the Rock dataset.
| Rock 51 songs: Full chord evaluation | ||||
|---|---|---|---|---|
| System | AccE | PS | RS | FS |
| semi-CRF | 70.1 | 58.8 | 53.2 | 55.9 |
| HMPerceptron | 61.3 | 41.0 | 29.9 | 34.6 |
Table 15
Event (AccE) and Segment-level (PS, RS, FS) results (%) on the Rock dataset.
| Rock 51 songs: Root only evaluation | ||||
|---|---|---|---|---|
| System | AccE | PS | RS | FS |
| semi-CRF | 86.1 | 68.6 | 61.9 | 65.1 |
| HMPerceptron | 80.7 | 51.3 | 36.9 | 42.9 |
| Melisma | 77.9 | 30.6 | 45.8 | 36.3 |
Figure 6
Measures 14–15 of ‘Let It Be’ by the Beatles, where HMPerceptron incorrectly predicts G:maj6 for measure 15 (bottom), while semi-CRF correctly predicts G:maj (top).