2015:Discovery of Repeated Themes & Sections Results

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Contents

Introduction

The task: algorithms take a piece of music as input, and output a list of patterns repeated within that piece. A pattern is defined as a set of ontime-pitch pairs that occurs at least twice (i.e., is repeated at least once) in a piece of music. The second, third, etc. occurrences of the pattern will likely be shifted in time and/or transposed, relative to the first occurrence. Ideally an algorithm will be able to discover all exact and inexact occurrences of a pattern within a piece, so in evaluating this task we are interested in both:

  • (1) to what extent an algorithm can discover one occurrence, up to time shift and transposition, and;
  • (2) to what extent it can find all occurrences.

The metrics establishment recall, establishment precision and establishment F1 address (1), and the metrics occurrence recall, occurrence precision, and occurrence F1 address (2).

Contribution

Existing approaches to music structure analysis in MIR tend to focus on segmentation (e.g., Weiss & Bello, 2010). The contribution of this task is to afford access to the note content itself (please see the example in Fig. 1A), requiring algorithms to do more than label time windows (e.g., the segmentations in Figs. 1B-D). For instance, a discovery algorithm applied to the piece in Fig. 1A should return a pattern corresponding to the note content of P1 and P2, as well as a pattern corresponding to the note content of Q1. This is because Q1 occurs again independently of the accompaniment in bars 19-22 (not shown here). The ground truth also contains nested patterns, such as P1 in Fig. 1A being a subset of the sectional repetition S1, reflecting the often-hierarchical nature of musical repetition. While we recognise the appealing simplicity of linear segmentation, in the Discovery of Repeated Themes & Sections task we are demanding analysis at a greater level of detail, and have built a ground truth that contains overlapping and nested patterns (Collins et al., 2014).


MozartK282Mvt2.png

Figure 1. Pattern discovery v segmentation. (A) Bars 1-12 of Mozart’s Piano Sonata in E-flat major K282 mvt.2, showing some ground-truth themes and repeated sections; (B-D) Three linear segmentations. Numbers below the staff in Fig. 1A and below the segmentation in Fig. 1D indicate crotchet beats, from zero for bar 1 beat 1.


For a more detailed introduction to the task, please see 2015:Discovery_of_Repeated_Themes_&_Sections.

Ground Truth and Algorithms

The ground truth, called the Johannes Kepler University Patterns Test Database (JKUPTD-Aug2013), is based on motifs and themes in Barlow and Morgenstern (1953), Schoenberg (1967), and Bruhn (1993). Repeated sections are based on those marked by the composer. These annotations are supplemented with some of our own where necessary. A Development Database (JKUPDD-Aug2013) enabled participants to try out their algorithms. For each piece in the Development and Test Databases, symbolic and synthesised audio versions are crossed with monophonic and polyphonic versions, giving four versions of the task in total: symPoly, symMono, audPoly, and audMono. There were no submissions to the symPoly category this year, so three versions of the task ran. Submitted algorithms are shown in Table 1.


Sub code Submission name Abstract Contributors
Task Version symMono
PLM1 SYMCHM PDF Matevž Pesek, Urša Medvešek, Aleš Leonardis, Matija Marolt
OL1'14 PatMinr PDF Olivier Lartillot
VM2'14 VM2 PDF Gissel Velarde, David Meredith
Task Version audMono
WHD1 VMO Motif Discovery PDF Cheng-i Wang, Jennifer Hsu, Shlomo Dubnov
WDH1 VMO Motif Discovery FML PDF Cheng-i Wang, Jennifer Hsu, Shlomo Dubnov
NF1'14 MotivesExtractor PDF Oriol Nieto, Morwaread Farbood
Task Version audPoly
WHD1 VMO Motif Discovery PDF Cheng-i Wang, Jennifer Hsu, Shlomo Dubnov
WDH1 VMO Motif Discovery FML PDF Cheng-i Wang, Jennifer Hsu, Shlomo Dubnov
NF1'14 MotivesExtractor PDF Oriol Nieto, Morwaread Farbood

Table 1. Algorithms submitted to DRTS. Strong-performing algorithms from 2014 (submission codes ending '14) are included for the sake of comparisons.

Results in Brief

(For mathematical definitions of the various metrics, please see 2015:Discovery_of_Repeated_Themes_&_Sections#Evaluation_Procedure.)

Pesek, Leonardis, and Marolt (2015) submitted a compositional hierarchical model – applied to automatic chord recognition and F0-estimation previously (Pesek, Leonardis, & Marolt, 2014) – to the symMono version of the task. Given that their submission SYMCHM (PLM1) is a general-purpose algorithm for which pattern discovery is one application domain and that this is a popular version of the task (four algorithms submitted in 2014; seven in 2013), SYMCHM (PLM1) did well (Figs. 4-12). It was still not as strong as the previous best performer, VM2 (Velarde & Meredith, 2014), with regards discovering at least one occurrence of each ground truth pattern (Fig. 2): this algorithm, VM2, tested significantly stronger according to Friedman's test than PLM1 (\chi^2(1) = 8.1,\ p < .05, Bonferroni-corrected). Likewise, it was not as strong as the previous best performer, OL1 (Lartillot, 2014), with regards discovering all occurrences of a given ground truth pattern (Fig. 3): OL1 tested significantly stronger according to Friedman's test than PLM1 (\chi^2(1) = 10.71,\ p < .01, Bonferroni-corrected), but we should note that the decision to average results for OL1 on piece 5 could be driving this result. It should also be noted that the runtimes for PLM1 (Fig. 13) are somewhat harsh, because the Windows Virtual Machine on which it ran is considerably slower than the Linux machines on which the other submissions ran.

Wang, Hsu, and Dubnov (2015a, 2015b) submitted a motif discovery system based on a Variable Markov Oracle to audMono and audPoly versions of the task. On the audMono task this algorithm, WHD1, was not significantly different to NF1 according to Friedman's test (\chi^2(1) = .23,\ p = .631) at discovering at least one occurrence of each ground truth pattern (Fig. 14). Similarly, WHD1 was not significantly different to NF1 according to Friedman's test (\chi^2(1) = .89,\ p = .346) at discovering all occurrences of a given ground truth pattern (Fig. 15). These results suggest that WHD1 is on a par with state-of-the-art performance on the audMono task. Results for the audPoly task were similar, and WHD1 was significantly better than previous state-of-the-art performance (\chi^2(1) = 6.43,\ p =< .05) with regards discovering at least one occurrence of each ground truth pattern (Fig. 26). (To avoid a bias toward the more numerous submissions of Wang et al. (2015), WHD1 was preselected over WDH1 for comparison with Nieto and Farbood's (2014a) submission, based on performance for the Development Database.)

Discussion

Since this task began in 2013, it has been observed that the discovery of repeated sections tends to be addressed well by submissions, and the discovery of shorter themes/motifs less well. This in itself is not a particularly surprising observation, since it mirrors the way music analysts might agree on the large-scale repetitive structure of a song/piece, but differ in interpreting its themes and/or motifs. It was exciting to see, however, that WDH1 and WHD1 (Wang et al., 2015a, 2015b) had high establishment recall compared with previous years for seven- and nine-note patterns in piece 1, a five-note pattern in piece 2, and nine- and thirteen-note patterns in piece 4 (see Fig. 14 for details). Whereas WHD1's establishment recall dropped off for six- and nine-note patterns in piece 5, establishment recall remained comparatively high for WDH1. The difference between these submissions was a fixed minimum length (FML) criterion that applied to WDH1 but not to WHD1. The criterion seems to have helped WDH1 to perform well on this aspect of the task.

The PLM1 submission (Pesek et al., 2015) is of interest because it (1) is the first deep architecture to be submitted to the task and (2) has been applied to other MIR tasks such as chord and multi-F0 estimation (Pesek et al., 2014). It outperformed previous algorithms on piece 1 (see Figs. 4-6), demonstrating its potential, but had lower establishment recall for pieces 2-5 (see Fig. 4). For those who have called for multipurpose, integrated MIR solutions, this approach represents an encouraging development.

It is good to see submissions from two new groups this year, and that the emphasis the task places on retrieving and evaluating hierarchical structure is being acknowledged and championed elsewhere (McFee, Nieto, & Bello, 2015). Next year we may switch to new training and test databases that focus not directly on the discovery task itself, but on an application of pattern discovery that can be used as a proxy to evaluate the extent to which algorithms have retrieved relevant repetitive material. If you are interested in helping out with the preparation of a new version of the task, you are welcome to get in touch.

Tom Collins, Leicester, 2015

Results in Detail

symMono

(Submission OL1 did not complete on piece 5. The task captain took the decision to assign the mean of the evaluation metrics for OL1 calculated across the remaining pieces.)

11symMonoEstRecPerPatt2015.png

Figure 2. Establishment recall on a per-pattern basis. Establishment recall answers the following question. On average, how similar is the most similar algorithm-output pattern to a ground-truth pattern prototype?


14symMonoOccRecPerPatt2015.png

Figure 3. Occurrence recall on a per-pattern basis. Occurrence recall answers the following question. On average, how similar is the most similar set of algorithm-output pattern occurrences to a discovered ground-truth occurrence set?


11symMonoEstRec2015.png

Figure 4. Establishment recall averaged over each piece/movement. Establishment recall answers the following question. On average, how similar is the most similar algorithm-output pattern to a ground-truth pattern prototype?


12symMonoEstPrec2015.png

Figure 5. Establishment precision averaged over each piece/movement. Establishment precision answers the following question. On average, how similar is the most similar ground-truth pattern prototype to an algorithm-output pattern?


13symMonoEstF12015.png

Figure 6. Establishment F1 averaged over each piece/movement. Establishment F1 is an average of establishment precision and establishment recall.


14symMonoOccRecP752015.png

Figure 7. Occurrence recall (c = .75) averaged over each piece/movement. Occurrence recall answers the following question. On average, how similar is the most similar set of algorithm-output pattern occurrences to a discovered ground-truth occurrence set?


15symMonoOccPrecP752015.png

Figure 8. Occurrence precision (c = .75) averaged over each piece/movement. Occurrence precision answers the following question. On average, how similar is the most similar discovered ground-truth occurrence set to a set of algorithm-output pattern occurrences?


16symMonoOccF1P752015.png

Figure 9. Occurrence F1 (c = .75) averaged over each piece/movement. Occurrence F1 is an average of occurrence precision and occurrence recall.


17symMonoR32015.png

Figure 10. Three-layer recall averaged over each piece/movement. Rather than using |P \cap Q|/\max\{|P|, |Q|\} as a similarity measure (which is the default for establishment recall), three-layer recall uses 2|P \cap Q|/(|P| + |Q|), which is a kind of F1 measure.


18symMonoP32015.png

Figure 11. Three-layer precision averaged over each piece/movement. Rather than using |P \cap Q|/\max\{|P|, |Q|\} as a similarity measure (which is the default for establishment precision), three-layer precision uses 2|P \cap Q|/(|P| + |Q|), which is a kind of F1 measure.


19symMonoTLF2015.png

Figure 12. Three-layer F1 (TLF) averaged over each piece/movement. TLF is an average of three-layer precision and three-layer recall.


20symMonoRuntime2015.png

Figure 13. Log runtime of the algorithm for each piece/movement.

audMono

31audMonoEstRecPerPatt2015.png

Figure 14. Establishment recall on a per-pattern basis. Establishment recall answers the following question. On average, how similar is the most similar algorithm-output pattern to a ground-truth pattern prototype?


34audMonoOccRecPerPatt2015.png

Figure 15. Occurrence recall on a per-pattern basis. Occurrence recall answers the following question. On average, how similar is the most similar set of algorithm-output pattern occurrences to a discovered ground-truth occurrence set?


31audMonoEstRec2015.png

Figure 16. Establishment recall averaged over each piece/movement. Establishment recall answers the following question. On average, how similar is the most similar algorithm-output pattern to a ground-truth pattern prototype?


32audMonoEstPrec2015.png

Figure 17. Establishment precision averaged over each piece/movement. Establishment precision answers the following question. On average, how similar is the most similar ground-truth pattern prototype to an algorithm-output pattern?


33audMonoEstF12015.png

Figure 18. Establishment F1 averaged over each piece/movement. Establishment F1 is an average of establishment precision and establishment recall.


34audMonoOccRecP752015.png

Figure 19. Occurrence recall (c = .75) averaged over each piece/movement. Occurrence recall answers the following question. On average, how similar is the most similar set of algorithm-output pattern occurrences to a discovered ground-truth occurrence set?


35audMonoOccPrecP752015.png

Figure 20. Occurrence precision (c = .75) averaged over each piece/movement. Occurrence precision answers the following question. On average, how similar is the most similar discovered ground-truth occurrence set to a set of algorithm-output pattern occurrences?


36audMonoOccF1P752015.png

Figure 21. Occurrence F1 (c = .75) averaged over each piece/movement. Occurrence F1 is an average of occurrence precision and occurrence recall.


37audMonoR32015.png

Figure 22. Three-layer recall averaged over each piece/movement. Rather than using |P \cap Q|/\max\{|P|, |Q|\} as a similarity measure (which is the default for establishment recall), three-layer recall uses 2|P \cap Q|/(|P| + |Q|), which is a kind of F1 measure.


38audMonoP32015.png

Figure 23. Three-layer precision averaged over each piece/movement. Rather than using |P \cap Q|/\max\{|P|, |Q|\} as a similarity measure (which is the default for establishment precision), three-layer precision uses 2|P \cap Q|/(|P| + |Q|), which is a kind of F1 measure.


39audMonoTLF2015.png

Figure 24. Three-layer F1 (TLF) averaged over each piece/movement. TLF is an average of three-layer precision and three-layer recall.


40audMonoRuntime2015.png

Figure 25. Log runtime of the algorithm for each piece/movement.

audPoly

21audPolyEstRecPerPatt2015.png

Figure 26. Establishment recall on a per-pattern basis. Establishment recall answers the following question. On average, how similar is the most similar algorithm-output pattern to a ground-truth pattern prototype?


24audPolyOccRecPerPatt2015.png

Figure 27. Occurrence recall on a per-pattern basis. Occurrence recall answers the following question. On average, how similar is the most similar set of algorithm-output pattern occurrences to a discovered ground-truth occurrence set?


21audPolyEstRec2015.png

Figure 28. Establishment recall averaged over each piece/movement. Establishment recall answers the following question. On average, how similar is the most similar algorithm-output pattern to a ground-truth pattern prototype?


22audPolyEstPrec2015.png

Figure 29. Establishment precision averaged over each piece/movement. Establishment precision answers the following question. On average, how similar is the most similar ground-truth pattern prototype to an algorithm-output pattern?


23audPolyEstF12015.png

Figure 30. Establishment F1 averaged over each piece/movement. Establishment F1 is an average of establishment precision and establishment recall.


24audPolyOccRecP752015.png

Figure 31. Occurrence recall (c = .75) averaged over each piece/movement. Occurrence recall answers the following question. On average, how similar is the most similar set of algorithm-output pattern occurrences to a discovered ground-truth occurrence set?


25audPolyOccPrecP752015.png

Figure 32. Occurrence precision (c = .75) averaged over each piece/movement. Occurrence precision answers the following question. On average, how similar is the most similar discovered ground-truth occurrence set to a set of algorithm-output pattern occurrences?


26audPolyOccF1P752015.png

Figure 33. Occurrence F1 (c = .75) averaged over each piece/movement. Occurrence F1 is an average of occurrence precision and occurrence recall.


27audPolyR32015.png

Figure 34. Three-layer recall averaged over each piece/movement. Rather than using |P \cap Q|/\max\{|P|, |Q|\} as a similarity measure (which is the default for establishment recall), three-layer recall uses 2|P \cap Q|/(|P| + |Q|), which is a kind of F1 measure.


28audPolyP32015.png

Figure 35. Three-layer precision averaged over each piece/movement. Rather than using |P \cap Q|/\max\{|P|, |Q|\} as a similarity measure (which is the default for establishment precision), three-layer precision uses 2|P \cap Q|/(|P| + |Q|), which is a kind of F1 measure.


29audPolyTLF2015.png

Figure 36. Three-layer F1 (TLF) averaged over each piece/movement. TLF is an average of three-layer precision and three-layer recall.


30audPolyRuntime2015.png

Figure 37. Log runtime of the algorithm for each piece/movement.

Tabular Versions of Plots

symMono

AlgIdx AlgStub Piece n_P n_Q P_est R_est F1_est P_occ(c=.75) R_occ(c=.75) F_1occ(c=.75) P_3 R_3 TLF_1 runtime FRT FFTP_est FFP P_occ(c=.5) R_occ(c=.5) F_1occ(c=.5) P R F_1
1 PLM1 piece1 5 18.000 0.700 0.731 0.715 0.726 0.419 0.531 0.378 0.499 0.430 29100.000 0.000 0.480 0.294 0.579 0.433 0.495 0.000 0.000 0.000
1 PLM1 piece2 5 31.000 0.209 0.454 0.286 0.755 0.505 0.605 0.222 0.413 0.289 19260.000 0.000 0.174 0.177 0.670 0.573 0.617 0.032 0.200 0.056
1 PLM1 piece3 10.000 8 0.426 0.277 0.336 0.834 0.695 0.758 0.501 0.305 0.379 180.000 0.000 0.242 0.505 0.834 0.695 0.758 0.000 0.000 0.000
1 PLM1 piece4 8 2 0.967 0.277 0.431 0.967 0.967 0.967 0.983 0.273 0.428 660.000 0.000 0.277 0.983 0.967 0.967 0.967 0.500 0.125 0.200
1 PLM1 piece5 13.000 35.000 0.366 0.331 0.348 0.785 0.406 0.535 0.354 0.372 0.363 69240.000 0.000 0.103 0.226 0.617 0.456 0.525 0.000 0.000 0.000
2 OL1_14 piece1 5 114.000 0.660 0.635 0.647 0.827 0.509 0.630 0.295 0.498 0.370 14013.284 0.000 0.368 0.389 0.723 0.559 0.630 0.009 0.200 0.017
2 OL1_14 piece2 5 98.000 0.117 0.737 0.202 0.842 0.868 0.855 0.148 0.611 0.238 126065.856 0.000 0.277 0.440 0.750 0.709 0.729 0.020 0.400 0.039
2 OL1_14 piece3 10.000 9 0.739 0.467 0.573 0.897 0.695 0.783 0.625 0.466 0.534 1751.959 0.000 0.348 0.622 0.728 0.608 0.663 0.111 0.100 0.105
2 OL1_14 piece4 8 4 0.950 0.405 0.568 0.950 0.967 0.958 0.974 0.400 0.567 204.197 0.000 0.405 0.974 0.950 0.967 0.958 0.500 0.250 0.333
2 OL1_14 piece5 13.000 56.250 0.617 0.561 0.498 0.879 0.760 0.807 0.510 0.494 0.427 35508.820 0.000 0.350 0.606 0.788 0.711 0.745 0.160 0.237 0.124
3 VM2_14 piece1 5 5 0.540 0.570 0.555 0.000 0.000 0.000 0.286 0.207 0.240 18.906 0.000 0.570 0.286 0.291 0.490 0.365 0.000 0.000 0.000
3 VM2_14 piece2 5 7 0.446 0.761 0.562 0.649 0.863 0.741 0.357 0.488 0.413 34.308 0.000 0.419 0.128 0.427 0.630 0.509 0.143 0.200 0.167
3 VM2_14 piece3 10.000 7 0.690 0.521 0.594 0.865 0.441 0.584 0.609 0.471 0.531 3.570 0.000 0.393 0.541 0.662 0.561 0.607 0.000 0.000 0.000
3 VM2_14 piece4 8 6 0.842 0.765 0.802 0.579 0.837 0.684 0.732 0.504 0.597 5.942 0.000 0.721 0.711 0.410 0.732 0.525 0.167 0.125 0.143
3 VM2_14 piece5 13.000 7 0.739 0.540 0.624 0.910 0.781 0.841 0.677 0.434 0.529 38.698 0.000 0.420 0.554 0.517 0.636 0.570 0.000 0.000 0.000

download these results as csv

Table 2. Tabular version of Figures 4-13.


AlgIdx AlgStub Piece n_P R_est R_occ(c=.75) R_occ(c=.5)
1 PLM1 piece1 5
0.941 1.000 0.312 0.600 0.800
0.614 0.410 0.000 0.000 0.267
0.614 0.410 0.000 0.000 0.267
1 PLM1 piece2 5
0.800 0.812 0.300 0.244 0.114
0.300 0.709 0.000 0.000 0.000
0.300 0.709 0.000 0.000 0.000
1 PLM1 piece3 10.000
0.409 0.442 0.846 0.227 0.361 0.263 0.222 0.000 0.000 0.000
0.00000 0.000 0.695 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.00000 0.000 0.695 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1 PLM1 piece4 8
0.00000 0.000 0.000 0.286 0.933 1.000 0.000 0.000
0.00000 0.000 0.000 0.000 0.933 1.000 0.000 0.000
0.00000 0.000 0.000 0.000 0.933 1.000 0.000 0.000
1 PLM1 piece5 13.000
0.255 0.193 0.117 0.079 0.545 0.357 0.417 0.155 0.177 0.829 0.591 0.342 0.246
0.00000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.406 0.000 0.000 0.000
0.00000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.406 0.000 0.000 0.000
2 OL1_14 piece1 5
1.00000 0.964 0.137 0.140 0.933
0.688 0.226 0.000 0.000 0.578
0.688 0.226 0.000 0.000 0.578
2 OL1_14 piece2 5
0.727 0.812 0.273 0.936 0.934
0.00000 0.734 0.000 0.936 0.934
0.00000 0.734 0.000 0.936 0.934
2 OL1_14 piece3 10.000
0.632 0.735 0.929 0.263 0.579 0.289 0.053 0.645 0.350 0.200
0.00000 0.000 0.695 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.00000 0.000 0.695 0.000 0.000 0.000 0.000 0.000 0.000 0.000
2 OL1_14 piece4 8
0.00000 0.000 0.000 0.308 0.933 1.000 0.000 1.000
0.00000 0.000 0.000 0.000 0.933 1.000 0.000 1.000
0.00000 0.000 0.000 0.000 0.933 1.000 0.000 1.000
2 OL1_14 piece5 13.000
0.528 0.528 0.528 0.528 0.528 0.528 0.528 0.528 0.528 0.528 0.528 0.528 0.528
0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276
0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276
3 VM2_14 piece1 5
0.727 0.719 0.625 0.111 0.667
0.00000 0.000 0.000 0.000 0.000
0.00000 0.000 0.000 0.000 0.000
3 VM2_14 piece2 5
0.538 0.812 0.600 0.920 0.934
0.00000 0.734 0.000 0.920 0.934
0.00000 0.734 0.000 0.920 0.934
3 VM2_14 piece3 10.000
0.786 0.744 0.962 0.278 0.395 0.360 0.250 0.677 0.571 0.190
0.384 0.000 0.498 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.384 0.000 0.498 0.000 0.000 0.000 0.000 0.000 0.000 0.000
3 VM2_14 piece4 8
0.667 0.571 0.600 1.000 1.000 0.714 0.800 0.769
0.00000 0.000 0.000 0.911 1.000 0.000 0.733 0.769
0.00000 0.000 0.000 0.911 1.000 0.000 0.733 0.769
3 VM2_14 piece5 13.000
0.609 0.087 0.974 0.982 0.633 0.600 0.333 0.111 0.084 0.800 0.667 0.652 0.488
0.00000 0.000 0.974 0.982 0.000 0.000 0.000 0.000 0.000 0.388 0.000 0.000 0.000
0.00000 0.000 0.974 0.982 0.000 0.000 0.000 0.000 0.000 0.388 0.000 0.000 0.000

download these results as csv

Table 3. Tabular version of Figures 2 and 3.

audMono

AlgIdx AlgStub Piece n_P n_Q P_est R_est F1_est P_occ(c=.75) R_occ(c=.75) F_1occ(c=.75) P_3 R_3 TLF_1 runtime FRT FFTP_est FFP P_occ(c=.5) R_occ(c=.5) F_1occ(c=.5) P R F_1
1 WHD1 piece1 5 131.000 0.250 0.651 0.362 0.506 0.133 0.211 0.098 0.338 0.152 845.000 0.000 0.089 0.112 0.416 0.213 0.282 0.000 0.000 0.000
1 WHD1 piece2 5 3 0.612 0.339 0.436 0.956 0.956 0.956 0.708 0.356 0.474 244.000 0.000 0.339 0.708 0.754 0.754 0.754 0.000 0.000 0.000
1 WHD1 piece3 10.000 7 0.611 0.402 0.485 0.000 0.000 0.000 0.562 0.399 0.467 92.000 0.000 0.344 0.551 0.603 0.486 0.538 0.000 0.000 0.000
1 WHD1 piece4 8 88.000 0.301 0.800 0.438 0.601 0.331 0.427 0.157 0.609 0.250 251.000 0.000 0.257 0.278 0.523 0.291 0.373 0.023 0.250 0.042
1 WHD1 piece5 13.000 3 0.644 0.221 0.329 0.947 0.947 0.947 0.743 0.231 0.353 519.000 0.000 0.221 0.743 0.821 0.821 0.821 0.000 0.000 0.000
2 WDH1 piece1 5 56.000 0.326 0.629 0.429 0.506 0.133 0.211 0.130 0.299 0.181 852.000 0.000 0.436 0.240 0.464 0.203 0.283 0.000 0.000 0.000
2 WDH1 piece2 5 11.000 0.307 0.494 0.379 0.956 0.956 0.956 0.258 0.419 0.319 243.000 0.000 0.317 0.268 0.754 0.754 0.754 0.000 0.000 0.000
2 WDH1 piece3 10.000 13.000 0.596 0.530 0.561 1.000 0.214 0.353 0.471 0.441 0.456 92.000 0.000 0.265 0.475 0.538 0.381 0.446 0.000 0.000 0.000
2 WDH1 piece4 8 45.000 0.312 0.800 0.448 0.815 0.536 0.647 0.206 0.609 0.308 259.000 0.000 0.208 0.247 0.706 0.458 0.555 0.044 0.250 0.075
2 WDH1 piece5 13.000 23.000 0.511 0.593 0.549 0.829 0.468 0.598 0.395 0.469 0.429 518.000 0.000 0.251 0.444 0.663 0.355 0.462 0.000 0.000 0.000
3 NF1_14 piece1 5 5 0.710 0.433 0.538 0.375 0.124 0.186 0.150 0.114 0.129 536.000 0.000 0.433 0.150 0.344 0.130 0.189 0.000 0.000 0.000
3 NF1_14 piece2 5 12.000 0.459 0.602 0.520 0.423 0.423 0.423 0.163 0.242 0.195 71.000 0.000 0.351 0.171 0.457 0.187 0.266 0.000 0.000 0.000
3 NF1_14 piece3 10.000 17.000 0.676 0.564 0.615 0.590 0.268 0.368 0.325 0.325 0.325 77.000 0.000 0.429 0.376 0.428 0.260 0.323 0.000 0.000 0.000
3 NF1_14 piece4 8 13.000 0.695 0.723 0.709 0.770 0.328 0.460 0.492 0.519 0.505 238.000 0.000 0.330 0.398 0.664 0.379 0.482 0.077 0.125 0.095
3 NF1_14 piece5 13.000 23.000 0.387 0.352 0.369 0.000 0.000 0.000 0.196 0.203 0.199 1598.000 0.000 0.258 0.218 0.365 0.147 0.210 0.000 0.000 0.000

download these results as csv

Table 4. Taublar version of Figures 16-25.


AlgIdx AlgStub Piece n_P R_est R_occ(c=.75) R_occ(c=.5)
1 WHD1 piece1 5
0.647 0.684 0.667 0.444 0.812
0.00000 0.000 0.000 0.000 0.133
0.00000 0.000 0.000 0.000 0.133
1 WHD1 piece2 5
0.058 0.104 0.019 0.552 0.960
0.00000 0.000 0.000 0.000 0.956
0.00000 0.000 0.000 0.000 0.956
1 WHD1 piece3 10.000
0.353 0.729 0.654 0.294 0.500 0.324 0.091 0.613 0.292 0.167
0.00000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.00000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1 WHD1 piece4 8
1.00000 0.286 0.400 1.000 0.933 1.000 0.778 1.000
0.250 0.000 0.000 0.146 0.933 0.889 0.778 1.000
0.250 0.000 0.000 0.146 0.933 0.889 0.778 1.000
1 WHD1 piece5 13.000
0.060 0.019 0.947 0.697 0.057 0.042 0.015 0.017 0.021 0.152 0.049 0.308 0.487
0.00000 0.000 0.947 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.00000 0.000 0.947 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
2 WDH1 piece1 5
0.647 0.684 0.667 0.333 0.812
0.00000 0.000 0.000 0.000 0.133
0.00000 0.000 0.000 0.000 0.133
2 WDH1 piece2 5
0.348 0.438 0.174 0.552 0.960
0.00000 0.000 0.000 0.000 0.956
0.00000 0.000 0.000 0.000 0.956
2 WDH1 piece3 10.000
0.538 0.729 0.654 1.000 0.500 0.324 0.200 0.613 0.571 0.167
0.00000 0.000 0.000 0.214 0.000 0.000 0.000 0.000 0.000 0.000
0.00000 0.000 0.000 0.214 0.000 0.000 0.000 0.000 0.000 0.000
2 WDH1 piece4 8
1.00000 0.286 0.400 1.000 0.933 1.000 0.778 1.000
0.250 0.000 0.000 0.146 0.933 0.889 0.778 1.000
0.250 0.000 0.000 0.146 0.933 0.889 0.778 1.000
2 WDH1 piece5 13.000
0.857 0.889 0.947 0.697 0.417 0.400 0.500 0.529 0.600 0.757 0.250 0.385 0.487
0.446 0.220 0.947 0.000 0.000 0.000 0.000 0.000 0.000 0.277 0.000 0.000 0.000
0.446 0.220 0.947 0.000 0.000 0.000 0.000 0.000 0.000 0.277 0.000 0.000 0.000
3 NF1_14 piece1 5
0.895 0.844 0.123 0.000 0.306
0.075 0.148 0.000 0.000 0.000
0.075 0.148 0.000 0.000 0.000
3 NF1_14 piece2 5
0.727 0.625 0.300 0.846 0.509
0.00000 0.000 0.000 0.423 0.000
0.00000 0.000 0.000 0.423 0.000
3 NF1_14 piece3 10.000
0.929 0.721 0.808 0.545 0.421 0.579 0.222 0.645 0.500 0.267
0.231 0.000 0.322 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.231 0.000 0.322 0.000 0.000 0.000 0.000 0.000 0.000 0.000
3 NF1_14 piece4 8
1.00000 0.857 0.000 1.000 1.000 0.571 0.667 0.692
0.250 0.214 0.000 0.167 0.917 0.000 0.000 0.000
0.250 0.214 0.000 0.167 0.917 0.000 0.000 0.000
3 NF1_14 piece5 13.000
0.400 0.250 0.194 0.195 0.421 0.485 0.121 0.176 0.321 0.557 0.457 0.615 0.385
0.00000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.00000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

download these results as csv

Table 5. Tabular version of Figures 14 and 15.

audPoly

AlgIdx AlgStub Piece n_P n_Q P_est R_est F1_est P_occ(c=.75) R_occ(c=.75) F_1occ(c=.75) P_3 R_3 TLF_1 runtime FRT FFTP_est FFP P_occ(c=.5) R_occ(c=.5) F_1occ(c=.5) P R F_1
1 WHD1 piece1 5 89.000 0.296 0.406 0.342 0.000 0.000 0.000 0.098 0.160 0.121 121.000 0.000 0.200 0.118 0.399 0.091 0.148 0.000 0.000 0.000
1 WHD1 piece2 5 2 0.967 0.410 0.576 0.966 0.966 0.966 0.967 0.405 0.571 275.000 0.000 0.410 0.967 0.966 0.966 0.966 0.000 0.000 0.000
1 WHD1 piece3 10.000 5 0.670 0.414 0.512 0.865 0.865 0.865 0.668 0.426 0.521 84.000 0.000 0.414 0.668 0.664 0.511 0.577 0.000 0.000 0.000
1 WHD1 piece4 5 33.000 0.353 0.570 0.436 0.670 0.451 0.539 0.193 0.401 0.261 55.000 0.000 0.311 0.313 0.506 0.264 0.347 0.000 0.000 0.000
1 WHD1 piece5 13.000 4 0.581 0.243 0.342 0.950 0.950 0.950 0.675 0.265 0.381 584.000 0.000 0.243 0.675 0.686 0.585 0.631 0.000 0.000 0.000
2 WDH1 piece1 5 110.000 0.305 0.413 0.351 0.000 0.000 0.000 0.097 0.170 0.124 124.000 0.000 0.200 0.118 0.354 0.109 0.167 0.000 0.000 0.000
2 WDH1 piece2 5 10.000 0.389 0.562 0.459 0.966 0.966 0.966 0.276 0.464 0.346 270.000 0.000 0.281 0.247 0.600 0.523 0.559 0.000 0.000 0.000
2 WDH1 piece3 10.000 14.000 0.572 0.562 0.567 0.865 0.865 0.865 0.445 0.465 0.455 84.000 0.000 0.356 0.566 0.521 0.356 0.423 0.000 0.000 0.000
2 WDH1 piece4 5 7 0.335 0.261 0.293 0.804 0.804 0.804 0.214 0.229 0.221 57.000 0.000 0.261 0.300 0.589 0.444 0.506 0.000 0.000 0.000
2 WDH1 piece5 13.000 16.000 0.529 0.466 0.495 0.950 0.950 0.950 0.475 0.405 0.437 545.000 0.000 0.253 0.493 0.674 0.453 0.542 0.000 0.000 0.000
3 NF1_14 piece1 5 1 0.168 0.108 0.132 0.000 0.000 0.000 0.095 0.064 0.076 118.000 0.000 0.108 0.095 0.000 0.000 0.000 0.000 0.000 0.000
3 NF1_14 piece2 5 12.000 0.323 0.509 0.395 0.408 0.408 0.408 0.145 0.236 0.180 80.000 0.000 0.410 0.254 0.493 0.288 0.363 0.000 0.000 0.000
3 NF1_14 piece3 10.000 10.000 0.645 0.524 0.578 0.393 0.297 0.338 0.394 0.323 0.355 122.000 0.000 0.354 0.399 0.438 0.285 0.345 0.000 0.000 0.000
3 NF1_14 piece4 5 1 0.895 0.193 0.317 0.817 0.817 0.817 0.897 0.203 0.332 31.000 0.000 0.193 0.897 0.817 0.817 0.817 0.000 0.000 0.000
3 NF1_14 piece5 13.000 12.000 0.428 0.344 0.382 0.000 0.000 0.000 0.215 0.183 0.198 1096.000 0.000 0.303 0.243 0.362 0.200 0.258 0.000 0.000 0.000

download these results as csv

Table 8. Tabular version of Figures 28-37.


AlgIdx AlgStub Piece n_P R_est R_occ(c=.75) R_occ(c=.5)
1 WHD1 piece1 5
0.647 0.567 0.143 0.189 0.484
0.00000 0.000 0.000 0.000 0.000
0.00000 0.000 0.000 0.000 0.000
1 WHD1 piece2 5
0.016 0.095 0.006 0.953 0.980
0.00000 0.000 0.000 0.953 0.978
0.00000 0.000 0.000 0.953 0.978
1 WHD1 piece3 10.000
0.415 0.869 0.688 0.526 0.214 0.149 0.119 0.624 0.333 0.205
0.00000 0.865 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.00000 0.865 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1 WHD1 piece4 5
0.714 0.250 0.333 0.750 0.804
0.00000 0.000 0.000 0.098 0.804
0.00000 0.000 0.000 0.098 0.804
1 WHD1 piece5 13.000
0.250 0.118 0.950 0.533 0.056 0.050 0.015 0.024 0.015 0.162 0.056 0.360 0.566
0.00000 0.000 0.950 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.00000 0.000 0.950 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
2 WDH1 piece1 5
0.529 0.567 0.182 0.189 0.600
0.00000 0.000 0.000 0.000 0.000
0.00000 0.000 0.000 0.000 0.000
2 WDH1 piece2 5
0.200 0.574 0.100 0.953 0.980
0.00000 0.000 0.000 0.953 0.978
0.00000 0.000 0.000 0.953 0.978
2 WDH1 piece3 10.000
0.537 0.869 0.688 0.727 0.275 0.489 0.471 0.624 0.520 0.423
0.00000 0.865 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.00000 0.865 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
2 WDH1 piece4 5
0.00000 0.000 0.000 0.500 0.804
0.00000 0.000 0.000 0.000 0.804
0.00000 0.000 0.000 0.000 0.804
2 WDH1 piece5 13.000
0.733 0.312 0.950 0.533 0.571 0.371 0.101 0.486 0.015 0.746 0.312 0.360 0.566
0.00000 0.000 0.950 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.00000 0.000 0.950 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
3 NF1_14 piece1 5
0.119 0.168 0.046 0.069 0.138
0.00000 0.000 0.000 0.000 0.000
0.00000 0.000 0.000 0.000 0.000
3 NF1_14 piece2 5
0.438 0.617 0.158 0.815 0.516
0.00000 0.000 0.000 0.408 0.000
0.00000 0.000 0.000 0.408 0.000
3 NF1_14 piece3 10.000
0.436 0.688 0.639 0.395 0.574 0.787 0.178 0.793 0.480 0.271
0.00000 0.000 0.000 0.000 0.000 0.098 0.000 0.396 0.000 0.000
0.00000 0.000 0.000 0.000 0.000 0.098 0.000 0.396 0.000 0.000
3 NF1_14 piece4 5
0.00000 0.000 0.000 0.070 0.895
0.00000 0.000 0.000 0.000 0.817
0.00000 0.000 0.000 0.000 0.817
3 NF1_14 piece5 13.000
0.439 0.203 0.526 0.657 0.296 0.329 0.084 0.125 0.161 0.649 0.057 0.533 0.415
0.00000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.00000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

download these results as csv

Table 9. Tabular version of Figures 26 and 27.

References

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  • Siglind Bruhn. (1993). J.S. Bach's Well-Tempered Clavier: in-depth analysis and interpretation. Mainer International, Hong Kong.
  • Tom Collins, Sebastian Böck, Florian Krebs, and Gerhard Widmer. (2014). Bridging the audio-symbolic gap: the discovery of repeated note content directly from polyphonic music audio. In Proc. Audio Engineering Society's 53rd Conference on Semantic Audio, London, UK.
  • William Drabkin. Motif. (2001). In S. Sadie and J. Tyrrell (Eds), The new Grove dictionary of music and musicians. Macmillan, London, UK, 2nd ed.
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  • Oriol Nieto and Morwaread Farbood. (2014b). Identifying polyphonic musical patterns from audio recordings using music segmentation techniques. In Proc. ISMIR, Taipei, Taiwan.
  • Oriol Nieto and Morwaread Farbood. (2013). Discovering musical patterns using audio structural segmentation techniques. 9th Annual Music Information Retrieval eXchange (MIREX'13), Curitiba, Brazil.
  • Matevz Pesek, Ales Leonardis, and Matija Marolt. (2015). Submission to MIREX Discovery of Repeated Themes and Sections. 11th Annual Music Information Retrieval eXchange (MIREX'15), Malaga, Spain.
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  • Arnold Schoenberg. (1967). Fundamentals of Musical Composition. Faber and Faber, London.
  • Gissel Velarde and David Meredith. (2014). Submission to MIREX Discovery of Repeated Themes and Sections. 10th Annual Music Information Retrieval eXchange (MIREX'14), Taipei, Taiwan.
  • Cheng-i Wang, Jennifer Hsu, and Shlomo Dubnov. (2015a). Submission to MIREX Discovery of Repeated Themes and Sections. 11th Annual Music Information Retrieval eXchange (MIREX'15), Malaga, Spain.
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