1. Tree structured representation of music for polyphonic music information retrieval David Rizo Departament of Software and Computing Systems University of Alicante

2. Funciona muy bien Muchas gracias por vuestra antención

3. Tree construction process (Rizo et al. ’03)  Based on the logarithmic nature of music notation  Each tree level is a subdivision of the upper level whole4 beats half2+2 quarter 4×1 8×½8×½eighth  Leaf labels can be any pitch magnitude  Rests are coded the same way as notes  Duration is implicitly coded in the tree structure......... F C EG 1 4/4 bar Initial time Duration Tree representation for monodies

4.  The complete melody is a forest  Bars can be grouped sequentially or hierarchically F C E G Inner nodes need to be labelled Rules for label propagation and for pruning less relevant branches Tree construction process A B C G Sequential grouping: CEGFABCG Tree representation for monodies

5. The distance is computed as the cost of the operations to transform one tree into the other. TREE EDIT DISTANCE TREE EDIT DISTANCE (Zhang & Shasha, 1989) C G C A A C C C G C A C C A A t1t1 t2t2 d(t 1,t 2 ) Weighted operations of insertion deletion replacement Melodic similarity metrics Tree edit distance  O( |T 1 |  |T 2 |  h(T 1 )  h(T 2 ) ) Previous prunning process helps to overcome this complexity (Zhang & Shasha, “Simple fast algorithms for the editing distance between trees...”. SIAM J Comput., 8(6): 1245-1262. 1989) Tree representation for monodies

6. Tree representation  Use key information of the melody in the labels: interval from tonic  Propagation of keys based on melodic rules (P.Roman et al. ICMC’07)  Development of algorithms to learn the tree edit distances costs European network of excelence (Pascal) project: “Pump Priming. Learning Stochastic Edit Distances from Structured Data: Application in Music Retrieval” Current work

7. Part II Tree model of symbolic music for tonality guessing

8. Polyphonic tree representation Recall tree representation. Process repeated for each voice {C,G} {C} {F} C F CG G E {G} {C,G,E}{C,G,E} {C,F,G}{C,F,G} {C,E,F,G}

9. Polyphonic tree representation Better tree summarization: Use harmonic profiles + rhythmic weights  Multiset E.g. Applying rhythmic weight = 1/level {C=0.5,E=0.5,G=0.5} {C=0.25} {F=0.25} {C=0.25,F=0.25,G=0.5} {C=0.75,E=0.5,F=0.25,G=1} Krumhansl-Schmuckler profiles multiply the rhythmic weight: worse results

10. Polyphonic tree representation Whole song representation for comparison – Ordered forest with a tree for each bar 0.5| 1|0 ….0.3|0|0.3…1|10|0|0.5|…0|1….0|0|1|0.3|…1|0|0.2|…..... Bar 1Bar 2Bar 3Bar 4Bar N Layers distance: -Let  be a tree level ot tree T, compose a sequence S  (T) with all nodes at that level in the forest -Distance between 2 songs A and B at a level  d(A,B,  a,  b )= stringDistance(S  a (A), S  b (B)) -Global distance d(A,B) = min 0  i , 0  j  d(A,B,i,j) Complexity: O(|bars A | * |bars B | *  2 ) Also other measures: LCS Shasha tree edit distance Selkow tree edit distance Drawback: - metered music required - use Melisma to get bars from unmetered music SaSa

11. Label substitution cost

12. Graphical representations P1, P2, P3 algorithms from Ukkonen, Lemstr ö m, Makinen ‘ 03 P2v5, P2v6: indexed versions of P2 – Not published yet

13. Classifier combination

14. Experiments Different corpora: – Helsinki: 7 different polyphonic tunes Covers made up of polyphonic piano files + “Band in a box” variations 68 files – Theme_variations_classical Bach Goldberg variations Bach english suites variations Some Tchaikowsky variations 78 files, all polyphonic – Corpus1000_with_queries MIDI files downloaded from internet 80 files, almost all polyphonic, some monophonic Leave one out – Avoid very good / bad queries

15. Results Corpus ICPS

16. Corpus Helsinki Results

17. Results Corpus Theme Variations Classical

18. Results

19. Conclusions and future (current) work Tree methods are 24 times faster when the tonality is known: they are also more accurate Very hard task when MIDI files are real ones – Preprocess songs: Use automatic tonal analysis + trees to remove non- important notes in songs Improve results by combining different classifiers Tune the tree comparison measures – Current learnt similarity measures Add LCS fast implementation from Hyyrö ‘04 Add confidence values to LCS Add the G.Valiente bottom-up tree edit distance Query MIDI