1. Learning to analyse tonal music Pl á cido Rom á n Illescas David Rizo Jos é Manuel I ñ esta Pattern recognition and Artificial Intelligence group University of Alicante Helsinki; 9th July, 2008

2. MML’08 Tonal analysis Musical analysis is a mean to better understand the thought of the composer when creating a piece Key: Bm composed How should it be played? Understanding it through analysis Sequence of notes  sequence of chords Chord has a Tonal Function: { T | D | SD } Equivalent in NLP to Syntax analysis Tonal function = {tension | relaxation}

3. MML’08Objectives To analyze a musical piece To get good correct analysis percentages describing the solution in a human-readable way To integrate harmonic analysis in other MIR and e-learning systems Automatic composition Expressive automatic performance Score reduction Pitch spelling Harmonic comparison of works Applications

4. MML’08 State of the art GrammarsWinograd 1968 / 1992: no melodic analysis Chemilier 2004, Steedman 1984: jazz chord progressions Expert systemsMaxwell 1992: problem with arpeggiated chords Probabilistic modelsRaphael 2004: no human readable explanation of solution Preference rulesTemperley 1999: errors in analysis Scoring techniquesPardo 2002: no tonal functions Neural networksHornel 1996: no human readable explanation of solution Model matchingTaube 1999: discontinued

5. MML’08Methodology

6. 1st: melodic analysis Target: get notes tagged as HT (harmonic tone) or NHT (non- harmonic tone) Rules system based on music theory Rules summary

7. MML’08 2nd: Key filtering w0w0 w1w1 w2w2 w3w3 w4w4 w5w5 w6w6 w7w7 w8w8 Split into time frames Remove the keys that do not match an expected semitones table Semitone differences from the tonic of the specified degree (the (1) value represents the Neapolitan, the (4) represents the Picardy ending)

8. MML’08 3rd. Weighted acyclic directed graph 3.1: Chord extraction Extract all possible chords for each time frame. Use backtracking to get all valid succesions of thirds 3 3

9. MML’08 3rd. Weighted acyclic directed graph

10. MML’08 3rd. Weighted acyclic directed graph etc. Extract of the actual graph 3.2: Construction of weighted acyclic directed graph Nodes are valid combinations of key+chord+tonal function for a time frame

11. MML’08 Edges correspond to cadences. Dashed lines represent invalid cadences. Weights are set according to the progression 3rd. Weighted acyclic directed graph Dynamic programming: get best path

12. MML’08Weights System performance is determined by a correct weight tuning Two approaches: – To use domain knowledge to set the weights As reported in a previous work (ICMC’07) – To learn the weights using a machine learning algorithm: genetic algorithm approach The approach presented here (MML’08)

13. MML’08 Genetic algorithm Chromosome: 1 gene for each weight – 25 genes, integer range [  3000, 1000] Fitness function – minimize number of incorrectly analyzed windows – ground-truth of 6 Bach chorales (BWV-253, 26, 437, 29, 272, and 438) Total: 832 time windows 300 iterations Iterations Fitness

14. MML’08 Output of trained system

15. MML’08Experiments Domain knowledge weights vs. Learnt weights – Tonal Function (TF) and Tonality (T) success rates Without GAWith GA TF (%)T (%)TF (%)T (%) BWV-2680548673 BWV-27261216650 BWV-2979507750 BWV-25379156420 BWV-43771567072 BWV-43872716186 Better TF than T suggests errors in tonality mode

16. MML’08Conclusion The system with weights learnt from data – avoids the arbitrariness or subjectivity of human expert – could learn different models for different styles Future works: – To build a larger tagged corpus to learn graph weights – To learn the model using examples from other genres – To construct chords from sequences of notes to cope with arpeggiated chords and monodies