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Similarity Measures for Rhythmic Sequences

Joao Martins Marcelo Gimenes J ô natas Manzolli Adolfo Maia Jr. Future Music Lab – University of Plymouth NICS – UNICAMP. Similarity Measures for Rhythmic Sequences. INTRODUCTION SCV EXAMPLES APPLICATIONS CONCLUSIONS. Outline ¦ Scope ¦ Other Measures. INTRODUCTION SCV EXAMPLES

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Similarity Measures for Rhythmic Sequences

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  1. Joao MartinsMarcelo GimenesJônatas Manzolli Adolfo Maia Jr. Future Music Lab – University of PlymouthNICS – UNICAMP Similarity Measures for Rhythmic Sequences 10º Simpósio Brasileiro de Computação Musical (SBCM2005)

  2. INTRODUCTIONSCVEXAMPLESAPPLICATIONSCONCLUSIONS Outline ¦ Scope¦ Other Measures • INTRODUCTION • SCV • EXAMPLES • APPLICATIONS • CONCLUSIONS 10º Simpósio Brasileiro de Computação Musical (SBCM2005)

  3. INTRODUCTIONSCVEXAMPLESAPPLICATIONSCONCLUSIONS Outline¦ Scope ¦ Other Measures • Similarity measures are fundamental in music information retrieval and play one of the most important roles in Artificial Intelligence towards the establishment of fitness functions. • The aim is to create a similarity measure for rhythmic sequences that can capture patterns in several hierarchical levels, spanning from a small rhythmic phrase to longer structures. 10º Simpósio Brasileiro de Computação Musical (SBCM2005)

  4. INTRODUCTIONSCVEXAMPLESAPPLICATIONSCONCLUSIONS Outline¦ Scope¦ Other Measures • Euclidean distance • Levenshtein distance • Mongeau and Sankoff (1990) 10º Simpósio Brasileiro de Computação Musical (SBCM2005)

  5. INTRODUCTIONSCVEXAMPLESAPPLICATIONSCONCLUSIONS Representation¦ Similarity Coefficient Vector ¦ Model • Representation of rhythmic sequences previously quantized discarding expressive timing info • Shmulevich, I. and Povel, D. (2000) 10º Simpósio Brasileiro de Computação Musical (SBCM2005)

  6. INTRODUCTIONSCVEXAMPLESAPPLICATIONSCONCLUSIONS Representation¦ Similarity Coefficient Vector ¦ Model • Similarity Coefficient Vector (SCV) • This vector is a measure of similarity between all the subsequences • It is built counting the sparsity of a distances matrix for a given k-level 10º Simpósio Brasileiro de Computação Musical (SBCM2005)

  7. INTRODUCTIONSCVEXAMPLESAPPLICATIONSCONCLUSIONS Representation¦ Similarity Coefficient Vector ¦ Model • Diagram 10º Simpósio Brasileiro de Computação Musical (SBCM2005)

  8. INTRODUCTIONMODELExamplesAPPLICATIONSCONCLUSIONS Building the Matrix ¦ ≠ Length¦ Finding the most similar • Example on how the algorithm builds the 3rd level matrix for two sequences of different lengths. 10º Simpósio Brasileiro de Computação Musical (SBCM2005)

  9. INTRODUCTIONMODELExamplesAPPLICATIONSCONCLUSIONS Building the Matrix ¦ ≠ Length¦ Finding the most similar • This is an example of the comparison between the sequences • V = 1 0 1 1 • W = 1 0 1 1 0 1 • The first sequence is completely included in the second, therefore we can find a positive value in the last level of the SCV • The sum of all coefficients of the SCV is 1.625 which can be seen as a single value expressing similarity between the sequences 10º Simpósio Brasileiro de Computação Musical (SBCM2005)

  10. INTRODUCTIONMODELExamplesAPPLICATIONSCONCLUSIONS = Length ¦ ≠ Length¦ Finding the most similar • Matlab application to explore the similarities in the rhythmic space • Gray code 0 0 0 0 1 0 1 1 0 1 0 0 1 0 1 1 1 1 0 1 1 0 0 1 10º Simpósio Brasileiro de Computação Musical (SBCM2005)

  11. INTRODUCTIONMODELEXAMPLESAPPLICATIONSCONCLUSIONS Musicology ¦ NetRhythms ¦ RGem ¦ Others • Computational musicology is broadly defined as the study of Music by means of computer modelling and simulation. • Complimentary approach to traditional musicology • What theories of music evolutionary origins make sense? • How do learning and evolved components interact to shape the musical culture that develops over time? 10º Simpósio Brasileiro de Computação Musical (SBCM2005)

  12. INTRODUCTIONMODELEXAMPLESAPPLICATIONSCONCLUSIONS Musicology ¦ NetRhythms ¦ RGem ¦ Others SARDNET (Sequential Activation Retention and Decay Network) is an extended Kohonen self-organising feature map. This network was developed to study sequences and organization of phonemes in the context of language (James and Miikkulainen (1995) • The input sequence • Each element of V is a vector in which the correspond to small rhythmic group with sampled events and amplitude • The network weights • The weight vectors W correspond to the internal representation of the agents Comparison using the SCV determines the winning node of the network 10º Simpósio Brasileiro de Computação Musical (SBCM2005)

  13. INTRODUCTIONMODELEXAMPLESAPPLICATIONSCONCLUSIONS Musicology ¦ NetRhythms ¦ RGeme ¦ Others Simulation dFL: date of first listening dLL: date of last listening nL: number of listenings W: weight Style Matrix 1 Style Matrix 2 time = 1 Every time a new music is listened to, new memes are included in the Style Matrix and the weights of all the memes are updated according to the similarity measure . time = 2 10º Simpósio Brasileiro de Computação Musical (SBCM2005)

  14. INTRODUCTIONMODELEXAMPLESAPPLICATIONSCONCLUSIONS Musicology ¦ NetRhythms ¦ RGem ¦ Others • Composition • Pedagogy 10º Simpósio Brasileiro de Computação Musical (SBCM2005)

  15. INTRODUCTIONMODELEXAMPLESAPPLICATIONSCONCLUSIONS Contributions ¦ Future work ¦ Acknowledgements • Contributions • This work contributes with a measure of similarity between sequences, exploring all hierarchical levels and keeping the information about the lower levels. • Future Work • Future developments involve the comparison between the SCV and other similarity measurements and how can we relate this measurement with human perception • Acknowledgements • The authors would like to acknowledge the financial support of the Lerverhulme Trust, São Paulo State Research Foundation (FAPESP) and CAPES (Brazil) 10º Simpósio Brasileiro de Computação Musical (SBCM2005)

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