Similarity Measures for Rhythmic Sequences

July / 2005 10º Simpósio Brasileiro de Computação Musical (SBCM2005)

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Joao MartinsMarcelo GimenesJônatas Manzolli Adolfo Maia Jr.

Future Music Lab – University of PlymouthNICS – UNICAMP

Similarity Measures for

Rhythmic Sequences


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INTRODUCTION SCV EXAMPLES APPLICATIONS CONCLUSIONS

INTRODUCTIONSCVEXAMPLESAPPLICATIONSCONCLUSIONS

Outline ¦ Scope ¦ Other Measures


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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.




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Euclidean distance Levenshtein distance Mongeau and Sankoff (1990)




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INTRODUCTION

SCVEXAMPLESAPPLICATIONSCONCLUSIONS

Representation ¦ Similarity Coefficient Vector ¦ Model

Representation of rhythmic sequences previously quantized discarding expressive timing info

Shmulevich, I. and Povel, D. (2000)


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INTRODUCTION



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


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INTRODUCTION



Diagram


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INTRODUCTIONMODEL

ExamplesAPPLICATIONSCONCLUSIONS

Building the Matrix ¦ ≠ Length ¦ Finding the most similar

Example on how the algorithm builds the 3rd level matrix for two sequences of different lengths.


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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

INTRODUCTIONMODEL


Building the Matrix ¦ ≠ Length ¦ Finding the most similar


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INTRODUCTIONMODEL


= Length ¦ ≠ Length ¦ Finding the most similar

Gray code0 0 0

0 1 0

1 1 0

1 0 0

1 0 1

1 1 1

0 1 1

0 0 1

Matlab application to explore the similarities in the rhythmic space


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INTRODUCTIONMODELEXAMPLES

APPLICATIONSCONCLUSIONS

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?


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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

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)

Comparison using the SCV determines the winning node of the network


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Musicology ¦ NetRhythms ¦ RGeme ¦ Others

# Meme dFL dLL nL W1 01011101 1 1 6 1.042 11011101 1 1 31 1.043 10001000 1 1 1 1.024 10010101 1 1 1 1.025 11011010 1 1 1 1.026 10011010 1 1 4 1.017 10011001 1 1 4 1.018 11111111 1 1 1 1.009 10000000 1 1 1 1.00

# Meme dFL dLL nL W1 01011101 1 2 7 1.072 11011101 1 2 37 1.083 10001000 1 1 1 1.024 10010101 1 2 21 1.065 11011010 1 2 2 1.046 10011010 1 1 4 1.027 10011001 1 2 10 1.048 11111111 1 1 1 1.019 10000000 1 2 2 1.0310 00010101 2 2 1 1.0411 10100101 2 2 1 1.0212 11011111 2 2 2 1.0213 10010111 2 2 4 1.0214 10011111 2 2 2 1.0215 11011000 2 2 1 1.0116 10000101 2 2 2 1.0117 11010101 2 2 1 1.01

Sty

le M

atrix

1

Sty

le M

atrix

2

time = 1

Simulation

time = 2

dFL: date of first listening

dLL: date of last listening

nL: number of listenings

W: weight

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 .


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Composition

Pedagogy


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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)

INTRODUCTIONMODELEXAMPLESAPPLICATIONS

CONCLUSIONS Contributions ¦ Future work ¦ Acknowledgements

Documents

Similarity Measures for Rhythmic Sequences