1. Measuring the Similarity of Rhythmic Patterns
Jouni Paulus, Anssi Klapuri
Tampere University of Technology
ISMIR 2002
8/3/2019
ISE by Frances Kao

2. Outline Background Proposal System Modules Simulation Results
Pre-processing
Pattern Segmenting
Acoustic Features for Similarity Judgments
Dynamic Time Warping (DTW)
Simulation Results
8/3/2019
ISE by Frances Kao

3. Background Music is composed of patterns
Measuring of rhythm similarity can be applied in musical database searching, and music context analysis
There lacks pragmatic methods, which can quantify the dissimilarity into some computer model
8/3/2019
ISE by Frances Kao

4. Proposal
A method for measuring the similarity of two rhythmic patterns
Patterns are performed using arbitrary percussion sounds, and presented as two acoustic signals
Four modules in the proposed system, including an optional pre-processing part.
8/3/2019
ISE by Frances Kao

5. System Overview Find recurring patterns Sin+noise model preprocessing
Feature
extraction
Similarity
measure
DTW
8/3/2019
ISE by Frances Kao

6. System Modules (1) - Preprocessing
Use sinusoids plus noise spectrum model to extract the stochastic parts of acoustic musical signal
Sin+noise model preprocessing
In order to suppress the sound of other instruments.
Acoustic signal
Noise residual
8/3/2019
ISE by Frances Kao

7. System Modules (2) – Pattern Segmenting
Signal modeling
Periodicity detection
Selecting tatum, tactus and measure lengths
To retain the metric percept of most signal, while reduce the amount of data needed to describe the signal. (DSP approach)
Use a fundamental frequency estimation algorithm. The figure is from a soft rock genre example. Output is used to for musical meter estimation. A dip means a period. The vertical line is the actual tactus and measure periods.
Tatum = time quantum. The shortest durational value. Tactus = beat, the tapping rate.
Different distribution functions and conditional probability are applied. Some parameters are assigned.
Authors mention about pattern phase, and also proposed a method to decide the temporal pattern starting point.
Finding recurring patterns
Acoustic signal without
preprocessing
Length of the
Tactus (beat)
Music measure
8/3/2019
ISE by Frances Kao

8. System Modules (3) – Feature Extraction
Three features are calculated in each of 23ms time frames
Loudness – mean square energy
Brightness – spectral centroid (SC)
Mel-frequency cepstral coefficients (MFCC)
Normalization of those feature vectors
SC: balance point of spectral power distribution, generally the expect value of magnitude spectrum.
MFCC: discrete cosine transform to the log-energy output of mel-scaling filterbank.
(detailed algorithm in the paper)
Normalization: absolute feature values to relative. We model only the deviations from the average. Output is 2-D matrix.
Matrix with normalized
feature vectors
Feature extraction
Pattern boundaries
Noise residual
8/3/2019
ISE by Frances Kao

9. System Modules (4) – Dynamic Time Warping (DTW)
A dynamic programming algorithm, which has been applied in template matching in speech and image pattern recognition
Allows flexibility in time alignment
Has been used to handle musical variations in pattern matching successfully
DTW can compare two patterns with different length.
8/3/2019
ISE by Frances Kao

10. System Modules (4) – DTW(cont’d)
DTW looks for optimal path in the matrix of points representing time alignment of two dataset
Starting from (0,0). Find the global cost (local cost + min global cost at adjacent cell) of each cell. The overall global distance is at top-right.
8/3/2019
ISE by Frances Kao

11. System Modules (4) – DTW(cont’d)
Three different local path constraints are tried, and type 3 is used in the algorithm.
With certain path constraints, the similarity measure is
(global cost) C(n.m)= D(n,m) + min (cost of three path)
(local cost) D(n,m) = sigma [ Weight * (F1(i, n)-F2(i, m))^2]
DTW
Feature vector sets of two acoustic signals
Similarity measure
8/3/2019
ISE by Frances Kao

12. Simulation Results (1) – Meter estimation and pattern segmenting
Estimated results vs. manual annotation
“Correct” criteria: deviation within ±10% range
Correct rate
Data size (piece)
Typical error
Tactus
67%
365
Tactus period doubling
Pattern (Measure)
77%
141
17% - doubling or halfing
6% - unclassified
Pattern phase
Around 50%
Database contains 365 tactus-annotated pieces; 141 pattern-annotated pieces. 7 different genres.
8/3/2019
ISE by Frances Kao

13. Simulation Results (2) – Similarity Measurements
Similarity of drum patterns
Successfully identifies that same rhythms played with different instruments are similar
Performance of different features
Normalized spectral centroid is the best
Experiments with complex music signals
In-song similarity of patterns is higher
Similarity of drum patterns:
Another database: 9 different patterns, totally 14 deviations, and each of the 14 was played with 3 different drum sets.
Performance of different features:
Assign weight to different features.
With SC alone, the result is more consistent.
MFCC would prefer identical sound sets.
Complex music
- Only SC; with preprocessing.
8/3/2019
ISE by Frances Kao

14. Simulation Results (2) – Similarity Measurements (cont’d)
Similarity of drum patterns:
Swing is played with only two drum sets. This experiment is with only one feature (SC), and no preprocessing. The input pattern boundary is manual annotation. White area with no data is that the pattern length of two patterns differ by a factor >2.
Complex music
- Only SC; with preprocessing.
8/3/2019
ISE by Frances Kao