Eigenrhythms:
Drum Track Bases
Dan Ellis and John Arroyo
Laboratory for Recognition and Organization of Speech and Audio
Dept. Electrical Eng., Columbia Univ., NY USA
dpwe@ee.columbia.edu
1.
2.
3.
4.
ja2124@columbia.edu
Eigenrhythms: Representing drum tracks
Basis projections
Aligning the data
Classification and Synthesis
Eigenrhythms - Ellis & Arroyo
2004-10-14
Drum Track Structure
• To first order,
All pop music has the same drum track:
• Can we capture this from examples?
.. including the variations
• Can we exploit it?
.. for synthesis
.. for classification
.. for insight
Eigenrhythms - Ellis & Arroyo
2004-10-14
Basis Sets
• Dataset reduced to
linear combinations of a few basic patterns
weights
data X
= W
×
H bases
1
=
0
×
-1
bases H: subspace that spans the data
weights W: dimension-reduced projection of data
Eigenrhythms - Ellis & Arroyo
2004-10-14
Different basis projections
•
•
PCA basis
6
5
Principal Component Analysis (PCA)
optimizes MSE of low-D reconstruction
4
3
2
1
0
0
2
4
ICA basis
6
0
2
6
6
Independent Component Analysis (ICA)
projections are independent (cf decorrelated)
• Linear Discriminant Analysis (LDA)
4
3
2
1
0
3
4
LDA basis
2
given class labels for data, find dimensions to
separate them
• Nonnegative Matrix Factorization (NMF)
each basis function only adds bits in
5
1
0
-1
-2
-3
-2
6
0
NMF basis
2
5
4
3
2
1
0
Eigenrhythms - Ellis & Arroyo
0
2004-10-14
2
4
6
Data
• Drum tracks extracted from MIDI
100 examples (10 × 10 genre classes)
fixed mapping of instruments to 3 classes
bass drum, snare, hi-hat
• Pseudo-envelope representation
40ms half-Gauss window sampled at 200 Hz
HH
•
•• Extract just one pattern from each MIDI
SN
BD
100
200
300
samples
looking for variety, quantity not a problem
Eigenrhythms - Ellis & Arroyo
2004-10-14
Aligning Data: Tempo
• Need to align patterns prior to PCA...
• First, normalize tempo
autocorrelation gives BPM candidates
Eigenrhythms - Ellis & Arroyo
2004-10-14
Sound Examples
Aligning Data: Downbeat
• Downbeat from best match of temponormalized pattern to ‘mean’ template
try every tempo hypotheses, choose best match
Original pattern scaled
Eigenrhythms - Ellis & Arroyo
2004-10-14
Aligned Data
• Tempo normalization + downbeat alignment
→ 100 2-bar excerpts:
• Can now apply basis projection(s)
Eigenrhythms - Ellis & Arroyo
2004-10-14
Eigenrhythms (PCA)
• Need 20+ Eigenvectors for good coverage
of 100 training patterns (1200 dims)
• Eigenrhythms both add and subtract
Eigenrhythms - Ellis & Arroyo
2004-10-14
Indirhythms (ICA)
Indirhythm 1
Indirhythm 2
HH
HH
SN
SN
BD
BD
Indirhythm 3
Indirhythm 4
HH
HH
SN
SN
BD
BD
0.1
Indirhythm 5
Indirhythm 6
HH
HH
SN
SN
BD
BD
0
1
50
100
2
150 0 200
3
250
300
4
350
0
-0.1
400
50
1
100
2
150
200
3
250
300
4
• 6 of 12 components from FastICA2_1
picking up fine timing shifts?
Eigenrhythms - Ellis & Arroyo
2004-10-14
350
samples (@ 2
beats (@ 120
Discrirhythms (LDA)
Discirhythm 1
Discirhythm 2
HH
HH
SN
SN
BD
BD
Discirhythm 3
Discirhythm 4
HH
HH
SN
SN
BD
BD
0.1
Discirhythm 5
Discirhythm 6
HH
HH
SN
SN
BD
BD
0
1
50
100
2
150
200
3
250
300
4
350
400
0
-0.1
0
1
50
100
2
150
200
3
250
300
4
• Trying to differentiate genre classes...
Eigenrhythms - Ellis & Arroyo
2004-10-14
350
samples (@ 2
beats (@ 120
Posirhythms (NMF)
Posirhythm 1
Posirhythm 2
HH
HH
SN
SN
BD
BD
Posirhythm 3
Posirhythm 4
HH
HH
SN
SN
BD
BD
0.1
Posirhythm 5
Posirhythm 6
HH
HH
SN
SN
BD
BD
0
1
50
100
2
150
200
3
250
300
4
350
400
0
-0.1
0
1
50
100
2
150
200
3
250
300
4
• Nonnegative: only adds beat-weight
• Capturing some structure
Eigenrhythms - Ellis & Arroyo
2004-10-14
350
samples (@ 2
beats (@ 120
Eigenrhythms for Classification
• Projections in Eigenspace / LDA space
PCA(1,2) projection (16% corr)
LDA(1,2) projection (33% corr)
10
6
blues
4
country
disco
hiphop
2
house
newwave
rock 0
pop
punk
-2
rnb
5
0
-5
-10
-20
-10
0
10
-4
-8
-6
-4
-2
• 10-way Genre classification (nearest nbr):
PCA3: 20% correct
LDA4: 36% correct
Eigenrhythms - Ellis & Arroyo
2004-10-14
0
2
Eigenrhythm BeatBox
• Resynthesize rhythms from eigen-space
Eigenrhythms - Ellis & Arroyo
2004-10-14
Conclusions & Future Work
• Basis projections
capture subspace of drum patterns
• Not genre, but something?
•
• Future work
use more data
extract drum patterns from audio
examine ‘feel’?
Eigenrhythms - Ellis & Arroyo
2004-10-14