Beat-Synchronous Chroma Representations for Music Analysisdpwe/talks/denmark-chroma-2007-05.pdf · Beat-Chroma Representations - Ellis 2007-05-23 - /23 1. Chroma Features • Chroma

Beat-Chroma Representations - Ellis 2007-05-23 - /231

1. Chroma Features2. Beat Tracking3. Matching Cover Songs4. Artist Identification

Beat-Synchronous Chroma Representations

for Music AnalysisDan Ellis

Laboratory for Recognition and Organization of Speech and Audio Dept. Electrical Eng., Columbia Univ., NY USA

[email protected] http://labrosa.ee.columbia.edu/

mailto:[email protected]

mailto:[email protected]

http://labrosa.ee.columbia.edu

http://labrosa.ee.columbia.edu


Beyond MFCCs...• MFCCs have been useful in Audio Music IR

“timbral similarity”artist ID, segmentation, thumbnailing, singing ...

• Separate tradition of Symbolic MIRmelody matching, chord detection, meter analysis

• It’s time to bring them together... with robust audio mid-level representations... that capture tonal (melodic-harmonic) content

= beat-synchronous chroma features2

time / sectime / sec

freq / k

Hz

Let It Be / Beatles / verse 1

2 4 6 8 100

1

2

3

4

freq / k

Hz

0

1

2

3

4Let It Be / Nick Cave / verse 1

2 4 6 8 10


1. Chroma Features• Chroma features map spectral energy

into one canonical octavei.e. 12 semitone bins

• Can resynthesize as “Shepard Tones”all octaves at once

3

Piano scale

2 4 6 8 10 100 200 300 400 500 600 700time / sec

freq

/ k

Hz

0

1

2

3

4

time / frames

ch

rom

a

A

C

D

F

G

Piano chromatic scale IF chroma

0 500 1000 1500 2000 2500 freq / Hz-60-50-40-30-20-10

0

2 4 6 8 10 time / sec

freq

/ kH

z

leve

l / d

B

0

1

2

3

4Shepard tone resynth12 Shepard tone spectra


Calculating Chroma Features• Method 1: Map every STFT bin

blurs non-tonal energy

• Method 2: Map only STFT peaksstill blurry at low frequencies

• Method 3: Instantaneous Frequency /tescapes frequency resolution limit

4

50 100 150 200 fft bin 2 4 6 8 10 time / sec 50 100 150 200 250 300 time / frame

freq /

kH

z

0

1

2

3

4

chro

ma

A

C

D

F

G

chro

ma

A

C

D

F

G

50 100 150 200 fft bin 2 4 6 8 10 time / sec 50 100 150 200 250 300 time / frame

freq /

kH

z

0

1

2

3

4

chro

ma

A

C

D

F

G

chro

ma

A

C

D

F

G

2 4 6 8 10 time / sec 50 100 150 200 250 300 time / frame

freq /

kH

z

0

1

2

3

4

chro

ma

A

C

D

F

G

chro

ma

A

C

D

F

G

0 2000 4000

!( )


2. Beat Tracking (1)• Goal: One feature vector per ‘beat’ (tatum)

for tempo normalization, efficiency

• “Onset Strength Envelope”sumf(max(0, difft(log |X(t, f)|)))

• Autocorr. + window → global tempo estimate

5

10203040

freq

/ mel

0

0

5 10 15time / sec

0 100 200 300 400 500 600 700 800 900lag / 4 ms samples

1000

0

168.5 BPM


Beat Tracking (2)• Dynamic Programming finds beat times {ti}

optimizes i O(ti) + i W((ti+1 – ti – p)/)where O(t) is onset strength envelope (local score)W(t) is a log-Gaussian window (transition cost)p is the default beat period per measured tempoincrementally find best predecessor at every timebacktrace from largest final score to get beats

6

C*(t) = ! O(t) + (1–!)max{W((" – "p)/#)C*(")}"

P(t) = argmax{W((" – "p)/#)C*(")}"

t"

O(t)

C*(t)


Beat Tracking Results• DP will bridge gaps (non-causal)

there is always a best path ...

• 2nd place in MIREX 2006 Beat Trackingcompared to McKinney & Moelants human data

7

10

20

30

40

0 5 10 150

20

40

freq / B

ark

band

Subje

ct #

time / s

test 2 (Bragg) - McKinney + Moelants Subject data

182 184 186 188 190 192 time / sec

10

20

30

40

freq / B

ark

band

Alanis Morissette - All I Want - gap + beats


Beat-Synchronous Chroma Features• Beat + chroma features / 30ms frames→ average chroma within each beatcompact; sufficient?

! "# "! $# $! %# %!

$

&

'

(

"#

"$

"#

$#

%#

&#

$

&

'

(

"#

"$

# ! "# "!)*+,-.-/,0

)*+,-.-1,2)/

34,5-.-6,7

89/,)-/)4,9:);

0;48+2-1*9/

0;48+2-1*9/

#


3. Cover Song Detection• “Cover Songs” = reinterpretation of a piece

different instrumentation, characterno match with “timbral” features

• Need a different representation!beat-synchronous chroma features

9

Let It Be - The Beatles Let It Be - Nick Cave

time / sectime / sec

freq / k

Hz

Let It Be / Beatles / verse 1

2 4 6 8 100

1

2

3

4

freq / k

Hz

chro

ma

chro

ma

0

1

2

3

4Let It Be / Nick Cave / verse 1

2 4 6 8 10

Beat-sync chroma features

5 10 15 20 25 beats

Beat-sync chroma features

5 10 15 20 25 beats

A

C

D

F

G

A

C

D

F

G

with Graham Poliner


Matching (1): Little Fragments• Cover versions may change song structure

multiple local matches at different alignments

• Match query and target as many small pieces?

10

how big are the pieces?

how do we combine individual scores?

do we have all day?

100 200 300 400 500 beats

100 200 300 400 500 beats

G

EDC

A

chro

ma b

ins

G

EDC

A

chro

ma b

ins

extract

cross-correlate

Query

Candidate


Matching (2): Global Correlation• Cross-correlate entire beat-chroma matrices

... at all possible transpositionsimplicit combination of match quality and duration

• One good matching fragment is sufficient...?

11

100 200 300 400 500 beats @281 BPM

-500 -400 -300 -200 -100 0 100 200 300 400 skew / beats

-5

0

+5

G

E

D

C

A

ch

rom

a b

ins

G

E

D

C

A

ch

rom

a b

ins

ske

w /

se

mito

ne

s

Elliott Smith - Between the Bars

Glen Phillips - Between the Bars

Cross-correlation


Filtered Cross-Correlation• Raw correlation not as important as precise

local matchlooking for large contrast at ±1 beat skewi.e. high-pass filter

12

-500 -400 -300 -200 -100 0 100 200 300 400

0

0.2

0.4

0.6

-500 -400 -300 -200 -100 0 100 200 300 400 skew / beats

skew / beats

-5

0

+5

ske

w /

se

mito

ne

s Cross-correlation

Cross-correlation @ skew = +2 semitones

raw

filtered


Results (1): Ellis 23 set• 23 pairs of cover songs from uspop2002 +...

one correct match per query

13

Test

Qu

ery

Ab Ad Al Am Be Be Bl Ca Ce Cl Co Co Da En Fa Go Go Gr Hu I_ I_ Le Ta

Abracadabra/sugar_ray

Addicted_To_Love/tina_turner

All_Along_The_Watchtower/dave_matthews_band

America/simon_and_garfunkel

Before_You_Accuse_Me/eric_clapton

Between_The_Bars/glen_phillips

Blue_Collar_Man/styx

Caroline_No/brian_wilson

Cecilia/simon_and_garfunkel

Claudette/roy_orbison

Cocaine/nazareth

Come_Together/beatles

Day_Tripper/cheap_trick

Enjoy_The_Silence/tori_amos

Faith/limp_bizkit

God_Only_Knows/brian_wilson

Gold_Dust_Woman/sheryl_crow

Grand_Illusion/styx

Hush/milli_vanilli

I_Can_t_Get_No_Satisfaction/rolling_stones

I_Love_You/faith_hill

Let_It_Be/nick_cave

Take_Me_To_The_River/annie_lennox

Cover Songs - dpwe23 - 12/23 correct


Results (2): MIREX 06• Cover song contest

30 songs x 11 versions of each (!)(data has not been disclosed)# true covers in top 108 systems compared (4 cover song + 4 similarity)

• Found 761/3300= 23% recallnext best: 11%guess: 3%

14

MIREX 06 Cover Song Results:# Covers retrieved per song per system

CS DE KL1 KL2 KWL KWT LR TP

cover song systems similarity systems

so

ng

-se

t (e

ach

ro

w is o

ne

qu

ery

so

ng

)

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

2

0correct

matchesretrieved

4

6

8


Where are the matches?• Look inside global cross-correlation to find

matching fragments...xcorr = t f (C1(t, f)⋅C2(t, f)) - view along time

15

Let It Be / Beatles (beats 11-441)

50 100 150 200 250 300 350 400

0 50 100 150 200 250 300 350 400

-0.2

0

0.2

0.4

Let It Be / Nick Cave (beats 13-443)

50 100 150 200 250 300 350 400 time / beats

time / beats

time / beats

ch

rom

a

A

C

D

F

G

chro

ma

A

C

D

F

G


What are the mistakes?• False reject - missed true match

cover version is too different, beat tracking wrong ...

• False alarm - invalid match“Cocaine” (Clapton) vs. “Satisfaction” (Stones)

16

Eric Clapton - Cocaine - beats 17:1027

100 200 300 400 500 600 700 800 900 1000

Rolling Stones - Satisfaction - beats 1:1011

100 200 300 400 500 600 700 800 900 1000

0 100 200 300 400 500 600 700 800 900 1000-2

-1

0

1

2

chroma

A

C

D

F

G

chroma

A

C

D

F

G


track

ae be br crdade fl gage gr mamepi qu ro ro t

aerosmithbeatles

bryan_adamsence_clearwater_revival

dave_matthews_banddepeche_modefleetwood_mac

garth_brooksgenesis

green_daymadonnametallica

pink_floydqueen

rolling_stonesroxette

tina_turneru2

-10

-5

0

5

10

15

recog

true

aebebr cr dade fl gagegrmamepi quro ro t

aebebrcr

dade

flgagegr

mame

piquroroti

u2

0

5

10

15

20

4. Artist Identification (AID)• Baseline system: “Bag of (timbral) frames”

MFCC frames, model as Gaussian or GMMdistance by likelihood or KL

• Dataset: [Mandel et al. 2006]18 artists x 5 or 6 albums each18x3 albums for training, 18x2 for test, 10x1 dev

17


Beat Chroma Features for AID?• Artists may use tonality in particular ways...

density, varietyparticular chords(influence of instruments on chroma features)

• Try bag-of-frames on beat-chroma rep’nuse several consecutive beats?key-normalization of each piece?

18

Northern Lad (1998) @ 1:35 (tatum=238 BPM)

20 40 60 80

2468

1012

Cars and Guitars (2005) @ 1:05 (tatum=333 BPM)

20 40 60 80

2468

1012


Aligned Global model

Taxman Eleanor Rigby I'm Only Sleeping

She Said She Said Good Day Sunshine And Your Bird Can Sing

Love You To Yellow Submarine

alig

ned

chro

ma

A

CD

FG

A C D F GA

CD

FG

A C D F GA

CD

FG

A C D F GA

CD

FG

A C D F GA

CD

FG

A C D F GA

CD

FG

A C D F GA

CD

FG

A C D F GA

CD

FG

A C D F GA

CD

FG

aligned chroma

Key Normalization• Could try matching at all possible rotations..• .. or just transpose every piece initially

single Gaussian model of one piecefind ML rotation of other piecesmodel all transposed piecesiterate until convergence

19


Timbre+Chroma AID• Preliminary Mandel18 Artist ID accuracy:

20

3 KEY NORMALIZATION

When applied, our key normalization operated by fitting asingle, full-covariance Gaussian to the chroma features tothe first track for a given training class. Then the like-lihood of each subsequent track in the training class isevaluated at all 12 possible chroma rotations; the rotationgiving the greatest likelihood is retained, and a new sin-gle Gaussian model is fit to all the training tracks rotatedby these indices. Best chroma rotations are calculated forthis model, and the entire process iterates until no changesoccur. In testing, the test track is also rotated to match thesame single Gaussian model prior to evaluating its likeli-hood under the full trained model (which is usually larger,involving concatenated time frames and/or multiple Gaus-sian components).

4 DATA

Following [3], we use the 18-artist subset of the “uspop2002”dataset for which at least five albums were available, andalso use the same division of three albums per artist as-signed to training, two for testing, and an additional albumfor nine of the artists available as a tuning set.

5 EXPERIMENTS

For both MFCC and beat-chroma features, we experimentedwith varying the number of frames used to train and testthe models, and the number of Gaussians used to modelthe distributions. For the MFCCs, we also investigatedthe effect of varying the range of coefficients used, vary-ing the highest coefficient up to 19, and including or ex-cluding the zero’th coefficient (average level). For thebeat-chroma features, we experimented with varying thenumber of temporally-adjacent frames modeled simulta-neously from 1 to 4, and with using the key normalizationfront-end.

The results are summarized in table 1. The test set con-sists of 451 items from the 18 classes, so a random base-line accuracy is 5.6% and based on a one-tailed Bernoullimodel we estimate a threshold for statistical significanceof around 5% in these values. We notice that MFCCsare intrinsically more useful than chroma features (as ex-pected), that Gaussian mixture models are preferable forthe chroma features (which we might expect to be multi-modal) but not for MFCCs, that key normalization seemsto give a slight improvement, but concatenating multiplebeats into a single feature vector does not. Fusing the bestMFCC and Chroma systems (shown in bold in the table)based on a weighted sum of separate model likelihoodstuned to the tuning set, we see a 4% absolute improve-ment in accuracy which is almost statistically significant.

6 CONCLUSIONS

We have shown that the simple approach of modeling thedistribution of per-beat chroma vectors very much as cep-

Feature Model T win Acc Exec. timeMFCC20 FullCov 1 48% 212 sMFCC20 64 GMM 1 33% 1952 sChroma FullCov 1 15% 46 sChroma FullCov 4 14% 117 sChroma 64GMM 1 24% 850 sChroma 64GMM 4 15% 2242 sChromaKN FullCov 1 17% 110 sChromaKN FullCov 4 14% 258 sChromaKN 64GMM 1 25% 2533 sChromaKN 64GMM 4 16% 5803 s

MFCC + Chroma fusion 52%

Table 1. Artist identification results for various con-figurations. “T win” is the size of temporal contextwindow. “FullCov” designates single, full-covarianceGaussian models. “ChromaKN” refers to per-track key-normalized chroma data.

stral vectors have been modeled in the past is a viable ap-proach for artist identification. Rotating the chroma vec-tors in order to transpose all pieces to a common tonalframework seems mildly helpful.

Our future plans are to pursue this idea of modelingsmall fragments of beat-chroma representation to identifythe most distinctive and discriminative fragments charac-teristic of each composer/artist.

AcknowledgementsThis work was supported by the Columbia Academic Qual-ity Fund, and by the NSF under Grant No. IIS-0238301.Any opinions, findings, etc. are those of the authors anddo not necessarily reflect the views of the NSF.

References[1] Jean-Julien Aucouturier and Francois Pachet.

Music similarity measures: What’s the use? InProc. 3rd International Symposium on Music In-formation Retrieval ISMIR, Paris, 2002. URLhttp://www.csl.sony.fr/downloads/papers/uploads/pachet-02g.pdf.

[2] D. P. W. Ellis and G. Poliner. Identifying coversongs with chroma features and dynamic pro-gramming beat tracking. In Proc. ICASSP,pages IV–1429–1432, Hawai’i, 2007. URLhttp://www.ee.columbia.edu/!dpwe/pubs/EllisP07-coversongs.pdf.

[3] M. I. Mandel and D. P. W. Ellis. Song-level featuresand support vector machines for music classification.In Proc. International Conference on Music Informa-tion Retrieval ISMIR, pages 594–599, London, Sep2005. URL http://www.ee.columbia.edu/!dpwe/pubs/ismir05-svm.pdf.


Artist Fragments• Idea: Find the most discriminant

beat-chroma fragments per artistk-means cluster 16 beat fragments within piece

keep fragments largest ratio(avg. similarity to same artist)/(avg. sim. to others)classify test pieces by ID of best-scoring fragment

21

!!"#$% &$!"#$%&'! ()'*+$),! %(! '!-)'*.),! ,%/01!23*#! *#)!/3/)!4567)'*!

($'0&)/*,!)8*$'9*):!7;!9.+,*)$3/0!#30#.30#*):<!

!

!

'$%()*+,*-./0%

!

'$&$%1232453%

%

=#)! &)*#%:! :),9$37):! #)$)! 2',! *),*):! %/! '! ,+7,)*! %(! *#)!

+,>%>?@@?! :'*',)*! ABC<! ! D+)! *%! *3&)! 9%/,*$'3/*,! '/:! *#)!

/'*+$)!%(! *#)!9$%,,69%$$).'*3%/!>$%9),,1! *#)! 3/3*3'.! ,)*!%(!4E!

'$*3,*,!2',!>'$):!:%2/!*%!F!'$*3,*,1!$'/:%&.;!,).)9*):<!!=#)!

9#%,)/! '$*3,*,! '$)! .3,*):!7).%2<! !=#)! *$'3/3/0!:'*',)*! G($%&!

2#39#! *$'3/3/0! ,%/0,! '/:! ($'0&)/*,! 2)$)! :$'2/H! 2',!

9%&>%,):! %(! I! '.7+&,! ($%&! )'9#! '$*3,*1! (%$! '! *%*'.! %(! 4F!

'.7+&,!23*#!45J!,%/0,<!!=#)!*),*!:'*',)*!2',!9%&>%,):!%(!?!

'.7+&,!>)$!'$*3,*1!23*#!'!*%*'.!%(!4I@!,%/0,<!!=#)$)!2',!'.,%!

'! K'.3:'*3%/! ,)*! 9%&>%,):! %(! 4! '.7+&! )'9#! (%$! B! %(! *#)! F!

'$*3,*,1!*%*'.3/0!BE!,%/0,<!!G=#)!:'*',)*!+/(%$*+/'*).;!:3:!/%*!

9%/*'3/!'!K'.3:'*3%/!'.7+&!(%$!*#)!L%..3/0!M*%/),1!'!('9*!*#'*!

2',!/%*!/%*):!2#)/!*#)!,+7,)*!%(!'$*3,*,!2',!,).)9*):<H!

!

N$*3,*,!O/9.+:):!3/!PK'.+'*3%/!M)*Q!

-)'*.),!

R':%//'!

S3/T!U.%;:!

L%..3/0!M*%/),!

V?!

%

'$6$%-5434%

%

=$'3/3/0! '/:! *),*! ,%/0! 9.',,3(39'*3%/! 2)$)! >)$(%$&):! (%$!

K'$;3/0!K'.+),!%(!W1!*#)!/+&7)$!%(!9#'$'9*)$3,*39!($'0&)/*,!

,).)9*):1! '/:! =1! *#)! *#$),#%.:! %/! '! ($'0&)/*X,! &)'/!

,3&3.'$3*;! ,9%$)<! ! =#),)! >'$'&)*)$,! 2)$)! *+/):! *%! 03K)!

%>*3&'.!>)$(%$&'/9)!%/!*#)!*),*!:'*',)*<!!=#)!)/*3$)!,;,*)&!

23*#! *+/):! >'$'&)*)$,! 2',! *#)/! *),*):! %/! *#)! K'.3:'*3%/!

:'*',)*<!

%

'$7$%8549:34%

%

=#)! 9.+,*)$3/0! ,*'0)! >$%:+9):! '! *%*'.! %(! 4B44! ($'0&)/*,!

($%&! *#)! 45J! *$'3/3/0! ,%/0,<! ! U30+$)! 4! ,#%2,! *#)! (+..!

9#$%&'!()'*+$),!(%$!'/!)8'&>.)!,%/01!23*#!*#)!.%9'*3%/,!%(!

)8*$'9*):! ($'0&)/*,! #30#.30#*):<! ! M3/9)! *#)! /+&7)$! %(!

($'0&)/*,! )8*$'9*):! 2',! :)>)/:)/*! %/! *#)! .)/0*#! %(! *#)!

,%/01!*#)!!

!!"#$% 6$! P8'&>.)! 9#$%&'! 9$%,,69%$$).'*3%/<! ! =#)! (+..!

9%$$).'*3%/! 3,! ,#%2/! '7%K)1! 23*#! '! $):! .3/)! :)/%*3/0! *#)!

9#$%&'!73/!$%*'*3%/!9%/*'3/3/0!*#)!#30#),*!>)'T<!!=#3,!73/X,!

9%$$).'*3%/!3,!,#%2/!7).%2<!

!

!

7$)'T:%2/!%K)$! *#)!'$*3,*,!2',!+/)K)/1!23*#! *#)! (%..%23/0!

:3,*$37+*3%/,Q!

!

-)'*.),! R':%//'! S3/T!U.%;:! L%..3/0!M*%/),! V?!

?@I! ?EY! IJ@! ?B@! I@Y!

!

"$%,,69%$$).'*3%/!2',!*#)/!>)$(%$&):!7)*2))/!)'9#!%(!*#),)!

($'0&)/*,! '/:! *#)! ,'&)! ,)*! %(! 45J! *$'3/3/0! ,%/0,<! ! N/!

)8'&>.)!9$%,,69%$$).'*3%/!$),+.*!3,!,#%2/!3/!(30+$)!?<!

P'9#! %(! *#)! 4B44! ($'0&)/*,! 2',! ,9%$):! 7',):! %/! *#)!

9%$$).'*3%/! $),+.*,<! ! =#)! 9.',,3(39'*3%/! >$%9):+$)! 2',! *#)/!

>)$(%$&):! (%$! K'$3%+,! >'$'&)*)$! ,)**3/0,<! ! U30+$)! I! ,#%2,!

*#)!9.',,3(39'*3%/!'99+$'9;!'9#3)K):!K)$,+,!*#)!*%*'.!/+&7)$!

%(! ($'0&)/*,! ,).)9*):! GWH1! (%$! ,)K)$'.! K'.+),! %(! *#)!

*#$),#%.:!=<! !W%*)! *#'*! '! ?@Z! ,+99),,! $'*)! 3,! )8>)9*):! 7;!

9#'/9)1!2#)/!9#%%,3/0!'&%/0!F!'$*3,*,<!

=#)!&'83&+&!'99+$'9;!3,!'9#3)K):!(%$!W![!I@@!'/:!=!

[! @<4I<! ! =#),)! >'$'&)*)$,! 2)$)! *#)/! '>>.3):! *%! *#)!

K'.3:'*3%/! ,)*<! ! =#)! 9.',,3(39'*3%/! '99+$'9;! '9#3)K):! %/!

K'.3:'*3%/! 2',! B?Z<! ! \*#)$! >'$'&)*)$! ,)**3/0,! 2)$)! /%*!

)8>.%$):!%/!*#)!K'.3:'*3%/!,)*<!

=#)!9%/(+,3%/!&'*$38!(%$!*#)!F!'$*3,*,1!,+&&):!%K)$!*#)!

*),*!'/:!K'.3:'*3%/!$),+.*,1!3,!,#%2/!3/!(30+$)!B<!

U30+$)! F! :3,>.';,! *#)! /+&7)$! %(! *3&),! '/;! 03K)/!

($'0&)/*! 2',! +,):! *%! 9.',,3(;! '! ,%/01! :+$3/0! *#)! 7),*!

>)$(%$&'/9)!$+/<!!\+*!%(!'!,).)9*):!I@@!($'0&)/*,1!%/.;!Y4!

+/3]+)! ($'0&)/*,!2)$)!+,):! *%!9.',,3(;! *#)!4I@! *),*! ,%/0,<!!

R%,*! ,%/0,!2)$)! +,):! %/9)! %$! /%*! '*! '..1!23*#! '! ()2!+,):!

&+.*3>.)!*3&),<!

with Courtenay Cotton


Artist Fragment Results• Preliminary, 5 way artist ID, ~32% correct

22

!!"#$%&$!"#$%%&'&($)&*+!$((,-$(.!'*-!/$-.&+0!/$#,1%!*'!2!$+3!

45!

!

!

'$%()*+,**)-.%

!

6#)7*,07! )71! %,((1%%! -$)1%! %7*8+! 71-1! $-1! +*)! )1--&9#.!

1+(*,-$0&+0! '*-! )7&%! $::-*$(7! )*! $-)&%)! (#$%%&'&($)&*+;! )71-1!

$-1! %1/1-$#! &<:*-)$+)! :*&+)%! )*! +*)15! ! =1%:&)1! )71! #*8!

$((,-$(.;! (#$%%&'&($)&*+! 9.! )7&%! <1)7*3! ,%,$##.! :1-'*-<%!

91))1-! )7$+! (7$+(1;! &'! *+#.! %#&07)#.;! */1-! $! -$+01! *'!

:$-$<1)1-!%1))&+0%5! !>1(*+3#.;! )71!:$-$<1)1-%! ),+13!'*-! )71!

)1%)! %1)! :1-'*-<13! 1/1+! 91))1-! *+! )71! /$#&3$)&*+! %1);! $+3!

%11<13!)*!3*!<,(7!91))1-!)7$+!(7$+(1!)71-15!!47&%!%11<%!)*!

&+3&($)1! )7$)! )71-1! &%! $)! #1$%)! %*<1! &+(-1$%1! &+! %&<&#$-&).!

91)811+!(7-*<$!'-*<!*+1!$-)&%)?%!<,%&(!$%!*::*%13!)*!*)71-!

$-)&%)%?!<,%&(5!

471! (*+',%&*+! <$)-&@! &%! &+)1-1%)&+0! 71-1;! 3,1! )*! &)%!

/$-&$9&#&).5! !48*!$-)&%)%;! )71!A1$)#1%!$+3!B&+C!D#*.3;!:-*/1!

/1-.!1$%.!)*!&31+)&'.!$+3!$-1!-$-1#.!<&%(#$%%&'&135!!E*81/1-;!

)71!B&+C!D#*.3!'-$0<1+)%!$-1!'-1F,1+)#.!,%13!)*!<&%(#$%%&'.!

*)71-! $-)&%)%?! 8*-C5! ! 47&%! <$.! 91! $! :-*9#1<! *'! %711-!

+,<91-%! G+*)1! )7$)! B&+C! D#*.3! 01+1-$)13! +1$-#.! )8&(1! $%!

<$+.! '-$0<1+)%! $%! %*<1!*'! )71!*)71-!$-)&%)%! )*!910&+!8&)7;!

3,1! )*! )71! -1#$)&/1#.! #*+0! %*+0%! &+! )71&-! (*##1()&*+H5! !I*-1!

#&C1#.!&)!&%!3,1!)*!%*<1!%:1(&'&(!(7$-$()1-&%)&(%!*'!)71!<,%&(;!

%&+(1! )71! B&+C! D#*.3! '-$0<1+)%! 81-1! $#%*! <*-1! #&C1#.! )*!

($,%1! :-*9#1<%! 8&)7! %:,-&*,%! (*--1#$)&*+%;! #1$3&+0! )*! )71!

+113!'*-!$!)7-1%7*#35!!47&%!<$.!&+3&($)1!)7$)!)71!)7-1%7*#3!&%!

%)&##!+*)! -1<*/&+0!1+*,07!*'! )71%1!,+8$+)13!'-$0<1+)%!'*-!

)7&%!$-)&%)5!!J+!*-31-!)*!:-1/1+)!)7&%!:-*9#1<;!(7$+01%!%7*,#3!

91! <$31! &+! )71! &+&)&$#! '-$0<1+)! 1@)-$()&*+! $+3! (#,%)1-&+0!

%)1:5!!E*81/1-!&)!&%!&+)1-1%)&+0!)7$)!)71!:-*9#1<!&%!%*!<,(7!

<*-1!:-1/$#1+)!'*-!*+1!$-)&%)!)7$+!)71!*)71-%5!!J+!(*+)-$%);!)71!

A1$)#1%!%7*8!$+!&+)1-1%)&+0!($%1!871-1!)71&-!<,%&(!&%!-$-1#.!!

!!"#$% /$! "*+',%&*+! <$)-&@! '*-! )71! K! $-)&%)%;! (*<9&+&+0! )1%)!

$+3!/$#&3$)&*+!-1%,#)%5!

!

!

<&%(#$%%&'&13;! $+3! )71&-! '-$0<1+)%! $-1! +*)! 1$%&#.! ,%13! )*!

<&%(#$%%&'.! *)71-! $-)&%)%! 1&)71-5! !47&%! &%! $!0**3!1@$<:#1!*'!

)71! %.%)1<!8*-C&+0! $%! )71*-&L135! !471!8*-C%!9.!I$3*++$!

$#%*! %7*8! $! %)-*+0! 3&$0*+$#! 1#1<1+);! 8&)7! $! <&+&<$#!

$<*,+)! *'!<&%(#$%%&'&($)&*+;! 1@(1:)! )7$)! $#-1$3.! +*)13! 3,1!

)*! )71! B&+C! D#*.3! '-$0<1+)%5! ! 471! '&+$#! )8*! $-)&%)%;! )71!

M*##&+0! >)*+1%! $+3!NO;! %7*8! /1-.! #&))#1! 31'&+&)&/1! :$))1-+5!!

471&-! 8*-C%! %11<! 1$%&#.! <&%(#$%%&'&13! $+3! ,%13! )*!

<&%(#$%%&'.!*)71-!8*-C%;!8&)7!#&))#1!(#1$-!%1#'P%&<&#$-&).5!!J)!&%!

3&''&(,#)! )*! 31)1-<&+1! 871)71-! )71! 3&''1-1+(1%! %11+! 71-1!

91)811+! $-)&%)%! &%! 3,1! )*! &+71-1+)! (7$-$()1-&%)&(%! *'! )71!

$-)&%)?%!<,%&(;!*-!%*<1!'#$8%!&+!)7&%!$::-*$(7!87&(7!9&$%!)71!

%.%)1<!)*!8*-C!91))1-!'*-!%*<1!$-)&%)%!)7$+!*)71-%5!

6!<$&+!:-*9#1<!8&)7!)71!$::-*$(7!:-1%1+)13!71-1!&%!)71!

)&<1! (*+%)-$&+)! *+! (-*%%P(*--1#$)&+0! #$-01! +,<91-%! *'!

'-$0<1+)%!8&)7!#$-01!+,<91-%!*'!%*+0%5!!6!-13,()&*+!&+!)71!

+,<91-! *'! '-$0<1+)%! 9.! (#,%)1-&+0!8$%! +1(1%%$-.! )*!<$C1!

)7&%! 8*-C! '1$%&9#15! ! E*81/1-;! )7&%! %)1:! <$.! 91! 8*-C&+0!

$0$&+%)! )71! 0*$#! *'! :$))1-+! 31)1()&*+;! $%! %*<1!:$))1-+%! )7$)!

<$.! 7$/1! 911+! ,%1',#! G&515! )71.! <&07)! 7$/1! $::1$-13! &+!

<,#)&:#1!%*+0%!9.!)71!$-)&%)H!7$/1!911+!)7-*8+!$8$.!&+!)7&%!

:-1#&<&+$-.! %)$015! !6! %&<&#$-! :-*9#1<! &%! )71! '$()! )7$)! *+#.!

)71! )*:P<$)(7&+0! '-$0<1+)! &%! 0&/1+! 81&07)! &+! )71!

(#$%%&'&($)&*+! *'! 1$(7! %*+05! ! 47&%! 8$%! 3*+1! 91($,%1! &)!

%11<13!)*!:-*3,(1!)71!91%)!-1%,#)%!'*-!)7&%!)$%C;!9,)!&)!&%!+*)!

+1(1%%$-&#.! )71! 91%)! $::-*$(75! ! 471! %&<&#$-&).! <1$%,-1%!

91)811+! <*%)! *'! )71! %*+0P'-$0<1+)! :$&-%;! 87&(7! <$.!

(*+)$&+! ,%1',#! &+'*-<$)&*+;! $-1! 91&+0! )7-*8+! $8$.5! ! 471!

&31$!*'!31)1()&+0!(7-*<$!:$))1-+%!8&)7&+!$+!$-)&%)?%!9*3.!*'!

8*-C!<$.!.1)!91!'1$%&9#1;!1/1+!)7*,07!)71%1!)1%)%!<1)!8&)7!

#&<&)13!%,((1%%5!

!

• need to search more fragments• way to choose phrase beginnings?

• a basis set for all tonal content?


Conclusions and Future Work• Beat-synchronous chroma features

are successful for matching cover songscaptures melody-harmony, not instruments

• Further uses:Beat-chroma fragments as musical building blockse.g. VQ over large body of musicfind recurrent motifsartist identification?

• Code available! Google “matlab chroma features”

23

Documents

Beat-Synchronous Chroma Representations for Music Analysisdpwe/talks/denmark-chroma-2007-05.pdf · Beat-Chroma Representations - Ellis 2007-05-23 - /23 1. Chroma Features • Chroma