Chord recognition using measures of fit, chord templates and by qpv40869

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									Introduction             Our system               Evaluation and results   Conclusions




               Chord recognition using measures of fit, chord
                      templates and filtering methods

                                                  e      e
                    Laurent Oudre, Yves Grenier, C´dric F´votte

                                      TELECOM ParisTech
                                         CNRS LTCI


                                      WASPAA 2009
                                      October 18-21
Introduction                Our system   Evaluation and results   Conclusions



Contents



      1   Introduction
            What is a chord ?
            Objectives
            State-of-the-art

      2   Our system

      3   Evaluation and results

      4   Conclusions
Introduction            Our system          Evaluation and results   Conclusions



What is a chord ?



       Definition
       Chord : aggregate of musical pitches played simultaneously

        Characterization of a chord
                 ex :   Cm    (C minor)
Introduction            Our system          Evaluation and results   Conclusions



What is a chord ?



       Definition
       Chord : aggregate of musical pitches played simultaneously

        Characterization of a chord
                 ex :   Cm    (C minor)
                root note upon which the chord
                     is perceived
Introduction            Our system          Evaluation and results   Conclusions



What is a chord ?



       Definition
       Chord : aggregate of musical pitches played simultaneously

        Characterization of a chord
                 ex :   Cm    (C minor)
                root note upon which the chord
                     is perceived
                type harmonic structure of the
                     chord
Introduction               Our system         Evaluation and results      Conclusions



Objectives



       Chord transcription
           Sequence of chords played successively, with their duration
               Compact representation of the harmonic content of a song

       Applications
           Song playback
               Song identification
               Query by similarity
               Musical structure analysis
Introduction                            Our system                    Evaluation and results    Conclusions



State-of-the-art

                      Chromagram of ’Eight days a week’

       C

    C#/Db

       D

    D#/Eb
                                                                      Most methods take the
       E                                                              chromagram as input
       F

    F#/Gb                                                             Many computational variants :
       G

    G#/Ab
                                                                      we use Bello & Pickens (2005)
       A                                                              based on the Constant-Q
    A#/Bb

       B
                                                                      Transform
            0   20   40    60       80     100      120   140   160
                                  time (s)




                             System input : N chroma vectors cn ∈ R12
                                                                   +
                                         (chromatic scale)
Introduction              Our system            Evaluation and results          Conclusions



State-of-the-art (ctd)



               HMM-based methods :
                   Sheh & Ellis (2003) : unsupervised HMM training
                   Bello & Pickens (2005) : introduction of musical knowledge
                   Papadopoulos & Peeters (2007) : large-scale study of HMM
                   methods
                   Lee & Slaney (2008) : joint key and chord estimation
               Template-based methods :
                   Fujishima (1999) : Pitch Class Profiles
                   Harte & Sandler (2005) : tuning algorithm in the computation
                   of the chromagram
Introduction                Our system   Evaluation and results   Conclusions



Contents


      1   Introduction

      2   Our system
           Overview
           Chord templates
           Measures of fit
           Filtering methods
           Example

      3   Evaluation and results

      4   Conclusions
Introduction                Our system               Evaluation and results   Conclusions



System overview



               Given a set of chord templates [p1 , . . . pK ] and a set of
               chroma vectors [c1 , . . . cN ]
               Fit a scale parameter : hk,n = argmin D (h cn |pk )
                                                     h
               Compute dk,n = D (hk,n cn |pk )
                            ˆ
               Detect chord kn on frame n as :
                                         ˆ
                                         kn = argmin {dk,n }
                                                 k
Introduction                           Our system                       Evaluation and results    Conclusions



Chord templates

           C major with 1 harmonic           C minor with 1 harmonic
    0.4                               0.4


    0.2                               0.2
                                                                        12-dimensional vectors each
     0                                 0
          CC#DD# E F F# GG#A A# B
           C major with 4 harmonics
                                            CC#DD# E F F# GG#A A# B
                                             C minor with 4 harmonics
                                                                        representative of a chord ;
    0.4                               0.4
                                                                        contain the theoretical
    0.2                               0.2
                                                                        amplitudes of the chromas.
     0                                 0
          CC#DD# E F F# GG#A A# B
           C major with 6 harmonics
                                            CC#DD# E F F# GG#A A# B
                                             C minor with 6 harmonics   1, 4 or 6 harmonics models,
    0.4                               0.4
                                                                        with exponentially decreasing
    0.2                               0.2
                                                                        spectral profile (Gomez, 2006)
     0                                 0
          CC#DD# E F F# GG#A A# B           CC#DD# E F F# GG#A A# B




                                            ⇒ K chord templates pk ∈ R12
                                                                      +
Introduction                        Our system                       Evaluation and results               Conclusions



Measures of fit


     1
                                                           EUC
                                                           KL
    0.9
                                                           IS



    0.8
                                                                     Euclidean :
    0.7
                                                                     DEUC (x|y) =             i   (xi − yi )2
    0.6
                                                                     Kullback-Leibler (2 variants) :
    0.5
                                                                     DKL (x|y) =
                                                                                xi
                                                                       i xi log yi − xi + yi
    0.4




    0.3




    0.2                                                              Itakura-Saito (2 variants) :
    0.1
                                                                                     x
                                                                     DIS (x|y) = i yii − log xii − 1
                                                                                               y
     0
          0.5   1   1.5   2   2.5    3    3.5    4   4.5         5
Introduction               Our system                      Evaluation and results   Conclusions



Filtering methods

       Exploiting persistence by introducing a post-processing step
           So far : chord detection done frame by frame
               In practice : unlikely for a chord to last only one frame

       Filtering
               Upstream filtering of the calculated measures dk,n (and not on
               the sequence of detected chords)
               2 filtering methods :
                                                L−1
                               ˜     1  n+ 2
                   low-pass : dk,n = L n′ =n− L−1 dk,n′
                                               2
                             ˜
                   median : dk,n = med {dk,n′ } L−1 ′ n−    2   ≤n ≤n+ L−1
                                                                        2

                                        ˆ            ˜
                                        kn = argmin {dk,n }
                                                k
Introduction                      Our system                                      Evaluation and results                       Conclusions



Example
                                                       Chromagram of ’Eight days a week’

                    C

                C#/Db

                    D

                D#/Eb

                    E

                    F

                F#/Gb

                    G

                G#/Ab

                    A

                A#/Bb

                    B
                         0   20         40     60                   80                  100      120       140     160
                                                                    time (s)




                                                    Chord transcription of ’Eight days a week’
                     C
                C#/Db
                     D
                D#/Eb
                     E
                     F
                F#/Gb
                     G
                G#/Ab
                     A
                 A#/Bb
                     B
                   Cm
               C#/Dbm
                   Dm
               D#/Ebm
                   Em
                   Fm
               F#/Gbm
                   Gm
               G#/Abm
                   Am
               A#/Bbm
                   Bm
                   N/A
                         0   20         40      60                     80                  100     120       140         160
                                                                     time (s)
Introduction              Our system   Evaluation and results   Conclusions



Contents



      1   Introduction

      2   Our system

      3   Evaluation and results
            Evaluation
            Results
            Comparison to MIREX 2008

      4   Conclusions
Introduction                       Our system                 Evaluation and results   Conclusions



Evaluation


       Corpus
                13 Beatles albums (180 songs) used in MIREX 08
                All chord types mapped to major/minor for the evaluation

       Overlap Score
                                          C major                    A minor
               ground truth :
                                    C major         F major             A minor
               transcription :

                 overlap :


                                                                     3+4
                                 Example : Overlap Score =            10     = 0.70
Introduction               Our system            Evaluation and results    Conclusions



Results


       Experimental set up
               5 measures of fit (EUC, IS1, IS2, KL1, KL2)
               2 filtering strategies with various window sizes (1 to 25)
               3 chord models (1, 4 or 6 harmonics)

                           → Total of 360 sets of parameters

       Conclusions
           KL2 tends to give best results DKL (pk |hk,n cn )
               Taking into account harmonics in the model is not really useful
               Filtering is definitely useful (opt. size ≈ 2s)
Introduction         Our system        Evaluation and results            Conclusions



Comparison to MIREX 2008




                                               AOS               Time
                 Our method (Maj-Min-7)        0.724              796s
                  Our method (Maj-Min)         0.718              790s
                     Bello & Pickens           0.707             1619s
                        a
                   Ryyn¨nen & Klapuri          0.705             1080s
                  Khadkevich & Omologo         0.663             1668s
               Pauwels, Varewyck & Martens     0.647            12402s
Introduction                Our system   Evaluation and results   Conclusions



Contents



      1   Introduction

      2   Our system

      3   Evaluation and results

      4   Conclusions
Introduction              Our system          Evaluation and results     Conclusions



Conclusions




               Fast and efficient chord recognition method
               Can easily handle many chord types
               No need for training
               The “optimal” parameters learnt from the Beatles corpus
               perform consistently on other datasets
Introduction              Our system          Evaluation and results     Conclusions



References



                                          e
               Oudre, L., Grenier, Y., & F´votte, C. (2009). Template-based
               chord recognition : influence of the chord types. Proceedings
               of the International Symposium on Music Information
               Retrieval (ISMIR). Kobe, Japan.
                                           e
               Oudre, L., Grenier, Y., & F´votte, C. (2009). Chord
               recognition by fitting rescaled chroma vectors to chord
               templates. Technical Report (online). Submitted to IEEE
               TASLP.

								
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