Music Structure Analysis

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1 Lecture Music Processing Music Structure Analysis Meinard Müller International Audio Laboratories Erlangen

2 Book: Fundamentals of Music Processing Meinard Müller Fundamentals of Music Processing Audio, Analysis, Algorithms, Applications 483 p., 249 illus., hardcover ISBN: Springer, 2015 Accompanying website:

3 Book: Fundamentals of Music Processing Meinard Müller Fundamentals of Music Processing Audio, Analysis, Algorithms, Applications 483 p., 249 illus., hardcover ISBN: Springer, 2015 Accompanying website:

4 Book: Fundamentals of Music Processing Meinard Müller Fundamentals of Music Processing Audio, Analysis, Algorithms, Applications 483 p., 249 illus., hardcover ISBN: Springer, 2015 Accompanying website:

5 Chapter 4: Music Structure Analysis 4.1 General Principles 4.2 Self-Similarity Matrices 4.3 Audio Thumbnailing 4.4 Novelty-Based Segmentation 4.5 Evaluation 4.6 Further Notes In Chapter 4, we address a central and well-researched area within MIR known as music structure analysis. Given a music recording, the objective is to identify important structural elements and to temporally segment the recording according to these elements. Within this scenario, we discuss fundamental segmentation principles based on repetitions, homogeneity, and novelty principles that also apply to other types of multimedia beyond music. As an important technical tool, we study in detail the concept of self-similarity matrices and discuss their structural properties. Finally, we briefly touch the topic of evaluation, introducing the notions of precision, recall, and F-measure.

6 Music Structure Analysis Example: Zager & Evans In The Year 2525 Time (seconds)

7 Music Structure Analysis Example: Zager & Evans In The Year 2525 Time (seconds)

8 Music Structure Analysis Example: Zager & Evans In The Year 2525 I V1 V2 V3 V4 V5 V6 V7 B V8 O

9 Music Structure Analysis Example: Brahms Hungarian Dance No. 5 (Ormandy) A1 A2 B1 B2 C A3 B3 B4 Time (seconds)

10 Music Structure Analysis Example: Folk Song Field Recording (Nederlandse Liederenbank) Time (seconds)

11 Music Structure Analysis Example: Weber, Song (No. 4) from Der Freischütz Introduction Stanzas Dialogues Kleiber Time (seconds) Ackermann Time (seconds)

12 Music Structure Analysis General goal: Divide an audio recording into temporal segments corresponding to musical parts and group these segments into musically meaningful categories. Examples: Stanzas of a folk song Intro, verse, chorus, bridge, outro sections of a pop song Exposition, development, recapitulation, coda of a sonata Musical form ABACADA of a rondo

13 Music Structure Analysis General goal: Divide an audio recording into temporal segments corresponding to musical parts and group these segments into musically meaningful categories. Challenge: There are many different principles for creating relationships that form the basis for the musical structure. Homogeneity: Novelty: Repetition: Consistency in tempo, instrumentation, key, Sudden changes, surprising elements Repeating themes, motives, rhythmic patterns,

14 Music Structure Analysis Novelty Homogeneity Repetition

15 Overview Introduction Feature Representations Self-Similarity Matrices Audio Thumbnailing Novelty-based Segmentation Thanks: Clausen, Ewert, Kurth, Grohganz, Dannenberg, Goto Grosche, Jiang Paulus, Klapuri Peeters, Kaiser, Serra, Gómez, Smith, Fujinaga, Wiering, Wand, Sunkel, Jansen

16 Overview Introduction Feature Representations Self-Similarity Matrices Audio Thumbnailing Novelty-based Segmentation Thanks: Clausen, Ewert, Kurth, Grohganz, Dannenberg, Goto Grosche, Jiang Paulus, Klapuri Peeters, Kaiser, Serra, Gómez, Smith, Fujinaga, Wiering, Wand, Sunkel, Jansen

17 Feature Representation General goal: Convert an audio recording into a mid-level representation that captures certain musical properties while supressing other properties. Timbre / Instrumentation Tempo / Rhythm Pitch / Harmony

18 Feature Representation General goal: Convert an audio recording into a mid-level representation that captures certain musical properties while supressing other properties. Timbre / Instrumentation Tempo / Rhythm Pitch / Harmony

19 Feature Representation Example: Chromatic scale C1 24 C2 36 C3 48 C4 60 C5 72 C6 84 C7 96 C8 108 Waveform Amplitude Time (seconds)

20 Feature Representation Frequency (Hz) Frequency (Hz) Intensity (db) Intensity (db) Example: Chromatic scale C1 24 Spectrogram C2 36 C3 48 C4 60 C5 72 Time (seconds) C6 84 C7 96 C8 108

21 Feature Representation Frequency (Hz) Frequency (Hz) Intensity (db) Intensity (db) Example: Chromatic scale C1 24 Spectrogram C2 36 C3 48 C4 60 C5 72 Time (seconds) C6 84 C7 96 C8 108

22 Feature Representation Example: Chromatic scale C1 24 Spectrogram C2 36 C3 48 C4 60 C5 72 C6 84 C7 96 C8 108 C8: 4186 Hz C7: 2093 Hz C6: 1046 Hz C5: 523 Hz C4: 261 Hz C3: 131 Hz Time (seconds) Intensity (db)

23 Feature Representation Example: Chromatic scale C1 24 Log-frequency spectrogram C2 36 C3 48 C4 60 C5 72 C6 84 C7 96 C8 108 C8: 4186 Hz C7: 2093 Hz C6: 1046 Hz C5: 523 Hz C4: 261 Hz C3: 131 Hz Intensity (db) Time (seconds)

24 Feature Representation Example: Chromatic scale C1 24 Log-frequency spectrogram C2 36 C3 48 C4 60 C5 72 C6 84 C7 96 C8 108 Pitch (MIDI note number) Intensity (db) Time (seconds)

25 Feature Representation Example: Chromatic scale C1 24 Log-frequency spectrogram C2 36 C3 48 C4 60 C5 72 C6 84 C7 96 C8 108 Pitch (MIDI note number) Intensity (db) Chroma C Time (seconds)

26 Feature Representation Example: Chromatic scale C1 24 Log-frequency spectrogram C2 36 C3 48 C4 60 C5 72 C6 84 C7 96 C8 108 Pitch (MIDI note number) Intensity (db) Chroma C # Time (seconds)

27 Feature Representation Example: Chromatic scale C1 24 C2 36 C3 48 C4 60 C5 72 C6 84 C7 96 C8 108 Chroma representation Chroma Intensity (db) Time (seconds)

28 Feature Representation Example: Brahms Hungarian Dance No. 5 (Ormandy) A1 A2 B1 B2 C A3 B3 B4 Time (seconds)

29 Feature Representation Example: Brahms Hungarian Dance No. 5 (Ormandy) Chroma (Harmony) Feature extraction A1 A2 B1 B2 C A3 B3 B4 Time (seconds)

30 Feature Representation Example: Brahms Hungarian Dance No. 5 (Ormandy) B b G D Chroma (Harmony) G minor Feature extraction G minor A1 A2 B1 B2 C A3 B3 B4 Time (seconds)

31 Feature Representation Example: Brahms Hungarian Dance No. 5 (Ormandy) B G B b G Chroma (Harmony) Feature extraction D D G minor G major G minor A1 A2 B1 B2 C A3 B3 B4 Time (seconds)

32 Overview Introduction Feature Representations Self-Similarity Matrices Audio Thumbnailing Novelty-based Segmentation

33 Self-Similarity Matrix (SSM) General idea: Compare each element of the feature sequence with each other element of the feature sequence based on a suitable similarity measure. Quadratic self-similarity matrix

34 Self-Similarity Matrix (SSM) Example: Brahms Hungarian Dance No. 5 (Ormandy)

35 Self-Similarity Matrix (SSM) Example: Brahms Hungarian Dance No. 5 (Ormandy)

36 Self-Similarity Matrix (SSM) Example: Brahms Hungarian Dance No. 5 (Ormandy)

37 Self-Similarity Matrix (SSM) Example: Brahms Hungarian Dance No. 5 (Ormandy)

38 Self-Similarity Matrix (SSM) Example: Brahms Hungarian Dance No. 5 (Ormandy)

39 Self-Similarity Matrix (SSM) Example: Brahms Hungarian Dance No. 5 (Ormandy)

40 Self-Similarity Matrix (SSM) Example: Brahms Hungarian Dance No. 5 (Ormandy) G major G major

41 Self-Similarity Matrix (SSM) Example: Brahms Hungarian Dance No. 5 (Ormandy)

42 Self-Similarity Matrix (SSM) Example: Brahms Hungarian Dance No. 5 (Ormandy)

43 Self-Similarity Matrix (SSM) Example: Brahms Hungarian Dance No. 5 (Ormandy)

44 Self-Similarity Matrix (SSM) Example: Brahms Hungarian Dance No. 5 (Ormandy)

45 Self-Similarity Matrix (SSM) Example: Brahms Hungarian Dance No. 5 (Ormandy) Faster Slower

46 Self-Similarity Matrix (SSM) Example: Brahms Hungarian Dance No. 5 (Ormandy) Faster Slower

47 Self-Similarity Matrix (SSM) Example: Brahms Hungarian Dance No. 5 (Ormandy) Idealized SSM

48 Self-Similarity Matrix (SSM) Example: Brahms Hungarian Dance No. 5 (Ormandy) Idealized SSM Blocks: Homogeneity Paths: Repetition Corners: Novelty

49 SSM Enhancement Block Enhancement Feature smoothing Coarsening Time (samples) Time (samples)

50 SSM Enhancement Block Enhancement Feature smoothing Coarsening Time (samples) Time (samples)

51 SSM Enhancement Block Enhancement Feature smoothing Coarsening Time (samples) Time (samples)

52 SSM Enhancement Challenge: Presence of musical variations Fragmented paths and gaps Paths of poor quality Regions of constant (high) similarity Curved paths Idea: Enhancement of path structure

53 SSM Enhancement Shostakovich Waltz 2, Jazz Suite No. 2 (Chailly) SSM

54 SSM Enhancement Shostakovich Waltz 2, Jazz Suite No. 2 (Chailly) SSM

55 SSM Enhancement Shostakovich Waltz 2, Jazz Suite No. 2 (Chailly) SSM

56 SSM Enhancement Shostakovich Waltz 2, Jazz Suite No. 2 (Chailly) Enhanced SSM Filtering along main diagonal

57 SSM Enhancement Idea: Usage of contextual information (Foote 1999) Comparison of entire sequences = length of sequences = enhanced SSM smoothing effect

58 SSM Enhancement SSM

59 SSM Enhancement Enhanced SSM with Filtering along main diagonal

60 SSM Enhancement Enhanced SSM with Filtering along 8 different directions and minimizing

61 SSM Enhancement Idea: Smoothing along various directions and minimizing over all directions Tempo changes of -50 to +50 percent

62 SSM Enhancement Path Enhancement Time (samples) Time (samples)

63 SSM Enhancement Path Enhancement Diagonal smoothing Time (samples) Time (samples)

64 SSM Enhancement Path Enhancement Diagonal smoothing Multiple filtering Time (samples) Time (samples)

65 SSM Enhancement Path Enhancement Diagonal smoothing Multiple filtering Thresholding (relative) Scaling & penalty Time (samples) Time (samples)

66 SSM Enhancement Further Processing Path extraction Time (samples) Time (samples)

67 SSM Enhancement Further Processing Path extraction Pairwise relations Time (samples) Time (samples) Time (samples)

68 SSM Enhancement Further Processing Path extraction Pairwise relations Grouping (transitivity) Time (samples) Time (samples) Time (samples)

69 SSM Enhancement Further Processing Path extraction Pairwise relations Grouping (transitivity) Time (samples) Time (samples) Time (samples) Time (samples)

70 SSM Enhancement Example: Zager & Evans In The Year 2525 I V1 V2 V3 V4 V5 V6 V7 B V8 O

71 SSM Enhancement Example: Zager & Evans In The Year 2525

72 SSM Enhancement Example: Zager & Evans In The Year 2525 Missing relations because of transposed sections

73 SSM Enhancement Example: Zager & Evans In The Year 2525 Idea: Cyclic shift of one of the chroma sequences One semitone up

74 SSM Enhancement Example: Zager & Evans In The Year 2525 Idea: Cyclic shift of one of the chroma sequences Two semitones up

75 SSM Enhancement Example: Zager & Evans In The Year 2525 Idea: Overlay & Maximize Transposition-invariant SSM

76 SSM Enhancement Example: Zager & Evans In The Year 2525 Note: Order of enhancement steps important! Maximization Smoothing & Maximization

77 Similarity Matrix Toolbox Meinard Müller, Nanzhu Jiang, Harald Grohganz SM Toolbox: MATLAB Implementations for Computing and Enhancing Similarity Matrices

78 Overview Introduction Feature Representations Self-Similarity Matrices Audio Thumbnailing Thanks: Jiang, Grosche Peeters Cooper, Foote Goto Levy, Sandler Mauch Sapp Novelty-based Segmentation

79 Audio Thumbnailing General goal: Determine the most representative section ( Thumbnail ) of a given music recording. Example: Zager & Evans In The Year 2525 I V1 V2 V3 V4 V5 V6 V7 B V8 O Example: Brahms Hungarian Dance No. 5 (Ormandy) A1 A2 B1 B2 C A3 B3 B4 Thumbnail is often assumed to be the most repetitive segment

80 Audio Thumbnailing Two steps 1. Path extraction Both steps are problematic! Paths of poor quality (fragmented, gaps) Block-like structures Curved paths 2. Grouping Noisy relations (missing, distorted, overlapping) Transitivity computation difficult Main idea: Do both, path extraction and grouping, jointly One optimization scheme for both steps Stabilizing effect Efficient

81 Audio Thumbnailing Main idea: Do both path extraction and grouping jointly For each audio segment we define a fitness value This fitness value expresses how well the segment explains the entire audio recording The segment with the highest fitness value is considered to be the thumbnail As main technical concept we introduce the notion of a path family

82 Fitness Measure Enhanced SSM

83 Fitness Measure Path over segment Consider a fixed segment

84 Fitness Measure Path over segment Consider a fixed segment Path over segment Induced segment Score is high

85 Fitness Measure Path over segment Consider a fixed segment Path over segment Induced segment Score is high A second path over segment Induced segment Score is not so high

86 Fitness Measure Path over segment Consider a fixed segment Path over segment Induced segment Score is high A second path over segment Induced segment Score is not so high A third path over segment Induced segment Score is very low

87 Fitness Measure Path family Consider a fixed segment A path family over a segment is a family of paths such that the induced segments do not overlap.

88 Fitness Measure Path family Consider a fixed segment A path family over a segment is a family of paths such that the induced segments do not overlap. This is not a path family!

89 Fitness Measure Path family Consider a fixed segment A path family over a segment is a family of paths such that the induced segments do not overlap. This is a path family! (Even though not a good one)

90 Fitness Measure Optimal path family Consider a fixed segment

91 Fitness Measure Optimal path family Consider a fixed segment Consider over the segment the optimal path family, i.e., the path family having maximal overall score. Call this value: Score(segment) Note: This optimal path family can be computed using dynamic programming.

92 Fitness Measure Optimal path family Consider a fixed segment Consider over the segment the optimal path family, i.e., the path family having maximal overall score. Call this value: Score(segment) Furthermore consider the amount covered by the induced segments. Call this value: Coverage(segment)

93 Fitness Measure Fitness Consider a fixed segment P := R := Score(segment) Coverage(segment)

94 Fitness Measure Fitness Consider a fixed segment Self-explanation are trivial! P := R := Score(segment) Coverage(segment)

95 Fitness Measure Fitness Consider a fixed segment Self-explanation are trivial! Subtract length of segment P := R := Score(segment) Coverage(segment) - length(segment) - length(segment)

96 Fitness Measure Fitness Consider a fixed segment Self-explanation are trivial! Subtract length of segment Normalization P := Normalize( Score(segment) - length(segment) ) R := Normalize( Coverage(segment) - length(segment) ) [0,1] [0,1]

97 Fitness Measure Fitness Consider a fixed segment Fitness(segment) F := 2 P R / (P + R) P := Normalize( Score(segment) - length(segment) ) R := Normalize( Coverage(segment) - length(segment) ) [0,1] [0,1]

98 Thumbnail Fitness Scape Plot Fitness Segment length Segment length Segment center Segment center

99 Thumbnail Fitness Scape Plot Fitness Segment length Fitness(segment) Segment length Segment center Segment center

100 Thumbnail Fitness Scape Plot Fitness Segment length Segment center

101 Thumbnail Fitness Scape Plot Fitness Segment length Segment center Note: Self-explanations are ignored fitness is zero

102 Thumbnail Fitness Scape Plot Fitness Segment length Segment center Thumbnail := segment having the highest fitness

103 Thumbnail Fitness Scape Plot Fitness A1 A2 B1 B2 C A3 B3 B4 Example: Brahms Hungarian Dance No. 5 (Ormandy)

104 Thumbnail Fitness Scape Plot Fitness A1 A2 B1 B2 C A3 B3 B4 Example: Brahms Hungarian Dance No. 5 (Ormandy)

105 Thumbnail Fitness Scape Plot Fitness A1 A2 B1 B2 C A3 B3 B4 Example: Brahms Hungarian Dance No. 5 (Ormandy)

106 Thumbnail Fitness Scape Plot Fitness A1 A2 B1 B2 C A3 B3 B4 Example: Brahms Hungarian Dance No. 5 (Ormandy)

107 Scape Plot Example: Brahms Hungarian Dance No. 5 (Ormandy)

108 Scape Plot Coloring according to clustering result (grouping) Example: Brahms Hungarian Dance No. 5 (Ormandy)

109 Scape Plot Coloring according to clustering result (grouping) A1 A2 B1 B2 C A3 B3 B4 Example: Brahms Hungarian Dance No. 5 (Ormandy)

110 Thumbnail Fitness Scape Plot Fitness I V1 V2 V3 V4 V5 V6 V7 B V8 O Example: Zager & Evans In The Year 2525

111 Thumbnail Fitness Scape Plot Fitness I V1 V2 V3 V4 V5 V6 V7 B V8 O Example: Zager & Evans In The Year 2525

112 Overview Introduction Feature Representations Self-Similarity Matrices Thanks: Foote Serra, Grosche, Arcos Goto Tzanetakis, Cook Audio Thumbnailing Novelty-based Segmentation

113 Novelty-based Segmentation General goals: Find instances where musical changes occur. Find transition between subsequent musical parts. Idea (Foote): Use checkerboard-like kernel function to detect corner points on main diagonal of SSM.

114 Novelty-based Segmentation Idea (Foote): Use checkerboard-like kernel function to detect corner points on main diagonal of SSM.

115 Novelty-based Segmentation Idea (Foote): Use checkerboard-like kernel function to detect corner points on main diagonal of SSM.

116 Novelty-based Segmentation Idea (Foote): Use checkerboard-like kernel function to detect corner points on main diagonal of SSM.

117 Novelty-based Segmentation Idea (Foote): Use checkerboard-like kernel function to detect corner points on main diagonal of SSM.

118 Novelty-based Segmentation Idea (Foote): Use checkerboard-like kernel function to detect corner points on main diagonal of SSM. Novelty function using

119 Novelty-based Segmentation Idea (Foote): Use checkerboard-like kernel function to detect corner points on main diagonal of SSM. Novelty function using Novelty function using

120 Novelty-based Segmentation Idea: Find instances where structural changes occur. Structure features Combine global and local aspects within a unifying framework

121 Novelty-based Segmentation Structure features Enhanced SSM

122 Novelty-based Segmentation Structure features Enhanced SSM Time-lag SSM

123 Novelty-based Segmentation Structure features Enhanced SSM Time-lag SSM Cyclic time-lag SSM

124 Novelty-based Segmentation Structure features Enhanced SSM Time-lag SSM Cyclic time-lag SSM Columns as features

125 Novelty-based Segmentation Example: Chopin Mazurka Op. 24, No. 1 SSM Time-lag SSM

126 Novelty-based Segmentation Example: Chopin Mazurka Op. 24, No. 1 SSM Time-lag SSM

127 Novelty-based Segmentation Example: Chopin Mazurka Op. 24, No. 1 SSM Time-lag SSM

128 Novelty-based Segmentation Example: Chopin Mazurka Op. 24, No. 1 SSM Time-lag SSM Structure-based novelty function

129 Conclusions Structure Analysis

130 Conclusions Score Audio MIDI Representations Structure Analysis

131 Conclusions Score Audio MIDI Representations Harmony Musical Aspects Timbre Structure Analysis Tempo

132 Conclusions Score Audio MIDI Representations Musical Aspects Structure Analysis Segmentation Principles Harmony Timbre Tempo Repetition Homogeneity Novelty

133 Conclusions Temporal and Hierarchical Context Score Audio MIDI Representations Musical Aspects Structure Analysis Segmentation Principles Harmony Timbre Tempo Repetition Homogeneity Novelty

134 Conclusions Combined Approaches Hierarchical Approaches Evaluation Explaining Structure MIREX SALAMI-Project Smith, Chew

135 Links SM Toolbox (MATLAB) MSAF: Music Structure Analysis Framework (Python) SALAMI Annotation Data LibROSA (Python) Evaluation: mir_eval (Python) Deep Learning: Boundary Detection Jan Schlüter (PhD thesis)

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