Music Structure Analysis Book: Fundamentals of Music ... · Shostakovich Waltz 2, Jazz Suite No. 2 (Chailly) SSM SSM Enhancement Shostakovich Waltz 2, Jazz Suite No. 2 (Chailly) Enhanced

Music Processing

Meinard Müller

Lecture

Music Structure Analysis

International Audio Laboratories [email protected]

Book: Fundamentals of Music Processing

Meinard MüllerFundamentals of Music ProcessingAudio, Analysis, Algorithms, Applications483 p., 249 illus., hardcoverISBN: 978-3-319-21944-8Springer, 2015

Accompanying website: www.music-processing.de







Chapter 4: Music Structure Analysis

In Chapter 4, we address a central and well-researched area within MIR knownas music structure analysis. Given a music recording, the objective is toidentify important structural elements and to temporally segment the recordingaccording to these elements. Within this scenario, we discuss fundamentalsegmentation principles based on repetitions, homogeneity, and novelty—principles that also apply to other types of multimedia beyond music. As animportant technical tool, we study in detail the concept of self-similaritymatrices and discuss their structural properties. Finally, we briefly touch thetopic of evaluation, introducing the notions of precision, recall, and F-measure.

4.1 General Principles4.2 Self-Similarity Matrices4.3 Audio Thumbnailing4.4 Novelty-Based Segmentation4.5 Evaluation4.6 Further Notes

Music Structure AnalysisExample: Zager & Evans “In The Year 2525”

Time (seconds)


Time (seconds)

Example: Zager & Evans “In The Year 2525”


V1 V2 V3 V4 V5 V6 V7 V8 OBI


Music Structure AnalysisExample: Brahms Hungarian Dance No. 5 (Ormandy)

Time (seconds)

A1 A2 A3B1 B2 B3 B4C


Time (seconds)

Example: Folk Song Field Recording (Nederlandse Liederenbank)

Example: Weber, Song (No. 4) from “Der Freischütz”

0 50 100 150 200

…...

Kleiber

Time (seconds)

.. ....


0 50 100 150 200

Introduction Stanzas Dialogues

20 40 60 80 100 12020 40 60 80 100 120

Ackermann

Time (seconds)


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

General goal: Divide an audio recording into temporal segments corresponding to musical parts and group these segments into musically meaningful categories.

Examples:


Homogeneity:

Novelty:

Repetition:

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.

Consistency in tempo, instrumentation, key, …

Sudden changes, surprising elements …

Repeating themes, motives, rhythmic patterns,…


Novelty Homogeneity Repetition

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 …

Overview

Introduction



Audio Thumbnailing


Thanks:

Clausen, Ewert, Kurth, Grohganz, …

Dannenberg, Goto Grosche, Jiang Paulus, Klapuri Peeters, Kaiser, … Serra, Gómez, … Smith, Fujinaga, … Wiering, … Wand, Sunkel,

Jansen …

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


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


C124

C236

C348

C460

C572

C684

C796

C8108

Example: Chromatic scale

Waveform

Time (seconds)

Ampl

itude


Freq

uenc

y (H

z)

Inte

nsity

(dB)

Inte

nsity

(dB)

Freq

uenc

y (H

z)

Time (seconds)

C124

C236

C348

C460

C572

C684

C796

C8108


Spectrogram


Freq

uenc

y (H

z)

Inte

nsity

(dB)

Inte

nsity

(dB)

Freq

uenc

y (H

z)

Time (seconds)

C124

C236

C348

C460

C572

C684

C796

C8108


Spectrogram


C4: 261 HzC5: 523 Hz

C6: 1046 Hz

C7: 2093 Hz

C8: 4186 Hz

C3: 131 Hz

Inte

nsity

(dB)

Time (seconds)

C124

C236

C348

C460

C572

C684

C796

C8108


Spectrogram


C4: 261 Hz

C5: 523 Hz

C6: 1046 Hz

C7: 2093 Hz

C8: 4186 Hz

C3: 131 Hz Int

ensi

ty (d

B)

Time (seconds)

C124

C236

C348

C460

C572

C684

C796

C8108


Log-frequency spectrogram


Pitc

h (M

IDI n

ote

num

ber)

Inte

nsity

(dB)

Time (seconds)

C124

C236

C348

C460

C572

C684

C796

C8108




Chroma C

Inte

nsity

(dB)

Pitc

h (M

IDI n

ote

num

ber)

Time (seconds)

C124

C236

C348

C460

C572

C684

C796

C8108




Chroma C#

Inte

nsity

(dB)

Pitc

h (M

IDI n

ote

num

ber)

Time (seconds)

C124

C236

C348

C460

C572

C684

C796

C8108




C124

C236

C348

C460

C572

C684

C796

C8108


Chroma representation

Inte

nsity

(dB)

Time (seconds)

Chr

oma

Feature RepresentationExample: Brahms Hungarian Dance No. 5 (Ormandy)

Time (seconds)




Feature extractionChroma (Harmony)

Example: Brahms Hungarian Dance No. 5 (Ormandy)

Time (seconds)





G minor G minor

D

GBb

Time (seconds)





G minor G major G minor

D

GBb

D

GB

Time (seconds)

Overview

Introduction



Audio Thumbnailing


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

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







G major

G m

ajor






Slower

Fast

er


Fast

er

Slower


Idealized SSM


Idealized SSM

Blocks: Homogeneity

Paths: Repetition

Corners: Novelty

SSM Enhancement

Feature smoothing Coarsening

Time (samples)

Tim

e (s

ampl

es)

Block Enhancement

SSM Enhancement

Block Enhancement


Time (samples)

Tim

e (s

ampl

es)

SSM Enhancement


Time (samples)

Tim

e (s

ampl

es)

Block Enhancement

SSM EnhancementChallenge: Presence of musical variations

Idea: Enhancement of path structure

Fragmented paths and gaps

Paths of poor quality

Regions of constant (high) similarity

Curved paths

SSM EnhancementShostakovich Waltz 2, Jazz Suite No. 2 (Chailly)

SSM


SSM


SSM


Enhanced SSMFiltering along main diagonal

SSM Enhancement

Idea: Usage of contextual information (Foote 1999)

smoothing effect

Comparison of entire sequences = length of sequences = enhanced SSM

SSM Enhancement

SSM

SSM Enhancement

Filtering along main diagonalEnhanced SSM with

SSM Enhancement

Filtering along 8 different directions and minimizingEnhanced SSM with

SSM Enhancement

Idea: Smoothing along various directionsand minimizing over all directions

Tempo changes of -50 to +50 percent

SSM Enhancement

Time (samples)

Tim

e (s

ampl

es)

Path Enhancement

SSM Enhancement

Time (samples)

Tim

e (s

ampl

es)

Path Enhancement

Diagonal smoothing

SSM Enhancement

Time (samples)

Tim

e (s

ampl

es)

Path Enhancement

Diagonal smoothing Multiple filtering

SSM Enhancement

Time (samples)

Tim

e (s

ampl

es)

Path Enhancement

Diagonal smoothing Multiple filtering Thresholding (relative) Scaling & penalty

SSM Enhancement

Time (samples)

Tim

e (s

ampl

es)

Further Processing

Path extraction

SSM Enhancement

Time (samples)

Tim

e (s

ampl

es)

Further Processing

Path extraction Pairwise relations

100 200 300 400

1

Time (samples)

234567

SSM Enhancement

Time (samples)

Tim

e (s

ampl

es)

Further Processing

Path extraction Pairwise relations Grouping (transitivity)

100 200 300 400

1

Time (samples)

234567

100 200 300 400Time (samples)

SSM Enhancement

Time (samples)

Tim

e (s

ampl

es)

Further Processing

Path extraction Pairwise relations Grouping (transitivity)

100 200 300 400

1

Time (samples)

234567

SSM Enhancement



SSM EnhancementExample: Zager & Evans “In The Year 2525”

SSM EnhancementExample: Zager & Evans “In The Year 2525”Missing relations because of transposed sections

SSM EnhancementExample: Zager & Evans “In The Year 2525”Idea: Cyclic shift of one of the chroma sequences

One semitone up

SSM EnhancementExample: Zager & Evans “In The Year 2525”Idea: Cyclic shift of one of the chroma sequences

Two semitones up

SSM EnhancementExample: Zager & Evans “In The Year 2525”Idea: Overlay Transposition-invariant SSM& Maximize

SSM EnhancementExample: Zager & Evans “In The Year 2525”Note: Order of enhancement steps important!

Maximization Smoothing & Maximization

Similarity Matrix Toolbox

Meinard Müller, Nanzhu Jiang, Harald GrohganzSM Toolbox: MATLAB Implementations for Computing andEnhancing Similarity Matrices

http://www.audiolabs-erlangen.de/resources/MIR/SMtoolbox/

Overview

Introduction



Audio Thumbnailing


Thanks:

Jiang, Grosche Peeters Cooper, Foote Goto Levy, Sandler Mauch Sapp

Audio Thumbnailing



General goal: Determine the most representative section(“Thumbnail”) of a given music recording.



Thumbnail is often assumed to be the most repetitive segment

Audio Thumbnailing

Two steps Paths of poor quality (fragmented, gaps) Block-like structures Curved paths

1. Path extraction

2. Grouping Noisy relations(missing, distorted, overlapping)

Transitivity computation difficult

Both steps are problematic!

Main idea: Do both, path extraction and grouping, jointly One optimization scheme for both steps Stabilizing effect Efficient

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 segmentexplains the entire audio recording

The segment with the highest fitness value isconsidered to be the thumbnail

As main technical concept we introduce the notion of a path family

0 50 100 150 2000

20

40

60

80

100

120

140

160

180

200

−2

−1.5

−1

−0.5

0

0.5

1

Fitness Measure

Enhanced SSM

Fitness Measure

Consider a fixed segment

Path over segment

Fitness Measure


Path over segment Induced segment Score is high

Path over segment

Fitness Measure

Path over segment



A second path over segment Induced segment Score is not so high

Fitness Measure

Path over segment



A second path over segment Induced segment Score is not so high

A third path over segment Induced segment Score is very low

Fitness Measure

Path family


A path family over a segmentis a family of paths such thatthe induced segments do not overlap.

Fitness Measure

Path family

This is not a path family!



Fitness Measure

Path family

This is a path family!



(Even though not a good one)

Fitness Measure

Optimal path family


Fitness Measure

Optimal path family


Consider over the segmentthe optimal path family,i.e., the path family havingmaximal overall score.

Call this value:Score(segment)

Note: This optimal path family can be computedusing dynamic programming.

Fitness Measure

Optimal path family


Consider over the segmentthe optimal path family,i.e., the path family havingmaximal overall score.

Call this value:Score(segment)

Furthermore consider theamount covered by theinduced segments.

Call this value:Coverage(segment)

Fitness Measure

Fitness


P := R :=

Score(segment)Coverage(segment)

Fitness Measure

Fitness


Self-explanation are trivial!

P := R :=


Fitness Measure

Fitness



Subtract length of segment

P := R :=


- length(segment) - length(segment) Normalize( )

Fitness Measure

Fitness



Subtract length of segment

Normalization

P := R :=


- length(segment)- length(segment)

]1,0[]1,0[

Normalize( )

Fitness Measure

Fitness


F := 2 • P • R / (P + R)Fitness(segment)

Normalize( ) Normalize( )

P := R :=


- length(segment)- length(segment)

]1,0[]1,0[

Thumbnail

Segment center

Segm

ent l

engt

h

Fitness Scape Plot

Segment length

Segment center

Fitness

Thumbnail

Segment center

Fitness Scape Plot

Fitness(segment)

Segment length

Segment center

Fitness

Segm

ent l

engt

h

Thumbnail

Segment center

Fitness Scape PlotFitness

Segm

ent l

engt

h

Thumbnail

Segment center

Fitness Scape Plot

Note: Self-explanations are ignored → fitness is zero

Fitness

Segm

ent l

engt

h

Thumbnail

Segment center

Fitness Scape Plot

Thumbnail := segment having the highest fitness

Fitness

Segm

ent l

engt

h

ThumbnailFitness Scape Plot


Fitness


Fitness




Fitness




Fitness




Scape Plot


Scape Plot

Coloring accordingto clustering result(grouping)


Scape Plot


Coloring accordingto clustering result(grouping)




Fitness


Fitness




Overview

Introduction



Audio Thumbnailing


Thanks:

Foote Serra, Grosche, Arcos Goto Tzanetakis, Cook


Find instances where musicalchanges occur.

Find transition between subsequent musical parts.

General goals: Idea (Foote):

Use checkerboard-like kernelfunction to detect corner pointson main diagonal of SSM.


Idea (Foote):



Idea (Foote):



Idea (Foote):



Idea (Foote):



Idea (Foote):


Novelty function using


Idea (Foote):





Idea: Find instances where

structural changes occur.

Combine global and localaspects within a unifying framework

Structure features


Enhanced SSM

Structure features


Enhanced SSM Time-lag SSM

Structure features


Enhanced SSM Time-lag SSM Cyclic time-lag SSM

Structure features


Enhanced SSM Time-lag SSM Cyclic time-lag SSM Columns as features

Structure features

Novelty-based SegmentationExample: Chopin Mazurka Op. 24, No. 1

SSM

Time-lag SSM


SSM

Time-lag SSM


SSM

Time-lag SSM


Structure-based novelty function

Example: Chopin Mazurka Op. 24, No. 1

SSM

Time-lag SSM

Structure Analysis

Conclusions

Representations

Structure Analysis

AudioMIDIScore

Conclusions

Representations

Musical Aspects

Structure Analysis

TimbreTempoHarmony

AudioMIDIScore

Conclusions

Representations

Segmentation Principles

Musical Aspects

Structure Analysis

HomogeneityNoveltyRepetition

TimbreTempoHarmony

AudioMIDIScore

Conclusions

Temporal and Hierarchical Context

Representations

Segmentation Principles

Musical Aspects

Structure Analysis

HomogeneityNoveltyRepetition

TimbreTempoHarmony

AudioMIDIScore

Conclusions Conclusions

Combined Approaches

Hierarchical Approaches

Evaluation

Explaining Structure

MIREX SALAMI-Project

Smith, Chew

Links SM Toolbox (MATLAB)

http://www.audiolabs-erlangen.de/resources/MIR/SMtoolbox/

MSAF: Music Structure Analysis Framework (Python)https://github.com/urinieto/msaf

SALAMI Annotation Datahttp://ddmal.music.mcgill.ca/research/salami/annotations

LibROSA (Python)https://librosa.github.io/librosa/

Evaluation: mir_eval (Python)https://craffel.github.io/mir_eval/

Deep Learning: Boundary DetectionJan Schlüter (PhD thesis)

Documents

Music Structure Analysis Book: Fundamentals of Music ... · Shostakovich Waltz 2, Jazz Suite No. 2 (Chailly) SSM SSM Enhancement Shostakovich Waltz 2, Jazz Suite No. 2 (Chailly) Enhanced