Daniel Müllensiefen

Department of Psychology

GoldsmithsUniversity of London

Similarity Algorithmsfor Music Plagiarism

StructureStructure1 Introduction2 Method and Examples3 Algorithms4 Empirical Study5 Summary – Future Research

IntroductionIntroduction: : The The BackgroundBackgroundHuge Public Interest:

Importance for the pop industry, interestingemphasis on tunes (melodic plagiarism)

Ambigity surrounding UK law in defining asubstantail part

Lack of Research, Exceptions: Timothy English: Sounds Like Teen Spirit, (2008) Stan Soocher: They Fought The Law, (1999) Charles Cronin: Concepts of Melodic Similarity in

Music-Copyright, (1998)

The 2-second rule The 1-bar rule The 5-notes rule

IntroductionIntroduction::No No hard hard and fast and fast rulesrules!!

It is more complicated than that!

What has been taken needs to be at least asubstantial part of the copyright work(Lord Millet, Designers Guild v. Williams [2000] 1 WLR 2426)

The first quantitative study on music plagiarism

IntroductionIntroduction: : MMüllensiefen üllensiefen &&Pendzich Pendzich (2009)(2009)

Questions: Can computer algorithms predict plagiarism

incidents from the melodic similarity of tunes? What is the predictive power of these algorithms

when superimposed on documented case law?

What is the frame of reference(directionality of comparisons)?

How can prior musical knowledge be takeninto account?

MethodMethod: : OutlineOutline

Selection of 20 cases* from 1970 to 2005 – focuson melodic aspects of copyright infringement

Transcription to monophonic MIDI files Analysis of judges' written opinions Reduction of court decisions to two categories

“pro plaintiff” = melodic plagiarism “contra plaintiff” = no infringement

Use of context: Corpus of 14,063 pop songsrepresenting pop music history from 1950-2006

*from UCLA/Columbia copyright infringement database: http://cip.law.ucla.edu/

The Chiffons He‘s So Fine, 1963 No. 1 in US, UK highest position 11

Example 1: Bright Tunes v.Example 1: Bright Tunes v.Harrisongs Harrisongs (1976, 420 F. Supp)(1976, 420 F. Supp)

George Harrison, My Sweet LordPublished in 1971 No.-1-Hit in US, UK & (West-)Germany

Ronald Selle, “Let It End” Unreleased (1975)

Example 2: Selle v. Gibb Example 2: Selle v. Gibb (1983, 567(1983, 567F.Supp 1173)F.Supp 1173)

Bee Gees, “How Deep Is Your Love” (1977)

AlgorithmsAlgorithms

Statistically Informed Similarity Algorithms:Importance of frequency of melodicelements for similarity assessment

Inspired from computational linguistics(Baayen, 2001) and text processing (Manning &Schütze, 1999; Jurafsky & Martin, 2000)

Conceptual Components: m-types (aka n-grams) as melodic elements Frequency counts: Type frequency (TF) and

Inverted Document Frequency (IDF)

Melodic elementsMelodic elements: : m-typesm-types

Word Type t Frequency f(t), Melodic Type τ (pitchinterval, length 2)

Frequency f(τ),

Twinkle 2 0, +7 1

little 1 +7, 0 1

star 1 0, +2 1

How 1 +2, 0 1

I 1 0, -2 3

wonder 1 -2, -2 1

what 1 -2, 0 2

you 1 0, -1 1

are 1 -1, 0 1

!

IDFC"( ) = log

C

m:" #m( )C Corpus of melodies

m melody

τ Melodic type

T # different melodic types

|m:τ ∈ m| # melodies containing τ

!

TF(m," ) =fm "( )

fm " i( )i=1

#

$

Melodic Type τ(pitch interval,length 2)

Frequency f(τ)

0, +7 1

+7, 0 1

0, +2 1

+2, 0 1

0, -2 3

-2, -2 1

-2, 0 2

0, -1 1

-1, 0 1

Type- and Type- and InvertedInvertedDocument FrequenciesDocument Frequencies

!

IDFC"( ) = log

C

m:" #m( )C Corpus of melodies

m melody

τ Melodic type

τ T # different melodic types

|m:τ ∈ m| # melodies containing τ

!

TF(m," ) =fm "( )

fm " i( )i=1

#

$

Melodic Type τ(pitch interval,length 2)

Frequency f(τ) TF(m, τ)

0, +7 1 0.083

+7, 0 1 0.083

0, +2 1 0.083

+2, 0 1 0.083

0, -2 3 0.25

-2, -2 1 0.083

-2, 0 2 0.167

0, -1 1 0.083

-1, 0 1 0.083

Type- and Type- and InvertedInvertedDocument FrequenciesDocument Frequencies

!

IDFC"( ) = log

C

m:" #m( )C Corpus of melodies

m melody

τ Melodic type

τ T # different melodic types

|m:τ ∈ m| # melodies containing τ

!

TF(m," ) =fm "( )

fm " i( )i=1

#

$

Melodic Type τ(pitch interval,length 2)

Frequency f(τ) TF(m, τ) IDFC(τ)

0, +7 1 0.083 1.57

+7, 0 1 0.083 1.36

0, +2 1 0.083 0.23

+2, 0 1 0.083 0.28

0, -2 3 0.25 0.16

-2, -2 1 0.083 0.19

-2, 0 2 0.167 0.22

0, -1 1 0.083 0.51

-1, 0 1 0.083 0.74

Type- and Type- and InvertedInvertedDocument FrequenciesDocument Frequencies

!

IDFC"( ) = log

C

m:" #m( )C Corpus of melodies

m melody

τ Melodic type

τ T # different melodic types

|m:τ ∈ m| # melodies containing τ

!

TF(m," ) =fm "( )

fm " i( )i=1

#

$

Melodic Type τ(pitch interval,length 2)

Frequency f(τ) TF(m, τ) IDFC(τ) TFIDFm,C(τ)

0, +7 1 0.083 1.57 0.13031

+7, 0 1 0.083 1.36 0.11288

0, +2 1 0.083 0.23 0.01909

+2, 0 1 0.083 0.28 0.02324

0, -2 3 0.25 0.16 0.04

-2, -2 1 0.083 0.19 0.01577

-2, 0 2 0.167 0.22 0.03674

0, -1 1 0.083 0.51 0.04233

-1, 0 1 0.083 0.74 0.06142

Type- and Type- and InvertedInvertedDocument FrequenciesDocument Frequencies

!

"C(s,t) =

TFIDFs,C(# ) $TFIDF

t,C(# )

# % sn&tn

'

TFIDFs,C(# )( )

2

$ TFIDFt,C(# )( )

2

# % sn&tn

'#% s

n&tn

'

TF-IDF CorrelationTF-IDF Correlation

Ratio Model (Tversky, 1977): Similarity σ(s,t) related to # features in s and t have common salience of features f()

!

"(s,t) =f (sn# tn )

f (sn# tn )+$f (sn \ tn )+ %f ( tn \ sn ),$,% & 0

features => m-types salience => IDF and TF different values of α, β to change frame of reference

Variable m-type lengths (n=1,…,4), entropy-weighted average

Feature-based SimilarityFeature-based Similarity

Tversky.equal measure (with α = β = 1)

!

"(s,t) =IDF

C(# )

# $ sn% t

n

&IDF

C(# )

# $ sn% t

n

& + IDFC(# )

# $ sn\ tn

& + IDFC(# )

# $ tn\ sn

&

Tversky.plaintiff.only measure (with α = 1, β = 0)

!

"plaintiff.only(s,t) =IDF

C(# )

# $ sn% t

n

&IDF

C(# )

# $ sn% t

n

& + IDFC(# )

# $ sn\ tn

&

Tversky.defendant.only measure (with α = 0, β = 1)

!

"defendant .only( t,s) =IDFC (# )# $ sn% tn

&IDFC (# )# $ sn% tn

& + IDFC (# )# $ tn \ sn&

Tversky.weighted measure with and

!

" =TF

s(# )

# $ sn% t

n

&TF

s(# )

# $ sn

&

!

" =TF

t(# )

# $ sn% t

n

&TF

t(# )

# $ tn

&

Feature-based SimilarityFeature-based Similarity

Ground Truth:20 cases with pro/contra decision (7/13)

Evaluation metrics Accuracy (% correct at optimal cut-off on

similarity scale) AUC (Area Under receiver operating

characteristic Curve)

EvaluationEvaluation

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EvaluationEvaluation

Evaluation: ROC CurvesEvaluation: ROC Curves

Observations: Decision sometimes based on ‘characteristic motives’ (incl. rhythm)

High-level form can be important (e.g. call-and-response structure)

Frame of reference can be different

Ronald Selle, “Let It End”

Bee Gees, “How Deep Is Your Love”

A Qualitative LookA Qualitative Look

SummarySummary Court decisions can be related closely tomelodic similarity Plaintiff’s song is often the frame ofreference when determining the question ofsubstantial part (“It depends upon its importance to thecopyright work. It does not depend upon its importance to thedefendants” per Lord Millet)

Statistical information about commonnessof melodic elements is important

Future ResearchFuture Research

Conduct analogous studies with cases fromthe UK and Germany and utilize additionalUS cases

Include rhythm in m-types Use higher level features of melodies in

addition to m-types Conduct listening experiment to determine

cognitive validity

Daniel Müllensiefen

Department of Psychology

Goldsmiths,University of London

Similarity algorithmsfor music plagiarism