pre-viva talk: parsing jazz: harmonic analysis of music...

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Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion Pre-Viva Talk: Parsing Jazz: Harmonic Analysis of Music Using Combinatory Categorial Grammar Mark Granroth-Wilding Supervisors: Mark Steedman Sharon Goldwater School of Informatics University of Edinburgh 15 th March 2013 Handout

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Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

Pre-Viva Talk:

Parsing Jazz:Harmonic Analysis of Music UsingCombinatory Categorial Grammar

Mark Granroth-Wilding

Supervisors:Mark Steedman Sharon Goldwater

School of InformaticsUniversity of Edinburgh

15th March 2013

Handout

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

1/24

Introduction

• Structures underly music

• Hierarchical structures

• Metrical structure

• Harmonic structure

1

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

1/24

Introduction

• Structures underly music

• Hierarchical structures

• Metrical structure

• Harmonic structure

1

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

2/24

Approaches to Musical Analysis

• Varying goals:

1. model/aid compositional process2. model listener’s cognition3. suggest interpretations

• Often not clearly defined

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

3/24

Thesis

• Tonal harmony has a syntax like that of language

• Statistical parsing can be used to infer harmonic structure

Contributions:

• Formal grammar for syntax of harmony

• Harmonic analysis by parsing

• Practical statistical parsing of chord sequences

• Extension to analysis of performance data

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

4/24

A Few Applications

• Automatic generation:• melodic variations• accompaniments

• Song identification

• Language modelling for transcription

(speculative)

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

5/24

Consonance and Harmony

• Simultaneous notes createdissonance / consonance

• Used by composers:tension / relaxation

• Harmony :formation of chord phrases

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• Relationships between chords

• Expectation / fulfilment

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

6/24

Approaches to Harmonic Analysis

Rameau (1722): Traite de l’harmonie

Roman numeral analysis

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Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

6/24

Approaches to Harmonic AnalysisRameau (1722): Traite de l’harmonie

Roman numeral analysis

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Functional analysis

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Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

6/24

Approaches to Harmonic AnalysisRameau (1722): Traite de l’harmonie

Roman numeral analysis

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Functional analysis

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Lerdahl & Jackendoff (1983):

A Generative Theory of Tonal Music

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Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

6/24

Approaches to Harmonic AnalysisRameau (1722): Traite de l’harmonie

Roman numeral analysis

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Functional analysis

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A Generative Theory of Tonal Music

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Winograd (1968), Keiler (1978),

Steedman (1984), Rohrmeier (2011)

Structured functional analysis

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

6/24

Approaches to Harmonic AnalysisRameau (1722): Traite de l’harmonie

Roman numeral analysis

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Functional analysis

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A Generative Theory of Tonal Music

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Winograd (1968), Keiler (1978),

Steedman (1984), Rohrmeier (2011)

Structured functional analysis

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

7/24

Tonal Space

• Longuet-Higgins’ formalization ofharmonic tonal theory

• Tonal relations between notes

• Ambiguous in performance

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G[

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A]

D[

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yMajor 3rd

4:5

xPerfect 5th

2:3

zOctave

1:2

• Harmonic analysis disambiguates tonal relations

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

8/24

Harmony in the Tonal Space

E[[[

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F[

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C[

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Dominant

Tonic

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

9/24

Functional Harmony

E[[[

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C]

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B]

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C[

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DominantTonic

Subdominant

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

10/24

Harmonic Analysis

• Functional harmonic structure

• Segmentation into chords

• Identification of keys

• Functional relationships between chords

C E7 A7 Dm7 G7 Dm7 D[7 C

dom dom dom

dom

dom dom

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

11/24

Harmonic Analysis

• Chords function as: dominant, subdominant or tonic

• Dominant-tonic resolution

• Subdominant-tonic resolution

• Recursion

• Substitution

• Delayed resolution: coordination

D[

F

A

A[

C

E

E[

G

B

G7 C

dom

F C

subdom

D7 G7 C

dom dom

D7 D[7 C

dom dom

D7 G7 D7 D[7 C

dom dom dom

dom

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

11/24

Harmonic Analysis

• Chords function as: dominant, subdominant or tonic

• Dominant-tonic resolution

• Subdominant-tonic resolution

• Recursion

• Substitution

• Delayed resolution: coordination

D[

F

A

A[

C

E

E[

G

B

G7 C

dom

F C

subdom

D7 G7 C

dom dom

D7 D[7 C

dom dom

D7 G7 D7 D[7 C

dom dom dom

dom

Mark bought and Greg read the book

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

11/24

Harmonic Analysis

• Chords function as: dominant, subdominant or tonic

• Dominant-tonic resolution

• Subdominant-tonic resolution

• Recursion

• Substitution

• Delayed resolution: coordination

D[

F

A

A[

C

E

E[

G

B

G7 C

dom

F C

subdom

D7 G7 C

dom dom

D7 D[7 C

dom dom

D7 G7 D7 D[7 C

dom dom dom

dom

C E7 A7 Dm7 G7 Dm7 D[7 C

dom dom dom

dom

dom dom

B[[

D[

F

A

F[

A[

C

E

C[

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G

B

G[

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F]

D[

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A

C]

A[

C

E

G]

E[

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B

D]

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

12/24

Harmonic Combinatory Categorial Grammar

G7 C

dom

C

D[

F

A

A[

C

E

E[

G

B

B[

D

F]

G7 ⇒ G/C : λx . dom(x)

C ⇒ C : C

G7 C

G/C C>

G –C

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

12/24

Harmonic Combinatory Categorial Grammar

G7 C

dom

C

D[

F

A

A[

C

E

E[

G

B

B[

D

F]

G7 ⇒ G/C : λx . dom(x)

C ⇒ C : C

G7 C

G/C : λx . dom(x) C : C>

G –C : dom(C)

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

13/24

Harmonic CCG: Recursion

D7 G7 C

dom dom

C

D7 G7 C

D/G : λx . dom(x) G/C : λx . dom(x) C : C>

G –C : dom(C)>

D–C : dom(dom(C))

Dom: G7 ⇒ G/C : λx . dom(x) Ton: C ⇒ C : C

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

13/24

Harmonic CCG: Recursion

D7 G7 C

dom dom

C

D7 G7 C

D/G : λx . dom(x) G/C : λx . dom(x) C : C>B

D/C : λx . dom(dom(x))>

D–C : dom(dom(C))

Dom: G7 ⇒ G/C : λx . dom(x) Ton: C ⇒ C : C

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

14/24

Harmonic CCG: Substitution

D7 D[7 C

dom dom

D7 D[7 C

D/G G/C C>B

D/C>

D–C

Dom: G7 ⇒ G/C Ton: C ⇒ C

Dom tritone: D[7 ⇒ G/C

D7 G7 C

D/G G/C C>B

D/C>

D–C

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

15/24

Harmonic CCG: Coordination

D7 G7 D7 D[7 C

dom dom dom

dom C

D7 G7 D7 D[7 C

D/G G/C D/G G/C C>B >B

D/C D/C&

D/C>

D–C

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

16/24

Derivation Model

• Supervised statistical parsing model

• Parsing model: Hockenmaier & Steedman (2002)1

• Model of CCG derivations: PCCG

• Supervised training, smoothing

• CKY parser with beam

D7 G7 D7 D[7 C

D/G G/C D/G G/C C>B >B

D/C D/C&

D/C>

D–C

1Generative models for statistical parsing with Combinatory Categorial Grammar. ACL

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

17/24

Supertagging

D7 G7 D7 D[7 C

D/G G/C D/G G/C C

>B >BD/C D/C

&D/C

>D–C

D/A G/D A[/D[ D[/G [ E

>B–E

B[/F A/D C/F B/E C/F

· · ·

• Experimented with n-gram models

• Small corpus: trigrams don’t help

• For parsing experiments:• bigram (HMM)• Katz backoff• Witten-Bell discounting• adaptive supertagging (Clark & Curran, 2007)2

2Wide-Coverage Efficient Statistical Parsing with CCG and Log-Linear Models

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

17/24

Supertagging

D7 G7 D7 D[7 C

D/G G/C D/G G/C C

>B >BD/C D/C

&D/C

>D–C

D/A G/D A[/D[ D[/G [ E

>B–E

B[/F A/D C/F B/E C/F

· · ·

• Experimented with n-gram models

• Small corpus: trigrams don’t help

• For parsing experiments:• bigram (HMM)• Katz backoff• Witten-Bell discounting• adaptive supertagging (Clark & Curran, 2007)2

2Wide-Coverage Efficient Statistical Parsing with CCG and Log-Linear Models

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

18/24

Baseline: HmmPath

• Construct path with HMM:

(0,0) (-1,0) (-1,0)

D7 G7 CM7

D[

F

A

A[

C

E

E[

G

B

B[

D

F]

F

A

C]

C E7 A7 Dm7 G7 Dm7 D[7 C

dom dom dom

dom

dom dom

B[[

D[

F

A

F[

A[

C

E

C[

E[

G

B

G[

B[

D

F]

D[

F

A

C]

A[

C

E

G]

E[

G

B

D]

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

18/24

Baseline: HmmPath

• Construct path with HMM:

(0,0) (-1,0) (-1,0)

D7 G7 CM7

D[

F

A

A[

C

E

E[

G

B

B[

D

F]

F

A

C]

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

19/24

Jazz Corpus

• Annotated training corpus

• Jazz chord sequences

• Full grammatical derivationannotated

• → full harmonic analysis

• 74 sequences: ∼3k chords

• Cross-validation

CM7 F♯φ7 B7♭9 Em7 A7 Dm7 Gm7 Dm7 G7 CM7

CM7 F♯φ7 B7♭9 Gm7 Dm7 Am7 Dm7 G7 CM7

F6 G♯φ7 G7 E♭7 Am7 Em7 Am7 Dm7 F F7

GM7 Bφ7 Em7 A7 Dm7 Am7 Fm7 GM7

CM7 F♯φ7 B7♭9 Em7 A7 Dm7 Gm7 Dm7 G7 CM7

C E7 A7 Dm7 G7 Dm7 D[7 C

dom dom dom

dom

dom dom

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

19/24

Jazz Corpus

• Annotated training corpus

• Jazz chord sequences

• Full grammatical derivationannotated

• → full harmonic analysis

• 74 sequences: ∼3k chords

• Cross-validation

CM7 F♯φ7 B7♭9 Em7 A7 Dm7 Gm7 Dm7 G7 CM7

CM7 F♯φ7 B7♭9 Gm7 Dm7 Am7 Dm7 G7 CM7

F6 G♯φ7 G7 E♭7 Am7 Em7 Am7 Dm7 F F7

GM7 Bφ7 Em7 A7 Dm7 Am7 Fm7 GM7

CM7 F♯φ7 B7♭9 Em7 A7 Dm7 Gm7 Dm7 G7 CM7

C E7 A7 Dm7 G7 Dm7 D[7 C

dom dom dom

dom

dom dom

Afternoon in ParisAlice in WonderlandAnthropologyBeauty and the BeastBlack OrpheusBlackberry WinterBlue in GreenBoplicityBud PowellByrd LikeCall Me IrresponsibleCan’t Help Lovin’ Dat ManChelsea BridgeA Child is BornChippieChitlins Con CarneComo En VietnamConfirmationCrescentDear Old Stockholm

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

20/24

Evaluation Metric

Tonal space edit distance

D[

F

A

A[

C

E

E[

G

B

B[

D

F]

F

A

C]

DDT,T

E[[

G[

B[

D

B[[

D[

F

A

F[

A[

C

E

C[

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BT,T

DT

Precision, recall, f-score

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

21/24

Evaluation: Dependency Recovery

• Dependency recovery of harmonic analysis

C D7 D[7 C

C

dom dom

C

C D7 D[7 C

E

dom

D[ C

Gold standard:

Parse result:

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

22/24

Results

• Tonal space metric:

P (%) R (%) F (%) Cov. (%)

HmmPath 77.44 84.87 80.98 100PCCG 92.29 88.78 90.50 97.37St+PCCG 90.18 92.79 91.46 100

• Dependency recovery:

P (%) R (%) F (%)

PCCG 90.25 86.83 88.51St+PCCG 88.22 90.78 89.48

(0,0) (-1,0) (-1,0)

D7 G7 CM7

D7 G7 D7 D[7 C

D/G G/C D/G G/C C>B >B

D/C D/C&

D/C>

D–C

D7 G7 D7 D[7 C

D/G G/C D/G G/C C

>B >BD/C D/C

&D/C

>D–C

D/A G/D A[/D[ D[/G [ EB[/F A/D C/F B/E C/F

· · ·

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

23/24

Conclusion

• Harmonic analysis in the tonal space

• Hierarchical structure in harmony

• Harmonic adaptation of CCG

• Statistical parsing, adapted from NLP

• Chord sequence treebank

D[

F

A

A[

C

E

E[

G

B

B[

D

F]

F

A

C]

D7 G7 D7 D[7 C

dom dom dom

dom

D7 G7 D7 D[7 C

D/G G/C D/G G/C C>B >B

D/C D/C&

D/C>

D–C

D7 G7 D7 D[7 C

D/G G/C D/G G/C C

>B >BD/C D/C

&D/C

>D–C

D/A G/D A[/D[ D[/G [ EB[/F A/D C/F B/E C/F

· · ·CM7 F♯φ7 B7♭9 Em7 A7 Dm7 Gm7 Dm7 G7 CM7

CM7 F♯φ7 B7♭9 Gm7 Dm7 Am7 Dm7 G7 CM7

F6 G♯φ7 G7 E♭7 Am7 Em7 Am7 Dm7 F F7

GM7 Bφ7 Em7 A7 Dm7 Am7 Fm7 GM7

CM7 F♯φ7 B7♭9 Em7 A7 Dm7 Gm7 Dm7 G7 CM7

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion

24/24

Conclusion

Thesis:

• Tonal harmony has a syntax like that oflanguage

• Statistical parsing can be used to infer harmonicstructure

• CCG grammar of harmonic structure

• Statistical parser for harmonic analysis

• Parser outperforms HMM baseline

• Extension to analysis of performances

Bibliography Atomic Categories MIDI Parsing Tonal Space Parsing Time Index

Extra slide

Bibliography I

Clark, S., & Curran, J. R. (2007).Wide-coverage efficient statistical parsing with CCG andlog-linear models.Computational Linguistics, 33 , 493–552.

Hockenmaier, J., & Steedman, M. (2002).Generative models for statistical parsing with CombinatoryCategorial Grammar.In Proceedings of the 40th Meeting of the Association forComputational Linguistics, (pp. 335–342). Philadelphia, PA:Association for Computational Linguistics.

Keiler, A. (1981).Two views of musical semiotics.In W. Steiner (Ed.) The Sign in Music and Literature, (pp.138–168). Austin TX: University of Texas Press.

Bibliography Atomic Categories MIDI Parsing Tonal Space Parsing Time Index

Extra slide

Bibliography II

Lerdahl, F., & Jackendoff, R. (1983).A Generative Theory of Tonal Music .Cambridge, MA: MIT Press.

Rameau, J. P. (1722).Traite de l’harmonie.Jean-Baptiste-Christophe Ballard.

Riemann, H. (1893).Vereinfachte Harmonielehre oder die Lehre von den tonalenFunktionen der Akkorde.Augener & Co.Trans. H. Bemerunge, as Harmony Simplified, or the Theory ofthe Tonal Functions of Chords.

Bibliography Atomic Categories MIDI Parsing Tonal Space Parsing Time Index

Extra slide

Bibliography III

Rohrmeier, M. (2011).Towards a generative syntax of tonal harmony.Journal of Mathematics and Music , 5 , 35–53.

Steedman, M. (1984).A generative grammar for jazz chord sequences.Music Perception, 2 , 52–77.

Winograd, T. (1968).Linguistics and the computer analysis of tonal harmony.Journal of Music Theory , 12 , 2–49.

Bibliography Atomic Categories MIDI Parsing Tonal Space Parsing Time Index

Extra slide

Atomic Categories

G7 C

G/C C>

G –C

C G7 C

C G/C C>

G –Cdev

C –C = C

BM7 G7 C

B G/C C>

G –Cdev

B–C

C –C

Bibliography Atomic Categories MIDI Parsing Tonal Space Parsing Time Index

Extra slide

Parsing Performances

• Can we parse a musical performance?

G C G C G D7 G

• Proof-of-concept extension

• HMM chord recognizer

• Parse chord labels as before

Bibliography Atomic Categories MIDI Parsing Tonal Space Parsing Time Index

Extra slide

Parsing Performances

• Parser beats baseline

• Much lower results than chord task

• Chord recognizer over-commits, parse a lattice

• Need rhythmic/metrical models

• Harder modelling task:voice-leading, polyphony, chord inversion, octave separation, . . .

• Evaluation harder: model does segmentation

• Unlabelled data

Bibliography Atomic Categories MIDI Parsing Tonal Space Parsing Time Index

Extra slide

MIDI Parsing

64 (C)

68 (E)

71 (G)

73 (A)72 (G♯)

75 (B)

66 (D)

63 (B)

MIDI input

Chord recognizer: lattice

Lattice-based supertagger/parser

Bibliography Atomic Categories MIDI Parsing Tonal Space Parsing Time Index

Extra slide

Tonal Space

E[[[

G[[

B[[

D[

F

A

C]

B[[[

D[[

F[

A[

C

E

G]

F[[

A[[

C[

E[

G

B

D]

C[[

E[[

G[

B[

D

F]

A]

G[[

B[[

D[

F

A

C]

E]

D[[

F[

A[

C

E

G]

B]

A[[

C[

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B

D]

F]]

E[[

G[

B[

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F]

A]

C]]

B[[

D[

F

A

C]

E]

G]]

F[

A[

C

E

G]

B]

D]]

C[

E[

G

B

D]

F]]

A]]

Bibliography Atomic Categories MIDI Parsing Tonal Space Parsing Time Index

Extra slide

Roman Numeral Tonal Space

[[[III−

[[V−

[[VII−

[II−

IV−

VI−

]I−

[[[VII−

[[II−

[IV−

[VI−

I−

III−

]V−

[[IV−

[[VI−

[I−

[III−

V−

VII−

]II−

[[I−

[[III−

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II−

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]VI−

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IV

VI

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I

III

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[[VI

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]]IV

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[VII

II

]IV

]VI

]]I

[[VII+

[II+

IV+

VI+

]I+

]III+

]]V+

[IV+

[VI+

I+

III+

]V+

]VII+

]]II+

[I+

[III+

V+

VII+

]II+

]]IV+

]]VI+

Bibliography Atomic Categories MIDI Parsing Tonal Space Parsing Time Index

Extra slide

Parsing Time

Average parse time per chord sequence:

Model Mean (std. dev.)

HmmPath 0:03 (0:01)PCCG 34:17 (75:23)St+PCCG 9:22 (33:32)

Bibliography Atomic Categories MIDI Parsing Tonal Space Parsing Time Index

Extra Slides

Bibliography

Atomic Categories

MIDI Parsing

Tonal Space

Parsing Time