Statistical Parsing for Harmonic Analysis of Jazz Chord ...of Jazz Chord Sequences Mark Granroth-Wilding and Mark Steedman School of Informatics University of Edinburgh 14th September

Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion

Statistical Parsing for Harmonic Analysisof Jazz Chord Sequences

Mark Granroth-Wilding and Mark Steedman

School of InformaticsUniversity of Edinburgh

14th September 2012

1/21

Introduction

• Hierarchical structure in music• Metrical structure• Harmonic structure

1/21

Introduction

1

1/21

Introduction

1

2/21

Applications of Automatic Harmonic Analysis

• Automatic generation:• melodic variations• arrangements• accompaniments

• MIR: e.g. identifying variations• Transcription of scores

2/21

3/21

Related WorkGrammars for music:

• Winograd (1968)Linguistics and the computer analysis of tonal harmony

• Lindblom & Sundberg (1969)Towards a generative theory of melody

• Keiler (1981)Two views of musical semiotics

• Lerdahl & Jackendoff (1983)A generative theory of tonal music

• Steedman (1984)A generative grammar for jazz chord sequences

• Bod (2002)A general parsing model for music and language

• Rohrmeier (2011)Towards a generative syntax of tonal harmony

3/21

4/21

Harmonic Analysis

• Functional harmonic structure• Tension-resolution patterns between chords

C E7 A7 Dm7 G7 Dm7 D[7 C

4/21

Harmonic Analysis

4/21

Harmonic Analysis

4/21

Harmonic Analysis

dom dom dom

dom

dom dom

5/21

Harmonic Analysis

• Chords function as: dominant, subdominant or tonic• Dominant-tonic resolution• Subdominant-tonic resolution• Recursion• Substitution• Delayed resolution: coordination

5/21

Harmonic Analysis

G7 C

dom

5/21

Harmonic Analysis

G7 C

dom

F C

subdom

5/21

Harmonic Analysis

G7 C

dom

F C

subdom

D7 G7 C

dom dom

5/21

Harmonic Analysis

G7 C

dom

F C

subdom

D7 G7 C

dom dom

D7 D[7 C

dom dom

5/21

Harmonic Analysis

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

5/21

Harmonic Analysis

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

5/21

Harmonic Analysis

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

6/21

Jazz Harmony

Jazz is interesting for harmonic analysis

• Large extended cadences• Complex embedding• Many substitutions• Chord sequences

D]◦7 Em7 Am7 E7 Bφ7 E7[9 A7 Dm7 G7 · · · C6dom dom dom dom dom dom

dom

Call Me Irresponsible

6/21

Jazz Harmony

dom

6/21

Jazz Harmony

dom

6/21

Jazz Harmony

dom

6/21

Jazz Harmony

dom

6/21

Jazz Harmony

dom

6/21

Jazz Harmony

dom

6/21

Jazz Harmony

dom

7/21

Tonal Space

• Longuet-Higgin’s formalization oftonal theory

• Distinguishes tonal relationsambiguous in performance

• Partly distinguished on a score E[[

G[

B[

D

F ]

B[[

D[

F

A

C]

F [

A[

C

E

G]

C[

E[

G

B

D]

G[

B[

D

F ]

A]

D[

F

A

C]

E]y

Major 3rd4:5

xPerfect 5th

2:3

zOctave

1:2

• Harmonic analysis disambiguates tonal relations

7/21

Tonal Space

G[

B[

D

F ]

B[[

D[

F

A

C]

F [

A[

C

E

G]

C[

E[

G

B

D]

G[

B[

D

F ]

A]

D[

F

A

C]

E]

7/21

Tonal Space

G[

B[

D

F ]

B[[

D[

F

A

C]

F [

A[

C

E

G]

C[

E[

G

B

D]

G[

B[

D

F ]

A]

D[

F

A

C]

E]

7/21

Tonal Space

G[

B[

D

F ]

B[[

D[

F

A

C]

F [

A[

C

E

G]

C[

E[

G

B

D]

G[

B[

D

F ]

A]

D[

F

A

C]

E]

7/21

Tonal Space

G[

B[

D

F ]

B[[

D[

F

A

C]

F [

A[

C

E

G]

C[

E[

G

B

D]

G[

B[

D

F ]

A]

D[

F

A

C]

E]

A7 Dm7 G7 C

7/21

Tonal Space

G[

B[

D

F ]

B[[

D[

F

A

C]

F [

A[

C

E

G]

C[

E[

G

B

D]

G[

B[

D

F ]

A]

D[

F

A

C]

E]

A7 Dm7 G7 C

dom dom dom

dom

dom dom

7/21

Tonal Space

G[

B[

D

F ]

B[[

D[

F

A

C]

F [

A[

C

E

G]

C[

E[

G

B

D]

G[

B[

D

F ]

A]

D[

F

A

C]

E]

A7 Dm7 G7 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]

8/21

Tonal Space Harmonic Analysis

G7 C

dom

G7 ⇒ dominant, G

C ⇒ tonic, C

8/21

G7 C

dom

G7 ⇒ dominant, G

C ⇒ tonic, C

8/21

G7 C

dom

G7 ⇒ dominant, G

C ⇒ tonic, C

8/21

G7 C

dom

G7 ⇒ dominant, G

C ⇒ tonic, C

8/21

G7 C

dom

G7 ⇒ dominant, G

C ⇒ tonic, C

D[

F

A

A[

C

E

E [

G

B

8/21

G7 C

dom

G7 ⇒ dominant, G

C ⇒ tonic, C

D[

F

A

A[

C

E

E [

G

B

B[

D

F ]

D[

F

A

A[

C

E

E [

G

B

9/21

Harmonic Grammar

D7 G7 C

dom dom

9/21

Harmonic Grammar

D7 G7 C

dom dom

D7 G7 C

>

9/21

Harmonic Grammar

D7 G7 C

dom dom

D7 G7 C

>

9/21

Harmonic Grammar

D7 G7 C

dom dom

D7 G7 C

D[

F

A

A[

C

E

E [

G

B

>

9/21

Harmonic Grammar

D7 G7 C

dom dom

D7 G7 C

D[

F

A

A[

C

E

E [

G

B

>

D[

F

A

A[

C

E

E [

G

B

B[

D

F ]

>

9/21

Harmonic Grammar

D7 G7 C

dom dom

D7 G7 C

D[

F

A

A[

C

E

E [

G

B

>

D[

F

A

A[

C

E

E [

G

B

B[

D

F ]

>

9/21

Harmonic Grammar

D7 G7 C

dom dom

D7 G7 C

D[

F

A

A[

C

E

E [

G

B

>

D[

F

A

A[

C

E

E [

G

B

B[

D

F ]

>

D[

F

A

A[

C

E

E [

G

B

B[

D

F ]

F

A

C ]

9/21

Harmonic Grammar

D7 G7 C

dom dom

D7 G7 C

D[

F

A

A[

C

E

E [

G

B

>B

>

D[

F

A

A[

C

E

E [

G

B

B[

D

F ]

F

A

C ]

10/21

Harmonic Grammar

D7 D[7 C

dom dom

D7 D[7 C

>B

>

10/21

Harmonic Grammar

D7 D[7 C

dom dom

D7 D[7 C

D[

F

A

A[

C

E

E [

G

B

>B

>

10/21

Harmonic Grammar

D7 D[7 C

dom dom

D7 D[7 C

D[

F

A

A[

C

E

E [

G

B

>B

>

D[

F

A

A[

C

E

E [

G

B

B[

D

F ]

F

A

C ]

11/21

Harmonic Grammar

D7 G7 D7 D[7 C· · · · · · · · · · · ·

&

>

D7 G7 D7 D[7 C

dom dom dom

dom

11/21

Harmonic Grammar

D7 G7 D7 D[7 C· · · · · · · · · · · ·

D[

F

A

A[

C

E

E [

G

B

&

>

D7 G7 D7 D[7 C

dom dom dom

dom

11/21

Harmonic Grammar

D7 G7 D7 D[7 C· · · · · · · · · · · ·

D[

F

A

A[

C

E

E [

G

B

&

>

D7 G7 D7 D[7 C

dom dom dom

dom

11/21

Harmonic Grammar

D7 G7 D7 D[7 C· · · · · · · · · · · ·

D[

F

A

A[

C

E

E [

G

B

&

>

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

12/21

Parsing with Grammars

A7 Dm7 G 7 CM7

X0 X1 X2 X3

X ′0 . . . X′1 . . . X

′2 . . . X

′3 . . .

X01

X012

X0123

• Chart parsing

12/21

A7 Dm7 G 7 CM7

X0 X1 X2 X3

X ′0 . . . X′1 . . . X

′2 . . . X

′3 . . .

X01

X012

X0123

• Chart parsing

12/21

A7 Dm7 G 7 CM7

X0 X1 X2 X3

X ′0 . . . X′1 . . . X

′2 . . . X

′3 . . .

X01

X012

X0123

• Chart parsing

12/21

A7 Dm7 G 7 CM7

X0 X1 X2 X3

X ′0 . . . X′1 . . . X

′2 . . . X

′3 . . .

X01

X012

X0123

• Chart parsing

12/21

A7 Dm7 G 7 CM7

X0 X1 X2 X3

X ′0 . . . X′1 . . . X

′2 . . . X

′3 . . .

X01

X012

X0123

Y12

Y123

Y0123

• Chart parsing

12/21

A7 Dm7 G 7 CM7

X0 X1 X2 X3X ′0 . . . X

′1 . . . X

′2 . . . X

′3 . . .

X01

X012

X0123

Y12

Y123

Y0123

• Chart parsing

12/21

A7 Dm7 G 7 CM7

X0 X1 X2 X3X ′0 . . . X

′1 . . . X

′2 . . . X

′3 . . .

X01

X012

X0123,Y0123,Z0123, . . .

Y12

Y123

Y0123

· · ·

• Chart parsing

12/21

A7 Dm7 G 7 CM7

X0 X1 X2 X3X ′0 . . . X

′1 . . . X

′2 . . . X

′3 . . .

X01

X012

X0123,Y0123,Z0123, . . .

Y12

Y123

Y0123

· · ·

• Chart parsing

12/21

A7 Dm7 G 7 CM7

X0 X1 X2 X3X ′0 . . . X

′1 . . . X

′2 . . . X

′3 . . .

X01

X012

X0123,Y0123,Z0123, . . .

Y12

Y123

Y0123

· · ·

• Chart parsing

13/21

Harmonic Analysis by Parsing

A7 Dm7 G 7 CM7

X0 X1 X2 X3X ′0 . . . X

′1 . . . X

′2 . . . X

′3 . . .

X01

X012

X0123,Y0123,Z0123, . . .

Y12

Y123

. . .

A7 Dm7 G7 CM7

domdomdom

D[

F

A

A[

C

E

E[

G

B

B[

D

F ]

F

A

C]

C

E

G]

• Many analyses: parsing is slow• Which are plausible?• Statistical parsing

13/21

A7 Dm7 G 7 CM7

X0 X1 X2 X3X ′0 . . . X

′1 . . . X

′2 . . . X

′3 . . .

X01

X012

X0123,Y0123,Z0123, . . .

Y12

Y123

. . .

A7 Dm7 G7 CM7

domdomdom

D[

F

A

A[

C

E

E[

G

B

B[

D

F ]

F

A

C]

C

E

G]

• Many analyses: parsing is slow• Which are plausible?• Statistical parsing

13/21

A7 Dm7 G 7 CM7

X0 X1 X2 X3X ′0 . . . X

′1 . . . X

′2 . . . X

′3 . . .

X01

X012

X0123,Y0123,Z0123, . . .

Y12

Y123

. . .

A7 Dm7 G7 CM7

domdomdom

D[

F

A

A[

C

E

E[

G

B

B[

D

F ]

F

A

C]

C

E

G]• Many analyses: parsing is slow• Which are plausible?• Statistical parsing

13/21

A7 Dm7 G 7 CM7

X0 X1 X2 X3X ′0 . . . X

′1 . . . X

′2 . . . X

′3 . . .

X01

X012

X0123,Y0123,Z0123, . . .

Y12

Y123

. . .

A7 Dm7 G7 CM7

domdomdom

D[

F

A

A[

C

E

E[

G

B

B[

D

F ]

F

A

C]

C

E

13/21

A7 Dm7 G 7 CM7

X0 X1 X2 X3X ′0 . . . X

′1 . . . X

′2 . . . X

′3 . . .

X01

X012

X0123,Y0123,Z0123, . . .

Y12

Y123

. . .

A7 Dm7 G7 CM7

domdomdom

D[

F

A

A[

C

E

E[

G

B

B[

D

F ]

F

A

C]

C

E

13/21

A7 Dm7 G 7 CM7

X0 X1 X2 X3X ′0 . . . X

′1 . . . X

′2 . . . X

′3 . . .

X01

X012

X0123,Y0123,Z0123, . . .

Y12

Y123

. . .

A7 Dm7 G7 CM7

domdomdom

D[

F

A

A[

C

E

E[

G

B

B[

D

F ]

F

A

C]

C

E

14/21

Statistical Parsing

• Supervised statistical parsing models• Guide parser and rank interpretations• Parsing model: Hockenmaier & Steedman (2002)1

• Model of CCG derivations, PCCG• Supervised training

A7 Dm7 G 7 CM7

X0 X1 X2 X3

X01

X012

X0123,Y0123,Z0123, . . .

1Generative models for statistical parsing with Combinatory CategorialGrammar. ACL

14/21

Statistical Parsing

A7 Dm7 G 7 CM7

X0 X1 X2 X3

X01

X012

X0123,Y0123,Z0123, . . .

14/21

Statistical Parsing

A7 Dm7 G 7 CM7

X0 X1 X2 X3

X01

X012

X0123,Y0123,Z0123, . . .

14/21

Statistical Parsing

A7 Dm7 G 7 CM7

X0 X1 X2 X3

X01

X012

X0123,Y0123,Z0123, . . .

14/21

Statistical Parsing

A7 Dm7 G 7 CM7

X0 X1 X2 X3

X01

X012

X0123,Y0123,Z0123, . . .

14/21

Statistical Parsing

A7 Dm7 G 7 CM7

X0 X1 X2 X3

X01

X012

X0123,Y0123,Z0123, . . .

14/21

Statistical Parsing

A7 Dm7 G 7 CM7

X0 X1 X2 X3

X01

X012

X0123,Y0123,Z0123, . . .

14/21

Statistical Parsing

A7 Dm7 G 7 CM7

X0 X1 X2 X3

X01

X012

X0123,Y0123,Z0123, . . .

15/21

Supertagging

A7 Dm7 G 7 CM7

X0 X1 X2 X3X ′0 . . . X

′1 . . . X

′2 . . . X

′3 . . .

X01

X012

X0123,Y0123,Z0123, . . .

Y12

Y123· · ·

• Reduce choice of lexical categories• Sequence model• Here: HMM

15/21

Supertagging

A7 Dm7 G 7 CM7

X0 X1 X2 X3X ′0 . . . X

′1 . . . X

′2 . . . X

′3 . . .

X01

X012

X0123,Y0123,Z0123, . . .

Y12

Y123· · ·

15/21

Supertagging

A7 Dm7 G 7 CM7

X0 X1 X2 X3X ′0 . . . X

′1 . . . X

′2 . . . X

′3 . . .

X01

X012

X0123,Y0123,Z0123, . . .

Y12

Y123· · ·

15/21

Supertagging

A7 Dm7 G 7 CM7

X0 X1 X2 X3X ′0 . . . X

′1 . . . X

′2 . . . X

′3 . . .

X01

X012

X0123,Y0123,Z0123, . . .

Y12

Y123· · ·

15/21

Supertagging

A7 Dm7 G 7 CM7

X0 X1 X2 X3X ′0 . . . X

′1 . . . X

′2 . . . X

′3 . . .

X01

X012

X0123,Y0123,Z0123, . . .

Y12

Y123· · ·

15/21

Supertagging

A7 Dm7 G 7 CM7

X0 X1 X2 X3X ′0 . . . X

′1 . . . X

′2 . . . X

′3 . . .

X01

X012

X0123,Y0123,Z0123, . . .

Y12

Y123· · ·

16/21

Baseline: HmmPathConstruct path directly

[II

IV

VI

[VI

I

III

[III

V

VII

[VII

II

]IV

IV +

VI+

]I+

16/21

(0,0)D

(-1,0)D

(-1,0)T

D7 G7 CM7

[II

IV

VI

[VI

I

III

[III

V

VII

[VII

II

]IV

IV +

VI+

]I+

16/21

(0,0)D

(-1,0)D

(-1,0)T

D7 G7 CM7

[II

IV

VI

[VI

I

III

[III

V

VII

[VII

II

]IV

IV +

VI+

]I+

16/21

(0,0)D

(-1,0)D

(-1,0)T

D7 G7 CM7

[II

IV

VI

[VI

I

III

[III

V

VII

[VII

II

]IV

IV +

VI+

]I+

DD

16/21

(0,0)D

(-1,0)D

(-1,0)T

D7 G7 CM7

[II

IV

VI

[VI

I

III

[III

V

VII

[VII

II

]IV

IV +

VI+

]I+

DDT

17/21

Jazz Corpus

• Annotated training corpus• Jazz chord sequences• Full grammatical derivation

annotated

• → full harmonic analysis• 74 sequences: ∼3k chords• Cross-validation

17/21

Jazz Corpus

annotated

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

17/21

Jazz Corpus

annotated

17/21

Jazz Corpus

annotated

17/21

Jazz Corpus

annotated

17/21

Jazz Corpus

annotated

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]

17/21

Jazz Corpus

annotated

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]

17/21

Jazz Corpus

annotated

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]

17/21

Jazz Corpus

annotated

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]

17/21

Jazz Corpus

annotated

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]

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

18/21

Evaluation Metric

Tonal space edit distance

D[

F

A

A[

C

E

E [

G

B

B[

D

F ]

F

A

C ]

E [[

G [

B[

D

B[[

D[

F

A

F [

A[

C

E

C [

E [

G

B

Precision, recall, f-score

18/21

Evaluation Metric

D[

F

A

A[

C

E

E [

G

B

B[

D

F ]

F

A

C ]

E [[

G [

B[

D

B[[

D[

F

A

F [

A[

C

E

C [

E [

G

B

18/21

Evaluation Metric

D[

F

A

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E

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B

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D

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F

A

C ]

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G [

B[

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A

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A[

C

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18/21

Evaluation Metric

D[

F

A

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E

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G

B

B[

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F ]

F

A

C ]

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A

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18/21

Evaluation Metric

D[

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A

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18/21

Evaluation Metric

D[

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18/21

Evaluation Metric

D[

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DDT,T

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18/21

Evaluation Metric

D[

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18/21

Evaluation Metric

D[

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18/21

Evaluation Metric

D[

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DDT,T

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18/21

Evaluation Metric

D[

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F ]

F

A

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DDT,T

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18/21

Evaluation Metric

D[

F

A

A[

C

E

E [

G

B

B[

D

F ]

F

A

C ]

DDT,T

E [[

G [

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F

A

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C [

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DT

18/21

Evaluation Metric

D[

F

A

A[

C

E

E [

G

B

B[

D

F ]

F

A

C ]

DDT,T

E [[

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A

F [

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C [

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DT

18/21

Evaluation Metric

D[

F

A

A[

C

E

E [

G

B

B[

D

F ]

F

A

C ]

DDT,T

E [[

G [

B[

D

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A

F [

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E

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DT

19/21

Results

Tonal space edit distance (%)

Precision Recall F-score Coverage

HmmPath 81.1 87.7 84.3 100St+PCCG 86.0 90.8 88.3 98.7

19/21

Results

HmmPath 81.1 87.7 84.3 100St+PCCG 86.0 90.8 88.3 98.7

19/21

Results

HmmPath 81.1 87.7 84.3 100St+PCCG 86.0 90.8 88.3 98.7

20/21

Backoff

• Use HmmPath where St+PCCG fails• HmmPath always produces an analysis

P R F Coverage

HmmPath 81.1 87.7 84.3 100St+PCCG 86.0 90.8 88.3 98.7St+PCCG+HmmPath 85.7 92.0 88.7 100

20/21

Backoff

P R F Coverage

20/21

Backoff

P R F Coverage

20/21

Backoff

P R F Coverage

21/21

Conclusion

• Syntactic grammars for harmonic analysis of chord sequences• Harmonic analysis in tonal space• Jazz grammar• Model of derivations, supertagging• Jazz corpus• Parsing with grammar helps recover harmonic structure

21/21

Conclusion

21/21

Conclusion

21/21

Conclusion

21/21

Conclusion

21/21

Conclusion

21/21

Conclusion

The End

1

References Tonal Space Roman Tonal Space MIDI Parsing New Results Index

Bibliography I

Bod, R. (2002). A general parsing model for music and language.In C. Anagnostopoulou, M. Ferrand, & A. Smaill (Eds.) Musicand Artificial Intelligence, vol. 2445 of Lecture Notes inComputer Science, (pp. 77–90). Springer Berlin / Heidelberg.

Hockenmaier, J., & Steedman, M. (2002). Generative models forstatistical parsing with Combinatory Categorial Grammar. InProceedings of the 40th Meeting of the ACL, (pp. 335–342).Philadelphia, PA.

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

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

Lindblom, B., & Sundberg, J. (1969). Towards a generative theoryof melody. Swedish Journal of Musicology , 10(4), 53–86.

Bibliography II

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

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

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

Extra slide

Tonal Space

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Roman Numeral Tonal Space

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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

Extra slide

New Results

P R F Coverage

HmmPath 80.3 87.2 83.6 100PCCG 92.0 90.4 91.2 97.4St+PCCG 90.3 92.1 91.2 100

Extra Slides

Tonal Space

Roman Tonal Space

MIDI Parsing

New Results

IntroductionIntroduction

Harmonic AnalysisHarmonic Analysis

ParsingParsing

Statistical ParsingStatistical Parsing

ConclusionConclusion

Extra SlidesTonal SpaceTonal Space

Roman Tonal SpaceRoman Tonal Space

MIDI ParsingMIDI Parsing

New ResultsNew Results

IndexIndex

Documents

Statistical Parsing for Harmonic Analysis of Jazz Chord ...of Jazz Chord Sequences Mark Granroth-Wilding and Mark Steedman School of Informatics University of Edinburgh 14th September