[PPT] - Parsing Jazz: Harmonic Analysis of Music Using Combinatory PowerPoint Presentation

SLIDE 1

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

15th March 2013 Handout

SLIDE 2

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 1/24

Introduction

Structures underly music
Hierarchical structures
Metrical structure
Harmonic structure

SLIDE 3

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 1/24

Introduction

Structures underly music
Hierarchical structures
Metrical structure
Harmonic structure

SLIDE 4

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 2/24

Approaches to Musical Analysis

Varying goals:
1. model/aid compositional process
2. model listener’s cognition
3. suggest interpretations
Often not clearly defined

SLIDE 5

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

SLIDE 6

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)

SLIDE 7

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 5/24

Consonance and Harmony

Simultaneous notes create

dissonance / consonance

Used by composers:

tension / relaxation

Harmony:

formation of chord phrases

Relationships between chords
Expectation / fulfilment

SLIDE 8

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 6/24

Approaches to Harmonic Analysis

Rameau (1722): Trait´ e de l’harmonie Roman numeral analysis

D:

I IV I IV V7 I IV6 V I

Key of D

VI
VII

V

II
I
IV
III

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Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 6/24

Approaches to Harmonic Analysis

Rameau (1722): Trait´ e de l’harmonie Roman numeral analysis

D:

I IV I IV V7 I IV6 V I

Riemann (1893): Vereinfachte Harmonielehre Functional analysis

T

S T S D T S D T

Key of D

Tp
D
D 7
Sp
T
S
Dp

SLIDE 10

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 6/24

Approaches to Harmonic Analysis

Rameau (1722): Trait´ e de l’harmonie Roman numeral analysis

D:

I IV I IV V7 I IV6 V I

Riemann (1893): Vereinfachte Harmonielehre Functional analysis

T

S T S D T S D T

Lerdahl & Jackendoff (1983): A Generative Theory of Tonal Music

SLIDE 11

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 6/24

Approaches to Harmonic Analysis

Rameau (1722): Trait´ e de l’harmonie Roman numeral analysis

D:

I IV I IV V7 I IV6 V I

Riemann (1893): Vereinfachte Harmonielehre Functional analysis

T

S T S D T S D T

Lerdahl & Jackendoff (1983): A Generative Theory of Tonal Music

Winograd (1968), Keiler (1978),

Steedman (1984), Rohrmeier (2011) Structured functional analysis

SLIDE 12

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 6/24

Approaches to Harmonic Analysis

Rameau (1722): Trait´ e de l’harmonie Roman numeral analysis

D:

I IV I IV V7 I IV6 V I

Riemann (1893): Vereinfachte Harmonielehre Functional analysis

T

S T S D T S D T

Lerdahl & Jackendoff (1983): A Generative Theory of Tonal Music

Winograd (1968), Keiler (1978),

Steedman (1984), Rohrmeier (2011) Structured functional analysis

SLIDE 13

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 7/24

Tonal Space

Longuet-Higgins’ formalization of

harmonic tonal theory

Tonal relations between notes
Ambiguous in performance

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 3rd 4:5 x Perfect 5th 2:3 z Octave 1:2

Harmonic analysis disambiguates tonal relations

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Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 8/24

Harmony in the 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♭ E♭ G B D♯ F♯♯ 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♯♯

Dominant Tonic

SLIDE 15

Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 9/24

Functional Harmony

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♭ E♭ G B D♯ F♯♯ 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♯♯

Dominant Tonic Subdominant

SLIDE 16

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

SLIDE 17

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

SLIDE 18

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

SLIDE 19

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♭ E♭ G B G♭ B♭ D F♯ D♭ F A C♯ A♭ C E G♯ E♭ G B D♯

SLIDE 20

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

SLIDE 21

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)

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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

SLIDE 23

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

SLIDE 24

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

SLIDE 25

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

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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

SLIDE 27

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 >B

D/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

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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 >B

D/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

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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♯

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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♯

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Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 19/24

Jazz Corpus

Annotated training corpus
Jazz chord sequences
Full grammatical derivation

annotated

→ 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

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Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 19/24

Jazz Corpus

Annotated training corpus
Jazz chord sequences
Full grammatical derivation

annotated

→ 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 Paris Alice in Wonderland Anthropology Beauty and the Beast Black Orpheus Blackberry Winter Blue in Green Boplicity Bud Powell Byrd Like Call Me Irresponsible Can’t Help Lovin’ Dat Man Chelsea Bridge A Child is Born Chippie Chitlins Con Carne Como En Vietnam Confirmation Crescent Dear Old Stockholm

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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♯ D D T,T E♭♭ G♭ B♭ D B♭♭ D♭ F A F♭ A♭ C E C♭ E♭ G B T,T D T

Precision, recall, f-score

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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:

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Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 22/24

Results

Tonal space metric:

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

Cov. (%)

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

Dependency recovery:

P (%) R (%) F (%) PCCG 90.25 86.83 88.51 St+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 >B

D/C D/C

&

D/C

>

D–C D/A G/D A♭/D♭ D♭/G♭ E B♭/F A/D C/F B/E C/F

· · ·

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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 >B

D/C D/C

&

D/C

>

D–C D/A G/D A♭/D♭ D♭/G♭ E B♭/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

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Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 24/24

Conclusion

Thesis:

Tonal harmony has a syntax like that of

language

Statistical parsing can be used to infer harmonic

structure

CCG grammar of harmonic structure
Statistical parser for harmonic analysis
Parser outperforms HMM baseline
Extension to analysis of performances

SLIDE 38

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 and log-linear models. Computational Linguistics, 33, 493–552. Hockenmaier, J., & Steedman, M. (2002). Generative models for statistical parsing with Combinatory Categorial Grammar. In Proceedings of the 40th Meeting of the Association for Computational 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.

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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). Trait´ e de l’harmonie. Jean-Baptiste-Christophe Ballard. Riemann, H. (1893). Vereinfachte Harmonielehre oder die Lehre von den tonalen Funktionen der Akkorde. Augener & Co.

Trans. H. Bemerunge, as Harmony Simplified, or the Theory of

the Tonal Functions of Chords.

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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.

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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–C

dev

C–C = C BM7 G7 C B G/C C

>

G–C

dev

B–C C–C

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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

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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

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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

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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♭ E♭ G B D♯ F♯♯ 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♯♯

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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− ♭V− ♭VII− II− ♯IV− ♯VI− ♭♭V ♭♭VII ♭II IV VI ♯I ♯III ♭♭II ♭IV ♭VI I III ♯V ♯VII ♭♭VI ♭I ♭III V VII ♯II ♯♯IV ♭♭III ♭V ♭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+

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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)

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Bibliography Atomic Categories MIDI Parsing Tonal Space Parsing Time Index