-
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
1/21
Introduction
• Hierarchical structure in music• Metrical structure• Harmonic structure
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
1/21
Introduction
• Hierarchical structure in music• Metrical structure• Harmonic structure
1
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
1/21
Introduction
• Hierarchical structure in music• Metrical structure• Harmonic structure
1
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
2/21
Applications of Automatic Harmonic Analysis
• Automatic generation:• melodic variations• arrangements• accompaniments
• MIR: e.g. identifying variations• Transcription of scores
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
2/21
Applications of Automatic Harmonic Analysis
• Automatic generation:• melodic variations• arrangements• accompaniments
• MIR: e.g. identifying variations• Transcription of scores
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
2/21
Applications of Automatic Harmonic Analysis
• Automatic generation:• melodic variations• arrangements• accompaniments
• MIR: e.g. identifying variations• Transcription of scores
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
2/21
Applications of Automatic Harmonic Analysis
• Automatic generation:• melodic variations• arrangements• accompaniments
• MIR: e.g. identifying variations• Transcription of scores
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
2/21
Applications of Automatic Harmonic Analysis
• Automatic generation:• melodic variations• arrangements• accompaniments
• MIR: e.g. identifying variations• Transcription of scores
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
2/21
Applications of Automatic Harmonic Analysis
• Automatic generation:• melodic variations• arrangements• accompaniments
• MIR: e.g. identifying variations• Transcription of scores
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
2/21
Applications of Automatic Harmonic Analysis
• Automatic generation:• melodic variations• arrangements• accompaniments
• MIR: e.g. identifying variations• Transcription of scores
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
4/21
Harmonic Analysis
• Functional harmonic structure• Tension-resolution patterns between chords
C E7 A7 Dm7 G7 Dm7 D[7 C
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
4/21
Harmonic Analysis
• Functional harmonic structure• Tension-resolution patterns between chords
C E7 A7 Dm7 G7 Dm7 D[7 C
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
4/21
Harmonic Analysis
• Functional harmonic structure• Tension-resolution patterns between chords
C E7 A7 Dm7 G7 Dm7 D[7 C
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
4/21
Harmonic Analysis
• Functional harmonic structure• Tension-resolution patterns between chords
C E7 A7 Dm7 G7 Dm7 D[7 C
dom dom dom
dom
dom dom
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
5/21
Harmonic Analysis
• Chords function as: dominant, subdominant or tonic• Dominant-tonic resolution• Subdominant-tonic resolution• Recursion• Substitution• Delayed resolution: coordination
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
5/21
Harmonic Analysis
• Chords function as: dominant, subdominant or tonic• Dominant-tonic resolution• Subdominant-tonic resolution• Recursion• Substitution• Delayed resolution: coordination
G7 C
dom
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
5/21
Harmonic Analysis
• Chords function as: dominant, subdominant or tonic• Dominant-tonic resolution• Subdominant-tonic resolution• Recursion• Substitution• Delayed resolution: coordination
G7 C
dom
F C
subdom
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
5/21
Harmonic Analysis
• Chords function as: dominant, subdominant or tonic• Dominant-tonic resolution• Subdominant-tonic resolution• Recursion• Substitution• Delayed resolution: coordination
G7 C
dom
F C
subdom
D7 G7 C
dom dom
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
5/21
Harmonic Analysis
• Chords function as: dominant, subdominant or tonic• Dominant-tonic resolution• Subdominant-tonic resolution• Recursion• Substitution• Delayed resolution: coordination
G7 C
dom
F C
subdom
D7 G7 C
dom dom
D7 D[7 C
dom dom
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
5/21
Harmonic Analysis
• Chords function as: dominant, subdominant or tonic• Dominant-tonic resolution• Subdominant-tonic resolution• Recursion• Substitution• Delayed resolution: coordination
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 Parsing Statistical Parsing Conclusion
5/21
Harmonic Analysis
• Chords function as: dominant, subdominant or tonic• Dominant-tonic resolution• Subdominant-tonic resolution• Recursion• Substitution• Delayed resolution: coordination
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 Parsing Statistical Parsing Conclusion
5/21
Harmonic Analysis
• Chords function as: dominant, subdominant or tonic• Dominant-tonic resolution• Subdominant-tonic resolution• Recursion• Substitution• Delayed resolution: coordination
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 Parsing Statistical Parsing Conclusion
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
dom
dom
Call Me Irresponsible
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
dom
dom
Call Me Irresponsible
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
dom
dom
Call Me Irresponsible
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
dom
dom
Call Me Irresponsible
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
dom
dom
Call Me Irresponsible
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
dom
dom
Call Me Irresponsible
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
dom
dom
Call Me Irresponsible
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
dom
dom
Call Me Irresponsible
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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]
• Harmonic analysis disambiguates tonal relations
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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]
• Harmonic analysis disambiguates tonal relations
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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]
• Harmonic analysis disambiguates tonal relations
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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]
A7 Dm7 G7 C
• Harmonic analysis disambiguates tonal relations
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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]
A7 Dm7 G7 C
• Harmonic analysis disambiguates tonal relations
C E7 A7 Dm7 G7 Dm7 D[7 C
dom dom dom
dom
dom dom
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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]
A7 Dm7 G7 C
• Harmonic analysis disambiguates tonal relations
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 Parsing Statistical Parsing Conclusion
8/21
Tonal Space Harmonic Analysis
G7 C
dom
G7 ⇒ dominant, G
C ⇒ tonic, C
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
8/21
Tonal Space Harmonic Analysis
G7 C
dom
G7 ⇒ dominant, G
C ⇒ tonic, C
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
8/21
Tonal Space Harmonic Analysis
G7 C
dom
G7 ⇒ dominant, G
C ⇒ tonic, C
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
8/21
Tonal Space Harmonic Analysis
G7 C
dom
G7 ⇒ dominant, G
C ⇒ tonic, C
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
8/21
Tonal Space Harmonic Analysis
G7 C
dom
G7 ⇒ dominant, G
C ⇒ tonic, C
D[
F
A
A[
C
E
E [
G
B
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
8/21
Tonal Space Harmonic Analysis
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
9/21
Harmonic Grammar
D7 G7 C
dom dom
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
9/21
Harmonic Grammar
D7 G7 C
dom dom
D7 G7 C
>
>
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
9/21
Harmonic Grammar
D7 G7 C
dom dom
D7 G7 C
>
>
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
9/21
Harmonic Grammar
D7 G7 C
dom dom
D7 G7 C
D[
F
A
A[
C
E
E [
G
B
>
>
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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 ]
>
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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 ]
>
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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 ]
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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 ]
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
10/21
Harmonic Grammar
D7 D[7 C
dom dom
D7 D[7 C
>B
>
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
10/21
Harmonic Grammar
D7 D[7 C
dom dom
D7 D[7 C
D[
F
A
A[
C
E
E [
G
B
>B
>
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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 ]
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
11/21
Harmonic Grammar
D7 G7 D7 D[7 C· · · · · · · · · · · ·
&
>
D7 G7 D7 D[7 C
dom dom dom
dom
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
Y12
Y123
Y0123
• Chart parsing
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
12/21
Parsing with Grammars
A7 Dm7 G 7 CM7
X0 X1 X2 X3X ′0 . . . X
′1 . . . X
′2 . . . X
′3 . . .
X01
X012
X0123
Y12
Y123
Y0123
• Chart parsing
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
12/21
Parsing with Grammars
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
12/21
Parsing with Grammars
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
12/21
Parsing with Grammars
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
16/21
Baseline: HmmPathConstruct path directly
[II
IV
VI
[VI
I
III
[III
V
VII
[VII
II
]IV
IV +
VI+
]I+
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
16/21
Baseline: HmmPathConstruct path directly
(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+
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
16/21
Baseline: HmmPathConstruct path directly
(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+
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
16/21
Baseline: HmmPathConstruct path directly
(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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
16/21
Baseline: HmmPathConstruct path directly
(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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
17/21
Jazz Corpus
• Annotated training corpus• Jazz chord sequences• Full grammatical derivation
annotated
• → full harmonic analysis• 74 sequences: ∼3k chords• Cross-validation
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
17/21
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
17/21
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
17/21
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
17/21
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
17/21
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
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 Parsing Statistical Parsing Conclusion
17/21
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
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 Parsing Statistical Parsing Conclusion
17/21
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
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 Parsing Statistical Parsing Conclusion
17/21
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
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 Parsing Statistical Parsing Conclusion
17/21
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
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
18/21
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 [
E [
G
BT,T
DT
Precision, recall, f-score
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
18/21
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 [
E [
G
BT,T
DT
Precision, recall, f-score
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
18/21
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 [
E [
G
BT,T
DT
Precision, recall, f-score
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
18/21
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 [
E [
G
BT,T
DT
Precision, recall, f-score
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
18/21
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 [
E [
G
BT,T
DT
Precision, recall, f-score
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
18/21
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 [
E [
G
BT,T
DT
Precision, recall, f-score
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
18/21
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 [
E [
G
BT,T
DT
Precision, recall, f-score
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
18/21
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 [
E [
G
BT,T
DT
Precision, recall, f-score
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
20/21
Backoff
• Use HmmPath where St+PCCG fails• HmmPath always produces an analysis
Tonal space edit distance (%)
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
20/21
Backoff
• Use HmmPath where St+PCCG fails• HmmPath always produces an analysis
Tonal space edit distance (%)
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
20/21
Backoff
• Use HmmPath where St+PCCG fails• HmmPath always produces an analysis
Tonal space edit distance (%)
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
20/21
Backoff
• Use HmmPath where St+PCCG fails• HmmPath always produces an analysis
Tonal space edit distance (%)
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
-
Introduction Harmonic Analysis Parsing Statistical Parsing Conclusion
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
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.
-
References Tonal Space Roman Tonal Space MIDI Parsing New Results Index
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.
-
References Tonal Space Roman Tonal Space MIDI Parsing New Results 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]]
-
References Tonal Space Roman Tonal Space MIDI Parsing New Results 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+
-
References Tonal Space Roman Tonal Space MIDI Parsing New Results 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
-
References Tonal Space Roman Tonal Space MIDI Parsing New Results Index
Extra slide
New Results
Tonal space edit distance (%)
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
-
References Tonal Space Roman Tonal Space MIDI Parsing New Results Index
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