Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion Handout 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
Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 1/24 Introduction • Structures underly music • Hierarchical structures • Metrical structure • Harmonic structure
Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 1/24 Introduction • Structures underly music • Hierarchical structures • Metrical structure • Harmonic structure
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
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 (speculative) • Automatic generation: • melodic variations • accompaniments • Song identification • Language modelling for transcription
Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 5/24 Consonance and Harmony • Simultaneous notes create • Harmony : dissonance / consonance formation of chord phrases � � �� � � � � �� � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � • Relationships between chords • Used by composers: • Expectation / fulfilment tension / relaxation
Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 6/24 Approaches to Harmonic Analysis Rameau (1722): Trait´ e de l’harmonie Roman numeral analysis IV V 7 IV 6 D: I IV I I V I � � �� � � � � �� � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � Key of D � �� � � � � � I II III � IV V � VI VII � � � � � � � � � � � � � �
Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 6/24 Approaches to Harmonic Analysis Rameau (1722): Trait´ e de l’harmonie Roman numeral analysis IV V 7 IV 6 D: I IV I I V I � � �� � � � � �� � � � � � � � � � � � Riemann (1893): Vereinfachte Harmonielehre � � � � � � � � � � �� � � � � � � � � Functional analysis T S T S D T S D T � � �� � � � � �� � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � Key of D � �� � � � � � � � � � � � � � � � � � � � � � T Sp Dp S D Tp D 7
Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 6/24 Approaches to Harmonic Analysis Rameau (1722): Trait´ e de l’harmonie Riemann (1893): Vereinfachte Harmonielehre Roman numeral analysis Lerdahl & Jackendoff (1983): Functional analysis IV V 7 IV 6 D: I IV I I V I T S T S D T S D T � A Generative Theory of Tonal Music � � �� � �� � � � � � � � �� � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � �� � � � � � � � � � � � � � � � � � �� � � � � �� � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � �
Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 6/24 Approaches to Harmonic Analysis Rameau (1722): Trait´ e de l’harmonie Riemann (1893): Vereinfachte Harmonielehre Winograd (1968), Keiler (1978), Roman numeral analysis Functional analysis Steedman (1984), Rohrmeier (2011) IV V 7 IV 6 D: I IV I I V I T S T S D T S D T � � � �� � �� � � � � � � � �� � � �� � � � � � � � � � � � � � � � Structured functional analysis � � � � � � � � � � � � � � � � � � � � � � � � � �� � � �� � � � � � � � � � � � � � � � Lerdahl & Jackendoff (1983): A Generative Theory of Tonal Music � � �� � � � � �� � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � �
Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 6/24 Approaches to Harmonic Analysis Rameau (1722): Trait´ e de l’harmonie Riemann (1893): Vereinfachte Harmonielehre Roman numeral analysis Functional analysis IV V 7 IV 6 D: I IV I I V I T S T S D T S D T � � � �� � �� � � � � � � � �� � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � �� � � � � � � � � � � � � � � � Lerdahl & Jackendoff (1983): Winograd (1968), Keiler (1978), A Generative Theory of Tonal Music Steedman (1984), Rohrmeier (2011) Structured functional analysis � � �� � � � � �� � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � �
Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 7/24 Tonal Space • Longuet-Higgins’ formalization of F ♯ C ♯ G ♯ D ♯ A ♯ E ♯ harmonic tonal theory y Major 3rd F ♯ C ♯ D A E B z 4:5 Octave • Tonal relations between notes 1:2 B ♭ F C G D A • Ambiguous in performance x G ♭ D ♭ A ♭ E ♭ B ♭ F Perfect 5th 2:3 E ♭♭ B ♭♭ F ♭ C ♭ G ♭ D ♭ • Harmonic analysis disambiguates tonal relations
Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 8/24 Harmony in the Tonal Space C ♯ G ♯ D ♯ A ♯ E ♯ B ♯ F ♯♯ C ♯♯ G ♯♯ D ♯♯ A ♯♯ F ♯ C ♯ G ♯ D ♯ A ♯ E ♯ B ♯ F ♯♯ A E B Tonic Dominant F ♯ C ♯ G ♯ D ♯ F C G D A E B D ♭ A ♭ E ♭ B ♭ F C G D A E B F C G B ♭♭ F ♭ C ♭ G ♭ D ♭ A ♭ E ♭ B ♭ G ♭♭ D ♭♭ A ♭♭ E ♭♭ B ♭♭ F ♭ C ♭ G ♭ D ♭ A ♭ E ♭ E ♭♭♭ B ♭♭♭ F ♭♭ C ♭♭ G ♭♭ D ♭♭ A ♭♭ E ♭♭ B ♭♭ F ♭ C ♭
Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 9/24 Functional Harmony C ♯ G ♯ D ♯ A ♯ E ♯ B ♯ F ♯♯ C ♯♯ G ♯♯ D ♯♯ A ♯♯ F ♯ C ♯ G ♯ D ♯ A ♯ E ♯ B ♯ F ♯♯ A E B F ♯ C ♯ G ♯ D ♯ F C G D A E B D ♭ A ♭ E ♭ B ♭ F C G D A E B Subdominant Dominant F C G B ♭♭ F ♭ C ♭ G ♭ D ♭ A ♭ E ♭ B ♭ Tonic G ♭♭ D ♭♭ A ♭♭ E ♭♭ B ♭♭ F ♭ C ♭ G ♭ D ♭ A ♭ E ♭ E ♭♭♭ B ♭♭♭ F ♭♭ C ♭♭ G ♭♭ D ♭♭ A ♭♭ E ♭♭ B ♭♭ F ♭ C ♭
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 dom dom dom dom dom dom E 7 A 7 Dm 7 G 7 Dm 7 D ♭ 7 C C
Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 11/24 Harmonic Analysis • Chords function as: dominant, subdominant or tonic • Dominant-tonic resolution A E B • Subdominant-tonic resolution F C G • Recursion D ♭ A ♭ E ♭ • Substitution • Delayed resolution: coordination dom dom dom dom dom dom D 7 G 7 D 7 D ♭ 7 C D 7 D ♭ 7 C dom dom subdom dom G 7 D 7 G 7 C F C C
Introduction Harmonic Analysis Harmonic CCG Statistical Parsing Conclusion 11/24 Harmonic Analysis • Chords function as: dominant, subdominant or tonic • Dominant-tonic resolution A E B • Subdominant-tonic resolution F C G Mark bought and Greg read the book • Recursion D ♭ A ♭ E ♭ • Substitution • Delayed resolution: coordination dom dom dom dom dom dom D 7 G 7 D 7 D ♭ 7 C D 7 D ♭ 7 C dom dom subdom dom G 7 D 7 G 7 C F C C
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