The Harmonic Musical Surface and Two Novel Chord Representation Schemes (original) (raw)
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An idiom-independent representation of chords for computational music analysis and generation
In this paper we focus on issues of harmonic representation and computational analysis. A new idiomindependent representation is proposed of chord types that is appropriate for encoding tone simultaneities in any harmonic context (such as tonal, modal, jazz, octatonic, atonal). The General Chord Type (GCT) representation, allows the re-arrangement of the notes of a harmonic simultaneity such that abstract idiom-specific types of chords may be derived; this encoding is inspired by the standard roman numeral chord type labeling, but is more general and flexible. Given a consonance-dissonance classification of intervals (that reflects culturallydependent notions of consonance/dissonance), and a scale, the GCT algorithm finds the maximal subset of notes of a given note simultaneity that contains only consonant intervals; this maximal subset forms the base upon which the chord type is built. The proposed representation is ideal for hierarchic harmonic systems such as the tonal system and its many variations, but adjusts to any other harmonic system such as post-tonal, atonal music, or traditional polyphonic systems. The GCT representation is applied to a small set of examples from diverse musical idioms, and its output is illustrated and analysed showing its potential, especially, for computational music analysis & music information retrieval.
A Directional Interval Class Representation of Chord Transitions
Chords are commonly represented, at a low level, as absolute pitches (or pitch classes) or, at a higher level, as chords types within a given tonal/harmonic context (e.g. roman numeral analysis). The former is too elementary, whereas, the latter, requires sophisticated harmonic analysis. Is it possible to represent chord transitions at an intermediate level that is transposition-invariant and idiom-independent (analogous to pitch intervals that represent transitions between notes)? In this paper, a novel chord transition representation is proposed. A harmonic transition between two chords can be represented by a Directed Interval Class (DIC) vector. The proposed 12-dimensional vector encodes the number of occurrence of all directional interval classes (from 0 to 6 including +/-for direction) between all the pairs of notes of two successive chords. Apart from octave equivalence and interval inversion equivalence, this representation preserves directionality of intervals (up or down). Interesting properties of this representation include: easy to compute, independent of root finding, independent of key finding, incorporates voice leading qualities, preserves chord transition asymmetry (e.g. different vector for I→V and V→I), transposition invariant, independent of chord type, applicable to tonal/post-tonal/ atonal music, and, in most instances, constituent chords from a chord transition can be uniquely derived from a DIC vector. DIC vectors can be organised in different categories depending on their content, and distance between vectors can be used to calculate harmonic similarity between different music passages. Preliminary tests are presented using simple tonal chord sequences and jazz sequences. This proposal provides a simple and potentially powerful representation of elementary harmonic relations that may have interesting applications in the domain of harmonic representation and processing.
Idiom-Independent Harmonic Pattern Recognition Based on a Novel Chord Transition Representation
2013
In this paper, a novel chord transition representation (Cambouropoulos 2012), that draws on the interval function between two collections of notes proposed by Lewin (1959), is explored in a harmonic recognition task. This representation allows the encoding of chord transitions at a level higher that individual notes that is transposition-invariant and idiom-independent (analogous to pitch intervals that represent transitions between notes). A harmonic transition between two chords is represented by a Directed Interval Class (DIC) vector. The proposed 12dimensional vector encodes the number of occurrence of all directional interval classes (from 0 to 6 including +/for direction) between all the pairs of notes of two successive chords. Apart from octave equivalence and interval inversion equivalence, this representation preserves directionality of intervals (up or down). A small database is constructed comprising of chord sequences derived from diverse music idioms/styles (tonal music...
The General Chord Type (GCT) representation is appropriate for encoding tone simultaneities in any harmonic context (such as tonal, modal, jazz, octatonic, atonal). The GCT allows the re-arrangement of the notes of a harmonic sonority such that abstract idiom-specific types of chords may be derived. This encoding is inspired by the standard roman numeral chord type labelling and is, therefore, ideal for hierarchic harmonic systems such as the tonal system and its many variations; at the same time, it adjusts to any other harmonic system such as post-tonal, atonal music, or traditional polyphonic systems. In this paper the descrip- tive potential of the GCT is assessed in the tonal idiom by comparing GCT harmonic labels with human expert an- notations (Kostka & Payne harmonic dataset). Addition- ally, novel methods for grouping and clustering chords, ac- cording to their GCT encoding and their functional role in chord sequences, are introduced. The results of both har- monic labelling and functional clustering indicate that the GCT representation constitutes a suitable scheme for representing effectively harmony in computational systems.
2015
The Theme And Variation Encodings with Roman Numerals (TAVERN) dataset consists of 27 complete sets of theme and variations for piano composed between 1765 and 1810 by Mozart and Beethoven. In these theme and variation sets, comparable harmonic structures are realized in different ways. This facilitates an evaluation of the effectiveness of automatic analysis algorithms in generalizing across different musical textures. The pieces are encoded in standard **kern format, with analyses jointly encoded using an extension to **kern. The harmonic content of the music was analyzed with both Roman numerals and function labels in duplicate by two different expert analyzers. The pieces are divided into musical phrases, allowing for multiple-levels of automatic analysis, including chord labeling and phrase parsing. This paper describes the content of the dataset in detail, including the types of chords represented, and discusses the ways in which the analyzers sometimes disagreed on the lower-...
A Hierarchical Approach for Music Chord Modeling Based on the Analysis of Tonal Characteristics
2006 IEEE International Conference on Multimedia and Expo, 2006
This paper first discusses how the signal segmentation and tonal characteristics of music notes effect in music chord detection. Two approaches, pitch class profile approach and psycho-acoustical approach, which differently represent these tonal characteristics, are examined for chord detection. The analysis of the tonal characteristics reveals that not only the fundamental frequency of music note but also its harmonics and sub-harmonies in different octaves contribute for detecting related music chord. A hierarchical approach, which transforms the music chord tonal characteristics in each octave onto probabilistic space, is then proposed for modeling the music chord. Our experimental results show that detection of chord type, Major, Minor, Diminish, and Augmented, and individual chords, 12 chords per chord type, are improved with the proposed hierarchical chord modeling approach. Experimental results also reveal that the tempo proportional signal segmentation is more effective extracting tonal characteristics than using fixed length segmentation.
Towards a general computational theory of musical structure
, for their guidance and support throughout this research study, and for all their invaluable comments and advice that helped me crystallise the views presented in this thesis. My colleagues from the Faculty of Music and the Department of Artificial Intelligence at the University of Edinburgh for providing an inspiring intellectual environment in which this work matured; especially, the meetings of the AI-Music Group and the Musical Communication Colloquium have been an indispensable source of ideas. The University of Edinburgh for making this research study possible by offering me a threeyear postgraduate research award. My friends who, with their constant support, love and good humour, have made my stay in Edinburgh unforgettable; especially, Evie Athanassiou for sharing so much with me in both stressful and happy times. My parents and brothers for their continuous wholehearted support throughout these years. v 5. Representation of the Musical Surface 5.1 The Common Hierarchical Abstract Representation for Music (CHARM) 5.1 Musical Surface 5.3 Pitch and Pitch Interval Representation 5.3.1 The General Pitch Interval Representation (GPIR) 5.3.2 Applications and Uses of the GPIR 5.3.3 Transcription of melodies based on the GPIR 6. Microstructural Module (Local Boundaries, Accents, Metre) 6.1 Musical Rhythm 6.2 The Gestalt principles of proximity and similarity in theories of rhythm 6.3 The Local Boundary Detection Model (LBDM) 6.3.1 The Identity-Change and Proximity Rules 6.3.2 Applying the ICR and PR rules on three note sequences 6.3.3 Applying the ICR and PR rules on longer melodic sequences 6.3.4 Further comments of the application of the LBDM rules 6.3.5 The refined LBDM 6.4 Phenomenal Accentuation Structure 6.5 Metrical Structure 7. Macrostructural Module I (Musical Parallelism and Segmentation) 7.1 Similarity and pattern-matching 7.2 Overlapping of patterns 7.3 Pattern-matching and pitch-interval representation 7.4 The String Pattern-Induction Algorithm (SPIA) 7.5 The Selection Function 7.6 Segmentation based on musical parallelism 7.7 Interaction with microstructural module 8. Macrostructural Module II (Musical Categories) 8.1 A working formal definition of similarity and categorisation 120 8.2 The Unscramble Algorithm 8.3 An illustrative example 8.3.1 Category formation 8.3.2 Category membership prediction 8.4 A musical example 8.5 Relative merits of the Unscramble algorithm vi 9. Overall Model and Four Analyses 9.1 Overall model based on the GCTMS 9.1.1 Musical input 9.
N-gram chord profiles for composer style representation
2008
ABSTRACT This paper studies the problem of using weighted N-grams of chord sequences to construct the profile of a composer. The N-gram profile of a chord sequence is the collection of all N-grams appearing in a sequence where each N-gram is given a weight proportional to its beat count. The N-gram profile of a collection of chord sequences is the simple average of the N-gram profile of all the chord sequences in the collection.
An Interactive Workflow for Generating Chord Labels for Homorhythmic Music in Symbolic Formats
2019
Automatic harmonic analysis is challenging: rule-based models cannot account for every possible edge case, and manual annotation is expensive and sometimes inconsistent, undermining the training and evaluation of machine learning models. We present an interactive workflow to address these problems, and test it on Bach chorales. First, a rule-based model was used to generate preliminary, consistent chord labels in order to pre-train three machine learning models. These four models were grouped into an ensemble that generated chord labels by voting, achieving 91.4% accuracy on a reserved test set. A domain expert then corrected only those chords that the ensemble did not agree on unanimously (20.9% of the generated labels). Finally, we used these corrected annotations to re-train the machine learning models, and the resulting ensemble attained an accuracy of 93.5% on the reserved test set, a 24.4% reduction in the number of errors. This versatile interactive workflow can either work i...