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Conceptual Blending of Harmonic Spaces for Creative Melodic Harmonisation
Abstract
In computational creativity, new concepts can be invented through conceptual blending of two independent conceptual spaces. In music, conceptual blending has been primarily used for analysing relations between musical and extra-musical elements in composed music rather than generating new music. This paper presents a probabilistic melodic harmonisation assistant that employs conceptual blending to combine learned, potentially diverse, harmonic idioms and generate new harmonic spaces that can be used to harmonise melodies given by the user. The key feature of this system is the application of creative conceptual blending to the most common chord transitions (pairs of consecutive chords) of two initial harmonic idioms. The proposed methodology integrates newly created blended chords and transitions in a compound probabilistic harmonic space, that preserves combined characteristics from both initial idioms along with those new chords and transitions within a unified setting. This methodology enables various interesting music applications, ranging from problem-solving, e.g. harmonising melodies that include key transpositions, to generative harmonic exploration, e.g. combining major–minor harmonic progressions or more extreme idiosyncratic harmonies.
... Structural blending in music exists in various forms such as grafting harmonic, melodic, rhythmic or timbral elements from one musical idiom to another, or integrating such elements from at least two different idioms into novel idioms. The CHAMELEON melodic harmonisation assistant has been developed in the context of the COINVENT project framework (Schorlemmer et al., 2014) and is capable of blending different harmonic idioms (Kaliakatsos-Papakostas, Makris, Tsougras, & Cambouropoulos, 2016;Kaliakatsos-Papakostas, Queiroz, Tsougras, & Cambouropoulos, 2017). Harmonic blending, as performed by CHAMELEON, involves two different processes. ...
... The next subsection briefly describes the idiom-independent harmonic learning and generating methodology while the following subsection includes a short overview of the harmonic blending methodology; finally, the last subsection gives some examples of the way the system works and its output. More details for both methodologies can be found in Kaliakatsos-Papakostas et al. (2016) and Kaliakatsos-Papakostas et al. (2017) respectively. ...
... Through this process, new chords are most likely to emerge as first or second chords in newly invented transitions. Transitions that incorporate newly invented chords that are not reachable from the two input spaces are filtered out (Kaliakatsos-Papakostas et al., 2017). A new chord is reachable if there are at least two transitions including this chord as the first and second chord respectively. ...
This article presents the CHAMELEON melodic harmonisation assistant that utilises the principles of conceptual blending theory as a means for the invention of hybrid or novel harmonic idioms and an empirical evaluation of a number of computer-generated melodic harmonisation blends. Melodies originating from various idioms were harmonised either according to the harmonic rules of the original idiom, according to the rules of a different idiom (melody–harmony blends), or by blending idioms, modes and transported versions of the same idiom (harmony–harmony blends). In two similar experimental set ups, the task of the listeners was to i) perform idiom, mode or type of chromaticism classification, ii) report their preference, and iii) rate the degree of expectancy characterising each harmonisation. The results show that harmonic blending (either melody–harmony or harmony–harmony) influences the identification of idiom, mode and type of chromaticism. This suggests that the harmonic blending system has indeed succeeded in producing perceivable blends under various conditions that were unexpected and also equally preferred compared to non-blends.
... Conceptual Blending Theory (CBT), as initially described by Fauconnier and Turner in [1], describes a process where concepts from two independent spaces are combined creatively to create new spaces that lead to the invention of original concepts in their own right. In music, possible effects of conceptual blending in musical works have been studied extensively by Zbikowski, e.g., in [2][3][4], while creative computational systems that are based on the mathematical formalization of Goguen [5,6] have been examined, e.g., for conceptual blending of harmonic spaces [7]. Jazz standards have commonly been notated as melodies accompanied by simplified harmonic frameworks of chords (lead sheets, fake books), allowing thus the necessary space for improvisation. ...
... A simple approach for composing melodic harmonizations under this scheme was presented by Kaliakatsos-Papakostas and Cambouropoulos [33], where constraints were added at phrase boundaries, ensuring appropriate cadential schemata at structurally important positions. This method is incorporated in the CHAMELEON melodic harmonization assistant [7,34,35], which is the core system we use in the current work. ...
This paper presents a methodology for generating cross-harmonizations of jazz standards, i.e., for harmonizing the melody of a jazz standard (Song A) with the harmonic context of another (Song B). Specifically, the melody of Song A, along with the chords that start and end its sections (chord constraints), are used as a basis for generating new harmonizations with chords and chord transitions taken from Song B. This task involves potential incompatibilities between the components drawn from the two songs that take part in the cross-harmonization. In order to tackle such incompatibilities, two methods are introduced that are integrated in the Hidden Markov Model and the Viterbi algorithm. First, a rudimentary approach to chord grouping is presented that allows interchangeable utilization of chords belonging to the same group, depending on melody compatibility. Then, a “supporting” harmonic space of chords and probabilities is employed, which is learned from the entire dataset of the available jazz standards; this space provides local solutions when there are insurmountable conflicts between the melody and constraints of Song A and the harmonic context of Song B. Statistical and expert evaluation allow an analysis of the methodology, providing valuable insight about future steps.
... The focus of this paper is on the CHAMELEON 1 melodic harmonization assistant (Kaliakatsos-Papakostas et al., 2017), which follows a paradigm of computational creativity that not only extrapolates musical styles, but also generates fundamentally new harmonic material through hybrid methods that are based on generative implementations of Conceptual Blending (CB) and statistical learning. CB Theory has been examined as a fundamental tool that humans use to understand and generate new concepts (Fauconnier and Turner, 2003;Goguen, 2006), whereby two input conceptual spaces are combined to generate a new conceptual space. ...
... At a second stage, all pairs of the most common transitions on the initial idioms are blended (Eppe et al., 2015), giving rise to new chord transitions that might potentially incorporate new chords, in a sense that these chords do not belong to any of the learned idioms. Such chords are appended in the augmented matrix (a new line and a new column are added for any new chord), while the probability assigned to the transitions generated by blending is the average probability of the input transitions (for more information please refer to Kaliakatsos-Papakostas et al., 2017). ...
CHAMELEON is a computational melodic harmonization assistant. It can harmonize a given melody according to a number of independent harmonic idioms or blends between idioms based on principles of conceptual blending theory. Thus, the system is capable of offering a wealth of possible solutions and viewpoints for melodic harmonization. This study investigates how human creativity may be influenced by the use of CHAMELEON in a melodic harmonization task. Professional and novice music composers participated in an experiment where they were asked to harmonize two similar melodies under two different conditions: one with and one without computational support. A control group harmonized both melodies without computational assistance. The influence of the system was examined both behaviorally, by comparing metrics of user-experience, and in terms of the properties of the artifacts (i.e., pitch class distribution and number of chord types characterizing each harmonization) that were created between the two experimental conditions. Results suggest that appreciation of the system was expertise-dependent (i.e., novices appreciated the computational support more than professionals). At the same time, users seemed to adopt more explorative strategies as a result of interaction with CHAMELEON based on the fact that the harmonizations created this way were more complex, diverse, and unexpected in comparison to the ones of the control group.
... Pioneer studies on automatic composition style transfer include (Pati 2018;Zalkow 2016;Kaliakatsos-Papakostas et al. 2017), where the first two deal with monophonic composition and the last two deal with polyphonic composition. The work (Pati 2018) builds pitch and rhythm models separately for different music genres and then create new melodies through the combination of the pitch model of one genre and the rhythm model of another genre. ...
... The work (Pati 2018) builds pitch and rhythm models separately for different music genres and then create new melodies through the combination of the pitch model of one genre and the rhythm model of another genre. The works by (Zalkow 2016;Kaliakatsos-Papakostas et al. 2017) rely on the power of explicit rules to modify melody and merge different chord progressions, respectively. The work (Lattner, Grachten, and Widmer 2016) enforces certain music structures by considering additional template-matching constraints in the optimization procedure. ...
Led by the success of neural style transfer on visual arts, there has been a rising trend very recently in the effort of music style transfer. However, "music style" is not yet a well-defined concept from a scientific point of view. The difficulty lies in the intrinsic multi-level and multi-modal character of music representation (which is very different from image representation). As a result, depending on their interpretation of "music style", current studies under the category of "music style transfer", are actually solving completely different problems that belong to a variety of sub-fields of Computer Music. Also, a vanilla end-to-end approach, which aims at dealing with all levels of music representation at once by directly adopting the method of image style transfer, leads to poor results. Thus, we see a vital necessity to re-define music style transfer more precisely and scientifically based on the uniqueness of music representation, as well as to connect different aspects of music style transfer with existing well-established sub-fields of computer music studies. Otherwise, an accumulated upcoming literature (all named after music style transfer) will lead to a great confusion of the underlying problems as well as negligence of the treasures in computer music before the age of deep learning. In addition, we discuss the current limitations of music style modeling and its future directions by drawing spirit from some deep generative models, especially the ones using unsupervised learning and disentanglement techniques.
... The Chameleon melodic harmonization assistant [7] learns harmonies from diverse musical styles and generate novel harmonisations of given melodies. The user may select the style of those harmonisations or select a 'blended' style that Chameleon creates, based on two styles selected by the user. ...
This paper presents current developments taking place in the context of the MusiCoLab project. MusiCoLab aims at delivering a comprehensive and efficient web platform for music learning and teaching, by building on prior research experience of project partners, as well as by investigating the integration of state-of-the-art tools in intelligent music composition, performance, and discovery within an educational context. Compared to existing relevant initiatives, MusiCoLab offers a suite of innovative tools that may be used to enhance collaboration and engagement in networked/virtual settings. These tools are sought both in the context of asynchronous student/teacher interactions (i.e., course preparation and scheduling, student assignments and self-practice) as well as synchronously, i.e., serving as groupware to facilitate live music lessons by manipulating intelligent collaborative digital artifacts.
... Contoh nyata interval tersebut tertera pada Gambar 6. Pada Gambar 6 terlihat bah wa not Eb berjarak tritone dari nada dasar nya (A). Dalam musik jazz, subtitusi tritone umum digunakan (KaliakatsosPapakostas et al., 2017) baik sebagai kadens (pola) rehar monisasi akord maupun atau melodi. Musisi jazz memandang dan memahami musiknya lebih besar dari sekadar satu atau sepasang akord yang terpisah (Keller et al., 2013). ...
Abstrak - Dialektika Riset Akuntansi dalam Perspektif Jazz
Tujuan Utama - Artikel ini berupaya menunjukkan potensi musik jazz sebagai metodologi dalam riset akuntansi.
Metode – Penelitian ini menggunakan metode deskriptif kualitatif dengan pengumpulan data melalui dokumentasi dan wawancara. Seorang penulis buku metodologi riset akuntansi dan musisi jazz menjadi informan penelitian ini.
Temuan Utama – Penelitian menunjukkan bahwa musik jazz dapat diabstraksi dan diturunkan menjadi metodologi melalui penggunaan metafora yang dibagi menjadi tiga elemen kunci yaitu proses, dimensi, dan tujuan. Metodologi musik jazz (MMJ) dapat digunakan pada ranah riset akuntansi emansipatoris untuk mengkonstruksi konsep akuntansi yang mengedepankan keberagaman dan mendorong keunikan. Selain itu MMJ memiliki nilai spiritual dan pendekatan yang holistik.
Implikasi Teori dan Kebijakan – Implementasi MMJ menempatkan manusia sebagai makhluk yang senantiasa mendambakan keindahan hakiki dalam bentuk keadilan dan keseimbangan. Jazz dapat dipahami sebagai sebuah cara pandang terhadap berbagai realitas kehidupan termasuk akuntansi.
Kebaruan Penelitian – Penelitian ini melihat diskursus akuntansi melalui perspektif musik.
Abstract - Dialectics of Accounting Research in Jazz Perspective
Main Purpose - This article attempts to demonstrate the potential of jazz as a methodology in accounting research.
Method - This study used a descriptive qualitative method. An author of accounting research methodology books and jazz practitioners were the informants of this research.
Main Findings – This study showed that jazz could be abstracted and derived into a methodology through metaphors divided into three key elements, namely process, dimensions, and objectives. Jazz music methodology (MMJ) can be used in emancipatory accounting research to construct accounting concepts that promote diversity and encourage uniqueness. In addition, MMJ has spiritual values and a holistic approach.
Theory and Practical Implications - The implementation of MMJ places humans as creatures who always crave beauty in the form of justice and balance. Jazz can be understood as a way of thinking about various realities of life, including accounting.
Novelty - This study portrays accounting discourses through a musical perspective.
... In the context of a generation (harmonisation) framework, constraints are inserted at phrase boundaries ensuring appropriate cadential schemata at structurally important positions, and, then, intermediate chord progressions are filled in according to the learned chord transition matrices. This method is incorporated in the Chameleon melodic harmonisation assistant ( [16], [17]) that is adaptive (learns from data), general (can cope with any tonal or non-tonal harmonic idiom) and modular (learns and encodes explicitly different components of harmonic structure: chord types, chord transitions, cadences, bass line voice-leading). ...
The difficulty of modelling musical structure in a general and cognitively plausible manner is due primarily to music’s inter-dependent multi-parametric and multi-level nature that allows multiple structural interpretations to emerge. Traditional AI symbolic processing methods, however, can be used effectively for modelling particular analytic and creative aspects of musical structure. In this paper three specific problems of music structure, namely, segmentation and streaming, pattern extraction, harmonic abstraction and generation, will be addressed with a view to highlighting the importance of problem definitions, music representation and multi-parametric hierarchical cognitively-inspired processing methodologies. Existing proof-of-concept models are used as a basis for a theoretical discussion.
... Performance style transfer can be either audio-to-audio or symbolicto-audio, the latter such as piano performance rendering [12,22] refers to the tasks of converting deadpan performance data (e.g., MIDI) into expressive performance with a specific interpretation of timing and dynamics. Finally, composition style transfer is usually a symbolic-to-symbolic style transfer problem, which aims at modifying the harmonic, rhythmic or structural attributes of music at the score level, and is applied in music genre transfer [5,21,23] or blending [15]. ...
Music-to-visual style transfer is a challenging yet important cross-modal learning problem in the practice of creativity. Its major difference from the traditional image style transfer problem is that the style information is provided by music rather than images. Assuming that musical features can be properly mapped to visual contents through semantic links between the two domains, we solve the music-to-visual style transfer problem in two steps: music visualization and style transfer. The music visualization network utilizes an encoder-generator architecture with a conditional generative adversarial network to generate image-based music representations from music data. This network is integrated with an image style transfer method to accomplish the style transfer process. Experiments are conducted on WikiArt-IMSLP, a newly compiled dataset including Western music recordings and paintings listed by decades. By utilizing such a label to learn the semantic connection between paintings and music, we demonstrate that the proposed framework can generate diverse image style representations from a music piece, and these representations can unveil certain art forms of the same era. Subjective testing results also emphasize the role of the era label in improving the perceptual quality on the compatibility between music and visual content.
... CHAMELEON is a computational melodic harmonisation assistant that can be used by human composers as a creativity support tool. It can harmonise a given melody according to a variety of harmonic idioms and/or their blends based on a generative implementation of Conceptual Blending theory and statistical learning techniques [7]. Thus, it can produce a number of diverge harmonic solutions to a melodic harmonisation task. ...
This paper presents an experiment designed to investigate the influence of a creativity support tool on music creation. Twenty five participants were asked to harmonise two very similar melodies, the first on their own and the second while given the opportunity to interact with the CHAMELEON harmonisation assistant. CHAMELEON can offer a variety of solutions in a melodic harmonisation task by harmonising according to a number of idioms and/or their blends. Comparison between the produced harmonisations by the participants and their selection of favourite CHAMELEON examples indicated that the majority of them were directly influenced by the solutions offered by the system. Three strategies by which participants exploited CHAMELEON were identified: borrowing of full measures or long chord sequences, borrowing of one or more single chords and finally, adoption of general concepts existing in the CHAMELEON examples. We argue that these findings indicate that the system has the potential to stimulate and promote creative thinking.
... root pitch class or presence of leading tone) and better blends were considered the ones that aggregated the higher 36 sum of importance values from the input low-level features. A similar approach was employed in the Chameleon * melodic harmonization assistant [6], where generic chord transitions, instead of mere cadences, were blended leading to the generation of new probabilistic harmonic spaces that allowed, for instance, meaningful connections between remote tonalities, or the generation of hybrid musical styles, e.g. blends between harmonies of Bach choral and Jazz standards. ...
Conceptual Blending (CB) theory discusses a basic mechanism that allows humans to understand and generate creative artefacts. CB theory has been primarily employed as a method for interpreting creative ideas and pieces of art, while recently algorithmic frameworks have been developed for methodologies that do generative use of CB towards achieving computational creativity. Regarding generative CB in music, most studies so far have focused on low-level musical information (e.g. chord roots, chord types or pitch classes) and how such information is combined to generate new musical objects (e.g. cadences) or even entire harmonic spaces. Recently, a new paradigm of CB theory has been proposed that incorporates information for high-level descriptive features of music, as pentatonicity or rhythm syncopation. The paper at hand presents results of a methodology that achieves high-level blending through low-level information recombination from input melodies using a genetic algorithm. Two evolutionary initialization schemes are presented that represent different version of CB, with and without blending completion. Specific examples are examined where Chinese Han melodies are blended with Jazz melodies and representative blends are analyzed to expose some strengths, weaknesses and possible improvements of this approach.
... For instance, in [5] a methodology was presented where the properties of the Perfect and the Phrygian cadences are combined to generate the tritone substitution cadence, which is a chord progression that was developed in Jazz centuries later in relation to the inputs. A similar approach was employed in the Chameleon 1 melodic harmonization assistant [6], where generic chord transitions, instead of merely cadences, were blended leading to the generation of new probabilistic harmonic spaces that allowed, for instance, meaningful connections between remote tonalities, or the generation of hybrid musical styles, e.g. blends between Bach choral and Jazz Harmonies. ...
Conceptual Blending (CB) theory has been primarily employed as a method for interpreting creative artefacts, while recently it has been used as a creative tool for the algorithmic invention of new concepts. In music, interesting examples have been presented where low-level musical information (e.g. chord roots, chord types or pitch classes) is combined to generate new musical objects (e.g. cadences) or even entire harmonic spaces. These generative frameworks, however, do not incorporate information for high-level descriptive features of music, as pentatonicity or rhythm syncopation. The paper at hand presents a methodology where high-level blending is achieved by recombining low-level information of melodies using a genetic algorithm. A test case is examined where a Chinese Han melody is blended with a Jazz melody and representative blends are analyzed to expose some shortcomings and possible improvements in this approach.
... In music, generative implementations based on conceptual blending have been presented for the invention of blended cadences [5,24], or the generation of blended harmonic spaces through blending chord transitions [11,14,15]. The concepts describing the cadences or the chord transitions in these works, incorporated the analytical description of specific elements, e.g. the root notes, chord types, existence of leading note to the tonic etc. Blending, therefore, involved the combination of such low-level structural elements and not concepts describing qualitative features of the blended spaces. ...
Dissonant stimuli or stimuli with high auditory roughness are often related to jagged shapes, while consonant stimuli or those with low auditory roughness are associated with curvy and smooth shapes. This empirical study explores auditory-tactile associations for roughness in diverse musical excerpts. We investigate whether auditory harmonic dissonance is perceptually associated with tactile roughness in sandpapers with varying grit values, and whether emotional dimensions mediate this cross-modal relationship. Participants were asked to listen to excerpts from several musical styles, accounting for possible effects of familiarity including Bach-style chorales, golden-era jazz, random, and non-Western polyphonic Indonesian styles (i.e., sléndro and pélog), and match them with sandpapers of different roughness. Western listeners matched the most dissonant and the least familiar harmonic organizations with rougher sandpapers. Other parameters such as note density and dissimilarity to 12-tone equal temperament contributed slightly to that relationship. Rough sandpapers and dissonant harmonizations share similar affective profiles (i.e., high arousal and negative valence), suggesting an emotional connection in the cross-modal association.
In this chapter, recent research in the domain of melodic harmonization and computational creativity is presented with a view to highlighting strengths and weaknesses of the classical cognitively inspired symbolic AI approach (often in juxtaposition to contemporary deep learning methodologies). A modular melodic harmonization system that learns chord types, chord transitions, cadences, and bassline voice leading from diverse harmonic datasets is presented. Then, it is shown that the harmonic knowledge acquired by this system can be used creatively in a cognitively inspired conceptual blending model that creates novel harmonic spaces, combining in meaningful ways the various harmonic components of different styles. This system is essentially a proof-of-concept creative model that demonstrates that new concepts can be invented which transcend the initial harmonic input spaces. It is argued that such original creativity is more naturally accommodated in the world of symbolic reasoning that allows links and inferences between diverse concepts at highly abstract levels. Moreover, symbolic representations and processing facilitate interpretability and explanation that are key components of musical knowledge advancement. Finally, reconciling symbolic AI with deep learning may be the way forward to combine the strengths of both approaches toward building more sophisticated robust musical systems that connect sensory auditory data to abstract musical concepts.
This article explores the notion of human and computational creativity as well as core challenges for computational musical creativity. It also examines the philosophical dilemma of computational creativity as being suspended between algorithmic determinism and random sampling, and suggests a resolution from a perspective that conceives of “creativity” as an essentially functional concept dependent on a problem space, a frame of reference (e.g. a standard strategy, a gatekeeper, another mind, or a community), and relevance. Second, this article proposes four challenges for artificial musical creativity and musical AI: (1) the 'cognitive challenge' that musical creativity requires a model of music cognition, (2) the 'challenge of the external world', that many cases of musical creativity require references to the external world, (3) the 'embodiment challenge', that many cases of musical creativity require a model of the human body, the instrument(s) and the performative setting in various ways, (4) the 'challenge of creativity at the meta-level', that musical creativity across the board requires creativity at the meta-level. Based on these challenges it is argued that the general capacity of music and its creation fundamentally involves general (artificial) intelligence and that therefore musical creativity at large is fundamentally an AI-complete problem.
Conceptual Blending (CB) theory describes the cognitive mechanisms underlying the way humans process the emergence of new conceptual spaces by blending two input spaces. CB theory has been primarily used as a method for interpreting creative artefacts, while recently it has been utilised in the context of computational creativity for algorithmic invention of new concepts. Examples in the domain of music include the employment of CB interpretatively as a tool to explain musical semantic structures based on lyrics of songs or on the relations between body gestures and music structures. Recent work on generative applications of CB has shown that proper low-level representation of the input spaces allows the generation of consistent and sometimes surprising blends. However, blending high-level features (as discussed in the interpretative studies) of music explicitly, is hardly feasible with mere low-level representation of objects. Additionally, selecting features that are more salient in the context of two input spaces and relevant background knowledge and should, thus, be preserved and integrated in new interesting blends has not yet been tackled in a cognitively pertinent manner. The paper at hand proposes a novel approach to generating new material that allows blending high-level features by combining low-level structures, based on statistically computed salience values for each high-level feature extracted from data. The proposed framework is applied to a basic but, at the same time, complicated field of music, namely melodic generation. The examples presented herein allow an insightful examination of what the proposed approach does, revealing new possibilities and prospects.
Computational Creativity (CC) is an emerging field of research that focuses on the study and exploitation of the computers’ potential to act as autonomous creators and co-creators. The field is a confluence point for contributions from multiple disciplines, such as Artificial Intelligence, which provides most of its methodological framework, and also Cognitive Science, Psychology, Social Sciences and Philosophy, as well as creative domains like the Arts, Music, Design, Poetry, etc.
Melodic harmonisation is a sophisticated creative process that involves deep musical understanding and a specialised knowledge of music relating to melodic structure, harmony, rhythm, texture, and form. In this article a new melodic harmonisation assistant is presented that is adaptive (learns from data), general (can cope with any tonal or non-tonal harmonic idiom) and modular (learns different aspects of harmonic structure such as chord types, chord transitions, cadences, and voice-leading). This melodic harmonisation system can be used not only to mimic given harmonic styles, but to generate novel harmonisations for diverse melodies and create new harmonic spaces, allowing for the imposition of user-defined chord constraints, leading to new unforeseen harmonic realisations. The various components of the proposed model are explained, then, a number of creative harmonisations of different melodies are presented to illustrate the potential of the system.
Conceptual blending is a powerful tool for computational creativity where, for example, the properties of two harmonic spaces may be combined in a consistent manner to produce a novel harmonic space. However, deciding about the importance of property features in the input spaces and evaluating the results of conceptual blending is a nontrivial task. In the specific case of musical harmony, defining the salient features of chord transitions and evaluating invented harmonic spaces requires deep musicological background knowledge. In this paper, we propose a creative tool that helps musicologists to evaluate and to enhance harmonic innovation. This tool allows a music expert to specify arguments over given transition properties. These arguments are then considered by the system when defining combinations of features in an idiom-blending process. A music expert can assess whether the new harmonic idiom makes musicological sense and re-adjust the arguments (selection of features) to explore alternative blends that can potentially produce better harmonic spaces. We conclude with a discussion of future work that would further automate the harmonisation process.
Conceptual blending is a cognitive theory proposing the combination of diverse conceptual spaces for the creation of novel blended spaces. Musical conceptual blending can be intra-musical, pertaining to the combination of diverse structural elements for the creation of new melodies, harmonies or textures, as well as cross-domain, involving the integration of musical and non-musical spaces for the creation of novel analogies or metaphors. The present paper presents a structural and hermeneutical analysis of 'Il vecchio castello' from Modest Musorgsky's 'Pictures at an Exhibition' in an attempt to disclose both the intra-musical (combination of modal, tonal and coloristic harmonic spaces) and the extra-musical (contextual, symbolic and programmatic aspects) conceptual blending that the work incorporates. The analysis reveals that the piece comprises seven strophes of a song form that emerge from a common melodic core, through the dynamic evolution of harmonic spaces from diatonic modality to impressionistic/coloristic chromaticism and with the combinatorial use of ten harmonization concepts. The reductional/prolongational analysis provides input for two distinct Conceptual Integration Networks, the first describing the intra-musical blending of melodic harmonization and the second proposing the cross-domain blending of the musical and pictorial input spaces into a blended hermeneutical space that projects the work's narrative/programmatic/emotional potential. The proposed analysis shows how musical structure promotes meaning construction through cross-domain mapping. This research suggests that conceptual blending theory as an analytical tool can promote a richer structural interpretation and experience of Musorgsky's work.
In this paper we critically investigate the application of Fauconnier & Turner's Conceptual Blending Theory (CBT) in music, to expose a series of questions and aporias highlighted by current and recent theoretical work in the field. Investigating divisions between different levels of musical conceptualization and blending, we question the common distinction between intra-and extra-musical blending as well as the usually retrospective and explicative application of CBT. In response to these limitations, we argue that more emphasis could be given to bottom-up, contextual, creative and collaborative perspectives of conceptual blending in music. This discussion is illustrated by recent and in-progress practical research developed as part of the COINVENT project, and investigating structural and cross-domain blending in computational and social creativity contexts.
While similarity and retrieval in case-based reasoning (CBR) have received a lot of attention in the literature, other aspects of CBR, such as case reuse are less understood. Specifically, we focus on one of such, less understood, problems: knowledge transfer. The issue we intend to elucidate can be expressed as follows: what knowledge present in a source case is transferred to a target problem in case-based inference? This paper presents a preliminary formal model of knowledge transfer and relates it to the classical notion of analogy.
Melodic harmonisation deals with the assignment of harmony (chords) over a given melody. Probabilistic approaches to melodic harmonisation utilise statistical information derived from a training dataset to harmonise a melody. This paper proposes a probabilistic approach for the automatic generation of voice leading for the bass note on a set of given chords from different musical idioms; the chord sequences are assumed to be generated by another system. The proposed bass voice leading (BVL) probabilistic model is part of ongoing work, it is based on the hidden Markov model (HMM) and it determines the bass voice contour by observing the contour of the melodic line. The experimental results demonstrate that the proposed BVL method indeed efficiently captures (in a statistical sense) the characteristic BVL features of the examined musical idioms.
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 rearrangement 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 descriptive potential of the GCT is assessed in the tonal idiom by comparing GCT harmonic labels with human expert annotations (Kostka & Payne harmonic dataset). Additionally , novel methods for grouping and clustering chords, according to their GCT encoding and their functional role in chord sequences, are introduced. The results of both harmonic labelling and functional clustering indicate that the GCT representation constitutes a suitable scheme for representing effectively harmony in computational systems.
Conceptual blending is a cognitive theory whereby elements from diverse, but structurally-related, mental spaces are 'blended' giving rise to new conceptual spaces. This study focuses on structural blending utilising an algorith-mic formalisation for conceptual blending applied to harmonic concepts. More specifically, it investigates the ability of the system to produce meaningful blends between harmonic cadences, which arguably constitute the most fundamental harmonic concept. The system creates a variety of blends combining elements of the penultimate chords of two input cadences and it further estimates the expected relationships between the produced blends. Then, a preliminary subjective evaluation of the proposed blending system is presented. A pairwise dissimilarity listening test was conducted using original and blended cadences as stimuli. Subsequent multidimensional scaling analysis produced spatial configurations for both behavioural data and dissimi-larity estimations by the algorithm. Comparison of the two configurations showed that the system is capable of making fair predictions of the perceived dissimilarities between the blended cadences. This implies that this conceptual blending approach is able to create perceptually meaningful blends based on self-evaluation of its outcome.
This research focuses on concept invention processes and suggests that structural blending is a powerful mechanism that gives rise to novel musical concepts. Structural blending is omnipresent across several formal musical levels, from individual pieces harmoniously combining music characteristics of different pieces/styles, to entire musical styles having emerged as a result of blending between diverse music idioms. In this paper, we focus on conceptual blending in the domain of musical harmony and present primarily computational examples in the following harmonic domains: chord-level blending, chord sequence blending, scale blending, harmonic structure level blending, melody-harmony level blending. Structural blending can be used not only for music analysis and music understanding, but more so it may form the basis for creative / generative music systems; processes of conceptual blending can be incorporated in computational compositional systems, facilitating the creation of original music structures/pieces/styles and contributing to a richer comprehension / experience of music.
Conceptual blending is a cognitive theory whereby elements from diverse, but structurally-related, mental spaces are " blended " giving rise to new conceptual spaces that often possess new powerful interpretative properties, allowing better understanding of known concepts or the emergence of novel concepts altogether. This paper provides an overview of the wide computational methodological spectrum that is being developed towards building an automatic melodic harmonization system that employs conceptual blending, yielding harmonizations that inherit characteristics from multiple idioms. Examples of conceptual blending in harmony are presented that exhibit the effectiveness of the developed model in inventing novel harmonic concepts. These examples discuss the invention of well-known jazz cadences through blending the underlying concepts of classical music cadences, as well as the construction of larger chord sequences. Furthermore, examples of a conceptual blending interpretation in human compositions that motivated the goals of the system's design are given. Finally, conceptual blending between harmonic and non-harmonic domains is discussed, offering tools that allow for intuitive human intervention in the harmonization process.
We present a framework for conceptual blending – a concept invention method that is advocated in cognitive science as a fundamental, and uniquely human engine for creative thinking. Herein, we employ the search capabilities of ASP to find commonalities among input concepts as part of the blending process , and we show how our approach fits within a generalised conceptual blending workflow. Specifically, we orchestrate ASP with imperative Python programming , to query external tools for theorem proving and colimit computation. We exemplify our approach with an example of creativity in mathematics.
We present a computational framework for chord invention based on a cognitive-theoretic perspective on conceptual blending. The framework builds on algebraic specifications, and solves two musicological problems. It automatically finds transitions between chord progressions of different keys or idioms, and it substitutes chords in a chord progression by other chords of a similar function , as a means to create novel variations. The approach is demonstrated with several examples where jazz cadences are invented by blending chords in cadences from earlier idioms, and where novel chord progressions are generated by inventing transition chords.
During the last decades, several methodologies have been proposed for the harmonization of a given melody with al-gorithmic means. Among the most successful are method-ologies that incorporate probabilistic mechanisms and sta-tistical learning, since they have the ability to generate har-monies that statistically adhere to the harmonic character-istics of the idiom that the training pieces belong to. The current paper discusses the utilization of a well–studied probabilistic methodology, the hidden Markov model (HMM), in combination with additional constraints that incorporate intermediate fixed–chord constraints. This work is moti-vated by the fact that some parts of a phrase (like the ca-dence) or a piece (e.g. points of modulation, peaks of ten-sion, intermediate cadences etc.) are characteristic about the phrase's or piece's idiomatic identity. The presented methodology allows to define and isolate such important parts/functions and include them as constraints in a proba-bilistic harmonization methodology. To this end, the con-strained HMM (CHMM) is developed, harnessed with the novel general chord type (GCT) representation, while the study focuses on examples that highlight the diversity that constraints introduce in harmonizations.
In this paper we focus on issues of harmonic representa-tion and computational analysis. A new idiom-independent 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 culturally-dependent notions of consonance/dissonance), and a scale, the GCT algorithm finds the maximal subset of notes of a given note simultaneity that contains only con-sonant intervals; this maximal subset forms the base upon which the chord type is built. The proposed representa-tion 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 representa-tion 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 comprehensive collection of essays in multidisciplinary metaphor scholarship that has been written in response to the growing interest among scholars and students from a variety of disciplines such as linguistics, philosophy, anthropology, music and psychology. These essays explore the significance of metaphor in language, thought, culture and artistic expression. There are five main themes of the book: the roots of metaphor, metaphor understanding, metaphor in language and culture, metaphor in reasoning and feeling, and metaphor in non-verbal expression. Contributors come from a variety of academic disciplines, including psychology, linguistics, philosophy, cognitive science, literature, education, music, and law.
This paper demonstrates knowledge representation mapping techniques common in both the domains of art and science. Analogical mapping systems take information from a source domain and map that data to a target domain located in another perceptual mode. I also explain conceptual blending, in which information from different sources combine into a new emergent structure. The theories that describe these visualization processes are conceptual metaphor theory (CMT) and conceptual blending theory (BT), which were orginally created by George Lakoff, Mark Johnson [15], Gilles Fauconnier and Mark Turner [4] more than thirty years ago. My own work of visualizing music also began in the late seventies, coincidentally during the same period of time that CMT and BT were being conceptualized and written down. I will illustrate the use of analogy as a basic visualization tool through describing visualizations of extant music, including the twentieth-century, intermedia masterpiece––the Ursonate by Kurt Schwitters. The cognitive space transfer is an important part of this process; it is a type of conceptual blend. I developed this method while creating art works, but predict that it can also contribute a rich, qualitative dimension to scientific visualization that adds in a substantial way to the story told by the information.
Hierarchical structure similar to that associated with prosody and syntax in language can be identified in the rhythmic and harmonic progressions that underlie Western tonal music. Analysing such musical structure resembles natural language parsing: it requires the derivation of an underlying interpretation from an unstructured sequence of highly ambiguous elements—in the case of music, the notes. The task here is not merely to decide whether the sequence is grammatical, but rather to decide which among a large number of analyses it has. An analysis of this sort is a part of the cognitive processing performed by listeners familiar with a musical idiom, whether musically trained or not. Our focus is on the analysis of the structure of expectations and resolutions created by harmonic progressions. Building on previous work, we define a theory of tonal harmonic progression, which plays a role analogous to semantics in language. Our parser uses a formal grammar of jazz chord sequences, of a kind widely used for natural language processing (NLP), to map music, in the form of chord sequences used by performers, onto a representation of the structured relationships between chords. It uses statistical modelling techniques used for wide-coverage parsing in NLP to make practical parsing feasible in the face of considerable ambiguity in the grammar. Using machine learning over a small corpus of jazz chord sequences annotated with harmonic analyses, we show that grammar-based musical interpretation using simple statistical parsing models is more accurate than a baseline HMM. The experiment demonstrates that statistical techniques adapted from NLP can be profitably applied to the analysis of harmonic structure.
Computational creativity is a flourishing research area, with a variety of creative systems being produced and developed. Creativity evaluation has not kept pace with system development with an evident lack of systematic evaluation of the creativity of these systems in the literature. This is partially due to difficulties in defining what it means for a computer to be creative; indeed, there is no consensus on this for human creativity, let alone its computational equivalent. This paper proposes a Standardised Procedure for Evaluating Creative Systems (SPECS). SPECS is a three-step process: stating what it means for a particular computational system to be creative, deriving and performing tests based on these statements. To assist this process, the paper offers a collection of key components of creativity, identified empirically from discussions of human and computational creativity. Using this approach, the SPECS methodology is demonstrated through a comparative case study evaluating computational creativity systems that improvise music.
An author's postprint (same content, but before it has been put into journal-specific formatting) is available via my institutional repository at https://kar.kent.ac.uk/cgi/users/home?screen=EPrint::View&eprintid=42379
Chorale harmonization is one of the most popular problem domains for AI-music researchers. The problem has been approached with various techniques ranging from a knowledge intensive approach on one end to a data intensive approach on the other end. Various approaches offer different strengths and pose different weaknesses. In this report, we explain our knowledge intensive approach. Here, we view chorale harmonization from a search control perspective. In this perspective, the harmonization activities are discretely captured as states. These states form a state space, which cannot be exhaustively examined since it is intractable by nature. To overcome the intractability problem, we propose a careful knowledge engineering approach. The approach offers a useful language specialized for the chorale harmonization task. This language controls the search at the meta-level through its three primitives, namely: rules, tests and measures. The harmonization outputs obtained from this method are very promising. The approach also offers a very promising application in the AI-education area.
This paper aims to propose a hierarchical, generative account of diatonic harmonic progressions and suggest a set of phrase-structure grammar rules. It argues that the structure of harmonic progressions exceeds the simplicity of the Markovian transition tables and proposes a set of rules to account for harmonic progressions with respect to key structure, functional and scale degree features as well as modulations. Harmonic structure is argued to be at least one subsystem in which Western tonal music exhibits recursion and hierarchical organization that may provide a link to overarching linguistic generative grammar on a structural and potentially cognitive level.
We describe a realtime tabla generation system based on a variable-length n-gram model trained on a large symbolic tabla database. A novel, parametric smoothing algorithm based on a family of exponential curves is introduced to control the relative weight of high-and low-order models. This technique is shown to lead to improvements over a back-off smoothing for our tabla database. We find that cross-entropy is lowest when the coefficient of the exponen-tial curve is between 1 and 2 and increases for values outside of this optimal range. The basic n-gram model is extended to model dependencies between duration, stroke-type, and meter using cross-products in a Multiple Viewpoints (MV) framework, leading to improvements in most cases when compared with independent stroke and duration models.
Many computational models of music fail to capture essential aspects of the high-level musical structure and context, and this limits their usefulness, particularly for musically informed users. We describe two recent approaches to modelling musical harmony, using a probabilistic and a logic-based framework respectively, which attempt to reduce the gap between computational models and human understanding of music. The first is a chord transcription system which uses a high-level model of musical context in which chord, key, metrical position, bass note, chroma features and repetition structure are integrated in a Bayesian framework, achieving state-of-the-art performance. The second approach uses inductive logic programming to learn logical descriptions of harmonic sequences which characterise particular styles or genres. Each approach brings us one step closer to modelling music in the way it is conceptualised by musicians.
Many systems use Markov models to generate finite-length sequences that imitate a given style. These systems often need to enforce specific control constraints on the sequences to generate. Unfortunately, control constraints are not compatible with Markov models, as they induce long-range dependencies that violate the Markov hypothesis of limited memory. Attempts to solve this issue using heuristic search do not give any guarantee on the nature and probability of the sequences generated. We propose a novel and efficient approach to controlled Markov generation for a specific class of control constraints that 1) guarantees that generated sequences satisfy control constraints and 2) follow the statistical distribution of the initial Markov model. Revisiting Markov generation in the framework of constraint satisfaction, we show how constraints can be compiled into a nonhomogeneous Markov model, using arc-consistency techniques and renormalization. We illustrate the approach on a melody generation problem and sketch some realtime applications in which control constraints are given by gesture controllers.
Creativity isn't magical. It's an aspect of normal human intelligence, not a special faculty granted to a tiny elite. There are three forms: combinational, exploratory, and transformational. All three can be modeled by AI - in some cases, with impressive results. AI techniques underlie various types of computer art. Whether computers could "really" be creative isn't a scientific question but a philosophical one, to which there's no clear answer. But we do have the beginnings of a scientific understanding of creativity. Copyright © 2009, Association for the Advancement of Artificial Intelligence. All rights reserved.
How is it possible to think new thoughts? What is creativity and can science explain it?
When The Creative Mind: Myths and Mechanisms was first published, Margaret A. Boden's bold and provocative exploration of creativity broke new ground. Boden uses examples such as jazz improvisation, chess, story writing, physics, and the music of Mozart, together with computing models from the field of artificial intelligence to uncover the nature of human creativity in the arts, science and everyday life.
The Second Edition of The Creative Mind has been updated to include recent developments in artificial intelligence, with a new preface, introduction and conclusion by the author. It is an essential work for anyone interested in the creativity of the human mind.
This paper examines the adaptation and expansion of Lerdahl' s & Jackendoff's Generative Theory of Tonal Music so that it may be applied on the analysis of 20th century modal music. Based on the premise that a considerable part of the theory's rules are universal — meaning that the principles of music perception and cognition are the same for all experienced listeners regardless of the musical idiom in which they are experienced — the application of GTTM to musical idioms other than the Western classical one requires formulation of idiom-specific well-formedness and preference rules, and description of the special tonal hierarchy. These tasks may be accomplished through the analytical study of a considerable quantity of music representing a certain idiom, and the description of its features in relation to the four parts of the GTTM methodology. The chosen analytical object — 44 Creek miniatures for piano — is representative of the musical idiom deriving from the amalgamation of Greek modal music and 20th century harmonization techniques, distinctive of the musical style of Greek composer Yannis Constantinidis. An inductive methodological process was used for the individual and comparative analysis of all 44 pieces. This paper includes three complete GTTM sample analyses from the 44 piano pieces, a summary of the stylistic characteristics of the analyzed music, and the formulation of the special well-formedness and preference rules, introduced as either new rules to the theory or adaptations of the existing ones.
Thus far, we have been automatizing the time-span analysis of Jackendoff and Lehrdahl's Generative Theory of Tonal Music (GTTM). We have also introduced the distance between two time-span trees and verified by an experiment that the distance was properly supported by the psychological similarity. In this paper, we synthesize a new piece of music using the algebraic operations on timespan trees, with this notion of distance. For this process, we need an operation to retain a certain number of pitch events as well as reduction, then we employ join operation on two input pieces of music. But, the result of the join operation is not obvious as two or more pitch events may occupy the same position on a score in a conflicting way. Therefore, in this research, we distinguish the tree representation from actual music written on a score and define join and meet in the domain of the tree representation in the algebraic manner. Then, to demonstrate the validity of our approach, we compose artificial variations of K.265/300e by Wolfgang Amadeus Mozart by a morphing technique using join and meet. We examine the results with human intuitive similarity and show that algebraic operations such as join and meet suffices to produce viable Mozartoid variations.
How is it possible to think new thoughts? What is creativity and can science explain it? And just how did Coleridge dream up the creatures of The Ancient Mariner? When The Creative Mind: Myths and Mechanisms was first published, Margaret A. Boden's bold and provocative exploration of creativity broke new ground. Boden uses examples such as jazz improvisation, chess, story writing, physics, and the music of Mozart, together with computing models from the field of artificial intelligence to uncover the nature of human creativity in the arts. The second edition of The Creative Mind has been updated to include recent developments in artificial intelligence, with a new preface, introduction and conclusion by the author. It is an essential work for anyone interested in the creativity of the human mind.
Allan F. Moore presents a study of recorded popular song, from the recordings of the 1920s through to the present day. Analysis and interpretation are treated as separable but interdependent approaches to song. Analytical theory is revisited, covering conventional domains such as harmony, melody and rhythm, but does not privilege these at the expense of domains such as texture, the soundbox, vocal tone, lyrics. Moore continues by developing a range of hermeneutic strategies largely drawn from outside the field (in the most part, within psychology and philosophy) but still deeply relevant to the experience of song.
This book shows how recent work in cognitive science, especially that developed by cognitive linguists and cognitive psychologists, can be used to explain how we understand music. The book focuses on three cognitive processes: categorization, cross-domain mapping, and the use of conceptual models, and explores the part these play in theories of musical organization. The first part of the book provides a detailed overview of the relevant work in cognitive science, framed around specific musical examples. The second part brings this perspective to bear on a number of issues with which music scholarship has often been occupied, including the emergence of musical syntax and its relationship to musical semiosis, the problem of musical ontology, the relationship between words and music in songs, and conceptions of musical form and musical hierarchy.
We introduce computational creativity theory (CCT) as an analogue in computational creativity research to computational learning theory in machine learning. In its current draft, CCT comprises the FACE descriptive model of creative acts as tuples of generative acts, and the IDEA descriptive model of the impact such creative acts may have. To introduce these, we simplify various assumptions about software development, background material given to software, how creative acts are per-formed by computer, and how audiences consume the results. We use the two descriptive models to perform two comparisons studies, firstly for mathematical dis-covery software, and secondly for visual art generating programs. We conclude by discussing possible addi-tions, improvements and refinements to CCT.
We discuss the problem of automatic four-part harmonization: given a soprano part, add alto, tenor and bass in accordance with the compositional practices of a particular musical era. In particular, we focus on the development of representational and modelling techniques, within the framework of multiple viewpoint systems and Prediction by Partial Match (PPM), for the creation of statistical models of four-part harmony by machine learning. Our ultimate goal is to create better models, according to the information theoretic measure cross-entropy, than have yet been produced. We use multiple viewpoint because of their ability to represent both surface and underlying musical structure, and because they have already been successfully applied to melodic modelling. To allow for the complexities of harmony, however, the framework must be extended; for example, we begin by predicting complete chords, and then extend the framework to allow part by part prediction. As the framework is extended and generalized, the viewpoints become more complex. This article discusses matters related to viewpoint domains (alphabets), such as their size and consequent effect on run time; and presents methods for their reliable construction. We also present an empirical analysis of the time complexity of our computer implementation.
Melody harmonisation is a centuries-old problem of long tradition, and a core aspect of composition in Western tonal music. In this work we describe FHarm, an automated system for melody harmonisation based on a functional model of harmony. Our system first generates multiple harmonically well-formed chord sequences for a given melody. From the generated sequences, the best one is chosen, by picking the one with the smallest deviation from the harmony model. Unlike all existing systems, FHarm guarantees that the generated chord sequences follow the basic rules of tonal harmony. We carry out two experiments to evaluate the quality of our harmonisations. In one experiment, a panel of harmony experts is asked to give its professional opinion and rate the generated chord sequences for selected melodies. In another experiment, we generate a chord sequence for a selected melody, and compare the result to the original harmonisation given by a harmony scholar. Our experiments confirm that FHarm generates realistic chords for each melody note. However, we also conclude that harmonising a melody with individually well-formed chord sequences from a harmony model does not guarantee a well-sounding coherence between the chords and the melody. We reflect on the experience gained with our experiment, and propose future improvements to refine the quality of the harmonisation.
This paper explores reasoning about space and time, e.g., in metaphors of time as space; an important method is to nd minimal assumptions needed to reach the same conclusions that humans reach. Some mathematical language, including the notion of triad, is introduced for this purpose, formalizing and generalizing the cognitive semantics ap- proaches to conceptual spaces (in the senses of both Fauconnier & Turner and of Gardenfors), blending, and metaphor; in particular, continuous mathematics is used to model space and time. A new explanation of emergent structure in blend spaces is also discussed, and proposed as a source of creativity. Four main examples illustrate the approach, and an appendix encapsulates the most dicult mathematics.
This paper reprots on a rule-based expert system called CHORAL, for harmonization and Schenkerian analysis of chorales in the style of J. S. Bach. The author first briefly compares his approach with some current trends in algorithmic composition and music analysis, and then describes the CHORAL system itself. 35 Refs.
This chapter proposes a new approach to style, arising from our work on computational media using structural blending, which enriches the conceptual blending of cognitive linguistics with structure building operations in order to encompass syntax and narrative as well as metaphor. We have implemented both conceptual and structural blending, and conducted initial experiments with poetry, including interactive multimedia poetry, although the approach generalizes to other media. The central idea is to generate multimedia content and analyze style in terms of blending principles, based on our finding that different principles from those of common sense blending are often needed for some contemporary poetic metaphors.
An abstract is not available.
The present paper builds on experimental data from earlier research to offer a new theoretical approach to a common problem in the study of music cognition – the way elementary musical concepts are constructed. Most literature on the conceptualization of music uses Conceptual Metaphor Theory as the framework of choice. While its cross-domain mappings based on embodiment are useful for targeting the possible motivation behind particular conceptualizations, this theory lacks clear mechanisms to explain underlying similarities among the seemingly disparate descriptions given by respondents from various cultural and linguistic backgrounds. Other theories, invoking conceptual primitives, offer a possible way to dismantle these responses into higher-order units, related at a more abstract level (Perceptual Meaning Analysis, Conceptual Semantics). However, when compared with the Conceptual Metaphor Theory, they seem to put less emphasis on either the emergent properties or the experiential grounding of the process in which the final (musical) concept is built. To reconcile the two contradicting tendencies, I propose the utilization of the four-space Conceptual Blending model, with a reinforced role of the generic space. In two sample analyses of typical conceptualizations obtained from the children I have worked with (musical pitches perceived as "high and low", "big and small" and "thick and thin"'; musical scales described as going "up and down", "forward and backward" and "to the goal and back"), I postulate that the generic space contains image schematic structures which may themselves be composed of conceptual primitives. The final conceptualization comes from blending the perceived physical properties of the music (input space 1) and the appropriate experiential, referential domain (input space 2). Both domains must comply with the image schematic structure of the generic space to produce an acceptable blend. In turn, all referential structures that are able to do so can be said to be based on the same set of conceptual primitives, since they are constrained by the abstract structure of the generic space. The paper discusses some candidates for conceptual primitives and image schemas in the two examples and others from my experimental work so far. If constantly supported by empirical data, the proposed model could: (1) help further clarify the notion of the image schema and conceptual primitive, (2) assist in the search for musical conceptual universals, by accounting for some cross-cultural and cross-linguistic differences in the conceptualizations.
This article offers a model of musical meaning that allows for the cultural construction of musical meaning, while at the
same time acknowledging the existence of constraints upon the meanings any given music may support under any given circumstances;
in this way it aims to fill the void between existing approaches that understand musical meaning as either inherent or socially constructed. I illustrate the argument through Tovey's and McClary's contrasting readings of the recapitulation
in the first movement of Beethoven's Ninth Symphony, and suggest some ways in which theory and analysis may enter into a constructive
relationship with the broadened critical agenda of contemporary musicology.
I summarise and attempt to clarify some concepts presented in and arising from Margaret Boden’s (1990) descriptive hierarchy of creativity, by beginning to formalise the ideas she proposes. The aim is to move towards a model which allows detailed comparison, and hence better understanding, of systems which exhibit behaviour which would be called “creative” in humans. The work paves the way for the description of naturalistic, multi-agent creative AI systems, which create in a societal context.I demonstrate some simple reasoning about creative behaviour based on the new framework, to show how it might be useful for the analysis and study of creative systems. In particular, I identify some crucial properties of creative systems, in terms of the framework components, some of which may usefully be proven a priori of a given system.I suggest that Boden’s descriptive framework, once elaborated in detail, is more uniform and more powerful than it first appears.
Over recent decades there has been a growing interest in the question of whether computer programs are capable of genuinely creative activity. Although this notion can be explored as a purely philosophical debate, an alternative perspective is to consider what aspects of the behaviour of a program might be noted or measured in order to arrive at an empirically supported judgement that creativity has occurred. We sketch out, in general abstract terms, what goes on when a potentially creative program is constructed and run, and list some of the relationships (for example, between input and output) which might contribute to a decision about creativity. Specifically, we list a number of criteria which might indicate interesting properties of a program’s behaviour, from the perspective of possible creativity. We go on to review some ways in which these criteria have been applied to actual implementations, and some possible improvements to this way of assessing creativity.
The following text is taken from the publisher's website.
"The experience of music is an abstract and elusive one, enough so that we're often forced to describe it using analogies to other forms and sensations: we say that music moves or rises like a physical form; that it contains the imagery of paintings or the grammar of language. In these and countless other ways, our discussions of music take the form of metaphor, attempting to describe music's abstractions by referencing more concrete and familiar experiences.
Michael Spitzer's Metaphor and Musical Thought uses this process to create a unique and insightful history of our relationship with music—the first ever book-length study of musical metaphor in any language. Treating issues of language, aesthetics, semiotics, and cognition, Spitzer offers an evaluation, a comprehensive history, and an original theory of the ways our cultural values have informed the metaphors we use to address music. And as he brings these discussions to bear on specific works of music and follows them through current debates on how music's meaning might be considered, what emerges is a clear and engaging guide to both the philosophy of musical thought and the history of musical analysis, from the seventeenth century to the present day. Spitzer writes engagingly for students of philosophy and aesthetics, as well as for music theorists and historians."
A musical chord can be represented as a point in a geometrical space called an orbifold. Line segments represent mappings from the notes of one chord to those of another. Composers in a wide range of styles have exploited the non-Euclidean geometry of these spaces, typically by using short line segments between structurally similar chords. Such line segments exist only when chords are nearly symmetrical under translation, reflection, or permutation. Paradigmatically consonant and dissonant chords possess different near-symmetries and suggest different musical uses.
Western musicians traditionally classify pitch sequences by disregarding the effects of five musical transformations: octave shift, permutation, transposition, inversion, and cardinality change. We model this process mathematically, showing that it produces 32 equivalence relations on chords, 243 equivalence relations on chord sequences, and 32 families of geometrical quotient spaces, in which both chords and chord sequences are represented. This model reveals connections between music-theoretical concepts, yields new analytical tools, unifies existing geometrical representations, and suggests a way to understand similarity between chord types.