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A Formal Model and Subjective Evaluation CONCEPTUAL BLENDING IN MUSIC CADENCES: A FORMAL MODEL AND SUBJECTIVE EVALUATION. Asterios Zacharakis Maximos Kaliakatsos-Papakostas Emilios Cambouropoulos School of Music Studies, School of Music Studies, School of Music Studies, Aristotle University of Aristotle University of Aristotle University of Thessaloniki, Greece Thessaloniki, Greece Thessaloniki, Greece [email protected] [email protected] [email protected] ABSTRACT portant interdisciplinary research advances from cognitive science, artificial intelligence, formal methods and com- Conceptual blending is a cognitive theory whereby ele- putational creativity. To substantiate its potential, a proof- ments from diverse, but structurally-related, mental spaces of-concept autonomous computational creative system that are ‘blended’ giving rise to new conceptual spaces. This performs melodic harmonisation is being developed. study focuses on structural blending utilising an algorith- Musical meaning is to a large extent self-referential; mic formalisation for conceptual blending applied to har- themes, motives, rhythmic patterns, harmonic progressions monic concepts. More specifically, it investigates the abil- and so on emerge via self-reference rather than external ity of the system to produce meaningful blends between reference to non-musical concepts. Since musical mean- harmonic cadences, which arguably constitute the most fun- ing largely relies on structure and since conceptual blend- damental harmonic concept. The system creates a variety ing involves mapping between different conceptual struc- of blends combining elements of the penultimate chords of tures, music seems to be an ideal domain for conceptual two input cadences and it further estimates the expected re- blending (musical cross-domain blending is discussed by lationships between the produced blends. Then, a prelimi- Antovic´ [1], Cook [6], Zbikowski [24]). Indeed, structural nary subjective evaluation of the proposed blending system conceptual blending is omnipresent in music making: from is presented. A pairwise dissimilarity listening test was individual pieces harmoniously combining music charac- conducted using original and blended cadences as stimuli. teristics of different pieces/styles, to entire musical styles Subsequent multidimensional scaling analysis produced spa- having emerged as a result of blending between diverse tial configurations for both behavioural data and dissimi- music idioms. larity estimations by the algorithm. Comparison of the two Suppose we have a basic tonal ontology where only configurations showed that the system is capable of mak- diatonic notes are allowed and dissonances in chords are ing fair predictions of the perceived dissimilarities between mostly forbidden (except possibly using minor 7th inter- the blended cadences. This implies that this conceptual vals as in the dominant seventh chord). We assume that blending approach is able to create perceptually meaning- some basic cadences have been established as salient har- ful blends based on self-evaluation of its outcome. monic functions around which the harmonic language of the idiom(s) has been developed, such as the authentic/per- 1. INTRODUCTION fect cadence, the half cadence, the plagal cadence and, Conceptual blending is a cognitive theory developed by even, older 15th century modal cadences such as the Phry- Fauconier and Turner [8] whereby elements from diverse, gian cadence (Figure 1). The main question to be ad- but structurally-related, mental spaces are ‘blended’ giving dressed is the following: Is it possible for a computational rise to new conceptual spaces that often possess new pow- system to enrich its learned tonal ontology by inventing erful interpretative properties allowing better understand- ‘new’ meaningful cadences based on blending between ing of known concepts or the emergence of novel concepts known cadences? altogether. The general framework within which the cur- rent work is placed, comprises a formal model for concep- tual blending [7] based on Goguen’s initial ideas of a Uni- fied Concept Theory [9, 18]. This model incorporates im- c Asterios Zacharakis, Maximos Kaliakatsos-Papakostas, Figure 1: Conceptual blending between the basic perfect Emilios Cambouropoulos. and Phrygian cadences gives rise to the Tritone Substitu- Licensed under a Creative Commons Attribution 4.0 International Li- tion progression/cadence. The Backdoor progression can cense (CC BY 4.0). Attribution: Asterios Zacharakis, Maximos also be derived as a weaker blend since less attributes of Kaliakatsos-Papakostas, Emilios Cambouropoulos. “Conceptual Blend- ing in Music Cadences: A formal model and subjective evaluation.”, 16th the two input spaces are retained leading to a lower rating International Society for Music Information Retrieval Conference, 2015. by the system. 141 142 Proceedings of the 16th ISMIR Conference, M´alaga, Spain, October 26-30, 2015 Figure 1 presents a conceptual blending example where plications of computational creativity to music pose the the perfect and the 15th century modal Phrygian cadences extra issue of aesthetic quality judgement since creativ- are used as input spaces. These have been chosen in this ity may not always be accompanied by aesthetic value and example as they are both final cadences to the tonic and vice versa. In terms of assessing a creative system, the at the same time, they are very different (i.e. the Phry- two usual approaches are to either directly evaluate the fi- gian mode does not have an upward leading note to the nal product or to evaluate the productive mechanism [16]. tonic but rather a downward ‘leading note’ from the IIb The present work is concluded by an empirical experiment to the I). Initially, these cadences are formally described that attempts to address the former by shedding some light as simply pitch classes with reference to a tonal centre (C on how the system’s output is perceived leaving -for the tonality was adopted in this case). Assuming that the fi- moment- the issue of aesthetic value intact. nal chord is always a common tonic chord, blending takes To this end, the output of the cadence blending system place by combining pitches of the penultimate chords be- described in the following section is used to set up a pre- tween different cadences. Rather than mere combination liminary subjective evaluation of the conceptual blending of pitches, other characteristic attributes of a cadence are algorithm applied to cadence invention. As stated previ- also taken into account. Weights/priorities that reflect rel- ously, the computational system is capable of creating a va- ative prominence (e.g., root, upwards or downwards lead- riety of blends combining elements of two input cadences ing note, dissonant note that requires resolution – see Fig- and it further estimates the expected relationships between ure 1 where lines of variable thickness illustrate relative the produced blends. A number of blends between the per- strength of voice-leading connections in cadences) are as- fect and the Phrygian cadence were produced in order to signed to each chord note according to a human expert. test the ability of the cadence blending system to accu- The ‘blended’ penultimate chord is also constrained to rately predict their perceived relations (i.e. the function- comply with a certain chord type such as the major or mi- ality of the blends) using an ‘objective’ distance metric nor chord (in this instance the characteristic major chord (see subsection 2.2). To achieve this, a pairwise dissim- with minor seventh was preferred). ilarity listening test for the nine cadences (two original, four blends and three miscellaneous) was designed and Let us examine the particular blending example be- conducted. Subsequent multidimensional scaling (MDS) tween the perfect and the Phrygian cadences more closely. analysis was utilised to obtain geometric configurations for Notes from the two input penultimate chords of the two both behaviourally acquired pairwise distances and dissim- cadence types create a large number of possible combina- ilarity estimations by the algorithm. Comparison of the tions. We start with combinations (at least 3 notes) of the two configurations showed that the system can model the highest priority/salience notes (notes connected with bold perceptual space quite accurately. lines in Figure 1). Many of these combinations are not triadic chords and may be filtered out using a set of con- straints (in this instance our constraint is to have a chord 2. FORMAL CONCEPTUAL BLENDING MODEL that is a standard characteristic tonal chord such as a dom- inant seventh), while also a note completion step might This section begins with a description of the conceptual be required (adding notes to incomplete blending results) blending mechanism utilised by the system for cadence if the examined combination incorporates too few notes; construction. It then proceeds with a consideration of a more details regarding constraints will be given in sub- naive distance metric for pairs of cadences based on repre- section 2.1. Among the accepted blends, the most highly sentation of cadences according to the system. rated one based on priorities values is the tritone substi- tution progression (IIb7-I) of jazz harmony. This simple 2.1 Cadence generation through chord blending blending mechanism ‘invents’ a chord progression that em- A cadence is described as a progression of (at least) two bodies characteristics of the Phrygian cadence (root/bass chords that conclude a phrase,
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