Cadence blending 211 CREATING MUSICAL CADENCES VIA CONCEPTUAL BLENDING: EMPIRICAL EVALUATION AND ENHANCEMENT OF A FORMAL MODEL ASTERIOS ZACHARAKIS, between different conceptual spaces that share some MAXIMOS KALIAKATSOS-PAPAKOSTAS, structural relations (combinational creativity). Boden COSTAS TSOUGRAS,& EMILIOS CAMBOUROPOULOS (2004) maintains that the latter (i.e., combinational Aristotle University of Thessaloniki, Thessaloniki, Greece creativity) has proved to be the hardest to describe for- mally. This paper explores aspects of combinational cre- THE COGNITIVE THEORY OF CONCEPTUAL BLENDING ativity in the domain of music, and more specifically, the may be employed to understand the way music becomes harmonic structure of music. meaningful and, at the same time, it may form a basis Conceptual blending is a cognitive theory developed for musical creativity per se. This work constitutes a case by Fauconnier and Turner (2003) whereby elements study whereby conceptual blending is used as a creative from diverse but structurally related mental spaces are tool for inventing musical cadences. Specifically, the per- ‘‘blended,’’ giving rise to new conceptual spaces that fect and the renaissance Phrygian cadential sequences are often possess new powerful interpretative properties used as input spaces to a cadence blending system that and allowing better understanding of known concepts produces various cadential blends based on musicolog- or the emergence of novel concepts altogether. Concep- ical and blending optimality criteria. A selection of tual blending theory is useful for explaining the cogni- ‘‘novel’’ cadences is subject to empirical evaluation tive process that humans undergo when engaged in in order to gain a better understanding of perceptual creative acts, and is akin to Boden’s notion of combi- relationships between cadences. Pairwise dissimilarity national creativity. A computational framework that ratings between cadences are transformed into a percep- extends Goguen’s formal approach (Goguen, 2006) has tual space and a verbal attribute magnitude estimation been developed in the context of the COINVENT (Con- method on six descriptive axes (preference, originality, cept Invention Theory) project (http://www.coinvent- tension, closure, expectancy, and fit) is used to associate project.eu) (Schorlemmer et al., 2014). According to this the dimensions of this space with descriptive qualities framework, two input spaces are described as sets of (closure and tension emerged as the most prominent qual- weighted properties and relations, and after their generic ities). The novel cadences generated by the computational space is computed, the amalgamation process (Eppe blending system are mainly perceived as single-scope et al., 2015) leads to the creation of consistent blends blends (i.e., blends where one input space is dominant), that are optimal according to some criteria relating to since categorical perception seems to play a significant role the blending process and to the knowledge domain of (especially in relation to the upward leading note move- the modeled spaces (the amalgamation process poten- ment). Insights into perceptual aspects of conceptual tially includes multiple ‘‘generalization paths,’’ leading bending are presented and ramifications for developing to many different blends). sophisticated creative systems are discussed. With regard to music, conceptual blending has been predominantly theorized as the cross-domain integra- Received: May 16, 2016, accepted May 1, 2017. tion of music structural and extramusical domains such Key words: conceptual blending, musical cadence, com- as text or image (e.g., Cook, 2001; Moore, 2012; Zbi- putational creativity, empirical evaluation, harmony kowski, 2002, 2008). Additionally, it has been studied in perception the context of ‘‘musicogenic’’ meaning (Koelsch, 2013), which refers to physical, embodied, emotional, and personality-related responses to music; such studies EW CONCEPTS MAY BE CREATED EITHER BY include work on music and motion by Johnson and Lar- ‘‘exploring’’ previously unexplored regions of son (2003) or empirical studies on pitch perception and N a given conceptual space (exploratory creativ- image schemata in children by Antovic´ (2009, 2011). ity), transforming established concepts in novel ways Finally, there have been studies that touch upon issues (transformational creativity), or making associations of structural mappings/blending between different spaces Music Perception, VOLUME 35, ISSUE 2, PP. 211–234, ISSN 0730-7829, ELECTRONIC ISSN 1533-8312. © 2017 BY THE REGENTS OF THE UNIVERSITY OF CALIFORNIA ALL RIGHTS RESERVED. PLEASE DIRECT ALL REQUESTS FOR PERMISSION TO PHOTOCOPY OR REPRODUCE ARTICLE CONTENT THROUGH THE UNIVERSITY OF CALIFORNIA PRESS’S REPRINTS AND PERMISSIONS WEB PAGE, HTTP://WWW.UCPRESS.EDU/JOURNALS.PHP?P¼REPRINTS. DOI: https://doi.org/10.1525/MP.2017.35.2.211 212 Asterios Zacharakis, Maximos Kaliakatsos-Papakostas, Costas Tsougras, & Emilios Cambouropoulos FIGURE 1. Conceptual blending between the tonal perfect cadence and a Renaissance Phrygian cadence gives rise to the tritone substitution progression / cadence (the backdoor progression can also be derived as a blend). within the music structure domain per se (such as map- 2015). The insight obtained by this proof-of-concept pings between incongruous tonalities (Ox, 2014) and approach will be exploited to develop a system capable different tonal pitch space theories (Spitzer, 2003)). of performing harmonic blending between different Almost all of the above studies examine conceptual musical idioms in a melodic harmonization task. blending in retrospect, analyzing and explaining existing The blending methodology is applied to two distinct metaphors/blends rather than taking a bottom-up, crea- cadential chord sequences, i.e., sequences that serve as tive perspective of generating novel blends. A more cadences when encountered at the end of musical extended discussion and critical examination of concep- phrases/sections: the tonal perfect cadence sequence, as tual blending processes in music is presented by Stefanou encountered in 18th and 19th century tonal music and and Cambouropoulos (2015). the modal Phrygian cadence sequence, as encountered in In this paper it is maintained that the creative poten- 16th century (Renaissance) modal music (Figure 1). The tial of conceptual blending (i.e., invention of new perfect cadence is described as a functional dominant-to- blends) in the domain of music is, probably, most pow- tonic chord progression (Aldwell & Schachter, 2003; (7) erfully manifested in processes that enable structural Caplin, 1998; Sears, 2015) consisting of a V chord in blending. To substantiate this potential, a proof-of- root position—prepared by a chord with pre-dominant concept autonomous computational creative system function—leading to a I chord in root position and with that performs melodic harmonization is being devel- the tonic in the upper voice (^1). The three- or four-voice oped (Kaliakatsos-Papakostas, Makris, Tsougras, & Phrygian cadence is described as a contrapuntal progres- Cambouropoulos, 2016). A core component of this sys- sion (Barnett, 2002; Collins Judd, 2002; Schubert, 2008) 6 tem is a transition blending mechanism that has been based on a two-voice linear movement consisting of a vii applied, among other things, to well-defined harmonic chord leading to a I or i or Iomit3 chord with the tonic in 1 concepts such as harmonic cadences (Eppe et al., 2015; the upper voice (^1) (see Figure 1). Zacharakis, Kaliakatsos-Papakostas, & Cambouro- poulos, 2015). The present work focuses on conceptual blending of musical cadences (with well-established 1 Both cadential progressions originate from the two-voice clausula, functional/voice-leading characteristics) and reports in called simple (Zarlino, 1558), parallel (Dahlhaus, 1990), or standard model cadence (Schubert, 2008), featuring stepwise motion 7-8 and 2-1 detail algorithmic and empirical findings that relate to and the progression from the imperfect consonance M6 to the perfect its application. The particular focus on cadences comes consonance P8. (For modes lacking the M6, like Dorian, Mixolydian, and from the fact that they constitute one of the most salient Aeolian, the leading note was created through musica ficta, while in the harmonic concepts and are of major importance in Phrygian mode the leading note was resolved with downward semitonal tonal music. The significance of the cadence lies not motion.) According to Dahlhaus (1990, and also in his article on "Har- mony" in GMO), this two-voice clausula evolved gradually into the four- only in its form-creating function (i.e., the delineation voice tonal cadential progression through the addition of a leap of a fourth of phrase/group boundaries that give rise to hierarchical or fifth on the fifth and first degrees of the mode in the lower voice (bass). grouping structure), but also in that its harmonic con- A similar descending fourth leap cadence may also appear in the Phrygian tent contributes, to a considerable extent, to the special mode, with the bass falling from the seventh to the fourth degree of the character of a harmonic idiom in which it functions as mode (Schubert, 2008), but it was much less common. When tonal har- mony was established, besides the upward leading note, the cadential bass an indispensable closure element (e.g., Aldwell & became fixed, while the Phrygian cadence was abandoned due to its Schachter, 2003; Bigand & Parncutt,