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- Bartok’s polymodality: the Dasian and other affinity spacesPublication . Martins, José OliveiraThe article proposes that a construct I call the Dasian space provides an effective framework to interpret harmonic aspects of scale relations in twentieth-century polymodality, particularly in the music of Bartok. Based on Bartok's intuition that the pitch space modeled after his notion of polymodal chromaticism retains integral "diatonic ingredients," the Dasian space (named after the medieval homonymous scale( establishes a system of relations between all potential diatonic segments, without relying upon traditional constraints, such as complete diatonic collections, harmonic functions, or pitch centricity. The Dasian space is a closed, nonoctave repeating scalar cycle, where each element is identified by a unique coordination of pitch class and modal quality. The dual description of each element enables both the specification of location in a given cycle and the emergence of a group structure, whose generators-named transpositio and transformatio-are also characteristic musical motions and relations. The proposed analytical methodology is probed in a couple of short pieces of Bartok's Mikrokosmos and in the third movement of his Piano Sonata. The article argues that, unlike other tonal and atonal classic approaches, the Dasian framework enables the analyst to reconcile the constructional character of a Bartokian idiomatic feature (the combination of distinct and integral scale strata) with the interpretation of harmonic space in terms of scale-segment interaction and formal processes. The article then contextualizes the structure of the Dasian space within a larger class of constructs, which I call affinity spaces, by generalizing some of its group-theoretical properties that model relations between non-diatonic scalar materials. The analytical pertinence of affinity spaces is probed in Bartok's "Divided Arpeggios," an intriguing posttonal piece appearing late in the Mikrokosmos set.
- Understanding and feeling music and time in LourençoPublication . Martins, José Oliveira
- What was new music: Arrigo and Bartók in LourençoPublication . Martins, José Oliveira; Dunsby, JonathanLourenço’s fragments about Arrigo’s Thumos and Bartók’s Music for Strings, Percussion and Celesta are richly implicative. We discuss what Lourenço calls ‘time in reverse,’ both from a music theory perspective and as to how his 1960s interpretations of modernism seemed so distinct from interpretations of the ‘classical’ in art music. Like his contemporary Adorno, he offers the image of ‘new music lighting up on the spot’, Arrigo’s ostinati being compositional examples. Techniques of that kind, we propose, stimulated Lourenço’s concept of music taking us ‘from future to past,’ music in which we live in ‘the abyss of our beginnings.’ In the Bartók, Lourenço finds paradoxes, such as ‘frozen velocity,’ that are inspired by the tension between the experience of musical process and its structural conditions and implications. We focus on three pertinent music‑analytical aspects: (1) how the arch design of perfect‑fifth entries creates a real-time, multivalent pitch structure; (2) how these multivalent relations are telescoped into the ‘new chromaticism’ of each subject statement; and (3) how relations between micro-level subject and macro-level arch form invoke the organization of certain out-of-time, that is, synchronic, periodic pitch structures, which we theorize as affinity spaces. Recovering a long-lost comparison, we drill down from Thumos in contemporary terms as relatively marginal, and unsurprisingly resistant to contemporary music‑analytical explanation, and Bartók’s masterpiece as now regarded as ‘classic’ and in many senses unproblematic. These works came over contemporaneously to Lourenço as equally and fundamentally modernist, a site of the ‘supremely coherent incoherence […] of a vacant universe.’
- Reframing the theorizing activity on twentieth-century multi-layered harmonyPublication . Martins, José Oliveira