Applications of DFT to the theory of twentieth-century harmony

Music theorists have only recently, following groundbreaking work by Quinn, recognized the potential for the DFT on pcsets, initially proposed by Lewin, to serve as the foundation of a theory of harmony for the twentieth century. This paper investigates pcset “arithmetic” – subset structure, transpositional combination, and interval content – through the lens of the DFT. It discusses relationships between interval classes and DFT magnitudes, considers special properties of dyads, pcset products, and generated collections, and suggest methods of using the DFT in analysis, including interpreting DFT magnitudes, using phase spaces to understand subset structure, and interpreting the DFT of Lewin’s interval function. Webern’s op. 5/4 and Bartok’s String Quartet 4, iv, are discussed.Accepted manuscrip

Sea surface temperature contributes to marine crocodylomorph evolution

During the Mesozoic and Cenozoic, four distinct crocodylomorph lineages colonized the marine environment. They were conspicuously absent from high latitudes, which in the Mesozoic were occupied by warm-blooded ichthyosaurs and plesiosaurs. Despite a relatively well-constrained stratigraphic distribution, the varying diversities of marine crocodylomorphs are poorly understood, because their extinctions neither coincided with any major biological crises nor with the advent of potential competitors. Here we test the potential link between their evolutionary history in terms of taxic diversity and two abiotic factors, sea level variations and sea surface temperatures (SST). Excluding Metriorhynchoidea, which may have had a peculiar ecology, significant correlations obtained between generic diversity and estimated Tethyan SST suggest that water temperature was a driver of marine crocodylomorph diversity. Being most probably ectothermic reptiles, these lineages colonized the marine realm and diversified during warm periods, then declined or became extinct during cold intervals

Decontextualizing contextual inversion

Contextual inversion, introduced as an analytical tool by David Lewin, is a concept of wide reach and value in music theory and analysis, at the root of neo-Riemannian theory as well as serial theory, and useful for a range of analytical applications. A shortcoming of contextual inversion as it is currently understood, however, is, as implied by the name, that the transformation has to be defined anew for each application. This is potentially a virtue, requiring the analyst to invest the transformational system with meaning in order to construct it in the first place. However, there are certainly instances where new transformational systems are continually redefined for essentially the same purposes. This paper explores some of the most common theoretical bases for contextual inversion groups and considers possible definitions of inversion operators that can apply across set class types, effectively decontextualizing contextual inversions.Accepted manuscrip

Immigrants in Québec: Toward an Explanation of How Multiple and Potentially Conflictual Linguistic Identities Become Integrated

The aim of this paper is to apply a newly developed theoretical model to the understanding of how a new linguistic identity becomes integrated in immigrants’ self-concept. While intergroup theories have addressed the situational changes in social identities, the longer-term processes underlying developmental changes in identities and their integration within the self remain to be identified. Relying on developmental and social cognitive principles, we aim to explain the specific processes by which a new linguistic identity develops and becomes integrated within the self over time. We focus on the particular situation of new immigrants in Québec who need to integrate new linguistic identities (French, English). The social factors that facilitate versus impede these change processes and the consequences associated with the integration of a new linguistic identity are also discussed.Cet article vise l’application d’un modèle théorique récemment développé afin de comprendre comment une nouvelle identité linguistique devient intégrée dans le concept de soi de nouveaux immigrants. Alors que les théories intergroupes classiques ont expliqué les changements situationnels dans les identités sociales, les changements plus profonds dans ces identités et leur intégration dans le soi restent à être identifiés. En nous basant sur des principes développementaux et cognitifs, les quatre stades du modèle seront élaborés afin d’expliquer les processus par lesquels une nouvelle identité linguistique devient intégrée dans le soi à travers le temps. Plus spécifiquement, nous nous penchons sur la situation vécue par les nouveaux immigrants qui, au Québec, doivent intégrer une et parfois deux nouvelles identités linguistiques (c.-à-d. le français et l’anglais). Les facteurs sociaux qui facilitent ou inhibent ces processus de changement identitaire et les conséquences associées à l’intégration d’une nouvelle identité linguistique sont aussi abordés

Scratching the scale labyrinth

In this paper, we introduce a new approach to computer-aided microtonal improvisation by combining methods for (1) interactive scale navigation, (2) real-time manipulation of musical patterns and (3) dynamical timbre adaption in solidarity with the respective scales. On the basis of the theory of well-formed scales we offer a visualization of the underlying combinatorial ramifications in terms of a scale labyrinth. This involves the selection of generic well-formed scales on a binary tree (based on the Stern-Brocot tree) as well as the choice of specific tunings through the specification of the sizes of a period (pseudo-octave) and a generator (pseudo-fifth), whose limits are constrained by the actual position on the tree. We also introduce a method to enable transformations among the modes of a chosen scale (generalized and refined “diatonic” and “chromatic” transpositions). To actually explore the scales and modes through the shaping and transformation of rhythmically and melodically interesting tone patterns, we propose a playing technique called Fourier Scratching. It is based on the manipulation of the “spectra” (DFT) of playing gestures on a sphere. The coordinates of these gestures affect score and performance parameters such as scale degree, loudness, and timbre. Finally, we discuss a technique to dynamically match the timbre to the selected scale tuning

Fourier phase and pitch-class sum

Music theorists have proposed two very different geometric models of musical objects, one based on voice leading and the other based on the Fourier transform. On the surface these models are completely different, but they converge in special cases, including many geometries that are of particular analytical interest.Accepted manuscrip

Shall We (Math and) Dance?

Can we use mathematics, and in particular the abstract branch of category theory, to describe some basics of dance, and to highlight structural similarities between music and dance? We first summarize recent studies between mathematics and dance, and between music and categories. Then, we extend this formalism and diagrammatic thinking style to dance.Comment: preprin

Spectroscopy of the a^3\Sigma_u^+ state and the coupling to the X^1\Sigma_g^+ state of K_2

We report on high resolution Fourier-transform spectroscopy of fluorescence to the a^3\Sigma_u^+ state excited by two-photon or two-step excitation from the X^1\Sigma_g^+ state to the 2^3\Pi_g state in the molecule K_2. These spectroscopic data are combined with recent results of Feshbach resonances and two-color photoassociation spectra for deriving the potential curves of X^1\Sigma_g^+ and a^3\Sigma_u^+ up to the asymptote. The precise relative position of the triplet levels with respect of the singlet levels was achieved by including the excitation energies from the X^1\Sigma_g^+ state to the 2^3\Pi_g state and down to the a^3\Sigma_u^+ state in the simultaneous fit of both potentials. The derived precise potential curves allow for reliable modeling of cold collisions of pairs of potassium atoms in their ^2S ground state