Maximal rationally connected fibrations and movable curves

A well known result of Miyaoka asserts that a complex projective manifold is uniruled if its cotangent bundle restricted to a general complete intersection curve is not nef. Using the Harder-Narasimhan filtration of the tangent bundle, it can moreover be shown that the choice of such a curve gives rise to a rationally connected foliation of the manifold. In this note we show that, conversely, a movable curve can be found so that the maximal rationally connected fibration of the manifold may be recovered as a term of the associated Harder-Narasimhan filtration of the tangent bundle.Comment: An error in the argumentation has been correcte

Tangential projections and secant defective varieties

Going one step further in Zak's classification of Scorza varieties with secant defect equal to one, we characterize the Veronese embedding of $\P^n$ given by the complete linear system of quadrics and its smooth projections from a point as the only smooth irreducible complex and non-degenerate projective subvarieties of $\P^N$ that can be projected isomorphically into $\P^{2n}$ when $N\geq\binom{n+2}{2}-2$.Comment: To appear in Bulletin of the London Mathematical Societ

Music Notation-to-Color Synesthesia and Early Stages of Music Education: A Grounded Theory Study

Problem Synesthesia is a neurological condition characterized by over-abundant neural connectivity between commonly highly specialized areas of the brain. The developmental form of the condition often results in automatic and consistent cross-sensory associations between perceived stimuli and commonly unrelated brain regions. This research contemplates the specific form of music notation-to-color synesthesia and its impact on early stages of music education. Synesthetes with this mode of the condition tend to involuntarily yet consistently associate music-notational concepts with colors, thus rendering their assimilation of these concepts unique and individualized. The purpose of this study is to determine the extent of these individualized experiences from original narratives. Method This study entails a grounded theory qualitative approach, through which 12 from participants were interviewed cross-culturally (7 featured nationalities). All participants were adults with music notation-to-color synesthesia who experienced music instruction in a Western cultural context. Data collection methodology involved a written survey, inperson (or live Zoom) interviews, and shared document analysis. Qualitative analytical methodology was used via coding strategies to discover surfacing themes, emerging issues, and commonalities among the narratives. Results Five overarching categories of commonalities were identified in this study. Firstly, participants shared generalities of synesthetic perceptions of music notation involving color, such as their awareness about their condition, the qualities of their experiences, the conceptual basis of their associations, among other characteristics. Interviewees also alluded to the mechanisms involved in the perception of music notation, such as the positive impact of their music notation-to-color synesthesia on memory as well as the negative implications of synesthetic incongruence. The spatial location of synesthetic perceptions varied among participants. Interviewees reported projecting on the page of music and associating in their mind\u27s eye —two common themes in the literature. Some participants, however, have also mentioned a middleground location that does not fit only one of these categories. Finally, this study analyzed themes relating to the implications of this form of synesthesia for music education, with attention to awareness on the part of educators, instructional intentionality, validation, reinforcement of student individuality, and conscious use of the condition. Moreover, other themes and future research possibilities were analyzed. -- Conclusion This study arrived at two grounded theory models. The first comprises a grounded theory of the experiences shared by participants. This theoretical model articulates the salient themes, such as positive and negative traits of notation-to-color perceptions and spatial location of perceptions. In special, this theory argues for a tendency for conceptually-based notation-to-color synesthesia among participants. The second grounded theory model advanced in this research entails an educational approach that would benefit awareness and intentionality in addressing students with music notation-to-color synesthesia. It discusses philosophical foundations, a theoretical framework, and methodological considerations that may transform how music notation-to-color students are accounted for in curricula. The study concludes by offering pedagogical suggestions derived from the methodological considerations. Firstly, it advances a linear process for identification, verification, and addressing of synesthesia. Secondly, it proposes the elimination of excessive notational information and gradual learning as initial strategies that could benefit music notation-to-color synesthetes in learning new notational elements

The Role of Proportion in the First-Movement Expositions of Mozart's String Quintets

This study aims at discussing the role of balance and proportion in the expositional scope within a Classical Sonata Form movement. While using the approach, model and labels proposed by James Hepokoski and Warren Darcy in Elements of Sonata Theory (2006), it also challenges the application of some of their analytical tools. Throughout this study, special attention is given to different treatments of expositional spaces, including a few significantly difficult cases for the repertoire. The intention here is to observe the interaction between these spaces in light of the dual function in the expositional trajectory: (1) to fulfill the harmonic requirement in destabilizing the tonic key; and (2) to attain a rhetorically reasonable organization of thematic material (HEPOKOSKI; DARCY, 2006, p.18). For this purpose, a careful examination of the medial caesura and the essential expositional closure is also taken into account throughout the present analysis. Finally, however limited the repertoire range used in this specific research, the present study fosters the idea of proportion and balance as feasible arguments (among many others) not only in determining the dimensions of expositional spaces, but also in the holistic process of analyzing entire Classical sonata forms as hermetic units

Music and ceremonial in Fernão Cardim’s Jesuit letters (1583-90)

This paper addresses Fernão Cardim’s letters to his Portuguese employer, in which he provides details on the missions of the Society of Jesus throughout Northeastern Brazil in late sixteenth century. This study dwells on the historical context of these letters and focuses on reports of ceremonial music, with special attention to themes such as Jesuit inculturation and adaptability. In analyzing the Jesuits’ peculiar musical engagement and interaction with the natives and their ceremonial practices, this paper evaluates the significance of this interrelationship for Jesuit Catholic ritual. This research also explores Cardim’s accounts on the intersection between Christian ceremonies and local rituals as one of the earliest documented signs of religious syncretism on Brazilian territory

Form and Structure in J. Haydn’s “Von deiner Güt’ o Herr und Gott”, from The Creation

In challenging SPITZER’s (2009) proposition of absence of structure and balance (parataxis) within “Von deiner Güt’, o Herr und Gott”, from J. Haydn’s The Creation, the present article addresses contemporary analytical theories of form that may reveal exactly the opposite. The analytical framework used in the study was drawn from theoretical tools designed by CAPLIN (1998; 2001; 2009), HEPOKOSKI, and DARCY (2006) for the analysis of Classical form. This paper argues that tonal balance is a fundamental organizational device and serves as a structuring agent in the composition discussed. Moreover, the tonal balance featured in “Von deiner Güt’” illuminates the underlying structure of the textual narrative, thus rendering a stronger rhetorical appeal to the climactic moment in which it is inserted. The most salient significance of this research lies in its applicability to other cases of less strict formal structure that may be dismissed as parataxis while they, in fact, feature careful formal construction on the composer’s part

Form and Structure in J. Haydn's "Von deiner Güt' o Herr und Gott" , from The Creation

In challenging SPITZER's (2009) proposition of absence of structure and balance (parataxis) within "Von deiner Güt', o Herr und Gott" , from J. Haydn's The Creation, the present article addresses contemporary analytical theories of form that may reveal exactly the opposite. The analytical framework used in the study was drawn from theoretical tools designed by CAPLIN (1998; 2001; 2009), HEPOKOSKI, and DARCY (2006) for the analysis of Classical form. This paper argues that tonal balance is a fundamental organizational device and serves as a structuring agent in the composition discussed. Moreover, the tonal balance featured in "Von deiner Güt'" illuminates the underlying structure of the textual narrative, thus rendering a stronger rhetorical appeal to the climactic moment in which it is inserted. The most salient significance of this research lies in its applicability to other cases of less strict formal structure that may be dismissed as parataxis while they, in fact, feature careful formal construction on the composer's part