Notation

The main objective of this article is to discuss the concept of modulation in extended harmonic structures. Tuning systems based on arithmetic divisions can be observed by means of the prime-factors in their constitutive interval ratios. According to this study, each prime-factor is represents a unique dimension in a geometrical depiction of interval cycles.
An extension of harmonic space may initially focus on the next prime-factors following the fifth proportion, i. e., seven, 11, and 13. All of them require thorough analysis by means of their inner structural and symbolic signification and through the harmonic vectors that each of them implies.
A conception of novel scales based on justly tuned partials may require the use of ratios taken from both the overtone and the theoretical undertone series. The consequences of this dualist model of harmonics (such as it has been proposed by Hugo Riemann and Hans Kayser) may be complemented by the use of subparticular scale models (such as Kathleen Schlesinger’s harmoniai) which may be applied to a consistent harmonic structure only under certain conditions.
Regarding the necessities for the consistent structural use of extended harmony, aspects of temperament as well as of just intonation will be discussed, along with the practical challenges to produce complicate intervals in unconventional harmonic surroundings. 
This article will refer to Schenkerian graphic analyses of some of my own scores. The investigations are not intended to serve as a portrayal of a personal artistic style. Rather, illustrating this approach in this way seems necessary because a similar attempt has not yet been proposed by other contemporary composers.

This thesis, in the field of music composition and performance practice, presents the results of a practice-research project into performance validity and notational reliability in vigilant musical practice. From my initial inquiry into what constitutes a valid performance, three ground principles were observed: non-normative cognitive states (how the performer thinks); embodied multimodal imagery across a full effort scale (the images a performer draws with their presence); and interpersonal communication (the performer’s readiness to react to the audience’s presence) and the performance environment. These three interconnected skills form what I come to call vigilant performance practice. This thesis aims to define a conceptual framework for vigilant music practice, at the stages of composition, rehearsal, and of performance. In support of vigilant practice, a set of developmental tools and activities were constructed that promote each of the three vigilance skills. These tools and activities are developed in practice in a sequence of sixty-four scores entitled Games for Musicians and Non-Musicians. This workbook promotes the development of vigilance skills in the context of improvised music performance in groups. Games for Musicians and Non-Musicians was rehearsed and performed publicly on several occasions. Reports of those events are presented here. Vigilant performance practice has the potential to be of use in music education and professional training, with different age groups (including children), as well as in other types of performance practice. It may be of use outside the performance environment altogether, in personal or community development.

The present paper seeks to expound the sociological prospects of a connection between the calculus of indications as presented in the Laws of Form (Spencer-Brown, 1994) and current sociological theory. Since sociology gets more and more interested in communication and perception, indeterminacy, boundaries, and difference, this attempt seems worthwhile. There is, however, a general condition that has to be met: A reasonable use of the calculus in sociology demands that the calculus is socialized. This paper is an attempt at such a socialization. It is not about how to use the calculus in sociology but rather about how to construe the calculus to develop a theory of social forms.
Keywords: sociology, social forms, methodology, communication, meaning, observer, sociological notation""

Notate sind ständige Begleiter unseres Lebens – egal ob im Privaten oder im öffentlichen Alltag. Insbesondere Schaffensprozesse machen von verschiedenen Visualisierungsstrategien Gebrauch. Zwischen Schrift und Bild werden diese Anordnungen im Material nicht nur zu externalisierten Speichern, sondern entwickeln sich aufgrund ihrer medialen und epistemischen Eigenheit zu Impulsgebern kreativer Prozesse. Vor dem Horizont von Schrift- und Bildtheorien sowie der Forschung zu Schriftbildlichkeit untersucht der vorliegende Band Wissens- und Handlungsstrukturen im Umgang mit Graphen, Bildern und Arbeitsmaterialen in verschiedenen Kontexten. Die Beiträge diskutieren epistemische Potenziale der Linie, Notate als hybride Handlungsräume, transitorische Eigenschaften von Notationen und das Wissen in diagrammatischen sowie zeichnerischen Anordnungen.

Both arithmetic and recording rely on semiotic systems, necessary for storing information. Search for indications of such human operations in prehistoric periods, before the existence of deciphered texts, can only be based on material culture and on the study of human cognition and behaviour. The archaeological record in the Near East and Europe comprises three-dimensional artefacts of unknown function, as well as two-dimensional marks on various artefacts, which have both been interpreted as the materialization of signs belonging to past reckoning and recording systems in a concrete form. This hypothesis is considered here for the evidence of the Greek Neolithic, in the light of previous studies on data from other areas.

In a recent paper, DeToffoli and Giardino analyzed the practice of knot theory, by focusing in particular on the use of diagrams to represent and study knots. To this aim, they distinguished between illustrations and diagrams. An illustration is static; by contrast, a diagram is dynamic, that is, it is closely related to some specific inferential procedures. In the case of knot diagrams, a diagram is also a well-defined mathematical object in itself, which can be used to classify knots. The objective of the present paper is to reply to the following questions: Can the classificatory function characterizing knot diagrams be generalized to other fields of mathematics? Our hypothesis is that dynamic diagrams that are mathematical objects in themselves are used to solve classification problems. To argue in favor of our hypothesis, we will present and compare two examples of classifications involving them: (i) the classification of compact connected surfaces (orientable or not, with or without boundary) in combinatorial topology; (ii) the classification of complex semisimple Lie algebras.

Português (English below): Considerando o potencial de preservação da performance por meio de sua guarda em acervos e de sua reexibição, propomos uma reflexão sobre soluções digitais a partir da aproximação com projetos de notação em dança. Entre eles, citamos o arquivo RePlay, da companhia de Siobhan Davies; a plataforma Motion Bank, mantida pela William Forsythe Foundation; e o TKB - A Transmedia Knowledge Base for Performing Arts, liderado pela Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa. A partir desses exemplos, discutimos as diferenças de objeto a serem ponderadas no possível desenvolvimento de uma iniciativa similar para a documentação de performance.

Abstract: Considering the potential of performance preservation through its collection and reexhibition, we propose a reflection on digital solutions from the approach with projects of notation in dance. Among them, we mention RePlay, the choreographic archive of Siobhan Davies Dance; the Motion Bank platform, maintained by the William Forsythe Foundation; and TKB - A Transmedia Knowledge Base for Performing Arts, led by the Faculty of Science and Technology of the New University of Lisbon. From these examples, we discuss the object differences to be considered in the possible development of a similar initiative for performance documentation.

Cet article porte sur le jugement professionnel des enseignants en matiere d'evaluation liee a l'attribution des notes dans le livret scolaire de l'eleve. Il est base sur une analyse d'entretiens avec 10 enseignants de 6 e primaire. Apres une presentation du concept de triangulation tel que defini dans les ouvrages de methodologie de recherche, on examine le degre de correspondance avec les pratiques d'evaluation des enseignants. Les resultats montrent que tous les enseignants ont recours a diverses formes de triangulation, tantot dans une visee de validation, tantot dans une perspective d'elargissement interpretatif.

The Fluxus Tree is an automatic composition centred around interactions with a collection of experimental interactive sculptures. Dancers (or anyone else) interacts with the sculptures and so creates data from sensors which generates electronic sounds and music notation live. This live notation is then played by a musician.