The wave equation for stiff strings and piano tuning

We study the wave equation for a string with stiffness. We solve the equation and provide a uniqueness theorem with suitable boundary conditions. For a pinned string we compute the spectrum, which is slightly inharmonic. Therefore, the widespread scale of 12 equal divisions of the just octave is not the best choice to tune instruments like the piano. Basing on the theory of dissonance, we provide a way to tune the piano in order to improve its consonance. A good solution is obtained by tuning a note and its fifth by minimizing their beats.Peer ReviewedPostprint (published version

"Sobre tenir lo Studi de Lleyda en Tortosa"

The lower medieval Catalan model of the estudi general (university) exemplified by the case of Lleida emphasises the weight achieved by the students as a body, the jurisdictional conflicts and, especially, the serious economic difficulties, that poisoned the relations with the poorly paid teaching staff and made the centre impossible to run. In that sense, the monarchy’s incapacity to provide the jurisdictional and financial bases, pushed higher education under a growing ecclesiastical weight snd municipal dependence. The local government, for its part, would have to increase the means of taxation needed to produce the necessary financing. All together, this generated difficulties that would burden the estudis generals throughout the lower Middle ages and into modern centuries, until their closure in the 18th century

Marginación e inadaptación : notas para un estudio sobre la llamada delincuencia juvenil en Barcelona

La pretension de sugerir unas notas para el tratamiento sociologico de la marginacion social y una de sus manifestaciones mas evidentes (la llamada «delincuencia juvenil», desde una perspectiva autonoma y teniendo a Barcelona como telon de fondo, es el objetivo del presente articulo. En una primera parte se repasan las grandes corrientes teoricas que han estudiado los temas de la marginacion social (localizadas fundarnentalmente en USA y Latinoamerica); a partir de todo ello y con la incorporacion de algun elemento original se intenta elaborar una sintesis util. En la segunda parte se indica una posible aplicacion de la sintesis al estudio de la llamada adelincuencia juvenil, proponiendo un modelo explicativo adecuado. Se examinan tambien las dificultades que se presentan al aplicarlo a la realidad social de Barcelona y se dan posibles lineas de solucion a estas dificultades

Suplement bibliogràfic 2012

Suplement bibliogràfic 201

Architecture and sustainability in the Mediterranean. The case of the Barcelo

LIMA, Low Impact Mediterranean Architecture, is an initiative that aims to demonstrate that reducing environmental impact of buildings in countries with warm climates is viable, both technically and economically. The project, which also improves the comfort and habitability of the building, can be applied to both new works, as well as to rehabilitation. A holistic view of the environmental impact thet we are presenting not only includes energy consumption during the building's period of use, but incoporation of construction materials throughout the building's lifecycle, likewise covering the water cycle and aspects such as health and comfort. The Taller Barceloneta, which was commissioned by the Town Hall of Barcelona, is an example of the LIMA Model under real conditions

The Catalonia of the 10th to 12th centuries and the historiographic definition of feudalism

The historiographic evolution of the concept of feudalism, from its formulation in the 17th century until today, has affected Catalonia differently. In the last quarter of the 20th century, it reached a prominent position as a paradigm of the mutationist model. The numerous sources still conserved, coupled with the enrichment of interpretative perspectives, facilitate a revision. However, it should be undertaken cautiously in light of the pitfalls of the documentation itself and the hermeneutic difficulties. Nonetheless, revision is a challenge that cannot be neglected given that the events that took place in the northeast of the Iberian Peninsula between the 10th and 12th centuries heavily conditioned the subsequent history