Cualidad sonora y geometríauna aproximación al análisis de "El Clave Bien Temperado" Vol. I (BWV 846-869), Johann Sebastian Bach

Abstract

The purpose of this PhD Thesis explores the connections between Music and Fine Arts, taking Geometry as a reference. The proposed research cannot forget the importance of the creative freedom, which evokes feelings far removed from reason, as well as the absolute necessity a performer must undertake in order to simulate the sound perception of a score, making the performance an added and particularly important value. During the development of this research work, we study the possibility of reinterpreting the Music by replacing the intangible nature of time – its usual support—with the plane – the physical and material support inherent in Fine Arts. That being said and taking into account that it is a reinterpretation, we will avoid, thus, transliterating for the sake of scientific rigour and accurate intuition, being helped by a versatile Geometry, able in this way to leave space for feelings without the stoppage entailed by established esthetic prejudices. In this sense, the proposed piece of music to this research will be Johann Sebastian Bach’s The Well-Tempered Clavier, specifically the vol. I BWV 846-869. Over time, this musical score has been increasing its great theoretical, conceptual and teaching value, bestowed by the composer himself, as it was addressed to his students and especially to his musician children, with no goal of being played neither known by the audience. The Well-Tempered Clavier (vol. I BWV 846-869) marks a turning point in History, becoming the indispensable closing of the Baroque and the begining of the Enlightment. It is, therefore, an everlasting work and a certain reference of the concept of tonality, thanks to the division of an octave into equal twelve sounds. This final adoption allows the tonality transit to another without impediments, modulating to either of the twenty-four tonalities, as well as standardizing and rationalizing the ruling laws of the harmony and counterpoint of the named equal temperament -- also known as twelve-tone equal temperament (TET) -- , become thereafter a facilitator reference of the music composition development until today...