ABSTRACT

Exact and heuristic tuning methods. Application to the trumpet


José Ibáñez Barrachina



       Our interest in studying tuning methods is due to three kinds of objectives: research itself, which has pursued the highest standards in the use of scientific methods, the applicability of the obtained results and the design of the experiments  for other musicians or acoustic scholars and, finally, the educational usefulness of the study.

       The first chapter provides a brief description of the historical evolution of the trumpet and its acoustics. The second chapter introduces describes some tuning systems (Pythagorean, Just Intonation, Holder’s and Equal Temperament of 12 notes). We have made an exhaustive study of each system. For each one, we have studied the internal distances between notes and have compared it with the others. In the third chapter, we have made some experiments to confirm the theory of the earlier chapters. Also, in this chapter it has been done a practical exercise with a piece composed from the calculations made by Kepler in Harmonices mundi (1619) to get his music describe the universal harmony. The fourth chapter provides the foundations to work with fuzzy musical notes and we have established the idea of degrees of compatibility between systems of tuning, in addition we provide some methods to calculate their degree of compatibility. Finally, in the fifth chapter we describe a test for measuring the perception of the notes of students and music teachers.