On The Mathematics of Musical Measures and Their Relation to Geometry

Abstract

The musical measures have been of primary importance throughout the history of music, because it is thanks to this tool that music is written and through it is performed and disseminated, however, those who study music formally understand the musical measures as only a tool to write and represent music, therefore, in this article we investigate the musical measures from another perspective: through mathematics, we will look for expressions that are able to describe the musical measures and thus find a new way to study them, in the second part, as a consequence, a possible analog to the Pythagorean theorem is constructed, which gives us the basis to begin to develop part of the geometry from the unique use of musical variables such as tempo, the rhythmic break, the time of a song and the number of measures.