Quadratic and non-dodecaphonic series as fundamental structures in the construction of a piece for brass quintet

In this work, we describe the compositional procedures used in the planning of a piece for brass quintet, whose materials come from quadratic and non-dodecaphonic series. The quadratic series allow for the creation of dodecaphonic matrices with ninety-six serial forms, that is, twice the possibilities available in traditional dodecaphonism. The non-dodecaphonic series, make it possible to manipulate series whose cardinality is less than twelve and, with them, produce matrices that can be mapped into different musical parameters, such as pitch, dynamics, articulations, etc. The theoretical bases for the construction of quadratic series originate from studies on musical symmetry with special focus on rotational operations around five axes. Additionally, repositories built from dissonant counterpoints will be used as elements of contrast.