The base for the present structure was founded around 1980. Wind orchestra Auletes was founded out of a wind quintet and a flute quartet. String orchestra Ma Non Troppo was established in 1980; a succesful choir workshop resulted in the formation of the mixed choir Vokollage. In 1986 Sambuca, the recorder ensemble, also joins the association. The string orchestra becomes a chamber orchestra in 2002, and was renamed to a symphonic orchestra in 2009. In 2016, Sambuca has unfotunatly been dissolved due to having too few members. Since 2002, ESMG Quadrivium consists of the following subassociations: wind orchestra Auletes, symphonic orchestra Ensuite and mixed choir Vokollage.

Besides the different orchestras and choir, Quadrivium also has several active ensembles that practice and perform music of their own accord. The association also owns three pianos and a grand piano and has several rehearsal rooms which can be used 24h a day by members for ensemble practice, or for individual practice. We also organize activities and provide musical coaching for ensembles and pianists.