Original unaccompanied literature currently stands as one of the most understudied bodies of music in the euphonium repertory. This is largely due to a lack of access to reference recordings, live performances, and study/performance guides. Many of the commissioning projects for new euphonium music in the late 20th and early 21st centuries have promoted the composition of large scale works for euphonium and large ensembles, but very few have generated new unaccompanied pieces for euphonium. Many of the most recent commissions for unaccompanied euphonium music have been for competitions such as the Lieksa Brass Festival (Finland) and Leonard Falcone International Festival (USA). These competitions are also where many students get their only exposure to the unaccompanied repertoire. Unfortunately, there is a small number of standard unaccompanied works that are continuously recycled for these competitions and the exposure to new pieces in the repertoire is further diminished for many developing euphoniumists. This study will examine the three works for unaccompanied euphonium by Torstein Aagaard-Nilsen and provide solutions for many common technical challenges and pose suggestions for approaching and preparing this genre of music. Connections are made throughout the study to specific etudes and other unaccompanied solos that can be used as complementary and precursory studies to aid in the mastery of this literature.

Neste trabalho, veremos que a noção de número de Nielsen pode ser estendida para aplicações entre variedades topológicas não necessariamente orientáveis ou compactas, com ou sem fronteira. / In this work, we are going to see that the concept of Nilsen Root Number can be extended to maps between not necessarily orientable nor compact manifolds, with or without boundary.

Neste trabalho, veremos que a noção de número de Nielsen pode ser estendida para aplicações entre variedades topológicas não necessariamente orientáveis ou compactas, com ou sem fronteira. / In this work, we are going to see that the concept of Nilsen Root Number can be extended to maps between not necessarily orientable nor compact manifolds, with or without boundary.