Different sections or movements of a piece are associated with each other and contain the composer essential thought. A vague affinity of mood and a resembling theme or form testifies to the relationship. However, the evidence is insufficient to reveal the unification of the different sections or movements since these are under restraint of external music proofs. In order to figure out the relationship, thus, identical musical substance should be discovered. In the study the substantial evidence, which can be called unity or unification, is mainly discussed. The unity is illustrated with Brahms's Horn Trio, Op.40 that is one of the Brahms's significant works. The unity found in the Horn Trio is based on the internal structure and structural voice-leading notes. The unity in the Horn Trio is the fundamental structural unity that is divided into initial ascent and voice exchange, and fundamental voice-leading motive. The fundamental unity seriously affects the master piece and penetrates the movements as a whole. Further, it reveals the hidden connections to the historical background of the Horn Trio and the philosophy of Brahms for the music. Even though a piece consists of several sections or movements, the entire piece presents homogeneity. The identity of the composer's underlying philosophical thought suffices to discern the musical unity in a piece. Thus, the investigation of unity is one of the critical ways to understand not merely a piece but also the philosophy of a composer. The study will help to enhance the audience's interpretation of music.