Traditional Ogene music (metal gong) is a music genre originating in the eastern communities of Nigeria which retains an intrinsic communicative function and music style of Igboland characterized by call and response vocals, polyrhythms and improvisation. Through applying a psychoacoustic approach using visualizations and sonifications of beat-class theory with ski-hill and cyclic graphs, a listener is enabled to represent their experience of both music and mathematics embodied acoustics. This paper demonstrates the evolution of Western music theory to have the capacity to represent rhythm, meter, and pitch by visualizing beat-class theory through ski-hill and cyclic graphs (mathematical music theory). This new approach is suitable for understanding Igbo music which, like the majority of the world's music, is transmitted aurally and not notated. Applying a psychoacoustic approach, this paper illustrates how Igbo music can be accurately preserved for future generations and included in the scholarly discussion. The paper also reveals structural details of the music which may not be accounted for previously through the use of traditional Western music theory.