We developed a new musical interface, CubeHarmonic, with the magnetic tracking system, IM3D, created at Tohoku University. IM3D system precisely tracks positions of tiny, wireless, battery-less, and identifiable LC coils in real time. The CubeHarmonic is a musical application of the Rubik’s cube, with notes on each little piece. Scrambling the cube, we get different chords and chord sequences. Positions of the pieces which contain LC coils are detected through IM3D, and transmitted to the computer, that plays sounds. The central position of the cube is also computed from the LC coils located into the corners of Rubik’s cube, and, depending on the computed central position, we can manipulate overall loudness and pitch changes, as in theremin playing. This new instrument, whose first idea comes from mathematical theory of music, can be used as a teaching tool both for math (group theory) and music (music theory, mathematical music theory), as well as a composition device, a new instrument for avant-garde performances, and a recreational tool.