In this research we studied the 12 tone equal temperament (TET) which consists
of the modern music system, and investigated the mathematical properties of it. Furthermore, we explored the possibilities of developing new music systems beyond the 12 TET. There are constraints in realizing the new music system. Since existing musical instruments have been designed for the 12-TET, it would require much effort and time to modify them for a new music system. However, it is possible to develop new music systems using present computer software due to the advancement of the IT industry and computer science. We can integrate music theory with mathematics by studying these new music systems. Musicians would be able to play current string instruments under new music systems because strings can hit a continuum of notes. We would also be able to sing songs composed under the new music systems. Further development in this area may drive the music industry to produce modified instruments, such as the wind instruments and the piano, compatible with new music systems. Possible consequences may include the discovery of exotic music systems, a renaissance within the music industry, and a myriad of new jobs within the industry.