In this research we studied the 12 tone equal temperament (TET) which consists of the modern music system, and investigated its mathematical properties. Furthermore, we investigated new music systems beyond the 12 TET and developed the 10 TET. 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 integrated music theory with mathematics by studying these new music systems. We will discuss mathematical properties of the 10 TET including major and minor scales, order of sharps and flats, and triad chords. 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.