Music and mathematics have a lot of structural similarities. Major and minor triads used importantly in music are in a relationship of inversion in which the sequence of the intervals is reversed, which is equivalent to reflection in mathematics. Geometrical expressions help understand structures in music as well as mathematics, and a diagram that shows tonal relationships in music is called Tonnetz. Relationships of reflection between major and minor triads can easily be understood by using Tonnetz, and also, transpositions can be expressed in translation. This study looks into existing Tonnetz and introduces S-Tonnetz newly formed by a mathematical principle.