The number of distinct operations in a system that map a set into itself is the set's degree of symmetry . The degree of symmetry, "specifies the number of operations that preserve the unordered pcsets of a partition; it tells the extent to which that partition's pitch-class sets map into (or onto) each other under transposition or inversion". Every set has at least one symmetry, as it maps onto itself under the identity operation T . Transpositionally symmetric sets map onto themselves for T where does not equal 0 (mod 12). Inversionally symmetric sets map onto themselves under TI. For any given T/TI type all sets have the same degree of symmetry. The number of distinct sets in a type is 24 (the total number of operations, transposition and inversion, for n = 0 through 11) divided by the degree of symmetry of T/TI type.