To transpose a given set, simply add the same number to each member of the set. The number should be between 0 and 11, and represent the amount of half steps contained in the interval of transposition. For example: to transpose a set up a minor third, you would add the number 3 to each member of the set. Given the pc set {10,0,1,3}, adding 3 to each member would yield the pc set {1,3,4,6} (note that 10 + 3 mod 12 = 1).

To determine if two sets are related by transposition, you would subtract the normal order of one set from the normal order of the second. If all the differences are the same, the two sets are related by transposition at that level. For example: given the pc sets {10,11,2,3} and {4,5,8,9}, subtract the second set from the first.

                                 10  11   2   3
                             -    4   5   8   9
                                  6   6   6   6

Notice in this case, all the differences are 6, therefore, these two sets are related by transposition at T6. Remember that 2 - 8 is the same as 14 - 8 and 3 - 9 is the same as 15 - 9. When you are subtracting a larger number from a smaller number, add 12 to the smaller number to achieve the correct results.