Magic Square Logology

A magic square, well-known to recreational mathematicians, consists of a set of numbers (integers) arranged in a square, such that the sum of each row and column and both of the principal diagonals is the same. Although magic squares date back thousands of years and have an extensive literature (see for example Magic Squares and Cubes by W.S. Andrews, published by Dover in 1960), the following logological problem involving magic squares appears to be new: construct a magic square in which the number-names in each row, column and diagonal share a letter (a different one in each case). Since there are in infinite number of solutions to this problem (just as there are an infinite number of magic squares), it is necessary to impose the further condition that the sum of the numbers in the square be as small as possible