  The motion of a particle in 6-dimensional phase space in the presence of
linear coupling can be written as the sum of 3 normal modes. A cubic equation
is found for the tune of the normal modes, which allows the normal mode tunes
to be computed from the 6x6 one turn transfer matrix. This result is similar to
the quadratic equation found for the normal mode tunes for the motion of a
particle in 4-dimensional phase space. These results are useful in tracking
programs where the one turn transfer matrix can be computed by multiplying the
transfer matrices of each element of the lattice. The tunes of the 3 normal
modes, for motion in 6-dimensional phase space, can then be found by solving
the cubic equation. Explicit solutions of the cubic equation for the tune are
given in terms of the elements of the 6x6 one turn transfer matrix.
