The above discussions are relevant. Just to put a cap on this thread, I would like to add the following: The correct mesh distribution has to deal with the order of the displacement function being assumed and the method of numerical integration being used.
In the early development of FEM, triangular elements were used, even for quads (four internal triangular elements with a central point at its CG). Five points were then the major points of interest. As the order increased, iso-parametric methods became popular which allowed more points (7, 9 and 16 points were typical) of interest to be considered, but yet swept out of the final stiffness formulation when establishing displacements.
Some planar mesh generators strictly use the triangular mesh and correct its distribution using an energy function. For three-dimensional problems often the tetrahedron is used as the primary building block element. The same distribution rules apply.
So, you have to understand the basic assumptions of the finite element and its distortion rules. Stress distributions or velocity gradients in CFD require localized fineness whereas that is not the case for dynamic (frequency) determinations.