Tapered gussets do three things.
Geometrically changing your section
Increase the stiffness of your base plate
Changes inherit natural frequency
1. Geometrically changing your section.
I'll quote square sections as i know the formulas off the top of my head
Second moment of inertia of a Square section BD^2/12*(A*h^2)
B= Bredth
D= Depth
A = Area
h = Hight from the neutral axis
For SHS sections the second term is negated as it is doubly symetrical.
by adding gussets you are in term adding depth in turn that relates to a higher Ixx value which is the measure of Stiffness.
2. The gusset goes into tension and compression hence stopping the base plate from bending (often used in structural steel connections to increase the capacity of the connection).
3. Is a byproduct of the previous two points. the stiffer the section the higher the natrual frequency. it can be simplified and calculated by the use of matrix manipulation in the form of eigen values. This can shoot you in the foot as if your natural frequency matches the induced frequency (motor mounts fans etc etc) the sinusoidal waves are coincidental and hence additive (much how noise cancelling works it throws a inverse wave to make the -ive appear as the + appears 1-1=0. 1+1=2. thats what the whole meaning of resonance. the only way you can kill resonance is dampening. You see the little rubber doova on a tennis racket.....
Dampening of the strings.