Hello there,
I think he wants to restrict the class of functions to those with integer frequency relationships, such as:
sin(w*t)+sin(3*w*t)+sin(8*w*t)+...+etc., ie sums that include terms like sin(n*w*t), n an integer, and not any that are like sin(x*w*t), where x is any number like pi, sqrt(2), etc.
In the case of integer frequency relationships i think the periodicity is as the inverse of lowest frequency, in this case the lowest is f=w/(2*pi) so it would be Tp=1/f.
If we dont restrict ourselves to the integer cases then we have a monumental task on our hands.