Every pendulum is “born” with a natural frequency. This frequency (and period) is not affected by the amplitude of oscillation.
The natural frequency of a spring-mass system depend on the stiffness (the spring constant of the spring) and the inertia (the mass of the mass) of the system.
The natural frequency of a pendulum is dependent only on its length. (The acceleration of free fall is the other factor, but we usually cannot choose the value of g.)