Notice that even though these new waveforms contain more than one frequency component, they are still periodic.
Because each of these frequency components are integer multiples of some fundamental frequency, they are called harmonics.
Signals with harmonic spectra have a fundamental frequency and therefore have a periodic waveform (the reverse is, of course, also true).
Pitch is our subjective response to the fundamental frequency.
The relative amplitudes of the harmonics contribute to the timbre of a sound, but do not necessarily alter the pitch.