Intuitive way to understand the triangle spectrum? Image on the top is in the time domain, image on the bottom is in the frequency domain. 

Why do we see -2T and 2T on image of the time domain and why do we see -1/2T and 1/2T of the image in the frequency domain?
Suppose there is a sound with frequency 440Hz. How large is each period of this periodic signal? It must be (1/440)s. The same applies in your case.