I have been studying quantum mechanics and I came across Planck's relation which describes the energy $E$ of a photon as being directly proportional to its frequency $f$, with Planck's constant $h$ as the proportionality constant, i.e. $E=hf$.
My question arises from the observation that this linear relationship between energy and frequency seems to hold true specifically when considering sinusoidal bases for frequencies. Why is it that using a sinusoidal frequency base results in a linear relationship in Planck's relation? If we were to use a different basis for frequencies, would we not see a linear relation? What is it about the sinusoidal nature of frequencies that makes this linearity apparent? I'm trying to understand the fundamental reasons behind this and would appreciate any insights into why the energy-frequency relationship in Planck's formula would change, if at all, with a different frequency base.