I would be careful here. Relative stability is data, which I am presuming to be correct for this problem. Hyperconjugation is an attempt to rationalize the stability order. The rationalization is not necessarily TRUE. It may be true, it may be partly true. So, if you do not understand it, the explanation may be more empirical than based upon physics. I suggest you simply recognize how hyperconjugation is applied.
If s, p, d, and f correspond with emission spectra, then where do sp3 bands occur? If they do not exist, then are there hybridized orbitals? As an organic chemist, I rather like hybridized orbitals. It seems to make sense. Can I explain them? I can understand how it was derived, but I cannot explain them.