I don't get the distinction you're making. Technically speaking, every sound we hear consists of a bunch of sin waves, each at a different frequency and amplitude, all superimposed together. Put differently: every real sound is a bundle of frequencies all piled together. These real sounds contain many frequencies we can hear, and some frequencies we can't hear. If you surgically remove the ones we can't hear, it sounds the same to us. By surgically, I mean, remove them without side effects that distort frequencies we can hear.
If you use a bandwidth wide enough to capture every frequency we can hear as a sin wave, you're done. It will transparently capture every real sound we can hear, regardless of fundamental vs. harmonic. No need to worry about or distinguish fundamentals from harmonics. SIY gave a good example: to me, a 14 kHz sin wave sounds the same as a 14 kHz square or triangle wave. I can only (barely) hear the fundamental, and all the harmonics that make them sound different are well above my hearing.