I don't think that quite explains it. The "cutting through" I believe is more a factor of what frequencies human ears are more sensitive to and where we expect to hear things in Western music.
"Frequency" describes the rate at which sound pressure waves peak and trough, and it is normally measured in cycles per second (aka 'hertz'). Humans can hear sounds that are roughly 20 hertz to 20,000 hertz; there are sounds above and below that range that other animals can hear (just as there is energy above and below visible light, but the wavelengths are usually measured in Angstroms because it would be many terahertz or better- any physicist jump in here ...).
Your bass guitar low E string makes a fundamental sound at 40hz (approximately). It also makes a harmonic at 80 hz, 160 hz, 320hz, and so on, and generally speaking, there is less energy present in each harmonic as you go up doubling the frequency. The difference in the loudness of different harmonics, determines the 'timbre' of an instrument (harmonic content). So... now your bass guitar 'E' is making a mixtures of 40/80/160/320/.. hz all at the same time in a pretty complex waveform, not just a pretty sine wave.
The other aspect of 'cutting through' has nothing to do with frequency; it's how quickly the sound starts and stops. Sort of the difference between a violin (with a gentle attack) and a piano (with a sharp attack) even though the instruments *might* have the same harmonic content. Things with faster attack cut through better.
