I think what Judith's alluding to is that even a tiny amount of 3rd or 7th order harmonic will add a discordant "edge" to a fundamental, thus giving it a sharpness that allows you to perceive it more easily.
Come to think of it I used to do the same thing as a kid by adding such a discordant harmonic to my Hammond organ playing by pulling out one of those upper "drawbars" to give color and definition to a melodic line. Listen to Jimmy Smith. It's that discordant upper harmonic that gets ya!
But alas not so great in amplifiers.
I use Pass Labs Alephs as a great compromise to achieve a neutral, clean, ultraquiet amplification that's regarded as somewhat tubelike, but with the advantages of only two solid-state gain stages.
Tubes act like natural compressors, so they get by with less wattage because their peaks are squashed, bursting forth with only even order stuff when clipping.
I prefer a CLEAN, unforced ss amp because of its linearity and lower noisefloor, and GREAT bass whomp, of course.
But tubes are great in a low-powered situation, like thosde great old radios of the 50s. Ahhh....