Conventional acoustic and audio knowledge has little enough to say about the sonic effects of harmonics when they're gross (ie, 50% to 0.5% of the fundamental). At lower levels, almost nothing is documented, and extrapolation of the high-level effects would seem presumptuous. I have witnessed experiments in which the effects of introducing at below –95dB a spray of harmonics, including the seventh, ninth, and eleventh, by loading-down an IC op-amp, are: a) perfectly audible, but b) perceived more as a dulling loss of detail and air than as dissonant in the usual sense of "anti-melodic" or "gritty." There is much yet to discover.
