Yes, however overtones of many notes also extend to the upper register, here are some pretty cool spectrographs to show that most musical notes contain their harmonics and also overtones: http://nastechservices.com/Spectrograms
There is definitely a LOT of things that are difficult to measure that qualify SQ in transducers, in fact FR is to me more of a filter, if something has good frequency balance then you can get into other stuff like detail retrieval, transient response, et cetera. We don't have square wave response measurements on these either which would be nice. I really wish more people with the equipment would simply run various chords and tones of various instruments and compare the reproduced spectrograph with one recorded directly from the instrument, that would be really useful. Another thing I would like good measurements on would be response when multiple tones are present, it's easy to have a transducer that can deliver a balanced FR but not easy to have one deliver a balanced 5khz tone whilst simultaneously playing a 100hz tone, that's normally limited by how much control the driver has at the extremes of it's excursion. It's almost frustrating the sheer lack of empirical objectivity that should be present in audio, it's what always makes me skeptical first of praise for any speaker/headphone. Measurements don't lie, thought they can be interpreted different ways.