Thank you Jimmy. Really appreciate your thorough and clear answer.
The monitors I use are: http://www.bhphotovideo.com/c/product/819559-REG/Audioengine_A5_B_A5_Plus_Speaker_System.html
(I also got their subwoofer).
What you say I have thought of... I have plugins for tape saturation, tube saturation -- you name it. And ones where I control the odd/even harmonics. I even have the Vienna Suite Pro exciter, which btw, is the only plugin where I can hear a difference more so than other plugins. Bottom line, when I apply these harmonic distortion plugins what I hear sounds negligible.
For a long time I suspected that it may be my hearing. I am 40, and 10 years ago I had my hearing checked where one ear showed a small dip in the mid high frequency (back then, I was going clubing every weekend). In general though, I don't feel I have any hearing difficulties. Anyway, I will try out using the online tools you mentioned. Curious of the result...
Going back to the monitor speakers, I hear some great things of those having "ribbon tweeters" for the high end range...