Those sorts of specifications (60Hz - 20kHz) are really not very useful on their own. In any case, we can only hear up to 20kHz at the very most - if you are an adult, especially a musician who has been subjected to a lot of high decibels, you probably won't hear anything much above 8 or 10 kHz.
What is more important is the spectrum of sound within those limits. Your speakers look OK but perhaps not adequate to represent the sound of real instruments such as piano, giving the full range and depth of sound.
We find headphones - ones of good quality, costing in the 80 - 250 euro range, say, very good at representing digital pianos - far better than speakers of a similar cost.
I'm quite happy with these Yamaha monitors, which should be better than yours. Even so, I am aware that the sound range is limited and the speakers are great as a reference for other sound systems (that is what reference monitors are supposed to do, anyway) http://www.thomann.de/es/yamaha_hs_7.htm
To get the sound you want, maybe you simply need to get larger, better designed, and consequently, more expensive speakers.
There are lots on the market - KRK, Yamaha, EV, JBL are a few names among very many. I think Behringer do well regarded monitors (their Truth range), too. Check those out, maybe. http://www.thomann.de/es/behringer_b2030a_truth_aktivmonitor.htm