If my reading is correct, using FFTs, we cannot be accurate in both frequency & phase - from wiki "When applied to filters, the result is that one cannot achieve high temporal resolution and frequency resolution at the same time; a concrete example are the resolution issues of the short-time Fourier transform – if one uses a wide window, one achieves good frequency resolution at the cost of temporal resolution, while a narrow window has the opposite trade-off." http://en.wikipedia.org/wiki/Uncertainty_principle
So again, the point is that the most used tool in signal processing, FFTs are less resolving than our hearing in regards to determining the full audio envelope. Decomposing this into an individual elements, such as frequency, and then showing that indeed measurements can be more accurate than the ear, in frequency determination, is missing the point - in the case of hearing it would appear that the whole is very much more than the sum of the parts!
The problem is you cannot get infinite resolution in zero time, and it is difficult to perform an FFT over infinite time... That is perhaps the fundamentla issue with FFTs as an analysis tool, you only get a window of time, and it acts on the whole window. They are great for steady-state, less so for moving (time-varying) waveforms.