There used to be a site that tested your ability to differentiate close pitches, but it is no longer active, and I am unaware of any other way of testing differentiation of pitch. So my question is: What is the smallest interval (in cents) audible by humans (and most importantly trained musicians)?
It's going to be difficult to come up with an absolute number, because it will vary greatly between individuals. I suspect it will also vary with age, exposure to music, and any number of other factors.
That being said, this question has been asked on some of our sister sites:
Perhaps the answers are of interest.
The smallest interval a human can hear depends somewhat on the register and timbre of the tone (and it varies from person to person), but generally speaking the smallest detectable difference is around 5-6 cents, according to this study from 2006:
D.B. Loeffler, "Instrument Timbres and Pitch Estimation in Polyphonic Music Archived 2007-12-18 at the Wayback Machine.". Master's Thesis, Department of Electrical and Computer Engineering, Georgia Tech. April (2006).
I have a small tool called dgen which is a very simple double sine wave generator which would be perfect to answer your question, at least for yourself. Maybe you can find something similar, even as an online tool.
In my own experience, there is a difference between really hearing two notes with close pitch and hearing one "blended" note and additionally the beat of the two notes.
Classical musicians train to hear this beat and use it to determine pitch correctness. This, by the way, does not only work whith to notes of the same frequency, but also on intervalls, where for example the frequencies are in a ratio of 2:3 (a quint intervall).
Of course it is a matter of training and experience, but organ and accordion tuners have to recognize the beat frequency for 2cents of difference (an equal-tempered fifth as opposed to a pure one) in their reference octave (which is tuned using fifths and fourths) to a precision of a fraction of a cent as well as hear whether they are flat or sharp compared to a pure fifth (or there will be gnashing of teeth when the circle of fifths is supposed to be completed).