While there are differences between tuners, the really interesting part of the problem is probably the autoharp.

Although we usually speak of a note a having a particular "pitch," mother nature is a pretty messy soul, and there really isn't often a sound that has a single frequency component. The tuner must, somehow, pick a "dominant" frequency from whatever sample it gets; and different tuners will use slightly different methods of determining which sound components are important, and which to discard.

Under any circumstances, a "typical" tuner would have a hard time separating two tones 5 cents apart in frequency, so it would likely just take whichever one was "loudest" and would show that as the "pitch" of the sound.

When you tune using the built-in microphone, you're obviously enough using the sound that's transmitted most strongly through the air, and - based on your description - that agrees with "what you hear." When you tune using the Matrix pickup, you're using the sound that's transmitted most strongly as a vibration of the part you clip onto, and that may not be the "note" that's most strongly transmitted out of the instrument.

The autoharp has multiple strings, and each string is a separate "resonant system." When two "resonant systems" are "coupled" or mixed, through a nonlinear connection you always get the frequency of each of the systems, and also a "note" at the frequency that is the difference between the two systems (and one at the sum frequency, as well). If, for example, you have an "A" string at 440 Hz, but there is an "a" string at 881 Hz that can rattle in sympathy with the A, the contact mike may pick up 440, 881, and (881-440) = 441 Hz. The tuner will have a very difficult time determining whether you want it to tell you about the 440 or the 441 Hz "pitch" that it's seeing. The "vagrant" 441 Hz noise that's rattling around inside the autoharp may never make it to the outside world - except via the Matrix pickup - but it may very definitely be there.

Everybody take a deep breath and say "HUH?" now.

Given the acoustic complexity of an autoharp, it's difficult to say whether you might be able to pick an attachment point for the pickup that might be less sensitive to the internal "shake-rattle-and-roll" that goes on, on the inside of the harp - so that the tuner can tell which is the "airborne acoustic output" pitch that you're looking for.

One possible solution would be to substitute a small, preferably directional, microphone for the Matrix pickup when tuning the autoharp. In other words, put a layer of air between the pickup and the instrument, so that you don't tune the "buzz" instead of the strings. Most tuners work quite well with the piezo "contact" pickups like the Matrix, with built in instrument pickups, or with most kinds of microphones, as their input. Although I've not had very good luck with them elsewhere, it's possible that one of the "suction cup" models (I believe Matrix makes one) would couple differently, and the softer cup connection might help discard the spurious frequencies.

Most piano tuners tune one or two strings and then "beat" the others to the tuned ones. I suspect that, even though it looks like it would be simpler just to use the tuner on all of the strings, it is probably the difficulty of discriminating the "note" from the "spurious beats" that makes it more efficient to tune that way.

John