The setup used for the test was an Axe-FX Ultra into an A&H MixWiz board. Everything was plugged into the same outlet and fed off a plug strip.
For the measurement I fed the signal to a laptop from an Aux output. I used a
Frequency Response Plotter to create the FFT.
I did some additional testing tonight with the following results:
(Y) = Yes, noise is present.
(N) = Noise is not present.
(Y) 1. XLR OUT of Axe to XLR IN on board. Axe grounded.
(Y) 2. XLR OUT of Axe to XLR IN on board. Axe ground lifted.
(Y) 3. XLR OUT of Axe to XLR IN on board. Axe grounded. XLR cable ground lifted.
(Y) 4. XLR OUT of Axe thru Ebtech Hum Eliminator to 1/4" IN on board. Axe grounded.
(Y)* 5. 1/4" OUT of Axe to 1/4" IN on board. Axe grounded.
(N) 6. 1/4" OUT of Axe thru Ebtech Hum Eliminator to 1/4" IN on board. Axe grounded.
(N) 7. 1/4" OUT of Axe thru Behringer DI to XLR IN on board. Axe grounded. DI grounded.
(N) 8. 1/4" OUT of Axe thru Behringer DI to XLR IN on board. Axe grounded. DI ground lifted.
* Noise was 60 cycle hum, not 3 kHz whine.
Also note that tests were performed with/without board phantom power applied.
So, I believe I can conclude that the whine is present only when using the balanced outs of the Axe.
I haven't concluded that this is/is not a ground issue. I'm in an old house and know for a fact that the outlet used is ungrounded. I've yet to dig out an extension cord to go into a grounded outlet.