Need help in trying to trace cause of distortion

RV, I think you are right and spenav 1++ Distortion like this is usually mechanical and the obvious culprit would be the driver that handles the midrange. It would only be in one speaker and just listening to each driver close up should be able to locate it. I assume you only use CDs so forget about miss tracking. I have seen cable connections do funny things, bad plugs or bad solder joints. First is to detect what channel has the problem as it is unlikely that both are doing exactly the same thing. If by chance both channels are involved the only common denominator would be the power supply of one of you electronic devices. If an amplification stage is not getting enough power it will clip early and there is a lot of energy at 1000 Hz but I think you would notice the distortion in loud passages and transients. Good Luck!

Thanks for the tips.

Both my GE Triton Ones an Triton References both play flute fine with zero distortions. 

Download REW  https://www.roomeqwizard.com/ and purchase a calibrated microphone  https://www.parts-express.com/dayton-audio-umm-6-usb-measurement-microphone--390-808

Learn how to use them and you will be able zero in on problems like this in short order.

Many years ago, during the period when I had gone over to the dark side (Muse Model 150 monoblocks, Thiel 3.8s), there was a particular passage in one particular Martinu piano CD (Chandos) that excited some kind of distortion in one channel.  "Luckily" it followed the monoblock when swopped, but I never found out whether it was just the monoblock, the interaction with the speaker, or something anomalous on the recording itself.  No other CDs, even of piano music, created the problem.  Muse went out of business shortly thereafter (surprise?), and I moved on to an SET + Proac.  Moral of the story: yes, these are very irritating and yes, they can be very hard to track down.