These measurements were from racket tune. Didn't know the frame could affect frequency but that makes some sense.
Well, this makes sense to me, too. Racquet Tune (as well as ERT-300 tennis computer) uses the physical model of standing waves in a fixed-fixed string as the first approximation. If you would use two rigid clamps spaced at a distance L from each other and clamped a piece of string with density P tensioned to the tension T, then its primary resonance frequency would be
F = (1/2*L) * SQRT (T/P)
Density P is the mass of the piece of clamped string divided by its length. These are input parameters into racquet tune.
When string vibrates, it deviates from a straight line, stretches a little, and exerts additional force on the clamps. If the clamps are not rigid, e.g., when a somewhat flexible frame serves as "clamps", then the frame starts vibrating as well, and it has its own resonance frequency which is probably fairly low, on a relative scale. This will create additional harmonics in vibrations of the whole thing, and this could conceivably shift the readings picked up by racquet tune.
Of course when you measure the complete string bed, you measure a very complex oscillation of multiple strings of different lengths and the frame, interconnected into the string bed. I looked at Fourier transform of the sound of the string bed after impact, picked up by a decent quality (about $150 - $200) studio microphone, and it is a freaking mess. Peak after peak after peak, all relatively small, like 5 to 10 dB or less. It is not like a piano or a guitar sound where you see the main note followed by harmonics.
A thought that you can measure tension with a racquet tune is a little bit of a stretch. There definitely is a correlation, but it is more complex than just tension vs frequency, and I am sure the frame (and grommets, for that matter) have an impact. When racquet tune gives you a shifted reading, it does not necessarily mean that your tension is different. It means that the resonance frequency, or whatever racquet tune is able to pick up as the resonance frequency, is different. You can theoretically have different resonance frequency of the string bed on a frame for exactly the same tension. I think you actually do have the same tension, regardless of what racquet tune tells you. But your string bed resonanates at a lower frequency for some reason, and usually this is percieved as a softer string bed. But you know, if you have a softer frame, its string bed, everything else being equal, would also be percieved as a softer one than with a stiff frame, for exact same strings and tension.
Since you are on it, a simple experiment could be to take a measurement with racquet tune on a free-standing racquet and on a racquet on the stringing machine. Grippers of the stringing machine would suppress some of the vibrations of the frame (6 points is much better than 4 and WAY better than 2 for the purpose of this test). I am curious what difference in reading you would see. I suspect, there may be some. I tried the same thing without measuring anything, and I could clearly hear the difference in sound.
[Ducks and runs for cover]
