A description of a "synodic frame" was one of the main ingredients in this excellent answer to a question about an animation of a funky-looking orbit that several different and distinctly interesting aspects to it.
As part of the background for this question I plotted historical orbit data for SOHO in a rotating frame centered on a point in space that is associated with the Sun-Earth L1 libration point. I say associated with because in real-world orbits, and not just circular-restricted ones, L1 is more of a "Gestalt" (or "area") than a specific, mathematically well-defined point.
If you look at the lengths to which I had to go to explain the frame of this plot, you can see that I could have used a better term, if one exists.
So here I'd like to ask both What is a "synodic frame"? so we could have a great answer and useful definition to link back to in the future. But I'd like to also ask Can one be defined for an elliptical orbit?
Here's the plot from the question where the math is described. It is the orbit of SOHO shown in a home-grown coordinate system. Note that the "Gestalt", faux-L1, or "instantaneous-L1" red point on the left is fixed in this frame, and the position of the Earth as a function of time, the blue elongated sausage on the right, defines only the axis.