If there's a scientific map that you know of that explains which 3D direction has what amplitude at a certain distance, that would be helpful as well.
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EDIT: I realized I didn't reply to the OP: :)
Thinking in "sonic ranges": the low frequencies of the violin are the most omnidirectional, if not totally; the highs tend to come out in a "slice of cake": considering as if you're playing in the middle of a clock quadrant, with your violin pointing at 12:00, your highs and high mid freqs spread better within 12:00 through 4:00, also in vertical.
I saw that the mids can have a strange behaviour.
But in general, the frequencies that make violin more audible and the sound travel more are, in my experience and general knowledge in the sound tech guys, are those that spread 12 - 4.
So, playing while having the listeners to your right, like first violins in an orchestra, is always a good move.
Lots of folks put their microphone(s) way too close to the instrument, so all we hear are the scrapes and squeaks which the audience never hears after the sound has developed in the performance space.
The amount of high frequency (HF) that the microphone picks up depends on the angle relative to the tone holes, and also the height of the microphone--the higher up you go above the level of the instrument, the more HF it picks up (as Cotton describes above).
While I love ribbon mics and was very fortunate to have a pair of Coles 4038 to use for awhile, good results are more a function of mic placement rather than getting the most expensive pieces of hardware out there. You can get very good results with basic cardioid condensers like a pair of Audio Technica AT2020 or a pair of sE7. Lots of my students recording for summer festivals and pre-screening auditions find a lot of success even with the very inexpensive Blue Yeti mic!
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