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It's been proven that you don't need to have the string touch the fingerboard to stop the string vibrating.
There are several bowed string instruments that don't even have a fingerboard. The side of the finger is used to just touch the edge of the string on these instruments - for any pitch along the length.
Bending the string too much will cause a change in pitch, so if you try to force the string to the fingerboard when the action is too high - you'll be bending all your notes out of tune.
I still believe WHAT'S IMPORTANT: is steel, gut and synthetic core strings, and their different rated tensions, ALL RESPOND DIFFERENTLY TO FINGER PRESSURE. If I understand this correctly, more initial finger pressure is needed, then we need to spring up to a spot the note quality can be sustained - it depends on our strings, but also how each of us uses our fingers.
Isn't it important for us to find out how to do this with the least amount of pressure vs. just learning to push or hammer the string to the fingerboard?
My favorite video on this topic:
@Katie L -
You are right - this is an excellent video (referring to your Finger Pressure Thread). 😊
Nathan Cole helps find the pressure we should be striving for, with the left hand, at 6 minutes into his video.
When it comes to string height, here's other factors to consider besides nut height - like the shape of the fingerboard, if it's too worn, and how much 'scoop' it has.
That said, it has been determined that a specific string height makes playing easier - and is usually adjusted at the top edge of the bridge.
Here's a GREAT video that explains the nuances of string height and how it's measured, by Edgar Russ!
This article at "Strings" also tells you how to measure the highest/lowest pitched strings - violin, viola and cello.
...closer to the bridge, strings are farther away from the fingerboard - and people learn to play there without distortion.