Bass- at what frequency does it change from sounding like a string to just a low tone?

I agree with gladmo but will try to answer directly. 60hz grabs the kick drum impact and is as high as you need to go with good speakers imo. At 80hz you are clearly into the bsss guitar range and it can get hard to match tone even with a highpass it sounds like a sub/sat combo to me. At 60hz you get bass slam but could lose a touch of texture at 40-50hz if you have VERY capable speakers  

But if you listen to just the subs with no speakers right around 35hz it is just tones or at least very slow cycles and it is just tones more or less. At 35 you are below an electric bass guitar. 35hz is what shakes the room for home theater. 
 

I have had subs in 3 systems while electronics and speakers changed a few times the subs always stayed. rough speaker specs and casual measurements in my room confirmed the specs more or less (large room with minimal nodes). It is different for each system room.  

thiel 2.4=flat to 32hz, used a 60hz highpass, thiels have great low bass but it is tuned too light for my tastes.   

revel 228be=flat to 45hz? used a 60hz highpass, Revel has no low bass, totally mixing in action… in bad need of subs  

JBl 4367=flat to 40hz, use a 40hz highpass. Amazing bass texture from these JBLs and they outperform the subs from 40hz up with more texture and tone but they drop lock a rock at 40hz.  
 

I would set the volume on the sub with test tones and a DB meter for starters then adjust to taste after that. 

I set my subs ruler flat and let the wife listen. She said there was no bass?!?  So I adjusters it for her by taste and she ended up 10db hot lol!  
 

As for sub setup. If you can not highpass the -6 or -10db point of your speakers is probably the place to start. The -3 might have too much over lap. A test tone/DB meter will save a lot of messing around. 
 

I think a highpass is well worth the effort. You can then just pick a frequent where both the subs and speakers work well. I have found it is best to use the 3db point of the woofer NOT the speaker as a whole. For ported speakers this cuts out the port and for sealed it minimizes boundary gain and you can get a cleaner sound. All in all it does not matter as long as you enjoy it. I stopped carrying about “correct” a long time ago. You can have all the other audiophile stuff and a frequency response that you enjoy.