What is the "reed" frequency?

Its the fundamental lateral natural freuquency of a beam, built in at one end and free at the other.

Picture a bed so reeds blowing back and forth in the wind. Sometimes used in the description of turbine blades.

I once saw a small hand-held box called a reed vibrometer: this had a glass front and contained about 40 small arms facing the glass. Each arm was 'tuned' to a slightly different frequency, with lowest at the left and getting higher to the right, with the centre arm tuned to 50Hz - by placing the box on a machine you could see the frequencies of vibration that were present. An interesting mechanical gizmo, probably used for electrical work

It was a reed tachometer; very common to see them setting on turbine 30 years ago.

This term is often used to describe the lateral frequencies of a vertical pumpset.
The frequency will be quite low, ie a few Hz to say 10 Hz depending primarily upon the height of the machine.
One of the charactereistics of reed-frequency vibration is that it can tolerate a fairly large vibration at the top of the motor without undue distress in the machine. (ie the frame vibration just carries the bearing and shaft along with it).

Thanks, all for your help. Byron