What is the proper term for the lowest natural frequency that is produced by a vibrating object, such as an instrument?

Fundamental frequency

Explanation:

Fundamental frequency is the lowest frequency which produced due to the oscillation of the body. This frequency is different from other higher frequencies. If the tube is closed at one end, the velocity of sound divided by 4 times the length of the tube gives the fundamental frequency. The higher frequencies can be obtained by integral multiple of the fundamental frequency.

i believe your looking for this word? "fundamental".