Certainly.
Lower hardness is achieved with longer tempering.
You can't achieve lower hardness with bad quenching.
You can, in a way, but the structure of steel would not be as it should be.
You must heat to a proper temperature, equally throughout the blade,
then keep that temperature for a certain amount of time
(some steels require 20 min or more, while people usually heat until demagnetizm)
then quench properly, regardless of the wanted hardness
then temper at least once, or more, till wanted hardness.
You are not supposed to, nor it is possible, to achieve proper STRUCTURE or hardness by only quenching.
Don't underestimate the serious misapprehension of inexperienced blacksmiths.
I admit, I haven't said thing properly, previously.
Cheers.
EDIT: In a way, I said all of this previously when I have said: "For the ping there is tempering"
As for the high hardness, isn't the cutting edge supposed to have high hardness ?
What is it with differential treatment then ?