Now I'm going to make a fool out of you. Piano tuners DO NOT use machines or tuners to set the tuning. I was trained by a guy in town who was regarded as the best in Kansas for 50 years. Every piano store in town and the surrounding area used DUKE. He taught me that the piano HAD to be tuned by ear, because the human ear doesn't like pianos tuned to perfect pitches of electronic tuners. The super trebles and sub basses need to be pitched RELATIVE (not exactly) to all other strings. You start at middle C and work out towards the last keys. Some strings sound better sharp, and some sound better flat to a human ear. It takes awhile to learn, and awhile to do the actual tuning. If it's been a long time since the piano was tuned - it will take a longer time to do. You'd have to do it 2 or 3 times to get right because of the immense tension on the soundboard. It's got to adjust.
I'll say it again - pianos tuned to exact pitches do NOT sound right to the human ear. Duke taught me to "tune it to the beating of the strings". That's relative tuning.