The proper way to tune a piano, the tried and true method that has been relied upon by composers and musicians throughout history is an aural tuning. This process involves setting one note to an external source (ie.-a tuning fork), and then tuning an octave around that note by widening 4ths and narrowing 5ths until each step is the same number of vibrations apart. The is called tempering the interval.
Practically every concert hall in the world will only rely on a properly done aural tuning. This is because it is really the only way that is truly consistently accurate when done by a skilled tuner.
Metered tuning basically involves an operator looking at a machine and turning the tuning hammer to stop revolving wheels. It is extremely difficult to properly tune a piano this way. In my opinion, built upon 38+ years and 18,000+ tunings, it is extremely difficult to properly tune a piano this way.
I probably do 50-100 tunings for new clients each year that have been extremely disappointed by a previously done metered tuning. It is my feeling that if you can’t do it right, don’t do it at all.