There is a defined pitch for every note on the piano keyboard. The frequencies are calculated according to the principles of equal temperament. This piano tuning system uses mathematics to divide an octave into 12 'equal' steps. Once the ratio for a semitone is established, harmonics are used to help the tuner fix the intervals in the scale.
These harmonics are used by the tuner to set the notes in the middle octave. The tuner uses these first 12 notes in the middle octave like a template, thus being able to tune the rest of the piano - hopefully achieving equal temperament across the whole piano keyboard. How close we tuners actually get to perfect equal temperament would interest perfectionists for a very long time.
The truth is that a tuning may not be perfect - the tuning will be as good as the particular piano will allow. To achieve a perfect tuning, one would need a perfect piano. Even an expensive new piano may not be quite as perfect as one might expect! After 50 or 60 years of wear, whatever perfection there might have been when it was a new piano, has been 'worn' away.
However, a well-tuned piano will always be a treat to play, a pleasure to listen to and the cause of great job-satisfaction for the piano tuner. The piano tuners who continually seek to excel in the job will everyday, be fine-tuning their skill.
© Steve Burden