Because of the inherent imperfections in all pianos, including variations in string manufacturing, cabinet, iron plate, bridges, ribs, soundboard, pinblock, etc., no two pianos are exactly alike.  Every string produces its own unique characteristics in tone.
 

When a string is hit and begins to vibrate, what you see is massive movement throughout the length of the string.  In reality however, the string has been mathematically divided into several sections.  These sub-divisions are referred to as "overtones".

Overtone Divisions:  When a wire or sound waves vibrate, it subdivides into simultaneously vibrating fractions referred to as Partials, or Overtones.

The first vibration is called the Fundamental, or 1st Partial.  This is the actual sound that you initially perceive.  For example, if the string is tuned to a "C", you will hear a "C".  In actuality, you are really hearing several pitches at once.  These are the divisions that are occurring within the string.  The following diagram shows how this division works: 

Divisions of a vibrating string generating individual audible pitches,  called Partials or Overtones.   (listen ~ click here) (listen ~ mp3)

The first division then, is much like taking your finger and placing it exactly half way in the middle of the string.  Because the string is now half the size, you will hear a pitch exactly one octave higher (from the initial "C" to the next higher "C").  This is natures 1st Overtone, or 2nd Partial.

If you had a "perfect" piano, the strings would subdivide into these various harmonics making tuning a breeze.  Unfortunately, this is never the case.  The deviations from the perfect divisions is termed inharmonicity. 
 
 

Six different brand new pianos of the same make and model were measured for the amount of inharmonicity in the temperament notes (F below middle C to the F above) using just the fourth partial.  These variations would cause some significant challenges in tuning using a "one size fits all" approach.

This diagram shows inharmonicity measurements of just  "middle C" between different types and sizes of pianos.

Through the use of advanced computer technology every string is measured for inharmonicity.  These variations, or deviations from the theoretical partials are then plotted and measured against other notes and partials.  The computer then simultaneously tunes up to 8 partials at once, continually measuring each partials inharmonicity, relative strength and weakness.  Targets are then calculated based on the measured inharmonicity, stretch choices (Style), temperament, and on the targets of other previously calculated targets.
 
 

The computer system that has been helping me achieve these incredible results, calculates nearly 2,000 measurements, individualizing each pianos temperament with absolute precision.

A typical aural tuner (including myself), and less sophisticated electronic tuning machines only listen for one partial at a time.  This requires some guess work on trying to find the perfect "stretch" (variations from the theoretical) for a piano.  Consistent optimize tunings are achieved and refined each time your piano is tuned.  Partly because of the tremendous amount of information that is kept on file for your piano.  Future tunings are even better, because of the stored memory of each strings partials.
 

With continual aural checks done by ear and the accuracy of the most advanced dedicated computer system available, I am able to produce exceptionally smooth rising beat rates in Equal Temperament.  Irregularities are easily compensated without guesswork.  Spinets and other difficult scales can be tuned with the best possible regularity.  Concert tunings are done with the type of precision that professional pianists expect and require. Note:  Sometimes I am asked if I tune by ear or with a machine.. the answer is yes to both questions.  I  know the very  best and latest techniques and systems for tuning by ear, I have studied and perfected the only system that is taught and endorsed by the Guild with the man who has been credited with co-writing and perfecting this system.  If done right, tuning is a combination of accuracy and musicality.  Knowing the skills to tune by ear to within 1 cent (one one-hundreth of a half step) helps guarantee a beautifully sounding piano. This was also necessary in order to pass the rigorous examinations of the Piano Technicians Guild and be granted the credential of Registered Piano Technician (RPT).