Some technical details related to piano tuning are offered here. This may be more information than some customers want to read. However, below is more information for those who love the details.
Pitch, Inharmonicity & Tuning:
To fine-tune a piano, first the overall tension must be correct. If it is not correct, the instrument may need a "pitch-raise" to establish the correct tension and enable the instrument to hold a tuning at concert pitch (A440). Once the correct tension is established, the technician must make very small adjustments to each string to fine-tune the instrument. Each piano is somewhat unique due to something called "inharmonicity". In addition to the full string length, which represents the fundamental frequency, strings vibrate in a number of shorter sections separated by "nodes". The nodes divide up additional related frequencies that piano tuners refer to as partials. Some musicians may refer to overtones or harmonics when speaking about related topics. We won't present an argument here regarding which term is correct (See Partials figure 2 below). However, piano tuners refer to them as partials. These related frequencies of a tuned piano may not match up exactly with the mathematically determined harmonic frequencies due to a number of issues relating to the size, tension, length, materials and sometimes even imperfections in the steel strings. (If you want a very short demonstration of partials/harmonics, ask me during your next tuning.)The "scale" of the piano, the design that includes string length, diameter, materials, and tension, also impacts the inharmonicity and tuning approach. The tuner must deal with the unique inharmonicity characteristic of each piano. Therefore, the technician does not simply match the strings to a given set of pitches. Years ago there were some tuners who carried a set of 12 tuning forks to set the initial middle octave. Experience has shown how small changes are needed in individual pianos to adjust for the inharmonicity that is unique for each acoustic piano. Your tuner assesses this, via listening to the interaction among notes and partials. A slight variation is applied from the theoretical standard to make your piano sound its best.