Basic answer: If a piano is too far out of tune, it will not stay in tune after one “pass.” It will require a preliminary “rough” tuning first, known as a pitch raise. A440 is the internationally established correct frequency for the note “A” above middle “C,” and is the starting pitch from which the rest of the piano is tuned.
More details: Tuning defines the relationship of one note to another, whereas “pitch“ describes the specific frequency at which a string vibrates. The note we call “A” above middle “C” has been set by International Committee to be at a frequency of 440 vibrations per second. This is known as “standard” or “concert” pitch. When we tune a piano, we start by making sure that this “A” is exactly at that frequency, and then the rest of the piano can be tuned by establishing the correct relationships that result from that starting pitch.
Theoretically, a piano can be in perfect tune with itself even if “A” is far from the “correct” frequency. However, to be “in tune” means not only in tune with itself but at the correct pitch. Tuning a piano is like shooting at a target. The farther you are, the harder it is to hit the bulls eye, let alone the CENTER of the bull’s eye.
As time and other factors act on a piano the tension on the strings tends to drop until the pitch is very low. If a tuner brings the strings to the correct frequency in one pass, he or she will find that no matter how carefully they try to do it, the increasing tension created by the tuning process will change the strings they first tuned, often significantly.
Therefore it is impossible to get a piano which is too far from correct pitch to stay in tune in one “pass.” We have found that one or two quick tunings to get everything “close” followed by a careful tuning can yield excellent results. This process of performing one or two “rough” tunings before the “real” tuning is called a pitch raise. It obviously take more time, and most tuners charge extra for this.
Pianos that have not been tuned in two years or more usually require this extra work, but new instruments where the strings are still stretching can require this process as well.