Tuning a Piano
Intervals
The most difficult part of tuning is to make sure that all 88 notes on the piano are in tune with each other. Out of the hundreds of ways of tuning pianos in earlier centuries, modern musicians settled on one - equal temperament. The "distance" between the bottom and top notes of an octave is "broken up" into 12 "even pieces." One way of imagining equal temperament is to think of the "distance" between two notes. For instance, the relationship between the two notes that make up a "fifth" on a piano stays the same, even though the pitches change. Every fifth on the piano has the same sound to your ear, even if the pitches are different. This is because the relationship between the two notes in any fifth is the same. This was not always the case.
After setting the A to 440, a piano technician starts to tune the piano by setting the pitches of all the notes in one octave so that they are in correct relationship with each other. This is called "setting the temperament," and it is the hardest part of piano tuning. It is like one of those wooden geometric puzzles, and the puzzle has 13 pieces. Whenever you move one piece, it affects all the other pieces in the puzzle. I tuned several hundred pianos before I could set a really excellent temperament.
Each technician develops his or her own pattern - the order in which the notes in the temperament are tuned. But the end result can be judged very objectively. There are test intervals which tell a well-trained technician if the intervals in the temperament are correctly tuned. The technician listens for "beats," or the sound of two sound waves interfering with one another. An experienced technician can sit down at any piano and tell whether it is properly tuned or not, and if not, where the errors are. There is some subjectivity in this judgment, but not very much!
After the temperament is set, the technician tunes the notes above and below those already tuned. When the piano is properly tuned and an interval is played chromatically up or down the keyboard, there should be an even sound. In other words, if chromatic thirds are played, there should not be one third that "sticks out" from its neighbors.
The design of the piano and the quality of its components and assembly affect how well it can be tuned. The result of a really fine tuning is that the piano is tuned the very best that that piano can be tuned. A good tuning is truly a joy to hear.
I hope this explanation gives you an idea of the amount of training and skill required to tune a piano really well. I will be happy to answer any questions you have about piano tuning.