Good question. The short answer is: “physics”.
The longer answer: The Greek philosopher Pythagorus discovered the natural intervals created by different string lengths. A 2:1 ratio creates an octave. A 3:2 ratio creates a 5th. A 4:3 ratio creates a 4th, and a 9:8 ration creates a whole step, a major second. The “major 3rds” are dissonant. If I start on the lowest note on the piano, A and go up in Perfect 5ths, I will end up on A again in the 7th octave, just below high C. I need to add the 3:2 ratio 12 times (3:2)^12 = 129.7463 times the original frequency. If I start on the same A and go up by octave to get to A7, I will have added the ratio 2:1 7 times (2:1)^7 = 128 times the original frequency. They are not the same A. If I start on the low B or low C, I end up with even a completely different set of frequencies or notes. The solution for this is called Tempering, where one note is set to specific frequency, usually A-440, and all of the other notes are made to sound good together regardless of what their theoretical frequency should be. It is common today to use Equal Temperament, where the distance between each successive note is the same, regardless of their theoretical frequency. - A guitar tuner uses theoretical frequencies and does not offer a tempered tuning. There is also something called inharmonicity in the strings themselves. The theoretical overtones of each string are exact ratios: 2:1, 4:1, 8:1, 4:2, 3:2, 6:4, 4:3, etc. Because of the physical properties of the metal wire, as the harmonics get higher, the part of the string that vibrates to make that harmonic gets stiffer, vibrates faster, and the harmonic goes sharper. For example, the harmonic that should match the note two octaves higher is too sharp, and the notes do not sound good together. The solution for this is called stretch. As one gets higher or lower on the keyboard, the octaves are stretched to be just a bit wider than theoretical so that they sound in tune with the rest of the keyboard. - A guitar tuner uses theoretical frequencies and does not offer frequencies for stretched octaves. If a piano is severely flat, it may take two or three passes to get it to pitch and stabilized. This is called a pitch raise. The strings are all tensioned, from lowest to highest a certain percentage just above the target pitch, knowing some of the tension will be immediately lost and the pitch will immediately go flat. Some tuners do a half-way pass with old and rusty strings. - A guitar tuner is no help for pianos that need a pitch raise, which many “inherited” pianos do. On a neglected piano, a solid tuning would take anywhere from an hour and a half to over two and a half hours for a professional. With more than 220 strings and tuning pins, a do-it-yourselfer may be making a commitment of anywhere from a half of a day to maybe 2 days or more. I have met several people who have tried the DIY method of piano tuning who were happy to commiserate about their learning experience. One gentleman watched the Youtube videos, bought a tuning kit from Amazon, and after breaking two bass strings, decided it was time to call a professional before he did any more damage. If you are adventurous, give it a shot. For the most part though, this is one best left to a professional. Support your local craftsperson.
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