[Todd Harrison] recently wrote in to tip us off on his submission to the Tektronix oscilloscope contest – using a scope to tune a piano. In his video he demonstrates how a Fast Fourier Transform can be used to determine the fundamental frequency of the note being played. This is a quick and easy way to determine if that key is in tune, and if not, how far off it is from the desired frequency and in which direction.
He goes on to explain that a scope can only be used as a starting reference point since “mathematically correct” tuning on a piano doesn’t sound right to the human ear. It turns out that when struck, the stretched wires in the piano behave less than ideally. In the case of a piano, the overtones (the other peaks shown on the scope higher in frequency than the fundamental) are actually slightly sharper (higher in frequency) than the expected harmonic whole-number multiple of the fundamental frequency. As a result, the frequency ranges of each octave must be “stretched” in order to accommodate this and sound correct when multiple notes are played together across octaves.
Typically, only the A4 key is actually tuned to its correct frequency of 440Hz and all of the other keys are manually tuned off of this baseline. The amount of necessary stretch applied to each octave increases as you get further away from this initial reference point in either direction and is unique to each and every individual instrument – thus there is no universal device capable of perfect tuning. Although [Todd] admits that he won’t attempt to tune the entire piano himself using this technique, he finds it a convenient way to keep the most heavily played center sections of the piano closer to true between professional tunings.