Great post that explain well why piano is so useful for tuning our system/room...
Thanks very much.....
My deepest respect....
Piano has stretched overtones. I believe it is somehow related to the fact that string has mass. Extremely long and thin string under extremely high tension would have straight harmonics, but it is not practical. Because of this stretching piano octave is not tuned to double frequency, but a little bit higher when the beating with overtones of lower octave stops, resulting in about 30 cents error at both ends. That is why tuning of the piano is so difficult and also why reproduction of the sound is very difficult as well. Any harmonics produced by the playback system might beat against stretched piano overtones. Overly warm systems produce even order harmonics that sound great with other instruments or voice, but piano sounds almost like out of tune.