tonights the night, page-60

re: min maj 6ths Actually by stoping the string half way it dampens the fundamental vibration.

Each string on a piano is a different pitch, obvioulsy, and the hammer only ever hits in the one spot. There are intervallic relationships between each noye of a piano.
Eg c - d is a major 2nd, c -e maj 3rd, c-f perfect 4th, c - g perfect 5th, c - a major 6th, c - b major 7th.

Perhaps you are confusing musical intervals with harmonics of a vibrating system.