My daughter's fiancé is a formally trained musician, flutist, and composer. We were discussing harmonics last night as he was tuning my nephew's new ukulele, and he explained the minor seventh occurs when a string is divided into seven equal parts. He explained that this is purely coincidence. Do we have a chart that shows the interval by string subdivision? I had only thought about the 1/2=octave before, but I doubt that the pattern is random. Does it go something like this? 1/2=octave (e.g., G on the G string), at the 12th fret 1/3=fifth (e.g., D on the G string), in two places 1/4=octave (e.g., G on the G string), in two places not counting the twelve fret, which is a different octave 1/5=major third (e.g., B on the G string), in four places 1/6=fifth (e.g., D on the G string), in three places (in addition to where the lower D notes are) 1/7=minor seventh (e.g., F on the G string), in six places 1/8=octave, etc. 1/9=ninth?