Here are a couple of down loaded charts showing the natural harmonics,usually recognized,you can take a pair of needlenose pliers and find extensions of these all the way to the vicinity of the bridge
.Banjoy [Frank Estes] has presented 3 nice vids on this subject so he is the one that is to be considered the maestro on this,never the less i feel the need to impart a little more fuel for the fire..
I do get the 0ne fifth string length harmonics on my banjo at the almost 4th fret 9th fret and so on.On the g string this is a b,i think earl mentioned this as a mystery in his book.The tempered scale is one reason is is not exactly over the fret.These charts even show a harmonic in the third fret region ,i'll have to try that.A d note on the 3rd string it says.
.A chimed note at the 12 is twice as fast as the root,the string is being cut in half and this makes the'' all of a sudden'' half lengths go twice as fast.,if you go to the 5th or seventeenth fret and chime,and you cut the string in fourths,making the note4 times as fast as the root.
Also the 7th fret chime cuts it in 3 pieces so it is 3 times as fast, (a high d note on the g string)the 4th fret chime slices it in 5 parts and is weak in comparison,on the g string this is a b note.
You can take a tape measure and measure from the nut up to a chime, then go to the bridge and measure down the same increment and find the same chime,since they are caused by equal increments .
Another chart i have included is one showing frequency and actual wave lengths of the individual notes,this is slightly related to this ,because the most strong natural harmonics are the major chord notes and this chart shows somewhat of reason.
In one instance it shows a g note wave of 1400 centemeters.when the string makes 4 excursions that is 5600 centimeters of travel in the air,the b note another note in the g chord is a shorter 1110 centimeters however you multiply by 5 you get 5550 centimeters,which is fairly close,the reason it can't be made perfect comes under discussion of the''tempered scale'',the d note the last note of the chord is an even shorter 940 centimeters but multiply it by 6 you get 5640 centimeters.Summarizing the the g and b are in sync every 5 th time and g and d every 6 times ,Keep in mind this is going on up to a few hundred times per second.--Tom