an index of basic chords possible using natural harmonics on the guitar (standard tuning)

Most writing that has been done on the topic of natural harmonics and the guitar take it as given that you can get natural harmonics at frets 12, 7, 5 and even 4 but not many writers go further than that.  You can, however, get natural harmonics around fret 3.  Depending on the instrument you can get a natural harmonic half-way between frets 2 and 4.  You can get a compound fifth harmonic slightly below fret 3 or, if you will, about 3.1 to 3.2 with variance for the length of your fingerboard.  You can get the septimal minor seventh natural harmonic about fret 2.55 and 5.9, roughly 3/4 of the way down from frets 2 and 5.  These harmonics don't speak as readily on nylon strings with normal tension but you can get them to sing out decently enough on steel stringed guitars. 

All of that is to say that you can play quite a variety of three factor chords using natural harmonics alone once you go to the effort to learn where all the natural harmonics are and account for the fact that there are inevitably microtonal differences between the F sharp harmonics you can get across the strings. 

So if you're a guitarist or a composer who has ever wondered whether chords in natural harmonics are even practical, yes, they are.  In fact a lot of them are fairly easy.

If you don't believe that then give these a try on your guitar.  You should find most of them fairly easy in principle but I suppose I should provide a caveat.  There's nothing like mastering chords played entirely in natural harmonics to show you how clean your left hand technique really is. 

This is not even close to being a comprehensive chart since it doesn't account for harmonics you can get between the fifth and sixth frets. 

The chart has two staves. The upper stave shows how the harmonics look when written at pitch. The lower staff shows how you would play the harmonics chords in terms of both the left and right hand placement needed to execute the chord.  Some of these will require a more flexible approach to left and right hand positioning than some guitarists may be used to but all of these chords, once you refine the basic technique of executing natural harmonics as a starting point, are pretty easy to play. 

So if someone like, say, Sofia Gubaidulina, wanted to know what kinds of chordal sonorities are possible on the guitar using only natural harmonics she's got an answer ... if someone were to send something like this her way.  I'd welcome whatever sort of work she'd write for classical guitar that makes use of all natural harmonics chords, personally, but that's just my own personal opinion. 

Just to be clear, even though I published this chart here I'm telling you that I think of this particular chord chart as something that is for anyone to use (i.e. public domain).  If you found this here at Wenatchee The Hatchet please do mention it when relevant, but also feel free to use it as a reference for your own guitar composing.