Lemme tell you:
Ever since I started playing autoharps back in Nov '73, I have been fiddling with the tunings and the chord patterns.
For some of these tunings, I can tune the harp to itself by means of a handy plastic template I made that slides under the strings. This template has harmonic points marked for each string (up to the 6th harmonic) which is a good way to check string ratios.
 
Otherwise, I use my handy Yamaha DX7 synthesizer or computer generated tones, or a an iPhone tuning app like Cleartone or Helix.
I started out with a 21-chord Oscar Schmidt Model C. 21 chords gives one lots of room for experimentation.
One of the simplest alterations one can do with an autoharp is to retune it in such a way as to turn the rather utilitarian chords into something more exotic. This is possible without making any changes to the harp itself or its chord bars. Here are a few suggestions:

Std AA#
Bb
BCC#
Db
D D#
Eb
EFF#
Gb
GG#
Ab
 
C Maj Modal ABBCCD EEFFGG F#,C#,G# flattened,
Bb, Eb sharpened
C Min Modal AbBbBCC D EbEbFFGAb A,C#,E,F# flattened
D Min Modal ABbBbCC#D DEFFGG B, Eb, F#,G# flattened
6's and 7's A H:B
M:B
L:A
BCC#
Db
D H:E
L:D
EFF#
Gb
GG#
Ab
only Bb and Eb affected;
Highest notes sharpened, lower ones flattened.
In the modal tunings, as you move from the "center" key of the tuning, instead of transposing, you get a different "mode". As you stray further from the center, the more unfamiliar the intervals become, as more changes are apparent in the tuning. Here's what happens to the 21 chords under C Major Modal:
Eb Bb F C G D A
F7 C7 G7 D7 A7 E7 B7
Ab Bb7 Cm Gm Dm Am Em
becomes:
Em Dm F C G Dm Am
F6 C6 G7 Dm7 Am7 Em7 BEFA
Am BFDA C G Dm Am Em

Here is an example of modal tuning as applied to Jesu, Joy of Man's Desiring (3063K).
Here is a tuning that I have on a little Chomoharp, a kid sized one with just 5 chords.
This harp is tuned to a scale of harmonics of a low F:
String 123 45 678910 1112 131415 16171819
Note name FFC FGAAB!CD! EbE FFGA B!CD!
Harmonic 446 891010111213 1415 16161820 222426
Ratio 1/11/13/2 1/19/85/45/411/83/213/8 7/415/8 1/11/19/85/4 11/83/213/8
Since these are true harmonics, 12 tone equal temperament doesn't fit this scale,
so some of the names are approximate (! indicates a 1/4 tone)
The Chords that "go" with this scale are like this:
  • X indicates a felt should be there;
  • * means a half height felt is there.
    If you push the bar in half way, you hear this note
    all the way down cuts it out.
Chord Name 123 45 678910 1112 131415 16171819
1-3-5-7*
Like F Maj and F7
FFC FXAAXCX Eb*X FFXA XCX
3-9-15
Like C Maj
XXC XGXXXCX XE XXGX XCX
1-3-9
Like C sus
FFC FGXXXCX XX FFGX XCX
9-11-13-15*
Not like anything;
The opposite of F7
XXX XGXXB!XD! XE* XXGX B!XD!
3-5-7-9*
Rootless F9
XXC XG*AAXCX EbX XXG*A XCX
1-3-5-7-9-
11-13-15
F15
(open strum; lets you play close groups of harmonics)

Now I'll give you a REAL headache: I have another 21 chord Schmidt that is set up to be tuned in a just intonation based on F, which has two kinds of Gs and two kinds of Bbs in it.
Here is a schematic of how the strings should be tuned:

G  - D - A - E        10/9 -  5/3  - 5/4 - 15/8
  \ / \ / \ / \         \   /    \ /    \ /    \
  Bb - F - C - G'        4/3 --- 1/1 -- 3/2  -- 9/8
    \ / \ / \ / \          \     / \     / \   /  \
     Db  Ab  Eb  Bb'         8/5 --- 6/5  - 9/5 -  27/20   
Or in other words, a 5-limit just scale built on 3/2 (perfect fifth) and 5/4 (major third) and their inversions 4/3 (perfect fourth) and 8/5 (minor third). There are twelve tones in this scale, although they are not equally tempered. The first trick is to retune the strings to this new scale. The second trick is to pick chords that make use of this scale.
The new tones are distributed as follows:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
F A C Db E F* G Ab A Bb' Bb C* D Db E Eb F G' G Ab A Bb' Bb C D Db E Eb F G' G Ab A Bb' Bb C
You may have noticed that some of the strings are "out of order" - this was a relic of an earlier scheme involving a 19-tone tuning... but I digress!
One of the interesting properties of the chords I ended up with is that each one has an F and a C in it (!) which allows me to put in two drone strings at spot #6 and #12 tuned an octave higher than normal. For this, I use a thinner guitar string. Sometimes I insert in a crude bridge to pull the drone string up above the thicker strings it's near, which makes it easier to pluck and often gives it a different, more muted timbre.
Each chord was made to be really rich, a pentad of piled-up thirds of various degrees, based in the keys of F and Ab :
just autoharp
F chords: made of pieces of F A C E G Bb D
F maj9F A C E G
G min9G Bb D F A
A min9A C E G Bb
Bb Maj9Bb D F A C
C9C E G Bb D
D mi9D F A C E
E 0 9E G Bb D F
Ab chords: made of pieces of Ab C Eb G' Bb' Db F
Ab maj9Ab C Eb G' Bb'
Bb mi9Bb' Db F Ab C
C mi9C Eb G' Bb' Db
Db maj9Db F Ab C Eb
Eb 9Eb G' Bb' Db F
F mi9F Ab C Eb G'
G' 0 9G' Bb' Db F Ab
Eb sus4Eb Ab Bb
suspended pythagorean chords
C sus4 7 C F G Bb
A sus 4A D E
Ab sus 4?Ab Db Eb
Augmented chords
F+F A C Db
Ab+Ab C E G'
That makes 19 chords: 7+7+3+2.
There's room for two "lock bars, but I only made one (F).
A lock bar had a special button that can keep the bar down
even when you aren't pressing it.
Lock Bars
F lockF G A Bb C D E
Ab lockAb Bb' C Db Eb F G'
All the chords have the drone strings open in them as well.
How are these bars arranged?
  BbM9 C9 Dm9 Eo9 Ab+ Absus   
  Lock FM9 Gm9 Am9 DbM9 Eb9 Fm9  
   F+ Csus Amsus G'09 AbM9 Bb'm9 Cm9
These are the basic F chords
These are the basic Ab chords
These chords are so rich, you can easily mistake them for one another! In practice, I usually put the "9th" of the chord only in the top octave so that there's not too much going on in the bass. Also, pressing combinations of chords tames them considerably. The lock bar lets me do a diatonic run in F and also helps deaden the non-F diatonic strings, as the felts on these bars are pretty beat up by now.
Clearly, close inspection shows that some of the chord choices could be tinkered with - some chords would benefit from using G' for G and vice versa, for example.

Here's a video about this Pentad tuning, made on Dec 26, 2013.
Just click the "play" control (ignore that loading... message if you see it; it will load then).


In 2019, I completely gut renovated that harp! The chord set had already moved to another body, and I changed it it into G-Bb(a/k/a GMajor/Gminor) with tetrads and a single G drone string (for now).
Here's a video about that conversion, when it was still in progress!


The chords currently on this incarnation are as follows. All the "fourth notes", which are 7ths or Major 7ths, are half-notched (or half felted if you are an optimist) and can disappear if pushed more forcefully. They all also have a "G", an octave higher, in the bass as a drone string. That G is propped up on a screw I put on the soundboard, held in place by its threads. This way, I can put it out of the way or make it easier to pluck. It's quieter than the other strings, so with softer strumming, you hear it more.
I added 7th chords on a circle of fifths to fill out the gap between Bb and G: An A7 to approach the D7, then a G7 as a way to resolve to CM or to D7, G7 and C7 to make their way to F7. A B7 allows modulating to E minor. So I can play a little bit of blues in there.
CM7 D7 Em7 F#o7   G7 C7   
  GM7 Am7 Bm7 EbM7 F7 Gm7 Ao7  
   A7 B7 Dsus7 BbM7 Cm7 Dm7 Fsus7
These are the basic G chords
These are the basic Bb chords
These are passing 7th chords

Of course they all have the drone string available. I've been experimenting with that drone string. By putting in a removable screw, the string can be lifted up above its neighboring strings and more obviously plucked with a thumb pick. This drone can be a G, but I also use A, D and E, each one adds character to the chords. The drone string is thin and quiet, so if you play the other strings quietly, it stands out more.

In August 2020, I silicone'ed the chord bars because the felt was too fuzzed up after some time. Here are some shots of that:

'Before': see how beat up, fuzzy and notched these felts are?

Here the chords arranged by 'key', G, Bb (or Gminor), and a bunch of 7ths.

Now they are sitting on wax paper, squooshed into toothpasty-lines of silicone.

The next morning: they are all dry.

Here's how gooey they are! They trim nicely with an art knife. You have to get those notches clear! This is much more tedious than cutting them in the first place.

'After': Back in the harp. Note: I put bamboo skewers in the chord bar slots to help get the felts closer to the strings. That way, you don't have to push so hard.


Todd Crowley has a tuning system called "Prizim Zither", a chord system that lets you play a lot of dense chords if you are willing to push two buttons at a time.
Here is a video of my version of this system, made on Dec 26, 2013, which runs in the keys of Eb -> A instead of F-> B
Just click the "play" control (ignore that loading... message if you see it; it will load then).

Here is something a lot simpler - I have one harp without any chords on it at all. It's tuned to 22 harmonics of a low F, like this:
String # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
harmonic 2 2 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 9 10 10 11 11 12 12 13 14 15 16 17 18 19 20 21 22 24
approx. pitch F F C C F F F A A A C C C Eb Eb Eb F F G A A B B C C D Eb E F F# G Ab A Bb' B C

Many of those note names are mere approximations to the true harmonic note... but anyway, you can beat the harp with a stick or your hand, strum it, pluck it. In a resonant space, it's quite something.
Here is an MP3 of it(306K).

2019!
Here it is a few years later, and I've taken the idea of that diatonic pentad harp, with its "circle of minor thirds", or rather "Major and Minor of the same key", and cleaned it up a little. I had a spare harp body with a cracked soundboard and a lot of bars made for 15-chord harps. I refelted them and left them uncut, and made this interesting video:



And then I cut three diatonic sets of 7 chords apiece. These chords are nominally triads, but use the "half felt" trick to add the fourth note in the top and middle octaves. You get tetrads unless you press the bar down harder. I also used foam mounting tape to get the chords closer to the strings, which makes it easier to play. So it's a lot cleaner sounding, and has some good transitions. But not much in the circle of fifths!

The chords are in the keys of D, F and Ab. Those who can multiply realize there are 21 chords there, but only space for 15. I swap parts of the sets out so I can hear what they are like. For a while, it was just F and Ab, like the Diatonic Pentad harp. Then it was D and F, which was great because I'm using the standard string schedule, and Ab basically has no bass that way. Another way is to take 4 chords from D, 7 from F and 4 from Ab. The chords I use are rich enough for substituting in most cases. It can also be organized as 5 chords x 3, IM, IIm, IIIm, V7, VIm for D, F and Ab, which is a little limiting, but can do some interesting things.

I arrange the chords in that same pattern as the pentad, roughly:

   
 GM7 A7  Bm7  C#o7     Bbm7  C7  Dm7  Eo7      DbM7  Eb7  Fm7  Go7
   DM7 Em7 F#m7          FM7   Gm7  Am7         AbM7  Bbm7  Cm7
  
   The VIIo7 chords can also be moved to the left of the IM7 
   (I have spare chord bar buttons in both top and bottom positions)
   
   Harmonically, the chords line up like this:
         
       DM --Em --F#m--GM --A7 --Bm --C#o    << D
      / \  /  \ /  \ /  \ /  \ /  \ / \
     Dm--Eo --FM --Gm --Am --BbM--C7 --Dm   << F
      \ /  \ /  \ /  \ /  \ /  \ /  \ /  
       Eb7--Fm --Go --AbM--Bbm--Cm --DbM    << Ab
      /  \ /  \ /  \ /  \ /  \ /  \ /  \  
    D#m--EM --F#7--G#m--A#7--BM --C#m--D#m  << B  key of B, no room for it
    


GM7 A6 BbM7 C7 Dm7 Eo7 DbM7 Eb7
DM7 Em7 FM7 Gm7 Am7 AbM7 Bbm7
These are D chords
These are F chords
These are Ab chords

Here's a video of it with F-Ab


October 2020:
Here's a trick involving drilling little screws on the chord bar ends so as to adjust the felts' distance to the strings. This makes pushing the buttons easier.

You might also want to listen to this cassette of Autoharp stuff I did in 1985 or so:
Une Harpe

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