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.
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#
D D#
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
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
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
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
Like F Maj and F7
Like C Maj
Like C sus
Not like anything;
The opposite of F7
Rootless F9
(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 tones 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 was to have 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. 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 Dmi9 E09 Ab+ Absus
Lock FM9 Gm9 Am9 DbM9 Eb9 Fmi9
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).

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).
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Henry Lowengard, jhhl-at-panix.com /324 Wall St., Apt. 5/ Kingston NY 12401/

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