If you pick every second note from a diatonic scale, there will be an interval of a third between each adjacent note.
In the following I will use examples from the C scale exclusively, for the sake of simplicity. It's all adaptable to any other scale, of course.
Example of a scale of a ladder of thirds: C E G B D F A C E G... etc.
Note that the thirds will vary between major and minor thirds. Any consecutive 3 notes will form a triad, either a major, a minor or a diminished chord. In this span of about 2 octaves, there will be 3 major, 3 minor and 1 diminished chord. Any 4 consecutive notes will form a tetrad, that is with the extra major or minor 7th on top.
The regular Richter tuning have parts which use this phenomenon. That's why chords such as C major, G major, d minor are available. The Paddy Richter tuning offers a-minor as well.
Here's a suggestion of a tuning, that I'm sure that many have thought of or even implemented.
As you can see, the first six holes are unaltered, as they offer good chord possibilities. Blow 4 to 6 and draw 2 to 6 are third ladders. Holes 7 to 10 are reversed between blow and draw, except that the new draw 10 is B instead of C. This way we have third ladders all the way from blow 4 to 10 and from draw 2 to 10.
As mentioned, ANY adjacent 3 or 4 holes will form a chord as in this table:
The letters represent the chord formed from a blow or draw in the corresponding hole and the next 2 or 3 to the right.
- C, G, F are major chords
- am, dm, em are minor chords
- B with a circle is a diminished chord, that is with a minor third and a diminished 5th
- M7 is a chord with a major 7th
- 7 is a chord with a minor 7th
- B with a ø7 is a "half-diminished" chord with a diminished 5th and a minor 7th
As an extra bonus there is no reversal of breath, and you can bend all draws. (Well, still not much on holes 5 and 7)
You can play all your regular melodies (unless you need the high C), and you can of course retune the blow 3 to a Paddy Richter A, extending the ladder of thirds, but the 3 bottom blow chords will be a-minor rather than C-major.
Haven't had one made yet, but I'll test it soon from an old harp.