Major Thirds Tuning Guitar Pattern Question Part 2

I want to thank the few people who answered my last question here that I posted yesterday (Turns out the answer was 192!). There are a few more restrictions I would like to implement right now when it comes to finding possible coordinate combinations. I could've edited my last question to add a few more restrictions but that would change the answer. Sorry about this, now for sure this will be the last time I ask such questions lol. Here below this line is my original post.

  Frets (1-4)
. . . .
. . . .
. . . .
. . . .


Hey everybody. The four dots above are the four frets (vertical) and four strings (horizontal) of the imaginary guitar (sorry I'm not good at giving visual help). Here I'm wondering how many possible chord shapes I can possibly make within the range of 4 strings and four frets using four (always four) coordinates at a time. Here are the examples I'm looking for

        . . x .               x . . .
. . x .               . x . .
x . . .               . . x .
. x . .               . . . x


The x's represent where I'm fretting on the fingerboard. Now here are the restrictions (examples I don't want counted)

      . . X X                   x . . .
. . X .                   . x x .
. . . X                   . x . .
. X . .                   . . . .


If there are two or more X's within the same string then it doesn't work due simply to the nature of the instrument. The second example is missing one string fretted so that's a no-no also in my book (I'm looking for all 4 strings to be fretted). One more restriction!

                    X . . .        . X . .
. X . .        X . . .
. . . X        . . . X
X . . .        . X . .


This also I can't allow to be counted as well since the Bottom and Top String is fretted at the same fret. This is just a specific rule though thanks to the nature of my guitar tuning (just the Bottom and Top String). I don't want to count chord shapes that contain repeating notes. So there you have it! Hopefully a Math Wizard would find out how many possible 4 note shapes I can form with these restrictions put in place.

Now the original post ends. The answer was 192 given the restrictions I placed so far. But now things are going to get tougher. We're still keeping in mind of the original restrictions placed in the original post now we're just adding new ones. Take a look at these

  X . . .         . X . .         . . X .     . X . .
X . . .         . . . X         X . . .     . X . .
. . X .         . X . .         X . . .     . X . .
. . X .         . . . X         X . . .     . . . X


These chords have notes that are exclusive to frets 1 and 3. And chords that have notes only in frets 2 and 4. All of these kinds of chords are to be eliminated since they serve the same function in terms of general sound, thus making it redundant to actually try to memorize these kinds of shapes. In other words chords that have notes exclusively in fret pairings of 1 & 3 and 2 & 4 are restricted and not allowed.

For the final restriction (something I probably should've also accounted for in the original post) is this

X . . .                  . X . .                . . X .
X . . .                  . X . .                . . X .
. X . .                  . . X .                . . . X
. X . .                  . . X .                . . . X


One of these chords (you pick!) is alright and therefore be counted in list of possible chord shapes to memorize. However the two chords that you didn't pick should not be counted since they are basically the same shape (sound) transposed in a different place. Here's another example:

              X . . .                  . X . .
. X . .                  . . X .
. X . .                  . . X .
. . X .                  . . . X


Again I pick one, but the other has to go. You get the picture. One more example:

                           X . . .      . . . X
X . . .      . . X .
. . X .      . X . .
. . . X      X . . .


These chords above are safe from this restriction. I count these in the list of possible chord shapes to remember and a unique property these chords has is that since these chord covers 4 frets apart it is safe from this last restriction since the whole shape can't move anymore.

And that's pretty much it. Since the Chord Possibilities in the original post is 192, these new chord restrictions should reduce it to an even lower number. Maybe you can help me figure this out! I would very gladly appreciate it

P.S I recommend looking at this problem at a laptop or computer because looking at this from a phone just makes it look weird (Patterns get jumbled up)

Part Three: Guitar Patterns Major Third Tuning Part 3

• Using a Maple program, I get a count of $130$. – quasi Oct 11 '17 at 4:57
• I think you might be right. So far I've written 112 chord shapes and its getting pretty difficult to find the rest. Thanks though! – pizzaking Oct 11 '17 at 21:02