Another member brought up a good idea about 7th chords built off the scale degrees. So, I guess I'll tackle that as well:
Scale Degree 7th Chords
Once you are able to form 3-note chords on each scale degree, the next step is to form 4-note chords. To be more specific, we're gonna talk about 7th chords. What we're gonna do is add one more note to the 3-note chords we already formed. Let's recap those:
1-3-5 = major 1 chord
2-4-6 = minor 2 chord
3-5-7 = minor 3 chord
4-6-1 = major 4 chord
5-7-2 = major 5 chord
6-1-3 = minor 6 chord
7-2-4 = diminished 7 chord
O.K., now using the same process as we did for those chords, we are gonna form 7th chords off each scale degree. Here's an illustration:
1 (skip 2) 3 (skip 4) 5 (skip 6) 7
2 (skip 3) 4 (skip 5) 6 (skip 7) 1
3 (skip 4) 5 (skip 6) 7 (skip 1) 2
4 (skip 5) 6 (skip 7) 1 (skip 2) 3
5 (skip 6) 7 (skip 1) 2 (skip 3) 4
6 (skip 7) 1 (skip 2) 3 (skip 4) 5
7 (skip 1) 2 (skip 3) 4 (skip 6) 6
Now, I'm gonna put them altogether:
1-3-5-7 = major 7th 1 chord
2-4-6-1 = minor 7th 2 chord
3-5-7-2 = minor 7th 3 chord
4-6-1-3 = major 7th 4 chord
5-7-2-4 = dominant 7th 5 chord
6-1-3-5 = minor 7th 6 chord
7-2-4-6 = half-diminished 7th 7 chord
Notice the chord qualities of each of the 7th chords above. A couple of them are different from the 3-note chord qualities. Take the 5 chord, when the 7th is added it becomes a dominant 7th chord. Then, look at the 7 chord, when the 7th is added it becomes a half-diminished 7th chord.
We still only use the notes of the major scale for these chords as well. So, using the scale degree formula above, here are all the chords in C:
C major scale: C=1 D=2 E=3 F=4 G= 5 A=6 B=7
1-3-5 = C-E-G-B
2-4-6 = D-F-A-C
3-5-7 = E-G-B-D
4-6-1 = F-A-C-E
5-7-2 = G-B-D-F
6-1-3 = A-C-E-G
7-2-4 = B-D-F-A
Again, the notes of these chords can also be altered to form more chords. This marks the end of the basic chords u can play with one hand. Anything larger than that and you will need to use 2 hands to play them, namely your 9ths, 11ths, 13ths, and various altered chords.