This is the 4th primary shape of 4-note Generic Shapes (GS)  and is probably more familiar to everyone compared to some of the others. This one has certain quirks and characteristics. I've been reading my own blogs and applying it to my melody making and there is definitely something new emerging even without practising it directly.
This 4GS is basically a scale fragment and can be placed anywhere in any diatonic 7-tone or 8-tone scale. So it could have a number of chromatics applied to an original. Since is is a tetrachord, I'll attempt to outline some chromatic alterations before moving on to working out the Basic Permutations (BP) and the Rotations (R) and Staggered Starts (S). Generally all these are described as tetrachords.
Some examples of 4GSD (1234) from C:
1234—Major tetrachord (CDEF)
12b34—Minor tetrachord (CDEbF)
1b2b34—Phrygian tetrachord (CDbEbF)
1b234—Harmonic tetrachord (CDbEF)
123#4—Lydian tetrachord (CDEF#)
1#23#4—Lydian #2 tetrachord (CD#EF#) (found in Harmonic scales)
12b3#4—Lydian b3 tetrachord (CDEbF#) (found in Harmonic scales)
1b2b3b4—Diminished tetrachord (CDbEbFb[E]) (found in Symmetrical Diminished scales)
12b3b4 Cliche tetrachord (CDEbFb[E])
1b2bb3b4 Cliche tetrachord retrograde (CDbEbb[D]Fb[E])
While all these tetrachords don't appear in every diatonic scale, they may appear in the source scales of Major, Harmonic Minor, Melodic Minor scales and Symmetrical Diminished scales [half-whole]—[whole-half]. NB for more on this refer to An Approach To Jazz Piano chapter 23 where I've outlined where tetrachords are found in these scales—or look it up.
Tetrachords (4GSD) found in the Major Bebop Scale
The Bebop scale is one source of the tetrachords (12b3b4 and 1b2bb3b4).
Here are the 4GSD found in a Major Bebop scale: See Figure 1.
Exploring the diversity of shapes within 4GSD through Basic Permutations (BP), Rotation (R) and staggered starts (S)
Using a simple example: CDEF a Major tetrachord in C Major etc. the first permutation device to be outlined in this series are the BP. See Figure 2.
Basic Permutations of note order in 4GSD using CDEF as an example.
Permutations using Rotations (R) in a 4GSD yields some surprising results visa-vis the variety of GS shapes. Using our example of 1234 in rotation (inversion) R, the result is:
R1 = 1234
R2 = 2348
R3 = 3489
R4 = 489
See Figure 3.
It starts with middle-CDEF (R1) S1 || DEFC[middle-C] R1 S2 || EFC[middle-C]D || FC[middle-C]DE. See Figure 4.
In Figure 5 is an outline of all (in C) 4GSD in BP (1—6), R (1—4) and S (1—4).
BP1-R1-S1 R1-S2 R1-S3 R1-S4 R2-S1 R2-S2 S3 S4
Try playing some of these in a scale tone sequence as exemplified in figure 4. There is a lot here and it is definitely overwhelming so I am going to take a couple of ideas and work with them in tunes.