Now that we have the diatonic scale. We're going to be looking at the modes of the scales, and how the modes are constructed.
 
        There are seven modes in total: ionian, dorian, phrygian, lydian, mixolydian, aeolian, and locrian. The ionian is just another name for the major scale, and aeolian is just the natural minor scale. Each mode is composed of two tetrachords combined by either a halfstep, or wholestep. We're going to look at the modes in two different ways. In one, we'll use C as the starting pitch for each mode, so you can see each mode differs, and in the other, use the key of C major (no sharps or flats) to show how the modes relate to each other. We'll start off with key of C major.
 
        C D E F G A B C
 
        The first tetrachord is going to be C D E F, and the second will be G A B C. The intervals of the first tetrachord are WWH. A wholestep between C and D (W), a wholestep between D and E, and a halfstep between E and F (H). So, it's two wholesteps, and a halfstep, WWH. This is a major tetrachord (M). Now, let's look at the next tetrachord, G A B C. It's the same thing. A wholestep between G and A, a wholestep between A and B, and a halfstep between B and C, WWH. So, now we have two tetrachords WWH and WWH, but there's an interval missing: the F to G. There's a wholestep between the two that connects the two tetrachords. When we put those together, we have WWH-W-WWH. The ionian mode is made of two major tetrachords with a wholestep in between them.
 
        The next mode, dorian, is two minor tetrachords (m) with a wholestep in between. Dorian used to be the typical minor key, but eventually aeolian became the minro. A minor tetrachord is WHW, instead of WWH. A dorian mode would look like this: WHW-W-WHW. If we want to stay in the key of no sharps or flats, we'll need to start the mode on D (D E F G A B C D). D up a wholestep is E. E up a halfstep is F, and F up a wholestep is G (WHW). The next tetrachord is A B C D. A to B is another wholestep. B to C is a halfstep, and C to D is a wholestep (WHW). The connecting interval is from G to A, which is a wholestep.
 
        The next mode starts on E, and is the phrygian mode. The phrygian is made of two phrygian tetrachords (ph) and a wholestep connecting the two. A phrygian tetrachord is HWW, so the mode would look like this HWW-W-HWW. E to F is a halfstep, F to G is a wholestep, G and G to A is a wholetep (HWW). B to C is a halfstep, C to D is a wholestep, and D to E is a wholestep, with the connecting interval from A to B being a wholestep.
 
So far, we have three different modes, and three different kinds of tetrachords:
 
M+M=ionian
 
m+m=dorian
 
ph+ph=phrygian
 
        Moving onto lydian. Lydian is made of a wholetone tetrachord (Wt), and major tetrachord with a halfstep connecting the two instead of a wholestep like the previous modes. A wholetone tetrachord is made of three wholesteps (WWW). Lydian is going to start on F. F to G is a wholestep, G to A is a wholestep, and A to B is a wholestep. The next tetrachord is major, and starts on C. C to D is a wholestep, D to E is A wholestep, and E to F is a halfstep. The connecting interval between B and C is a halfstep, so the mode would look like this, WWW-H-WWH.
 
        Mixolydian is the next mode, and it's made of a major, and a minor tetrachord, with a wholestep connecting the two (WWH-W-WHW). This mode will start on G. G to A is a wholestep, A to B is a wholestep, and B to C is a halfstep. The connecting interval being C to D is a wholestep, leads us to the next tetrachord. D up a wholestep is E, which up a halfstep is F, and up a wholestep is back to G.
 
        The last mode we'll learn about is the aeolian, which is commonly known as the natural minor scale. The aeolian mode is made of a minor tetrachord and a phrygian tetrachord, with a wholestep connecting the two (WHW-W-HWW). This one will start on A. A to B is a wholestep, B to C is a halfstep, and C to D is a wholestep. E to F is a halfstep, F to G is a wholestep, and G to A is a wholestep, with the wholestep from D to E being the connecting interval.
 
So, to review the modes and tetrachords:
WWH=Major
WHW=minor
HWW=phrygian
WWW=Wholetone
 
M+M=ionian
m+m=dorian
ph+ph=phrygian
Wt+M=lydian
M+m=mixolydian
m+ph=aeolian.
 
We aren't going to do locrian, because it's never used, but if you want to figure it out yourself, go for it.