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A major chord (CD7) |
A minor chord (Cm7) |
A dominant chord (C7) |
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Let's have a look at the chords on the clock.

The root note, C, is shown in black. Both the major and minor chord forms are symmetric around a line but the C7 is not. However, if we add the note just above the root (the b9), we can form a square that has a corner one hour after the root. The b9 is often played on dominant chords, so including it for the sake of creating symmetry isn't as far-fetched as it might appear at first. Chords in other keys than C can be constructed by rotating the shapes on the clock. For example, if you want to find out which notes are in a Ebmin7, you add three hours to the four notes in Cmin7.
It is rare that you will hear chords played in the basic form demonstrated above. Rather, they will be inverted and decorated. Inversion of a chord means that some of its notes are transposed up an octave. For example, the 1-5-7-3 voicing (the third up an octave) is used a lot. Decoration means that extra notes are added to the chord in order to make it sound more interesting. Since this is an extension of the basic chord, which is made up of the 1st, 3rd, 5th, and 7th, it is notated by numbers greater than 7, so 9 is used instead of 2, 11 (or sus, short for suspended) instead of 4, and 13 instead of 6. Here are some of my favourite decorated chords.
A major chord (CD9), voicing 1-9-5-7
A minor chord (Cm9), voicing 1-b3-b7-9
A dominant chord (C13), voicing 1-b7-3-13
Notation of extended chords is tricky to explain in a single paragraph, even in crash course style, and since its entertainment value is close to zero I will quitely skip the subject. Suffice to say that there are several ways to write the same chord, and that the system is not entirely consistent. It takes a little getting used to.
Consider the very common voicing, 1-b7-b3-5, of a minor 7th chord in the key of G. On the 6-string in conventional tuning, there are two ways to play this voicing. Either you anchor the chord at the 3rd fret on the 6th string, or at the 10th fret on the 5th string. The two positions are obviously quite far apart, seven frets, so in a given situation the nearest Gm7, voiced as 1-b7-b3-5, isn't necessarily that near at all. The fingerings are also different in the two positions, so you will essentially have to learn two Gm7 chords. On the M3, on the other hand, the symmetry dictates that patterns repeat every four frets. The desired Gm7 voicing can be anchored at the 3rd fret on the 7th string, or at the 7th fret on the 5th string (and, of course, the next one up is at the 11th fret on the 6th string). Not only are the 'good' positions closer than on the 6-string in conventional tuning, the fingerings are also the same everywhere. You only have to learn a certain chord once.

