I found an old word doc and knocked up this first draft, but it's pretty much illegible at the moment. It will be a permanent document a bit like this once I've discovered if people prefer diagrams or numbers such as 0202. The problem with the pictures is formatting the way they combine with text.

Stringy will recognise the shapes if he plays them on his guitar.

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The following all looks infinitely more complicated than it actually is. You can learn it by playing each chord in sequence and realising that you are only chanign one note at a time and they all follow a pattern.

I'm going to assume a soprano or concert or tenor uke tuned to GCEA

Google CAGED for guitar and you'll find lots of stuff about how guitar chords have 5 shapes.

If you transpose each up a perfect fourth for uke yoyu get FDCAG, of cycled around, CAGFD so that it looks a bit like CAGED.

But CAGED has 5 shapes becuase guitars have 5 unique strings (it has two E strings).

The uke only has four strings and doesn't need the D shape (the guitar's A shape) because the uke doesn't have the D string that would take the place of the guitar's A string. The uke only needs the CAGF shapes. We can call it CAGE, since the F shape is based on the E string.

You'll often see 2020 listed as D7 (aka the Hawaiian D7). It's not D7, it's the notes ACF#A which can be substitued for D7, but lacks the note D (the guitar shape 02020 would be A7), so it's not D7. Thus the D shape doesn't exist on the uke.

In the 4-shape system notice that each shape has a string that always and only supplies the tonic (marked beneath it as 1), a string that only supplies the mediant (3, major or minor), a string that only supplies the dominant (marked as 5), which can be augmented if need be, and one that provides all the variations that define the chord. If you loook at jazz chord progressions, you'll mostly find they change one note at a time, and that is usefully reflected in this system, wehre that work is done onf hte fourth string (the one that's not 1,3 or 5)

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The C shape: -

This is called the C-shape because the C string supplies the tonic, and we play C as 0003

The specific chord above is variations on the D chord (2225), but it is known as the C shape.

The systemic D7 shape is 2223, C7 moved a tone, or 2 frets, upwards, as opposed to the Hawaiian D7 above.

We draw the D chord as the C shape to demonstrate how we play C minor by flattening the E string.

This is a bit easier than demonstrating with the C# chord.

The way to get a feel for what these pictures mean is to play C# (1114) then C#M7 (1113) then C#7 (1112) then C#6 (1111) then C#m (1104), C#mM7 (1103), C#m7 (1102), C#m6 (1101).

(1104 is probably not the usual way to play C#m: that would, according to taste, be 1444, which is a variant of the A-minor shape below. I chose C# because the E string can’t be flattened.)

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The A-shape: -

 (because the A chord is played 2100, and the tonic is the A string) is treated the same way:

Play Bb (3211), BbM7 (2211), Bb7 (1211), Bb6 (0211), Bbm (3111), BbmM7 (2111), Bbm7 (1111), Bbm6 (0111). Here we can’t flatten the G-string for A6, so I chose Bb as an illustration.

It’s very useful to know that, as well as 0003, you can play C as 5433, using the A-shape.

One of the results of CAGE is that to play any chord, you can cycle through the 5 shapes in that order C, A, G, E up the fretboard. 

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The G shape: -

Play G (0232), GM7 (0222), G7 (0212), G6 (0202), Gm (0231), GmM7 (0221), Gm7 (0211), Gm6 (0201).

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We normally play the chord of F as 2010, but the basis for the F shape is the F7 chord 2313

FM7 is (2413), F7 (2313, although 2310 is possible) F6 (2213), FmM7 (1413 ignorable), Fm7 (1313), Fm6 1213).

These shapes are just shifted up the fretboard to produce new chords.

Yes, there are other ways to play most of these chords, but the point is that they are not systematic. And if you want to play jazz progressions (which typically tend to change one note at a time), then using non-systematic chords will be a nightmare.

Note that the notes of G6 are the same as the notes of Em7: GBDE. Also the shapes are the same on the uke. G6 is 0202, and Em7 is one fret down from Fm7, also giving 0202. The same goes for C6 and Am7 (CEGA) – both are played 0000, and you can see the equivalence of the C6 and Am7 shapes above. What varies is which string supplies the tonic.

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We can use the above shapes for all of the extended chords:

C9 is an extension of C7. The notes are CEGBbD.

We must drop one of these notes, as there are only 4 strings available. We usually drop the tonic and play EGBbD. These are exactly the same notes as Gm6 and the shape we use is 0201, the Gm6 shape. Note that also this comes from playing C7 0001 and then playing fret 2 of string 3, changing the note from C to D.

CM9 is CEGBD, for which we play G6 (0202, note that string 1 is now supplying 7 instead of b7)

Cm9 is CEbGBbD, for which we would play EbM7, but we can’t flatten string 2, so we illustrate by using a transposed example: for Dm9 we play FM7 (2413) (and we can also think about it thus: Dm is 2210, Dm7 is 2213, Dm9 is 2413 by dint of raising string 3 from fret 2 to fret 4, D to E).

C11 is obtained not only by raising the C to D but also by raising the E to F (so here we needn’t worry about major and minor variants any more). CEGBbDF then becomes GBbDF, Gm7.

C13 is the above but in addition we raise the G to A, i.e. CEGBbDFA becomes BbDFA or BbM7.

So, to recap, in sequence, play C7 (0001), C9 (0201), C11 (0211), C13 (2211). Singing a C while playing these might help with the musical context.

You can work out the rest!