If the sound of the music is in the key of Eb and I want to play using chord shapes in the key of C, what fret do I put the capo on?
This depends upon what you mean by "music is in the key of…" and "I want to play it in the key of…".
If you mean that you want to play chords written in the key of C and have them sound in the key of Eb, put the capo on fret 3. Eb is three semitones higher than C (C-C#-D-Eb). (This seems likely.)
If you want to play chords written in the key of Eb and have them sound in the key of C, put the capo on fret 9. C is nine semitones higher than Eb (Eb-E-F-F#-G-G#-A-Bb-B-C). (This seems less likely.)
(Reading between the lines, I'm guessing that you actually want to change chords written in Eb, to be played in C, but still sounding in Eb - in which case, there is more about this in the third and fifth bullet points below.)
Each fret on a guitar is a semitone higher than the one below it (or one semitone higher than the open string, for fret 1). To find out where to position a capo for any particular transposition, work out how many semitones higher the key you want the music to sound in is from the key you want to play chords written in.
Here's an example: suppose you are playing chords in D Major, but you want the music to sound in B Major; you have to go up nine frets and so place the capo at fret 9 (D-D#-E-F-F#-G-G#-A-A#-B).
A few things to note:
The reason these two approaches are needed when using a capo (counting up and counting down), is because there are two main reasons for transposing using a capo:
Although your question is a little ambiguous, I'm guessing that you want to play music written in Eb, using chords in C, but keeping the music sounding in Eb. So, you put the capo on fret 3 and rewrite all your chords three semitones lower. However, just giving you this answer won't help you understand how to work out where to put a capo should you need to work out a different transposition, so what follows is a description of how to work out which fret to place a capo on for any particular transposition.
There are three things to consider when using a capo to transpose guitar music: the key the original music is written in; the key you want to play chords in; the key you want the music to sound in.
Usually you will only need to consider two of these, for instance: 1. using a capo to play written chords so that they sound at a different pitch; 2. using a capo to play chords in an easier, different key to the original music, but staying at the same pitch as the original music. However, it is possible to change both the chords played and the sounding pitch of the original music.
As I say, these are the most likely ways to use a capo. You could, though, change the chords played and the sounding pitch from the original key. This is a little more complicated. Firstly, count down by semitones from your original, written key to the key you want to play in and rewrite all chords this number of semitones lower; secondly, count up by semitones from the key you want to play in to the key you want the music to sound in and place the capo at this fret.
Here's an example: the music is written in Eb, you want to play in A and have the music sound in F. Firstly, count down from Eb to A, that's six semitones, rewrite all chords six semitones lower. Secondly, count up from A to F, that's eight semitones, so place the capo on fret 8. Voila, chords originally written in Eb, played in A, sounding in F…
Finally, a couple of things to note:
I only mention transposing chords here, to transpose single notes you wouldn't usually need a capo, instead you would simply move up or down the required number of frets.
Here is the list of chromatic pitches, to help you count up or down by semitones (notes between natural notes are listed with both their flat and sharp names):
C - C#/Db - D - D#/Eb - E - F - F#/Gb - G - G#/Ab - A - A#/Bb - B - C
If you need to count "further" than the beginning or end of the sequence, you simply continue counting from the opposite end.
E♭ is three semitones above C. So you should put the capo on the third fret.
Some of the other answers are quite thorough, but it is really a simple answer!
Simple, completely effective answer:
For Eb, don't use a capo. Rather, lower the tuning of each string. Re-tune the strings, low to high, Eb, Ab, Db, Gb, Bb, Eb. Then play the regular chord shapes that you already know.
I think the other answers are good, but wanted to condense the most important bit into one answer. You just have to count the semitones.
Here are all the notes, and the number of semitones they are away from A.
0 1 2 3 4 5 6 7 8 9 10 11 12 A A# B C C# D D# E F F# G G# A A Bb B C Db D Eb E F Gb G Ab A
D is five semitones up from A -- so if you want to play an A shape and have it sound like a D, put a capo on the 5th fret.
Eb is three semitones up from C -- so if you want to play a C shape and have it sound like an Eb, put a capo on the 3rd fret.
This formula works for any pair of keys. Note that to play an A shape and get a G sound, you have to capo the 10th fret, which turns your guitar into a soprano instrument with a very short fretboard. It can sound nice, but may not be what you want -- in which case you have to choose a different set of chord shapes, or tune down (see below)
You can do the same thing at the instrument by making the chord shape and shifting it up.
A capo can only shift the tuning up, not down. If you want to go down, you can change the tuning on your guitar. For example, to play E shapes and hear Eb shapes, just tune every string down by one semitone.
Doing this will reduce the tension of your strings. Playing will feel different. The timbre of the guitar will change. Intonation might be affected. Lower than 2 semitones down and these effects become quite pronounced. Keep going lower and the guitar will become unplayable -- of course there will come the point where the strings are completely slack.
I think I know exactly what you mean, so I will just give a simple answer in case you are confused by the others (but I highly recommend studying them, anyway).
The answer is to place the capo over the 3rd fret. This makes your "C Chord shape" (what you would play to get a C chord should there be no capo at all) be an Eb chord. Thus, you can easily access the key of Eb now.