two quick questions

There are four ways to do it.

ONE
The first one is to just use whatever key the melody's in and use the standard chords for that key (i.e. C, Dm, Em... etc in C)

TWO
The second is to use chords borrowed from the parallel minor and use them as appropriate. So what's appropriate? Well if you're playing in the key of C and the melody is singing a C, you could throw in an Ab. For instance, let's take the I-vi-ii-V "doo-wop" progression and fool around with it. We can substitute the ii for a IV (they're both considered predominant) which gives us I-ii-IV-V. Then we can substitute the V for a bVI.
Let's play that. C-Am-F-Ab.
Sounds a bit strange, even UNPALATABLE, especially when going back to the I. Well, let's smooth things out with the bVII.
Now play one bar each of C, Am and F, then for the last bar play an Ab and a Bb.
Sounds a bit better, huh. Of course, you can just mix and match, which brings us to...

THREE
This way gives you a LOT of freedom, but can sound terrible. Say we had a C in the melody. Over that, we could play any chord containing a C. That includes, Ab, Dbmaj7, F, Fm, D7, hell, ANYTHING. The rule for this one is whatever sounds good works. I've only come across this method in the last few days so correct me if I'm wrong.

FOUR
Use the circle of fifths. This way gives you more structure. Picture the circle of fifths for a second. Find out what key you want to play in (let's say E) and cycle back a few notes on the circle. The song "Hey Joe" is in E, but the verse is C-G-D-A-E. Why? Look at the circle of fifths and see if that seems familiar.

If you're familiar with the song "Tente Outra Vez", which is in A, it uses the progression A-C-G-D-A-C-G-E7 (this is a VERY bad representation of the timing in that song). Same principle. It starts off on A, then the "C-G-D-A" bit is just cycling through to A over the circle of fifths. "C-G" is the chorus, and E7 is reinforcing the key center (A) in our head.
Using this technique, you can cycle through chords like butter.

Any questions or corrections?

Bit of an addition, I was going to go into it before but forgot.

Jazz players use the ii-V-I prgression for two reasons:
1. It follows the circle of fifths.
2. Going from a dominant to the tonic (V to I, vii can also be considered dominant but it sounds like crap to me) is good, but going from a predominant (IV or ii) to a dominant to the tonic is better. You'll find IV-V-I used in a lot of songs (how many times have you seen F-G-C used?).

And ONE more thing...

Another way to add a bit of feeling to a song is to use secondary dominants. What are they? I'll show you.

Let's use the I-vi-ii-V progression in C, so C-Am-Dm-G.

We can use the V of each of these chords to make is sounds different. How do we use them? Let's tuck them in before each chord is played.

C-E7-Am-A7-Dm-D7-G-G7

or in roman numerals

I - V7/vi - vi - V7/ii - ii - V7/V - V - V7

Notice that the V7 can be labelled V7/I. Of course, you don't have to play 7th chords, you can just use the normal major ones. It's a different sound and you might not find it to your liking, but it's something to add to your toolbox.

The Beatles used it to great effect. They even used progressions like this:

A (x2) - D - B7 - A

or in other words

[pre]
| I   |     | IV  | V/V |
| I   |
[/pre]

Here's hoping the whole thing raises less questions than it answers.

Um, Chris, I think this would go more smoothly if you realised that chords are numbered with Roman numerals, capital for major chords and lower case for minor or diminished chords:

I    
ii
iii
IV
V
vi
viidim

While notes are numbered with Arabic numerals, i.e.

1_2_34_5_6_78

OK, the I chord (C major) is constructed with 1-3-5, the ii chord (Dm) 2-4-6 and so on up to the vii chord (Bdim) which is 7-9-11.

When we number notes into the second octave:

9 is the same note as 2.
11 is the same note as 4.
13 is the same note as 6.

Occasionally (rarely), the 3 is called a 10.

I hope this helps.

OK, you've got me interested... when would a 3 be called a 10?

OK, you've got me interested... when would a 3 be called a 10?

I've only seen it occasionally.

First, when people want to emphasise that the 3rd is played in the second octave.   This is often done on the bass to give a cleaner sound.

Second, when there is both a minor and a major 3rd involved, one or the other is generally played an octave higher.

Ahhh... kind of like an inversion of a #9 chord then, or am I way off the mark?

I've got a book of Lennon's solo stuff in Piano Vocal Guitar format.  One of the chords listed there is an A7-10.  

I always thought it looked peculiar as a chord notation, but I think that's what Helgi's mentioned.

They're usually just called 10ths when you're referring to an interval rather than a chord.  Helgi is right, it signifies either the third an octave higher (hence a tenth interval), or a chord using two thirds... but the notation for that gets pretty tricky fast.  I think most composers and copyists would prefer to treat the 10th as a double-flatted 11th.  That makes the accidentals clearer to read.

Inverting a #9 gets you a diminished 7th:

C-D# becomes
D#-C

The rule on inversions is pretty simple where number is concerned: simple intervals (less than an octave) and their inversions must add up to 9; compound intervals (more than an octave) must add up to 16.  For simple intervals:

2nds invert to 7ths
3rds invert to 6ths
4ths invert to 5ths

and vice-versa

For compound intervals:

9ths invert to 7ths
10ths invert to 6ths - although intervals of 10ths and larger are usually reduced by an octave before they're inverted (and often, in theory books, before they're even named!)

Tom

The two bass lines in "Take a Walk on the Wild Side" (Lou Reed) have two basses alternating between the root and the 3rd of the E and A.  However, if you want to play it on one bass, the best way is to play the root on the E-string and the 3rd an octave up on the G-string.

G-13---6---/13
D-----------------
A-----------------
E-12---5---/12

In that case, I always call it the 10th, to make clear that it's an octave up, though its "meaning" is the 3rd. I think David teaches somewhere that if you have a 9th or 11th chord, it implies that the 7th is included.

I have no idea whether this pertains to the topic at hand.  I'll go back with the other bottom-feeders. ;D

-Laz