I'd first off like to thank everyone for the helpful reviews on Part 1. It got good acclaim, though some said it didn't go in depth enough. Well, I've finally gotten the time to throw another article together, and I hope this one will help just as much as the last; perhaps even more. Okay, now let's get down to business!
Intervals
Though I explained intervals in Part 1, there is actually much more to them than that. I said that thirds, fourths, fifths, and octaves were the most common intervals to use while harmonizing. Silly me, I forgot that the sixth was the second-most common of all-time, right along with the third! A major sixth is 9 semitones above the root, and a minor sixth is 8. Of the two, the major sixth is used more often. Not sure how exactly to use these intervals? Read on.
How To Utilize Intervals
There is a "rule", so to speak, that was used very prominently in classical music and still holds true today. It states that, when harmonizing, never to use more than three notes in a row that are the same interval apart. For instance, if you're harmonizing in minor thirds, don't put more than three minor thirds above the melody in a row. The rule goes on to say that you should experiment with octaves, sixths, fifths, fourths, whatever. Too much of the same interval in harmonizing gives off the impression that it's not going anywhere, whereas using different intervals within a harmony can give quite a good sense of counterpoint. Not familiar with the term? Don't worry, I've got you covered.
Counterpoint
According to wikipedia, "Counterpoint is a musical technique involving the simultaneous sounding of separate musical lines." Now, let's expand on that a bit more.
What counterpoint basically states is that you are harmonizing in more than one interval. Which means that whatever harmony you are creating can move upwards or downwards in any fashion while still keeping the same key against the original melody. Johann Sebastian Bach is the undisputed master of contrapuntal movement, and it is evident in many of his works. Take the Bourree, for example:
e|--0--2----|---3----2--0--------0--2--|-------------------------|
B|----------|---------------4----------|--0----2--4--5----3--1---|
G|----------|--------------------------|-------------------------|
D|----------|--------------------------|-------------------------|
A|----------|--------0------2----0-----|-------------------------|
E|--3--2----|---0----------------------|--3----2-----0----2------|
e|----------------------|--------------------------|
B|-0--------------------|-0------------------------|
G|------2--0-------0--2-|----2--0------------------|
D|------------4---------|-----------4--2-----------|
A|------0-----2----0----|-------2------------------|
E|-3--------------------|-3------------0-----------|
Judging just by those first 5 measures, we can already tell that great counterpoint is happening. There is a melody on top, which is good, but look at the lower notes. If you can play that (it's a bit tough, I know), you should be able to hear the magnificent counterpoint going on within the two sets of notes. Bach really was the musical genius behind counterpoint.
Okay, I'll bet you're thinking to yourself, "How can I get my harmony to sound like that?" I know how you feel. Be patient, darlings, it's coming.
How To Harmonize
Writing a harmony is based a lot off of experimentation and trial-and-error, but I know you don't want to read this article to hear that crap. In fact, before you can experiment at all, you must know which notes will sound good against the original melody beforehand, otherwise you'll probably end up with a bad-sounding or just plain wrong harmony. The best way to find which notes will work well in a harmony is to find out which notes are the key you're in. For example:
In the Key of C major
Play your basic open C chord:
|0---|
|1---|
|0---|
|2---|
|3---|
|X---|
The C on the 3rd fret of the A string is your root note. Now, if we wanted to start harmonizing on, say, a major third up, we must identify which note is a major third above the C. In this case, it's E, which is located on the 2nd fret of the D string. Now that we've identified that, how do we start harmonizing? Simple; just know your C major scale. Let's use this 2-octave version, for example:
|----------------------3-5-7-8-|
|----------------3-5-6---------|
|----------2-4-5---------------|
|----2-3-5---------------------|
|3-5---------------------------|
|------------------------------|
That is your basic C major scale (it's also your A minor scale, and I'll cover that in this article, too). Knowing that those are the notes you can use in your scale, you already know all the notes you can use to harmonize! Yes, you can play any two or more of those notes together in any order, and no matter what it'll sound good. This will work with any scale; I can guarantee it.
Majors And Relative Minors
Take note that I said above that a C major scale is also an A minor scale. This is because A minor is the relative minor of C major, meaning that the notes of both scales are exactly the same, only you start on different root notes. To find the relative minor of a certain key, take the major sixth of the root of the key/scale, and that's your relative minor. The major sixth of a C is an A, so that's why it's your relative minor. C major obviously starts on C while A minor starts on an A; but the notes within are exactly the same. Why is this important? Because if you're in, say, C major, for example, and you wanted a bridge or interlude or something, you could very well put it in A minor. This is good to know in harmonizing because if you know one scale, you already know the relative minor's scale, and you can make a harmony in a minor key, too, depending on which notes you are emphasizing more. To help you out, here's a list of all the majors and their relative minors:
C major - A minor
C#/Db major - A#/Bb minor
D major - B minor
D#/Eb major - C minor
E major - C#/Db minor
F major - D minor
F#/Gb major - D#/Eb minor
G major - E minor
G#/Ab major - F minor
A major - F#/Gb minor
A#/Bb major - G minor
B major - G#/Ab minor
Knowing those keys and which notes are in them, you can easily -- and I stress easily -- harmonize. Once you know the notes of the scales, all it takes is expermimentation and you'll have a brilliant harmony in no time.
I hope this goes more in depth than Part 1. Some people were saying it was too simple, so I hope I got more explained, while still being as clear as possible.
Enjoy!
/ my profile 
already do a lot of harmonizing, but it was still interesting to read
can anyone help?