This is something that I wrote some time ago that I keep on hand as a FAQ when people ask about how chords work. This explanation of harmony really depends on your understanding the major scale and how it works. If you don't drop me a line and I'll take a stab at that.
Given that the major scale is the thing that sounds like "Do re mi fa sol la ti (do)", let us change each of those syllables to the numbers "1 2 3 4 5 6 7 (8)." In the following model of how chords are built, each number represents the corresponding scale degree above. So... "4" would mean the fourth degree of the major scale, "fa." #4 means that the fourth scale degree is raised by a half step, or one fret, and b4 means it is lowered by 1/2 step.
The simplest thing that is treated as a chord (in common practice, not in theory) is the "power chord" or "Five" chord. Compared to a major scale, it is:
R - 5 ...(Root - fifth or Do - sol...get the idea?)
Next comes the most common form of harmony, tertiary. It consists of chords built as stacked thirds. In other words, start at someplace in the scale and select every other note. The simplest of these are triads. They are, compared to a major scale:
Major R - 3 - 5 ex: G
Minor R -b3 - 5 ex: Gmi or G-
diminished R -b3 -b5 ex: Go (pretend "o" is a degree symbol)
augmented R -#3 -#5 ex G+
Aside from suspensions, those are all of the triads.
Next come seventh chords. Those are produced simply by adding and altering "7." As a rule, unless the word "major" appears in the name of the chord, the seventh will be flatted. There are a lot more possible combinations with seventh chords, for example:
Major 7 R - 3 - 5 - 7 ex: Gma7
minor 7 R -b3 - 5 -b7 ex : Gmi7
Dominant 7 R - 3 - 5 -b7 ex : G7
half diminished R -b3 -b5 -b7 ex : Gmi7(b5)
diminished 7 R -b3 -b5 -bb7 ex : Go7
Augmented 7 R - 3 - #5 - b7 ex G+7
major 6 R - 3 - 5 - 6
minor 6 R -b3 - 5 - 6 (note NOT b6)
get the idea? There are lots more. In case you were wondering about chords with higher numbers, it continues on in the same way. If you were to put two octaves of a major scale together, you would have
1 2 3 4 5 6 7 8 9 10 11 12 13 14 (15).
So any sort of 9th chord is some type of 1 3 5 7 9, any type of 11th chord is 1 3 5 7 9 11, and any type of 13th chord is some type of 1 3 5 7 9 11 13. It doesn't go any farther. When you get to 15, you have started over.
It is always assumed that these extended notes are as they would be in a major scale whose root is the root of the chord. If they are to be altered, they must be addressed individually. For example, a Dominant9 with a sharped 11 and a flat 13 would be notated G9 (#11 b13).
Now it is usually not possible to play all of the notes of some of these chords. Many notes are optional. Those that are not are the third, the seventh, and the highest extension. The root is kind of important, too, but less so... and usually the bass player will play that.
That's tertiary harmony in a nutshell. Something else that some people experiment with is "quartal," or stacked fourths, "quintal," or stacked fifths, etc... I, myself, am unaware of any treatises on discerning between qualities of these kinds of chords, and if anyone knows if anything has been made up in this area or how different kinds of these harmonies are notated (I've seen Q3 to represent a quartal triad, Q4 to represent four stacked fourths, etc) I'd really apreciate hearing about it.
- Tim Fullerton.