I know the major/minor scale and some of the theory behind it (tonics and such) but nothing substantial off the top of my head. I could probably point it out but wouldn't be able to explain what it meant.
I'd be up to drilling some stuff in but I usually stumble upon something like what you said in your last question and wind up completely out of my depth. I wouldn't be opposed to starting from the basics (and I probably need to anyway).
The last question I asked was regarding the use ("function") of the different chords that are available to you in a given key. Common chord progressions are no accident and often come about because they often use chord function in the most natural and obvious ways possible. Having said that, understanding basic chord function is usually good enough, with some practice, to analyse basically any music concerned with major scale harmony, regardless of how difficult it is.
This is something of a copy-paste job but hopefully it's still useful to you.
The first step to understanding this kind of question (assuming you already know the major scale) is figuring out what triads you can get for it. Why triads? Because they are essentially the building blocks of western harmony; certainly, there is great value to chords that aren't triads (or extensions of triads, like seventh chords) but they are far less fundamental to an understanding of how western harmony works.
A triad can be thought simply as any chord consisting of three notes, but usually when we refer to triads we talk about situations where the notes are spaced two letters apart (C E G and not C D E).
C major gives you these notes:
C D E F G A B
Noting the rule above, there are seven triads that you can get from the major scale.
C E G - C major (C to E is a major third, C to G is a perfect fifth -- this makes a major chord)
D F A - D minor (D to F is a minor third, D to A is a perfect fifth -- this makes a minor chord)
E G B - E minor
F A C - F major
G B D - G major
A C E - A minor
B D F - B Diminished (B to D is a minor third, B to F is a tritone -- this makes a diminished chord)
(If you're not familiar with intervals like major third, perfect fifth and tritone, there are a lot of resources on that subject that should catch you up.)
You can do this for any starting note, and the pattern will always come out the same: Major minor minor major major minor diminished. Similarly, if you do this with the (natural) minor scale, you will get minor diminished major minor minor major major.
The most important chords in C major, by idiom and by design, are the chords that fall on C and on G. It is, for everyone's benefit, a good idea to ignore why this is for now as a full answer is quite complex and probably won't do you any good right now anyway. But what is easy to understand is that the relationship between these two chords makes a resolution that is satisfying and easy to hear. You will often find that G goes to C, and that A goes to D, and that E goes to A, and that F# goes to B. In the case of G and C, C is called the
tonic and G the
(primary) dominant. The primary dominant of a given tonic can always be found on the fifth degree of its scale; in other words, a dominant chord is a perfect fifth above (or a perfect fourth below) a given pitch.
As an aside, dominant chords are often played as dominant sevenths (G7 instead of G), not triads. It is therefore advisable, when you're actually playing and hearing these sounds, to go G7 > C, not G > C.
Looking back at C major, we have now identified the function of two of its chords: C major is the tonic chord, and G is the dominant chord. The next most important chord in the key of C is F major. F major is called the
subdominant chord; in terms of resolution it is still appealing to go from F major to C major but it is not as strong as G major to C major. Similarly, F major to G major is a significantly smoother transition than C major to G major. In this way, the subdominant chord can be thought of an intermediate between the tonic and dominant.
If you look at the chord progression of La Bamba, you will notice that it consists entirely of these three chords -- C F G. There are, indeed, a huge number of pieces of music that rely exclusively on this relationship in one form or another. The twelve bar blues, in its most basic form, relies on this relationship.
This is, again, no accident, and it's due to the fact that from the major scale, where 99% of western music gets its harmonic information from, there are only three chord functions: Tonic, subdominant and dominant. The chords on the first, third and sixth note of the major scale are tonic chords. The chords on the second and fourth note of the major scale are subdominant chords. The chords on the fifth and seventh* degree of the major scale are dominant chords.
* - The chord on the seventh degree is complicated and its use relatively challenging.
Back at the C major scale, that gives you this:
C major - Tonic
D minor - Subdominant
E minor - Tonic ("Mediant")
F major - Subdominant
G major/G7 - Dominant
A minor - Tonic ("Submediant")
B diminished - Dominant
These are the basics of chord-scale function. It's quite a bit more difficult to explain what chord-scale function can help you with, but the implications are quite vast: When you are looking to make tension and when to remove it, it is chord-scale function that tells you where tension comes from. Similarly, when you want to substitute a chord for another one or be creative with an arrangement, you can use chord-scale function to inform your decision; in the key of C you can substitute an F major for a D minor easily, but substituting it for an A minor would be a significant alteration.