Chord Families

Diminished and augmented chords would fit into the dominant family if there were such a thing.  That is their function.

do you mean dominant as in chord V, or like b7?

if you mean V then that would be a major/minor and not a family of its own, and the b7 would just be a major/minor chord with a b7, i suppose it has a function but its still a major/minor chord enhanced for a dominant function.

there are tons of different chord types besides major and minor..

yeah including augmented, diminished etc etc, chromatic chords, like Augmented 6th's, Neapolitan's, then you have suspended chords etc.

If you want to set your mind on putting chords into buckets, the simplest way is just two categories:

1. Chords that can stay put
2. Chords that need to move

The chords that need to move, like dominant chords, have a tension to them; chords that can stay put, like major chords, can end a progression without having any tension left over to resolve.

Moving a little further, the chords that can stay put fall into two buckets:

1. Major chords
2. Minor chords

and the chords that need to resolve to something else group into:

1. Dominant chords (7ths, 9ths, 11ths, 13ths)
2. Everything else (dim, aug, altered dominants)

That's in traditional harmony, of course, where everything is built on thirds.  There are other types of harmonization, like quartal harmony, that need their own sets of buckets :)

If you really want to strip everything down and keep it simple there are only two types of chords: major and minor. Major is anything with a natural third (3) in it such as major, major7, dominant, augmented, and minor has a minor third (b3): minor, minor7, diminished, diminished 7th, minor-major (1,b3,5,7). Of course, you can go into much more detail if you want.

Yes, chords can be broken into as few as two groups (as I did above - chords that can stay put / chords that want to move), but I have to disagree with Major / minor as a useful pair of categories.  There are a few reasons it's not helpful to identify chords just by the third:

1. It gives you no information what to do with the chords.  At least the stay put / move combination addresses tension and release.
2. There are a fair number of chords that don't have thirds: suspended chords and power chords spring immediately to mind.
3. The Major / minor categories group VERY dissimilar sounds together - Am in the same group as Aº7?  G in the same group as G7+11?  The Am and G are very simple sounds, so why put them with complex structures based on a single interval?

I think the Tension-release group makes some sense too, but they won't be the same in all cases. For example, an A major chord. If this chord is used in the key of D, it will want to move back to the D chord, but if you're playing in A, it will sound resolved.

With the major-minor grouping, every chord you can think of will have either a major or minor third, whether it is actually played or not. Sus and power chords will be either major or minor depending on the progression/key they are played in. (Dsus2 in G = major;  Dsus2 in C = minor).

Some of the chords will sound very different, but in general the minor chords will be more dissonant than the major, unless you use some strange alterations or extensions.

Now you're talking about the context of a progression, which makes things much more difficult to categorize.

Play an A chord, all by itself.  It's satisfied -- it doesn't need to move anywhere.  The only reason it wants to move to another chord in the key of D is because your ear is remembering what's happened before, and wants conclusion to the entire sequence of chords.

If you try to sort chords into categories, and base that sorting on progressions, you'll get lost quickly.

Sus and power chords do not have a third -- that's a great example of the confusion your method will lead to: you need to know the chords surrounding it in order to name the category -- a power chord can be major sometimes, and minor sometimes.  If you're trying to categorize chords, categories that change with their surroundings are not very useful...

Also, I think you're confusing tone color with dissonance.  Although it may be true that a minor third sounds more dissonant to your ear than a major third, both minor and major chords are made up of one major and one minor third each -- so the amount of dissonance you hear has a lot more to do with the inversion being played than with the character of the chord itself.