Understanding major, minor, augmented and diminished

Hey, DVC!

Jerome's answer was spot on! I'd like to give your question a shot, too... just in case I am able to add anything helpful.

People convert the letters into numbers, or rather intervals, because although the letters change for every key, the intervals of chords and scales do not. For example:

CDEFGABC
becomes
12345678

Two notes are cannot be a chord because they are only an interval, so the fundamental foundation of a chord must be three notes. Also chords can only be built by stacking thirds. This means that the most basic chord possible is a triad, meaning: 1-3-5 (Root-third-fifth).

Now the root can never change, but the 3rd and 5th can. So that gives us these variations.

Maj: R-3-5
Min: R-b3-5
Dim: R-b3-b5
Aug: R-3-#5

Augmented triads are kind of rare; but if you wanna hear a good example, check the intro to "Stardust" by Nat King Cole.
Diminished chords are a lot more common; they often act as transitions between diatonic chords. Check out the Jazz standard "Bewitched" as an example.

Now, about the 7... The seven is just following the formula used to find triads, stacking 3rds.

Most common 7th chords:
Maj7 chord: 1-3-5-7
Min7 chord: 1-b2-5-b7
(Dom)7 chord: 1-3-5-b7

Notice that those 7th chords are built from the Maj and Min triads. Other 7th chords can be build from Dim and Aug triads.

So now about the 9, 11, 13... you may have noticed that while stacking thirds, we skipped over the 2, 4 and 6. A quick recap:
CDEFGABC = 12345678

Well 8 is the same as 1 again, C and C. If we stack thirds beyond the point of 1-3-5-7, well moving a third over 7 will pass over 8 and lands at 9, which is the same as two... check it out, CDEFGABCD = 123456789. C is 1 also 8. D is 2 and also 9. A third above the 2/9 is 4/11. A third above 4/11 is 6/13.

9, 11 and 13 are considered extensions or scale tones. as where 1-3-5-7 are considered chord tones. Anything in between a chord tone and a scale tone are passing tones.

Hope that helps.

P.S. A quick tip, try adding a 9, just as an example, to any chord you play. It's never a "wrong" note, unless you are playing with someone who knows to altered a functioning Dom chord.

All the best, dudes! Check out my youtube channel if you want to see some videos with weird chord voicings (and normal ones too) and other lessons :-).

Thanks, Funster!

Huge props to you guys for being able to tackle stuff on your own. These days with sweet forums and stuff on the internet - self-teaching, so to speak is made ultra viable.

I had always had private lessons and eventually went on to the Musicians Institute in CA and I can say this much in regard to music theory; it's worth really comes through after what I would call some kind of third stage.

Example:
1st stage - Attaining general understanding of what the heck is going on with all this mumbo jumbo.
2nd stage - Knowing it... and particularly, I should add, how to apply it. Focusing on it's usefulness as a tool, rather than as an end in itself.
3rd stage - "Forgetting it". Not literally, haha, but after truly internalizing this stuff it becomes unconscious and effortless.

Main point:
Knowing theory has been an invaluable asset to me as an artists who creates original music. Knowing the theory means that when I sit down, I know exactly how to achieve the effect I want to create with a progression, how complex or direct/straight-forward it might be "emotionally" or "intellectually". Best of all, I don't have to sit around fishing for what I want when inspiration hits!

Analogy:
Stage 1 - Courtship
Stage 2 - Companionship
Stage 3 - Inter-dependant symbiosis

Lee your statement "the root can never change" is incorrect altered chords change the root because you can arrange the notes or intervals in several different forms C E G could also be expressed as  E G C OR G C E this more common in chords like 11s or 13ths 9ths but simple triad can be change to follow a leading tone like choir arrangements

ok a rose is a rose by any other name I get it, on a side note your website listed in your personal section has the http// twice so when anyone clicks on your website on your avatar the page cannot be found I tried to edit it for you but it keeps reverting back so you will have to do it. the signature link is ok RH moderator

A good rule of thumb to know when it's an inversion vs a whole different chord, is this:

*If the 3, 5 or 7 are the lowest note in the voicing - It's a 1st, 2nd or 3rd inversion.
*If the 9, 11 or 13 (i.e. 2, 4 or 6) are the lowest note in the voicing - it's perceived as a different chord.

For example, a G triad with an A in the bass will be perceived as an A7sus chord. This is one example of how one could go about re-harmonizing a progression. It's important to note however, that one must be careful to be certain that the new chord embraces the melody and does not clash against it (unless it's the clash they seek).

Stacking thirds just refers to putting two or more notes together that are in the interval of a third.

C E G

This is a C major chord, which is a major third (C to E) stacked on top of a minor third (e to g).