I made a post on davie gravy's scale intervals page on the modes of the major scale and I touched base with what you can do with them as far as chords go, but first I felt I should touch base with people who are first starting into theory because that will not make sense more than likely, I accidentally jump around a lot. My punctuation and typing also suck, excuse the ADD anyways, here is a decent lesson explaining intervals. If you still have problems contact me and I will try to explain in better terminology.
Intervals are used to define the distance from one note to the next. As we all know the musical alphabet is 12 tones(standard)
There are also double flats- bb and double sharps- x and sometimes E is considered to be an Fb or B a Cb. Yeah, I used to think it was stupid but then I realized of course you try to keep one of each note on the scale which you are using. It makes things difficult if you use one note more than once and totally drop another note from your scales. It doesn't make sense once you look into the logic in it. Anyways, there are Major, Minor, Perfect, Augmented, Diminished, Doubly Augmented, and Double Diminished. This is how we refer to intervals.
Labelling intervals consists of a qualitative value next to a quantitative value. basically one of the names next to a number which shows which degree of a scale it is found.
Perfects - P
If you play an A on one string and play it on the next, exact same note same octave. You have played a Perfect 1st(P1) or a Unison. If you play an E on the low string and an A on the next string. you have played a Perfect 4th(P4). If you play an E on the low string and play a B on the next string you have just played a Perfect 5th(P5) which is also a basic power chord. The only other one refered to as a perfect is the octave which is the exact same note except one octave higher hence it is thereby called the "octave." Yeah, I'm not trying to sound condescending, but I think I may be succeeding.
Majors - M
As far as Majors they contain the steps of the major scale so C-D is a M2 C-E is a M3. Yeah pretty easy, now I'm having to rush a bit so yeah. Check the scale intervals lesson to find out the steps of the major scale if you don't already know.
Minor - m
Minors contain the steps of the minor scale. So A-G is a m7 and C-Eb is a m3. That type shindigg.
Augmented - a
You take one of the steps that are perfect and raise it by one half step this turns perfects into augmented it can do the same to major as well though, if you augment a M2 it technically becomes a m3 but depending on how the writer/theorist wants you to interpret it he will write it. Instead of just putting the natural minor 3rd degree he will put the Major 2nd with a cute little # sign. If you augment it twice it becomes doubly augmented or A.
Diminished - D
To diminish is to take away in this case taking away a half step. Pretty much the same rules apply as augmented. If you diminish twice it becomes doubly diminished or d. I call the half step augmentation "a" because it doesn't raise it as much. As for diminished it is taking away so I refer to a half step diminish as D because it is still larger or greater.
I'm too much of a geek sometimes. There is no standard for music though. Hence, I hate common chord progressions because it is an attempt to standardize music. If that happens I would go insane. I guess I'm too progressive for my own good.
If you invert the intervals
Quality: Major becomes minor, Perfect stays perfect, minor becomes Major. Augmented becomes diminished and diminished becomes augmented Doubly augmented becomes Doubly diminished and Doubly diminished becomes Doubly augmented.
Quantity: If it is a complex interval such as a M9 then subtract 7 and you get what the lower octave is(M2) and it helps to determine the difference between the notes. Some call this the rule of 7 it helps determine what the simple interval would be.
If you invert say a M6 it becomes a m3 or a P4 it becomes a P5 when inverted the two numbers on the ends of the quality will add up to 9 thats one of the only other rules concerning inversions in music.
Anyways, I'm about to get out of this stupid class, sorry I didn't have more time but I'll eventually fix this lesson if anybody has any problems. If there are problems let me know as always. I'll try to clarify or lamerize. Anyways, hope this helps beginners... later.