I'm sure M.Ted is right that technically this isn't necessarily music theory. However, in the general sense of theory vs. practice--book larnin' vs. doin' it--I would call it theory.

Now we all learn to talk without formal education, but instruction in reading and writing helps us expand and cement our understanding and command of language. Likewise, learning some of this music theory can help enrich our playing and singing.

In language, we start by learning the alphabet, then learn how to spell words, then learn the rules for putting words together to make proper sentences, etc. (We also find that sometimes we can make a point more effectively by violating those rules, although it's usually best to avoid this.) In music, we can learn and profit from similar basic knowledge.

Let's start with the alphabet--the chromatic scale. This is something that really should be committed to memory. It's a matter of definition and convention in Western music, and you gotta know it to fully understand the rest.

Our music is made of notes that have certain physical relationships to each other (based essentially on the lengths of vibrating strings). These notes are given names. There are only twelve names, and they are re-used as we continue going up or down the scale, which is theoretically infinite. If we start with A, going up, we have:

A-A#/Bb-B-C-C#/Db-D-D#/Eb-E-F-F#/Gb-G-G#/Ab-A-A#/Bb-B-C-etc.

Note that some notes have two names. For example, A# is the same note as Bb. Which name you use generally depends upon what key you are in (more to follow).

The next thing to learn is the major scale pattern. The distance (interval) from any note in the chromatic scale to an adjacent note (up or down) is called a half step. So, from A to A#(=Bb) is one half step. Likewise, it is a half step from A# to B, and from B to C, etc. The major scale pattern is a counting of half steps as follows:

2-2-1-2-2-2-1.

You start at a chosen note, find successive notes in the major scale by counting half steps according to the pattern, and end on a note with the same name as where you started. This comprises eight notes, and hence is called an octave. (The eight note has a vibration frequency that is twice that of the first note, and they sound very harmonious together, though obviously one is higher pitched than the other.)

We'll begin with an example in the key of C:

Start on C. Go two half steps, land on D. Go two half steps, land on E. Go one half step, land on F. Go two half steps, land on G. Go two half steps, land on A. Go two half steps, land on B. Go one half step, land on C. We now have named the notes of one octave in the key of C: C, D, E, F, G, A, B, C.

Note that in the key of C, none of the notes in the major scale are sharps (#) or flats (b). Note also, that if you play this scale on a piano keyboard, you play only white keys (the black keys are the sharps/flats). This is a convention, the piano keyboard is set up to play the C major scale on only white keys. I find it very helpful to know the notes on a keyboard, it makes a good visual aid to grasping this.

Now let's try it in the key of D. We start on D and count up in the 2-2-1-2-2-2-1 pattern:

D--E--F#/Gb-G--A--B--C#/Db-D

So, do we call the third note F# or Gb? The seventh note C# or Db? The rule, to minimize confusion, is to use each letter name once. Thus we'll call the third one F#, so that we can use "F" and not use "G" twice. Likewise, the seventh note is called C#. So a D major scale is:

D--E--F#-G--A--B--C#-D

Note that there are two sharps in the key of D. This is the only key with two sharps, and its key signature in sheet music will have two sharps.

Let's try the key of F.

F--G--A--Bb--C--D--E-F

We call the fourth note Bb rather than A#, so as to use "B" once and not use "A" twice. This key has one flat, and is the only key with one flat; its key signature has one flat.

To quickly find the notes in any major scale, write out the note names, at first without sharps or flats. For example, the key of A:

A--B--C-D--E--F--G-A

Now add sharps or flats as needed to make the intervals fit the 2-2-1-2-2-2-1 pattern:

A to B, two half steps--okay. B to C, one half step--not okay. Make it a C#, now it's two half steps--okay. C# to D, one half step--okay. D to E, two half steps--okay. E to F, one half step--not okay. Make it an F#, now it's two half steps--okay. F# to G, one half step--not okay. Make it a G#, now it's two half steps--okay. G# to A, one half step--okay. So now we have:

A--B--C#-D--E--F#--G#-A

There are three sharps, which is unique to the key of A.

Let's try the key of Eb:

E--F--G-A--B--C--D-E

Since the chosen key is Eb, we know the first and last ones must be Eb. Two half steps takes us to F. Two half steps takes us to G. One half step takes us to Ab. Two half steps takes us to Bb. Two half steps takes us to C. Two half steps takes us to D. One half step takes us to Eb. Now we've got:

Eb--F--G-Ab--Bb--C--D-Eb

Three flats (we only count Eb once), unique to the key of Eb. Here we're using Ab and Bb over G# and A# to follow the rule of using each letter name once. By writing each letter name out to begin with, then adding either a sharp or flat as and when needed to fit the pattern, you automatically do this.

What if you had wanted to call this the key of D#, which is the same note as Eb? You'd get something like these:

D#--F--G-G#--A#--C--D-D# [No "E", no "B", two "G's", two "D's"--rather confusing]

D#--E#--F##(=G)-G#--A#--B#(=C)--C##(=D)-D# [Uses each letter name once, but double sharps add to confusion]

The standard keys, and the number of sharps or flats in each are:

B--five sharps
E--four sharps
A--three sharps
D--two sharps
G--one sharp
C--no sharps or flats
F--one flat
B--two flats
Eb--three flats
Ab--four flats
Db--five flats

The key of F#/Gb is a bit trickier than the others. If you call it F#:

F#--G#--A#-B--C#--D#--F-F# or F#--G#--A#-B--C#--D#--E#(=F)--F#

You either have to use "F" twice and not use "E" or use E# to indicate F.

If you call it Gb:

Gb--Ab--Bb-B--Db--Eb--F-Gb or Gb--Ab--Bb-Cb(=B)--Db--Eb--F--Gb

You either use "B" twice and not use "C" or use Cb to indicate B.

I would say the second choice in each of the above is more technically correct, as the key signature will have either six sharps (F#) or six flats (Gb).

Okay, that's an introduction to the chromatic scale and the major scales. Next installment we'll look at chords.