The Complete Idiot''s Guide to Music Theory

Part 1:
Tones
These black keys are called 
sharps
and 
flats.
Sharps and flats are halfway between
the pitches represented by the white keys on a piano; a sharp is above a specific
key and a flat is below a specific key.
Put another way, a sharp raises the natural note; a flat lowers the note.
Take the black key above the middle C key, for example. You can refer to this key
as 
C-sharp,
because it raises the pitch of C. It also can be called 
D-flat,
because
it lowers the next white key up, D. It may be a little confusing, but it’s true—
C-sharp is the same note as D-flat. And whenever you have two notes that
describe the same pitch—like C-sharp and D-flat—the notes are 
enharmonic
.
Here are the dual names you can use for a piano’s black keys:
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An
interval 
is the
space between two pitches.
The smallest interval in
Western music is a half
step; intervals are typically
measured in the number of
half steps between the two
notes.
Definition
Two notes that
sound the same but can
be spelled differently are
called
enharmonic 
notes.
Definition
The black keys on a piano keyboard.
On a music staff, sharps and flats are designated by special characters placed
before
the affected note. These characters, called 
accidentals, 
look like this:
Any modification
to a natural note is called
an
accidental.
Sharps and
flats are accidentals; the
natural sign (used to return
a sharped or flatted note
to its natural state) is also
an accidental.
Definition
A sharp, a flat, and a natural sign.
That third character is called a 
natural.
When you see a natural sign on a piece
of music, it means to return the specific note to its natural state, without any
sharps or flats.
It’s important to know that you can add sharps and flats to any note—even those
keys on a piano that don’t have black notes between them. So, for example, if
you add a flat to the C note, you lower it to the next note on the keyboard—
which happens to be B natural. (This means B natural is the same pitch as C-flat.)
Steppin’ Out …
The smallest interval in Western music is the 
half step
. On the piano keyboard,
half steps appear between the white keys B and C and between E and F. In all
other cases they appear between a white key and a black key—for example, D
to D-sharp, or F-sharp to G.

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Chapter 2:
Intervals
Two half steps equal one 
whole step
. The interval between F and G is a whole
step; the interval between B and C-sharp is also a whole step.
Now that you know about steps, it’s a little easier to understand how sharps
and flats work. When you sharpen a note, you move the pitch up a half step.
When you flatten a note, you move the pitch down a half step.
Take the note C, for example: When you add a flat to C, you take it down a half
step. Because the first key (white or black) to the left of C is the white key B,
this means C-flat equals B. When you add a sharp to C, you take it up a half
step. The first key to the right of C is the black key we call C-sharp. (This black
key is also the first key to the left of D, which means C-sharp is the same as 
D-flat.)
19
In some musical
circles, a 
half step 
is called
a
semitone,
and a 
whole
step
is called a 
tone.