The Complete Idiot''s Guide to Music Theory

Part 1:
Tones
Here are the three perfect intervals, with C as the root.
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Three perfect intervals, starting on C.
Augmented and Diminished Intervals
Okay, now you know that perfect intervals can’t be major or minor. That doesn’t
mean that they can’t be altered, however. You 
can
raise and lower fourths and
fifths—however, the result is not called major or minor. When you raise a per-
fect interval a half step, it’s called an 
augmented
interval. When you lower a per-
fect interval a half step, it’s called a 
diminished
interval. So don’t call the new
intervals major or minor—call them augmented or diminished.
For example, if you use C as the root, F is a perfect fourth away from the root.
If you sharpen the F, the resulting note (F-sharp) is an augmented fourth above
the root.
Along the same lines, G is a perfect fifth above C. When you flatten the G, the
resulting note (G-flat) is a diminished fifth above the root.
Here are the key augmented and diminished intervals, with C as the root.
An augmented fourth and
a diminished fifth are
enharmonically the same
note.
Note
Augmented and diminished intervals, starting on C.
Now, just to confuse things, other types of intervals can also be called dimin-
ished and augmented—and these intervals have nothing to do with the perfect
intervals.
To start, you can also create a diminished interval by lowering a minor interval
by another half step. For example, F to D-flat is a minor sixth; if you flatten the
D-flat (yes, there’s such a thing as a double flat), the resulting interval is called a
diminished sixth.
You can also create an augmented interval by raising a major interval by another
half step. For example, F to A is a major third; if you sharpen the A (to A-
sharp), the resulting interval is an augmented third.
Fortunately, you don’t have to deal with either type of diminished or augmented
interval that often. But you still need to know what they are, just in case!

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Chapter 2:
Intervals
Beyond the Octave
You don’t have to stop counting intervals when you get to the octave. Above the
octave are even more intervals—ninths, tenths, elevenths, and so on.
Intervals that span more than an octave are called 
compound intervals
because
they combine an octave with a smaller interval to create the larger interval. For
example, a ninth is nothing more than an octave and a second; an eleventh is an
octave and a fourth … and so on.
The following table describes the first six intervals above the octave.
Compound Intervals