The Complete Idiot''s Guide to Music Theory

Part 3:
Tunes
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Seventh, ninth, and eleventh chords see frequent use in modern jazz music,
which often employs sophisticated harmonic concepts.
Elevenths … and Beyond
An eleventh chord adds another note a third above the ninth, for six notes total:
1-3-5-7-9-11. You can set an eleventh on top of any type of triad, along with all
sorts of seventh and ninth variations—although the most common eleventh
chord always uses the unchanged note from within the underlying key or scale.
As with the ninth chord, you have to make a few assumptions with the eleventh
chord. You have to assume the underlying triad, of course, but you also have to
assume the presence of both the seventh and the ninth.
Different types of eleventh chords.
Above the eleventh, it’s possible to construct both thirteenth and fifteenth
chords. Just keep adding more notes; each a third above the last.
By the way, the fifteenth chord is pretty much the highest you’ll find, because
the new note for the next chord up—the seventeenth chord—is exactly two
octaves up from the chord root. There’s no point in calling it a new chord when
all you’re doing is doubling the root note.
Altered, Suspended, and Power Chords
To ensure that you have a comprehensive background in chord theory, there are
three other chord types you need to know about. These are variations on the
basic chord types that crop up from time to time—and can help you notate
more complex musical sounds.
Altered Chords
When you get into seventh and ninth and eleventh chords, you run into the pos-
sibility of a lot of different variations. It’s math again; the more notes in a chord,
the more possible combinations of flats and sharps and such you can create.
This is why we have something called 
altered chords.
Altered chords take stan-
dard, easy-to-understand chords and alter them. The alteration—a lowered
fifth, perhaps, or maybe an added ninth—is typically notated in parentheses,
after the main chord notation.
For example, let’s say you wanted to write a C Major seventh chord, but with a
lowered fifth. (I know … that’s a really weird-sounding combination.) To notate
this, you start with the basic chord—CM7—and add the alteration in parenthe-
ses, like this: