Chord Formula Lesson Two covers the augmented, diminished, and extended chords.
I am assuming that if you came to this page, you are serious about seeking information, so let's get started!
Remember that the numbers in a chord formula refer to notes in major scale.
A discussion of how these chords function can be found here.
Augmented Triad--1 3 #5
(EXAMPLE: C E G#) (NOTATION: C+ or C aug) Just start with the MAJOR TRIAD and sharp the third note(the 5th note in the scale).
Diminished Triad--1 b3 b5
(EXAMPLE: C E G#) (NOTATION: Cdim)
Begin with the MINOR TRIAD and flat the third note (the 5th note in the scale)
Half Diminished Chord--1 b3 b5 b7
(EXAMPLE: C Eb Gb Bb) (NOTATION: Cø or Cm7b5)
Start with the MINOR TRIAD and flat the second and third notes (the 3rd and 5th notes in the scale.) Then add the flatted seventh note of the scale.
"Extended Chords" refers to chords to which notes PAST THE SEVENTH have been added. The added notes are numbered by starting with the second note in the scale as the ninth.
Ninth--1 3 5 b7 9(EXAMPLE: C E G Bb D) (NOTATION: C9) Please note that this chord has the FLATTED SEVENTH--in other words, it is an extension of the DOMINANT SEVENTH chord.
Major Ninth--1 3 5 7 9 (EXAMPLE: C E G B D)(NOTATION: Cmaj9 or CM9) This chord has the NATURAL SEVENTH degree of the scale. It is an extension of the MAJOR SEVENTH chord.
Minor Ninth--1 b3 5 b7 9 (EXAMPLE: C Eb G Bb D) (NOTATION Cm9 or Cmi9) The flatted 3rd and flatted seventh make it an extension of the MINOR SEVENTH chord.
All of these ninth chords can be further extended by adding the ELEVENTH or the THIRTEENTH. Their function remains the same as the ninth chord to which they were added.
INTERESTING NOTE: The ELEVENTH and THIRTEENTH chords are actually a combination of TWO chords. EXAMPLE: a C11 chord(C E G Bb D F) is a Bb MAJOR triad on top of a C MAJOR TRIAD.
Try extended some of the chords in progressions that you play. It will give your playing a whole new "color". Just remember to maintain the proper chord function. Use the extended chords as you would seventh chords.