3. CHORD FORMATION  
 
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Most chords are based on a pattern of odd notes (1 - 3 - 5 - 7 - 9 etc.).   A major chord uses notes 1 - 3 - 5.   So C major (usually written as just C) is C - E - G.   (In Table 1, the note C, is the first, E is the third, and G is the fifth.)   Minor chords use the notes 1 - b3 - 5 (root, flatted third, fifth).   So C Minor (written as Cmin) is C - Eb - G.  
 
A diminished chord uses the notes 1 - b3 - b5.   So C dim (or C0) is C - Eb - Gb.   An augmented chord, denoted by +, uses the notes 1 - 3 - #5, so that C+ uses the notes C - E - G#.

A dominant seventh chord (usually just called a seventh chord) uses the notes 1 - 3 - 5 - b7.   A major seventh chord varies only in the last note, using 1 - 3 - 5 - 7.   We saw above that a minor chord differs from a major chord in that the third is flatted in the minor chord.   So if we take a dominant seventh chord and flat the third, we get the notes 1 - b3 - 5 - b7.   This is the definition of a minor seventh chord.   But be careful!   The seventh chords seem to be inconsistent with the others (using b7 rather than 7), and this affects chords 'above' them, such as the ninths, elevenths, and thirteenths.

So C7 (C Dominant Seventh, usually just called C Seventh) uses the notes C - E - G - Bb (recall Bb = A#).   CMaj7 (C Major Seventh) uses C - E - G - B.   CMin7 (C Minor Seventh) uses C - Eb - G - Bb.   You can also have a (dominant) seventh (flatted fifth) chord – it uses 1 - 3 - b5 - b7.   C7 (b5) [this is pronounced C seventh, flatted fifth] uses C - E - Gb - Bb.

You can also have a major seventh (flatted fifth), a minor seventh (flatted fifth), a diminished (dominant) seventh, a diminished major seventh, a diminished minor seventh, a diminished (dominant) seventh (flatted fifth), a diminished major seventh (flatted fifth), a diminished minor seventh (flatted fifth)   .   .   .   virtually ad nauseum.

To construct a major seventh (flatted fifth) chord, use the construction for a major seventh chord (1 - 3 - 5 - 7), and flat the fifth to get the notes 1 - 3 - b5 - 7.   For a diminished minor seventh, start with the construction for a minor seventh chord, which uses 1 - b3 - 5 - b7, and make it diminished by flatting the fifth (giving 1 - b3 - b5 - 7.   So a diminished minor seventh chord is the same as a diminished minor seventh (flatted fifth) chord.   Note that a diminished chord has both the third and the fifth flatted, so a diminished (flatted fifth) chord is redundant.   Similarly, a minor seventh (flatted fifth) chord is the same as a dominant diminished seventh chord.

You can even have a Major minor seventh!   We saw above that a major seventh uses the notes 1 - 3 - 5 - 7, and a minor seventh uses the notes from a dominant seventh (which are 1 - 3 - 5 - b7) and flats the third (yielding 1 - b3 - 5 - b7).   So if we take the notes from the major seventh, and flat the third, we get 1 - b3 - 5 - 7.
 
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A (dominant) ninth chord is a dominant seventh, with a ninth note added; it uses 1 - 3 - 5 - b7 - 9.   So C9 uses C - E - G - Bb - D.   Remember the ninth is the same as the second.   So another way of looking at it is that the ninth chords uses 1 - 2 - 3 - 5 - b7.   Also see that the b7 that was used in the (dominant) 7th carries over here.

A major ninth chord uses the same notes as a major seventh, with the ninth note added; it uses 1 - 3 - 5 - 7 - 9 (or 1 - 2 - 3 - 5 - 7).   A minor ninth chord uses the same notes as a minor seventh, with the ninth node added; it uses 1 - b3 - 5 - b7 - 9 (or 1 - 2 - b3 - 5 - b7).   A diminished ninth chord flats the third and the fifth, so it uses 1 - b3 - b5 - b7 - 9.   An augmented ninth uses 1 - 3 - #5 - b7 - 9.   Using these rules, we can see which notes are used in the chords CMaj9, CMin9, C9dim (or C90), and C9+.   They are in Table 3A.

A (dominant) eleventh chord is a ninth chord, with the eleventh note added; it uses 1 - 3 - 5 - b7 - 9 - 11.   Remember the eleventh is the same as the fourth, so another way of looking at that is that the eleventh chord uses 1 - 2 - 3 - 4 - 5 - b7.   So C11 uses C - D - E - F - G - Bb.   In the same way we constructed major, minor, diminished and augmented chords for C9, we can do the same for C11.   I won't go through that; I'll just list the results in Table 3A.
 
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      Table 3A.   Notes Used In Several Chords In The Key of C.    
   
Chord Name
Notes Used
   
   
C9
C
E
G
Bb
D
   
   
CMaj9
C
E
G
B
D
   
   
CMin9
C
Eb
G
Bb
D
   
   
C9dim
C
Eb
Gb
Bb
D
   
   
C9+
C
E
G#
Bb
D
   
   
C11
C
E
G
Bb
D
F
   
   
CMaj11
C
E
G
B
D
F
   
   
CMin11
C
Eb
G
Bb
D
F
   
   
C11dim
C
Eb
Gb
Bb
D
F
   
   
C11+
C
E
G#
B
D
F
   
   
C13
C
E
G
Bb
D
F
G
   
   
CMaj13
C
E
G
B
D
F
G
   
   
CMin13
C
Eb
G
Bb
D
F
G
   
   
C13dim
C
Eb
Gb
Bb
D
F
G
   
   
C13+
C
E
G#
B
D
F
G
   
 
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A (dominant) thirteenth chord is an eleventh chord, with the thirteenth note added; it uses 1 - 3 - 5 - b7 - 9 - 11 - 13.   Since the 13thnote is the same as the 6th note, we could also say that the the 13th chord uses 1 - 2 - 3 - 4 - 5 - 6 - b7.   So C13 uses C - D - E - F - G - A - Bb.   So C13 uses every note in the key of C!   (Except the 7th, B, is flatted).   In the same way that CMaj9 and CMaj11 replaced the flatted 7th with a natural 7th, a major 13th chord will also replace it.   (If you've been paying close attention, you know this means a major 13th chord will use every note in the corresponding key.)   The bottom part of Table 3A shows the notes used in several 13th chords in the key of C.

If something about this makes you uneasy, there's a good reason for it.   13th chords have seven notes.   The guitar has six strings.   So you can't play a complete 13th chord on the guitar.   However, it turns out, you can sometimes leave out a note from a 13th chord, and it will still sound okay.   But don't ask me how to do this, or how to figure it out.   It's way above my level of expertise.

In the same way we constructed major, minor, diminished and augmented chords for 9th and 11th chords, we can do the same for 13th chords.   And we can also have a major ninth (flatted fifth), and a minor ninth (flatted fifth), and a major 11th (flatted fifth), and a major thirteenth (flatted fifth).   And we can make any and all of these diminished, or augmented, as well.   I'm not going to do that.   If you need to play one of these chords, you can either figure it out from the rules that I listed above, or go on the web and find a diagram.
 
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There are other types of chords that I do want to discuss.   A fifth chord uses only the first and the fifth (the third is omitted).   It's a 1 - 5 chord.   C5 [also written as C (no 3rd)] uses the notes C - G.   A suspended second chord uses 1 - 2 - 5, while a suspended fourth chord uses 1 - 4 - 5.   (You would think that suspended means something is left out - and the third is left out of both types of chords - but in this case suspended means it is put in.   Go figure.)   So Csus2 uses C - D - G and Csus4 uses C - F - G.   Suspended fourth chords are also just referred to as suspended.   Obviously, these chords deviate from the 1 - 3 - 5 - 7 - 9 - 11 - 13 formula.

A sixth chord (also called major sixth) uses the notes 1 - 3 - 5 - 6 in the appropriate key.     A minor sixth uses notes 1 - b3 - 5 - 6.   So C6 uses the notes C - E - G - A, and Cmin6 uses C - Eb - G - A.

Given the rules I've outlined here, you can probably (with some pain) construct just about any chord.   Table 3 summarizes these rules for a number of common chords (but not all those I’ve described).   As I stated before, if you need to play one of these really complicated chords, you can either figure it out from the rules I've listed, or go on the web and find a diagram.   Table 4 lists the actual notes used in major chords, minor chords, diminished chords, and augmented chords.   It is derived by applying the rules I've outlined (which are summarized in Table 3) to the notes in Table 2.

But all this information about how to form various chords doesn't tell us what their purpose is, how they are used, where they come from   .   .   . That's the purpose of the next file.
 
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