harmonizing the major scale (in extended chords; 9th, 11th, 13th)


Recall, in previous lessons ( http://simianmoon.com/snglstringtheory/chords/harmtri.html)we took the major scale and stacked it upon itself in 3rds to yield first intervals, and then triads (3 note chords), then 7th chords (4 note chords).

Recall also that we determined the chords (triads) built off the 7 notes in the major scale (in order) are: major, minor, minor, major, major, minor, diminished. And putting these together with roman numerals, and an intervallic notation for the scale we get:
I-ii-iii-IV-V-vi-viio.
(In the key of C, these chords would be: C-Dm-Em-F-G-Am-Bo).

This was given in more detail explaining how and why last lesson. Check the archive above or www.deja.com for the lesson.

Recall, the following intervals (equivilencies):
major ninth (9) = 14 half-steps
minor ninth (b9) = 13 half-steps
augmented ninth = 15 half-steps

Recall, that a triad is a 3-note chord, and that the triads we considered consist of a root note, a third (of some sort), and a fifth (of some sort).

Recall a seventh chord (any arbitrary seventh chord) as a 4-note chord (4 distinct notes) containing some form of the following notes: a root note, a third (of some sort), a fifth (of some sort), and a seventh (of some sort).

We defined 4 seventh chords we find in the harmonized form of the major scale:

major seventh chord = 1,3,5,7
dominant seventh chord = 1,3,5,b7
minor seventh chord = 1,b3,5,b7
half-diminished seventh chord = 1,b3,b5,b7

NINTH CHORDS

Let us now define a ninth chord (any arbitrary ninth chord) as a 5-note chord (5 distinct notes) containing some form of the following notes: a root note, a third (of some sort), a fifth (of some sort), a seventh (of some sort) and a ninth (of some sort).

Let us now define the 5 ninth chords we will find in the harmonized form of the major scale:

major ninth chord (maj9) = 1,3,5,7,9
dominant ninth chord (9) = 1,3,5,b7,9
minor ninth chord (m9) = 1,b3,5,b7,9
minor seven flat nine chords (m7b9) = 1,b3,5,b7,b9
half-diminished seven flat nine chord (m7b9b5)= 1,b3,b5,b7,b9

Note that both the major ninth chord and the dominant ninth chord contain the major triad (major chord) within them (from the root note), but they have different sevenths. Also note that the m9 and m7b9 chords both contain minor seventh chords within them but have different ninths Taking an arbitrary seventh and adding a ninth note to it, we can create many more ninth chords. the 5 above; however, are the ones we will find when we harmonize the major scale.

So recall the C major scale (C,D,E,F,G,A,B,C).
We will find the following intervals (9ths) using whatever method we prefer (familiarity with keys, transposition chart, rote memorization, counting 1/2-steps, etc.):
C to D = 9 (major ninth)
D to E = 9
E to F = b9(minor ninth)
F to G = 9
G to A = 9
A to B = 9
B to C = b9

Recall that we found our triads by stacking thirds. we can continue in this fashion to find 7th chords. (Below is in standard notation)

TRIADS (form major scale)

                              O
|-------------------------O-----|
                      O       O
|-----------------O-------O-----|
              O       O       O
|---------O-------O-------O-----|
      O       O       O
|-O-------O-------O-------------|
      O       O
|-O-------O---------------------|
      O
 -O- 

SEVENTH CHORDS (from major scale)


                              O
                         -O-
                      O       O
|-----------------O-------O-----|
              O       O       O
|---------O-------O-------O-----|
      O       O       O       O
|-O-------O-------O-------O-----|
      O       O       O
|-O-------O-------O-------------|
      O       O
|-O-------O---------------------|
      O
 -O- 

NINTH CHORDS (from major scale)



                              O
                         -O-
                      O       O
                 -O-     -O-
              O       O       O
|---------O-------O-------O-----|
      O       O       O       O
|-O-------O-------O-------O-----|
      O       O       O       O
|-O-------O-------O-------O-----|
      O       O       O
|-O-------O-------O-------------|
      O       O
|-O-------O---------------------|
      O
 -O- 

So a third from the top of the seventh (the 7th) is the 9th. and we just analyzed those notes. so taking a note in the scale, and all the notes stacked above it we find the following chords:

C-E-G-B-D = 1,3,5,7,9 = major ninth chord
D-F-A-C-E = 1,b3,5,b7,9 = minor ninth chord
E-G-B-D-F = 1,b3,5,b7,b9 = minor seven flat nine chord
F-A-C-E-G = 1,3,5,7,9 = major ninth chord
G-B-D-F-A = 1,3,5,b7,9 = dominant ninth chord
A-C-E-G-B = 1,b3,5,b7,9 = minor ninth chord
B-D-F-A-C = 1,b3,b5,b7,b9 = half-diminished seven flat nine chord
(where each 1 refers to the bottom note of the respective chord)

So harmonizing the C major scale in 3rds and creating 9th chords, we find the following (in C):
C major ninth - D minor ninth - E minor seven flat nine - F major ninth - G dominant ninth - A minor ninth - B half-diminished seven flat nine.

We often use abbreviations for chord names. The following are commonly used:

For major ninth chords: maj.9. Also used though not feasible with this font are a greek letter delta (a triangle) after the letter before a 9, or M9.

For dominant ninth chords: dom.9 or 9 are written after the letter.

note: although there are many types of ninth chords, the one referred to without a qualifier is the dominant ninth chord. So if I say to you, "play a 'G nine' chord" then that chord would be a dominant ninth chord, written as G9. If instead i want you to play a 'G major nine chord', Gmaj9, I must specify the word major before the nine, to let you know that i am talking about a major ninth chord rather than a dominant ninth chord. I bring this up so that you'll not be confused, or confuse others, and because i've been loosely using the term ninth chords to discuss a broad range of chords having a root, some third, some fifth, some seventh, and some ninth.

For minor ninth chords: m9 or -9 (ex. Cm9, C-9).

For minor seven flat nine chords: m7b9

For half-diminished seven flat nine chords: m7b9b5, m7-9-5.

So looking back above we can say we have the following chords (in C):
Cmaj9-Dm9-Em7b9-Fmaj9-G9-Am9-Bm7b9b5

We recall that we can keep this in context but not refer to a specific key by using roman numerals. Then we get:
Imaj9-ii9-iii7b9-IVmaj9-V9-vi9-vii7b9b5

Recall that the relative minor contains the same notes (and therefore the same chords) as its relative major scale/key in the same order but starting on a differnet note.

The relative minor of C major is A minor, so we have the notes:
A-B-C-D-E-F-G-A, and the chords: Am9-Bm7b9b5-Cmaj9-Dm9-Em7b9-Fmaj9-G9

These are the same chords as above but in a different context. we can see the change in context by changing to roman numerals, we get:
i9-ii7b9b5-bIIImaj9-iv9-v7b9-bVImaj9-bVII9

So we we create progressions from the two listings of chords that would go well with the major and minor scales respectively.

For example, Imaj9-ii9-iii7b9-IVmaj9 would go well with the major scale. We could say that the major scale starting on the same root note as Iwould be an inside choice of a scale to play over (solo, improvise) this progression. We could also say that this is a major (scale) progression or an ionian (mode) progression.

Now consider the progression ii7b9b5-v9-i9. This would be a minor (scale) progression or an aeolian (mode) progression, and a minor scale starting on the same root note as i9 would fit easily over these chords (it would be an "inside" choice).

Ok. So you could use these groups of chords to analyze a song, which might help you choose a scale to use over a group of chords rather than changing scales with every chord (which is another option often heard in jazz).

ELEVENTH CHORDS

Let us now define an eleventh chord (any arbitrary eleventh chord) as a 6-note chord (6 distinct notes) containing some form of the following notes: a root note, a third (of some sort), a fifth (of some sort), a seventh (of some sort), a ninth (of some sort), and an eleventh (of some sort).

Let us now define the 6 eleventh chords we will find in the harmonized form of the major scale:

major eleventh chord (maj11) = 1,3,5,7,9,11
major nine sharp eleventh chord (maj9#11) = 1,3,5,7,9,#11
dominant eleventh chord (11) = 1,3,5,b7,9,11
minor eleventh chord (m11) = 1,b3,5,b7,9,11
minor eleven flat nine chords (m11b9) = 1,b3,5,b7,b9,11
minor eleven flat nine chord flat five chords (m11b9b5)= 1,b3,b5,b7,b9,11

Note how the 11th chords shown contain smaller chords we already know inside of them.

So recall the C major scale (C,D,E,F,G,A,B,C).
We will find the following intervals (9ths) using whatever method we prefer (familiarity with keys, transposition chart, rote memorization, counting 1/2-steps, etc.):
C to F = 11 (Perfect 11th = perfect 4th+octave)
D to G = 11
E to A = 11
F to B = #11(augmented eleventh = augmented 4th +octave)
G to C = 11
A to D = 11
B to E = 11

Recall that we found our triads, seventh chords and ninth chords by stacking thirds. we can continue in this fashion to find 11th chords. (Below is in standard notation)

ELEVENTH CHORDS (from major scale)




                              O
                         -O-
                      O       O
                 -O-     -O-
              O       O       O
         -O-     -O-     -O-
      O       O       O       O
|-O-------O-------O-------O-----|
      O       O       O       O
|-O-------O-------O-------O-----|
      O       O       O       O
|-O-------O-------O-------O-----|
      O       O       O
|-O-------O-------O-------------|
      O       O
|-O-------O---------------------|
      O
 -O- 

So a third from the top of the ninth chord (the 9th) is the 11th. and we just analyzed those notes. so taking a note in the scale, and all the notes stacked above it we find the following chords:

C-E-G-B-D-F = 1,3,5,7,9,11 = major eleventh chord
D-F-A-C-E-G = 1,b3,5,b7,9,11 = minor eleventh chord
E-G-B-D-F-A = 1,b3,5,b7,b9,11 = minor eleven flat nine chord
F-A-C-E-G-B = 1,3,5,7,9,#11 = major ninth sharp eleven chord
G-B-D-F-A-C = 1,3,5,b7,9,11 = dominant eleventh chord
A-C-E-G-B-D = 1,b3,5,b7,9,11 = minor eleventh chord
B-D-F-A-C-E = 1,b3,b5,b7,b9,11 = minor eleven flat nine flat five chord
(where each 1 refers to the bottom note of the respective chord)

So harmonizing the C major scale in 3rds and creating 11th chords, we find the following (in C):
C major eleventh - D minor eleventh - E minor eleven flat nine - F major nine sharp eleventh - G dominant eleventh - A minor eleventh - B minor eleven flat nine flat five.

We often use abbreviations for chord names. The following are commonly used:

For major eleventh chords: maj.11. Also used though not feasible with this font are a greek letter delta (a triangle) after the letter before 11, or M11.

For dominant eleventh chords: dom.11 or 11 are written after the letter.

note: although there are many types of eleventh chords, the one referred to without a qualifier is the dominant eleventh chord. So if I say to you, "play a 'G eleven' chord" then that chord would be a dominant eleventh chord, written as G11. If instead i want you to play a 'G major eleven chord', Gmaj11, I must specify the word major before the eleven, to let you know that i am talking about a major eleventh chord rather than a dominant eleventh chord. I bring this up so that you'll not be confused, or confuse others, and because i've been loosely using the term eleventh chords to discuss a broad range of chords having a root, some third, some fifth, some seventh, and some ninth, and some eleventh.

For major nine sharp eleventh chords: maj9#11

For minor ninth chords: m11 or -11 (ex. Cm11, C-11).

For minor seven flat nine chords: m11b9

For minor eleven flat nine chords flat five: m11b9b5, m11-9-5.

So looking back above we can say we have the following chords (in C):
Cmaj11-Dm11-Em11b9-Fmaj9#11-G11-Am11-Bm11b9b5

We recall that we can keep this in context but not refer to a specific key by using roman numerals. Then we get:
Imaj11-ii11-iii11b9-IVmaj9#11-V11-vi11-vii11b9b5

Recall that the relative minor contains the same notes (and therefore the same chords) as its relative major scale/key in the same order but starting on a differnet note.

The relative minor of C major is A minor, so we have the notes:
A-B-C-D-E-F-G-A, and the chords:
Am11-Bm11b9b5-Cmaj11-Dm11-Em11b9-Fmaj9#11-G11

These are the same chords as above but in a different context. we can see the change in context by changing to roman numerals, we get:
i11-ii11b9b5-bIIImaj11-iv11-v11b9-bVImaj9#11-bVII11

So we we create progressions from the two listings of chords that would go well with the major and minor scales respectively.

Ok. So you could use these groups of chords to analyze a song, which might help you choose a scale to use over a group of chords rather than changing scales with every chord (which is another option often heard in jazz).

THIRTEENTH CHORDS

Let us now define an thriteenth chord (any arbitrary thriteenth chord) as a 7-note chord (7 distinct notes) containing some form of the following notes: a root note, a third (of some sort), a fifth (of some sort), a seventh (of some sort), a ninth (of some sort), an eleventh (of some sort), and a thirteenth (of some sort).

Let us now define the 7 eleventh chords we will find in the harmonized form of the major scale:

major thirteenth chord (maj13) = 1,3,5,7,9,11,13
major thirteenth sharp eleventh chord (maj13#11) = 1,3,5,7,9,#11,13
dominant thirteenth chord (13) = 1,3,5,b7,9,11,13
minor thirteenth chord (m13) = 1,b3,5,b7,9,11,13
minor eleventh flat thirteen chord (m11b13) = 1,b3,5,b7,9,11,b13
minor eleven flat thirteen flat nine chords (m11b13b9) = 1,b3,5,b7,b9,11,b13
minor eleven flat thirteen flat nine chord flat five chords (m11b9b5)= 1,b3,b5,b7,b9,11,b13

Note how the 13th chords shown contain smaller chords we already know inside of them.

So recall the C major scale (C,D,E,F,G,A,B,C).
We will find the following intervals (9ths) using whatever method we prefer (familiarity with keys, transposition chart, rote memorization, counting 1/2-steps, etc.):
C to A = 13 (Major 13th = major 6th+octave)
D to B = 13
E to C = b13 (Minor 13th = minor 6th+octave)
F to D = 13
G to E = 13
A to F = b13
B to G = b13

Recall that we found our triads, seventh chords, ninth chords and eleventh chords by stacking thirds. we can continue in this fashion to find 13th chords. (Below is in standard notation)

THIRTEENTH CHORDS (from major scale)


O -O- O O -O- -O- O O O -O- -O- -O- O O O O -O- -O- -O- -O- O O O O |-O-------O-------O-------O-----| O O O O |-O-------O-------O-------O-----| O O O O |-O-------O-------O-------O-----| O O O |-O-------O-------O-------------| O O |-O-------O---------------------| O -O-

So a third from the top of the eleventh chord (the 11th) is the 13th. and we just analyzed those notes. so taking a note in the scale, and all the notes stacked above it we find the following chords:

C-E-G-B-D-F-A = 1,3,5,7,9,11,13 = major thirteenth chord
D-F-A-C-E-G-B = 1,b3,5,b7,9,11,13 = minor thirteenth chord
E-G-B-D-F-A-C = 1,b3,5,b7,b9,11,b13 = minor eleven flat thirteen flat nine chord
F-A-C-E-G-B-D = 1,3,5,7,9,#11,13 = major thirteenth sharp eleven chord
G-B-D-F-A-C-E = 1,3,5,b7,9,11,13 = dominant thirteenth chord
A-C-E-G-B-D-F = 1,b3,5,b7,9,11,b13 = minor eleven flat thirteenth chord
B-D-F-A-C-E-G = 1,b3,b5,b7,b9,11,b13 = minor eleven flat thirteen flat nine flat five chord
(where each 1 refers to the bottom note of the respective chord)

So harmonizing the C major scale in 3rds and creating 13th chords, we find the following (in C):
C major thirteenth - D minor thirteenth - E minor eleven flat thirteen flat nine - F major thirteen sharp eleventh - G dominant thirteenth - A minor eleventh flat thirteenth - B minor eleven flat thirteen flat nine flat five.

We often use abbreviations for chord names. The following are commonly used:

For major thirteenth chords: maj.13. Also used though not feasible with this font are a greek letter delta (a triangle) after the letter before 13, or M13.

For dominant thirteenth chords: dom.13 or 13 are written after the letter.

note: although there are many types of thirteenth chords, the one referred to without a qualifier is the dominant thirteenth chord. So if I say to you, "play a 'G thirteen' chord" then that chord would be a dominant thirteenth chord, written as G13. If instead i want you to play a 'G major thirteen chord', Gmaj13, I must specify the word major before the thirteen, to let you know that i am talking about a major thirteenth chord rather than a dominant thirteenth chord. I bring this up so that you'll not be confused, or confuse others, and because i've been loosely using the term thirteenth chords to discuss a broad range of chords having a root, some third, some fifth, some seventh, some ninth, and some eleventh, and some thirteenth.

For major thirteen sharp eleventh chords: maj13#11

For minor thirteenth chords: m13 or -13 (ex. Cm13, C-13).

For minor seven flat thirteen flat nine chords: m11b13b9

For minor eleven flat thirteen flat nine chords flat five: m11b13b9b5, m11-13-9-5.

So looking back above we can say we have the following chords (in C):
Cmaj13-Dm13-Em11b13b9-Fmaj13#11-G13-Am11b13-Bm11b13b9b5

We recall that we can keep this in context but not refer to a specific key by using roman numerals. Then we get:
Imaj13-ii13-iii11b13b9-IVmaj13#11-V13-vi11b13-vii11b13b9b5

Recall that the relative minor contains the same notes (and therefore the same chords) as its relative major scale/key in the same order but starting on a differnet note.

The relative minor of C major is A minor, so we have the notes:
A-B-C-D-E-F-G-A, and the chords: Am11b13-Bm11b13b9b5-Cmaj13-Dm13-Em11b13b9-Fmaj13#11-G13

These are the same chords as above but in a different context. we can see the change in context by changing to roman numerals, we get:
i11b13-ii11b13b9b5-bIIImaj13-iv13-v11b13b9-bVImaj13#11-bVII13

So we we create progressions from the two listings of chords that would go well with the major and minor scales respectively.

OMITTED NOTES/ SLASH CHORDS

It's not possible or convienient sometimes to play every note of a chord as we add more extensions. Since most guitarists play 6 string guitars, it is not possible, generally to play 7 notes at once making complete 13th chords more of a theoretical construct than a playable structure (of course we could do it with arpeggios). We can omit notes, and often do for larger chords.

Generally the 5 is the 1st interval to go, and i would suggest removing it first unless it has been altered (Try not to remove a #5, or b5). After the 5, the 4 is usually removed unless it has been specified (don't remove the 4 if it has been altered or it is an 11th chord). Next the 9, unless it has been specified in the chord (don't remove the 9 if it is a 9th chord or if it has been altered). One could also remove the root note, especially if playing with another player who could emphasize the root note ( a bassist, pianist, or another guitar player).

Sometimes, we see slash chords with extensions after the slash. What this is saying is play the Chord before the slash and add the particular extension.

ex.
m7/11 is the minor seven chord with the 11 added. (m7/11 = 1,b3,5,b7,11 )
6/9 is the major6 chord with the ninth added. (6/9 = 1,3,5,6,9 )

Ok. The upcoming lessons will cover the 5 ninth chords above. We'll discuss ways to create "altered" chords. Eventually i'll post lessons on 11th and 13th chords covered above, as well as alternate harmonization schemes and chords from other scale families (besides the major scale and it's modes).

Until then,
Peace,
Christopher Roberts
snglstringtheory@aol.com


How do I change all those numbers to letters (for notes, chords, etc.)? Here's a transposition chart simianmoon.com/snglstringtheory/guitar/8theory3.html

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Last updated August 15, 2002
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