Harmonizing the major scale (seventh chords)

Recall, last lesson we took the major scale and stacked it upon itself in 3rds to yield first intervals, and then triads (3 note chords).

Recall also that we determined the chords 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:
(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 below for the link to the lesson.

Recall, the following intervals (equivilencies):
major seventh (7) = 11 half-steps
minor seventh (b7) = 10 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).

Now, let us define 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).

Let us now define the 4 seventh chords we will 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

Note that both the major seventh chord and the dominant seventh chord contain the major triad (major chord) within them (from the root note), but they have different sevenths. Taking an arbitrary triad and adding a seventh note to it, we can create many more seventh chords. the 4 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 (7ths) using whatever method we prefer (familiarity with keys, transposition chart, rote memorization, counting 1/2-steps, etc.):
C to B = 7 (major seventh)
D to C = b7 (minor seventh)
E to D = b7
F to E = 7
G to F = b7
A to G = b7
B to A = b7

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

                      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 triad (the 5th) is the 7th. 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 = 1,3,5,7 = major seventh chord
D-F-A-C = 1,b3,5,b7 = minor seventh chord
E-G-B-D = 1,b3,5,b7 = minor seventh chord
F-A-C-E = 1,3,5,7 = major seventh chord
G-B-D-F = 1,3,5,b7 = dominant seventh chord
A-C-E-G = 1,b3,5,b7 = minor seventh chord
B-D-F-A = 1,b3,b5,b7 = half-diminished seventh chord
(where each 1 refers to the bottom note of the respective chord)

So harmonizing the C major scale in 3rds and creating 7th chords, we find the following (in C):
C major seventh - D minor seventh - E minor seventh - F major seventh - G dominant seventh - A minor seventh - B half-diminished seventh.

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

For major seventh chords: maj.7. Also used though not feasible with this font are a greek letter delta (a triangle) after the letter before a 7, or a delta without a 7 after it, or a seven with a line through it. Also sometimes seen are M7 and maj. after the letter.

For dominant seventh chords: dom.7 or 7 are written after the letter.

note: although there are many types of seventh chords, the one referred to without a qualifier is the dominant seventh chord. So if I say to you, "play a 'G seven' chord" then that chord would be a dominant seventh chord, written as G7. If instead i want you to play a 'G major seven chord', Gmaj7, I must specify the word major before the seven, to let you know that i am talking about a major seventh chord rather than a dominant seventh chord. I bring this up so that you'll not be confused, or confuse others, and because i've been loosely using the term seventh chords to discuss a broad range of chords having a root, some third, some fifth, and some seventh.

For minor seventh chords: m7 or -7 or just "-" after the letter (ex. Cm7, C-7, C-).

For half-diminished seventh chords: m7b5, m7-5, or a circle with a line through it after the letter before a 7.

So looking back above we can say we have the following chords (in C):

We recall that we can keep this in context but not refer to a specific key by using roman numerals. Then we get:

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: Am7-Bm7b5-Cmaj7-Dm7-Em7-Fmaj7-G7

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:

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

For example, Imaj7-ii7-iii7-IVmaj7 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 ii7b5-v7-i7. This would be a minor (scale) progression or an aeolian (mode) progression, and a minor scale starting on the same root note as i7 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). Take for example a minor 7th chord followed by a dominant 7th chord a perfect 4th higher. We find these two chords as being either ii7-V7 (in major) or iv7-bVII7 (in minor). If we consider it the first then we can find the key by going down a whole-step from the ii7. (this is a convenient way to approach jazz compositions)

Consider the following:

In a jazz context, I would note that there are 3 segments of ii7-V7 progressions (one of them being a ii-V-I cadence). so Fm7-Bb7 would be ii7-V7 in the key of Eb. Am7-D7 would be ii7-V7 in the key of G. and C#m7-F#7-Bmaj7 would be ii7-V7-Imaj7 in the key of B. So i might use key of Eb over Fm7-Bb7 (Eb-major, F-Dorian, Bb-Mixolydian, etc.). The key of G over Am7-D7 (G-major, A-Dorian, D-Mixolydian, etc.). The key of B over C#m7-F#7-Bmaj7 (B-major, etc.)

Many jazz players would use dorian mode over these progressions, and it becomes a matter of preference as to what type of mood you want to create over the changes. these are not your only options, but they are some inside (relatively safe) ones. I will discuss modes soon if you are not already familiar with them.

Here is a common jazz progression, where the old I becomes the new ii.


So here we have 3 ii-V-I progressions. which keys are they in? Answer at bottom of the page, but try to figure out for yourself to confirm the answers.

Ok. The upcoming lessons will cover the 4 seventh chords above, a lesson on inversions and voicings, and the modes of the major scale. then at some point (after going over the seventh chords), we'll return to harmonizing the major scale to get 9th, 11th, and 13th chords. this is done in the same fashion as triads (3 note chords), and 7th chords (4 note chords) by stacking 3rds to get 9th chords (5 notes), 11th chords (6 notes), 13th chords (7 notes). If you've understood the discussion so far, it's not a stretch to come up with 9th, 11th, and 13th chords built off the major scale.

Here are some definitions for the ambitious:
maj9 = 1,3,5,7,9
dom9 = 1,3,5,b7,9
m9 = 1,b3,5,b7,9
m7b9 = 1,b3,5,b7,b9
m7b9b5 = 1,b3,b5,b7,b9

maj11 = 1,3,5,7,9,11
maj9#11 = 1,3,5,7,9,#11
dom11 = 1,3,5,b7,9,11
m11 = 1,b3,5,b7,9,11
m11b9 = 1,b3,5,b7,b9,11
m11b9b5 = 1,b3,b5,b7,b9,11

maj13 = 1,3,5,7,9,11,13
maj13#11 = 1,3,5,7,9,#11,13
dom13 = 1,3,5,b7,9,11,13
m13 = 1,b3,5,b7,9,11,13
m11b13 = 1,b3,5,b7,9,11,b13
m11b13b9 = 1,b3,5,b7,b9,11,b13
m11b13b9b5 = 1,b3,b5,b7,b9,11,b13

The answer for the question above was
F#m7-B7-Emaj7 (key of E)
Em7-A7-Dmaj7 (Key of D)
Dm7-G7-Cmaj7 (Key of C)

Chris Roberts

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 December 31, 2002.
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