Intervals Series Part 2: Naming Intervals in Scales and Chords

 

When talking about chords people use the terms Root, Major 3rd, Perfect 5th, Flat 7th, etc...

What is that all about?
 

When chords are built they are built in relation to the notes of a Major scale. While these notes/chords are simply groups of Intervals they are still related 
to the Interval Structure of the Major scale.

In reality, chord building is as easy as counting notes in the Major scale. But let's see if I can explain the 'names' of the Intervals in relationship to the 
Major scale.

All examples will be from the C Major Scale. But as you know and will see further with Intervals, this could be moved to any Major scale replacing the notes of the C Major Scale with the notes of any Major Scale.

Let's look at a C Major scale:

C  D  E  F  G  A  B  C

Let's look at the Interval Relationship between the notes in the C Major Scale:

C    D    E    F    G   A   B    C
  \   /  \   /  \  /  \  /  \  /  \  /  \  /
   W   W   H   W  W  W   H

Every Major scale has the same series of Intervals, regardless of the starting point. This series of Intervals in the Major scale make up the "Major Scale Formula".

All Major scales will have the Intervals: W W H W W W H from starting note to end. So, if you start on an A note, making it an A Major Scale and you use the W W H W W W H Major Scale Formula starting on A, you get the notes: A B C# D E F# G# A.

So again, it's important to realize that even though we are looking at examples from the C Major Scale, this information is directly related to every other Major Scale. Because Interval Structure never changes in the Formula, it's a static Formula of Intervals.


Now let's give each of the notes in the C Major Scale numbers:

C  D  E  F  G  A  B  C
1   2   3  4  5   6   7   8

But wait, C is 1 AND 8...actually no. When C is repeated again it is still 1, like this:

C   D   E   F   G   A   B   C
1    2    3   4    5   6    7   1

Now with C being 1 again, everything repeats, basically like this:

C   D   E   F   G   A   B   C   D   E   F   G   A   B   C   ...continuously repeats itself, octave after octave.
1    2    3   4    5   6    7   1    2    3   4    5   6    7    1

The list above is the basic idea but, in chord building we take it one step further. All chords are built using a TWO OCTAVE Major scale, similar to what is 
listed above. The difference is the count doesn't go 1-7, then 1-7 again. It basically goes from 1-15 with a few modifications. But for simplicity sake let's 
look at it as 1-15 for right now. Like this (this is not the correct why to think of it but it will help us understand the correct way a little better):

C    D    E    F    G    A    B    C    D    E    F    G    A    B    C
1     2     3    4    5     6     7     8    9    10  11   12  13   14   15

Now let's fix one piece at a time. Since we understood the C was just 1 and not 1 and 8, let's make our first change:

C    D    E    F    G    A    B    C    D    E    F    G    A    B    C
1     2     3    4    5     6     7    1     9    10  11   12  13   14   1

So, we can see that C is now just 1, and not 1, 8 and 15 anymore.

Building chords is nothing more than counting EVERY OTHER note in a Major scale. Every other note is also three notes from the note you are on, IOW:

C   D   E   F   G   A   B   C   D   E   F   G   A   B   C   and we repeat again...

When including the C note can you see how E is 3 notes from C? When including the E note can you see that G is three notes from E, and so on? This relates to a term people use when building chords...Stacking Thirds. Which means 
playing/adding a 3rd on a 3rd on a 3rd, etc...or "stacking 3rd's"...stacking every third note on top of each other.

The other thing to notice here is that when you stack 3rd's and get back to the beginning (in this case C), you'll find you have used ALL the note that are in 
a Major scale (in this case the C Major scale). Look at it like this using the every third note we just listed:

C   E   G   B   D   F   A   C

We covered EVERY note in the C Major scale:

C   D   E   F   G   A   B   C

Hopefully you can see by using the scale in two octaves and counting every other note we actually account for every note in the scale.


Ok, so how does all this relate to Interval and Chord names?

For the note names we had the Cycle of Notes, right?

In chord building we have Chord Formulas. Chord formulas are made up of these 3rd's stacked on each other as I listed above.

There are are two primary Chord Families: Major Chord, and Minor Chords.

Each of these Families has a static formula that never changes. You'll see them in books and discussions listed like this:

Major chord = R M3 5
Minor chord = R b3 5


Now I need to show what the R, M3, b3, and 5 are relating to.

The Root equals the starting point, or foundation, of where a scale or chord is built from. In a C Major scale or a C Major chord, or a C Minor chord...the 
Root is C. C is the foundation, or the Root, or the home, or the starting point. Hopefully that makes sense.

The M3 is another name for "Major 3rd". The Major 3rd, or M3, equals the third note of the Major scale. If the Root of the C Major scale is C, then the third 
note , or the M3, is E. Just count from the Root to the third note of a major scale, this note is the M3.

The 5 in the formula is nothing more than the 5th note of a Major scale. If the Root of the C Major scale is C, then the 5th note, or the 5, is G. Just count 
from the Root to the fifth note of a major scale, this note is the 5.

It's as easy as counting the notes in the scale. Hopefully that makes sense.

Ok, well what's the b3 in the Minor chord then?

The b3 is another name for flatting/lowering the M3 by one Half-step. It can also be called the "Minor 3rd" because it is the "3rd" in a Minor chord. If you find the M3 in a Major scale and flat it by one fret, it's called the b3.

The Root and 5 of the Minor chord should be self-explanatory since they haven't changed, or don't change, when comparing a the Intervals of Major and Minor 
chords.

The only thing that changes between the Major and Minor chord is the 3rd. The 3rd is a M3 in the Major chord and the 3rd is a b3 in the Minor chord.

Ok, that was an example of using some of the Intervals we've been working with, and how they are used in a common application, Major and Minor chords.

Now on to the other notes...

When we create the basic Major and Minor chords we end up with a three note chord. The three note chord is also called a "Triad". So, you can call them a 
Major chord or a Major triad, or you could have a Minor chord or a Minor triad.

On the guitar you can play a common Open E Major Chord using six strings, but remember the Major chord ONLY has three note in it. Hmmm, six strings, an E 
Major chord, only three notes in the chord...now I'm confused...

In the case of the basic triad: regardless of what octave you play the Root, the M3 or b3, or 5th in, they are still the R, M3, b3, and 5. These are the notes 
that develop the basic Major and Minor chords and the formulas.

Notice in an open C chord we can play six strings but are really only playing three note names:

high --0-- = E = M3
        --1-- = C = R
        --0-- = G = 5
        --2-- = E = M3
        --3-- = C = R
low  --3-- = G = 5


This shows the chord fingering, the names of the note we are playing, and the Interval relationship based on the Root of C. It also shows that the C 
Major chord is made up of only three note names: C E G = R M3 5.

So, with this information let's redraw the list of notes/Intervals. We will renumber all the E's to 3 and all the G's to 5, regardless of what octave they are in:

C    D    E    F    G    A    B    C    D    E    F    G    A    B    C
1     2     3    4    5     6     7     1    9     3   11   5    13   14    1

So in C, regardless of where we find a C, E, or G...they are the R, M3, or 5 of the scale/chord, regardless of whether or not they are in the same octave.

We're getting there, just a couple of more steps

The next basic level of Chord Families is the "7" or the "Extended Chord Families[/b]

This is another "foundation"/Chord Family that all chord are based on. This will move us from a three note triad to a four note chord. And, this is the 
beginning of what are called "Extended Chords".

If you've understood this tutorial so far, and understand the triad type Major and Minor chords...then you only have to add one more note into the mix. And, 
the new note is the next note when stacking thirds.

So, for a C Major chord we have the First, third, and fifth note of the scale. To make a "7" type chord we now add the Seventh note to the triad. So with C as 
the Root of the Major scale we'll have:


C    E    G    B
R   M3   5    7

This formula equal a Cmaj7 chord (spoken as 'C Major 7'). And, regardless of the Root note, the formula for ANY maj7 chord will always be:

maj7 = R M3 5 M7

I labeled the 7 as a M7, or a "Major 7"...because it's the seventh note of the Major scale.

Here's the formulas for the Extended Chord families, there are three of them:

maj7 (Major 7) = R M3 5 M7

m7 (Minor 7) = R b3 5 b7

7 (Dominant 7) = R M3 5 b7

You're familiar with the Intervals listed in the formulas, except for maybe the b7. But, if you remember how we got a b3 by flatting the M3 by a Half-step, 
you can assume the b7 is the M7 flatted by a Half-step...and your assumption would be correct.

Something to note about these three Extended Chord Families is, The Root and 5th are the same in each formula, it's the 3's and 7's that are changing.

Another way to look at them is:

1. The maj7 has a Major triad with the M7 added.

2. The m7 is a Minor triad with the a b7 added.

3. The Dominant 7 has a Major triad with a b7 added.

The Dominant 7 chord has a little of both worlds, doesn't it? More on this in a future lesson.

Just as we saw in the triad, regardless of what octave the R, M3, and 5 are in...the same is true for the 7 note. So, with C as the Root of the scale or a 
chord, the B note would always be considered the M7, or Bb would be considered the b7.

So, let's redraw the list of Intervals in the C Major scale again, now showing the B note as a 7...always:

C    D    E    F    G    A    B    C    D    E    F    G    A    B    C
1     2     3    4    5     6     7     1    9     3   11    5    13   7     1

And, I'll redraw it one more time using the "M" signifying "Major".

C    D     E     F     G     A     B     C     D     E     F    G    A     B    C
R     2    M3   4     5      6     M7   R     9     M3  11   5    13   M7   R

Now we can see that the R, M3, 5, and M7 are consistent throughout the scale, regardless of what octave they are in.

The next lesson will take the Interval numbering/naming even further.

 

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