Intervals Series Part 4: The Complete Interval List

 

At this point the list below should look familiar and you should understand what it represents. If not please see the previous lessons in the series.

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

We've taken a long time to get here but now we can see the two octave Interval relationship of all the notes of a Major scale in one octave.

Well, that's fine and dandy for the notes of a Major scale. But, the Major scale doesn't account for EVERY note on the fretboard, or every note in the "Cycle of Notes". Remember the Chromatic Cycle of Notes? The scale made up of all Half-steps, all 12 notes on the fretboard, including the Natural Notes and the Enharmonic Notes!

The Cycle of Notes accounted for every note, the Natural Named Notes (A, B, C, etc...), and the Sharped and Flatted Notes (A#/Bb, C#/Db, F#/Gb, etc..)...

So, what are all of those other notes in relationship to a Root?

Well, just as we understood in the Cycle of Notes that we could take a Natural Named Note (like A, B, C, D, etc..) and sharped or flatted it to be Enharmonic (like A#/Bb, D#/Eb, etc...) we can also use the same principle when dealing with the Interval Names (M3, 5, 13, M7, etc...).

We've already done a bit of this in the last lesson. Remember how we took the M3, flatted it by one Half-step and got b3? Remember how we took the M7, flatted it by one Half-step and got b7?

Well we can apply that basic idea to the Interval names. And, some of them are even Enharmonic in a sense that they can have two name even though they are the same note, or fret.

Let's draw out a Chromatic Scale starting with C:

C     C#/Db     D     D#/Eb     E     F     F#/Gb     G     G#/Ab     A     A#/Bb     B     C ...and you could repeat it forever.

Now let's redraw it again using some of the Interval names in relation to the Root of C:

Note Name:       C        C#/Db      D       D#/Eb       E       F      F#/Gb      G       G#/Ab      A       A#/Bb       B       C
Interval Name:    R                       2/9                      M3   4/11                    5                      6/13                    M7      R

You can see that even though we've covered a lot so far, there are still quite a bit of notes left. And, we'll need to show how those notes relate to the Root.

Well, in our previous lesson we saw that flatting the M3 and the M7 gave us a b3 and a b7, respectively.

So, lets redraw the scale again including these two Interval Names:

Note Name:      C      C#/Db      D      D#/Eb      E        F      F#/Gb      G      G#/Ab      A      A#/Bb      B      C
Interval Name:   R                     2/9        b3        M3    4/11                    5                     6/13      b7        M7     R

Well now, it's starting go to fill up, and we really haven't learned anything new yet, we've just put things into a perspective that people use when dealing with Interval Names.

We only have three more Intervals to name.

If you've ever seen larger "extended chords" in a song chart, one thing you've never seen is something like: C#root, or CaddC#, or maybe this one Cmaj#root, etc...all of these are referring to a C Major chord with a C# note in the chord. While a chord like this can exist, it isn't written like I just did.

But if we take the 2/9 and flatten it we can get a b2/b9 Interval Name. So, in relationship to the C note, C#/Db is known as the b2 or the b9, or b2/b9.

So, in my goofy examples two paragraphs above, those chords could be written out as: Caddb9, or Cmajb9. More on these names later.

That covers the note between the Root and the 2/9. It's a b2/b9.

The next note to deal with is the note between the 4/11 and the 5. Well, this Intervals name is going to essentially be Enharmonic. If we remember, Enharmonic is a note that can have two names but both can be the same note, or at the same fret.

So, the note between the 4/11 and the 5 could be #4/#11 or b5.

Ok, two down.

The last unnamed Interval is between the 5 and 6/13. This is another Interval that can be considered Enharmonic. This Interval can be #5 or b6/b13.

Now again, lets redraw the list of Intervals adding these new Intervals in relationship to the C note:

Note Name:      C      C#/Db      D      D#/Eb       E         F           F#/Gb       G         G#/Ab           A      A#/Bb      B      C
Interval Name:   R       b2/b9     2/9        b3         M3    4/11     #4/#11-b5     5       #5-b6/b13      6/13      b7        M7     R

WOW! We've come a long way.

Now if you see a chord formula like this:

Cmaj#11 = R M3 5 M7 9 #11

You'll be able to look at the Chromatic Interval Name list and decipher the notes that are in the chord when C is the Root.

You'd have:

Cmaj#11 = R    M3    5    M7   9    #11
                  C     E      G     B    D      F#

Wow! A six note chord! Cool!

How about this formula and then the notes:

Cmaj13/#11 = R    M3     5    M7    9     #11    13
                       C      E      G     B     D       F#       A

Wow! A seven note chord! Cooler!

More on the actual Formulas later.

The Chromatic Interval Names are the basis of what every chord formula uses. And, by knowing these Interval Names and memorizing Chord Formulas, you'll be able to look at any chord, know what Intervals are in it, and based on the Root find what notes the Intervals are.

Ok, you think you're at the finish line? We'll not quite, but if you are with me so far you are in the home stretch.

If you understand things so far the rest we'll be kind of common-sense.

I want to look at a few other notes and their Enharmonic functions: the b3, M3, and 6/13.

In some cases these three notes could function as other Interval Names, such as:

the b3 could equal a #2/#9. This happens if a chord formula is a Major chord but also has a note in it a Half-step below the M3. In a Major chord you won't have a M3 and a b3, you'd have a M3 and a #2/#9.

the M3 could equal a b4/b11. This happens if a chord formula is a Minor chord but also has a note in it a Half-step above the b3. In a Minor chord you won't have a b3 and a M3, you'd have a b3 and a b4/b11.

the 6/13 could equal a bb7 (double-flatted 7). This Interval Name is used when building a Diminished 7 chord. More on this later but, the Diminished 7 chords formula is: R b3 b5 bb7 and with this information and using the Chromatic Interval Name list you should be able to decipher the notes in the Formula for a Cdim7 chord:

Cdim7 = R b3 b5 bb7 = C Eb Gb A, respectively.

Now with these three additional Interval names, if we redraw the list things are going to get really crazy. This is what we get:

Note Name:      C      C#/Db      D       D#/Eb            E              F              F#/Gb         G          G#/Ab          A               A#/Bb      B      C
Interval Name:   R       b2/b9     2/9      #9-b3     M3-b4/b11    4/11       #4/#11-b5       5       #5-b6/b13      6/13-bb7        b7       M7     R


Ok, take a break...whew!

Ok, breaks over :)

Now re-read that list above, write it on paper 10 times, pick up your guitar and pick C as a Root and starting getting familiar visually with a frets relationship to C, and for the rest of your life...repeat this process over and over.

And, don't forget to listen to the notes against the Root as you'll develop audio recognition of Intervals. This is very important.

If you have a grasp on what was covered you are now ready to put it in real life practice and start building chords from Chord Formulas using the Chromatic Interval Names list.

 

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