2008 week 14 lesson: Tertachords and where they exist in almost every common scale

[gennation]

Part 1:

 

Introduction to the Tetrachords...

 

The Wikipedia definition:

 

 

Traditionally, a tetrachord is a series of four tones filling in the interval of a perfect fourth.

 

 

So, a Tetrachord will have ONLY four notes and they will all be BETWEEN a Root and the 4th.

 

What does this mean to you? You will soon find out, but it's meant A LOT to A LOT of people over the years.

 

The fundamental concepts are two different types of Tetrachords, the Major Tetrachord and the Minor Tetrachord.

 

The Major Tetrachord:

 

Interval Names = R 2 M3 4

Interval spacing = W W H

C Major Tetrachord = C D E F

 

The Minor Tetrachord:

 

Interval Names = R 2 b3 4

Interval Spacing = W H W

C Minor Tetrachord = C D Eb F

 

The note names themselves are not so important as much as the idea and the Interval awareness, that you will soon realize.

 

The Major and Minor Tetrachords are the two fundamental Tetrachords. And, the ONLY difference is that the 3rd is a M3 in the Major Tetra and the 3rd is a b3, or m3, in the Minor Tetra. Other wise they each have the same R, 2, and 4.

 

To play them as a true chord on guitar is next to impossilbe unless you tune you guitar to soemthing other than Standard Tuning. The reason being is they all happen in the same octave and the four notes would need to "live" on two strings only. Since you can't play more than one note at a time on one string, there is no way to play the in standard tuning.

 

"Well if I can't play them as chords, what the hell good do they do me?"

 

Let's not worry about "the chords" right now, let's just focus on the Intervals themselves and exactly where you might already be using them, and may have been for a long time (without knowing it).

 

When we use these two types of Tetrachords in different combinations, these two 4 note "groups of Intervals", they are at the basis of MOST Western Music and it's most common theories.

 

If you've delved into Music Theory and never realized Tetrachords importance, or that they even existed, you are going to say "why the hell haven't I known this all along?"

[gennation]

Part 2:

 

Let's see how it fits in YOUR everyday life...

 

Let's take the fundamental reference to everything we call "Theory" in Western Civilization...the Major scale.

 

The Interval Spacing/Formula of the Major Scale is: W W H W W W H

 

Can you see TWO "W W H" sets in there? The "W W H" Interval group creates a Major Tetrachord...

 

the Major scale has TWO Major tetrachords.

 

Now notice this, there's a Whole-step between the highest note of the first one and the loweest note of the second one. So, if you look at the two sets like this: [W W H] W [W W H]. The Major scale is nothing but two Major Tetrachords stacked on top of each other with a Whole-step between them.

 

This is like saying, a Major Scale consists of a Major Tetrachord from the "Root" note, and a Major Tetrachord from the "5th" note. Many improvisers look at a Major Scale as Two Major Tetrachords, a 5th from each other.

 

Here's a C Major Scale "bracketed" into two Major Tetrachords:

 

[C D E F][G A B C]

 

That's a C Major Tetrachord and a G Major Tetrachord, but together they equal a C Major scale.

 

Notice the last one ends where the first one begins, containing the whole scale Root to Root.

 

Hopefully you can see that a C Major scale consists of a C Major Tetrachords AND a G Major Tetrachord, or two Major Tetrachords a 5th apart.

[gennation]

Part 3:

 

Ok, so we see what we get when we have two Major Tetrachords a 5th apart. Let's see what we get when we stack two Minor Tetrachords together the same way (I'll use D as the Root since I know they will contain no #'s or b's).

 

The other very important scale in Western Music is the Dorian scale, let's look at D Dorian's Note Names and Intervals Spacing.

 

D Dorian:

 

Note Names: D E F G A B C D

Interval Spacing: W H W W W H W

 

Can you see two sets "W H W" in there? And if you notice, there's a Whole-step between the two sets: [W H W] W [W H W]

 

The "W H W" Intervals create Minor Tetrachords...

 

the Dorian scale has TWO Minor Tetrachords.

 

So many improvisers look at a Dorian Scale as Two Minor Tetrachords, a 5th from each other. So, a Dorian Scale consists of a Minor Tetrachord from the "Root" note, and a Minor Terachord from the "5th" note.

 

Here's a D Dorian Scale "bracketed" into two Minor Tetrachords:

 

[D E F G][A B C D]

 

That's a D Minor Tetrachord and an A Minor Tetrachord. Which can also be thought of as two Minor Tetrachords a 5th apart.

 

Notice the last one ends where the first one begins, containing the whole scale Root to Root.

 

Hopefully you can see that a D Dorian scale consists of a D Minor Tetrachord AND an A Minor Tetrachord, or two Minor Tetrachords a 5th apart.

[gennation]

Part 4:

 

Ok, "blah, blah...", But, let me show you around a few other VERY common scales in Western Music. Hopefully by now you can "see" or hear Tetrachords, so I'll try and make these other scales short now that you have the idea...but these scales are just as important.

 

So far we've seen "major on major" and "minor on minor" Tetrachords a 5th away. What happens if we start mixing things up???

 

1. Let's take a Major Tetrachord and a Minor Tetrachord a 5th apart (I'll use G since I know it won't contain any #'s or b's):

 

G Major Tetra = G A B C

and a 5th higher...

D Minor Tetra = D E F G

 

The Note Names we get are: G A B C D E F G

The Interval Spacing is: W W W H W W H W

 

This equals a G Mixolydian Scale!

 

So a Major Tetra and Minor Tetra a 5th higher equals a Mixolydian Scale.

 

2. Let's take a Minor Tetrachord and a Major Tetrachord a 5th apart (I'll use D since I know it will contain a minimal amount of #'s or b's):

 

D Minor Tetra = D E F G

and a 5th higher...

A Major Tetra = A B C# D

 

The Note Names we get are: D E F G A B C# D

The Interval Spacing is: W H W W W W H

 

This equals a D Melodic Minor Scale!

 

So a Minor Tetra and Major Tetra a 5th higher equals a Melodic Minor Scale.

[gennation]

Part 5:

 

Now remembering the definition of Tetrachords:

 

Traditionally, a tetrachord is a series of four tones filling in the interval of a perfect fourth.

 

We can see that the Major and Minor Tetrachords are not the only tetrachords since flatting the 2 (b2) of either the Major or Minor scale STILL create a Tetrachord by definition. Let's call it a "Major b2 Tetrachord" and a "Minor b2 Tetrachord".

 

Adding these into the mix, we arrive at these combinations creating many of our other common scales:

 

A Major b2 Tetra and a Major b2 Tetra a 5th higher = Double-Harmonic scale

 

A Minor b2 Tetra and a Minor b2 Tetra a 5th higher = Phyrigan Scale

 

A Major b2 Tetra and a Minor b2 Tetra a 5th higher = Phrygian Dominant Scale

 

A Minor b2 Tetra and a Major b2 Tetra a 5th higher = I'm going to let you find the name to this one on your own

 

Now combine the regular Major and Minor Tetra's with the Major b2 and Minor b2 Tetra's, us get even more familiar scales:

 

A Minor Tetra and a Major b2 Tetra a 5th higher = Harmonic Minor

 

A Major Tetra and a Minor b2 Tetra a 5th higher = Mixolydian b6 (5th Mode of the Melodic Minor scale)

 

A Minor b2 Tetra and a Minor Tetra a 5th higher = Dorian b2 (2nd Mode of the Melodic Minor)

 

A Major b2 Tetra and a Major Tetra a 5th higher = I'm going to let you find the name to this one on your own

[gennation]

Part 6:

 

As you can see, these Tetrachords a 5th apart are the building blocks of SO MANY of our day to day scales. And by understanding them you can even put together a few of the "crazier" scales, Invervals, and sounds for youself.

 

The scales in that last section are definitely used but their use, at least in Western Music, is more minimal compared to the common Major, Dorian, Mixolydian, Harmonic Minor, and Melodic Minor. But, none the less they can still be broken down to two Tetrachords.

[gennation]

Part 7:

 

Learning to use Tetrachords in solo'ing is easier by starting with the Common scales.

 

For instance, a lot of guitarist will solo using a Major Scale played up and down for a riff. To start using Tetrachords for solo, just take a pause between the 4 and the 5 of the scale. This translates to pausing between the "Root Major Tetra" and the "5th Major Tetra" chords.

 

Not only will you break one scale into two entities, you'll also break it into two "sounds". One, a secund scale based on the Root of the Major scale. Two, a scale directly related to the "tension" of the Major scale, starting on the 5th (V) and resolving to the Root (I) by way of the leading-tone (M7).

 

So, try this out...play a C Major or Cmaj7 vamp, "view" your scale from the 2nd Tetra chord (G A B C). You'll still have TWO Major sounds PLUS the Tension...one being the notes ARE from the Major scale...two being the G Major Tetra starts with a straight Major scale sound of it's own, and the last half-step created the tension to resolve to the Root of C.

 

Using it this way gives you "color". And, it gives you a line starting on something other than the Root, but is also a Harmony to the base Cmaj7 chord.

[gennation]

Part 8:

 

Some of the very common Dorian Modal lines start on the 5th (A) using an A Minor Tetrachord.

 

Even look at the main Bass line (the underlining theme) and many of Miles lines in So What...it finish simliar to this "A Tetra" to Root line:

 

 

Dm7

E----------------------------

B-----------------------------

G-------------9------7-----------

D---7--9--10-----10---------------------

A---------------------------------

E---------------------------------

 

 

The more you listen to Miles and especially Coltrane you'll find they start MANY lines on the 5th, or 2nd Tetra.

[gennation]

Part 9:

 

That explains quite a bit, I'll try and follow up with more solo'ing ideas. I ran into something about 3 years ago that opened my eyes big time. The closest common Theory piece I have found to explain it is the Tetrachords. If you delve into these let me know, because after you are fully acclimated...I have some serious stuff to show you that will open up even more doors.

 

Practice these from the view of two different scales you can use over a chord as opposed to one big scale (2 Tetra's v/s one Major, Dorian, Mixo, etc...). It'll help you separate out some sounds and break up that "scaley" sound.

 

Proceed through the next section for examples of placing and to help separate these sounds.

[gennation]

Part 10:

 

The Common forms

 

 

C Major Tetrachord (from the E String):

 

E---------------

B---------------

G---------------

D---------------

A---------7--8--

E--8--10--------

 

E-------------

B-------------

G-------------

D-------------

A-----5--7--8-

E--8----------

 

E---------------

B---------------

G---------------

D---------------

A-------------8-

E--8--10--12----

 

 

C Major scale:

 

C Maj Tetra + G Maj Tetra

 

E----------------|-----------------

B----------------|-----------------

G----------------|-----------------

D----------------|----------9--10-----

A----------7--8--|--10--12---------------

E---8--10--------|-------------------

 

 

C Minor Tetrachord (from the E String):

 

E---------------

B---------------

G---------------

D---------------

A-------------8-

E--8--10--11----

 

E-------------

B-------------

G-------------

D-------------

A-----5--6--8-

E--8----------

 

E--------------

B--------------

G--------------

D--------------

A---------6--8-

E--8--10-------

 

 

C Dorian scale:

 

C Min Tetra + G Min Tetra

 

E-----------------|-----------------

B-----------------|-----------------

G-----------------|-----------------

D-----------------|--------------10-

A--------------8--|--10--12--13-----

E---8--10--11-----|-----------------

 

 

[mugwump]

Good rundown. Very cool, Mike...

 

Thanks!

[Brewski]

I want you to know this stuff is great!! Please keep it up!!

 

 

 

That's a C Major Tetrachord and a G Major Tetrachord, but together they equal a C Major scale. Notice the last one ends where the first one begins, containing the whole scale Root to Root. Hopefully you can see that a C Major scale consists of a C Major Tetrachords AND a G Major Tetrachord, or two Major Tetrachords a 5th apart.

 

[Brewski]

Like this: [W W H] W [W W H]. The Major scale is nothing but two Major Tetrachords stacked on top of each other with a Whole-step between them.

 

Here's a C Major Scale "bracketed" into two Major Tetrachords:

 

[C D E F][G A B C]

 

So if you cut it up it would be notionally since the root is where you start:

 

[Cw Dw Ew Fh] [Gw Aw Bw Ch] works for me. seems kind of obvious once you put it on paper doesn't it?

 

minor tetra

 

C D Eb F or [RootWHW]