Week 5: 4th and 5th

Welcome back!

The fourth is quite the peculiar interval.  While the interval of a 4th doesn't appear as "material" until the mid sixties (if anyone can correct that statement, please do) and primarily (most awesomely) in the work of McCoy Tyner and Alice Coltrane.

the below just isn't for the keyboard players in the group....we all should be able to make our way on the piano.

In the key of C, they note F is a 4th away.  a Perfect 4th away.

The distance of a 4th is also the same as two whole steps (C - D , D - E) and one half step (E - F)



quickly, the interval of a 4th can be used as material much in the same way as the interval of a third--namely stacked:

C - F - Bb

Yes, it's a triad (a three note chord), but there is no third.  There is, however a dominant 7th--another story for another time.

If you dig the sound of two fourths stacked, then pass them through the progressions!  All four ways!

Also, try putting in an Augmented fourths--or space 3 whole steps!  (C - D , D - E, E - F#) both in the beginning:

C - F# - B

As well as in the middle

C - F - B

and why not...hold up...is that a 4th at the end?

C - F# - Bb

put them through all the progressions!  What do you have to loose?



The 4th, when paired with the diminished arpeggio sounds especially cool

C - F - C ... Eb - Ab - Eb ... F# - B - F# ... A - D - A ...

F - C ... Ab - Eb .. B - F# ... D - A ...

this "diminished material" is priceless....




The Fourth as progression is also priceless.  Movement by the interval of a 4th has been a mainstay in western music for at least 400 years. 

If you have heard of a progression called a "two-five-one" (or ii-V-I) you probably have heard of it in a context like "the ii-V-I is the most frequent heard three chords in Jazz" or something equally spectacular. 

Believe the hype and then some! 

Lets look at movement by 4th.

C  -  F  -  Bb  -  Eb  -  Ab  -  Db/C#  -  F#  -  B  -  E  -  A  -  D  -  G  -  (and back to) C

it is perhaps because one can start at any note, move in one direction by 4ths and end up at the original note, 11 notes later that this phenomena is given the name "circle" as in

THE CIRCLE OF FOURTHS

No matter--it could be called the hotdog-hamburger of 4ths--you just need to apply ALL MATERIAL to this progression (movement by fourths) until it is fluid.

C - B - C ... F - E - F .... Bb - A - Bb (etc)

D - C ... G - F ... C - Bb ... (etc)

C - D - C - B - C ... F - G - F - E - F .... Bb - C - Bb - A - Bb (etc)

D - B - C ... G - E - F .... C - A - Bb ... (etc)

D - C# - C ... G - F# - F ... C - B - Bb ... (etc)



Here's another completely and totally vital exercise! 

1.  Take 3 consecutive 4ths

     D  -  G -  C  

2.  play a minor triad on D

3. play a major triad on G and C

4 put that three note pattern through the progressions, following steps 2 and 3.

so...

Eb  - Ab  - Db  =  Eb minor triad ... Ab Major triad ... Db Major triad
E - A - D = E minor triad ... A Major triad ... D Major triad

and so forth.


Here is a similar sounding exercise which is of extreme mega importance.  Can you write the instructions?


D - E - F - D .... G - A - B - G .... C - D - E - C ..... then
G - A - Bb - G ... C - D - E - C ... F - G - A - F .....  then
C -  _ -  _ -  C  ... _ - G - _ -  _  ....   Bb - _  - D - Bb then
then
then
then........................



There is a CIRCLE OF FIFTHS as well.  It goes like this

C - G - D - A - E - B - F# - C #/Db - Ab - Eb - Bb - F - C

If you look carefully, you'll find it is the CIRCLE OF FOURTHS in the opposite direction. 

That said, you'll find (hear) a distinct difference when you play notes separated by a Perfect fifth as contrasted with notes separated by a Perfect fourth.

As with fourths, you can play fifths stacked on top of one another

C - G - D ... C# - G# - D# ... D - A - E ...

though that sound did not find it's way into jazz history, it could be it is a sound waiting to become a part of music history going forward.

do put it through all the progressions, give it all the treatment, go wild!


What I would like to point out about the 5th is that it is the "other end" of a triad.

If we look at a Major triad

C - E - G 

we see that the outer notes ( C - - G) are a Perfect 5th apart.

that is the same for the minor triad

C - Eb - G

It is not the same for the Augmented triad

C - E - G# 

(C - - G#) are an Augmented 5th apart

nor is it the same for the diminished triad

C - Eb - Gb

(C - - Gb) are a diminished 5th apart.

...but they are all the interval of a 5th.




Here's a super fun project for the Holiday break!

1.  Take a Major triad (C - E - G)
2.  Add a Major 2nd or, in this case a D  (C - D - E - G)
3.  Take that new material (C - D - E - G) and put it through the progression of movement by 4th

C - D - E - G ....  F - G - A - C ....  Bb - C - D - F ....  Eb - F - G - Bb

Next, do the same with a minor triad

1.  Take a minor triad (C - Eb - G)
2.  Add a Major 2nd or, in this case a D  (C - D - Eb - G)
3.  Take that new material (C - D - Eb - G) and put it through the progression of movement by 4th

Next, movement by 5th

Then, movement by minor 3rd (and heck, major 3rd too)

C - D - Eb - G .... Eb - F - Gb - Bb ... F# - G# - A - C# ... A - B -  C - E

Then, movement by whole step

Then, movement by half step .





These two materials (C - D - E - G) and (C - D - Eb - G) are of ultra mega central importance...as are all the many variations (C - Eb - F - G for instance) and permutations (like C - G - E - D)

We'll get deep into that situation upon your return!

Have a great holiday be safe and practice practice practice!

Week 4 = Week 3 again

In the last class, we ended by playing an Augmented, Major, minor and diminished triad, one after another.

We also noted how each triad was a combination of thirds stacked on each other (where M3 is a major third and m3 is a minor third)

Augmented = M3 + M3 = C - E - G#

Major = M3 + m3 = C - E - G

minor = m3 + M3 = C - Eb - G

diminished = m3 + m3 = C - Eb - Gb


we all unanimously decided it was an excellent idea to run through this material through all 12 keys.

Db - F - A
Db - F - Ab
Db - Fb - Ab
Db - Fb - Abb

D - F# - A#
D - F# - A
D - F - A
D - F - Ab

and so forth. 

It is an excellent idea if for no other reason than we will soon add a 4th note to the triads, and doing the same exercise.  If you have the first 3 notes under control, that 4th one won't pose any problem!




We also touched on the idea of moving each of these 4 triads through each of the progressions

1.  movement by half step C - E - G ... Db - F - Ab ... D - F# - A .... Eb - G - Bb  (etc)
2.  movement by whole step C - E - G ... D - F# - A ... E - G# - B (etc)

and, the newest addition, movement by minor third

C - E - G ... Eb - G - Bb ... F# - A# - C# ... A - C# - E
Db - F - Ab ... E - G# - B ... G - B - D ... Bb - D - F

(you can figure out the third one!)

Of course, you will also want to put the Augmented, minor and diminished through the same progressions.




Then, we touched ever so briefly on the fact that the triad itself can a progression.  This will make more sense in the weeks to come.  In the mean time, can you run the "material" through the triads?

C   -  E  -  G   -------> B - C  Eb - E  F# - G
where C - E - G is a major triad and we are preceding each note in the triad with a note a half step below.

remember preceding notes with a note a half step below?

Then there is C - B - C - D - C  -- E - D# - E - F# - E...................
OR IS THERE?
Does it sound right?

(does it sound right compared to what?)

compare!

C - B - C - D - C  ....  E - D# - E - F# - E  ....  G - F# - G - A - G

versus

C - B - C - D - C  ....  E - D# - E - F - E  ....  G - F# - G - A - G

if you had to describe in narrative form what the difference is between these two examples, what would you say?  (I would say something about the different use of whole steps and half steps based on starting note)


For now, let's use the 2nd example as our prototype, for all twelve keys

D - C# - D - E - D  ...   F# - F - F# - G - F# ... A - G# - A - B - A 





And minor?  compare

C - B - C - D - C  ....  Eb - D - Eb- F - Eb  ....  G - F# - G - A - G

C - B - C - D - C  ....  Eb - D - Eb - F - Eb  ....  G - F# - G - Ab - G

I'll let you choose!  For now!




Lastly, try practicing your triads like this:

C - E - G ... G# - F - C# ... D - F# - A ... Bb - G - Eb

as well as

G - E - C - C# - F - G#  ... A - F# - D ... Eb - G - Bb


and so on.




HEY!  You have already learned many of the intervallic movements in COUNTDOWN.  Now it's just a matter of committing them all to muscle memory.  Anyone (who is willing to work) can do that!

spoiler -- where this is all headed.

If you aren't getting what you want / need from me, just ask my best friend YOUTUBE for help.

Week 3: Minor and Major 3rds

Welcome Back!

This week we explore an interval that is central to our conception of "western music" and "Jazz" especially.

Unless you are a big fan of McCoy Tyner, listening to him exclusively, most of the music you hear in "the west" (from the 1600's to the present) is based on Tertian Harmony--that is, scales and chords based on 3rds.


There are two different Thirds.  The minor third and the Major third.  [If it isn't a convention in western music to capitalize Major and keep minor lowercase, it is in this course]


The interval of a minor third is the same as one whole and one half step.

W + H = m3  (whole step plus half  step= minor 3rd)

C - D (whole step) D - Eb (Half Step)

and so

The distance from C to Eb is the interval known as a minor third.  So is the distance from D to F (and so on)



The interval of a Major third is the same as two whole steps.

W + W = M3 (whole plus whole = Major 3rd)

C - D (whole step) D - E (whole step)

and so

The distance from C to E is the interval known as a Major third.  So is the distance from D to F#.



Getting back to the real world, your first task is simple, but not easy. Become fluent in playing notes a minor and major 3rd apart from one another!

Material: Minor Thirds!
Progression: Half steps

All four ways !

1.  "up and up"             C - Eb  ...  C# - E  ...  D - F  ...  Eb - Gb  ...  E - G   and so on --
2.  "down and up"        Eb - C  ...  E - C#   ...  F - D ...  and so on
3.  "up and down"        Eb - Gb ... D - F ...  C# - E ... C - Eb  and so on
4.  "down and down"   F - D ... E - C# ... Eb  - C ...  D ... F  and so on

guess what comes next?

Material: Major Thirds!
Progression: Half Steps

All four ways !

1. "up and up"             C - E ... C# - F ... D - F#  and so on
2.  "down and up"       E - C .... F - C# .... F# - D ... and so on
3.  "up and down"       C - E ... B - Eb .... Bb ... D  .... and so on
4.  "down and down"  E - C ... Eb - B .... D - Bb .... and so on


Can you put the same material through last week's progression?  Do you remember last week's progression?

Material:  Minor Third
Progression:  Whole Steps

All four ways!  And both scales!

1.  "up and up"               C - Eb ... D - F ... E - G ... F# - A  and so forth
                                       C# - E ... D# - F# .... F - Ab and so forth....
2.  "down and up"
3.  "up and down"
4.  "down and down"

Material:  Major Third
Progression:  Whole Steps

1.  up and up
2. down and up              E - C ...  D - Bb .... C - Ab ...  and so forth
                                      F - Db ... Eb - B ....  Db - A ...
3. up and down
4  down and down


remember: the aim of the game is first to memorize, then to play by reflex--without thinking, but by muscle memory.  that takes practice.  Hundreds upon hundreds of hours of practice. 






Now, what happens when we make a progression made of minor thirds?  We get this

1.  C  - Eb - F# - A - C

we also get

2.  C# - E - G - Bb - C#

we also get

3.  D - F - Ab - B - D

we also get

(1.)   Eb - F#....but wait, that's a repeat of the first one!

In sum, there are three progressions by minor third, all of which you must master--and by "master" I mean successfully run ALL the collected material thus far through these three progressions.  Because there are only three, you will do this in no time at all.

 for example

C - B - C ...  Eb - D - Eb ...  F# - F - F#
and so forth, all four ways, starting on C# and D as well.

then there was our ol friend

D - C# - C ....  F - E - Eb ....   Ab - G - F#

 and, more to the point, there was this one

B - C .... D - Eb .... F - F# ...  G# - A ...  B - C 

hold up...that's exactly like the H - W - H - W - H - W scale from last class!  We will talk more about this amazing coincidence in a later class.





In "Jazz" you might hear people use the word "vocabulary".  You might also hear people use the phrase "Music (Jazz included) is a language"

This material moved through this progression can be heard all through the history of Jazz, from the 40's (at least) to the present.  John Coltrane made handy use of this harmonic convention.

certainly you remember 

"note, down a half step, note, up a half step, note, up a whole step, note, down a whole step"
C - B - C - D - C

put that material through all three minor third progressions.




Then there was this one
 C - D - C - B - C 

put that material through all three minor third progressions 





Now...and this is not easy...some new material that utilizes the minor third!
D - B - C     F - D - Eb  (etc)

D - (down a minor third) - B - (up one half step) C

Analysis: We started a whole step above (D) our "target" (C) then we moved down a minor third (a whole step and a half step) to (B).


As well as putting that material through all progressions hitherto explored, make a special effort and put this material through all three minor third progressions 




This isn't easy either
B  - D - C    ..... D - F - Eb   (etc)

Put that material through all three minor third progressions






Now, consider this by now familiar progression:  C - Eb - F# - A - C

what if we did this

D - C ....  F - Eb.....  B - A ....   D - C ..... G# - F#  ..... B - A ....  F - Eb  ..... G# - F#





Our next  Progression is made up of minor thirds, but they aren't in the usual sequence.

1st                                                                              D - C ....... F - Eb 
2nd                                                             B - A ...   D - C
3rd                                       G# - F # ....... B - A
4th                       F - Eb.... G# - F#
5th        D - C..... F - Eb

Can you play it?  It sounds RAD!

Let's analize.

1.  note - down a whole step -
2.  note - up a minor third...from the previous (first) note
3.  note - down a whole step
4.  note - down a minor third...from that first note


We will continue to explore this one for weeks going forward. 








Now we must turn our attention to the effects of playing minor and major triads one after another.

Triads!

That the combination of Major and minor 3rds are what make triads is a great reason to make sure you have your 3rds under control on your instrument...and by under control I mean all progressions, all 4 ways, without mistakes.

moving on.....  

A "triad" is any three note chord (notes played at the same time.)  Horn players can also play triads, but they must play them in the form of an "arpeggio" --one note after another.

For now, we are going to concentrate on four types of triads.

1. Diminished.  minor 3 + minor 3 
        (or m3 + m3)
             ((or note - whole step plus half step - note - plus whole step plus half step - note))
                      C - Eb (minor third) or [C - whole step - D - half step - Eb]
                                Eb - Gb (minor third) or [Eb - whole step - F - half step - Gb]
thus and so, a C diminished triad i.e. with C as the Root = m3 + m3 = C Eb Gb.

"C dim" = C Eb Gb

Using this formula (or better yet, your EAR) play, learn, and internalize all 12 diminished triads.



2.  minor.  minor3 + Major 3
          C
             C up one m3 = Eb    (C to D to Eb)
                  Eb up one M3 = G  (Eb to F to G)
thus, a C minor triad = C Eb G

"Cmin" or "C-" = C Eb G

memorize, internalize.  Totally and completely essential foundational stuff. 


3.  Major.  Major + minor 3

Does anyone else find it interesting that construction-wise, the Major triad is the opposite of the minor triad...
     Major = M3 + m3
     Minor = m3 + M3
...especially so because minor and Major are thought to evoke opposite "feelings" in the listener.  Music in Major keys is"happy" while music in minor keys is "sad".

In any event,
        C
             C + M3 = E
                   E + m3 = G
"C maj" = C E G

know it like you know your own name, in all progressions, in all directions.


4.  Augmented.  M3+M3
Just minor and Major have opposite constructions, so does diminished and Augmented.  Does the diminished scale and the Augmented scale sound like "opposites" to you?
 
C
    C + M3 = E
        E + M3 =  G#

 "C aug" or "C+" = C E G#




NOW!  Are you ready for this one?  What if I told you triads are also their own "progressions"?

Check it!  C B C .... E D# E ..... G F# G ....C.  

Analysis:  Very early "material" put through a major triad progression!


Try putting all material, through all triads (48)!


If this is dizzying, don't worry.  We are going to go over all this (and more!) next week!

until then, can you hear any of our materials and progression on this fantastic album?