Alternate Harmonizations: harmonizations in 4's

Recall,
tertian harmonization harmonizes a scale by stacking it in 3rds.

|--------------------------|
|                       O  |
|--------------------O-----|
|                 O     O  |
|--------------O-----O-----|
|           O     O        |
|--------O-----O-----------|
|     O     O              |
|--O-----O-----------------|
      O
  -O-
C major harmonized in 3rds.

We then continue stacking 3rds to create triads, 7th chords, 9th chords, 11th, and 13th chords. (see http://simianmoon.com/snglstringtheory/chords/harmtri.html)
This is common way we are taught to harmonize but it is not the only way.

Today we consider what happens when we harmonize in 4ths instead of 3rds (there will be an upcoming lesson on harmonizing in 5ths.)

Confining ourselves to the major scale (and its modes) for the moment, we harmonize the C major scale in 4ths.

|-----------------------O--|
|                    O     |
|-----------------O--------|
|              O        O  |
|-----------O--------O-----|
|        O        O        |
|-----O--------O-----------|
|  O        O              |
|--------O-----------------|
      O
  -O-
  p4  p4 p4 a4 p4 p4 p4 p4
We see that notes except the 4th have a p4 (perfect 4th). The 4th position (sub-dominant) has an augmented 4th (a4). (discussion of intervals at http://simianmoon.com/snglstringtheory/scales/intervals.html)

Continuing we stack the next group of 4ths.

                        O
                    -O- --
                  O
|--------------O--------O--|
|           O        O     |
|--------O--------O--------|
|     O        O        O  |
|--O--------O--------O-----|
|        O        O        |
|-----O--------O-----------|
|  O        O              |
|--------O-----------------|
      O
  -O-
   1  1  1  1  1  1  1  1
   4  4  4 #4  4  4  4  4
   7 b7 b7  7 b7 b7 b7  7
Here the intervals stacked are the 1,4,and7.
Stacking 2 p4s gives us: 1,4,b7
Stacking a4 on top of p4 gives: 1,4,7
stacking a p4 on top of a4 gives: 1,#4,7.

Looking back at the harmonized scale in 4ths we see that the tonic is {1,4,7}, the 2nd,3rd,5th, 6th, and 7th are {1,4,b7}, and the 4th is {1,#4,7}. There is not a standard notation for these types of chords. One could use 7sus4(no5), maj7sus4(no5), and maj7sus#4(no5), but that's a lot to write for such minimal chords.

Applying to standard tuning (which is largely in 4ths) we have the following moveable shapes.

1,4,b7
X|---|---|---| X|---|---|---|  X|---|---|---|   |---|-O-|---|
X|---|---|---| X|---|---|---|   |---|-O-|---|   |---|-O-|---|
X|---|---|---|  |-O-|---|---|   |-O-|---|---|   |-R-|---|---|
 |-O-|---|---|  |-O-|---|---|   |-R-|---|---|  X|---|---|---|
 |-O-|---|---|  |-R-|---|---|  X|---|---|---|  X|---|---|---|
 |-R-|---|---| X|---|---|---|  X|---|---|---|  X|---|---|---|

1,4,7
X|---|---|---| X|---|---|---|  X|---|---|---|   |---|---|-O-|
X|---|---|---| X|---|---|---|   |---|---|-O-|   |---|-O-|---|
X|---|---|---|  |---|-O-|---|   |-O-|---|---|   |-R-|---|---|
 |---|-O-|---|  |-O-|---|---|   |-R-|---|---|  X|---|---|---|
 |-O-|---|---|  |-R-|---|---|  X|---|---|---|  X|---|---|---|
 |-R-|---|---| X|---|---|---|  X|---|---|---|  X|---|---|---|


1,#4,7
X|---|---|---| X|---|---|---|  X|---|---|---|   |---|---|-O-|
X|---|---|---| X|---|---|---|   |---|---|-O-|   |---|---|-O-|
X|---|---|---|  |---|-O-|---|   |---|-O-|---|   |-R-|---|---|
 |---|-O-|---|  |---|-O-|---|   |-R-|---|---|  X|---|---|---|
 |---|-O-|---|  |-R-|---|---|  X|---|---|---|  X|---|---|---|
 |-R-|---|---| X|---|---|---|  X|---|---|---|  X|---|---|---|

Continuing we stack another 4th on top for 4-note 4th chords.

                       -O-
                     O
                 -O- -- --
               O        O
           -O- -  - -O- --
         O        O
|-----O--------O--------O--|
|  O        O        O     |
|--------O--------O--------|
|     O        O        O  |
|--O--------O--------O-----|
|        O        O        |
|-----O--------O-----------|
|  O        O              |
|--------O-----------------|
      O
  -O-
   1  1  1  1  1  1  1  1
   4  4  4 #4  4  4  4  4
   7 b7 b7  7 b7 b7 b7  7
   3 b3 b3  3  3 b3 b3  3
maj7(4) = 1,3,4,7
maj7b5 = 1,3,b5(#4),7
7(4) = 1,3,4,b7
m7(4) = 1,b3,4,b7

Looking at some shapes we find:

maj7(4)
X|---|---|---| X|---|---|---|   |---|---|-O-|
X|---|---|---|  |---|---|-O-|   |---|---|-O-|
 |---|-O-|---|  |---|-O-|---|   |-O-|---|---|
 |---|-O-|---|  |-O-|---|---|   |-R-|---|---|
 |-O-|---|---|  |-R-|---|---|  X|---|---|---|
 |-R-|---|---| X|---|---|---|  X|---|---|---|


maj7b5
X|---|---|---| X|---|---|---|   |---|---|-O-|
X|---|---|---|  |---|---|-O-|   |---|---|-O-|
 |---|-O-|---|  |---|-O-|---|   |---|-O-|---|
 |---|-O-|---|  |---|-O-|---|   |-R-|---|---|
 |---|-O-|---|  |-R-|---|---|  X|---|---|---|
 |-R-|---|---| X|---|---|---|  X|---|---|---|

7(4)
X|---|---|---| X|---|---|---|   |---|---|-O-|
X|---|---|---|  |---|---|-O-|   |---|-O-|---|
 |---|-O-|---|  |-O-|---|---|   |-O-|---|---|
 |-O-|---|---|  |-O-|---|---|   |-R-|---|---|
 |-O-|---|---|  |-R-|---|---|  X|---|---|---|
 |-R-|---|---| X|---|---|---|  X|---|---|---|


m7(4)
X|---|---|---| X|---|---|---|   |---|-O-|---|
X|---|---|---|  |---|-O-|---|   |---|-O-|---|
 |-O-|---|---|  |-O-|---|---|   |-O-|---|---|
 |-O-|---|---|  |-O-|---|---|   |-R-|---|---|
 |-O-|---|---|  |-R-|---|---|  X|---|---|---|
 |-R-|---|---| X|---|---|---|  X|---|---|---|

Looking at the C major scale in 4-note chords (in 4ths), we have:
Cmaj7(4)-Dm7(4)-Em7(4)-Fmaj7b5-G7(4)-Am7(4)-Bm7(4)
if we use these chords for a progression
such as I-ii-iii-IV, we get:
Cmaj7(4)-Dm7(4)-Em7(4)-Fmaj7b5
and we could use the chords based on root note 5th string to get:

|---------------| 
|--5--6--8--10--| 
|--4--5--7--9---| 
|--3--5--7--9---| 
|--3--5--7--8---| 
|---------------| similar iseas are used in jazz.

Further extensions and comparisons with tertain harmonization.
If we consider the major scale:
major scale = 1,2,3,4,5,6,7
and then we look at which notes are added by successively stacking thirds we get:
1,3,5,7,9(2),11(4),13(6)
1,3,5,7,2,4,6.
And harmonizing in 4ths we get:
1,4,7,3,6,2,5.

The more notes we stack, the more the chords resemble the extended chords from other harmonization schemes.

Types of chords (all based on I) as an extra pitch is stacked.
C{1,4,7}, Cmaj7(4), Cmaj7/11(6), Cmaj13(no5), Cmaj13.

Where does one hear playing in 4th chords?
It's not common but I've heard both jazz players and some oriental (chinese) players. And if we include just 4ths (intervals, doublestops), then the number of genres dramstically increases, but we're not so I will give a few examples (in TAB), and a common jazz convention.

Jazz Convention
7th chords are at the basis of much jazz. jazz also makes use of more extensions. It's not possible to play full 13 chords on a six-string guitar (arps are possible), and the note that usually gets omitted first is the 5th. (which is probably being covered by the basist or pianist anyways).

A nice jazzy voicing for 7th chords is to stack them in 4ths (omitting the 5). Here we have voicings with a 7th and a 4th stacked on top of that (the 7th is 2 stacked 4ths).

maj7
X|---|---|---| X|---|---|---|   |---|---|-O-|
X|---|---|---|  |---|---|-O-|   |---|---|-O-|
 |---|-O-|---|  |---|-O-|---|  X|---|---|---|
 |---|-O-|---| X|---|---|---|   |-R-|---|---|
X|---|---|---|  |-R-|---|---|  X|---|---|---|
 |-R-|---|---| X|---|---|---|  X|---|---|---|


7
X|---|---|---| X|---|---|---|   |---|---|-O-|
X|---|---|---|  |---|---|-O-|   |---|-O-|---|
 |---|-O-|---|  |-O-|---|---|  X|---|---|---|
 |-O-|---|---| X|---|---|---|   |-R-|---|---|
X|---|---|---|  |-R-|---|---|  X|---|---|---|
 |-R-|---|---| X|---|---|---|  X|---|---|---|


m7
X|---|---|---| X|---|---|---|   |---|-O-|---|
X|---|---|---|  |---|-O-|---|   |---|-O-|---|
 |-O-|---|---|  |-O-|---|---|  X|---|---|---|
 |-O-|---|---| X|---|---|---|   |-R-|---|---|
X|---|---|---|  |-R-|---|---|  X|---|---|---|
 |-R-|---|---| X|---|---|---|  X|---|---|---|
Note: this does not serve well with altered 5ths (7b5, m7b5, dim7,maj7#5, etc.)

Try the following: (ii-V-I)

|-----------|-----------|
|--8-----7--|--6-----5--|
|--7--6--6--|--5--4--4--|
|-----5-----|-----3-----|
|--7-----5--|--5-----3--|
|-----5-----|-----3-----|

Oriental Music
We'll consider a faux oriental sound, as we're not looking to seriously study chinese or gamelan music at this time.

Consider the pentatonic major scale, and the 4ths that occur in it.
C-maj-pent. = C,D,E,G,A.

|--------------------|
|                    |
|--------------O-----|
|           O     O  |
|--------------------|
|        O     O     |
|-----O-----O--------|
|                    |
|--------O-----------|
      O
  -O-

Throwing in the 4th (F) when using C, we can create a faux-Oriental sound such as

|---------------------------|
|---------------------------|
|--------2--5--7--7--10--5--|
|--3--5--2--5--7--7--10--5--|
|--3--5---------------------|
|---------------------------|
We could try using Kumoi or another pentatonic scale as well, such as hirojoshi. But Pentatonic major works well for this kind of sound.

Next lesson on Harmonizations in 5ths.

Peace,
Christopher Roberts
snglstringtheory@aol.com


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 March 11, 2004
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