Buy Modalogy Preview Modalogy Modalogy Home Modalogy Reviews Ask the Modalogists More Books

To submit a question, click here:



Perfect Chords

Type of stable chord that can "stand alone" in isolation without regard to either the previous or subsequent chord,
ie. without any harmonic or temporal reference.

All perfect chords (those built by stacking alternating quality thirds) are inherently stable, other thirds-stacking patterns are not.
The maximum number of notes in a perfect chord is 7.
· All perfect chords can be derived from radially symmetric structures.
   ∑ The relative majors of perfect minor chords are also perfect.
   ∑ Supersets of perfect chords constructed by adding the alternate quality third to either end of the chord also results in a perfect chord.
   ∑ Preserving the root and select components, subsets of perfect structures also remain stable.


In addition to the perfect chordsí other attributes, the greater structures possess interlocking P5 pairs

1-5, 3-7, 5-9, 7-#11, 9-13

or

1-5, b3-b7, 5-9, b7-11, 9-13

 

 

The Perfect Chords

 

RS


type 1

C major

 |
C | E
M3
|
   


type 2

E minor

|
E | G
m3
|
   



type 1

Am7 & C6

|
A C | E G
m3 M3 m3
|
   


type 2

Cmaj7

|
C E | G B
M3 m3 M3
|
   



type 1


Fmaj9#11

|
F A C | E G B
M3 m3 M3 m3 M3
|
   


type 2

Am11 and
Cmaj13 (no 11)

|
A C E | G B D
m3 M3 m3 M3 m3
|
   

 


both type 1 and type 2
 

Dm13 & Fmaj13#11

|
D F A C | E G B D
|
m3 M3 m3 M3 m3 M3 m3
|

|
  A C E G B D F# A
|
m3 M3 m3 M3 m3 M3 m3
|

Am13 & Cmaj13#11
    
 

 


"not" RS


min

A C E
m3 M3
 


maj

C E G
M3 m3
 



The minor / Major Dichotomy
The two primary and two secondary consonants
of the D centric pentatonic scale:


axis
|
a  c | e  g

A C E g

a C E G

a  c | e  g

axis
 


Of all the possible five chord roots in this RS pentatonic set,
only two are capable of producing a triad:

A (A C E) and C (C E G)

 

 

Minor Triad and Major Triad Combined

  axis
   
|
     
R
b3
|
3
5
m3
h
m3
   
|
     
  axis


 


"Relatively Stable" RS Chords


Out of all the 14 permutations of four stacked major and minor thirds (see addenda to this article), there are only two structures which possess radial symmetry:

The 9th chord and the mM9

 

The 9th chord

The RS stacking pattern {M3 m3 | m3 M3} forms the "dominant" 9th chord:


axis
|
G
B
D
F
A
M3
m3
|
m3
M3
|
axis


Although the harmonic series is not radially symmetrical itself (because it goes up and up and up), its lower harmonics generate a radially symmetrical structure (the 9th chord).

Along with the 9th chordís RS and its intimate relationship with the natural harmonic series, it is also interesting because it has the complementary attributes of being capable of either acting as a force of tension for propelling forward circular motion [not stable] or simply remaining at rest [stable] (ie. its tritone can be regarded as either functional or non-functional [as with its little brother the 7th]).

 

The 9th chord may function as:

Dominant V (major & composite minor) / Secondary Dominant (V of x),

Or as the tonic of a mixolydian (for example).

 

Since this chord is not a member of the set of "perfect" chords, it is not categorized as "inherently" stable. Its dual nature prevents this anyway (unstable sometimes and stable sometimes).

 

 

The mM9 chord

When encountering the "mM7" as a final chord in a piece, many jazz musicians interpret that symbol to mean "play a mM9".

In Levineís "Jazz Theory" book (pg 77), he states that the R b3 5 7 9 (aka "mM9") are the characteristic notes of the jazz minor.


The mM9 chordís radial symmetry

axis
|
G
Bb
D
F#
A
m3
M3
|
M3
m3
|
axis

 

The mM9 chord (the 9th chordís "mirror", eg. {M3 m3 | m3 M3} vs {m3 M3 | M 3 m3}) is also not a perfect chord, so itís not "inherently" stable.

There is, without a doubt, some "clashiness" within this chord.

To many, the mM7 sounds harsher than the mM9. The presence of the 9th degree mellows out the clashes some.

 

 

Both the 9th and mM9 chords can be described as radially symmetric mirrored triads,
conjoined and centered at D:


G9

Dm
G

|
G B D F A
M3 m3 | m3 M3
|
   


GmM9

D
Gm

|
G Bb D F# A
m3 M3 | M3 m3
|
   

 

 

Compare:



G9

Dm
G

G B D F A
M3 m3 m3 M3
 



Gmaj9

D
G

G B D F# A
M3 m3 M3 m3
 

 
Gm9

Dm
Gm

G Bb D F A
m3 M3 m3 M3
 


GmM9

D
Gm

G Bb D F# A
m3 M3 M3 m3
 



Note the stable triads both top and bottom in all the above 4 structures.

 

 

The First Level RS Quintal

|
G      D      A
|


The central axis D note and its two primary consonants G and A (first level of radial symmetry) are constant in each of the four unique pentads analyzed here
.

The unifying factor in this remarkable family of four-interval tertian chord structures is the two conjoined stacked P5s quintal.

The only variables are the permutations of the respective qualities of the thirds and sevenths that can be inserted into the underying stable quintal foundation.

axis
primary consonant
|
primary consonant
G
D
A
|
|
|
G
B
D
F
A
G
Bb
D
F
A
G
Bb
D
F#
A
G
B
D
F#
A
G
B
D
F
A
|
|
|
G
D
A
primary consonant
|
primary consonant
axis


None of the other "four-interval tertian pentads" exhibit these characteristics.

The radially symmetrical stable quintal formed by the two conjoined P5s (G-D | D-A) greatly contributes to the perceived relative stability of the 9th and mM9 chords.

 

Alternate Visualization

Stable Quintal Frame

Quintal Frame

Gm9

Gm9
 

Gmaj9

Gmaj9
 

G9

G9

GmM9

GmM9



ADDENDA TO THIS ARTICLE


(back to top)


To submit a question, click here.

Buy Modalogy Preview Modalogy Modalogy Home Modalogy Reviews Ask the Modalogists More Books

MODALOGY.NET © MMXI