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Friday, February 1, 2019

155. PERTURBATING WITH AUGMENTED AND DIMINISHED CHORDS A DIATONIC SCALE OF CHORDS

(This post has not been written completely yet)

See also posts 36 and  153 for other types of perturbations of a diatonic scale of chords called harmonic personalities.

The concept of harmonic personality is a concept of chromatic tonal music and not a concept of multi tonal or atonal music. (See post 263 )

The resolution relation of two chords e.g. G7->C (or Bdim->C) suggests a general method of creating waves of tension with diminished or augmented chords  and relaxed resolution to minor or major chords. And this is done in a most familiar way with a scale of chords of a diatonic scale.

I, ii, iii, IV, V vi, vii I or 1M, 2m 3m 4M 5M 6m 7dim 1M

The perturbation is the next scale of chords



7dim 1M, 1# dim
2b dim 2m 2#dim
 3bdim 3m 3#dim
 4bdim 4M 4#dim
 5bdim 5M 5#dim
6bdim  6m  6#dim


or

7aug 1M, 1# aug
2baug 2m 2#aug
 3baug 3m 3#aug
 4baug 4M 4#aug
 5baug 5M 5#aug
6baug  6m  6#aug

and in general


7x 1M, 1# y
2bx 2m 2#y
 3bx 3m 3#y
 4bx 4M 4#y
 5b x5M  5#y
6bx  6m  6#y

with Abx=Abdim or Abaug and  A#x=A#dim or A#aug  for A=1,2,3,4,5,6 

Actually when for two successive chords X1 X2 with roots one tone apart in the diatonic scale of chords,one of them is minor, then the intermediate chord X2b  sounds better if it an augmented chord. While if both X1 X2 and major chords then  it sounds better if it is an diminished chord

This creates an abundance of alternatives in a improvisation in the "flow".

But we must not forget that the time spent in tension chords of diminished or augmented should in general be less than the time spent in the relaxing major or minor chords.

And we even may use as relaxing chords the power chords, that  are even more harmonic.

For improvisational solos, that fit harmonically to each the 3-notes minimal number of fret chords, in the guitar (mainly 4-courses string guitar), the simple rule of 2 only notes outside the notes of the chords plus all notes of the triad chord and duration of the note in the average about equal is a rule that works very well.


MORE HARMONIC PERSONALITIES BY PERTURBING  THE DIATONIC HARMONIC PERSONALITY

Starting from the diatonic harmonic personality in a sequence of chords in harmonic transitions (as if an arc of the wheel by intervals of 4 )we may create more harmonic personalities e.g.

1M->4M
2m ->5M
3m ->6m
4M ->7dim
5M ->1M
6m ->2m
7dim ->3m

We substitute all seconds parts with all minors and diminished or all majors and diminished 
The general rule is that we change the major to minor (or vice versa) but if the sound is better with a diminished or #diminished we prefer the 2nd choice.
e.g

1M->4M
2m ->5M or 5#dim
3m or 3M  ->6M or 6dim
4M ->7dim
5dim  or 5M ->1M
6m ->2M (or 2dim)
7dim ->3M

or

1M->4dim (or 4m)
2m ->5#dim
3m ->6m
4M ->7dim
5M ->1#dim
6m ->2m or (2dim)
7dim ->3m or 3dim


Which is in accordance with what we wrote in post 148 ,145 etc to obtain new scales of chords from connected arcs in the wheel by intervals of 4 and changing minors to majors or vice versa. Here the first column of chords remain with choices minors or majors as in the diatonic scale.


Triads of chromatic tonality that are often met and are based in one of the chromatic 7-notes scales the harmonic minor, the meapolitan and the double chromatic minor are the next

3M7-6m-2m  (harmonic minor)

7M7-3m-6m (Neapolitian)

6M7-2m-5m (harmonic minor)

All the three above triads (double harmonic minor)

2M7-5m-1m

5M7-1m-4m

1M7-4m-7m

4M7-7m-3m

Chromatic shifts of them by an interval of 2nd are e.g. the next

7M7-3m-6m->
1M7-4m-7m

Or 

1M7-4m-7m->
2M7-5m-1m

Or 

6M7-2m-5m->
1M7-3m-6m

Etc

Cycles of 6 chords in harmonic relations are the next 7

1M7-4m-7m->
3M-6M-2M

2M7-5m-1m->
4M-7M-3M

3M7-6m-2m->
5M-1M-4M

4M7-7m-3m->
6M-2M-5M

5M7-1m-4m->
7M-3M-6M

6M7-2m-5m->
1M-4M-7M

7M7-3m-6m->
2M-5M-1M




According to musicologists of Jazz and Ethnic music (as appearing e.g. in music arrangement software like the music machines of Microsoft), the next scales of chords (that cover the steps of the chromatic 12-tone scale) correspond to the next harmonic personalities.

I BELIEVE THAT THE MAIN USE OF THIS CONCEPT IS IN JAZZ WHERE THE ROLE OF  THE DIATONIC SCALE (TONALITY) IS RATHER LOOSE,IN THE SENSE THAT IT IS REQUIRED AT LEAST 50% OF THE TIME THE NOTES OF THE MELODY AND CHORDS TO BE IN THOSE OF THE DIATONIC SCALE AND THE REST OF THE TIME IN THE 12-NOTES FULL CHROMATIC SCALE. THUS THE TYPES OFTHE CHORDS WITH ROOTS ON THE REST OF THE NOTES OF THE 12-NOTES CHROMATIC SCALE COMPARED TO THE 7-NOTES DIATONIC SCALE IS SO AS TO APPLY FOR THE REST OF THE MELODY AND ITS CHORDS. E.G. THE SOFTWARE MIDI-GUITAR ALLOWS WITH AN ARPEGGIATOR TO ACCOMPANY AUTOMATICALLY ANY MELODY WITH CHORDS OVER THE MELODY'S NOTES, THAT IN PRACTICE ARE CHORDS THAT  SOUND ONLY FOR THE CENTERS OF THE MELODY THAT ARE NOTES THAT SOUND LONGER. 
THERE ARE THOUGH OTHER USES OF THIS 12-NOTES SCHEME OF HARMONIC PERSONALITIES.

As we see in the harmonic personality of Righteous(Major) and Honest (major) the perturbation of the 7-notes  diatonic scale to the 12-notes fully chromatic scale is by diminished 7nth chords.


Steps of the chromatic scale/Harmonic Personality
1
1#
2
2#
3
4
4#
5
5#
6
6#
7

Righteous(Major)
M(ajor)
Dim7
m(inor)
Dim7
m
M
Dim7
7
Dim7
m
4,2
Dim7

Honest (major)
M
Dim7
m
Dim7
m
M
Dim7
7
Dim7
m
M
dim

Hopeful (Mixolydian)
M
M
m
M
dim
M
m
m
M
m
M
dim

Serious (Phrygian)
m
M
6,3
M
6,3
m
6,3
dim
M
6,5
m
6,5

Upbeat(Mixolydian)
M
M
m
M
m
M
M
M
M
m
M
dim

Searching(Dorian)
m
M
m
M
dim
M
dim
m
M
dim
M
dim

Lonely (major)
7
Dim7
m7
Dim7
7
7
Dim7
7
7
7
7
7

Funky(Mixolydan)
7#9
7
m7
9
m7
9
7
7
7
m7
6,3
7

Sad(minor)
m7
M
6,3
M7
6,3
m7
6,3
m7
M7
6,5
M
6,5

Romantic(major)
M
6,3
m7
6,3
m7
M7
6,3
9s
6,3
m7
M
m7b5

Boogie(major)
7
Dim7
7
Dim7
7
7
Dim7
7
Dim7
7
7
7

Noble(major)
M
6,3
m
6,3
6,3
M
6,3
M
4,3
6,3
4,2
6,3

Bittersweet(Harmonic minor)
m
6,5
m7b5
M
Dim7
m
Dim7
7
M
m7b5
M
dim7

Adventurous(H-minor)
m
M
6,3
M
6,3
m
6,3
m
M
6,5
M
6,5

Striving(minor)
M7
M
6,3
M7
6,3
m7
6,3
m7
M7
6,5
M
6,5

Sophisticated(major)
6,9
Dim7
m11
Dim9
m7
M9#11
Dim7
13
Dim7
m11
9#11
Dim9

Miserable(mixolydian)
13
Dim7
m11
Dim9
m11
13
Dim7
13
Dim7
m11
9#11
Dim9

Complex(major)
2
6,3
m11
Dim7
m6,7
2M7
6,3
9s
2M7
6,3
2
6,3









We may compare it with the standard Jazz harmonic personality with the 5 blue notes that complement the 7 notes diatonic scale to the 12-notes full chromatic scale



Steps of the chromatic scale/Harmonic Personality
1
1#
2
2#
3
4
4#
5
5#
6
6#
7


JAZZ PERSONALITY
1M(ajor) or 1m
1#Dim or 6M
2m(inor) or 2M(ajor)7
7M
3m or 3M(ajor)7
4M or 4m or 4Dim
2M7
5M7 or 5m
5#Dim or 3M7
6m or 6M7
5m
7Dim or 7Major7




IN SUMMARY BOTH EARLY WESTERN AND EASTERN (GYPSY) JAZZ MAY MAKE THE NEXT 7 TEMPORARY CHANGES IN THE CHORDS OF THE DIATONIC SCALE DUE TO THE 5  BLUE NOTES 

3m becomes 3M
7dim becomes 7M
5M becomes 5#dim or 5m 
2m becomes 2M
6m becomes 6M
4M becomes 4m or 4dim
1M becomes 1m or 1#dim

Obviously not all of these changes occur necessarily simultaneously in a single song. maybe only few of them. And usually at least 50% of the time the chords are the normal of the diatonic scale. Other ways to organize them and perceive them are as triads of harmonic pairs of chords (see post 215  
IMPROVISATION OVER A PAIR OF CHORDS . TRIADS OF HARMONIC PAIRS OF CHORDS. ). This awareness of these alterations of the normal chords of a diatonic scale (by blue notes) allows for a consistent and rich system of harmony for composing and improvising early jazz type of jazz.

1ST CHROMATIC TONALITY 7-CHORD-SCALE OR 7-CHORD CYCLE  

THEREFORE IT IS A VERY COMMON IN WESTERN JAZZ GYPSY JAZZ CLASSICAL MUSIC ANDEAN MUSIC ETC THE NEXT CYCLE OF CHORDS OR SCALE OF CHORDS THAT CAN BE CALLED  1ST CHROMATIC TONALITY 7-CHORD-SCALE OR 7-CHORD CYCLE  THE NEXT

6m->2m->5M->1M->4M->7M->3M->6m

or with 7nths in Jazz

6m7->2m7->5maj7->1maj7->4maj7->7M7->3M7->6m7

AS WE MAY NOTICE THIS SYSTEM OF HARMONY WITH THE FIRST 4 BLUE NOTES (AND  5TH BLUE NOT 6#=7b  MAY BE ADDED) IS ESSENTIALLY A METHOD TO PLAY SOONER OR LATER IN THE MELODY ALL THE 12 NOTES OF THE FULL CHROMATIC SCALE STARTING FROM THE 7 NOTES OF THE DIATONIC SCALE AND RETURNING TO THEM AGAIN.