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.

154. SWING JAZZ MELODIC RE-HARMONIZATION OF SONGS VERSUS THE HARMONIC RE-HARMONIZATION

(This post has not been written completely yet)

It is know that in Gypsy Jazz , it is  usual to  adopt lovely and well known songs to swing Gypsy jazz, usually by extending the major chords X to the X6 version of them (X+ lower relative minor of X), plus use a fast (sometimes 4 times faster than a calm beat ofthe heart) tempo , which gives its dancing swing character.

Now is it possible to have a rather simple rule for such re-harmonizations?  The answer is yes,and it is the melodic re-harmonization, which is most often interpolating chords X0 ,X1 X2  between the Chords X -> and Y if Y, X are apart by intervals of 4th or 5th of the original chord progression, so that X=X0->X1=Ybdim->X2=Y or X=X0->X1=Ybbdim->X2=Y , or X=X0->X1->X2=Y etc and X0 X1 (or also X1,X2 in the last case)  is  a  pair of  chords in a diatonic scale that their roots are apart by an interval of 3rd . Alternatively if the initial harmony is a scale of chords which is a connected arc in the wheel by 4ths then a rule is to substitute major chords with their lower (or sometimes upper) minor relative chords (thus are a minor 3rd apart therefore a melodic re-harmonization) resulting nevertheless again to a connected arc in the wheel by 4ths. Of course there is also a kind of opposite which is substituting a  minor chord with major chord with the same root. This also allows for easier solo improvisation fitting the new melodic re-harmonization of the original chord progression. Now because such chord-relations by intervals of 3rds are relative chords and is called melodic relation of chords we call this re-harmonization melodic re-harmonization. In this minor and major chords alternate with diminished chords as well.

https://www.youtube.com/watch?v=80ZlQ0iTY_g&ab_channel=CoenModder-PianoCouture
https://www.youtube.com/watch?v=T2WV80h3P04&ab_channel=MangoldProject

We may compare this re-harmonization with the chromatic re-harmonization of the post 153 andthe harmonic re-harmonization which is to interpolate between two chords X1->X2 a third chord  Y (X1->Y->X2) so that the Y is a 7nth chord in harmonic relation to X2 and resolving to X2 (e.g. if X1=C and X2=G then Y may be Dm7, in total C->Dm7->G . Other example is X1=Am X2=F and then Y=C7 , in total Am->C7->F)

Of course the best songs to modify so are those that their scale of chords is an harmonic one in the sense that is a connected arc of chords in the wheel by 4ths.

OTHER TYPES OF RE-HARMONIZATION HERE IN JAZZ HERE 

7-LEVELS OF RE-HARMONIZATION

https://www.youtube.com/watch?v=ys0zXG_sZ4Y&ab_channel=8-bitMusicTheory

https://www.youtube.com/watch?v=1KqJrjYcgnI&ab_channel=RuslanSirota

153. SWING JAZZ CHROMATIC RE-HARMONIZATION OF SONGS

(This post has not been written completely yet)

It is know that in Gypsy Jazz , it is  usual to  adopt lovely and well known songs to swing Gypsy jazz, usually by extending the major chords X to the X6 version of them (X+ lower relative minor of X), plus use a fast (sometimes 4 times faster than a calm beat ofthe heart) tempo , which gives its dancing swing character.

This usually increases the percentage of  minor chords to the original chord progression, resulting to a higher than 50%  percentage of minor chords.

The most common chord progressions in such minor jazz ar based on the simulteneous and rather fast modulations between the next minor chords with the same root e.g. D4

1) D4 natural minor,
2) D4 harmonic minor
3) D4 double harmonic minor
4) Melodic minor

And in the above example of D4 the most common chord progressions (with various permuations)  is  the tetrad

B7  E7  Am  Dm  

We should notice that no single minor scale has the above progression but , a shifting among the 1) 2) 3) scales does have this chord progression.

Now is it possible to do a similar adoption of songs, that will result at about 50% of minor and major chords? The answer is yes,and it is the chromatic re-harmonization, which is most often interpolating chords X0 ,X1 X2 ...Xn between the Chords X -> and Y of the original chord progression, so that X=X0->X1->X2->X3 ....Xn=Y etc are a shortest possible path of successive chords in a diatonic scale , in other words differing by an interval of 2nds. When doing so we may start from a minor chord to end at a major chord or vice versa (from sadness to joy or vice versa) Alternatively if the initial harmony is a scale of chords which is a connected arc in the wheel by 4ths then a rule is to create a perturbation of  these  chords with their 1 semitone neighboring diminished or augmented chords (that are an interval of 2nd apart thus chromatic perturbation) keeping nevertheless the basic harmony as a connected arc in the wheel by 4ths .  This also allows for easier solo improvisation fitting the new chromatic re-harmonization of the original chord progression. Now because in a diatonic scale the minor chords are about equal in number with the major chords, the resulting re-harmonization w ill tend to have about 50% minor and 50% major chords.

We may compare this re-harmonization with the melodic re-harmonization of the post 154 and the harmonic re-harmonization which is to interpolate between two chords X1->X2 a third chord  Y (X1->Y->X2) so that the Y is a 7nth chord in harmonic relation to X2 and resolving to X2 (e.g. if X1=C and X2=G then Y may be Dm7, in total C->Dm7->G . Other example is X1=Am X2=F and then Y=C7 , in total Am->C7->F)

Of course the best songs to modify so are those that their scale of chords is an harmonic one in the sense that is a connected arc of chords in the wheel by 4ths.

https://www.youtube.com/watch?v=80ZlQ0iTY_g&ab_channel=CoenModder-PianoCouture

https://www.youtube.com/watch?v=T2WV80h3P04&ab_channel=MangoldProject

OTHER TYPES OF RE-HARMONIZATION HERE IN JAZZ HERE 

7-LEVELS OF RE-HARMONIZATION

https://www.youtube.com/watch?v=ys0zXG_sZ4Y&ab_channel=8-bitMusicTheory

https://www.youtube.com/watch?v=1KqJrjYcgnI&ab_channel=RuslanSirota

152. Why improvising in Swing Jazz is rather easier than the improvisation in other forms of music.

(this post has not been written completely yet)

Swing jazz was initiated by the swing dancing so the rhythmic rather fast (usually 4 times faster than the beat of the heart).
A remarkable example of such improvisations is with the Stephan Grappelli on the violin.
In this Jazz is included also the Gypsy jazz which relative to the rest of the Swing jazz has a percentage of  minor chords significant larger than the percentage of major chords.

There are mainly 4 reasons why improvisation in Swing Jazz is easier


1) The rhythm is fast enough so that , in the improvisation we may have one note per beat, thus the beat is leading the improvisation.

2) As swing is dancing we may imagine the improvisation over notes as dancing steps, that repeat notes more when they are notes of the underlying chord therefore the improvisation fits with the chords easier. The steps  are usually intervals of 2nd (one or 2 semitones) and not larger as in Irish or Latin folk music. A rule is that the transient notes to the chords are 1 or 2 semitones away from notes of  the chord and always between lowest and highest note of the chord (either 3-notes or 4 notes chord) . If about equal time per note will guarantee that as the notes of the chord  are more compared to the transient notes, they also sound more time time. Another general rule is that  : "The improvisation is done mainly by using in variable order tones and semitones only , as "continuous" moving inside the 12-note chromatic scale till it finds the note that sounds as desired , then stays longer on that and so on".  In other words the melodic triplets used are statistically mostly 2-1, 1-2, and more rarely 2-2, 1-1. Some people conceive its as if using the diminished scale all the time : 2-1-2-1-2-1-2-1 . Completely chromatic long moves by semitones is avoided but also is avoided moving with intervals larger than 2nds. These two rules are quite easy for an intuitive  improvisation on any scale and chord progression.

3) The chords are larger in number per number of melodic notes compared to other folk music , and follow a close harmonic contingency transition progression, therefore,  it is easier to find improvisation melodies to fit such chord progressions, as most of the motions is already determined by the chord progression. About half of each melodic theme is within one chord (3-4 different notes per 3-notes chord or 4-5 different notes per 4-notes chord) .

4) Because is was essentially dancing music, the melodic and harmonic meaning and pattern of repetitions of the music should be simple enough for the dancer to follow. But this makes also easy for the improviser to create melodic movements too.

151. Internal and external harmony of a chord in a scale and chords-melodies fitting

(this post has not been written completely yet)


We are used to think that the harmony of  chord are the intervals between its notes. Nevertheless this is only the internal harmony of  chord! The external harmony of the chord in scale is the structure of intervals between any note of the scale and the notes of the chord.

The degree of fit of melody to a chord is mainly based on the extenal hamony of each note of the melody relative to the chord.


And as there are good and bad internal harmonies for chord so there are good and bad external harmonies of chord relative to a scale.
We classify here some external harmonies based on the total harmonic score of the external intervals in post 40

In the next we will compare the external harmony in a major-mode diatonic scale of the I-step major chord, with the external harmony of the IV-step and V-step major chords.