57. Extrapolating major, minor, diminished and augmented triad chords to 4,5,6,7,8 notes scales in improvisation and musical composition

Extrapolating major, minor, diminished and augmented triad chords to 4,5,6,7,8 notes scales  in improvisation and musical composition. This is a very important concept, in other words an enveloping local  sub-scale for each chord which allows when soloing to play notes outside the chord in at most 1/3 of the dime duration, while at 2/3 of the duration notes of the chord.

One of the most well know technique is the extrapolation of minor or major chord to a pentatonic (minor or major) with the same root.

Other well known extrapolations is to take the arpeggio of chord extensions to 4 or 5 notes chords like C->C6, C-C6add9 etc

Discussion of examples


A1) 4-scale 1-3-1
Minor Chord 3-4-5  -----> 3-4-(1-3-1) (tetra-chord 1-3-1)
Major Chord 4-3-5 ------> 4-3-(1-3-1) (tetra-chord 1-3-1)
Augmented Chord 4-4-4  -------> 4-4-(3-1)-----> 4-3-1-3-1 (tetra-chord 1-3-1)

A2) Pentatonic 
Minor chord 3-4-5 ---->     3-4-(3-2) ------> 3-(2-2)-(3-2) pentatonic western
Major Chord 4-3-5 ------>  4-3-(2-3)-------> (2-2)-3-(2-3) western pentatonic
Major Chord 4-3-5 ------>  4-3-(3-2)-------> (2-2)-3-(3-2) dominant pentatonic
Minor chord 3-4-5 ---->     3-4-(2-3) ------> 3-(2-2)-(2-3) dominant pentatonic


Here is a nice video about soul and blue scales  as extrapolation of chords

https://www.youtube.com/watch?v=mjttaiOq-8Q 


And more about blues arpeggio extrapolation of minor and major chords

In fact, a blue arpeggio of a 7nth chord with interval structure 

3-1-3-4-1  (called here blue pentatonic scale of a chord)

may be considered a pentatonic scale corresponding exclusively to that chord!


https://www.youtube.com/watch?v=y-gV5RGJbLo


A3) Diatonic scale
Major Chord 4-3-5----->  (2-2)-(1-2)-(2-2-1) diatonic
Major chord 4-3-5----->   (2-2)-(2-1)-(2-2-1) diatonic
Minor Chord 3-4-5----->  (2-1)-(2-2)-(2-1-2) diatonic
Minor Chord 3-4-5------>(1-2)-(2-2)-(1-2-2) diatonic

Diminished chord 3-3-6 ------>  3-3-3-3 dim7

A4) Melodic minor (Hindu), characteristic 4-subscale 1-2-1
Major Chord 4-3-5------> (2-2)-(1-2)-(1-2-2)  Hindu or melodic minor
Minor Chord 3-4-5------> (2-1)-(2-2)-(2-2-1)  Hindu or melodic minor

(Melodic minor=6,7,1,2,3,4#,5#,6'=(in semitones) (2-1)-(2-2)-(2-2-1))

A5) Melodic double minor (Arabic or leading wholetone or neopolitan major scale see also post 21) characteristic 3-subscale 1-1
Minor Chord 3-4-5------->(1-2)-(2-2)-(2-2-1) Arabic or melodic double minor
Major Chord 4-3-5------->(2-2)-(1-1-1)-(1-2-2) Arabic or melodic double minor

A6) Harmonic Minor ,characteristic 4-subscale 1-3-1
Minor Chord 3-4-5----->  (2-1)- (2-2)-(1-3-1) harmonic minor
Major Chord 4-3-5----->  (3-1)-(2-1)-(2-2-1) harmonic minor

A7) Harmonic double Minor, characteristic two  4-subscales (1-3-1)-(1-3-1)
Major Chord 4-3-5------>  (1-3)-(1-2)-(1-3-1) harmonic double minor
Minor Chord 3-4-5------>  (1-2)-(1-3)-(1-1-3) harmonic double minor

A good concept when creating melody after the choice of a chord (see harmonic method of composition post 9) , is to determine also the extrapolation scale of the chord before the choice of the melodic pattern. Then choose a butterflying pattern, and finally the melody. In other words, determine at first the triple (chord, extrapolated scale, butterflying pattern). The notes of the simplicial sub-melody (see post 9 about the concept of simplicial sub-melody) are  centers and are notes of the chord, while the rest of the melody (the part that sounds parallel to the particular chord) is a butterflying within the extrapolated scale around the centers of the simplicial melody. 


Here is a video showing a practical way to figure out which scales are define by a chord progression. Strictly speaking there is an algorithm that could be programmed in a software program that you give the chord progression and it defines the smallest set of scales that contain these chords. 

https://www.youtube.com/watch?v=wimGlqwYrjY


The easiest algorithm to find the smallest set of scales that have the chords of a chord progression is based on the rule that represents the chords of a diatonic scale on the 24 cycle, which is the next (see post 34)
The chords of a diatonic scale in this 24-cycle are easily defined as the chords of an arc of 3 consecutive major chords together with their 4 relative minors. The root of the diatonic scale is the middle major chord. In the symbolism above it is the next arc of 7 chords  (x-2, X-1,x-1,X,x,X+1,x+1)=(vii,V,iii,I,vi,IV,ii).

Summarizing in  simplistic way the correspondence of melodic pitch dynamics and the 4-basic emotions in music (joy, sadness, anxiety, serenity) we have 

1) Up pitch moves correspond to joy

2) Down pitch moves to sadness

3) Small pitch intervals of 1 or 2 semitones (chromatic or interval of 2nd) correspond to anxiety

4) Large pitch intervals (e.g. 4th, 5th octave etc) correspond to harmony and serenity. 

1) In the part of the chord progression with minor chords, utilize descending melodic moves so that sadness from melody and sadness from harmony fit
2) In the sad melody parts of the melody (and minor chords) utilize rhythmic patterns that start with faster notes and end with slower notes, and the reverse for the happy part (and major chords).
3) In a triad or 7 nth 4-notes chord the most characteristic notes are the middle 2nd note (in 1-3-5 interval notation  is the 3) and the 7 nth (if it exists). So for the anxiety part of the melodic moves we may utilize 1-semitone trills around these two notes, or waving with 1 or 2 semitones steps and notes outside the chord in the interval of minor 3rd (3 semitones) of the chord. Alternatively instead of trill or small amplitude waves we may utilize chromatic monotone scaling by steps of 1 semitone , or scaling with steps by intervals of 2nd of the scale,  that go from these previous notes of the chord to the same such notes in the next octave. But always make sure that the notes of the chord sound in the average longer, than the notes of these anxiety transition moves with notes outside the chord. 
4) Alternate up (happy) and down (sad) pitch moves , or chromatic moves (anxiety), with harmonic (on chord notes) moves (serenity-harmony).
5) Utilize at least 2 octaves, or even 3 for the melodic moves repeating the notes of the underlying chord on the next octaves , so there is sufficient space for melodic moves, to express with sufficiency the emotions.
6) For the duality of emotions anxiety-serenity, it may be utilized also harmonic waves or monotone scaling over 2 octaves at least,  on the notes of the chord, but also chromatic trill wave over the notes of this wave or scaling (modulated wave on wave or move) and then return to the pure harmonic wave or scaling on the notes of the chord.


7) A chromatic wave by 1-semitones steps or all notes of the scale (steps by intervals of 2nd) that goes up and down at least 2 octaves, corresponds to a chord sub-progression of the song , of our choice that utilizes almost all the chords of the scale!

DEFAULT MELODIES  FOR A CHORD PROGRESSION.

Given a  chord progression it is direct how to create a melody that fits the chords, with the following rules

1) During  each chord, the entry note of the simplicial submelody , is the middle note of the chord.

2) During  each chord, the exit note of the simplicial submelody (two notes per chord here), for major chords (including 7nth chords and extensions) is the upper note of the chord, for minor, diminished and augmented chords it is the lower note of the chord.

3) During the chord the melody follows an harmonic theme in one or more octaves span, in other words from notes of the chords, and is walking the chord by a spike, straight scaling or waving (these are parameters for the composer or improviser to choose) from middle and down to up (joy) if the chord is major, or from middle and upper to down (sadness) if it is minor, diminished or augmented. Alternatively  any descending , ascending or waving sequence of notes at diatonic speed such that the odd or even number of them is exactly the notes of the chord (extended probably by 7nth or 6th) and these motes sound e.g. 3 times more than the notes of the rest of the scaling is a melody that fits the particular chord! Irish melodies do it often. If the chord is simply major or minor we may enhance its harmony by extending it with its upper and lower relatives thus  by an interval of 3rd at the highest note and up , or at the lowest note and lower (in normal position). In other words making it a chord with 6th and/or 7nth. 

Another characteristic of the happy and joyful melodies is to define two notes (or interval) for the simplicial sub-melody for each chord so that in over all the melody is maximally harmonic (see post 40) and we  may use almost exclusively  the maximum large intervals (within a scale) that exist in the chords of the song. And this would be intervals of 8th, 6th (for triad-chords) , 5th and 4th. In other words we use almost exclusively the maximum harmonic melodic  speed that the chords allow (see post 68). 

This idea of maximum harmonic speed in melodies is also an idea that can give pretty directly improvisation melodies over a chord progression! This is good for happy melodies. It directly defines improvisational beautiful melodies from the chord progression,  because the maximum intervals of a chord are unique or very few for each chord! In fact a single large such interval from each chord can define the melodic-rhythmic pattern for each chord! 

The standard preference is to use 

a1) For  a major chord x1-x2-x3, the 1st x1-3rd x2   notes interval of pure 5th (7 semitones), or the 1st nx1-2nd x2 notes interval of major 3rd (4 semitones)

a2) For  a minor chord x1-x2-x3, the 1st x1-3rd x2   notes interval of pure 5th (7 semitones), or the 1st x1-2nd x2 notes interval of minor 3rd (3 semitones)

a3) For  a dominant 7th and major 7th chord x1-x2-x3-x4, the 1st x1-3rd x2   notes interval of pure 5th (7 semitones), or  the 1st x1-4th x4   notes interval of minor 7th (8 semitones), or of  major 7th (9 semitones). 
An interesting case of simplicial submelody is  the first choice  always  (interval of 5th or 4th). 

Or we may allow this interval of 4th or 5h of each chord sound 2/3 of the time of the chord sounding and 1/3 of the time the other middle x2 note for minor or major  , or 7th note of the 7th chords.
 Still another case is the minimal harmonic simplicial submelody (but always with notes of the chords) where we take always the 2nd choice (the x1-x2 interval of 3rd, or x1-x4 interval of 7th) where this sounds 2/3 of the time and 1/3 of the time the 3rd note of the chord. This simplicial submelody gives emphasis to the character of each chord, that is being minor , major or 7th etc. 

But another more maximal  harmonic  method is based on the next rules

b1) For each chord the simplicial submelody consists of at least two notes one entry and one exit (that may though coincide)

b2) Complementary chords (e.g. Cmajor, Dminor) can transition with intervals of 5 or 7 semitones (e.g. exit note of Cmajor is the c, and entry note of Dminor is the f).

b3) Successive chords in the cycle of 4ths or 5ths, and relative chords have common notes, this the exit note of the first chord and the entry note of the 2nd chord are identical.

b4) If the entry note of the a chord and its exit  note is an interval of minor 3rd  (3 semitones) we may add two more notes during the chord which is twice the 3rd note of the chord, but at one octave distance, and convert the minor 3rd interval to major 3rd (4 semitones) which has higher harmonic score (see post 40). E.g. G7-->C-->E7 , entry of C=g3, exit of C=e2, so we add c2, c3, and the simplicial submelody goes like this g3-c2-c3-e2, duringthe chord C. We converted the minor 3rd interval g-e, to a major 3rd c-e. 

b5) It is prefered that intervals of 1,2,3,4 semitones are converted to their complemntary of 11,10,9,8 semitones, by changing octave.

The so derived simplicial submelody singles less melody than the chord progression itself!

E.g. for the Chord progression Am->F->G7->C->G7->C->G7->C->E7->Am, the sumblicial submelody with these rules would be a3-a2a2-f2f2-g3g3-g3g3-g3g3-g3g3-g3g3-c2c3e2e2-e3e3-a3.
This simplicial submelody can be the centers of  full melody over this chord progression

4) At chord transitions x->y , the melody utilizes a dense melodic move (anxiety), with steps from 1 or 2 semitones, and within a scale (including the chromatic 12-notes scale) from the exit note of x of to the entry note of y , of the simplicial submelody.

5) As more general alternative to the above rules 1)-4) , we may define melodic moves not for each chord but for each chord-transition, and preferably for the        X7-->x+1 type of transitions (see the symbolism of post 34) e.g. E7-->Am.
Then the chord X7 has only one note x1 for simplicial submelody  the starting note of the melodic move, and the end note x2 of the melodic move is the next simlicial submelody note and one note of the chord x+1 not common with the chord X7. If the latter note x2 is not the root of x+1, it is created a tension that has to be resolved later where x2 would be the root of x+1. In between the x1 and x2, the rule is that at least 2/3 of the notes belong to the underlying chord, and this can be achieved by repeating notes of the underlying chord if necessary. The move x1->x2 may involve  each of the chords X7, x+1 , twice in two octaves each instead of once in one octave only, which may create very impressive melodic effects. This gives an even better opportunity to use in the melodic move, intervals of 8th, 4th and 5th (high harmonic speed, see post 68) , that have higher harmonic score than the other intervals (see post 40). The at most 1/3 of the total duration of the move x1->x2 ,of notes that play with underlying the 1st chord but may be outside the starting chord, might be unusually at chromatic and diatonic speed (see post 68), and sometimes might belong to the next chord or even to none of the two chords. The chromatic or diatonic speed applies usually when approaching the ending note of the melodic move.  The melodic moves x1-->x2 can be called chord-transition melodic moves and must have an element of repetition in length and rhythm. In the transitional Irish melodies that utilize 2-3 only major chords, while the melodic moves are 4-5 or 6-7 , but also in the traditional Greek music of the Aegean Islands, the starting and ending point of the melodic move is during the duration of a single chord and are notes of the chord! But still the rule 2/3 -1/3 for notes internal and external to the chord still holds, and the starting and ending notes of the melodic move may define the simplicial submelody.
6) The harmonic move   lasts longer than the transitional dense (chromatic or diatonic harmonic speed) melodic move , as the latter  takes less than 30% of the duration of x, and y.

7) From the rule of local fitness of a melody to a  chord  progression , such a default melody will fit the chord progression.

In the example below the chord progression is Am E7 Am E7 Am E7 Am E7 Am A7 Dm G7 C F E7 Am and the centers of the melody are correspondingly for each of the above chords the  E E E E E  B A B A A F G E F D A . The melody-moves consist of 10 notes ,the first 9 belong to the first chord and the last 10th to the next. All the moves are on the chord transitions of the form X->(x+1) in the symbolism of the cycle of 24 chords (see post  34). E.g. E7->Am, or Am->E7, or A7->Dm, or G7->C. An exceptions is the transition F->E7.  The notes that belong to the chord for each of these moves are 6 from the 9, that is 2/3 of the notes. They achieve it ,as we said , by repeating notes of the chord. And even in the transition F->E7 the notes hat do not belong to the chord F, while F sounds , do belong to the next chord E7 and so they prepare the ear for the next chord. The melody has all the 4 harmonic speeds (see post 68).  They start (ignoring the repeating notes) from the root A of Am and end to the root E of E7,they go back and forth, then from the root A of Am go to the dominant B of E7 and back to the root A of Am. Then they repeat. Then from the root A of Am which is also of A7, they go to the middle note F of Dm. Then from the root G of G7 to the middle E of C. Then from the root of F to the chord F to the 4th note (7th) D of E7, and close back to the root A of Am.  Starting from the root of X7 and ending in the middle (2nd note)  or dominant (3rd note) of (x+1), (e.g. starting at a of A7 and ending at f of Dm) creates a tension, which resolves at the end of the cycle of 16 moves by ending at the root of minor chord (x+1) (here at a of Am).

Here is the result.

https://www.youtube.com/watch?v=CEPsAIqnVao

The characteristic of at least  4-notes sub-scales (tetra-chords) of the above extrapolation scales are the next


Diatonic
2-2-1, 
1-2-2
2-2-2, 
2-1-2
Melodic minor  
1-2-1
Melodic double minor
2-1-1, 1-1-2
Harmonic minor 
1-3-1
Harmonic double minor
(1-3-1)-(1-3-1) , 


And if we restrict to only 4-notes sub-scales (tetra-chords) , having inverse such scales not different, then we are left with a small number of 10 of such characteristic tetra-chords
They are also all such tetra-chords containing intervals of 1,2,3, and where inverses and cyclic permutations of them do not count as different 

Diatonic

2-2-1, (major, natural minor rast, ussak)

2-2-2, (major, augmented)

Melodic minor, double minor (shabach)

1-2-1

Harmonic minor (Hijazz,Huzam)

1-3-1

Harmonic double minor

1-2-3,
 Diminished 

3-3-3 , (diminished 7nth)

3-3-1, 

Pentatonic

3-3-2, 
2-2-3

Chromatic

1-1-1

We shall also show how these extrapolations of the chords can be realized on the guitar fretboard.

For example The  pentatonic scale as extrapolation of major and minor chord in of the shapes D, E, A at the 3-highest strings is the next 

                                                                   D major shape

E major shape

A major shape 

E minor shape

D minor shape

A minor shape 

See also the next video on how to relate chords with their arpeggios and relevant scale.

https://www.youtube.com/watch?v=W_fWUeYZEAw