9. The Harmonic method and sequence of composing songs and music. 1)Scale of Chords or progression Harmony, 2) the simplicial submelody, 3) the rhythm, 4) the melody and 5) the lyrics if at all

We must remind here the fundamental philosophy of musical composition and improvisation.

Musical improvisation is not a technical skill that one “learns to do.” It is a natural spontaneous process that occurs first in the imagination. It is often a natural language of the soul, as we have the language of words. But that is why it is understood by people that do not even speak the same language of words

The main goal of musical composition and improvisation is not the output musical piece, but the EXISTENTIAL FUNCTION of the process of creating and listening the musical piece. 

Here is an example of mediative improvisation by Estas Tonne

https://www.youtube.com/watch?v=7gphiFVVtUI

The basic triangle that functions here is the next:

   1) Feelings identity of the music (poetical symbol: Waters)   
                                                    

 2) Mental identity of  the music     (poetical symbol: Air)                                

3) Instrumental-fingers action identity    of the music

       (poetical symbol: Material Solidity)

1)-3) is mainly practical improvisation

2) -1) is mainly composition (or the way at the  first steps of improvisation when finger skills are not evolved yet)

2)-3) is mainly organized method of acquiring skills on the instrument.

We must remark here that the 2), the mental musical theoretical or harmonic identity of the music should be simpler than the 3) the instrumental-fingers identity of the music.

The improvisation should be 60%-80% due to feelings  15%-30% due to simple mental images about the music and 5%-10% only due to hands skills!

THE KEY-WORD HERE IN THE 4TH GENERATION DIGITAL MUSIC FOR THE MUSICAL-THEORETIC IDEAS OF THIS   POST (AS FAR AS MORDEN SOFTWARE FOR MUSIC MAKING IS ) IS MELODY-SEQUENCERS , CHORD-SEQUENCERS AND ARPEGGIATORS

THE TERM  SEQUENCER MEANS HERE A LOOP OR RHYTHMIC CYCLE OF   A  MELODIC THEME THAT IS VARIATED INTERACTIVELY BY THE USER  IN A MELODIC SEQUENCER.

THERE MANY GOOD SOFTWARE PROGRAMS FOR THIS COMPOSITION AND IMPROVISATION LIKE FUGUE MACHINE, YAMAHA MOBILE SEQUENCER, THUMPJAM ETC. ALSO ARPIO  AND ARPEGGIONOME FOR GENERAL ARPEGGIOS ALTERNATED WITH MELODIC IMPROVISATIONS AND NAVICHORD FOR CHORD SEQUENCER

THE HARMONIC METHOD IN COMPOSITION AND IMPROVISATION 

The basic idea of this method is to create the music from the SIMPLE AND ABSTRACT towards the MORE COMPLEX AND CONCRETE . Quite similarly as we write a book , starting from a design of the contents and outline of the plot. If music is the language of  the soul consciousness,  then this method of composition and improvisation starts with the soul feelings, or the heart, which is closer to the abstract mind, before it results in to more concrete decisions of the melody, which is the final output of a more detailed  and specific "musical speech"
Here the simple, is first the rhythm, then the chords progression, then the simplicial melody (as chanel ofthe final melody) , then the full melodic patterns and finally the lyrics (that may not exist too).
This method follows the next sequence of steps
 1)Chord progression Harmony, 
2) the simplicial submelody, 
3) the rhythm, 
4) the  melody and 
5) the lyrics. 

The harmonic method of composition, which composes first the chord progression and then the melody, is identical with the method of improvisation in jazz, where the chord progression is predetermined and then the melodies and soloing is freely created. This method of improvisation of Jazz, is also identical with the much older method in ethnic music (Greece, Spain,Portugal, South American  countries etc) where hundredths of folk songs have identical chord progressions, but different melodies and soloing improvisation. 

In order to create the melody over a chord progression we may proceed as follows.

1)We compose a simplicial sub-melodies one for each part of the song ,  with one note per chord, over the chord progression preferably at a chromatic sequence ascending and descending . 

2) We create moves or waves or cycles for each note of the simplicial sub-melody by sequencing during the chord with two types of notes a fast (usually outside the chord) and a slow of double duration on the notes of the chord again ascending or descending with smaller waves

3) We arrange a continuous sound instrument to play the simplicial sub-melody only and a discrete sound (guitar mandolin etc) to play the full waves melody.

Here is a nice video which shows how the chord progression, through the arpeggios of the chords, can be used to compose melodies and parallel soloing. 

https://www.youtube.com/watch?v=fxSieB5o81A

https://www.youtube.com/watch?v=OcmiQCsPy58

We may compare the harmonic method of musical composition, with the way that we shape sentences of meaning in our minds before we choose the exact words to speak  them. We need at first an analogy between the musical language and speaking language.

Here is a table of the analogy and correspondence of the levels of the musical language and Speaking languages

MUSICAL LANGUAGE	SPEAKING LANGUAGE
Note	Letter  of the alphabet
Interval (3 elementary melodic moves)	Syllables
Melodic moves or themes (5 basic  melodic patterns)	Words that make a simple proposition (subject verb object)
Chords duration may contain many musical themes	Sentences from a point to  a next point , that may contain many simple propositions

There are attempts by various software developers to create software that assists this method of compositions. Here is one which is free

The  palette
http://www.palette-mct.com/manual_eng/table_of_contents.html

See also

http://howtomakeelectronicmusic.com/how-to-make-a-song-start-with-the-chords



This harmonic-first method, is based on the philosophy that the emotional content of the harmony of the chord progressions is different and is not included in the emotional content of the sequence of notes of the melody. In other words the harmony is not summarizing only the emotions of the melody but is carrying and suggesting a sequence of emotions by itself. The emotions of the harmony and the emotions of the melody must of course be compatible. 

Let us see an example. Le us see at first in the next video  how a chord pregression can create a melody.

Here is  a very simpler but also beatiful way to create chord-melodies from chord progressions. The melody is a simple oscillation (waving or butterflying) around the highest note of the chord with intervals of 2nd or 3rd. We may emnhance this method by  chosing different inversions of the same chord so that the desired note is always the highest in the chord. 

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

Now to add the concept of invariants as in the post 41. Let us say for convenience that we are doing musical composition rather than improvisation.

We lay down the chord progression R1, R2,...Rn, and we chose let us say one pitch order pattern and also rhythmic pattern P for the melody. Pitch order patterns say which note is high from which but they do not specify how much and as what interval. So we set the pattern to fit in the first chord R1, e.g. by having only notes of the chord R1,  and symbolize it by P1, then similarly for the rest of the chords P2,P3,....Pn. We also keep invariant the rhythmic pattern of the P1 etc.  We make sure that the notes of the melody P1,P2,....Pn are higher than the chords. We already have composed a song. We may chose also two or more different patterns , and do the same, by making also sure that the same pattern goes to similar according to some rule chords (e.g. minor or major etc). As patterns have the character of joy and sadness we may correspond the sad pattern to sad chords and the joyful pattern to joyful chords.

Concluding the invariant here is the pitch order pattern. But we may already have other harmonic invariants in the chord progression and the coupling with the appropriate rhythm.

Here is a song composed by me in that way. In composing it I used also on more technique to define the patterns, which I call simplicial submelody (similar to the melody of the bass) but for this I will enlarge later.

https://www.youtube.com/watch?v=vMcPrrxJ-d8

Here is also more video, to see how a chord progression can define a melodic and improvisational composition.

https://www.youtube.com/watch?v=binjvIqAN1s

(https://www.youtube.com/watch?v=cAxB5bQfF5s

https://www.youtube.com/watch?v=R-P06FDk4NA)

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

https://www.youtube.com/watch?v=yxeOjqNK2Cw


And still another video

https://www.youtube.com/watch?v=T-SUJySXKUQ



GENERAL RULE FOR GOOD CHORD PROGRESSIONS OF IMPROVISATION AND COMPOSITION

Chord progressions that two successive chords  are always either 
1) an interval of  4th , that is successive n the wheel of 4ths 
2) Relative chords where major turns to minor and vice-versa, thus roots-distance  an interval of 3rd 3) Chromatic relation , in other words the roots differ by a semitone 

are best chord progressions for parallel translations of melodic themes by intervals of octave, 4th-5th, 3rd and semitone. 

Example  

C-> Am->Dm_->G->C->F->Dm->Dm7->G7->C etc
ARPEGGIOS AND DEA SYSTEM OF 4-STRING INSTRUMENTS (SEE POST 67) FOR SUCH CHORD PROGRESSIONS:

For the 4-string (double or simple strings) instruments of post 67, that are most of the ethnic music instruments , the chord shapes theory simplifies to the DEA instead of the CAGE of the 6-string guitar. Similarly the arpeggios of the chords, although are not identical with the shapes of the chords in a 6-string guitar, for the above 4-string instruments , they are identical with the chord shape! Thus knowing the chords means knowing their arpeggios of them too, which gives immediately a way of easy improvisation along a chord progression! The randomness is double a) in the choice of the chord progressions as above , in particular the chord transitions as described b) in the choice of the way to play soloing inside the arpeggio of such chords in particular the melodic themes 4 transformations.This  is easiest done with the 4-string instruments of the ethnic music (see post 67) . Such arpeggios can be extended to contain the 6th and 7th thus being arpeggios of the chord as with 6th  or 7nth (Notice that 6th are identical with minor 7ths X6=Ym7 and Xm6=Ym7b5, where X and Y are a minor 3rd apart as in relative chords). Some times extended so as to contain the chord with 2nd or 4th too. The transformations of the melodic themes, (see post 76) and in particular the 4 basic translations, inversions, rhythm variations and melodic density expansion or contraction can be conducted with a mini 4-or-5-notes-scale when a chord is playing which its arpeggio or extended 6th or 7th  arpeggio! In this way the melody always remains in accordance with the underlying chord and chord progression. Thus arbitrary such 3-types of chord transitions as above and arbitrary such 4 transformations of melodic themes will result in to a rich , free but well harmonic and melodic improvisation and composition! 

THE GENERAL PATTERN OF PROGRESSIONS WITH ALTERNATING CHORD-RELATIONS OF 
CHROMATIC-MELODIC ,CHROMATIC-HARMONIC , HARMONIC-MELODIC , HARMONIC-HARMONIC, MELODIC-MELODIC, CHROMATIC-CHROMATIC CHORD-TRANSITIONS.

This is a progressions X1->X2->X3->...->Xn  where the Xi->Xi+1  and Xi+1->Xi+2 is an alternation of chord relation and  transitions of the chromatic-melodic   , chromatic-harmonic,  melodic-harmonic,  chromatic-chromatic, melodic-melodic or harmonic-harmonic relations. 

Such constant alternating patterns of chord relations somehow determine also that the melodic themes (either within a single chord or within a chord transition), are structured and translated or inverted or expanded with similarly alternating intervals of 2nd, 3rd or 4th/5th. 

THE GENERAL PATTERN OF A CHROMATIC DOUBLE SCALE OF CHORDS 

Here is an alternative way to produce not harmonic scales of chords (based on the harmonic relation of chords) but chromatic scales of chords based on the harmonic relation of chords but which still involve the other two chord relations the melodic and the harmonic 

WE START WITH A CHROMATIC CADENZA OR ASCENZA  in semitones 2->2->1  or 1-3-1 or 1-3-1-1-3-1 in harmonic and double harmonic minor scales,   and we paralel chords rooted on such notes X1->X2->X3->X4 with chords 

Y1->Y2->Y3->Y4, such that the relation of Xi with Yi is either in a relation of being  relative chords (melodic relation of chords) or a 4th apart (harmonic relation of chords) 

Of course the less total number of different chords that we may use is better and it sounds more familiar if such chords belong to an harmonic personality (diatonic or harmonic minor or double harmonic minor etc).We may use either minor or major chords. 

TRIPLE ALTERNATION OF CHORD-TRANSITIONS

More generally   and we paralel chords  X1->X2->X3->...->Xn  that are in  one of the relations chromatic, melodic harmonic , with chords X1->X2->X3->...->Xn so that the relation of Xi with Yi is always constantly in one of the 3 basic relations  relative chords (melodic relation of chords) or a 4th apart (harmonic relation of chords) .

When playing the scale as progression X1->Y1->X2->Y2->... it is equivalent with having a triple alternation of chord relation and  transitions of the chromatic-melodic   , chromatic-harmonic,  melodic-harmonic,  chromatic-chromatic, melodic-melodic or harmonic-harmonic relations and a third which is variable. 

Such constant alternating patterns of chord relations somehow determine also that the melodic themes (either within a single chord or within a chord transition), are structured and translated or inverted or expanded with similarly alternating intervals of 2nd, 3rd or 4th/5th. 

TO BE MORE SYSTEMATIC WE MAY FOLLOW THE NEXT STEPS

1) Choice of the chord progression (the cycle of 24 chords may be used here, some rule of chord-relations invariants , together with joy-sadness, tension-release considerations). 

Based on the idea of the three relations of the chords (see post 30) , we may compose beautiful chord progressions. Two general rules are the next:

A11 . 1st general rule for harmonic chord progressions:  Progressions by arcs in the 12-chord cycle by intervals of 4th

This cycle defines by every connected arc of it a chord progression , where a chord may be substituted  with its same root relative major or minor chord , or its lower or upper minor relative chord. Of course  as they are an arc of the above 12-cycle they are successive chords or in the harmonic relation of resolution.

E.g. B7->Em->Am->D7->G->Bm-> etc 

Or B7->Em->Am->D7->G->C->(Am orA7)->D7 etc

E.g. The well known song of Frank Sinatra "Fly me to the moon" is using this technique in its sequence of chords 

https://www.youtube.com/watch?v=U8zvLvfUzCQ

Another example is the song of Nat King Cole L.O.V.E.

(main arc is the (Em or E7)->A7->D7->G(or Bm or Gm7) ->E7 etc with backwards retraces by one chord)

https://www.youtube.com/watch?v=cZ4TfRt1NK0&list=PLCD6F28C13A0A9AC2&index=12

Such arcs of the 12-chords wheel of 4ths can be considered as cycles, if the end-chord links with the beginning-chord with what maybe called a mutation. And there are mainly two mutations a) the relatives chords mutation that gives small cycles of 4 chords and b) the chromatic mutation that gives cycles of 6 chords. Here we present some examples that have a center of 3-major chords that we return in it. Many country music songs follow such chord progressions. But also many songs of  Latin music of Andes follow such chord progressions. Also the songs of the famous Greek composer Theodorakis follow such chord progressions.

WHEEL OF 4THS
1) The short 3-chords sub-cycle of the wheel of 4ths is a set of chords X1, X2, X3 where the previous chords are successive in the wheel of 4ths but they may be either minor or major and alternating also. Thus there are 2^3=8 types of such small sub-cycles. Essentially they define a diatonic scale or a mode of it

2) The medium size sub-cycle is a sequence of 6-chords X1, X2, X3, X4 X5, X6,  which they are again successive chords in the wheel of 4ths and again they may be either major or minor or alternating in any combination (e.g. two successive minor then one major etc).For this to be a sub-cycle, the X1, and X6 must differ in their root notes only a semitone.  For the choices of major or minor there are 2^6 such types of sub-cycles. We may also add the possibility that they are dominant 7tnth or major 7nth chords, or chords with 6th etc.

3) Similarly the 4 or 5 successive chords in the wheel of 4ths  X1, X2, X3, X4 X5 maybe considered closing if X5 and X1 ar relative chords e.g.

Bm->Em->Am->Dm->G, as G and Bm are relative chords

But also the 4-chords sequence is also

Em->Am->Dm->G, as G and Em are relative chords.

We enlarge more:

1) The minimal 3-chords cycle.
This is 3 successive chords in the wheel of 4ths

e.g. G->C->F->G
or Em->Am->Dm->Em.

Slight enlargement to this is the  Small 4 chords cycles of relatives mutation (by // we denote the relatives mutation)

Examples:  A->D->G//Em    or D->G->C//Am    or   G->C->F//Dm

2) Medium  6 chords cycles of chromatic mutation (by // we denote the chromatic mutation)

Examples:  A->D->G//F#->Bm->E    or A->D->G//F#->B7->Em

or  A->D->G->C->F->Bb//A

D->G->C//B7-> Em->A7  or D->G->C//B7-> E->Am

G->C->F//E7->Am->D  or G->C->F//E7->A->Dm

o

(Notice here that if we would restrict to a diatonic scale the cycle G->C->F//E7->Am->D  or G->C->F//E7->A->Dm   would be

G->C->F//Em7->Am->Dm  .

This cycle can be extended to an 8-cycle in the following way:

The 6-cycle  A->D->G->C->F->Bb//A  can be extended to the 8-cycle

A->D->G->C->F->Bb->D#->Edim7->A

or the A->D->G//F#->Bm->E  will become A->D->G->C->C#dim7->F#->Bm->E

With double chromatic mutation we have the progression 7-chords cycles

A->D->G//C#->F#->Bm->E  or D7->G7->C7->F7->Bb//E7->A7, which also can be alternating in minor major: Dm7->G7->Cm->F7-<Bbm//E7->Am7  or D7->Gm7->C7->Fm7-<Bb//E7->Am7 etc.

See also the double Andaluzian cadenza above and the standard Jazz 7-chords progression

So the  suggested cycles already contain a modulation that combines e.g. two diatonic scales o a diatonic and a harmonic minor etc, and is necessary so as to have 2/3 or more major chords in the chord progression. So the rule is: The 2/3 rule of major chords in the chord progression of 6 chords necessarily   involves modulations, and cannot be conducted within a single diatonic scale!!!

C->F->Bb//A7->Dm->G or C->F->Bb//A7->D->Gm

etc.

Notice that an alternating even only or odd only sequence of chords in such 7 chords cycles with double chromatic mutation gives the Andaluzian cadenza and Jazz 7-chords progression.

Example of  beautiful chord progressions that one can obtain with the above 6 or 7 chords cycles are the next with the next rules

1) All chords are from the above 7-cycle cycle with chromatic mutation and are with 7th chords

2) Any two successive chords are either successive in the above cycle ( that is successive in the wheel of 4th too or are in chromatic 1 semitone relation) or are relative chords, or inverses in order in the above relations

3) All successive chords alternating are minor then major or major then minor.

4) There is a starting and ending pair of chords which is successive in the wheel of 4ths and are both major chords.

An example of a chord progression with the above rules is the next

C7 F7 Bbm A7 Dm7 D7 Gm7 C7 Am7 D7 Gm7 C7 Am7 Bbmaj7 A7 Dm7 D7 Gm7 C7 Am7 F7 Dm7 A7 Am7 D7 Gm7 C7 F7.

When playing such chord progressions we may move slowly all the way  up and then all the way down in th fretboard.

3) Full 12 chords cycle: A->D->G->C->F->Bb->D#(=Eb)->G#(=Ab)->C#(=Db)->F#->B->E

where at most 1/3 that is at most 4 chords can be minor chords.

c) Full 12 chords cycle: A->D->G->C->F->Bb->D#(=Eb)->G#(=Ab)->C#(=Db)->F#->B->E

where at most 1/3 that is at most 4 chords can be minor chords. 

 A12 . 2nd general rule for harmonic chord progressions:  Two arcs  in the 12-chord cycle by intervals of 4th (substituting any of the chords with its minor if it is major or vice versa) that have distance at the closest ends either 1 , or 2 or 3 or 4 or 6 semitones!

E.g. D7->G ,(1 semitone apart)  Db7->Fm 

or D7->G, (2 semitones apart) E7->Am         

or E7->Am-> F#7->Bm (E7, F#7 2 semitones apart)

or D7->G , (3 semitones apart) B7-> Em 

or F-> Bb -> A7-> Dm or F#7->B7-> E or D7->G->F#7->Bm

or F-> Bb-> E7-> A or G7->C-> F#7->B

or Am->D7->G, (1 semitone apart ) F#7->B7->Em

or Am Dm G7 C F (6 semitones apart) , B7 Em

or Dm Gm C F A# (6 semitones apart) E7 A7

or Em (E7) ->Am (A7)-> D7-> G-> C->(6 semitones apart)  F#7-> B7 

e.g. in the valse indifference

https://www.youtube.com/watch?v=pph5IOXWlHU

or G7 C  F#7 B ( or Bm)

or F Bb E7 A  (or Am)

or C  F  B7  E (or Em)

A13 3rd general rune for harmonic chord progressions:

We may define the HARMONIC 2 OCTAVES , 7 NOTES SCALE of 7 notes that spans 2 octaves, and every 3 or 4 successive notes is a chord of the above types 

Here it is (STARTING FROM THE  C3)

etc -C3-E3-G3-B3-D4-F4-A4-C5- etc  (all steps intervals of 3rds)

As a structure of intervals over semitones it is the next sequence

-4-3-4-3-3-4-3-

And the sequence of 3-notes chords , by successive 3 notes in this scale is the chord progression

C->Em->G->Bdim->Dm->F->Am 

Such a sequence of relative chords alternating minor and major is a standard harmonic chord progression! And it can be extended up to 24 steps 

COMBINING THE PREVIOUS GENERAL RULES WE RESULT TO A SINGLE GENERAL RULE :

GENERAL RULE FOR GOOD CHORD PROGRESSIONS OF IMPROVISATION AND COMPOSITION

Chord progressions that two successive chords  are always either 
1) an interval of  4th , that is successive n the wheel of 4ths 
2) Relative chords where major turns to minor and vice-versa, thus roots-distance  an interval of 3rd 3) Chromatic relation , in other words the roots differ by a semitone 

are best chord progressions for parallel translations of melodic themes by intervals of octave, 4th-5th, 3rd and semitone. 

Example  

C-> Am->Dm_->G->C->F->Dm->Dm7->G7->C etc

SIMPLIFICATION AND UNIFICATION OF RULES FOR GOOD CHORD-PROGRESSIONS

A GOOD IMPROVISED OR COMPOSED CHORD PROGRESSION X(1) X(2) X(3),...X(N) IS ONE THAT HAS ONLY THE NEXT 3 CHORD-TRANSITIONS

1) X(I)->X(I+1) IS RESOLVING , THAT SUCCESSIVE IN THE WHEEL OF 4THS
OR  ANY OF THE TWO HAS BEEN SUBSTITUTED WITH RELATIVE CHORD OF IT WITH 2 COMMON NOTES (ALTERNATING MINOR TO MAJOR OR VICE VERSA)
OR
2) X(I)->X(I+1) ARE RELATIVE CHORDS WITH 2 COMMON NOTES, ALTERNATING MINOR TO MAJOR OR VICE VERSA (SUCCESSIVE IN THE WHEEL OF 3RDS)
OR
3) X(I)->X(I+1) HAVE ROOTS IN DISTANCE OF ONE SEMITONE OR ONE TONE (SUCCESSIVE IN THE WHEEL OF 2NDS)

An example of such a chord-progression improvisation is the next progression, that can be played from the 4th neighborhood of the guitar to the first open chords neighborhood

Em->G->Bm->Bb->F->E7->Am->D7->Em->G->D->F#m->F->C->Em->D#->Bb->A7->D

Now we can extend these rules and at the same time simplified them for guitar players. We always assume playing only on the higher 4 strings of the guitar, and the chords are essentially the triads played  only on the 3 higher strings.

A GOOD IMPROVISED OR COMPOSED CHORD PROGRESSION X(1) X(2) X(3),...X(N) IS ONE THAT HAS ONLY THE NEXT 2  CHORD-TRANSITIONS:

1) WHEN THE CHORDS ARE DISTANT IN DIFFERENT OCTAVES, THEN THE CHORD TRANSITION    X(I)->X(I+1)  MUST BE EITHER A) RESOLUTION AS SUCCESSIVE CHORDS IN THE WHEEL OF 4THS B) RELATIVES (ALTERNATING MINOR TO MAJOR AND VICE VERSA) AS SUCCESSIVE CHORDS IN THE WHEEL OF 3RDS. IT IS SUGGESTED THAT THE TRANSITIONS AS SUCCESSIVE CHORDS IN THE WHEEL OF 4THS ARE MUCH MORE THAN THE TRANSITIONS AS RELATIVE CHORDS

2) WHEN THE CHORDS, AND THEIR EXACT VOICING ON THE FRETBOARD, ARE IN THE SAME OCTAVE (AND WE DO NOT REDUCE THEM TO EQUIVALENT IN THE SAME OCTAVE) THEN THE CHORD TRANSITION X(I)->X(I+1) MUST BE SUCH THAT THEIR SHAPES AS PLAYED HAVE AT LEAST ONE FRET IN COMMON (MAYBE 2 OR 3 COMMON FRETS TOO AND MAYBE ONE, OR TWO NOTES IN COMMON). IT IS SUGGESTED THAT THE TRANSITIONS AS SUCCESSIVE CHORDS IN THE WHEEL OF 4THS ARE MUCH MORE THAN THE TRANSITIONS AS RELATIVE CHORDS AND THE REST OF THE TRANSITIONS AS CHROMATIC TRANSITIONS WITH ROOTS ONE OR TWO SEMITONES APART, OR ONE ONLY COMMON FRET ARE MUCH LESS IN NUMBER. ALSO IF JOYFUL SONGS ARE INTENDED THEN AT LEAST 2/3 OF THE CHORDS ARE TO BE MAJOR AND  LESS THAN 1/3 MINOR CHORDS. IN ADDITION THE PATTERN OF CHORD TRANSITIONS AS OF THE 3 BASIC TYPES MUST SOMEHOW REPEAT IN THE CHORD PROGRESSION EVEN WITH DIFFERENT CHORDS.

3) BASED ON THE IMPROVISED CHORD PROGRESSION, THEIR ARPEGGIOS DEFINE AT A SECONDARY ORGANIZATION LEVEL SECONDARY MELODIC AND SOLOING IMPROVISATION AT THE LEVEL OF NOTES NOW AND NOT CHORDS!

NOW WE DO NOT NEED TO PLAY ALL THE CHORDS OF AN IMPROVISED CHORD-PROGRESSION WITH EQUAL SIGNIFICANCE OR TIME DURATION. SOME CHORDS MAY BE GHOST-CHORDS

GHOST-CHORDS PROGRESSION METHOD OF IMPROVISATION OVER A SINGLE CHORD:

MOST OF THE TEACHERS OF IMPROVISATION SUGGEST  USING THE ARPEGGIO OF THE UNDERLYING CHORD, EITHER AS PURE TRIAD OF NOTES OR AS EXTENSION TO 4 OR 5 NOTES SUCH CHORD. BUT THERE IS ANOTHER INTERESTING TECHNIQUE THAT INVOLVES GHOST-CHORDS (NAMELY THAT ARE NOT REALLY HEARD). E.G. OF WE ARE TO IMPROVISE SAY ON C MAJOR CHORD, THEN IT IS NOT ENOUGH TO USE ITS ARPEGGIO, BUT DO THE NEXT: CONSIDER C IN THE CHORD PROGRESSION OF THE SONG, AND TAKE TWO OTHER CHORDS OF THE SONG PREFERABLY IN THE WHEEL OF 4THS,  THE 2 NEIGHBORHOOD CHORDS (EITHER AS MAJORS OR MINORS) HERE E.G. LET US TAKE THE MAJORS G->C->F ASSUMING THEY WHERE IN THE SONG. IF THERE IS NOT SONG YET WE JUST TAKE . IN THE WHEEL OF 4THS,  THE 2 NEIGHBORHOOD CHORDST (that define here the C major-mode diatonic  scale) . THEN  TAKE THE ARPEGGIOS OF THESE THREE CHORDS AND PLAY THEM IN RHYTHMIC , FAST AND RATHER RANDOM PERMUTATION  WAY, AS IF A VERY FAST CHANGE OF CHORDS IS MADE IN THE THREE  G->C->F, SO FAST THAT G, F CHORDS ARE RATHER TRANSIENT WHILE WE REMAIN MOST OF THE TIME ON C. THE SEQUENCE OF THE CHORDS THROUGH THEIR ARPEGGIOS DEFINE ALSO A SOLOING. THE RESULT WILL BE AN IMPROVISATION ON ALMOST A WHOLE 7-NOTES SCALE, WITH UNDERLYING SINGLE CHORD THE C.IN ADDITION THE SOLOING TAKES IN CONSIDERATION   AT LEAST TWO  OTHER CHORDS OF THE SONG. IF THERE IS MELODY IN THE SONG WE MAY CONSIDER MIMICKING THE MELODY WITH WAVINGS AND "DANCING AROUND THE NOTES OF IT, IN NOTES THAT EXIST IN THE CHORDS OF THE MELODY. OR WE MAY APPLY DIFFERENT TRANSFORMATIONS IN THE MELODIC THEMES THAN THE TRANSFORMATIONS THAT EXIST IN THE MELODY. THE RESULT WILL BE A DIALOGUE BETWEEN THE MELODY AND THE SOLOING

ARPEGGIOS AND DEA SYSTEM OF 4-STRING INSTRUMENTS (SEE POST 67) FOR SUCH CHORD PROGRESSIONS:

For the 4-string (double or simple strings) instruments of post 67, that are most of the ethnic music instruments , the chord shapes theory simplifies to the DEA instead of the CAGE of the 6-string guitar. Similarly the arpeggios of the chords, although are not identical with the shapes of the chords in a 6-string guitar, for the above 4-string instruments , they are identical with the chord shape! Thus knowing the chords means knowing their arpeggios of them too, which gives immediately a way of easy improvisation along a chord progression! The randomness is double a) in the choice of the chord progressions as above , in particular the chord transitions as described b) in the choice of the way to play soloing inside the arpeggio of such chords in particular the melodic themes 4 transformations.This  is easiest done with the 4-string instruments of the ethnic music (see post 67) . Such arpeggios can be extended to contain the 6th and 7th thus being arpeggios of the chord as with 6th  or 7nth (Notice that 6th are identical with minor 7ths X6=Ym7 and Xm6=Ym7b5, where X and Y are a minor 3rd apart as in relative chords). Some times extended so as to contain the chord with 2nd or 4th too. The transformations of the melodic themes, (see post 76) and in particular the 4 basic translations, inversions, rhythm variations and melodic density expansion or contraction can be conducted with a mini 4-or-5-notes-scale when a chord is playing which its arpeggio or extended 6th or 7th  arpeggio! In this way the melody always remains in accordance with the underlying chord and chord progression. Thus arbitrary such 3-types of chord transitions as above and arbitrary such 4 transformations of melodic themes will result in to a rich , free but well harmonic and melodic improvisation and composition! 

2) Choice of an appropriate rhythm (the rhythm also must fit the joy-sadness  considerations). We utilize appropriate software to test the rhythm. The rhythm is not the 2 numbers that is written in the musical pentagrams.  (See also post 

91. HARMONIC AND MELODIC ORGANIZATION BASED ON A 2 OR 3 LEVEL RHYTHMIC/MORPHOLOGICAL ORGANIZATION OF MELODIC THEMES PROGRESSION , INHERITED FROM POETRY MEASURE ORGANIZATION.).

3) Choosing the lyrics (the meaning of the lyrics must fit the joy-sadness, tension-release considerations).

4) Discovering  a  simplicial sub-melody from the chord progression (The simplicial submelody as starting ending notes of melodic themes and as the channel of a waving melody). The simplicial submelody is a simplification of the melody to simpler one. See also post  91. HARMONIC AND MELODIC ORGANIZATION BASED ON A 2 OR 3 LEVEL RHYTHMIC/MORPHOLOGICAL ORGANIZATION OF MELODIC THEMES PROGRESSION , INHERITED FROM POETRY MEASURE ORGANIZATION.


1) Chromatic simplicial sub-melody. A second a but more sophisticated way is to do exactly the same except that the 1st voice is defined not by the highest note in the chords but through the simplicial submelody.  The simplicual submelody is defined by the next rules. 
1.1) When two successive chords of the chord progression have notes that are one semitone distance only, we chose these two notes as notes of the simplicial sub-melody. For reasons of flexibility we allow two notes per chord if necessary. This happens for all cases that the two consecutive chords in a diatonic scale that are at roots distance of an interval of pure 4th (5 semitones) or pure 5th (7 semitones) or if they are mutually complementary chords (with roots of one step of  the scale apart). In general it is a good idea to chose as notes of the simplicial submelody for two successive chords in the chord progression, two notes, one from each chord with the minimum distance in semitones from the notes of the two chords. And alternatively for a 2nd voice we may take the 2 notes in the chords respectively with the maximum distance  between them for maximum action of waving movements! This in general may lead to two notes per chord in the chord progression, the second note is reserved for the 2nd voice etc.  The more correct rule to find the simplicial submelody  is as few notes per chord as possible that give the basic feeling of the melody. 
1.2) If the two consecutive chords are mutually relative with two common notes, the notes of the simplicial submelody for each chord are either a common note or the note that the other chord does not contain! 
1.3) Chromatic links simplicial submelody (also bass lines) In general we may have the next rule. If X1, X2 are two succesive chords of the chord progression, and we are at X1, a chromatic ling or chromatic bridge  is defined by finding two notes a1 in X1, a2 in X2, so taht a1-a2 is at the minimum interval distance among all other chord notes. Then the chromatic link starts with a1, b1,b2....,bn,a2 , and with a2 and all the intermediate steps are one semitone distance. 

The previous rules of minimum distance notes and disjoint notes of relative chords for two consecutive chords of the chord progression, determine at least one simplicial submelody for each chord progression! Then we extend as in 1) the simplicial submelody to the full melody where the original simplicial submelody are centers of the full melody. This means notes that sound more time than the other notes. The rules of the simplicial sub-melody give a  more passionate melody with conflicts and resolutions according to the chord progression. After we defined fine the notes of the simplicial sub-melody, then we  create the full melody by composing bridges between its notes , with other sizes of intervals. 


1.4) Minimal chromatic drone sub-melody (MCD sub-melody).
This simplicial sub-melody is like the chromatic sub-melody, except that we utilize preferably the common notes of the chords, and we require it  
1.4.1) of as few notes as possible and
1.4.2)  of as little distance as possible. 
The rules are the next

Rule 1: We start from the chord and we find a common note with its next chord. If there are two common notes, we look at the next 3rd chord and chose this that is also either a note of the 3rd--next chord or minimal distance of a note of it. We proceed in this way till the last chord of the underlying chord progression. 
It can be proved that if the chord progression are chords of a diatonic scale, then the minimal  chromatic drone melody, can have only some or all of the first 3 notes of the scale (e.g. in a C major mode diatonic scale the c, d, e)  



A minimal chromatic drone sub-melody need not be a kind of bass-line! It very well be a kind of very high register or octave simple melodic line. Personally I prefer the latter.

2) Harmonic simplicial sub-melody. Finally a third and probably best method is based on creating first the simplicial sub-melody in a different way which is based on preffering intervals distances of the notes of the simplicial sub-melody (opposite to the previous method) that are large intervals ,namely intervals of 5ths , 4th 6th or 8th.  . The simplicial sub-melody is somehow the centers of the final melody and most often it is one note per chord of the chord progression . It can also be considered as a very simple bass line parallel to the melody. So the rule to choose the simplicial sub-melody is the next
2.1) If we have two successive chords X(1) -> X(2) in the chord progression, and a is the note of the simplicial sub-melody belonging to chord X(1) , and b is the not of the simplicial sub-melody belonging to the chord X(2), then a->b is an interval in the following order of preference 5th, 4th, 8th, 6th. 
If the X(1) -> X(2) are two chords of a diatonic scale in the relation of resolution (succesive in the wheel by 4ths) e.g. G->C then we have 3 choices for a->b, the g->c, or b->e, or d->g. If the X(1) -> X(2) are in the relation of relative chords (two common notes) e.g. C->Em then we have 2 choices for a->b, c->g, or e->b. And if the X(1) -> X(2) are in the chromatic or complementary relation of  chords (roots that differ by one step of the scale) e.g. C->Dm, then we have one only choice or a->b, here the c->f. After we have defined the simplicial sub-melody then we create bridges between its notes by smaller intervals e.g. 3rds or 2nds. 


3) Default simplicial sub-melody.  This is simply the melody created by the roots of the chords of the chord progression.

 An important remark is that we may have HIGHER ORDER SIMPLICIAL SUBMELODIES. In other words except the 1st simplification of the melody, which is the 1st order simplicial submelody, we may have the 2nd order simplicial submelody, the 3rd order simplicial submelody, each one simpler that its previous. A path of grids from the complexity to simplicity. One of them should correspond of course to the complexity of the chord-progression, that is have one note for each chord of the chord progression. It is supposed that it will be the centers of the melody , in other words the notes that will sound longer. But most often it is the starting and ending notes of the melodic themes (see post 72) while the centers of the melody are a higher order simplicial submelody. In choosing the simplicial submelody from the chord progression, we have some degrees of freedom, and we may take advantage of them, so as to make the simplicial submelody itself , as an independent melody, to have parts of it that are melodic themes, repeating and transformed by translation, inversion and rhythm variation. Of course, as in the simplicial submelody , we choose on note per chord, these symmetries of the melodic themes, are reflections of the structure of the chord progression and a reflection of the 3 basic relations of chords, namely resolution by 4ths, relative and complementary chords. 

See also post 114 about higher-order syntax of the Dolphin language for melody composition

As we remarked in this post about the simplicial sub-melody , and also in post 72 and in post 69, the simplicial sub-melody can be multi-layered, in other words there are simplicial sub-melodies of simplicial sub-melodies This is an idea of that exists also in other sciences (e.g. stratified-sampling in statistics, multi-scale organisation of data in digital maps like google-maps , fractals with self-similarity , multi-order syntax of languages in linguistics, higher-order formal languages of logic , etc) and is a simplifying organization idea, where similar organization patterns in different scales are used to create an entity.
Here of course this entity is the full melody. Researcher of Bach have proved that he was utilizing also this method in counterpoint, where a single melodic theme, occurs in very slow time and large range, then in faster time-scale and finally in fastest recognizable time-scale as the main theme of the counterpoint.

In the post 114  for reasons of simplicity we describe a 2-levels Dolphin language for melody composition.

We showed in post 101 how the order-topological shapes of melodic themes or Dolphin-words are used to compose a melody. We also discussed in post 72, how the simplicial sub-melody can be used to organize a full melody as starting or ending points of melodic themes of the full melody. Nevertheless what we point-out here in this post is that the simplicial sub-melody could have been composed also my order-topological shapes of the Dolphin language, and in particular that it can be one or 1-3 only Dolphin words that are not only longer in time duration but also larger in pitch-range.  Then the next rule may be applied 

Rules of  interaction of simplicial sub-melody and full melody

Rule of melodic centers 

The  Dolphin words, or order-topological shapes of the full melody, end at a note of the simplicial sub-melody, which is its center or goal. 

Rule of harmony of the centers 

The duration of the center or goal note (a note of the simplicial sub-melody) is the longest among the duration of the notes of the Dolphin word or order-topological pattern, and preferably is larger, than the total duration of all the notes of the Dolphin word. 

Usually of course the center-note together with 2 other notes of the Dolphin word, are the chord-notes of an underlying chord of the Dolphin-word, and these 3 notes in total last longer that the total duration of all other notes of the Dolphin word.

Since in post 104 we described how to derive a simplicial sub-melody from a chord-progression, then we may understand that also a chord-progression may have the structure (e.g. at the roots of the chords) of very few Dolphin-words! 

As the simplicial sub-melody is simpler than the full melody it is natural to start composing from the simplicial sub-melody. And this is the main reason that on post 9 I suggest a composition method of songs that starts with the harmony of the chord-progression (which corresponds to a simplicial sub-melody) as this is a simpler setting (It is also the setting of the jazz improvisation) 

See also post 102 which essentially a similar idea.

One of the best methods to choose the simplicial sub-melody and in particular the one note per-chord, is to choose the notes so that the intervals between the notes are minimized (1 semitone) or maximized (interval of 5th or octave and inverses). For successive chords in the wheel of 4th both extremes are feasible. For chords that are  relatives, intervals of 4ths are possible, while for chords with roots one tone apart, intervals of 5th are also possible. For chords with roots one semitone apart, obviously the minimum 1 semitone is feasible.  


The simplicial sub-melody should have the highest possible repetitive pattern symmetry in the intervals, a symmetry in general higher than that of the chord progressions!  (Here improvising with an instrument, or even the computer ,with melodic lines after the chord progression may be helpful). The root of the chords may define the bass, but it is not the simplicial submelody always. Another obvious choice is the highest note of each chord, as the ear-perception identifies and discriminates   chords easier  with their highest note!  In a triad or 4-notes with 7 nth chord , the most characteristic notes are the middle 2nd note (in 1-3-5 interval notation  is the 3) and the 7th (if it exists) as they define their character as minor-major and 7nth or extended in general. Therefore these two notes have higher probability to be the notes of the simplicial submelody.  Here is video discussing it. https://www.youtube.com/watch?v=itLSHk5jnTI . If we intent for a super simple simplicial sub-melody, then the common notes of  maximal sub-sequences of the chords of the chord progression may be a candidate. The best simplicial submelody is discovered if we improvise with the chord progression and the sound-feeling results in substituting the chords with single notes. The more correct rule is as few notes per chord as possible that give the basic feeling of the melody. In the simplicial submelody we have most often, exactly one note per chord but some times two notes per chord. It is a decision of at least one note of the chord that would be the simplicial submelody. When we improvise the chord progression with the simplicial submelody in the mind, we perceive each chord essentially as one note, that of the simplicial submelody, which gives a chord-melody meaning to the chord progression of higher and simpler symmetry that that of the chord progressions itself! The root of the chord defines the melodic position of the chord in the octaves, the 3rd the emotional quality (sad-happy) and the 5 the anxiety-peace interplay. The full melody created after the simplicial submelody should be tried to be chosen in such a way that if we would fit chords for it , it would be exactly the chords of the initial chord progression. One way of course to have it so is to extend the simplicial melody to a full melody by using all the notes of the chord for each chord of the chord progression. In other words  it should not miss the important distinguishing character of each chord in the chord progression that defines it compared to other alternative chords in its place, that would make it less good. This may not always be possible for the simplicial submelody only.  But this will become will easier and exact  if we have the full melody in the next step , not only the simplicial submelody that may contain more notes from each chord of the chord progression.  Discovering the simplicial submelody of the chord progression should be easier than defining the full melody that fit to it  as melody. Personally when two successive chords of the chord progression have notes that are one semitone distance only, I like to chose these two notes as notes of the simplicial submelody. This happens for all cases that the two consecutive chords are at roots distance of an interval of pure 4th (5 semitones) or pure 5th (7 semitones) or if they are mutually complementary chords (with roots of one step of  the scale apart). In general it is a good idea to chose as notes of the simplicial submelody for two successive chords in the chord progression, two notes, one from each chord with the minimum distance in semitones from the notes of the two chords.    And alternatively for a 2nd voice we may take the 2 notes in the chords respectively with the maximum distance  between them for maximum action of waving movements! This in general may lead to two notes per chord in the chord progression, but as we remarked the rule one note per chord is about true not always. The more correct rule is as few notes per chord as possible that give the basic feeling of the melody. If the two consecutive chords are mutually relative with two common notes, the notes of the simplicial submelody for each chord are the notes that the other chord does not contain! 
The previous rules of minimum distance notes and disjoint notes of relative chords for two consecutive chords of the chord progression, determine at least one simplicial submelody for each chord progression! 

The next video in jazz improvisation music shows that in fact any of the 12 notes of the chromatic scale and not only the 3 or 4 notes of the chord can be chosen as the note of the simplicial sub-melody during a chord!

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

In order to create the melody over a chord progression we may proceed as follows.

1)We compose a simplicial sub-melodies one for each part of the song ,  with one note per chord, over the chord progression preferably at a chromatic sequence ascending and descending . 

2) We create moves or waves or cycles for each note of the simplicial sub-melody by sequencing during the chord with two types of notes a fast (usually outside the chord) and a slow of double duration on the notes of the chord again ascending or descending with smaller waves

3) We arrange a continuous sound instrument to play the simplicial sub-melody only and a discrete sound (guitar mandolin etc) to play the full waves melody.

A melodic  theme-move, can easily have three factors that characterize it

1) If it is sad (-) or joyful (+) (we may call it minor or major  melodic move, although its underground chords sometimes , rarely  may be a  major or a minor chord respectively).

2) Its melodic density (see the 4 melodic speeds or densities, chromatic, diatonic, middle harmonic and high harmonic in post 68)

4) Its range as an interval (this is related somehow by inequality to the density as in 2). melodic theme-moves that their range is more than one octave are special in stressing the nature of being sad or joyful. 

These three parameters still do not define the melodic move-theme even if we know its first note. As we see melodic theme-moves are much more complicated than 3 or 4 notes chords! When creating a melody through melodic theme-moves, ideas similar to those that structure a good chord progression may apply.

We may device a symbolism for a melodic theme move based on the above three factors as follows An1Bn2(-)(x) or An1Bn2(+)(x) where An1 is the first note and Bn2 the last note of the move (n1 n2 denote the piano octave of it) and a minus - or plus + sign if its is sad (minor)  or joyful (major) and (x)=1,2,3,4 denotes the dominating density of it is chromatic x=1, if it is diatonic x=2, if it is middle harmonic x=3 and high harmonic x=4  (see post 68)  e.g. G5A4(-)(2) . In this way we write the dynamics of he melody as a theme-progression ,much like a chord progression. 

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 aver 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 ofthe 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) Itis 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. forthe 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

Still an alternative but very simple way of defining a simplicial submelody, is such that the notes of the simplicial submelody are the starting and ending notes of the chord-transition melodic moves or intra-chord melodic moves (see below in 5)  for this. This involves defining usually one note per chord, and the chords in pair as chord-transitions, or a very simple sequence of notes inside a chord that is the simplicial submelody within the chord duration, which are the starting and ending points of the melodic moves.  See for more details post 72.  We repeat here some of the content.
The three harmonic relations of the chord transitions define also three melodic speeds or densities. 
1) The complementary chords in a 2-chords transition corresponds to the chromatic/diatonic melodic speed or density. 
2) The relative chords in a 2-chords transition corresponds to the middle harmonic melodic speed or density. 
3) The successive resolutional  chords in a 2-chords transition corresponds to the high harmonic melodic speed or density. 

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 traditional 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.

In this way of composing chord-transition melodic moves, the starting ad ending points are of paramount importance. Generally speaking, they are not identical with the centers of the melody, as they do not last in general longer than the other notes. They can be used though to define the simplicial submelody.    

By substituting the melodic move with its starting and ending notes we get a simplicial submelody, which shows in a simplified way the general move of the melody as a whole, whether it is ascending or descending and how much, and how this is done based on the 3 notes of each of the underlying chords. 

In the harmonic method of composition (see post 9) we conversely start with the chord progression, and its chord transitions, we select the starting and ending points of the melodic moves, and then  the morphological type of the melodic move , their length , their  rhythm , harmonic speeds etc. 

The chord-transitional melodic move is as a generalized interval which is defined by the starting and ending notes of the melodic move (and which belong respectively to the starting and ending chords of the chord transition). 

The simplicial submelody can be viewed also the channel submelody.  With this we mean that the simplicial submelody defines a channel in the pitch-time diagram, where the melody waves. But the shape of the move of the channel is defined by the simplicial submelody. We described how to derive the simplicial submelody from the full melody. But in the harmonic method of composition, the converse is of interest. In other words how to derive a full melody, from the simplicial submelody. And the idea to conceive the simplicial submelody as defining the channel where the full melody waves and being the staring and ending notes of the themes (here usually waves of the channel), is the key to do so. We just sing a waving with small waves that are at 2/3 inside the chord and 1/3 outside it and  that start and end at the notes of the simplicial submelody. 

The relation of the starting-ending notes of the melodic patterns as notes of the simplicial submelody and the morphological type of the basic melodic moves are as follows.

4.1) Straight scaling up or down (including spikes) in one or more of the melodic speeds (straight sadness or joy). Here the notes of the simplicial submelody are the starting and ending notes.

4.2) Ascending or descending waving (complex sadness or joy). Here the notes of the simplicial submelody are the starting and ending notes.

4.3) Flat equilibrium waving (serenity and equilibrium emotion).Here the notes of the simplicial submelody are the upper level and lower level ofthe flat channel.

4.4) Flat diminishing waving (serenity and diminishing emotions). Here the notes of the simplicial submelody are the starting upper or lower level and h ending note of the diminishing channel

4.5) Flat expanding waving resolving up or down  (serenity emotions exploding to either sadness or joy). Here the notes of the simplicial submelody are the starting note and the ending note at the upper or lower level of the expanding channel.

5) Creating the final melody (that has to fit not only the chord progression but also the meaning of the words in the lyrics). (see also post 69) In the harmonic method of composition,  after the determination of the chord-progression and then the simplicial submelody, the next step is to chose the melodic speed to fill the simplicial submelody to a full melody (see also post 68 for the melodic speeds). If it would be the chromatic speed, it would be an oriental-like melody. If it would be a diatonic speed, it would be a "lazy"  an easy to sing melody. If it would be the middle or high harmonic speed, it would be an exotic and beautiful but difficult to sing melody.  

A single melodic theme has a simple emotional meaning and this is a simple interplay or move inside the duality of emotions (positive-negative emotions).

Here are some techniques to compose the melody from ethnique folg music

"MUSICAL WORDS" OR MELODIC MICRO-THEMES WITH SYLLABLES, LONG  IN THE CHORD AND SHORT OUT OF THE CHORD : THE SMALL SECRET OF MAKING BEAUTIFUL FOLK MELODIES LIKE THOSE IN THE IRISH  CELTIC OR ANDEAN-INCAS FOLK MUSIC.

As we wrote in post 92 much of the beautiful folk melodies , come from ancient times that melodies where the mode of speaking and singing the poetry, was melody and which poetry already had organization levels in number of syllables, (e.g. 16-1=15 syllables , 12-1=11  syllables per poetic line) in long sounding and short sounding syllables of the words E.g. all words of ancient but also modern Greek language are divided to long and short according to the vowels although only in ancient times the speaking of the syllable was lasting longer when the syllable was long. Furthermost there was the organisation of the lines of poetry according to the rhyme, that together with all the above symmetries created multi-layer organisation in the rhythm (notice the similarity of the word rhyme with rhythm) , which is not existing in the writing of the music anymore. Normally we only have the concept of musical measure but not higher layer measures.

Here we concentrate one only simple organization structure which the closest corresponded in the poetic language and lyrics is the word. So we introduce a concept of micro-melodic theme, called

MUSICAL WORD that we may agree to symbolize say by w. It consists of a very small number of beats higher than 2 e.g.  3 or 4, and we may symbolize it with 0,s and 1,s , which means that at this beat if no sound is heard it is zero, while if a sound is heard it is 1. E.g. (0101) or (011) etc Now we divide the word in its LONG PART , that symbolize by L(w) , and SHORT PART . that we symbolize by S(w) and so that in time duration, or beats it holds that L(w)/S(w)>=2 (e.g. L(w)/S(w)=3 etc).

The musical-words or melodic micro-themes need not be by intervals of 2nds! They can be by intervals of 3rds and 5ths or 4ths! 

PITCH OSCILLATIONS AND THE MELODIC MICRO-RHYTHMIC-THEME
The musical-words or melodic micro-themes need not be by intervals of 2nds! They can be by intervals of 3rds and 5ths or 4ths! Actually as we shall see in the RULE OF OSCILLATION below its ends may be the required oscillation which most often is an interval of 5th or 4th. E.g.on of the most common such dancing pattern is the (1,1,1), where 2 of the 1's is the long part and 1 is the short part. It may start so  that these 3, 1's are the notes of the underlying chord a kind of harping) , but then it dances away so that only two of the 1's are eventually notes of the underlying chord. The number 3 here most often in dancing comes from the 3-like steps of the running horse. It corresponds also to the basic harping of a 3-notes chord.  It is also a micro-rhythmic pattern that repeat either inside or outside the chord. In this way by going up and down the diatonic scale,   this very micro-rhythmic structure of the melodic micro-theme, by odd and even steps creates chords and diatonic harmony. Of course the chord changes may be fast , so actually we are talking about ghost-chords! (see post 87 about ghost chords ). 
When playing or improvising  such melodies, with the vibraphone (metallophone) , the 2 , 3 or 4  mallets, correspond to this oscillating melodic micro-theme.

Such musical words may be ascending, descending or waving. Ascending as excitation may be small (intervals of 2nd) low middle (intervals of 3rds) or high middle (interval of 5th or 4th) or high (intervals of  8th or higher) Of course, as they are combined, they definitely create the effect of waving. BUT the waving is not the very standard by intervals by 2nds but a richer one, that involves many intervals of 3rds and even 5ths, and 8ths. The simplicial sub-melody of such melodies are movements mainly with intervals by 3rds and 5ths. There is also acceleration and deceleration as the melodic theme starts and ends.

E.g. we may descend with a chord say Am and its relative C (out of chords would be notes of G), and ascend with its chromatic-complementary thee G7 (out of chord notes would be those of Am or C ) etc. In other words, we ascend with even or odd notes and descend conversely. Here although we may utilize only 3 chords (Am, C, G) the alternating-changing may be fast covering practically all waving and melodies of the pentatonic or diatonic scale. The scale-completion of the melody (see post 86)  , may be at the next octave rather than in the same octave!
The rhythmic repetition 3 times then the 4th is different is more common than 2 times repeated then 2 times a different. The total range of waving say of the first 3 repetitions may be of size a 5th, while the 4th measure a range of size an 8th, or vice versa.

Let us also assume that the chord progression that underlines the melody is the X(1), X(2) ,...X(n).

As we wrote in previous posts, the melody consists by a progression of melodic themes, that are transformed, by the 4 main transformations or translation, inversion, dilation and rhythmic transformation. This is indeed happening in to the melodic micro-themes or melodic or musical words during the part of the melody that sounds during say the chord X(i) i=1,2...n, BUT we impose here a very important structure which is the key to the beautiful folk melodies, and makes them compatible with the chord progression that underlines, the melody. And this rule is a

THE CHATTY-COURT MELODY: 

RULE1 OF TRANSIENT AND CHORD NOTES. Obligatory part: In simple words, each musical-word w , that has underlined chord X(i) has the notes of its long part L(w) , to be notes of the chord X(i), (which includes extended forms of X(i) like X(i)maj7 or X(i)7 or X(i)add9 or X(i)sus4 ) while , the notes of its short part S(w) to be transient and belonging to the notes of the neighboring chord that is X(i-1) or  X(i+1), (which includes extended forms of X(i+1) like X(i+1)maj7 or X(i+1)7 or X(i+1)add9 or or X(i+1)sus4) or and more rarely to the rest of the chords of the chord progression. And if so if it contains a note from a non-adjacent chord Y(j) of the progression, then usually somewhere in the progression there is a transition X(i)->Y(j) or Y(j)->X(i) . We keep the transient notes sound at most 1/3 of the time only and the notes of the chord at least 2/3 of the time, because of the rule of long and short parts of the musical word or micro-theme. No mentioning of any scale is necessary in this definition (as usually there are more than one) but only of the chord progression, which is compatible with our enhanced concept of modern harmony. Nevertheless the chord progression over which this technique produces fast melodies may contain very fast chord changes, and may not be identical with the actual chord progression that the instruments play as background to the melody. This is the concept of "ghost chords" in the melody as described in the post 87. E.g. The full ghost-chord progression may be D G D G D A D. While the chords really played is only D. 


RULE2 An alternative rule is that a musical-word w , that has underlined chord X(i) has the notes of its long part L(w) , to be notes of the chord X(i), (which includes extended forms of X(i) like X(i)maj7 or X(i)7 or X(i)add9 or X(i)sus4 ) while , the notes of its short part S(w) to be transient and is one only intermediate not between the notes of the  chord X(i) (usually a 2nd away from the notes of X(i) and preferably but not obligatory this additional note to be a note of the other chords of the progression, again preferably and if possible of the previous or next chord, rarely on  of other chords. And if so, if it contains a note from a non-adjacent chord Y(j) of the progression, then usually somewhere in the progression there is a transition X(i)->Y(j) or Y(j)->X(i) .In this way we keep the transient notes sound at most 1/3 of the time only and the notes of the chord at least 2/3 of the time, in addition to the rule of long and short parts of the musical word or micro-theme. Even if we did not have the structure of micro-themes as musical-words with long and short notes , and we are playing in a random way the three notes of the chord plus one transient, in equal time in the average, we are still in the harmony of this chord, because of the proportion 3:1. And this would still hold if we used 2 transient notes in which case we would have the time proportion 3:2.  But in addition to this rule if we want also the intervals of 3rds, 4ths, 5th and 8th to be more than 2/3 of all the intervals the way is to apply harping in a chord say with 6 or 8 steps on notes, where it is added only one intermediate note in the chord (e.g. 7nh, 6th, 4th or 2nd) and so that the created intervals of 2nd are only 2 in the 6 or 8 intervals. Then we shift to a relative chord an interval of  3rd away or to a resolution transition which is a chord in an interval  5th or 4th away , or we even shift to a chord a 2nd away in which case we do not use any additional note, and we continue so.  So finally %3rds+%4ths/5ths/8ths>=2*(% 2nds) . Again the chord progression over which this technique produces fast melodies may contain very fast chord changes, and may not be identical with the actual chord progression that the instruments play as background to the melody. This is the concept of "ghost chords" in the melody as described in the post 87. E.g. The full ghost chord progression may be D G D G D A D. While the chords really played is only D. 

THEREFORE EVERY CHORD PLAYS THE ROLE OF A MINI CENTRAL SUB-SCALE AROUND WHICH THE MELODY DANCES FOR A WHILE ALTHOUGH IT  IS STEPPING ON OTHER NOTES TOO BUT NOT FOR LONG, THAT ARE MAINLY THE NOTES OF THE NEXT CHORD-SUB-SCALE. 

RULE 3 OF OSCILLATION OR BALANCE
THE COURT-MELODY USUALLY  OSCILLATES INSIDE AN INTERVAL OF 5TH OR 8TH. AND IT MAY BE OF THE NOTES OF THE HARMONIC SIMPLICIAL SUBMELODY (oscillating link or bridge of chords) OR THE ROOR-DOMINANT OF THE CHORD, OR MIDDLE 3RD AND 6TH OR 7NTH OFTHE CHORD (internal bridge of a chord).A simple and common way to crate such an oscillations is to take for example a simple chord harping-waving that conatins also with the previous rules less than 50% of the time also notes outside the chord , and then half of this simple theme translate it one octave higher, and so oscillate between the two octaves. The interval of 3rd will become 6th , the interval of 5th, a 4th and an interval of 2nd , will become 7nth. See e.g. the folk Irish melody Kerry Polka below

RULE 4 OF AFFINE STRUCTURE BALANCE
The melody if ir ascend then it descends and vice versa. The imblanace of thsi rather slight to indicate joy or sadness respectively. (For the Affine structure of a melody see post 97)

RULE 5 OF PITCH SCALE-COMPLENTESS
THE MELODY IS DESIRD TO USE AS EVENTUALLY MANY AS POSSIBLE OF ALL THE NOTES OF AN INTERVAL EITHER OF THE 12-TONES CHROMATI SCALE OR OF A 7 NOTES DIATONIC SCALE.


WE MAY CALL SUCH A CHATTY FAST MELODY THE CHORD-COURT MELODY OR SIMPLER THE CHATTY COURT MELODY OF THE CHORD PROGRESSION.
IT IS IMPORTANT TO REALIZE THAT THE COURT-CHATT MELODY MAY USE OSCILLATIONS BETWEEN THE NOTES OF THE HARMONIC SIMPLICIAL SUBMELODY THAT ARE MAILY INTERVALS OF 4TH, 5TH AND 8TH.  (SEE POST 9, 65, 72 )

WE MAY CALL SUCH A CHATTY FAST MELODY THE CHORD-COURT MELODY OR SIMPLER THE CHATTY COURT MELODY OF THE CHORD PROGRESSION.
IT IS IMPORTANT TO REALIZE THAT THE COURT-CHATT MELODY MAY USE OSCILLATIONS BETWEEN THE NOTES OF THE HARMONIC SIMPLICIAL SUBMELODY THAT ARE MAILY INTERVALS OF 4TH, 5TH AND 8TH.  (SEE POST 9, 65, 72 )

GENERAL REMARKS ABOUT MELODY-CHORD CORRELATION 

0) When a melody is created without reference to any chord-progression (see e.g. post 82 about INDEPENDENT MELODIES ), then an statistical profile with high percentages of intervals of 5ths, 4ths, and 3rds compared to 2nds is sufficient to make it an beautiful harmonic melody. But if there is already a chord progression, and we improvise with a melody on it, 

1) then during the time interval that a chord is sounding, we may want to have notes of the melody that include at least one note of the chord and in overall the time that notes of the melody that belong to the chord ,sound, is longer that the total time that the rest of the notes not in the chord is sounding during the chord. This is a quite strong rule. 

2) A weaker rule is simply the requirement that the notes of the melody during the sounding of the chord, contain  notes of the sounding chord, and probably that compared to their neighboring notes, the notes in the melody of the chord, sound longer during the sounding of the underlying chord.

3) If we abolish even this rule then we have an independent melody parallel to an independent chord progression, which is entirely acceptable in Jazz. In an independent melody, from the chord progression, we feel the harmony of the chord progression, but we apply all , some or none of the previous rules to some or of the chords.

Here is the way to create melodies with at least 2/3 of the intervals that  are the larger intervals of 3rds , 5ths/4ths or 8ths. The way is to apply harping in a chord say with 6 or 8 steps on notes, where it is added only one intermediate note in the chord (e.g. 7nh, 6th, 4th or 2nd) and so that the created intervals of 2nd are only 2 in the 6 or 8 intervals. Then we shift to a relative chord an interval of  3rd away or to a resolution transition which is a chord in an interval  5th or 4th away , or we even shift to a chord a 2nd away in which case we do not use any additional note, and we continue so.  So finally %3rds+%4ths/5ths/8ths>=2*(% 2nds) 

A way to take short notes of such beautiful melodies is to write the chord progression, and then one note with small letters above or below the chord denoting which neighboring note (by interval of 2nd usually)  is the extension of the chord in the melody.

Usually the pattern of the melody e.g. in Celtic folk music is with underlying chords two successive in the wheel by 4ths, that is e.g. D7->G (actually the requirement is to cover the diatonic scale so it could also be D->A, D->Bm etc) . E.g. there is an ascending  excitation movement to the next octave, maybe also one more fifth higher (may be called upwards melodic movement) , during the D7, while there is descending waving return to G (maybe called downwards melodic movement) , which goes quite low so that finally the melody closes with waving ascending return to D from where it started. In general the repeated waving of the melody is large within an interval of 8th , or  large-medium within an interval of 5th or medium within an interval of 3rd.


Furthermore, the rule can be extended to the optional part    of the rule which is that we are at least 1/3  of the time (preferably more than 2/3 of the time) at intervals of 3rds in the 2-octave 7-notes scale by thirds, which is always chords, or higher intervals of 4ts and 5ths and the rest of the time with intervals of 2nds. If the chords are mainly in the resolution relation (4ths) or relatives (3rds) the faster the changes of the chords relative to the duration of the musical-words, that may be with intervals by 2nds, the more the higher intervals of 3rds, 4ths, 5ths are in the total melody. The shifting a musical-word or micro-theme which is based, say, in intervals by 3rds inside the underlying chord X(i), is already a translation of the theme by intervals of 3rds, 4ths or 5ths. And at the transition of the chords X(i)->X(i+1), we may consider that the musical-word micro-theme translates also by the interval of the roots of the chords (although this is not absolutely necessary always). Therefore if the chord transitions X(i)->X(i+1) are mainly in the relation of resolution (intervals by 4ths or 5ths) or relative chords (interval of 3rd) then transitioning in the next chord again translated the micro theme by intervals by 3rds 4th or 5ths. Therefore in total, we may have at least more than half of the successive intervals of the melody by intervals of 3rds , 4th, 5ths or 6ths. 
This works even better if for every resolution pair X(i)->X(i+1) we involve as parallel mirror of it its relative pair Y(i)->Y(i+1) where Y(i) relative chord to X(i) and Y(i+1) relative chord to X(i+1). (e.g. to the resolution pair Am->Dm the relative pair is the C->F In the language of intervals for the simplicial sub-melody, this means that we may descend with an interval of 4th (5 semitones) and ascend by a lower relative intervals of 4th again E.g. f4->c4-> e3->a3 ). 
When we solo around say a major chord e.g. C , that we may consider as root chord of a major diatonic scale , the out of chords notes are the 7th, 2nd, 4th, and 6th (b, d, f, a) . But the 2nd, 4th, 6th are the notes of the minor chord ii (Dm)  , which is the lower distant relative chord of the IV (F). Thus it also belong to the V6 (F6)  . While the 7nth (b) is in the V (G) or in the same chord C7. Also the 6th, may be considered as belonging to the I6 (C6). Therefore the sequence C7->F6 , or the G->C->F6, which is in the wheel by 4ths, covers such soloing. Different soloing is a permutation of such triads or pairs. We may also consider that it is covered in the wheel by 3rds, as the ascending sequence of 5 chords  with 3 minors 2 majors (minor oriented) Em->C->Am->F->Dm  or the 5 chords sequence with 2 minors and 3 majors (major oriented)  G->Em->C->Am->F. The latter consideration in the wheel by 3rds seems more natural. Therefore soloing around a chord like C,=(c,e,g) as interval of 7 notes b-c-d-e-f-g-a, is covered by an arc of 5 successive chords in the wheel by 3rds , and the soloing can be patterned by permutations of these chords, as fast-ghost chord progression (see post 87 ) while in reality we may play only 2 major or 3 major chords only.  The same method as we may continue further left or right in the wheel by 3rds defines also the modulations that lead us away from the initial diatonic scale.

For example, 
1) if X(i)->X(i+1) are two chords successive in the wheel by 4ths e.g. G->C, then the chord-pair sub-scale od join-arpeggio of the two successive chords is the pentatonic  scale (B,C,D,E,G) with interval structure 1-2-2-3-4.
2) if X(i)->X(i+1) are two chords successive in the wheel by 3rds e.g. C->Em then the chord-pair sub-scale of join-arpeggio of the two successive chords is the 4-notes scale (B,C,E,G) with interval structure 1-4-3-4. If it is the pair C->Am, then the chord-pair sub-scale of join-arpeggio of the two successive chords is the well known and standard  5-notes major pentatonic scale (C-D-E-G-A) with interval structure 2-2-3-2-3 

3) if  X(i)->X(i+1) are two chords successive in the wheel by 2nds e.g. Dm->Em then the chord-pair sub-scale of join-arpeggio of the two successive chords is the 6-notes scale (B,D,E,F,G,A)
with interval structure 3-2-1-2-2-2. Or if it is the pair F->G then it is the 6-notes scale (F,G,A,B,C,D) with interval structure 2-2-2-1-2-2. On the other hand if it the pair E->Am then it is a pentatonic  scale  (C,E,G#,A,B) with an interval structure 4-4-1-2-1. While if it is the pair Am->G it is the 6-notes scale (A,B,C,D,E,G). And if the G is with dominant seventh G7, so Am->G7, then it is all the 7-notes diatonic scale (A,B,C,D,E,F,G)! If it is the power chord Gpower, so Am->Gpower, then the chord-pair sub-scale of join-arpeggio of the two successive chords is the minor pentatonic scale (A, C, D, E, G)! 
The same if we have the chord progression 
Am->Gpower->C, again the chord-triad sub-scale of join-arpeggio of the three successive chords is the minor pentatonic scale (A, C, D, E, G)! Some beautiful folk songs have this chord progression, and melody in the corresponding pentatonic scale as above.
In the same way, the chord progression G->Am->C  would as join-arpeggio scale the 6-notes scale C-D-E-G-A-B, with internal structure (2-2-3-2-2-1)
Or the progression C-E7->Am the join arpeggio the 7-notes scale C,D,E,G,G#,A,B with interval structure 2-2-3-1-1-2-1.
And of course the join-arpeggio of the chords progression C-F-G or Em-Am-Dm is all the diatonic scale.


W e may strengthen the harmony of the melody by the following observations
THE BEAUTIFUL PROPORTIONS MELODY:  % of intervals of 5ths/4ths> % of intervals of 3rds>% % of intervals of 2nds.

The musical-words or melodic micro-themes need not be by intervals of 2nds! They can be by intervals of 3rds and 5ths or 4ths! 

As we wrote in the post 40, the intervals of  5th/4ths have higher harmonic score than the intervals of 3rd which in their turn have higher harmonic score than the intervals of 2nd.

So many beautiful melodies have this distribution of  the percentage   of  intervals in them. In other words % of 5ths/4ths> % of 3rds>% % 2nds.

Some of the melodies of the music of Incas, Andes etc, but also of all over the world composers have this property.

We should notice also that although the diatonic 7-notes scale is closed to intervals of 2nd, 3rds and 5ths or 4ths (but not both) the standard pentatonic scale is  closed  to intervals by 5th and by 4ths .

We say that a scale is closed to  intervals by nth, if and only if starting from any note of it if we shift higher or lower by an interval by nth, we are again in a note of the scale.


Nevertheless , other proportions of  percentages of 5ths/4ths/8ths, of 3rds and of 2nd are known to give characteristic types of melodies among the different cultures.

Other observed profiles of percentages are


%2nds> %3rds+%4ths/5ths/8ths 
(e.g. the 2nds double more than the rest of the intervals, ratio 3:1 ) :
Oriental and Arabic Music,  GypsyJazz, and Jazz Stephan Grappelli soloing

%3rds+%4ths/5ths/8ths>% 2nds :
(e.g. the 2nds less than half compared to the rest of the intervals,ratio 3:1 )
 Music of Incas, and countries of the Andes. Celtic music Ancient Egyptian  music

The way to create melodies with at least 2/3 of the intervals to by the larger intervals of 3rds , 5ths/4ths or 8ths, is to apply harping in a chord say with 6 or 8 steps on notes, where it is added only one intermediate note in the chord (e.g. 7nh, 6th, 4th or 2nd) and so that the created intervals of 2nd are only 2 in the 6 or 8 intervals. Then we shift to a relative chord an interval of  3rd away or to a resolution transition which is a chord in an interval  5th or 4th away , or we even shift to a chord a 2nd away in which case we do not use any additional note, and we continue so.  So finally %3rds+%4ths/5ths/8ths>=2*(% 2nds) 

%4ths/5ths/8ths/6th>%3rds>% 2nds :
(e.g. the 2nds +3rds less than half compared to the rest of the intervals,ratio 3:1,  )
The way to create such melodies with at least 2/3 of the intervals to by the larger intervals of 5ths/4ths or 8ths, compared to 3rds ,  and 2nds is to apply the same technique as before, but when harping inside the chord we use the intervals of 4th and 5th and 8th of the  normal position and   2  inversions, instead of the 3rds in  the normal position! In this way in the fast soloing or harping on the notes of the the chord has more intervals of 4th, 5th and 8th than of 3rds!

Another characteristic of such beautiful melodies with the "right harmonic proportions" is that the exhibit the effect of acceleration/deceleration in the movement exactly as the physical bodies. In other words, they start with slow speed (intervals of 2nds), accelerate (intervals of 3rds and then intervals of 5ths/4ths) and finally decelerate when reaching to the right center-note (from intervals of 5ths/4th to intervals of 3rds and then to intervals of 2nds), Of course there many shortcuts where intermediate level of melodic-speed or melodic-density (see post 68 ) are omitted.

The melody understands the chord sequentially rather than simultaneously, and therefore the chord is mainly two poles of notes roots and dominant that are 7 semitones or an intervals of 5th apart. So the melody waves between these two poles, utilizing the middle note but also another intermediate not in the chord, which creates also a few intervals of 2nd. This is normally the high-middle excitation in the waving. For high excitation we jump to intervals at an octave or higher.

A fast and good melody requires appropriately organized symmetry and further organization patterns based on pitch-order emotions dynamics, rhythm, and harmony.

In order to understand better this rich concept, and separate it from the harmony, we will consider the part of the melody, which is parallel to a single chord, from all the chord progression of the song.

The organization of the symmetries of the melody is understood better over the "melodic corridor"

(See post 94 )

We have already mentioned types of symmetry for the melodic themes that are

1) Reflection to a horizontal axis (time)

2) Reflection to a  vertical axis (pitch)

3) Point symmetry to a time point

4) Pitch translation

5) Recursive pitch waving ascending or descending.

6) Cyclic behavior in ascending-descending.

7) Dilation on the size of intervals (waved changing of the 3 melodic densities or speeds). Usually the melody starts with low melodic speeds or densities , accelerates to higher speeds or densities and then decelerates again to lower speeds or densities, as is also the motion of bodies in dancing.

8) Statistical types of symmetries.

9) Furthermore, the melodic themes may be organized at small time level by the rhythm of the "melodic words" e.g. 3:1 or 2:1 time duration ratio of the long-short notes, the long inside the underlying chord and the short possibly outside the chord. The melodic word is a basic micro-theme of 

the melody. The interval of the long-short notes is a basic step-interval of the melody and it is avoided to me an interval of 2nd , instead an interval of 3rd, 4ths/5th, 6th , 7th or 8th (see post  92 ). The next basic interval in the melody, is the pitch distance among two successive melodic words, which is usually  zero, an interval of 3rd, 4th, 5th etc.

10) or at a larger time scale, by the relevant poetic measure (11-syllables poetry, 15-syllables poetry, 17-syllables poetry) that determine the pattern of repetitions in the melodic themes E.g. 3 repetitions at 4th measure resolution-change or 4 repetitions and at he 5th resolution-change .

11) We may determine a statistical profile of statistical frequency of intervals in the melody such that the highest statistical  frequency of intervals of the melody are mainly the next intervals in the next preference order 5th, 4th, 8th, 6th, 3rd, 2nd. A happy melody tends to avoid sad and dissonant intervals and use instead happy harmonic intervals

12) As the micro-themes (melodic "words") develop over notes ascending and descending over even or odd number steps of the diatonic scale (as in such a way that chords are shaped) the total results, as intended,  is to use eventually all the notes of he diatonic scale, so that the melody has high scale-completeness measure (see post 86 about chromatic music ). This principles somehow determines the preferred chord progressions (E.g. I, IV, V7) .

13) Although we may focus in such an organized symmetry of the melody during a single underlying chord, the true harmony of the fast melody may use "ghost chords" around this single chord (see post 87 about ghost chords ).  

 E.g. if the chord progression is I, IV, V7 used where IV and V7 are ghost chords, then substituting IV with ii or vi and V7 with vii or iii, we get at least 9 more combinations and variations for the ghost-harmony of the melody , that essentially only the chord I is sounding. E.g. (I,ii,vii), (I,ii,V), (I,vi,V), (I,iv,vii) ,(I,ii, iii) ,(I,vi,iii), (I,vi,V), (I,IV,vii), (I,IV,iii).

14) A fast melody should balance properly repetition and  innovation during its development

It is obvious that a simple guitar harping is not a sufficient concept to grasp the required above high organization of the melody even during a single chord. The guitar has only 6-strings while to lay-out the previous organization structures may require many notes and the chord considered at two octaves rather than one only octave.

ASCENDING OR DESCENDING AT WILL THE MELODIC BRIDGES IN CHORD CHANGES.

The alternative positions of the D, A, E shape chords in the 2nd, 3rd and 4th neighborhood of the fret-board (see post 13 ) has a utility by far more than just varying the sound and voicing of the chords! Its main utility is in creating melodic bridges among chords in chord transitions so that the bridge will be ascending or descending from one octave to a higher or lower, without altering its start and end chords! If we had to play these melodic bridges while playing at the same time only open chords we would have to alter ascending such bridges by re-entrance to a lower octave to descending and vice versa. But with the chords distributed among the 3 neighborhoods, we may do as we like with the ascending or descending character of the melodic bridges!

The pitch translation homomorphism between melodic themes and underlying chords. (see post 80) 

When the melody is composed from little pieces called melodic themes M1, M2, M3 etc and each one of them or a small number of them (e.g. M1, M2)  , have the same underlying chord C1, then we have a particular simple and interesting relation between the chords C1, C2 , C3 and the melodic themes (M1, M2), (M3, M4) ,...etc. This is not the case when the melodic themes start at one chord and end to the next, that we usually call in the book, as "external melodic Bridges" . We are in the case of "internal melodic Bridges". This relation is based on the pitch translations of the melodic themes and of the chords. Actually this is also a scheme of composition of melodies based on small melodic themes (see post 9), when the chord progression is given or pre-determined.

So let us say that the melodic themes (M1, M2), have underlying chord C1. Then as we have said there are only 3 possible chord-transition relations in a chord progression (see post 30 ): C2 will be either in resolution relation with C1 which means that the rood of C2 is a 4th lower or higher relative to the root of C1, or the root of C2 is an interval of  3rd  away from the root of C1 , or and interval  of 2nd away from the root of C1. Let us symbolize by tr4(), tr3(), tr2() , where tr() is from the word translation, of these three pitch shifts. Then we may also translate the melodic themes similarly

tr4(M1), tr4(M2), or tr3(M1), tr3(M2), or tr2(M1), tr2(M2), Then automatically the new translated melodic themes will have as appropriate underlying chord the C2. Actually in the case of intervals of 3rd or 5th, the melodic themes tr3(M1), tr3(M2)  or tr5(M1), tr5(M2) may as well as appropriate underlying chord the C1 again as the 3rd and 5th of the chord is a pitch translation that leads to a note again inside the chord. This is the reason we called this relation homomorphism and not isomorphic. In mathematics , and correspondence H is call homomorphism relative to some relations R, if the the objects H(x1), H(x2) are in relation R , if the objects x1, x2 are in relation R. Here H(M1)=C1 and H(tr(M2))=C2 and C2=trn(C1) that is are in distance of interval of n (=2,3,4 etc) if tr(M1) and M1 are in distance of interval of n. It may happen that H(x1)=H(x2). But if when x1 is different from x2 then always also H(x1) is different from H(x2) we say that H is an isomorphism. Here because it may happen that H(M1)=C1, and H(tr(M1))=C1 again the correspondence of melodic themes and chord is not 1-1, that is H is an homomorphism not an isomorphism in general. 

By continuing in this way translating in pitch the initial melodic themes M1, M2 according to the interval shifts of the roots of the chord progression an remaining inside a diatonic scale , we compose a melody (or simplicial sub-melody too, see post 9). Of course in order for the melody not to be too monotonous we may vary also the melodic themes from ascending to descending etc.


Now even when we are at external melodic bridges e.g. M1 which starts at underlying chord C1 and ends in underlying chord C2, even then this homomorphism is of use! The way to make it work is to take the range of the melodic theme (usually starting and ending note as simplicial submelody) equal as interval to the interval of the roots of the underlying chords C1, C2. 

Here is a video of jazz improvisation which uses this idea. The chord progression id C, F, G, and the of pitch translations of the initial melodic themes are always intervals of 4th or 5th.  

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

INTERACTIVE SINGING METHOD OF MELODY COMPOSITION AFTER THE CHORD PROGRESSION: In this method we start e.g. from the  triad of major  chords of the chord progression , and we start singing the melody with our voice and appropriate emotions. Then we develop the melody, note by note by containing it, that  at each turn of it, we may utilize only a chord of the chord progression. So at each turn of the melody we try chords from the chord progression that best suit the note, and if we find none, then we alter the note so that at least one chord fits. 

 Other way based on the concept of bridges:  After the chord progression and simplicial submelody we chose, 
THE DEFINITION OF MELODIC BRIDGES THAN LINK TWO SUCCESSIVE CHORDS BETWEEN THEM AND START AND END AT THE NOTES OF  THE SIMPLICIAL SUBMELODY.

1) WHICH CHORD-TRANSITIONS (PAIRS OF CHORDS) WILL HAVE A MELODIC BRIDGE! (Usually the chord-trasnitions that are in resolutional relation, or resolutional-like relation)

2) THEN WHICH BRIDGES WILL BE ISOMORPHIC IN PITCH AND RHYTHMIC DYNAMIC SHAPE AND WHICH DIFFERENT, DEFINING THEREFORE A PARTITIONING IN THE BRIDGES.

3) THEN IF IN EACH EQUIVALENCE CLASS OF  ISOMORPHIC MELODIC BRIDGES IN THIS PARTITIONING, THE BRIDGES ARE  EVENTUALLY ASCENDING OR DESCENDING (This besides the emotional significance, determines also where to play the chord in one of the 3 neighborhoods of the fretboard)

4) FINALLY  HOW IN EACH EQUIVALENCE CLASS OF  ISOMORPHIC MELODIC BRIDGES IN THE PARTITIONING, THE COMPLICATED PITCH DYNAMIC SHAPE  OR WAVING AND RHYTHM WILL BE AS A REPETITION  OF SUCH PATTERNS OF PREVIOUS ISOMORPHIC MELODIC BRIDGES, OR VARIATION OF  SUCH PATTERNAS S SO NOT TO BE TOO BORING. (This pitch dynamic shape has again a significant emotional meaning)

5) THE JUSTIFICATION OF THE CHORD PROGRESSION USUALLY IS NOT DONE BY THE CHOICE OF THE MELODIC BRIDGES (THAT IS GIVEN THE MELODIC BRIDGES MAYBE A SIMPLER CHORD PROGRESSION MAY COVER THEM HARMONICALLY). BUT AN INTERMEDIATE HARPING OR STRUMMING OF EACH CHORD WILL ENHANCE  THE MELODY OF THE BRIDGES SO THAT ONLY THIS CHORD PROGRESSION IS JUSTIFIED!

MELODIC THEMES TRANSFORMATIONS AND SIMPLICIAL SUBMELODY

We have mentioned in post 72 that the simplicial submelody is usually  the starting or ending notes of simple melodic themes, can be external bridges (see post 72) of the chord transitions (of density diatonic or middle harmonic etc). Therefore here we apply the 3 basic transformations and starting from a single melodic theme ending to the first note of the simplicial submelody we translate or invert or vary rhythmically this theme, and make it end (or start) on the next note of the simplicial submelody.  The transformed melodic themes derived in this way cover most often two chords or a chord transition or chord relation

 The full melody created after the simplicial submelody should be tried to be chosen in such a way that if we would fit chords for it , it would be exactly the chords of the initial chord progression. 
One way of course to have it so is to extend the simplicial submelody to a full melody by using all the notes of the chord for each chord of the chord progression. In other words  it should not miss the important distinguishing character of each chord in the chord progression that defines it compared to other alternative chords in its place, that would make it less good. This may not always be possible for the simplicial submelody only.   (see e.g. https://www.youtube.com/watch?v=LlvUepMa31o or how one melody could be created parallel to chords where in this example we eliminate the chords and leave only the one melody https://www.youtube.com/watch?v=JhLhsbza1Ic or https://www.youtube.com/watch?v=tCuxVS3CI3U or https://www.youtube.com/watch?v=tCuxVS3CI3U ) 
As general alternative  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. The tension is highest if the x2 is the 3rd note, middle of it is the 2nd note and resolving if it is the root note. 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 melodic moves x1-->x2 can be called chord-transition melodic moves and must have an element of repetition in length and rhythm. In the traditional 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.

A good concept when creating melody after the choice of a chord and simplicial melody, is to determine also the extrapolation scale of the chord (see post 57) before the choice of the melodic pattern. The rules of the 24-cycle of chords apply very wel to determine the smallest number of scales that contain the chords of the chord progression . The step from the simplicial submelody to the full melody involves the choices of the 4-basic melodic moves as described e.g. in post 59. The themes of the melody are a plot (sequence) of the 4 basic moves which by itself says an emotional story without the help of the harmony. The centers of the melody or notes of the simplicial submelody are usually the notes of the 4 basic melodic moves that sound longer, and these would most probably be the tops and bottoms of the 4 basic melodic moves but also notes of the underlying chord. Do we want emotional clarity and intensity or emotional ambiguity on Sadness or joy? etc. Then we choose a butterflying pattern, if any at all, and finally the part of the melody corresponding to the particular chord. In other words, we determine at first the triple (chord, extrapolated scale, butterflying pattern) for the part of the melody that corresponds to a chord. The notes of the 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 or simply transient notes within the extrapolated scale around the centers of the simplicial melody.  We usually prefer that the note of the melody is either the highest note of the chord inversion or of higher pitch than the highest note of the background chord inversion. Any descending , ascending or waving sequence of notes at diatonic speed (see post 68) 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 est of the scaling is a melody that fits the particular chord! Irish melodies do it often. We may even break the duration of each  note of each chord of the chord progression to many times repeating same note and then create fast waving melodies from all these small notes that both make an trill harping of he chord and the same with the bridge to the next chord. Different variations of doing it create different voices but already harmonized due to the initial chord progression! (See e.g. https://www.youtube.com/watch?v=uoqFH-i7jYY and https://www.youtube.com/watch?v=T2aR9eq1fzQ or https://www.youtube.com/watch?v=tbWqPnRbq3M&index=1&list=RDtbWqPnRbq3M) The final melody usually contains more notes than the simplicial sub-melody, and it may also contain notes outside, the chords. I do not say outside a scale, as there is no assumption at all that the song will be in a single scale-tonality in the classical sense. On the contrary, it is desired to have a rule of modulations in it based on some chords relations logic. But  certainly the  notes of the part of the melody that sounds parallel to a chord will be inside the chord-extrapolation scale which is usually one of the next 5 scale, diatonic, melodic minor and double minor, Harmonic minor and double minor. By changing the chord during the chord-progression the scale may change too. (see e.g. post 42, 57). The concept of the centers of a melody within a time interval , can be defined more precisely in  mathematical-statistical way as follows: Divide all notes of the melody in to equal smaller ones (e.g. by the smallest duration note on the melody), and then create s a statistical histogram with statistical probabilities of how often the particular note and pitch occurs in the melody. The highest 3 peaks of this histogram define the top 3 centers of the melody within the particular time interval. If we utilize a moving time interval (e.g. of one or few measures) we may define the centers for all the melody. (See in post 27 also the scientific papers  http://research.microsoft.com/en-us/um/redmond/projects/songsmith/ and  http://research.microsoft.com/en-us/um/people/dan/mysong/ )

An alternative way is not to use any simplicial sub-melody but to use the rule of utilizing (almost) ALL the notes of each chord in the melody, and of course the minimum of some more. That is use in a maximal way the chords and minimal number outside the chords just to fit for the theme needs, rather than in a minimal way as the simplicial submelody . In that case the we simply design the theme as a plot of the 4 basic moves and almost entirely from notes of the chords. The result is of course a dominance of intervals of 3rds, 4ths, and 6ths in the melody! And such a melody may still have its centers, that could be defined as simplicial sub-melody, but the order of creation is different.

The themes of a melody consist of a plot or sequence of the 4 basic moves (see post 59)  which by itself says an emotional story without the help of the harmony. If we have (as here we assume we do) an underlying chord progression, then utilizing almost all the notes of the chords and one theme for each of the 3-harmonic-types of chord transitions , we may define the set of themes of the melody in easy way. Alternatively we may define a theme for each type of emotion, sad, joy, anxiety or serenity, or a theme for each type of chord respectively minor (sad) major (happy), 7nth or diminished or augmented (anxiety) and r5 (serenity.) The chord progression serves as a way to transform and make variations of the themes. The notes of the simplicial submelody are the centers of the melody that sound longer and are usually the tops and bottoms of the 4 basic melodic moves that create the themes of the melody but also the notes of the underlying chord. 

For the correlation of melodies with chords that fit to them, or conversely , melodies that can be improvised over a chord progression the next local concept is very significant: The closure of a chord: This is defined as the closed interval of notes from all the 12-tone (chromatic) scale) with lower end the lowest note of the chord, and highest end the highest note of the chord. The chord is assumed within an octave, and normal positions, 1st inversion, and 2nd inversion have different closures. All of them may span all the octave. It holds the next interesting theorem. If we define randomly a melody within a the closure of a chord  in normal position  and no other note outside it, with uniform probability of occurrence of any of the notes of the closure, then according to the local condition of fit of a piece of melody with a chord  the only chord in normal position of the chords of the diatonic scale that would fit this melody is the one with this as its closure!. Or more generally if we  define  as probabilities of sounding a note on all the octave an equal value for all notes    except at the notes of the chord X where we have as probability the double this value (e.g. sound each note of the octave once as a scaling that covers all the octave but the notes of the chord once more by just harping the chord) then any such random melody with this probability structure will have as its fitting underlying chord the chord X. 

A very useful remark for improvisation of melody within a particular chord is the next.

Suppose we are at a note y1 of the melody which fits the underlying chord with notes x1x2x3 (whatever that may mean), then depending on the particular position of y1 relative to the x1x2x3, a shift by an interval of 3rd, 4th, 5th, and 6th wil lead to a note y2 that will again fit the chord!. This is because the relative positions of the notes x1x2x3 of the chord are intervals of major, minor 3rd and pure 5th, and their complementary intervals relative to the octave are minor or major 6th, and pure 4th 
The next is a useful concept when creating melodies over chords of a chord progression
HARMONIC BUTTERFLYING 
This butterflying is very often utilizing intervals of 3rds (3 or 4 semitones) and 4ths (5 semitones) and their complementary (6th,  8 and 9 semitones and 5th, 7 semitones when changing octave too),   thus it is ascending or descending chords (chord-scales or chord-arpeggios  , that is why it is called harmonic butterflying) and it is thus chord-harping too, but it involves also intervals of 2nd (1 or 2 semitones) which correspond to chord transitions. We must be utilizing the chord progression as rules of transformation of the theme. A hidden simplicity or invariant in this  butterflying is obviously the underlying chord.  This butterflying maybe of  waving type of melodic move but the amplitudes of the waves may be intervals of 3rds (3 or 4 semitones) and 4ths (5 semitones), instead of intervals of 1 or 2 semitones as in eastern folk music butterflying. And it can be of course of non-waving and monotone scaling type of melodic move . Obviously this butterflying prefers changing strings tuned by 4ths, rather than moving along a single string as in the Greek Bouzouki butterflying.

Summarizing in  a 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. 

More instructive remarks in creating the final melody based on the chords are the next.

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. Similarly ascending melodic moves for  major chords.
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!
8) Although a chord may be simply a minor o major, the part of the melody which the harmonic theme over this chord can be so as if  the chord was with 6th or 7nth. In other words as if we extended the chord with its upper and lower relative chords that is with an interval of  a 3rd higher than its highest note or lower than it lowest not (in normal position) .

For a scientific analysis of the concepts of creating melodies , after a chord progression , composed by elementary melodic moves and chord transitions, see the next paper and software by R.M. Keller , where such melodic moves or chord transitions are called "Bricks"

http://computationalcreativity.net/iccc2012/wp-content/uploads/2012/05/155-Keller.pdf

https://www.cs.hmc.edu/~keller/jazz/improvisor/

6) Writing it with appropriate software, and  produce the musical score. This includes creating a midi file for the song.

( Optional 

7) Create a video for this song )

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 est 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 aver 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 ofthe 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) Itis 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. The tension is highest if the x2 is the 3rd note, middle of it is the 2nd note and resolving if it is the root note. 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.

We summarize the basic concerns in the melodic improvisation and composition of a voice or melody (similar to the syntax of phrase with subject verb and object etc).

1) Always use a finite set of melody motives , themes or moves. A theme may consists of the basic 4 melodic moves.  (The theme entity for melodies is so important as the chord in harmony. A theme can  be inside a chord or over a chord transition. Conversely any of the 3 types of chord transitions may define a theme for the melody, thus a finite set of themes for a chord progression)

2) Transform these melodic themes or moves  which will be the invariant of their transformations. The simpler the themes the easier the transformations.

3) Close it by returning to the initial theme. 

The ways to transform a theme are at least the next 5 and combinations of them

1) Translate it in different pitches (within a scale or not changing possibly the pitch distances )

2) Translate in time (repeat it)

3) Invert it in time or change its rhythm (if at the begging is slower and at the end faster it will be now the reverse etc)

4) Invert it or distort it in pitch (Create 1st 2nd 3rd or 4th voice versions, utilizing the chord progression as rules of transformation of the theme, or if it is ascending now it will be descending etc)

5) Change it as morphology  (from a non-waving ascending it may become waving ascending or iso-kratic) . We prefer spikes and scaling as  the main  morphological types, while the waving and isokratic as intermediate bridges. 

Of course if we want more elementary classification of the pitch moves compared to the 4 basic melodic moves (like not analyzing substances to their chemical type but resort t the 3 elementary particles of electron , neutron and proton), then there are only 3-types  a) the (non-waving) up move of pitch (upward vector) , b) the (non-waving) down move of pitch (downward vector) c) and the sustained sounding of a note (horizontal vector)

In the next video about improvisation is presented a similar philosophy, according to which we first compose before we improvise. So essentially we improvise what we can compose or have composed. And as far as the melody is concerned  we first sing mentally a melody after  a chord progression , BEFORE  we express it on the instrument. We pass at first the melody from the consciousnesses and emotions before we run it with the fingers. 

https://www.youtube.com/watch?v=6-pO0LArVh8


In the next video we see a very cute way to improvise on the chord progression Bm, G, Em, F# (A)
(As shift of F, E, Am, Dm, G)

https://www.youtube.com/watch?v=PLEhGSQqCfQ&feature=em-subs_digest-vrecs

The characteristic of at least  4-notes sub-scales (tetra-chords) of the above extrapolation scales Diatonic, Melodic minor, Melodic double minor, Harmonic minor, Harmonic double minor 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) , 

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  exactly 10 of  characteristic tetra-chords (=4-notes sub-scales)  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)
2-2-2, (major, augmented)
Melodic minor  and double minor
1-2-1
Harmonic minor 
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