72. The importance of the starting and ending notes of a transformed melodic theme, as simplicial submelody. The simplicial submelody as the channel of the full melody and centers of the middle melodic themes

We have described in post 9, 63, 65 how chord-transition melodic moves can be composed. 

 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 sub-melody for each chord progression! We may allow two notes per chord for reasons of flexibility. 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. 


1.2.1) 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  
1.2.2) of as few notes as possible and
1..2.3)  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. Probably best method of  creating first the simplicial sub-melody is based on preferring 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 OR OSCILLATION BOUNDARIES, of the final melody (e. g. Chord-Court melody see post 92) 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. But also bass-lines can be created by the chromatic links or bridges of the chords.  So the rule to choose the simplicial sub-melody is the next

3.1) 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 in a diatonic scale and in the relation of resolution (successive 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. 
IT IS IMPORTANT TO NOTICE THAT IN A CHORD ITI S NOT ONLY THE ROOT AND DOMINANT THAT CREATE AN INTERVAL OF 5TH, BUT ALSO THE MIDDLE NOTE WITH THE 6TH AND THE 7NTHOF THE CHORD.


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

THE NOTES OFTHE SIMPLICIAL SUBMELODY ARE NOT MOST OFTEN INDICATING THE CHORDS OF THE ACCOMPANYING CHORD PROGRESSION BUT ALSO ARE CENTERS OFTHE MIDDLE-SCALE MELODIC THEMES. WHILE THE NOTES OF THE SIMPLICIAL SUBMELODY MEY DEFINE A (SIMPLICIAL) MACRO-SCALE MELODIC THEME.

This perception of the melody, is used also in an excellent way to write the basic bone-structure of the improvised melody, with as high simplicity as the chord progression. We simply chose one of the closest 7-notes diatonic scales, and we indicate the sequence ofthe melodic centers as ordinal numbers of the diatonic scale. 


We summarize some techniques from posts 9, 63,65.

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 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 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. 


VERY SIMPLE MELODIC THEMES OF MELODIC SPEED OF 2NDS AND WITH ONLY ONE CENTAL NOTE OF THE SIMPLICIAL SUBMELODY .

Such melodic themes have as center only one note, usually that of a note of the simplicial sub-melody, and of course usually a note of the underlying chord. The start and end on this note or only end on this note while the waving is by intervals of 2nd. Very simple melodic themes occur often in jigs and reels of Celtic and Irish music, but also of Cretan Lyra music or Pontian Lyra music in Greece. 

LONG-SHORT TWO-STEP PATTERN TO COMPOSE A MELODY 
A very simple trick to create beautiful melodies like those of Irish songs is to use a two-step rhythmic and melodic scheme of one short-duration note and one long duration (like in ancient Greek language that vowels are divided into two categories long and short duration). The long duration is, say two or three times longer, and the long duration is a note belonging to the chord while the short duration it does not! Usually, the two-step pattern id of diatonic density that is the interval of the two notes is a tine or semitone. But sometimes it may be 3 or 4 semitones, that is, of middle harmonic density. One of the goals of the melody is e.g. to walk down or up an octave or an interval of pure fifth or fourth that is to go from simplicial submelody center to another. In this way, both internal and external bridges among the chords can be created. We compose small ripples of this walking up or down (bridges) by the two-step pattern so that the long note is always a note of the underlying chord. thus given a chord progression we may easily compose such beautiful melodies! If there are lyrics and the lyrics e.g. are in the Greek language we immediately derive an appropriate rippling of the melody. When composing melodies through bridges, the bridges themselves are not sufficient to justify the choice of the chords, and we have to walk through the notes of each chord like harping and between the bridges so as to have a full melody that justifies the particular choice of the chords. But when composing melodies after a chord progression through the 2-step patterns (internal-long, external-short notes for the chord) we walk the octave at the area of each chord, therefore, the melody immediately justifies the choice of the chord.

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.    

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. 

MELODIC THEMES TRANSFORMATIONS AND SIMPLICIAL SUBMELODY

We have mentioned in this post that the simplicial submelody is usually  the starting or ending notes of simple melodic themes, that can be external bridges 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 thsi 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 3 elementary melodic themes, as we mentioned earlier (e.g. in posts  66 and 69 ) , are  the ascending melodic interval of two notes, the isokratic melodic interval of two equal notes and the descending melodic interval of two notes.

The 4 basic transformations of them are

1) the translation (either with intervals of 2nd , (or diatonic density) or intervals of 3rd (or middle harmonic density) or  of intervals of 4th or 5th (or high harmonic density))

2) The inversion where the ascending move becomes descending.

4) The expansion-contraction or dilation, in which the theme changes melodic velocity or melodic density. In other words while it is by intervals of 2nd it becomes by intervasl of 3rds or 4ths etc, or vice-versa.

3) Rhythm transformation (which may vary)

The 5 basic melodic moves (see e.g. post 69)  , being more complicated have more types of transformations, as derived by the writing in a pentagram :

1) Translation

2) Inversion relative to a point

3) Reflection relative to an horizontal line

4) Reflection relative to a vertical line.

5) Rhythm transformation

to the above five we may add the

6) Acceleration-deceleration  or Dilation  (e.g. from the diatonic speed or density to the middle harmonic speed or density) or Deceleration (vice-versa).
7) Extension in 2 or more  octaves

Bach has often used the above 6 transformations in his fugue.

More complicated  ways to transform a theme are at least the next 5 and combinations of them (see also post 41)

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 isocratic). We prefer spikes and scaling as the main morphological types, while the waving and isocratic as intermediate bridges. 

Often melodic bridges from a chord to the next, may start with harmonic speed or density covering the first chord A and then decelerate to diatonic speed or density when reaching to the next chord B

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. 

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. 

When we have the full melody, by substituting the melodic move with its starting and ending notes we get a simplicial submelody, which shows in a simplified way the general channel 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. 

It is very instructive to improvise with melodic moves starting and ending at the notes of the simplicial sub-melody , that is at notes of different successive chords (usually at diatonic density) . We may call the external melodic bridges of successive chords. In general this may involve moving on 1 , 2 or more strings. Each part belonging to single string may be called 1-string sub-theme of the external melodic bridge. Most important 
are the diatonic density 1-string sub-themes   from which a diatonic density melodic bridge may consists
But is also very instructive to improvise with melodic moves (usually at diatonic density) starting and ending at the notes of  a single chord . Such melodic moves maybe called internal melodic bridges of the notes of a chord, and again we may define the 1-string sub-themes   of the internal melodic bridges.  Again most important  are the diatonic density 1-string sub-themes   from which a diatonic density melodic bridge may consists.
Besides the simplicial sub melody, there is one more note at each chord which is of importance and this is the one note bass, for each chord which is usually one of the two lower frequency strings of the 4-string chord. 

The IMPROVISATION OF MONOTONE MESMERIZING MUSIC IS USUALLY  a repetitive alternation of two chords, rarely more. 

Thus improvisations with one or two notes bass and internal melodic bridges of a chord with their 1-string melodic sub-themes , as in post 72, become important as a single chord may last for quite of a time duration. This IMPROVISATION may be called BASS-AND-INTERNAL BRIDGES OF A SINGLE CHORD.

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!


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!

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

Here is the result.

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

The 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.

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.

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

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) 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

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.

Internal bridges in a chord are nothing else than extended arpeggios. Here is a video about such an internal bridge called blues arpeggio!

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

(This post has not been written completely yet)

71. Dialogue of a simple human singable melody and dense chatty-birdy instrumental multiplied (counter) melody

Countermelody:

Most of the suggestions about soloing parallel to chords are of the type:

1) Play the arpeggio or chord-tone of the chord

2) Play the pentatonic scale, minor or major, with the same root

3) Play a mode or scale that the song is in it

etc

And although applying the above will not sound ugly when soloing, still all of the above are inadequate for good licks and multiplicative (meaning dense and chatty)  soloing by an instrument in a song! The reason is the next: A song has a singable melody and chords and when soloing, the soloing must not only fit the chord progressions but also resemble the melody that the singer sings especially at the pattern of repeating and transforming simple melodic themes!

Now the melody has simple themes that repeat, ascend or descend and expand or contact. So the soloing must refect the simple theme repetition and transform them in more complicated ways. That is why all the 1),2), 3) are not really adequate.

Here is an example of the fitting of the melody that the singers sings and the instrumental multiplicative soloing

https://www.youtube.com/watch?v=RYXYoUb13nM

In other posts of this book, we have enlarged on the structure of the melody from simple themes that somehow repeat and the simplicial sub melody. E.g. the soloing must have also the same simplicial sub melody. 

This  improvisation is very very common is traditional and folk music. (E.g. Moden Greek songs with companionship with bouzouki, or Latin songs with companionship with charango or ukulele).

This morphology of the songs is as important as accompanying a melody with chords. But it is done only with the dialogue of two melodies! The first is the main simple melody that a human sings and the second is a multiplied melody or a twitting , bird-singing-like soloing. 

The dialogue usually respects, that when one of the two is playing the other is most often silent but not always. But there is a radical difference between the two. Although both play supposedly the melody of the same song, the singable melody is simple with fewer notes and possible to sing by a human voice. While the instrumental dialogue melody, is with many notes, it is chatty, it utilizes almost all the 4 melodic harmonic-speeds (see post 68), the diatonic and chromatic speeds mostly at the chord transitions.   Most often it is so densely complicated with possibly so abrupt jumps that a voice can hardly  sing it . This second instrumental melody is like a singing bird in dialogue with a singing human voice.
Still, the chords that fit to both the human voice and the instrumental chatty-birdy reply are most usually the same sequence of chords. So the  chatty-birdy  instrumental instrumental reply is essentially a variation  embellishment  of the melody with the same harmony and the same simplicial sub-melody. The chatty-birdy reply is done usually during the longer playing of the last chord of the melodic phrase.

Different playing of the song by different groups may respect the melody of the human voice but may largely improvise and vary on the second birdy instrumental melody.
The Birdy-chatty instrumental melody maybe  utilizing more of  of waving around the human singable melody, or fast melodic patterns of the chromatic, diatomic, and harmonic middle and high harmonic speeds, BUT always within the same chord progression of the simple human-voice melody.
Because this birdy-chatty instrumental accompanying melody follows in composition and improvisation both the chord progression AND the simple human voice melody its composition and improvisation is easier, than the composition of a melody after a chord progression. Still what we have write about how to compose default melodies from a chord progression applies here too (see posts 9, 27, 69 etc) . That is why in the method of composing melodies after a chord progression (see post 9) we use the technique of composing at first a simplicial submelody (which plays the role of the simple human singable melody) and then the full melody (which plays the role of the birdy-chatty instrumental dialogue melody.  Of course here we have an additional element to compose, that of the way the two melodies make the dialogue as they both sound, while in the previous reference the simplicial submelody may not sound as a separate melody in the song.

I give here three example. One from a song of traditional music of Andes with charango , and two from modern Greek music with bouzouki.

1) https://www.youtube.com/watch?v=EW5-w-Dr34w

2) https://www.youtube.com/watch?v=SoGdeg2K81c

3) https://www.youtube.com/watch?v=nNE1bBVyImE


Improvisation with  3-string Greek bouzouki, requires learning scales essentially on two successive strings, which is a lot easier than learning guitar scale shapes on 6 strings!

We will  discus here, how such a dialogue between the human singable simple melody and the chatty-birdy melody can me composed.

A way to make the dialogue is to chose some of the human voice melody intervals, and consider them as starting and ending points of melodic moves of the chatty-birdy instrument melody, so that this 2nd melody extrapolates the 1st. And the way to compose these chatty-birdy melodic moves are as in the post 72. For example we may take a simplicial submelody or all of the 1st human-voice melody and consider it as  simplcial submelody to the 2nd melody to compose the chatty-birdy instrumental 2nd melody. Then we embellish the simplicial sub-melody with standard waving that are preferred by the player of the instrument.

ACCOMPANYING A MELODY WITH INTERVALS INSTEAD OF WITH CHORDS.
Another simple idea is that the countermelody (especially when it is on a simpler scale e.g. a pentatonic ) can be used to accompany the melody not with chords but with intervals from the simpler scale of the countermelody. E.g. we may utilize intervals by 3rds as in the role of minor  diminished or augmented chords and the intervals of 4th or 5th as major or power chords



IN MY APPROACH IN THIS BOOK I FAVOR MIXTURE OF AN IN ADVANCED COMPOSED MUSIC PIECE AND  A LATER IMPROVISATION OVER IT, RATHER THAN A 100% PRIMA-VISTA IMPROVISATION. THE REASON IS OBVIOUS. THERE ARE ADVANTAGES OF MUSICAL COMPOSITION THAT WILL TAKE MORE TIME THAN THE DURATION OF THE MUSICAL PIECE OVER A DIRECT IMPROVISATIONAL CREATION OF IT AS WE LISTEN TO IT. THE FORMER GIVES US THE OPPORTUNITY OF A BETTER QUALITY MUSICAL CREATION AND A BETTER BALANCE OF THE PREVIOUS TRIANGLE OF MUSICAL MENTAL IMAGES, SOUND FEELINGS AND FINGER ACTIONS WHEN WE IMPROVISE LATER ON THE ALREADY COMPOSED MUSICAL PIECE.

(this post has not been written completely yet)

70. Memorizing melodies. How ordinary memory people can remember incredible complex things. Cicero's method and the subconscious method.

See also post 285 and 282
Most musical instruments players, memorize their musical pieces, by just playing them sufficient many times, and letting the subconscious memorize them.

There are neverthless short notes about a melody that helps to remember it (especially when the target is an improvisation over the melody) which are not more complicated than the  chord progression which underlies the melody.

Here are hints for it

1) Determine and take note of the root of at least one main diatonic scale from which the melody may deviate and the melody has  maximal number of notes in it among other diatonic scales  (there may be more than one!) . 
2) Determine and take  a note of the parts A B C etc and repetion (loop) pattern of them
3) Determine initial-final note of  each melodic theme in the parts as it varies , as well as lowest and highest note of it and take a note of it attached to  the part
4) Determine and take a note of the longest central notes that define the simplicial submelody that should not me more than the chords of the chord progression

After all the above 4) aspects of  partial information about the melody , listen to it sometimes to refresh the memory about it, and then improvise on  it without changing the information that you took notes. Chose the best version that you feel better , and play it as your own version of the melody.

On the other hand  one may have heard about national or world memory completions, where memory athletes memorize in seconds  the order of whole decks of cards, or hundreds of random numbers etc. And most people thing that such people have extraordinary memory! WRONG! Al these people have average memory abilities, BUT have learned the standard  method of memorizing complex sets of information. Boldly speaking the method (an ancient Greek method, Cicero's method) is to link the elements of the information you want to memorize in to  larger pleasant story! This obviously applies to long and complex melodies, and chord progressions, where the basic parts of the melody are linked between them with a story ...with much more information. 

Below are two video that explain how Cicero's method may make an average man a memory champion! 

http://www.ted.com/talks/joshua_foer_feats_of_memory_anyone_can_do

https://www.youtube.com/watch?v=9ebJlcZMx3c 

69 The simplest hidden symmetry of the composition of beautiful melodies of songs

See also post 114.

From the morphological point of view the basic melodic patterns as  we have mention in earlier posts are the next 5

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

Therefore we may start by choosing the morphology of the melody as a  sequence of the above 5 patterns, that say an emotional story e.g.
1) serenity emotions exploding to  sadness (pattern 5)
2) serenity emotions exploding to  joy (pattern 5)
3) Serenity and diminishing emotions(pattern 4)


Another way to put it is the next
We remind at first that except the melody itself 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. E.g. the starting ending notes of the meloduc themes may be a simplicial submelody while the centers of the melody a higher order simplicial submelody.

Now the best simple  hidden symmetry and simplicity  of the melody that is the subject of this post, is that one of the higher order simplicial submelodies of the melody  has a single or simple sequence 2-3 only,  of the basic 5 melodic patterns! 


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
Chords	Sentences
Simplicial submelody	Subject-verb-object

These sequence of the 5 patterns are best realizable with a very simple simplicial sub-melody! For this it helps very much if the simplicial submelody has long lasting notes  (even for more than one chord!) so that each of these patterns is e.g. 3-4 notes of  the simplicial submelody. The first note of the pattern and the last note may serve as notes of the simplicial submelody. See also a more detailed correspondence below in this post

The simplicial submelody with these 5 patterns may serve as a pattern for self-similar (fractal) repetition with shorter duration notes , and shorter duration similar patterns when composing the full melody ( a  method sometimes utilized by Bach) 

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

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

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

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

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

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

b5) 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

Then correspond this emotional story with the emotional story of the chord progression
E.g. 1) is parallel to  cycle of minor chords like Em, Am, Dm  2) is parallel to a cycle of major chords like
G, C, F, and 3) parallel to  cycle of major chords like A, D, E. (major relative scale A major of A major that were the previous 2 cycles)

If we make sure that the parts with middle and high harmonic speed  of the melody last say more than 70% compared to the parts with chromatic and diatonic speed of the melody, then the correspondence of chords is almost unique and easy! 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. Notice that e.g. since for the C major scale , both the minor cycle (Em, Am, Dm) and the major cycle (C, G, F) cover all the notes of the scale, corresponding a pattern on the major or minor cycle , is simply the way we start to span in middle harmonic speed the scale. Taking the middle notes as roots of the minor chords in the sequence Dm->Am->Em we get the sequence of the major chords F->C->G , and both triads are in the middle harmonic melodic speed. 

Notice that although a chord may have duration  for many notes of the melody, the above 5 melodic patterns may have duration for many chords of the chord progression. Thus these 5 melodic patterns are intended to by more macroscopic than a chord. By utilizing the inversions of a chord, and shifts in higher or lower octaves, the chords themselves, if they have been determined before the above 5 melodic patterns in the harmonic method of composition, can serve as vectors of move at middle or high harmonic melodic speed, to shape on of the above 5 melodic patterns. 

Of course as the approach of composition in this book, favors the greater simplicity, it is desirable to start composing from the more macroscopic and abstract patterns first to the smaller and more detailed patterns afterwards. Thus we may very well have at first a composition of a sequence of the above 5 melodic patterns, then the chord progression, then the simplicial submelody and  finally the detailed full melody

As an example we may discover exactly such a design in the song tico-tico non fuba by  Zequinha de Abreu in 1917(see https://en.wikipedia.org/wiki/Tico-Tico_no_Fub%C3%A1  and https://www.youtube.com/watch?v=lsMNvmqRdC0 and https://www.youtube.com/watch?v=Vo-OpQS2zdQ) which had huge success internationally during the 20th century. The melody of the song is designed with
1) serenity emotions exploding to  sadness (pattern 5)
2) Serenity and equilibrium emotion (pattern 3)
2) Serenity and diminishing emotions(pattern 4).
The pattern 5 is created in 2-3 variations with combination of chromatic, diatonic and middle harmonic speed over the mainly minor (sadness) chords B7, E, Am, Dm . Then a variation of pattern 3 is repeated parallel to the major (joy) chords G, C, F. And finally, the pattern 4 is created in 1 or 2 variations over the major (joy) chords E, A, D.

Other examples are celebrated musical pieces of Paganini , who loves to design whole pieces over the patterns 2 and 3

The way that patterns 1,2,3,4,5 can be realized with different melodic speeds (see post 68), the appropriate rhythm,  "sketching" or variations of them and over different chord progressions is practically unlimited! But the hidden simplicity of the emotional story of the 5 patterns behind it may always be very simple!

THE BASIC CONCEPT OF MUSICALLY BEAUTIFUL  IN THIS BOOK IS THE CONCEPT OF HIDDEN SIMPLICITY OF  RULES OF PROPORTIONS OF 2 AND 3 , AND IN GENERAL OF VERY SMALL INTEGER NUMBERS IN FREQUENCIES, (INTERVAL HARMONY) MELODIC MORPHOLOGY (VOICES), RHYTHM (ORDER AND DIMENSION OF RHYTHMS) AND EVEN PERCENTAGE OF MAJOR (=2/3)-MINOR(=1/3) CHORDS ETC. 

THE 5 BASIC MELODIC PATTERNS ARE REDUCED TO THE ELEMENTARY 3 MELODIC PATTERS THROUGH THEIR CRITICAL MELODIC INTERVAL!

We explain: The basic melodic patterns are 5 as we mentioned at the beginning of this post. But elsewhere we have mentioned the elementary melodic patterns that re only 3 (the up the down , the isoskratic or plain). Now the way to derive an elementary pattern from a basic pattern is through their critical melodic interval. A melodic interval is of course always  up , down , or the isokratic  plain. The critical melodic interval of the basic melodic pattern is the most characteristic interval of the pattern, that subconsciously the subjective listening would simplify in it the basic pattern. Usually it is the first and last notes of the pattern but not always. As with the critical path in the flow charts of the projects scheduling, the critical interval is usually the longest in the pattern or the one that sounds more time.

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)

1/3-2/3 POETIC MELODIC PATTERNS

These are melodic simple patterns where at the 1/3 of their duration sound transient short notes and 2/3 of their duration a long lasting note. E.g. S1+L,  or S1+S2+L or S1+S2+S3+L where the duration of the short notes S1 or S1+S2 or S1+S2+S3 is 1/2 of the duration of the long note L. Then the short note serve also as transient notes, while the Long note is always a note of the underlying chord. In this way the harmonic part of the melody (L-notes) is always double of the transient-chromatic part of the melody. 
Such melodies are very common on Irish traditional music, but also in Greek Islands traditional music.

 In traditional  poetry the poetic measures can define such melodic patterns. 
The poetic measures e.g. in the ancient and modern Greek poetry are the next 4 
1) Iamviko      S+L   duration(S)=1/2duration(L)
2) Trochaiko  L+S  duration(S)=1/2duration(L)
3) Anapestiko  S1+S2+L   duration(S1+S2)=1/2duration(L)
4) Daktiliko     L+S1+S2  duration(S1+S2)=1/2duration(L)
5) Amphivrachi   S1+L+S2 duration(S1+S2)=1/2duration(L)

68. The 4 basic melodic speeds or densities: The chromatic (chromatic ripples), the diatonic ( ripples), the middle harmonic (waves), and the high harmonic(spikes). The melodic pitch accelerations. Fretboard angles and melodic densities

(this post has not been written completely yet)
We define and discuss in this post an important concept in composing beautiful melodies, that of the basic melodic speeds or densities.  This speed has nothing to do with the time speed of laying the melody. It only has to do with how large intervals is the steps of the melody, that is is called harmonic speed. 

1) The chromatic melodic speed or density (chromatic ripples) is melodic themes composed in such a way that successive notes are always in a distance of 1  semitone.
2) The diatonic speed or density (ripples)  is  melodic themes composed in such a way that successive notes are always in a distance of 1  step of the diatonic scale, thus 1 or 2 semitones.
3) The melodic or middle harmonic  speed or density (waves) is  melodic themes composed in such a way that successive notes are always in a distance of an interval of 3rd and alternating (major minor)  thus of 3 or 4 semitones. Any 3 successive notes define a major or minor chord.
4) The harmonic or high (maximum) harmonic  speed or density (spikes) is  melodic themes composed in such a way that successive notes are always in a distance of an interval of perfect 4th or 5th   thus of 5 or 7 semitones. 

Besides the 4 melodic speeds we have also the 2 melodic accelerations   which are sequential combination of acceleration=speed1+speed2 , where speed2>speed1 E.g.

1) Diatonic acceleration=chromatic speed+diatonic speed
2) Harmonic acceleration=diatonic or chromatic speed+harmonic speed (middle or high) 

Here the acceleration is not in the time but in the pitch change. 

Correspondence of chord transitions of chord progressions to the 3-melodic densities or speeds  of the melodies that fit to such chord progressions

(See also post 30)
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. 

ANGLES IN FRETBOARD AND MELODIC SPEEDS

1) When playing the melodies on the fretboard in the guitar, the chromatic/diatonic speed is played mainly along the length of a string, so it is the zero angle.

2)  When playing the melodies on the fretboard in the guitar, the middle harmonic  speed is played mainly at an angle which relative to the horizontal is about 45 degrees and moves from the keys of the guitar to the sounding body as the melody descends in pitches! This is is because it consists of intervals of 3 or 4 semitones that in two successive strings is such an angle.

3)  When playing the melodies on the fretboard in the guitar, the high  harmonic  speed is played mainly at an vertical  angle  relative to the horizontal because the strings are tuned at intervals of 5 semitones (and one string in 4 semitones). Also the interval of 7 semitones (5th) when played in descending the pitches makes an angle  larger than vertical or 90 degrees (e.g. 135 degrees) and moves from  the the sounding body of the guitar to the keys of the guitar  as the melody descends in pitches!

A characteristic of melodies of Andes ,Incas, Bolivia, Chile etc is that there is often the melodic pattern of non-waving ascension, which escalates from chromatic or diatonic melodic speed , to middle harmonic and then high harmonic , giving thus the feeling of acceleration of joy or sadness! 

The famous jazz violin player,  Stephan Grappelli soloing is utilizing the diatonic speed , with almost no (middle harmonic speed)  waving but approximation of continuous movements at diatonic speed together with occasional spike jump intervals  at high harmonic speed or even higher jumps. If waving are like dancing steps, the Grappelli soloing is like fast walking from point to point with rather small (diatonic) but not very small (Chromatic) steps. 

See e.g. https://www.youtube.com/watch?v=vi10rCh73j8

Another characteristic of the happy and joyful melodies of the Andes , is that the often 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 they use almost exclusively the maximum harmonic melodic  speed that the chords allow. 

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 (like that of ethnic music of Andes). It directly defines improvisational beautiful melodies from the chord progression,  because the maximum intervals of a chord are unique or very few for each chord! In fact a single large such interval from each chord can define the melodic-rhythmic pattern for each chord! 

The standard preference is to use 

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

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

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

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

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

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

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

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

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

b5) Itis prefered that intervals of 1,2,3,4 semitones are converted to their complementary 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 sumplicial 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


The next beautiful melody from Andes (La partida/Quiero ser tu sombra ) is an example of a a melody with all the 4 melodic speeds, chromatic, diatonic, mid and high harmonic

https://www.youtube.com/watch?v=MIgyAvDvoR0

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 9 for the harmonic method of composition). 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.