213 . MELODIC IMPROVISATIONS BY SHIFTING FROM THE IONIAN MODE TO THE CELTIC MINOR TO THE INDIAN PENTATONIC AND TO THE GREEK PENTATONIC SCALE

For the next see post 204
The celtic 6-notes minor scale 2-2-3-2-2-1 is a subscale of the 7-notes diatonic scale 2-2-1-2-2-2-1

The Greek pentatonic (5-notes) scale 2-2-3-4-1  is a subscale of the Celtic 6-notes  minor scale.

But also the India or Egyptian pentatonic scale 2-2-3-2-3 is also a a subscale of  the 6-notes celtic minor

This allows for interesting improvisations shifting from 

1) Ionian more of diatonic 2-2-1-2-2-2-1

2) Celtic minor  2-2-3-2-2-1

3) Greek pentatonic 2-2-3-4-1

4) Indian pentatonic 2-2-3-2-3

where in all cases the 3 first notes and interval structure in semitones 2-2 remain stable 

212 MELODIC IMPROVISATIONS BY SHIFTING FROM 1) AEOLIAN MODE ( NATURAL MINOR) TO 2) DORIAN MODE 3) MELODIC MINOR 4) HARMONIC MINOR

 This improvisation and modulations of these 4 changes

1) Aeolian mode or natural minor a-b-c-d-e-f-g-a  (of D diatonic)

2) Dorian mode of  the diatonic scale of one tone higher thus here of D  diatonic
     a-b-c-d-e-f#-g-a
3) Melodic minor of C diatonic
   a-b-c-d-e-f#-g#-a

4) harmonic minor

   a-b-c-d-e-f-g#-a

ALL HAVE THE FIRST PART OF 5 NOTES OF PENTA-CHORD THE SAME AND STABLE

a-b-c-d-e or in  intervals in semitones   2-1-2-2

THEREFORE THE IMPROVISATION HAS ONLY CHANGES ON THE LAST 4 NOTES OR LAST TETEA-CHORD WHICH MAKES IT STABLE AND INTERESTING.
WHEN CHANGING THESE MODES AND SCALES WE MAY ALSO CHANGE OCTAVE TOO,WHICH IS VERY EASY IN AN OCTAVE TUNING AS IN POST 210.

      

211. AN OCTAVES AND FIFTH AND OTHER ALTERNATIVE TUNINGS OF THE VIOLIN FOR SPECIAL IMPROVISATIONS

As we wrote in post 209, there is a system of melodic improvisation based on drone (isocratic) interval of  an octave and melodies derived by alternating intervals 5th and 4rth so as to create successive power-5 chords among octaves. But this requires alo in string instruments special tuning and a space of 3 to 4 octaves.

happily for the violin have been created the octave-violin strings which are one octave lower from the standard. So instead of  G3-D4-A4-E5 these strings will tune the violin to G2-D3-A3-E4.

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


This allows for  mixed low-standard tunings of the violin for melodic improvisations as inpost 209 that are 8-5-8 meaning that the 1st-2nd string are one octave apart , the 2nd-3rd one fifth apart and the 3rd-4th one octave apart E.g.

G2-G3-D4-D5 (utilizing strings octave G2, standard G3, octave D3, standard E4 for the D5 ) or

A2-A3-E4-E5 (utilizing strings octave G2 for A2 , standard A3, octave E4, standard E5)

The 2nd requires one tone loosening one standard string and the 1st one octave string and one standard string tightening by one tone.


ALTHER ALTERNATIVE TUNINGS

1) THE OCTAVES 3 STRING TUNING:

This is utilizing again the D3 octave string of the violin and it is simply the

D3-D4-D5

For the D5 we use obviously the E5 string

The advantage is obviously very easy grasping of the notes on the fingerboard , as known one strings is known all the violin.

2) THE PANDURI OR OPEN MAJOR CHORD  3 STRING TUNING:

This is not utilizing octave strings of the violin and it is simply the open G3 major chord. The advantage is obviously very easy arpeggios (harpisms) on all chords of the (G major) diatonic scale.

G3-B4-D5

For the D5 we use obviously the E5 string and for the B4 the A4 string of the violin.

If we want a more bass version of the open major chord tuning,then we may utilize the G2 octave string of the violin and have the tuning as follows:

G2-B4-D5


FRETBOARD VIOLIN (FRET-LIN OR METRIC-LYRA ) PLAYED AS CRETAN LYRA (OR  SMALL CELLO)


Many companies of electric violins manufacture them with frets on the fingerboard.

If we apply on the violin fingerboard ready made auto-sticking fretboards, we still can have tremolo and vibrato and even a type of glissanti while we do not spent so much time  learning the fingerboard. Then if we know fretboard string instruments like mandolin , ukulele, guitar it helps a lot to start playing the violin as an instrument without artificial difficulties.

(Here is such a product from a canadian musician http://www.frettedfiddle.com/ )

In addition it is by far more convenient to play it as they play the folk Lyra in Greece (Crete) and other places in other words like a small cello, on the knees. If we want to have also the bow falling with its own weight in stable way on the strings as in the standard position of the violin we may use simple bow drivers like these here https://www.aliexpress.com/item/32878752247.html?spm=a2g0s.9042311.0.0.21cd4c4deuojvB )

FRENCH AND GERMAN BOW HOLDING

The bow in case of this modification of the violin which is essentially a new instrument that could be called FRET-LIN OR METRIC-LYRA can be either with the German or French way. The French way gives more control because of more efficient use of the bones of muscles of wrist for difficult moves of the bow, but the German way is more relaxing. A best result is if we use both ways for difficult bowing the French way and for stand more easy bowing the German way.

210.OCTAVES TUNING

This is simply the tuning where each string is tuned one octave higher than the previous

Obviously there are limitations due to  the material of strings that have also to be of equal (scale-length) length.

E. g. in 3-string instruments like saz, tambouras, Bouzouki , balalaika , panduri etc

it will be

D2-D3-D4 or C2-C3-C4 or E2-E3-E4 etc

But utilizing digital fretboards like Artiphon  (https://artiphon.com/ )we can even setup 6 strings with octaves tuning

C1-C2-C3-C4-C5-C6  OR  C2-C3-C4-C5-C6-C7 ETC.

THen improvisations as in post 209 will sound beautifully and will resemble a bit the style of Alexey Archipofsky improvisations

 https://www.youtube.com/watch?v=CIaL-mrWOWA&t=165s

209. MELODIC TETRA (4) OR PENTA (5) -CHORDS: SOLO COMPOSITION AND IMPROVISATIONS BASED ON ALTERNATING MELODIC QUARTETS OR QUINTETS OF INTERVALS OF 4TH AND 5TH.

THE ANCIENT MUSICAL THEORY SIMPLE DESCRIPTION OF RAPSODY MUSIC STIL LIVING IN THE AEGEAN ISLANDS LIKE THAN OF CRETE IN GREECE :

Such music was created in ancient times it  is mesmerizing with complicated melodic lines but in reality very simple musical description.

For these Aegean islands (Greece) improvisational folk melodies with violin or Lyra, the next factors prevail.

1) "Poetic meters" over the same note sometimes note up to 8 notes

3) Straight vectors ascending or descending usually of 4 or 5 notes so as to reach a new chord neighborhood.

2) Mainly waves by intervals of 2nds (chromatic) inside intervals of 3rds (melodic, either standing or ascending descending, and usually inside a chord  so as to reach the neighborhood of a new chord.

A) THE UNDERLYNG CHORD OF THE SONG IS ONLY ONE AND IS A POWER  CHORD AT ROOT POSITION OF SAY A DIATONIC SCALE (ALTHOUGH IN ANCIENT TIMES THEY DID NOT HAVE THE CONCEPT OF A  7-NOTES SCALE BUT ONLY OF A 4-NOTES SCALE THE  TETRACHORD WHICH WAS A SCALE SPANING ONLY AN INTERVAL OF 4TH INSTEAD OF AN INTERVAL OF 8TH, THUS POWER CHORD WOULD BE THE ROOT POSITION ON THE TETRACHORD). 

B) THE SOLOING IS ANY REPEATING PROGRESSION OF SHORT RYTHMIC MELODIC THEMES WITHIN A TETRACHORD WHICH  IS USUALLY  THE 1-2-2 IN SEMITONES THUS THE FRYGIAN TETRACHORD AT THE 3RD POSITION OF A  DIATONIC SCALE WITH UNDERLYING POWER CHORD AT THE ROOT POSITION OF THE TETRACHORD OR THE 3RD POSITIONOF A MODERN 7-NOTES DIATONIC SCALE. (SOMETIMES ALTERNATING WITH ANOTHER TETRACHORD E.G. THE IONIAN TETARCHORD AT ROOT POSITION OF THE 7-NOTES DIATONIC SCALE , AND IN ANY CASE THE ACCOMPANYING CAN BE ALSO BY THE POWER CHORD AT THE ROOT POSITION OF THE 7-NOTES DIATONIC SCALE IN INSTEAD OF THE 3RD POSITION OF THE DIATONIC SCALE)

THE MORE COMPLICATED BUT NOT  ALWAYS MORE ENLIGHTENING DESCRIPTION WITH MODERN SCALES AND CHORDS: 

MELODIC TETRA (4) OR PENTA (5) -CHORDS: SOLO COMPOSITION AND IMPROVISATIONS BASED ON ALTERNATING MELODIC QUARTETS OR QUINTETS OF INTERVALS OF 4TH AND 5TH.

(This post has not been written completely yet)

In post 208 we discussed a similar idea but with alternating major/minor 3rds creating thus underlying harmony of major /minor chords of diatonic scale. The optimal tuning for this is string instruments  tuned uniformly by intervals of 5ths.

Here the idea is the same but we alternate intervals of 4th-5th to create power-5 chords. The optimal tuning here is the octaves tuning of post 210.

When improvising is a solo in an almost random way but which tries to listen also to the inner emotions, a good path is to walk by intervals of 2nd small distances of total length and interval of alternating intervals of 4th (5 semitones) and 5th  (7 semitones) exactly as it happens in a power-5 chords of diatonic scale, as this also creates an underlying  simple and string harmony. 

This type of walking vector-intervals (see also post 183 1nd 159) in other words intervals closed together with all the intermediate notes of diatonic scale that it belongs to it we have called previous post as vector-chord improvisation as contrasted to arpeggio improvisations.

Therefore instead of the concept of scale (and as here we do not assume a chord progression or scale of chords) we have the concept of tetra-chords and penta-chords   as vector intervals of  4th and 5th respectively.
In ancient Greece the dominant concept was not the 7-notes scale but the tetra-chord and penta-chord. By combing two such we get 7-notes scales  

Of course here also a 4-chord and a 5-chord (or vice versa) of length an interval of 4th and an interval of 5th create a 7 -notes scale . Some of them are modes of the diatonic scale, the harmonic minor  the double harmonic minor and the melodic minor.

Of course we add wavings by intervals of 2nd and we go up or down according to the alternation of sad and happy changes of the emotions. 

The 4th/th  alternation also corresponds to alternation of sad and happy emotions. 

If we are on string instruments tuned by octaves (see post 210), then we can also accompany this solo with the interval of 8th of the two immediately lower strings as a kind of drone power-8 chord. The melodic themes created in one or two consecutive such (vector) intervals of 4th-5th can be varied of course with translations, inversions, rotations (including expansions)  and mutations. In an octaves tuning this can be done by shifting octaves which means shifting among the strings.
Normally two tetra-chords/pentachords  are for the first poetic line (8 beats) and two more for the 2nd poetic line (7 syllables) in lyrics of 15-syllables poetry.

ALL 6 TETRACHORDS   (also called vector intervals of  4ths)

DIATONIC FAMILY

(containing only 2 and 1)

2-2-1  syntono major  , Ionian/mixolydian

1-2-2  syntono minor  , Phrygian/Locrian

2-1-2   minor, Dorian/Aeolian

CHROMATIC FAMILY

(containing 3)

1-3-1   2nd chromatic

1-1-3    parachromatic tonal

3-1-1    1st chromatic 

ALL 20 PENTACHORDS   (also called vector intervals of  5ths)

All pentachords contain a single power-5 chord that power-5 chord which is defined by the end-notes of the pentachord.

DIATONIC FAMILY

(containing only 2, and 1)

2-2-2-1       Major Lydian    Contains a major chord (known also as Natzi/Zaouil)

2-2-1-2        Major Ionian/Mixolydian    Contains a major chord.(known also as Rast/Mahour)

2-1-2-2       Minor Dorian    Contains a minor chord (known also as Bousselik/Nichavent)

1-2-2-2       Minor Frygian/Aeolian    Contains a minor chord (known also as Qourdi)

CHROMATIC FAMILY

(containing  3 )

1-1-3-2

1-1-2-3

1-3-2-1   Contains a major chord and a diminished chord

1-2-3-1   Contains a minor chord and a diminished chord

1-2-1-3   Contains a minor chord and a diminished chord

1-3-1-2   Contains a major chord and a diminished chord (known also as Hijaz)

3-2-1-1    Contains  a diminished chord

2-3-1-1

3-1-2-1   Contains a major chord and a diminished chord

2-1-3-1   Contains a minor chord and a diminished chord (known also as Nevesser/Nikriz)

3-1-1-2   Contains a major chord (known also as Saz-kar)

2-1-1-3   Contains a minor chord (known also as Samba)

ENHARMONIAN FAMILY

(containing  4 )

1-1-1-4   Contains a minor chord

1-1-4-1

1-4-1-1

4-1-1-1   Contains a major chord

Of course a 4-chord and a 5-chord (or vice versa) of length an interval of 4th and an interval of 5th create a 7 -notes scale . Some of them are modes of the diatonic scale, the harmonic minor  the double harmonic minor and the melodic minor.

In composing melodic themes based on melodic tetra-chords/penta-chords  we should use also the concept and technique  of  variational  independent base of melodic shapes or melodic seed (see post 106). I other words the melodic themes shapes that are mutually variational independent, in other words neither translation neither , inversion, neither rotation can derive any one of them from the others , and in addition all other melodic themes of  the song can be derived with variations from them.

208. MELODIC TRIADS: SOLO COMPOSITION AND IMPROVISATIONS BASED ON ALTERNATING (MELODIC TRIADS AS VECTOR) INTERVALS OF MAJOR(HAPPY) /MINOR(SAD) 3RD:RECIPES OF HAPPINESS AND SADNESS

(This post has not been written completely yet)

MELODIC TRIADS: SOLO COMPOSITION AND IMPROVISATIONS BASED ON ALTERNATING (MELODIC TRIADS AS  VECTOR) INTERVALS OF MAJOR(HAPPY) /MINOR(SAD) 3RD:RECIPES OF HAPPINESS AND SADNESS

HERE IS EXAMPLE OF SUCH  IMPROVISATION

https://www.youtube.com/watch?v=Hxym5yTmdC8&t=1420s

When improvising is a solo in an almost random way but which tries to listen also to the inner emotions, a good path is to walk by intervals of 2nd small distances of total length an interval of 3rd and alternate  major (4 semitones happiness ) and minor (3 semitones, sadness ) exactly as it happens in a diatonic scale, as this also creates an underlying  major or minor chord. If on the other hand it is two consecutive intervals of minor 3rd it would create an underlying diminished chord and if consecutive major intervals of 3rd an augmented chords (that occur in the harmonic and double harmonic minor) , both more  rare compared to major and minor chords. 

This does not mean that we create a specific diatonic scale or mode of it but rather pieces of diatonic scales, therefore it is more probable that we are in a bebop scale (union of two diatonic scales).

This type of walking vector-intervals (see also post 183 1nd 159) in other words intervals closed together with all the intermediate notes of diatonic scale that it belongs to it we have called previous post as vector-chord improvisation as contrasted to arpeggio improvisations.

Therefore instead of the concept of scale (and as here we do not assume a chord progression or scale of chords) we have the concept of TRIAD  as vector interval of 3rd MINOR (SAD) OR MAJOR (HAPPY) . By composing triads we get various types of scales known or unknown but with recognizable hidden harmony.
OF COURSE WE MAY VERY WELL WALK BY TRIADS A DIATONIC SCALE GIVING SEQUENCES OF MAJOR (HAPPINESS) AND MINORS (SADNESS) 3RDS IN THE PROPORTION AND COMBINATION WE WANT.
KNOWING THIS IN MAJOR-MINOR 3RDS WE ALWAYS KNOW WHERE TO FIND HAPPINESS AND MORE HAPPINESS AND SADNESS AND MORE SADNESS.
Inharmony a chord is a triad, and triads of chords define usually in  a minimal way the harmony of a scale. Similarly here in melodic composition, the basic composition element is a melodic triad as above, and and triads of melodic triads define somehow an scale of an octave.

The usual  triads  are the next 3 in semitones

1-2
2-1
2-2
  giving in total  semitones 3 or 4 or an interval of  3rd

Of course we add wavings by intervals of 2nd and we go up or down according to the alternation of sad and happy changes of the emotions. The major/minor 3rds alternation also corresponds to alternation of sad and happy emotions. We may of course alternate to the solo also triad chords. If we are on string instruments tuned by 5ths, then we can also accompany this solo with the interval of 5th of the two immediately lower strings as a kind of power-5 chord. The melodic themes created in one or two consecutive such (vector) intervals of 3rd can be varied of course with translations, inversions, rotations (including expansions)  and mutations.
Normally two triads are for the first poetic line (8 beats) and two more for the 2nd poetic line (7 syllables).

If we do not walk the intermediate notes of the vector interval of 3rd and we just jump-play it, alternating major minor such intervals of 3rd we are simply in t what we have called in post 94 the melodic corridor, which e.g. how the siku pan-fludes and pan--flutes with double rows of pipes are designed in the folk music of andes.

In composing  melodic themes based on melodic triads we should use also the concept and technique  of  variational  independent base of melodic shapes or melodic seed (see post 106). I other words the melodic themes shapes that are mutually variational independent, in other words neither translation neither , inversion, neither rotation can derive any one of them from the others , and in addition all other melodic themes oft he song can be derived with variations from them.

We should not confuse the melodic triads, which is a concept similar to that of  a scale of notes with the shapes of melodies in a melodic triad (as e.g. in post 100-106).

207. CHORDS MIDDLE NOTES SIMPLICIAL SUB-MELODY AND IMPROVISATION BASED ON THEM

See also posts 65, 72, 92, 103, 104 (concepts of chord-local 7-notes scale and chord-courtyard)

The chord-middle note simplicial sub-melody (CMNSS) this is one of the most simple tupes and most characteristic sub-melodies for the chord progression. The reason is that the middle note characterises a chord of it is major or minor, and thus this sub-melody involves notes that sometimes are the critical notes of modulations e.g. from the natural minor o the harmonic minor or double harmonic minor

In post 104 we have described more types of simplicial sub-melodies.

Here we describe a basic technique of the composition method that starts first from the chord progression and then the melody introduced in post 9  (as in jazz improvisation).

A simplicial (or simplistic) sub-melody is a bit more varying than a drone (isocratic)  melody, and is also the  source  of the bass lines. 

1) Chromatic simplicial sub-melody (CSS , minimum distance notes) .  The simplicial submelody is defined by the next rules. 

 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. E.g. if the chords are , the first chord is the C major=(c4,e4,g4) and the 2nd chord is the F major=(f4,a4,c5), then the notes are e4-f4 that is 3rd-1st. If the chords are the first chord is the C major=(c4,e4,g4) and the 2nd chord is the D minor=(d4,f4,a4), then the notes are e4-f3 that is 3rd-3rd. 

 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! That is the 1st-5th order notes. E.g. If the first chord is the C major=(c4,e4,g4) and the 2nd chord is the E minor=(e4,g4,b4) then the notes are b4-c5, that is 5th, and higher 1st. But if the chords are  C major=(c4,e4,g4) and the 2nd chord is the A minor=(a3,c4,e4), then the notes are a4-g4  , that is the higher 1st. and the 5th. If the chords are major-minor relatives : C major=(c4,e4,g4) and the 2nd chord is the C minor=(c4,eb4,g4), then the notes are eb4-e4 , that is 3rd-3rd. 

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 link or chromatic bridge  is defined by finding two notes a1 in X1, a2 in X2, so that a1-a2 is at the minimum interval distance among all other chord notes of X1 , X2. Then the chromatic link starts with a1, b1,b2....,bn,a2 , and ends with a2 and all the intermediate steps are one semitone distance. 

1.3) 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  
1.3.1) of as few notes as possible and
1..3.2)  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)  
This is very useful in double flutes or whistles or double reed-winds playing where in the first it is played a minimal chromatic drone sub-melody, and in the 2nd a full melody.

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 (HSS, maximum distance notes) . Probably the best method of creating  the simplicial sub-melody which 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 oscilaltion boundaries of the final melody and most often it is one note per chord of the chord progression . They may be also the start and end of the melodic themes. Or they can be just centers that the melodic theme must pass from them. 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 note of the simplicial sub-melody belonging to the chord X(2), then a->b is an interval of maximum distance and the preference in intervals is in the following order of preference 5th, 4th, 8th, 6th. 
For the notes of maximum distance between successive chords we have the next choices : 

If the X(1) -> X(2) are 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 best choice of a->b, here the c-> f, and a 2nd best choice the c-> which is an interval of 6th.
The notes of maximum distance would be two notes per chord. The 1st would be the maximum distance from the previous chord and the 2nd the maximum distance from the next chord. We prefer usually to simplify it it in to one only note but either two or one only note  if necessary we shift to the next octave so as to have the rule that two successive notes of two successive chords of the harmonic simplicial sub-melody have always distance large intervals of  5th, 4th, 8th, 6th. 
2.2) After we have defined the simplicial harmonic and the chromatic sub-melody then we may create bridges between its notes by smaller intervals e.g. 3rds or 2nds for a  full melody. The best ways is to start from the first note of the Chromatic Simplicial submelody (CSS) of the chord relevant to the previous chord, pass from the unique note of the Harmonic simplicial submelody (HSS)  of the chord and end at the 2nd note of the chromatic simplicial submelody (CSS) of the chord relevant to the next chord. (See post 109).
The notes of the harmonic submelody of a chord progression may be used to be  somehow the centers or oscilaltion boundaries of a final melody and most often.  They may be also be the start and end of the melodic themes. It depends if we create melodic themes inside the chord and around of a note of it which serves as it center or melodic themes linking two of them  and their successive chords. For the first way , the melodic themes inside the chord and around the note of the harmonic simplicial submelody can be created as in the post 103 using the chord-local 7-notes scale for each one note of the harmonic simplicial submelody.


There are also the 


3) CHORD-PROGRESSION SIMPLICIAL SUB-MELODIES (CPSS) 
 This is defined in the most easy way as consisting from one note per chord of the chord progression and always at the same degree (1st or 3rd or 5th, or 6th, or 7nth or 9nth or 2nd etc) 
Here is relevant video that by extrapolating  this simplicial sub-melody , we get an improvisational melody, an idea of Jerry Bergonzy

https://www.youtube.com/watch?v=2X-WsnWCAaA&t=21s


4) The chord-middle note simplicial sub-melody (CMNSS) this is one of the most simple tupes and most characteristic sub-melodies for the chord progression. The reason is that the middle note characterises a chord of it is major or minor, and thus this sub-melody involves notes that sometimes are the critical notes of modulations e.g. from the natural minor o the harmonic minor or double harmonic minor 
IN THE NEXT WE DESCRIBE HOW TO CALCULATE THE SIMPLICIAL SUB-MELODY OF THE MELODIC CENTERS OF A MELODY

For improvisation in general over a known  or unknown a tune we need two types of concepts 
1) Simplifying to the melody concepts like chord-progression, simplicial sub-melody , bas etc
2) Enhancing to the melody concepts like counter-melody on the vector-chord underlying at that time the melody etc From the chord the middle (3rd note together with the root 1st note) is considered tobe the most characteristic from the chord as it differentiates it from major and minor.
Because 5 notes are played statistically almost equally in time and 3 are inside the chord while 2 only outside the overall result is harmonic with the chord. taking the middle note (3rd) ofthe chord as it its geometric center rather than its root, we have that this soloings is a kind of  almost random "dancing" around the geometric center of the chordand inside the underlying scale. Since for each chord there is usually one note of a simplicial submelod, and we may take as note of the simplicial sub melody the geometric center (3rd in1-3-5) we may alsos say that this way of improvising is a "dancing" around the notes of this (middle note) simplicial submelody

The chord-closure or vector-chord as defined in post 159 is only for the normal position of a chord.

The random playing of the notes at an equal time each, or "rotations" or permutations of a vector-chord (or chromatic and diatonic neighborhood of  a chord) ,  leads to a melody that the chord that fits to it harmonically to accompany it, is the chord of the vector-chord. In this way, a pre-defined chord progression visualized as a progression of vector chords, defines almost completely an improvisational melody. 

2ND LAYER FASTS HARMONIZATIONS OF VECTOR-CHORDS IMPROVISATIONS

Furthermore, when improvising by "waving" or "rotating" inside the vector chord, we may also add some harmony by playing the improvisational solo as 1st-2nd voice or doubles by intervals of 3 and of course changing them to major minor 3rds so that it belongs to the scale if the roots are in  the scale or keeping it the same to the closest such that is in the scale. It can be with doubles or even triads (3-notes chords) which of course will create a fast-changing harmony which is reasonable to accompany with only stable power chord of 5 (interval of  5). Usually, the fast changing of the chords is of the chords I, IV, V (or  substituting any one of them with its lower relative minor chord. see also post 159)

E.g. here is a good example of such melodic wavings in the next midi file. It can be considered as chromatic or diatonic waving around each note of the chord but in addition, harmonized with doubles by intervals of 3rds http://www.greeksongs.gr/midis/arampasperna.mid 

Because 5 notes are played statistically almost equally in time and 3 are inside the chord while 2 only outside the overall result is harmonic with the chord. taking the middle note (3rd) ofthe chord as it its geometric center rather than its root, we have that this soloings is a kind of  almost random "dancing" around the geometric center of the chordand inside the underlying scale.

We should notice that besides such "chromatic waving" or "rotating" within the closure of a triad chord in the normal position, we may have also waving ascending and waving descending or translating, if we expand the chord in two or 3 octaves. And this may be done again with fast-changing harmonization (I, IV, V)  with doubles or triads , as long as the duration of the notes outside the chords (the initial and maybe two more within the pattern I, IV, V) are less than the duration of the notes inside the chords or as long as the intervals created by the notes of the melody and the notes of the chords have more 3rds 4ths and 5ths compared to intervals of  2nds.

We must remark here that if there is a melody in the song which is say using the chords X1, X2 X3,...Xn , the melodic improvisational fillings parallel and in between the parts of the melody with instruments like Bouzouki or mandolin or violin or lyre etc , need not keep the same chord-progression X1,...Xn but a permutation of it as well ,although in general, it will use the same chords and rarely more chords but of the same notes-scale or same scale of chords  (chord-scale). 

In all cases, a variational chord progression X(a1), ...,  X(ak)  will determine as above after determining the vector-chord wavings an improvisational solo.

If we are composing e.g. in a midi editor the above perceptions are adequate for easy composition of melodies. But if we are playing an instrument and we want to improvise, then instead of having as center the arpeggio of a chord to improvise diatonically or chromatically around it it ir ending at it it  is easier to think of waving around or ending at centers that are not chords but notes that are away by intervals of 3rd, 4th, 5th 8th (e.g. the notes of a simplistic sub-melody).

See also post 159