287. IMPROVISATIONAL SONGS THAT THEIR CHORD PROGRESSION IS A SLIGHTLY CHANGING SEQUENCE OF REPEATING CYCLE OF CHORDS.

 See also post 280 about IMPROVISATIONAL SONGS THAT THEIR CHORD PROGRESSION IS A  REPEATING CYCLE OF CHORDS.

The most obvious slightly changing sequence of repataing cycke of chords is when the cycle of chords is a triangle.

E,g. From sad to joyful


3m->6m->2m  (repeated n-times) and then
5M7->6m->2m (repeated n-times) and then
5M7->1M->2m (Blues triangle repeated n-times) and then
5M7->1M->4M (repeated n-times)

Or

3m->6m->2m  (repeated n-times) and then
3m->6m->4M (repeated n-times) and then
3m->1M->4M (repeated n-times) and then
5M7->1M->4M (repeated n-times)

Or

3m->6m->2m  (repeated n-times) and then
3m->1M->2m (repeated n-times) and then
5M7->1M->2m (Blues repeated n-times) and then
5M7->1M->4M (repeated n-times)

Or

3m->6m->2m  (repeated n-times) and then
3m->1M->2m (repeated n-times) and then
3m->1M->4M ( repeated n-times) and then
5M7->1M->4M (repeated n-times)


Or

3m->6m->2m  (repeated n-times) and then
3m->6m->1M (repeated n-times) and then
3m->5M7->1M ( repeated n-times) and then
5M7->1M->4M (repeated n-times)

Or

2m->3m->6m  (repeated n-times) and then
5M7->3m->6m (repeated n-times) and then
5M7->1M->6m ( repeated n-times) and then
5M7->1M->4M (repeated n-times)

etc

286. HOW TO COMPOSE IMPROVISATIONAL INTRODUCTORY COUNTER-MELODIES TO A KNOWN SONG.

(This post has not been written completly yet)


The main idea is to apply the method below to a selected subset of chords of the chords of the song. Usually at thre "refren" or happier repeating part of  the song.

 IMPROVISATION METHOD BASED ON  A SET OF CHORDS AND MELODIC LINES BRIDGING THE HIGHEST NOTES OF EACH OF THEM. APPLICATION WITH STRUMMING WITH CUATRO, CAVAQUINHO, UKULELE , HARMONICA VIOLIN, WINDS ETC

The application idea is that when the chord is realized with a voicing on the highest 4 (or all 4) strings , we create melodic lines on the highest string bridging the highest notes of two succesive chords. Because of a inherent phenomenon of the human sound perception , when we are strumming and chaning the chords with in-between such melodic lines, the musical perception clearaly heres a melody, which is that of the highest notes. If it was not the highest notes the melodic lines would be more often lost in listening in the strumming.
Such chord-bridging melodic lines use a last small part of the previous chord duration and a small initial part of the new chord duration. During the rest ofthe time there is strumming of the chord or a achord arpeggio or variations of small melodic themes inside the chord by intervals of 3rd or 4th/5th. Thus melodic-harmonic variations. While when bridging two succesive chords there may be melodic themes variations by intervals of 2nd 3rd or 4th/5th (thus chromatic-melodic-harmonic).
This technique utilizes the simplicity of the information of the set of chord and translates it it to a simple information about the partition of the types of variations of simple melodic themes with the time placement and duration of the chords.
With this technique we may create simplicial counter-melodies parallel to melody.

It applies verty easily when utilizing a chromatic harmonica (see post 274), but also a violin (especially marked at a particular diatonic scale, so that we can identify chord-triad  shapes on it after a convenient tuning) and finally also on a diatonic wind.

285. HOW IS IT POSSIBLE WHEN LEARNING AND REMEMBERING MELODIES TO REDUCE THEIR INFORMATION TO AS LITTLE AS THE INFORMATION OF ITS CHORD PROGRESSION? THE ROLES OF SIMPLICIAL SUBMELODY AND SIMPLICIAL MELODIC THEMES ("DOLPHIN WORDS")

(This post has not been written completly yet)
See also post 70 and post 282

Dolphin words are beatifully composed with the arpeggiator

Dot Melody of https://www.olympianoiseco.com/

https://www.olympianoiseco.com/apps/dot-melody/

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.

When creating improvisational variations, or remembering melodies that we must improvise, we must start from the simple and proceed to the more complicated.

And the simple in a song is the chord progression. The corresponding simplicity in the melody is the simplicial sub-melody as defined  in various types of it (melodic harmonic , chromatic etc) in previous posts.

The next level of simplicity is of course the progression of simplicial melodic moves or melodic themes as defined in post 282, which is also called the "Dolphin words".

Once these levels of simplicity are defined and remain invariant,  the rest of the variation  is creating connecting and transient notes, between them (the notes of the simplicial sub-melody and the notes of the simplicial move-themes) which can be quite arbitrary, without spoiling the compatibility of the  melody with the chord progression and which will create an improvisational variation of the melody. 

An excellent example is the well known song Petite Fleur by Sidney Bechet in G major scale.

We will utilize only the simplicial submelody not the simplicial melodic moves in this song .

The chord progression (simplified) is the next

C->B7->Em->F#->B7

C->B7->G->Am->G->Am->Em->F#->B7

C->B7->Em->F#->Em->E7->Am->D7->G

C->B7->Em->F#->Em->E7->Am->D7->G

A less simplified chord progression would be the next

C->B7->Em->F#->B7

C->B7->(D7)->G->Am->(D7)->G->(B7->Em)->Am->(B7)->Em->(C)->F#->B7

C->B7->Em->F#->(B7)->Em->E7->Am->D7->G

C->B7->Em->F#->(B7)->Em->E7->Am->D7->G

And with the simplicial sub-melody notes in parenthesis (one note per chord of the simplified chord progression) it becomes

C(c)->B7(b)->Em(g)->F#(f#)->B7(b)

C(c)->B7(b)->G(d)->Am(c)->G(b)->Am(a)->Em(g)->F#(f#)->B7(f#)

C(c)->B7(b)->Em(g)->F#(f#)->Em(e)->E7(d)->Am(c)->D7(c)->G(b)

C(c)->B7(b)->Em(g)->F#(f#)->Em(e)->E7(d)->Am(c)->D7(c)->G(b)

Now any convenient linking notes between those of the simplicial sub-melody that we feel we like to play within the rhythm will create an improvisational variation of the melody.

Other examples are in Cretan mandinodies (kondilies) . In such cases because the chord progressions is very short of two only chords, the successful layer of simplicity that will remain invariant is the simplicial melodic moves.

A METHOD T O CREATE THEORETICALLY BUT ALSO PRACTICALLY SIMPLICIAL COUNTER-MELODIES:

 IMPROVISATION METHOD BASED ON  A SET OF CHORDS AND MELODIC LINES BRIDGING THE HIGHEST NOTES OF EACH OF THEM. APPLICATION WITH STRUMMING WITH CUATRO, CAVAQUINHO, UKULELE , HARMONICA VIOLIN, WINDS ETC

The application idea is that when the chord is realized with a voicing on the highest 4 (or all 4) strings , we create melodic lines on the highest string bridging the highest notes of two succesive chords. Because of a inherent phenomenon of the human sound perception , when we are strumming and chaning the chords with in-between such melodic lines, the musical perception clearaly heres a melody, which is that of the highest notes. If it was not the highest notes the melodic lines would be more often lost in listening in the strumming.
Such chord-bridging melodic lines use a last small part of the previous chord duration and a small initial part of the new chord duration. During the rest ofthe time there is strumming of the chord or a achord arpeggio or variations of small melodic themes inside the chord by intervals of 3rd or 4th/5th. Thus melodic-harmonic variaonions. While when bridging two succesive chords there may be melodic themes variations by intervals of 2nd 3rd or 4th/5th (thus chromatic-melodic-harmonic).
This technique utilizes the simplicity of the information of the set of chord and translates it it to a simple information about the partition of the types of variations of simple melodic themes with the time placement and duration of the chords.
With this technique we may create simplicial counter-melodies parallel to melody.

It applies verty easily when utilizing a chromatic harmonica (see post 274), but also a violin (especially marked at a particular diatonic scale, so that we can identify chord-triad  shapes on it after a convenient tuning) and finally also on a diatonic wind.

284. COMPOSING THE 3 SIMPLICIAL "DOLPHIN WORDS" (CYCLIC OR ASCENDING/DESCENDING MELODIC THEMES) WITH THE 3 BASIC TYPES OF CHORD TRANSITIONS: HARMONIC, MELODIC , CHROMATIC

(This post has not been written completely yet)

We may create such nice loops, of 2 or 3 or more chords and parallel melodic themes as "dolphin words"  with arpeggiator applications in ipad like chordion, dot melody, arpeggist , fugue machine, ioniarics polyrhitmic arpeggiator etc (see post  12 )
We must notice that many application create looping melodic themes that are any sequence of notes, which allows for the loop to be acctually a repeating sequence of smaller melodic thems M1 M2 M3 ...Mn  (or "dolphin words")  one for each chord  C1 ,C2 C3,...Cn of the cycle of chords.

1) As a first step we must compose the progression of cycles and vectors of the independent parts of the melody of the song (as Simplicial Dolphin Words) and their repetition pattern


2) Next we correspond the  range of the melodic cycles or vectors among the octaves numbered as in the piano (1st 2nd...6th 7nth etc)


3) As a 3rd step we  compose the harmony  by choosing the "scale" of chords that will make the chord progression.  This is the tools of harmony which are somehow independent from the tools of the melody.

4) As a 4th  step we compose the chord sub-progression that accompanies (harmonizes) the cycle (of simplicial melodic moves) and the chord sub-progression that accompanies (harmonizes) the vectors (of simplicial melodic moves).

283. THE SIMPLICIAL SUB-MELODY AND THE SIMPLICIAL MELODIC MOVES AS A METHOD OF CREATING IMPROVISATIONAL VARIATIONS OF A MELODY

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 

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. ALAO ARPIO  AND ARPEGGIONOME FOR GENERAL ARPEGGIOS ALTERNATED WITH MELODIC IMPROVISATIONS

When creating improvisational variations, we must start from the simple and proceed to the more complicated.

And the simple in a song is the chord progression. The corresponding simplicity in the melody is the simplicial sub-melody as defined  in various types of it (melodic harmonic , chromatic etc) in previous posts.

The next level of simplicity is of course the progression of simplicial melodic moves or melodic themes as defined in post 282, which is also called the "Dolphin words".

Once these levels of simplicity are defined and remain invariant,  the rest of the variation  is creating connecting and transient notes, between them (the notes of the simplicial sub-melody and the notes of the simplicial move-themes) which can be quite arbitrary, without spoiling the compatibility of the  melody with the chord progression and which will create an improvisational variation of the melody. 

An excellent example is the well known song Petite Fleur by Sidney Bechet in G major scale.

We will utilize only the simplicial submelody not the simplicial melodic moves in this song .

The chord progression (simplified) is the next

C->B7->Em->F#->B7

C->B7->G->Am->G->Am->Em->F#->B7

C->B7->Em->F#->Em->E7->Am->D7->G

C->B7->Em->F#->Em->E7->Am->D7->G

A less simplified chord progression would be the next

C->B7->Em->F#->B7

C->B7->(D7)->G->Am->(D7)->G->(B7->Em)->Am->(B7)->Em->(C)->F#->B7

C->B7->Em->F#->(B7)->Em->E7->Am->D7->G

C->B7->Em->F#->(B7)->Em->E7->Am->D7->G

And with the simplicial sub-melody notes in parenthesis (one note per chord of the simplified chord progression) it becomes

C(c)->B7(b)->Em(g)->F#(f#)->B7(b)

C(c)->B7(b)->G(d)->Am(c)->G(b)->Am(a)->Em(g)->F#(f#)->B7(f#)

C(c)->B7(b)->Em(g)->F#(f#)->Em(e)->E7(d)->Am(c)->D7(c)->G(b)

C(c)->B7(b)->Em(g)->F#(f#)->Em(e)->E7(d)->Am(c)->D7(c)->G(b)

Now any convenient linking notes between those of the simplicial sub-melody that we feel we like to play within the rhythm will create an improvisational variation of the melody.

Other examples are in Cretan mandinodies (kondilies) . In such cases because the chord progressions is very short of two only chords, the successful layer of simplicity that will remain invariant is the simplicial melodic moves.

 IMPROVISATION METHOD BASED ON  A SET OF CHORDS AND MELODIC LINES BRIDGING THE HIGHEST NOTES OF EACH OF THEM. APPLICATION WITH STRUMMING WITH CUATRO, CAVAQUINHO, UKULELE , HARMONICA VIOLIN, WINDS ETC

The application idea is that when the chord is realized with a voicing on the highest 4 (or all 4) strings , we create melodic lines on the highest string bridging the highest notes of two succesive chords. Because of a inherent phenomenon of the human sound perception , when we are strumming and chaning the chords with in-between such melodic lines, the musical perception clearaly heres a melody, which is that of the highest notes. If it was not the highest notes the melodic lines would be more often lost in listening in the strumming.
Such chord-bridging melodic lines use a last small part of the previous chord duration and a small initial part of the new chord duration. During the rest ofthe time there is strumming of the chord or a achord arpeggio or variations of small melodic themes inside the chord by intervals of 3rd or 4th/5th. Thus melodic-harmonic variaonions. While when bridging two succesive chords there may be melodic themes variations by intervals of 2nd 3rd or 4th/5th (thus chromatic-melodic-harmonic).
This technique utilizes the simplicity of the information of the set of chord and translates it it to a simple information about the partition of the types of variations of simple melodic themes with the time placement and duration of the chords.
With this technique we may create simplicial counter-melodies parallel to melody.

It applies verty easily when utilizing a chromatic harmonica (see post 274), but also a violin (especially marked at a particular diatonic scale, so that we can identify chord-triad  shapes on it after a convenient tuning) and finally also on a diatonic wind.

282. THE MISSING SIMPLICITY LAYER BETWEEN ONE NOTE OF A MELODY AND ITS UNDERLYING CHORD: THE PROGRESSION OF THE SIMPLICIAL MELODIC THEMES (DOLPHIN WORDS) OF A COMPLICATED MELODY. SIMPLICIAL DOLPHIN WORDS

THE MISSING SIMPLICITY LAYER BETWEEN ONE NOTE OF A MELODY AND ITS UNDERLYING CHORD: THE PROGRESSION OF THE SIMPLICIAL MELODIC THEMES (DOLPHIN WORDS) OF A  COMPLICATED MELODY.

We may create such nice loops, of 2 or 3 or more chords and parallel melodic themes as "dolphin words"  with arpeggiator applications in ipad like chordion, dot melody, arpeggist , fugue machine, ioniarics polyrhytmic arpeggiator , touchscaper etc (see post  12 )
We must notice that many application create looping melodic themes that are any sequence of notes, which allows for the loop to be acctually a repeating sequence of smaller melodic thems M1 M2 M3 ...Mn  (or "dolphin words")  one for each chord  C1 ,C2 C3,...Cn of the cycle of chords.

When listening to fast and complicated melodies e.g. in Gypsy jazz or in Irish reels or in Cretan kondilies (mantinodies), the subconscious perception of them perceives a betaifull simplicity which is not the harmony of the underlying chord. Where does it come from?

We have developed in these online notes the very useful concept of simplicial sub melody of a complicated melody. It may be identified from the durations of the notes (longer lasting note are correlated with the centers of the melody) but also from the notes of the underlying chord. Now because we extract and focus on the simplicial sub-melody of a complicated melody, the melodic themes of the simplicial sub-melody are the simplest possible this is "oriented intervals" or "vector intervals". We may call the simplicial melodic themes In other words intervals of two only notes that sound sequentially and not simultaneously with a specific order.

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. 

During a singly underlying chord we may have more than one such simplicial melodic themes. And they may be created on after its previous by some variation transformation like "translation" by an interval of 3rd or 5th or 8th  or "inversion" etc. This is very significant simplistic pattern of the ontology of the moves of the melody even during a sing;y underlying chord. We may have an increasing-ascending  progression of such simplicial melodic themes or oscillating-stationary  or decreasing-descending etc progression of such simplicial melodic themes. E.g. in Cretan Kondilies that have usually only two underlying chords (e.g. 1M->5M7->1M ) this progression during each chord (statistically determined rather than deterministically) defines the local style of the improvisational melody. E,g, 2 simplicial melodic themes for first 1M one for 5M7 and one back to 1M. In total 4 simplicial themes, the first 3 in a kind of variational repetition (translation or inversion) and one last and 4th closing one that may be mutated. Therefore the rhythm , and scale and underlying chord are not adequate to define the characteristic sound of such improvisations we need also the statistical profile of the progression of the simplical melodic themes.

In post  114, 231   such a progression of simplicial melodic themes has been called DOLPHIN WORD

Dolphin words are beatifully composed with the arpeggiator

Dot Melody of https://www.olympianoiseco.com/

https://www.olympianoiseco.com/apps/dot-melody/

This additional and missing simplicity layer in between the notes of a of a fast and complicated melody and its underlying chord has significance only when the melody is sufficient fast and complicated. This progression of simplicial melodic themes, together with the chord progression  , not only define the style but can be also an initial composition determination to be supplemented with an improvisational enhancement to the full melody when composing such songs. 

As alternative way to identify the style would be to use not the almost minimum number of chords to accompany it, but the maximum number of chords (usually of the diatonic scale) that can accompany it, and change them almost every beat. In this  way we define also an intermediate simplicity layer , between the notes of the  melody and the slow changing underlying chords, that can be lsos used both to define the style as well as to compose new ones.

Examples of such progressions of simplicial melodic themes (or Dolphin words) are the next  (each vector-arrow is an oriented interval that fits to a single or more  underlying chord(s)).

Or

Or

Or

AS THE COMBINATION SIMPLICIAL MELODIC MOVES (ORIENTED INTERVALS) CREATE PATTERNS THAT ARE CALLED "DOLPHIN WORDS" , WE MAYS AS WELL CLASSIFY THE "SIMPLICIAL DOLPHIN WORDS" . The simplest such patterns are of course the 3: 1) THE CYCLE 2) THE ASCENDING SEQUENCE 3) THE DESCENDING SEQUENCE. They can be defined also by requiring that the Simplicail dolhin words are also the connected components of the melody. The mathematical topology that should be defined b th concept of "contact of a notea nd the melody so far " in order to define also the connected components . And the contact is  defined by 1) Loooking back  n-notes (e.g. n=4) 2) Assuming that the contact of the note and  of the previous melody so far  is broken if an interval larger than 2nd appears between the note and the last n-notes.

SEE ALSO POST 293

HERE THE PREVIOUS SIMPLICITY CAN BECOME COMPATIBE WITH THE SIMPLICITY OF THE HARMONIZING SET OF UNDERLYING CHORDS:

   IMPROVISATION METHOD BASED ON  A SET OF CHORDS AND MELODIC LINES BRIDGING THE HIGHEST NOTES OF EACH OF THEM. APPLICATION WITH STRUMMING WITH CUATRO, CAVAQUINHO, UKULELE , HARMONICA VIOLIN, WINDS ETC

The application idea is that when the chord is realized with a voicing on the highest 4 (or all 4) strings , we create melodic lines on the highest string bridging the highest notes of two succesive chords. Because of a inherent phenomenon of the human sound perception , when we are strumming and chaning the chords with in-between such melodic lines, the musical perception clearaly heres a melody, which is that of the highest notes. If it was not the highest notes the melodic lines would be more often lost in listening in the strumming.
Such chord-bridging melodic lines use a last small part of the previous chord duration and a small initial part of the new chord duration. During the rest ofthe time there is strumming of the chord or a achord arpeggio or variations of small melodic themes inside the chord by intervals of 3rd or 4th/5th. Thus melodic-harmonic variaonions. While when bridging two succesive chords there may be melodic themes variations by intervals of 2nd 3rd or 4th/5th (thus chromatic-melodic-harmonic).
This technique utilizes the simplicity of the information of the set of chord and translates it it to a simple information about the partition of the types of variations of simple melodic themes with the time placement and duration of the chords.
With this technique we may create simplicial counter-melodies parallel to melody.

It applies verty easily when utilizing a chromatic harmonica (see post 274), but also a violin (especially marked at a particular diatonic scale, so that we can identify chord-triad  shapes on it after a convenient tuning) and finally also on a diatonic wind.

281. WHY WHEN LEARNING A NEW INSTRUMENT IT IS BETTER TO START WITH IMPROVISATION RATHER THAN PLAYING FROM MUSICAL SHEETS (SCORES)

(this post has not been written completely yet)


There are  many reasons why  WHEN LEARNING A NEW INSTRUMENT IT IS BETTER TO START WITH  PLAYING IMPROVISATIONS RATHER THAN PLAYING FROM MUSICAL SHEETS (SCORES).

1) It is the natural way that the brain learns , as when we learned to speak and talk, which also gives a better internalisation of the music. Educating the subconscious so as  to be able to create hundreds of different melodies over a single chord progression is by far more efficient and profound than just education the memory to remember one melody over a chord progression to repeat it note by note.

2) It is more pleasant and self-rewarding to improvise melodies where there are not wrong and right notes (except by very tolerant rules: e.g. more than 50% of the time notes inside the underlying chord or diatonic scale). Therefor we manage to play satisfying melodies within less time.

3) It is a better fit of the music played with our underlying emotions, which feeds back our desire to go on learning.

4) It feeds easier and faster our self-esteem in learning.

5) The standard writing and notation system  of the musical melodies in a  pentagram , with its sharps and flats and two only numbers for the rhythm ,is not the most efficient , smart and with clarity system of notating music. The appearance of software for music has made it quite clear.

In conclusion it is more natural, more efficient and faster in  producing and playing music, more profound, more pleasant , and eventually more beautiful and attractive from the point of view of the listeners. 

Of course at a particular phase of the learning process we will have to learn reading music sheets and play melodies from them, as it was also the case when we learned reading and writing on our natural language.

In addition to improvise requires having listened to melodies that we like a lot many more hours, than just playing a melody that we do not know from a musical sheet. So although it feels easier at the end, ir requires more work in educating the subconscious by listening carefully and repeatedly to melodies and music that we like.

280. IMPROVISATIONAL SONGS THAT THEIR CHORD PROGRESSION IS A REPEATING CYCLE OF CHORDS

(This post has not been written completely yet)

VECTORS, WAVES AND SPIKES

The identification and method of composition of them is based on the next concepts

1) As melody it has 3 layers (Simplicial submelody of the harmony, melodic arpeggio , diatonic chromatic arpeggio or ostinado)

2) Within each chord, it has 

2.0) A single note from the simplicial submelody

2.1) A projected and simplified melodic arpeggio

2.2) The full diatonic chromatic ostinado, which consists from

a) Diatonic chromatic maxima VECTORS

b) Diatonic chromatic RIPPLES or waves or cycles or oscillations

c) SPIKES (jumps with intervals higher than 2nd)

THERE ARE HUNDREDS OF DIFFERENT SONGS ON THE SAME CHORD-CYCLE  AND THOUSANDS OF DIFFERENT IMPROVISATIONAL SONGS ON THE SAME CHORD-CYCLE.

(see also post 17 and 29 , 145 ,148, 150)

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 example for Aegean islands (Greece) improvisational folk melodies (mandinades) condylies) with violin or Lyra, the next factors prevail.

1) "Poetic meters" over the same note sometimes notes up to 8 notes. The density of the notes is high. E.g. with 4 notes per  measure-bar and a beat of 80-100 bars per minute gives a tempo of 320-400 beats-notes per minute.

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. The simplistic sub-melody of such a waving melody is essentially an arpeggio of the underlying 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). 

SINGLE CHORD IMPROVISATION: We may as well alternate the root chord of a scale as power chord (only an  interval of 5th) with melodic themes (of 3 or 4 notes and inside  a three-chord or tetrachord ) based on each of the  the 3 notes of the root 3-notes or 4 notes chord and translated or inverted melodically by intevals of 3rd across the 3 or 4 notes of the roor chord. 

E.g. in  the Dorian mode of the C diatonic sacle and with an harp,  here

https://www.youtube.com/watch?v=NomPFFmycDo&ab_channel=rharp111

https://www.youtube.com/watch?v=9BD1y0TOk3o&t=774s&ab_channel=Buddha%27sLounge

MANY CHORDS-CYCLE  IMPROVISATION: We do the same as with the one chord for each chord of the chord-cycle. with melodic themes (of 3 or 4 notes and inside  a three-chord or tetrachord ) based on each of the  the 3 notes of the underlying  3-notes or 4 notes chord and translated or inverted melodically by intevals of 3rd across the 3 or 4 notes of the roor chord. We may sure thatthe melodic centers are notes of the underlying chord. At the chord transition one of the previous three-chords or tetrachords of the melodic theme becomes the bridge between the 2 consecutive chords and we constinue as before.  

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: 

We may create such nice loops, of 2 or 3 or more chords and parallel melodic themes as "dolphin words"  with arpeggiator applications in ipad like chordion, dot melody, arpeggist , fugue machine, ioniarics polyrhitmic arpeggiator , touchscaper etc (see post  12 )
We must notice that many application create looping melodic themes that are any sequence of notes, which allows for the loop to be acctually a repeating sequence of smaller melodic thems M1 M2 M3 ...Mn  (or "dolphin words")  one for each chord  C1 ,C2 C3,...Cn ofthe cycle of chords.
We may also utilize chord sequencers or chord progressions sequencer applications

The symbols here mean M=major m=minor ,  dim=diminished , aug=augmented, the numbers 1,2,3,4,5,6,7 are the steps of a diatonic scale (ionian mode).


E.G.

1) 1M


2) 5M7->1M


3) 6m->1M



4) 1M->4M->5M->1M    (Cretan matinodies, kondilies) 
or only 1M (3rd note) ->1M->5M7(5th note)->1M (3rd note)
or only 1M (3rd note) ->1M->1M->1M (3rd note)
e.g. as order of notes in a diatonic scale 
3 3 3 4 3 5 5 5 4  2 3 4 5 5 3
as rhythm from 15-syllables poetry
(1M         )
10010100
(5M7)1M
1001  010
(combination of poetry rhythms of anapestik  100 with trochaic 10 )
In addition to  rhythm, scale and chord progression we need also the statistical profile of the progression of the simplical melodic themes (see post 282) so as to determine the local style of the particular improvisations.
E.g. in Cretan Kondilies that have usually only two underlying chords (e.g. 1M->5M7->1M ) this progression during each chord (statistically determined rather than deterministically) defines the local style of the improvisational melody. E,g, 2 simplicial melodic themes for first 1M one for 5M7 and one back to 1M. In total 4 simplicial themes, the first 3 in a kind of variational repetition (translation or inversion) and one last and 4th closing one that may be mutated.

Examples of such progressions of simplicial melodic themes (or Dolphin words) are the next  (each vector-arrow is an oriented interval that fits to a single or more  underlying chord(s)).

Or

Or

Or

Dolphin words (=abstract order patterns of melodies) are beatifully composed with the arpeggiator

Dot Melody of https://www.olympianoiseco.com/

https://www.olympianoiseco.com/apps/dot-melody/

5)  5M7->1M7->4M   (Jazz, Celtic folk)


6) 2m7->5M7->1M    (Blues)


7) OTHER TRIAD CYCLES 
One of the simplest cycle of chords is 3 consecutive chords in the cycles of 4ths.

E.g. in the C major diatonic scale

Dm->G->C  (Western Jazz)  (2m-5M-1M) (happy)

G->C->F  (Irish folk)  (5M- 1M- 4M) (happy)

Em->Am->Dm (Eastern folk and latin too)  (3m-6m-2m)  (sad)
E.g.

https://www.youtube.com/watch?v=BgS3zqzIpmU

Bdim->Em->Am  (Eastern Jazz) (7d-3m-2m)  (sad)

other combinations of major M, minor m, diminished d and augmented aug are

d-M-M  (happy)

aug-M-M  (happy)

aug-m-M  (sad)

aug-m-m  (sad)

M-m-m  (sad)

d-m-M (sad)

d-d-M (sad)

d-d-m (sad)

aug-aug-M (sad)

aug-aug-m (sad)

d-aug-M (sad)

d-aug-m (sad)

d-aug-d (sad)

aug-aug-d (sad)

etc

In the next video the next 4 triads are harmonizing the 4 known minor scales

5m->1m->4m =natutal minor (diatonic)

5m->1m->4M= Dorian minor (diatonic)

5M->1m->4M=melodic minor (chromatic)

5M->1m->4m=harmonic minor (chromatic)

https://www.youtube.com/watch?v=kobgAsDZxsw&t=125s

and of course

there are also the combinations

5M->1M->4M =ionnian mode , major (diatonic)

5m->1M->4M

5m->1M->4m

5M->1M->4m

If the triad is harmoni only at one pair we get also the triads

1M->2m->5M7  (blues)

1M->6m->5M7  

1M->3m->5M7  

4-CYCLES

8) 5M7->1M7->6m->4M  (Popular Pop)

(E.G. https://www.youtube.com/watch?v=eObM-tAgeG0&t=1273s )



9) 6m7->2m7->5M7->1M  (Pop music 50s)

(E.G. https://www.youtube.com/watch?v=gUNWjgaJEik&t=50s )


10) 6m->5M->4M->3M (Andalusian cadenza, part of the 1st chromatic tonal cycle as in 10))

(E.G.   https://www.youtube.com/watch?v=Li4izrMnd-I  or https://www.youtube.com/watch?v=2KE48jD5aVw  )

11) 3m->1M->6m->7M7 (flamenco pharaon or tonal 2nd chromatic 4-cycle)

E.g.    https://www.youtube.com/watch?v=BwDJ0e1fssw


12)   6m->4M->2m->3M7   (tonal 1st-chromatic 4-cycle)

E.g. https://www.youtube.com/watch?v=XgJFV5K3NLc


13)   1M->7M7>3m->5M7_1M   (tonal 2nd-chromatic 4-cycle)

14)  1M->7M7>3M7->6m   (tonal 2nd-chromatic 4-cycle b)




15) CHROMATIC INVERSE OF HARMONIC RESOLUTION PAIRS: DIATONIC SCALE 
In the chords of a diatonic scale, , we may reverse chromatically by 4 or 5 chords any harmonic resolution transition of two chords and this is already a cycle of chords:

E.g,  5M7->1M ,which reversed chromatically as a cycle it is 

1M->7dim->6m->5M7  (or  with 5 chords 1M->2m->3m->4M-5M7)

similarly 

4M->3m->2m->1M7     (or with 5 chords 4M->5M->6m->7dim->1M7 )

and 

6m->5M->4M->3m7    (or with 5 chords  6m->7dim->1M->2m->3m7)

and 

2m->1M->7dim->6m7  (or with 5 chords 2m->3m->4M->5M->6m7)


16) CHROMATIC INVERSE OF HARMONIC RESOLUTION PAIRS : 1ST CHROMATIZATION OF DIATONIC SCALE:  In the chords of the 1st chromatic version of the  diatonic scale, , we may reverse chromatically by 4 or 5 chords any harmonic resolution transition of two chords and this is already a cycle of chords:

E.g,  3M7->6m ,which reversed chromatically as a cycle it is nothing else than the Andalussian cadenza

6m->5M->4M->3M

And also the next such cycles

1M->7M7->6m->5M7  (or  with 5 chords 1M->2m->3M7->4M-5M7)

and  similarly 

4M->3M->2m->1M7     (or with 5 chords 4M->5M->6m->7M7->1M7 )

and 

6m->5M->4M->3M7    (or with 5 chords  6m->7M7->1M->2m->3M7)

and 

2m->1M->7M7->6m7  (or with 5 chords 2m->3M->4M->5M->6m7)


17) MELODIC INVERSIONS OF HARMONIC RESOLUTION PAIRS. 1ST CHROMATIZATION OF DIATONIC SCALE:  In the chords of the 1st chromatic version of the  diatonic scale,  we may reverse MELODICALLY (in other words with chord transitions in relatives relation) by 4 or 5 chords any harmonic resolution transition of two chords and this is already a cycle of chords:

5M7->1M->6m->4M->2m->5M7

or 

5M7->1M->6m->4M->2m->7M7->5M7

18) 3M7->6m->5M7->1M  (4-cycle from 1st chromatic diatonic chord cycle, Andean Music)


5-CYCLES

19) 3M7->6m->2m7->5M7->1M  (5-cycle from 1st chromatic diatonic chord cycle)



20) 6m->2m->5M->1M->4M   (5-cycle ,Most popular Pop)

20.1)  1M->4M->3M7->6m->6M7->2m->1M (Scandinavian folk tunes)


6-CYCLES

21) 3m->6m->2m->5M7->1M->4M  (6-chords diatonic cycle)


22) 6m->2m->5M7->1M->4M->3M7  (6-chords 1st chromatic tonal chords in melodic (relatives) relations).

23) 1M->-6m->4M->2m->5M7->3m->1M  (6-cycle of melodic relations tonal chords)


7-CYCLES

24) 7dim->3m7->6m7->2m7->5maj7->1maj7->4maj7  ( 7-chords diatonic cycle))




25) 6m7->2m7->5maj7->1maj7->4maj7->7M7->3M7

(7-chords 1st chromatic diatonic cycle Jazz, Gypsy Jazz, Beethoven)


26)  6M7->2m7->5maj7->1maj7->4maj7->3M7->6m (Gypsy jazz)

In the next 7-cycles only one of the 3 minor chords or diminished is turned in  to a major chord

24.1)   5M7->1Μ->4Μ->7dim->3m->6M7->2m->5M7  (Scandinavian folk)

24.2)   5M7->1Μ->4Μ->7dim->3m->6m->2M7->5M7  

24.3)   5M7->1Μ->4Μ->7M7->3m->6m->2m->5M7  
24.4)   5M7->1Μ->4Μ->7dim->3M7->6m->2m->5M7  25) 7-chords melodic diatonic cycle (by relative chord transitions)

24.5)   5m7->1Μ->4Μ->7dim->3m->6M7->2m->5m7  (Scandinavian folk with 6M7 and 5m7)

6m->1M->3m->5M->7dim->2m->4M->6m

27) 7-chords melodic 1st chromatic diatonic cycle (by relative chord transitions)

6m->1M->3M7->5M->7dim->2m->4M->6m

28) 7-chords melodic 2nd chromatic diatonic cycle (by relative chord transitions partly mixed with harmonic relations)

1M->6m->4M->2m->7M7->3m->5M7->1M  (3melodic  2harmonic transitions )or

6m->1M->3M7->5M->7M7->2m->4M->6m (6melodic  1 chromatic  transitions )

or 

1M->7M7->3M7->6m->4M->2m->5M7->1M (2melodic  1 chromatic 3 harmonic transitions )
or


1M->6m->4M->2m->7M7->3M7->5M7->1M (4melodic  1 chromatic 2 harmonic transitions )

7-chords melodic-harmonic 2nd chromatic diatonic cycle


or

1M->3m->6m->4M->2m->5M7->3M7->1M (4melodic  1 chromatic 3 harmonic transitions )

or

1M->3m->6m->4M->2m->5M7->7M7->1M (3melodic  2 chromatic 2 harmonic transitions )

or

1M->7M7->3m->4M->3M7->6m->2M7->5M7->1M 

(0 melodic  3 chromatic 5 harmonic transitions )

or

1M->7M7->3m->3M7->6m->4M->2m (or 2M7)->5M7->1M 

(3 melodic  1 chromatic 4 harmonic transitions )

or

1M->4M->3M7->6m->6M7->2m (or 2M7)->5M7->1M 


(1 melodic  1 chromatic 5 harmonic transitions )

or

1M->4M->7M7->3m->3M7->6m-> 2M7->5M7->(5aug)->1M 


(1 melodic  1 chromatic 6 harmonic transitions )

or 

1M->7M7->3m->4M->3M7->6m->2m (or 2M7)->5M7->1M 


(0 melodic  3 chromatic 5 harmonic transitions )

or 

1M->4M->7M7->3M7->6m->2m (or 2M7)->5M7->1M 


(0 melodic  1 chromatic 6 harmonic transitions )

or 

1M->7M7->3m->4M->2m->5M7->3M7->(5aug)->1M


(3 melodic  2 chromatic 3 harmonic transitions)

29) Small 4-chords melodic chromatic tonal cycle

1M->3m->5M->7M7->1M or



30) Small 5-chords melodic chromatic tonal cycle

1M->6m->4M->2m->7M7->1M  or

1M->6m->4M->2m->7M7->3M7->1M  

29) more than 7 chords:

6m->6M7->2m->5M7->1M->4M->2m->7M7->3M7->6m


31)  Other examples are , the next cycle of chords

 Bdim->Em->Am->Dm->G->C->F 

is a scale of chords of the simple type, that is a connected arc in the wheel of chords by 4ths, and the specifications of diminished, minor or major are set so that the particular scale of chords is also the chords of the major diatonic scale of notes!

Nevertheless we can alter that specification of the chords in which case more than one scale are produced:

B7->Em->A7->Dm->G7->Cm->F  or 

Bm7->E7->Am7->D7->Gm7->C7->Fm or 

B7->E->A7->Dm->Gm7->Cm->F  etc

Or 

B7->E(m)->A(m)->D(m)->G(m)->C->F

The E(m) means either major chord E or minor chord Em etc

The next scales of 7-chords have only two minor chords which complies with a desired ratio of minor chords not more than 1/3 of all chords

B7->E(m)->A(m)->D->G->C->F

B(m)7->E(m)->A->D->G->C->F

B7->E->A(m)->D(m)->G->C->F

B7->E->A->D(m)->G(m)->C->F

B7->E->A->D->G(m)->C(m)->F

B7->E->A->D->G->C(m)->F(m)


Or we may alternate minor major once at odd chords and once at even chords e.g.

B7->Em->A->Dm->G7->C->F->Bb->B7->E->Am->D7->Gm->C7->F->Bb->B7->E 
Larger scales are from 12-chords 

G#->C#->F#->B->E->A->D->G->C->F->Bb->Eb

or 


G#->C#->F#->B->Em->Am->Dm->G->C->F->Bb->Eb



Other simpler scales from chords are of 4 only chords e.g.


G->C->F ->Bdim7 etc

or 

G->C->F ->Caug(or G#aug) etc

or they can be based on wheel by 3rds and alternating minor major relative chords 
e.g. 

G->Em->C->Am->F >Dm->G etc


32) THE GENERAL PATTERN OF CHORD-CYCLES  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. 

ETC.

In order to create the melody over such a  cycle of chords we may proceed as follows.

1)We compose 2 or 3  simplicial sub-melodies one for each part of the song ,  with one note per chord, over the cycle of chords preferably at a chromatic sequence ascending and descending . 

2) We create moves or waves 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.

Other determinations of these songs or improvisations;


0) THE HARMONY.

Although the cycle of chords is fixed, the order and duration that these chords are played may vary, from song to song, or even inside the same song ("random" permutation of the chords of the cycle).
E.g. 1M->4M->5M->1M    (Cretan matinodies, kondilies) 
or only 1M (3rd note) ->1M->5M(5th note)->1M (3rd note)
or only 1M (3rd note) ->1M->1M->1M (3rd note)



1) The rhythm:
The duration of the beat is determined by clock-standards. Then each chord of the cycle is determined how many beats has duration. Furthermore, the rhythm is specified as in post 10. Usually, the powers of 2 are utilized. So a triad of chords will have a repetition of a chord in duration. E.g. a cyclic pattern A B C A, of 4 groups of beats so that each chord has equal duration will also determine a variational repetition pattern of the variating melodic themes, usually 3 variations and the last time a resolution.  The melody itself can be classified to the simplicial say in 4 chord-durations, or the normal in 8 chord half durations, or embellishing in 16  chord quarter durations, or fast embellishing  32 , eighths chord durations etc.
Initially, it seems that the rhythm of the main melody was patterned over 15-syllables poetry, with 4+4 beats at the first line of 8 syllables and 4+3 beats at the 2nd line of 7 syllables.
The term mantinodies is quite similar and meanings and methods with the term rhapsody of the ancient poetry of homer (Iliada, Odyssia etc)

E.g. for Cretan mantinodies (condilies)

as rhythm from 15-syllables poetry

10010100

1001010

(a combination of anapestik  100 with trochaic 10 )

2)  The pitch order pattern of the roots of the chords of the chord-cycle.
In general, there are 4 classes:
1)The ascending (happy)
2) The descending (unhappy)
3) The upper cyclic (happily sad),
4) The lower cyclic (sadly happy).

This is a general pitch order pattern which of course has emotional significance: Increasing pitch order in the roots =joy, decreasing pitch order in the roots=sadness.

e.g. as order of notes in adiatonic scale (Cretan mantinodia, condilia)
3 3 3 4 3 5 5 5 4  2 3 4 5 5 3


3) The pitch order pattern of the induced by the melody harpism (permutation) of the notes of each chord.  

Although the part of the melody accompanied by a single chord may have notes outside the chord, it will have also notes of the chord that it is expected that they have a longer duration. Thus this part of the melody induces a permutation or harpist of the notes of the chord.

4) The variational repetition pattern of the melodic themes as part of the melody accompanied by a single chord.

279. A CLASSICAL GROUP OF MELODIC THEME VARIATIONS FOR BEAUTIFUL DIATONIC TONAL MUSIC TRANSLATIONS EXPANSIONS,INVERSIONS MUTATIONS

 A  CLASSICAL GROUP OF MELODIC THEME VARIATIONS FOR BEAUTIFUL DIATONIC TONAL MUSIC. TRANSLATIONS , EXPANSIONS, INVERSIONS, MUTATIONS

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 

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 ARE MANY GOOD SOFTWARE PROGRAMS FOR THIS COMPOSITION AND IMPROVISATION LIKE FUGUE MACHINE, YAMAHA MOBILE SEQUENCER, THUMPJAM ETC

By studying e.g. the art of Vivaldi melodic themes variations (but other folk music too, e.g. Celtic and Irish music), we can directly get the idea of a nice finite group of melodic themes transformations. We use of course the term finite group in the standard mathematical algebraic meaning of a set of transformations closed to composition and inversion. The transformations  are most often  tonal translations (in other words shifting the melody inside the diatonic scale and preserving the nature of intervals as 2nds, 3rds, 4ths, 5ths etc). From the mathematical algebraic point of view such a finite group has a finite set of generators and a  finite set of defining relations for the presentation of the group (https://en.wikipedia.org/wiki/Presentation_of_a_group).

And the group of such transformations are of course 

1) Tonal translations by 3rds (melodic translation) , 5ths or 4ths (harmonic translation) , when we ae inside the accompanying of a single chord (but also in different chords related melodically or harmonically to the first) And by 2nds (chromatically) which requires usually changing the underlying chord too. This tranasformation includes the  Harmonic Complementation (Blue Shaffling). If the instrument is harmonica tuned as a Zamponia panflute (double row of odd-even notes of a diatonic scale, called also cyclic tuning, or melody king tuning) we have an additional variational transformation that we may call complementation (Blue shuffle) . E.g. if the melodic theme has notes 1,1 , 2, 3,3 a complementation of it would be to inverse even with odd numbers e.g. 2,2,3,4,4 etc

2) Tonal inversion . It is an inversion of the pitch order of the notes of the melodic theme which results in melodic theme again inside the initial diatonic scale. Besides the pitch-inversion there is of course also the time-inversion of the melodic theme, which is a different concept.

3) Tonal expansions-contractions: It is when we keep an initial part of the melodic theme fixed while expand or contract the rest of it , but always resulting again inside the initial diatonic scale. E.g. the initial melodic theme over chord A maybe within ione octave and when we translate it to fit the next chord B we also expand it to span 2 octaves. 

 The statistical frequency of such tonal translations is at least 2/3 of the times by intervals of 3rds and 5ths/4ths (melodic and harmonic tonal translations) and at most 1/3 of the time by intervals of 2nds (chromatic tonal translations). A more tolerating quantification would be to require that the statistical frequency of such tonal translations is at least 50% of the times by intervals of 3rds and 5ths/4ths (melodic and harmonic tonal translations) and at most 50% of the time by intervals of 2nds (chromatic tonal translations).

In the formation of such group of variations of melodic themes and in creating such nice melodies and music we utilize of course the closure properties of the diatonic scale in shifts by intervals of 3rds, and 5ths or 4ths. (Which is also a good opportunity for the reader to refresh and re-discover. E.g. For every note of the diatonic scale there is an interval of 3rd and of 5th or 4th such that up or down of the note and away by that interval it is again a note of the diatonic scale). So that such variations create cycle of melodic themes that repeat.

The above group of variations of the melodic theme can be both in the context of tonal music but also in the context of chromatic tonal music as in the post 263

As we mentioned in post 263  the order of the chromatic notes 5#, 4#, 1# , 2#, 6# would give the next order of altering majors to minors or vice versa

3 minor ->3 major or 4 major->4 minor (for 5#) 
2 minor-> 2 major (for 4#)
6 minor -> 6 major (for 1#)
1 major-> 1 minor (for 2#)
5 major-> 5 minor (for 6#)

Boldly speaking, the topological shape of the melodic themes are of three  kinds:
A) Oscillations (arpegios of a chord or vector-chord)
B) Up or down Continuous Moves 
C) Discontinuous  jump (Spike) by an interval of 5th/4th or larger.

THE DIATONIC-GUITAR OR HARMONICA-GUITAR  AS IN POST 90 HAS A DIRECT ADVANTAGE OF APPLYING THE CLASSICAL GROUP OF VARIATIONS OF MELODIC THEMES AS DESCRIBED IN THIS POST  (TONAL TRANSLATIONS BY 3RDS AND 5THS OR 4THS IN AT LEAST 2/3 OF THE CASES AND CHROMATICALL IN AT MOST 1/3 OF THE CASES). THE MELODIC THEME SUCH TONAL  TRANSLATION BY 3RDS OR 5THS/4THS IS SIMPLY SHIFTING THE MELODIC THEME FROM ONE STRING ON THE SAME FRET  VERTICALLY TO  THE ADJACENT STRING ( A 3RD) OR NEXT TO ADJACENT STRING (5TH OR 4TH). (SEE POST 90).

See also about chromatic inversion  (pitch inversion)

https://www.youtube.com/watch?v=0oI2iFrzA0o