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

206. HOW TO CREATE LONG SYMMETRIC CHORD PROGRESSIONS AND THEIR SIMPLICIAL SUB-MELODY FOR BEAUTIFUL SONGS FROM THE 7 CHORDS OF A DIATONIC SCALE.

AN EXCELLENT SOFTWARE TOOL TO UNDERSTAND THE BASIC 3 CHORD REATIONS IS THE SOFTWARE NAVICHORD (FOR IOS). IT HAS A HEXAGONIC TOUCH-SCREEN KEYBORD OF THE NOTES WHERE THE CHORDS ARE TRIAGNGLES AND ARE PLAYED BY TOUCHING THE CENTER OFTHE TRIANGLE

SUCH HEXAGONIC KEYBOARDS HAVE BEEN PATENTED ALSO IN THE TERPSTRA KEYBOARD.    THE 3 BASIC LOCAL RELATIONS OF THE CHORDS (NO-COMMON NOTE OR CHROMATIC RELATION, ONE COMMON NOTE OR HARMONIC RELATION AND TWO COMMON  NOTES OR MELODIC RELATION) ARE IMMEDIATELY VISIBLE.

THE NAVICHORD IS  ALSO A CHORD LOOP SEQUENCER WHICH PRODUCES CHORD PROGRESSIONS AND BACKTRACKS.

WE DESCRIBE TWO METHODS , ONE WITH TRIANGLES OF CHORDS AND ONE WITH PARALLELOGRAMS OF CHORDS.

The two methods to create chord progressions from the 7 chords of a diatonic scale are like creating words of a language which has as alphabet the 7 chords of the diatonic scale. It allows of unlimited combinations with varying degrees of symmetries.Of course always of a diatonic scale. we include also modulations of a certain type which are change of the natural minor of the diatonic scale to a same root harmonic minor or double harmonic minor.

A) THE CHORD PROGRESSION IS A CYCLE OR SEQUENCE OF TRIADS (TRIANGLES) OF CHORDS AS BELOW.

For happy melodies obviously, the triad is  the I, IV, V. According to the degree of sadness we want to impose, we substitute any of the major chords with its lower minor relative. In other words  vi for I, ii for IV and iii for V. 

About the symbols: In a C major scale the symbols denote the next chords

I=1M=C

ii=2m=Dm

iii=3m=Em

IV=4M=F

V=5M=G

vi=6m=Am

vii=7d=Bdim

So the possible combinations are 

I, IV, V   (1M, 4M,5M majors harmonic triad)

vi , IV, V  (4M, 5M , 5m,  chromatic triad, e.g, part of the Andalusian cadenza when reversed) 

I , ii, V    ( 2m, 5M ,1M harmonic triad)

I, IV, iii   (3m 1M, 4M,   melodic-harmonic triad)

IV , ii, V   ( 1M, 4M, 2m, harmonic-melodic triad)  

I , ii, iii  (3m, 1M, 2m, melodic chromatic or only chromatic triad)

vi, IV, iii   (3m, 6m, 4M, harmonic-melodic triad)

vi, ii, iii   (3m, 6m, 2m, harmonic triad)

vi-vii-iii (7d, 3m, 6m, harmonic triad)

I -vii -V  (5M, 1M , 7d, harmonic-chromatic triad)

In case we want to alter the natural minor ofthe scale to an harmonic minor or double harmonic minor the the usual changes of the harmonic personality as in post 158 apply.

In more detail: 

In general starting from a diatonic harmonic personality 

1M, 2m 3m 4M 5M 6m 7dim 1M

the next are the effects of turning the natural minor to harmonic minor or double harmonic minor.

The effect of the 1st blue note 5# of the harmonic minor on the harmonic personality is that 

the 3m  turns in to 3M and the 5M may turn  into  5b5  or better sounding  5#m or 5#dim or 5aug,  or  1dim  

Also the 7dim may turn in to 7m7b5 as 4 notes chord.

While the effect of  the 2nd blue note of the double harmonic minor 2# (or 3b) is that the 7dim turns in to 7M  or 7b5  and , the 1M may become 1aug and also the 2m may become 2#dimb3 or  better sounding 2#dim or 2#M. 

Further changes with augmented chords because of the harmonic and double harmonic minor we involve not only diminished chords but also augmented chords.

E.g.

In C major

Am  Bdim E  Am (repeated many times)  then

C Bd  G C  (repeated many times)  then

Am Dm E Am (repeated many times)  then again

Am  Bdim E  Am (repeated many times)  etc

Listen also to

https://www.youtube.com/watch?v=NwIw2BQW_jE

and to

https://www.youtube.com/watch?v=HcVD-6w4A8k

Of course the next critical issue is to determine the simplicial sub-melody that goes parallel to the chord progression. This determines also the chord progression as triads of notes and the correct voicing of the chord progression, so as to play directly also the simplicial submelody through the correct voicing of chord progression as triads of notes only. In other words

THE SIMPLICIAL SUBMELODY IS OF EQUIVALENT DETERMINATION WITH THE VOICING OF THE CHORD PROGRESSION AS TRIADS OF NOTES. 

Triads of chords with minor chords in them most often are correlated with straight descending shape of the theme of the simplicial sub-melody. While triads of chords with all three chords major chords are correlated with straight ascending shape of the theme of the simplicial sub-melody. Usually we prefer the middle note (3 from 1-3-5) of the chord for the note of the simplicial sub-melody. But we should study also the harmonic, chromatic and default  simplicial sub melodies discussed in posts 66, 109. 

Then we proceed with the embellishments and waving around the simplicial submelody to derive a full dense and even fast melody.

For example if we chose the next two triads of chords for te chord progression in a song in the C major scale 

(Am ,Bdim, E)  and (C Bdim G7) then the chord progression is 

Am-> Bdim-> E-> Am  repeated 4 times and 

C-> Bdim->G7->C  repeated 4 times and   

and all together repeated 3 times.

Then the first triad of chords  which has the minor chord Am signifies sadness and the simplicial submelody is chosen descending with a middle waving . So it is the a5->d5->e5->a4 . One note for each occurence of a chord which belongs to the chord . And the triads of chords C-> Bdim->G7->C has more major chords which signifies happiness so the simplicial submelody is defined as straight ascending . So corresponding one note (which belongs to the chord) to each chord it may be the c4->d4->g4->c5 .  We may also create an introductory part A of the song which is both parts B , C of the simplicial submelody with the necessary waving embellishments around it c4->d4->g4->c5->a5->d5->e5->a4 which we repeat two times each time we repeat the parts B and C above   of the two triads of chords.

The two methods to create chord progressions from the 7 chords of a diatonic scale the one here with triads (triangles) if chords and the one in post 148 with parallelogram diagrams of chords are like creating a language which has as alphabet the 7 chords of the diatonic scale. It allows of unlimited combinations with varying degrees of symmetries.

The next  Irish reel example is made more or less with thsi way.

https://www.youtube.com/watch?v=NwIw2BQW_jE

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

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

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

THE GENERAL PATTERN OF A CHROMATIC PARALLELOGRAM 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. 

PRODUCING CHORD PROGRESSIONS FROM CHORD-SCALES

Now when we want to improvise based on such a scale of chords (harmony first), we may start with one such chord from this scale and play a melodic theme that fits it. Then we move to the next melodic theme, with all the know so far rules of good melody composition (e.g. variations of translation, inversion, homeomorphism) and try to fit it also to one of the chords of the previous scale of chords. If we succeed in this we repeat it , with the next melodic theme, and appropriate chord from this set of chords or scale of chords, and so on. In this way we have an inter play with harmony and melody at the very process of improvisation or composition. 

This method of composing a melody, is more general and more comprehensive than composing a melody within a single scale of notes. It results composing melodies in many different scales and modulations between them, but the simplicity is still kept as set of chords (scale of chords) rather than scale of notes.

Here is a way when the scale of chords is identical with the chords of diatonic scale of notes.


An relatively easy and safe way to produce such  mesmerizing  monotone but beautiful flows of improvisation , is to use scale of chords as in post 148. And in particular a very familiar  scale of chords that are the chords of diatonic scale:

I , ii, ii, IV, V vi, vii, I' (=1M, 2m, 3m, 4M, 5M, 6m, 7dim 1'M)

and in addition to an instrument tuned by the harmonic tuning (see post 90) so that there is a densest possible opportunity of major or minor chords per number of frets.

Some of the variation techniques to walk this scale of chords are

1) Walk in the chromatic order up and down (all then only odds then only even) 

2) Walk in the relative chords order up and down

3) Walk in the resolution or harmonic order by 4ths or 5th order up and down

4) Walk only the minor chords first descending and then the major chords ascending 

5) Walk in the 4-notes chords (major 7nth extension of the chords) up and down, all then only even then only odd

6) Walk in a half scale (in the chromatic order) up down then other half  up and down.


7) Walk in a random way either 3-note chords or 4 notes chords

8) Alter some chords to include the 5#, or 2# of the harmonic minor or double harmonic minor, or other like 6#. E.g. alter the 3m to 3M7 or 3dim etc

We cannot stress much the importance of triads of chords (but also of notes intervals and scales) in improvisation.

A good application is to realize that as a diatonic scale is characterized as chords on the wheel by 4ths by its 3 chords on the steps 1M, 4M , 5M  (harmonic triplet of chords) ,  OR 7d 1M 2m (chromatic tripler of chords) the same can apply for the modes of the diatonic scale.

Besides the basic harmonic triplets (in other words a sequence of 3 chords X1,X2,X3 so that X1-X2 , X2-X3 are harmonic relations od chords, in other words chords that their roots differ by an interval of 4th (5th)) , there are also the chromatic triplets (in other words a sequence of 3 chords X1,X2,X3 so that X1-X2 , X2-X3 are chromatic relations od chords, in other words chords that their roots differ by an interval of 2nd). BOTH  ARE BASIC TYPES OF TRIPLETS. In other words with the 3 CHORDS OF THE TRIPLET WE CAN ACCOMPANY ANY MELODY IN THE DIATONIC SCALE. WE CANNOT HAVE THIS PROPERTY OF BEING HARMONICALLY A BASE OF 3 CHORDS FOR MELODIC TRIPLETs (in other words a sequence of 3 chords X1,X2,X3 so that X1-X2 , X2-X3 are melodic relations of chords, in other words chords that their roots differ by an interval of 3rd) 

The chords of a mode of a diatonic scale at the steps 1,4,5 (or 7,1, 2) of it characterize its mood.

For example for the mixolydian mode of the diatonic scale from C ,(G, A, B , C, D, E, F, G) the chords at the steps 1,4 ,5 are the G, C, Dm) thus the 1, 2, 5 or I, ii, V of the original ionian and are the base of blues jazz.


Based on this perception, the 7 modes of the diatonic scale have the following chord triads:

(that is chords on their 1st 4th and 5th step, and we symbolize by m=minor M=major d=diminsihed.

1. IONIAN  :  CHROMATIC TRIPLET (7d, 1M, 2m)
2. DORIAN  :  CHROMATIC TRIPLET (1M, 2m, 3m )
3. PHRYGIAN : CHROMATIC TRIPLET(2m,3m, 4M)
4. LYDIAN:  CHROMATIC TRIPLET(3m, 4M, 5M)
5. MIXOLYDIAN: CHROMATIC TRIPLET (4M, 5M, 6m)
6. AEOLIAN:  CHROMATIC TRIPLET (5M, 6m, 7d)
7. LOCRIAN:  CHROMATIC TRIPLET (6m, 7d, 1M)

We may compare the basic chromatic triplets with the basic harmonic triplets (see also post 222)

1. IONIAN  :  HARMONIC TRIPLET (1M, 4M, 5M)
2. DORIAN  : HARMONIC TRIPLET (2m, 5M, 6m)
3. PHRYGIAN : HARMONIC TRIPLET (3m, 6m, 7d)
4. LYDIAN: HARMONIC TRIPLET  (4M, 7d,1M)
5. MIXOLYDIAN: HARMONIC TRIPLET  (5M, 1M,2m)
6. AEOLIAN: HARMONIC TRIPLET (6m, 2m, 3m)
7. LOCRIAN: HARMONIC TRIPLET  (7d, 3m, 4M)


Besides these 2 types of basic triplets we have also a 3rd type X1 X2 X3 , where X1-X2 is a chromatic relation and the X2-X3 is an harmonic relation or vice versa. We may call them the mixed
basic chromatic-harmonic triplets. E.g.  the basic triplet that is used sometimes in blues 1M 2m, 5M , is such as 1M-2m have chromatic relation while 1M-5M harmonic relation.

To convert a basic harmonic triplet to another chromatic or mixed basi triplet we utilize correspondences where we correspond each of the 3 main major chords of the diatonic scale with their lower minor relative and the 5M7 with the 7d. Therefore

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

The same arguments may apply for the chromatic tonality where some of the mnor chords become major and some of the major chords minor. E.g. We have the harmonic triplet (3M7, 6m ,2m ) of the frygian mode and the harmonic triplet (7M7-3M7-6m) of the Locrian mode which are combined with the more standard harmonic triplets of the diatonic tonality of the dorian mode (2m-5M7-1M) or the myxolydian mode (5M7-1M7-4M) .

For  alternative basic chromatic triplets of the chromatic tonality (that corresponds to the harmonic minor and double harmonic minor) we have the triplets (we notice that thsi type of chromatic tonality gives for the basic chromatic triplets, cases of 2 major chords and one minor, thus the major chords are dominating!)


IONIAN MODE: 7M-1M-2m
DORIAN MODE: 1M-2m-3M
FRYGIAN MODE: 2m-3M7-4M
LYDIAN MODE: 3M-4M-5M
AEOLIAN MODE: 5M-6m-7M
LOCRIAN MODE: 6m-7M-1M

205. HOW TO CREATE CHORD PROGRESSIONS AND A SIMPLISTIC SUB-MELODY FROM TRIADS OF CHORDS OF THE DIATONIC SCALE AND ALSO ALTER THEM FOR THE HARMONIC AND DOUBLE HARMONIC MINOR MODULATIONS OF ITS NATURAL MINOR

THE CHORD PROGRESSION IS A CYCLE OR SEQUENCE OF TRIADS OF CHORDS AS BELOW.

(we contrast this method with the alternation of pairs in harmonic-chromatic-melodic relations as inpost 148 at the end of it. Here we use triads of chords instead of pairs of chords  and the symmetry is different.
The two methods to create chord progressions from the 7 chords of a diatonic scale the one here with triads (triangles) if chords and the one in post 148 with parallelogram diagrams of chords are like creating a language which has as alphabet the 7 chords of the diatonic scale. It allows of unlimited combinations with varying degrees of symmetries.)

For happy melodies obviously, the triad is  the I, IV, V. According to the degree of sadness we want to impose, we substitute any of the major chords with its lower minor relative. In other words  vi for I, ii for IV and iii for V. 

About the symbols: In a C major scale the symbols denote the next chords

I=1M=C

ii=2m=Dm

iii=3m=Em

IV=4M=F

V=5M=G

vi=6m=Am

vii=7d=Bdim

So the possible combinations are 

I, IV, V   (1M, 4M,5M majors harmonic triad)

vi , IV, V  (4M, 5M , 5m,  chromatic triad, e.g, part of the Andalusian cadenza when reversed) 

I , ii, V    ( 2m, 5M ,1M harmonic triad)

I, IV, iii   (3m 1M, 4M,   melodic-harmonic triad)

IV , ii, V   ( 1M, 4M, 2m, harmonic-melodic triad)  

I , ii, iii  (3m, 1M, 2m, melodic chromatic or only chromatic triad)

vi, IV, iii   (3m, 6m, 4M, harmonic-melodic triad)

vi, ii, iii   (3m, 6m, 2m, harmonic triad)

vi-vii-iii (7d, 3m, 6m, harmonic triad)

I -vii -V  (5M, 1M , 7d, harmonic-chromatic triad)

In case we want to alter the natural minor ofthe scale to an harmonic minor or double harmonic minor the the usual changes of the harmonic personality as in post 158 apply.

In more detail: 

In general starting from a diatonic harmonic personality 

1M, 2m 3m 4M 5M 6m 7dim 1M

the next are the effects of turning the natural minor to harmonic minor or double harmonic minor.

The effect of the 1st blue note 5# of the harmonic minor on the harmonic personality is that 

the 3m  turns in to 3M and the 5M may turn  into  5b5  or better sounding  5#m or 5#dim or 5aug,  or  1dim  

Also the 7dim may turn in to 7m7b5 as 4 notes chord.

While the effect of  the 2nd blue note of the double harmonic minor 2# (or 3b) is that the 7dim turns in to 7M  or 7b5  and , the 1M may become 1aug and also the 2m may become 2#dimb3 or  better sounding 2#dim or 2#M. 

Further changes with augmented chords because of the harmonic and double harmonic minor we involve not only diminished chords but also augmented chords.

E.g.

In C major

Am  Bdim E  Am (repeated many times)  then
C Bd  G C  (repeated many times)  then
Am Dm E Am (repeated many times)  then again
Am  Bdim E  Am (repeated many times)  etc

Listen also to

https://www.youtube.com/watch?v=NwIw2BQW_jE

and to

https://www.youtube.com/watch?v=HcVD-6w4A8k

Of course the next critical issue is to determine the simplicial sub-melody that goes parallel to the chord progression. This determines also the chord progression as triads of notes and the correct voicing of the chord progression, so as to play directly also the simplicial submelody through the correct voicing of chord progression as triads of notes only. In other words

THE SIMPLICIAL SUBMELODY IS OF EQUIVALENT DETERMINATION WITH THE VOICING OF THE CHORD PROGRESSION AS TRIADS OF NOTES. 

Triads of chords with minor chords in them most often are correlated with straight descending shape of the theme of the simplicial sub-melody. While triads of chords with all three chords major chords are correlated with straight ascending shape of the theme of the simplicial sub-melody.

Then we proceed with the embellishments and waving around the simplicial submelody to derive a full dense and even fast melody.

For example if we chose the next two triads of chords for te chord progression in a song in the C major scale 

(Am ,Bdim, E)  and (C Bdim G7) then the chord progression is 

Am-> Bdim-> E-> Am  repeated 4 times and 
C-> Bdim->G7->C  repeated 4 times and   
and all together repeated 3 times.

Then the first triad of chords  which has the minor chord Am signifies sadness and the simplicial submelody is chosed descending with a middle waving . So it is the a5->d5->e5->a4 . One note for each occurence of a chord which belongs to the chord . And the triads of chords C-> Bdim->G7->C has more major chords which signfies happiness so the simplicial submelody is defined as straight ascending . So correpsonding one note (which belongs to the chord) to each chord it may be the c4->d4->g4->c5 .  We may also creare an introductory part A of the song which is both parts B , C of the simplicial submelody with the necessary waving ebelishments around it c4->d4->g4->c5->a5->d5->e5->a4 which we repeat two times each time we repeat the parts B and C above   of the two triads of chords.

The two methods to create chord progressions from the 7 chords of a diatonic scale the one here with triads (triangles) if chords and the one in post 148 with parallelogram diagrams of chords are like creating a language which has as alphabet the 7 chords of the diatonic scale. It allows of unlimited combinations with varying degrees of symmetries.

We cannot stress much the importance of triads of chords (but also of notes intervals and scales) in improvisation.

A good application is to realize that as a diatonic scale is characterized as chords on the wheel by 4ths by its 3 chords on the steps 1M, 4M , 5M  (harmonic triplet of chords) ,  OR 7d 1M 2m (chromatic tripler of chords) the same can apply for the modes of the diatonic scale.

Besides the basic harmonic triplets (in other words a sequence of 3 chords X1,X2,X3 so that X1-X2 , X2-X3 are harmonic relations od chords, in other words chords that their roots differ by an interval of 4th (5th)) , there are also the chromatic triplets (in other words a sequence of 3 chords X1,X2,X3 so that X1-X2 , X2-X3 are chromatic relations od chords, in other words chords that their roots differ by an interval of 2nd). BOTH  ARE BASIC TYPES OF TRIPLETS. In other words with the 3 CHORDS OF THE TRIPLET WE CAN ACCOMPANY ANY MELODY IN THE DIATONIC SCALE. WE CANNOT HAVE THIS PROPERTY OF BEING HARMONICALLY A BASE OF 3 CHORDS FOR MELODIC TRIPLETs (in other words a sequence of 3 chords X1,X2,X3 so that X1-X2 , X2-X3 are melodic relations of chords, in other words chords that their roots differ by an interval of 3rd) 

The chords of a mode of a diatonic scale at the steps 1,4,5 (or 7,1, 2) of it characterize its mood.

For example for the mixolydian mode of the diatonic scale from C ,(G, A, B , C, D, E, F, G) the chords at the steps 1,4 ,5 are the G, C, Dm) thus the 1, 2, 5 or I, ii, V of the original ionian and are the base of blues jazz.


Based on this perception, the 7 modes of the diatonic scale have the following chord triads:

(that is chords on their 1st 4th and 5th step, and we symbolize by m=minor M=major d=diminsihed.

1. IONIAN  :  CHROMATIC TRIPLET (7d, 1M, 2m)
2. DORIAN  :  CHROMATIC TRIPLET (1M, 2m, 3m )
3. PHRYGIAN : CHROMATIC TRIPLET(2m,3m, 4M)
4. LYDIAN:  CHROMATIC TRIPLET(3m, 4M, 5M)
5. MIXOLYDIAN: CHROMATIC TRIPLET (4M, 5M, 6m)
6. AEOLIAN:  CHROMATIC TRIPLET (5M, 6m, 7d)
7. LOCRIAN:  CHROMATIC TRIPLET (6m, 7d, 1M)

We may compare the basic chromatic triplets with the basic harmonic triplets (see also post 222)

1. IONIAN  :  HARMONIC TRIPLET (1M, 4M, 5M)
2. DORIAN  : HARMONIC TRIPLET (2m, 5M, 6m)
3. PHRYGIAN : HARMONIC TRIPLET (3m, 6m, 7d)
4. LYDIAN: HARMONIC TRIPLET  (4M, 7d,1M)
5. MIXOLYDIAN: HARMONIC TRIPLET  (5M, 1M,2m)
6. AEOLIAN: HARMONIC TRIPLET (6m, 2m, 3m)
7. LOCRIAN: HARMONIC TRIPLET  (7d, 3m, 4M)


Besides these 2 types of basic triplets we have also a 3rd type X1 X2 X3 , where X1-X2 is a chromatic relation and the X2-X3 is an harmonic relation or vice versa. We may call them the mixed
basic chromatic-harmonic triplets. E.g.  the basic triplet that is used sometimes in blues 1M 2m, 5M , is such as 1M-2m have chromatic relation while 1M-5M harmonic relation.

To convert a basic harmonic triplet to another chromatic or mixed basi triplet we utilize correspondences where we correspond each of the 3 main major chords of the diatonic scale with their lower minor relative and the 5M7 with the 7d. Therefore

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

The same arguments may apply for the chromatic tonality where some of the mnor chords become major and some of the major chords minor. E.g. We have the harmonic triplet (3M7, 6m ,2m ) of the frygian mode and the harmonic triplet (7M7-3M7-6m) of the Locrian mode which are combined with the more standard harmonic triplets of the diatonic tonality of the dorian mode (2m-5M7-1M) or the myxolydian mode (5M7-1M7-4M) .

For  alternative basic chromatic triplets of the chromatic tonality (that corresponds to the harmonic minor and double harmonic minor) we have the triplets (we notice that thsi type of chromatic tonality gives for the basic chromatic triplets, cases of 2 major chords and one minor, thus the major chords are dominating!)


IONIAN MODE: 7M-1M-2m
DORIAN MODE: 1M-2m-3M
FRYGIAN MODE: 2m-3M7-4M
LYDIAN MODE: 3M-4M-5M
AEOLIAN MODE: 5M-6m-7M
LOCRIAN MODE: 6m-7M-1M

204. THE CELTIC HEXATONIC MINOR THE CRETAN HEXATONIC AND THE GREEK PENTATONIC SCALES

Studying the Celtic fast dancing melodies (reels) and the Cretan fast dancing melodies (condilies) we find particular scales that are 6-notes and 5-notes (pentatonic).

The Celtic minor is a well-known scale (with various modes) that has also been used to tune hang percussion instruments. In these notes in music here, we have adopted the definition of a scale as a sequence of notes that give one or more octaves and also all cyclic permutations of them. In this way starting from a different note of the scale gives only a different mode, not a different scale.

The Celtic minor 6-notes scale has the next interval pattern in semitones 

2-2-3-2-2-1 

or
3-2-2-1-2-2

Thus as C major scale we just omit the f 4th note

E.g.

c4-d4-e4-g4-a4-b4-c5

 It has 5 chords: C major (I), Em (iii),  Am (vi) ,G (V), Bdim (vii). 


As an alternative at its mode 2-2-1-2-2-3, it is again just the 7-notes diatonic scale 2-2-1-2-2-2-1 where we omit the 7nth note and it becomes 2-2-1-2-2-3.

As alternative if we omit the 3rd note in major mode diatonic scale we get the 6-notes scale 

2-3-2-2-2-1 and its 6 modes. (e.g. 2-2-1-2-3-2 or 3-2-2-2-1-2 etc) We could call it 2nd celtic 6-tonic scale.

It is a 6-notes scale with a maximal number of major/minor chords (See post 117)

The chinese Bawu direct blowing or transverse blowing flutes, and the hulusi flutes as well utilize a celtic minor scale in the mode (starting from the lowest note ) 2-2-1-2-2-3. They name the Bawu or Hulusi tuning of the flute by the 4th note. The Bawu and Hulusi flutes are free-reed winds as the Crumhorn, the Schalmei, the harmonica and the Accordeon. I call them here free-reeds not mainly because they do not touch a surface when they vibrate (the Slamei does touch a surface) but because the lips do not touch the reed.

THE HAPPY ENHARMONIC MAJOR  6-NOTES SCALE

In a diatonic scale there are 3 intervals of major 3rd 1-3, 4-6 , 5-7 (e.g. in C major C-E, F-A , G-B) and 4 minor 2-4, 3-5, 6-1, 7-2. If we want a  scale with more happy intervals of 3rd (major) than sad (minor) then should start with the 3 major 3rds 1-3, 4-6 , 5-7, and create the 6-notes enharmonic generation scale 

1-3-4-5-6-7-1 (e.g. in C major C-E-F-G-A-B-C) with interval structure

4-1-2-2-2-1  

WE may call it the happy enharmonic  MAJOR 6-notes scale

Also in Japanese folk music are used a few enharmonic gendre 5-notes scales with more intervals of major 3rd than minor 3rd. See also post 274 where harmonicas are tuned in this hexatonic scale.

In  the Celtic Minor scale which can be derived by the 3 minor 3rd intervals of the diatonic scale 2-4, 3-5, 6-1 or in C major

C-D-E-F-G-A-C with interval structure 2-2-1-2-2-3 (see also post  276)

The Cretan  6-notes scale is identical with this enharmonic gendre hexatonic scale and it has the next interval pattern in semitones 

4-1-2-2-2-1

It is derived from taking the major 3rd 1-3 of a root chord 1-3-5 and inverting it to be from 3 to next root 1'

Thus as C major scale we just omit the d 2nd note

E.g.

c4-e4-f4-g4-a4-b4-c5

 It has 4 chords all of them major or minor. They are the C major (I) , F major (IV), Em (iii), Am (vi). 

It is met most often in "condilies" with 2-3 cadenzas in the part 1-2-2-2-1.

We may compare it with the Hexatonic scale

3-2-2-1-2-2.  (Celtic minor)

which  can also be  derived by  taking the minor 3rd 3-5 of a root chord 1-3-5 and inverting it to be from 5 to next octave  3'.

Both  scales occur in the Cretan mantinodies or kondilies.

The hexatonic scale is most often an embelishment extension ofthe stanrd diatonic tetrachord 1-2-2.
Common pattern of simplicial submelody of Cretan folk rapsody music: : As intervals of a scale they are in pitch order 1-2-2. In other words  the most common pattern of simplicial submelody is a descending tetrachord , in semitones and in temporal order it is 2-2-1. An example  the andalusian cadenza that in ordinal numbers of the diatonic scale it is 6-5-4-3. 

The Greek pentatonic (5-notes) scale has the next interval pattern in semitones 

2-2-3-4-1 

Thus as C major scale we just omit the f 4th note and the  6th note

E.g.

c4-d4-e4-g4-b4-c5

It has the 3 chords C major G major E minor.  
It appears also in the Richter Tuning of the harmonica at the first octave andthe Chords 1M-5M.

The Greek pentatonic scale is a pentatonic scale with maximum number of major and minor chords. We must not be confused with the standard pentatonic scale (Egyptian, Mongolic, Western Indian  etc of interval structure  2 2 3 2 3.  (1st mode of the pentatonic minor. The 5th mode  3-2-2-3-2 is  also the pentatonic minor, and there is also  the 2nd mode or Egyptian scale 2-3-2-3-2 and the 
3-2-2-2-3 pentatonic which is not a different mode of it )

The greek pentatonic (5-notes) scale  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 (known also as Raga Chitthakarshini)

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 

The way that these scales derive from folk fast solos over two only chords (I-V-I) is as  in the  post 203.

203. A SIMPLE SYSTEM OF FAST FOLK IMPROVISATION (DACTYLADA OR TROCHADA) WITH BEGINNING AND ENDING NOTES OF A SCALE AND TWO OR THREE ONLY CHORDS INSPIRED BY IRISH REELS AND CRETAN "CONDILIES".

See also posts 159 and 201, and 280

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)

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). 

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: 

SHORT DESCRIPTION

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


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 adiatonic scale 
e.g. as order of notes in adiatonic scale 
(3 3 3 4 )(3 5 5 5) (4  2 3 4) (5 5 3) (15 syllables) and spans an interval   2-5 ,of 4th around e.g. a chord 1-3-5.
As intervals of a scale they are in pitch order 1-2-2. In other words  the most common pattern of simplicial submelody is a descending tetrachord , in semitones and in temporal order it is 2-2-1. An example  the andalusian cadenza that in ordinal numbers of the diatonic scale it is 6-5-4-3. 
Or a different again of cyclic type:
(1'2'3'3')(1'1'2'2')(771'1')(7655)
(5566)(71'2'2')(1'71'1')(1'1')(again 16+14 half syllables  or 8+7 syllables) and spans an interval 5-3' of 6th around e.g. an inverted  chord 5-1'-3'

Alternatively the action of the melody can be in the upper minor 3rd and in detail  descending from 3' to 5 (in intervals of semitones 2-2-1-2-2) , or in the lower major 3rd, or in detail from 1' to 3 (in in intervals of semitones 1-2-2-2-1)
as rhythm from 15-syllables poetry
(1M         )
10010100
(5M7)1M
1001010
(combination of anapestik  100 with trochaic 10 )

Other thythms are 

100111010 or a more extreme that spans 3 powers of 2 , 10000011100100
(e.g. in Bardakis castrines condilies) .

DANCING FAST INSTRUMENTAL MELODY
Most often each half line of the poetic line is with 8 notes , thus all the first 8-syllables line 
16 notes, and the 2nd 7-syllables line from 16 notes again or possible 14 notes, in total 32 or 28. This is the dancing fast instrumental melody.
The half-poetic line is the middle melodic theme, and also one measure, that follows the pattern of the above rhythm most of the time, and is translated up or down , and also changing shape. The trasnlations are melodic (intervals of 3rd) harmonic (intervals of 4th or 5th) or more rarely (less than 30% of the cases) chromatic (intervals of 2nd).
But inside each measure and middle melodic theme, there are the micro-melodic-themes that are oscilaltions around one note, most often by intervals of 2nds.
SLOW SINGING MELODY: this is by no means following in syllables the exact pattern of the 15-syllables poetry. Maybe it was in ancient times. But in modern times, is may vary significaly depending on the  emotional state ofthe singer.

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 (mandinodies)  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

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


4) 2m7->5M7->1M    (Blues)

ETC.

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 
3 3 3 4 3 5 5 5 4  2 3 4 5 5 3

Common pattern: As intervals of a scale they are in pitch order 1-2-2. In other words  the most common pattern of simplicial submelody is a descending tetrachord , in semitones and in temporal order it is 2-2-1. An example  the andalusian cadenza that in ordinal numbers of the diatonic scale it is 6-5-4-3. 

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.




  A SIMPLE SYSTEM OF FAST FOLK IMPROVISATION (DACTYLADA OR TROCHADA) WITH BEGINNING  AND ENDING  NOTES OF A  SCALE AND TWO OR THREE ONLY CHORDS   INSPIRED BY IRISH REELS AND CRETAN "CONDILIES".

Dactylades in the Cretan, Greek language or dactylic melodies in the ancient Greek language  means FINGERINGS MELODIES
Notice also that the term trochaic measure in Greek means wheels measure or reels measure which coincides with the Irish term for such melodies. Trochada or Trochaico or Trochaices melodies mean in Greek rolling or reels melodies.

About the symbols: In a C major scale the next symbols denote the next chords

I=1M=C
ii=2m=Dm
iii=3m=Em
IV=4M=F
V=5M=G
vi=6m=Am
vii=7d=Bdim

We may also denote the 7 notes of the major diatonic scale by 1-2-3-4-5-6-7

THE MAIN IDEA TO COMPOSE AND IMPROVISE SUCH FAST DANCING SOLOING IS TO RESTRICT THE HARMONY AND THE USED NOTES TO REALLY SIMPLEST POSSIBLE  SCHEMES AND CONVERSELY ENHANCE THE COMPLEXITY IN WAVING OR ROTATING, VARIATIONAL PATTERNS

This system can play practically on any of the well-known instruments: Guitar, mandolin, piano, violin, Bouzouki, Saz, Ukulele, Irish Whistle, transverse flute, Celtic harp, santouri, saxophone, clarinet etc

This simple system of simple improvisation has the next determination requirements

A) THE RHYTHM

The temporal speed  is usually 4 times the normal beat of a heart so it is in between

200-280 beats. So it has dancing implications strongly correlated to joy rather than sadness

Examples of rhythms may be (1110) in 4/8 or (1010100010001000) in 16/8. in general multiples of 4 beats. So the measures could of 4 beats. Each dactylada or "rotation"  has 8 measures 4+4 , and 32 beats.

THE IMPROVISATION IS A SEQUENCE OF "ROTATIONS". EACH "ROTATION" HAS THE NEXT 3-LEVEL  RHYTHMIC OR MORPHOLOGICAL STRUCTURE

THE 4 PARTS A1 A2 A3 BI STRUCTURE 

This structure is rhythmic morphological and comes as a pattern from the 15-syllable poetry.

2 lines in a 15-syllables poetry are divided to 4 parts A1 A2 A3 B1, each of the Ai having 4 syllables and the B1 3 syllables. Similarly here in the melody the A1 A2 A3 , B1 are of 2 measures.  Each of the A1 A2 A3 B1 contain at least one melodic theme. If we put the restriction that both the melodic theme and its variations are consisting from intervals that are 2nds in less that 1/3 (=33%) of the cases, then we get an "Irish" but also "south american", melodic/harmonic sound in the melody. The melodic theme of A1 is translated or inverted to that of the A2 and that of the A2 to that of A2. Finally the melodic theme of A3 is mutated to that of B1. The simplicial sub-melody has one note in each measure therefore two notes in each of the A1 A2 A3 B. These two notes signify a MELODIC MOVEMENT (VECTOR) which is the basis of an emotion.  If we superimpose the melody at the first two levels, the detailed improvisational notes of the melodic theme (1st level) and the melodic move or vector of the simplicial submelody (2nd level) we get a new musical entity and concept that we may call WAVING MELODIC VECTOR. The wavings are as in the 7 melodic themes patterns asin post 231. Another classification of them is that they are of 3 classes a) Chromatic (of length an interval of 2nd) b) Melodic (of length an interval of 3rd) c) Harmonic (of length an interval of 5th). The choice in the improvisation of one of these 3 classes is similar to the choice in a chord progression if the chord-transition will me chromatic , melodic or harmonic. Very often the wavings are of diminishing amplitude as we reach the melodic center-end note of it. This is very convenient to have in mind when we improvise because we think that we will move from a persisting note a (melodic center) to a persisting note b (melodic center ) in a scale but with improvisational waving way that we may change each time at willAll the melodic movements of the A1 A2 A3 B make a DOLPHIN WORD (as defined also in post 101, 114 ). Each part A (thus melodic move too) has an underlying chord. The chords of two parts like A1 A2 may be the same or different chords. The melodic move can be also a melodic triad (alternating major minor vector interval of 3rd as in post 208) . The Dolphin word of the "rotation" may be a closed polygon (e.g, triangle) of waving melodic vectors , so that the length of the melodic vector indicates also the length-interval of the waving melodic vector, which may also be the distance as musical interval of the middle notes of the underlying chords, of the melodic move.
This melodic polygone allows for simple and very concise, simple and visually beautiful  methods of writing the improvisation with not less information than the necessary but no more than a minimum too, so that each time we see the written paper and play the melody a different melody will emerge (mainly at the first layer/level of it) while still it will be "the same" song. 

When playing again such an improvisation the simplicial sub melody is repeated (thus the "rotation" A1 A2 A3 B or Dolphin word of it), but the other notes inside the measures that are embellishments may change. All together the "rotations" or Dolphin words make the total melodic phrases of the song. Therefore we have here at least a 3-level structures of the melody a) notes b) melodic moves c) "rotations" or Dolphin words,and in time it is 1, 2^3=8 (2 measures)  and 2^5=32 (A1A2A3B parts).

B) THE SCALE 

B1) In the case of using three chords for the improvisation which are the I-IV-V-I, we utilize all the major mode of the diatonic scale and starting note is the root and ending note is either the root 1st the 3rd or the 5th. 
Similarly if we would use 2 chords the I (major) , ii (minor) , them again the 7 notes diatonic scale would be OK. 

The harmonic transition of the melodic theme when played on an overtone flute as in post 233,is just repeating the melody on the holes but on a higher harmonic. E.g. from the 2nd to 3rd harmonic will give a transition by a fifth. So the scale maybe just the range of the holes of the overtone flute which is an interval of 5th (pentachord).
Dividing the octave in two parts at the 5th note of the diatonic scale we have 2 subscales , a pentachord and a tetrachord to play the melodic theme and translate it to the 2nd such subscale.

Special considerations are required when we want to use only 2 major chords and be the I V. 

B2) But if we are using only two chords I-V-I, then here is how we find the appropriate 6-notes or 5-ntes scale. Again starting note is the root and ending note is either the root 1st  the 3rd or the 5th. 

The scale can even be all the diatonic scale but in particular two notes are pointed as beginning and end: [a1, a2] It can, of course, be also a mode with  a2=a1' E.g. a1=e4 in a c4 major scale thus the Phrygian mode. Or it can be a subscale of the diatonic scale. Here we utilize as default a 6-notes subscale and a1=e4 a2=b4. The reason we prefer 6-notes or 5-notes scales from 7-notes is that the intended underlying chords I and V have in total 5 notes, so with 6-notes or 5 notes, we have fewer notes outside the chords in the solos and never more than the notes of the underlying chord. 
Here we utilize the Cretan minor 6-notes scale as  default choice (e4,f4,g4,a4,b4, c5). We do so because the underlying chords of the solo will be only two chords. In the major diatonic scale, it will be the C major (I) and the G major (V).  As in soloing, we do not use only the arpeggio of the chords but the vector-intervals of it (see post 183)  we will combine vector intervals of 3rds one from each chord to derive the subscale where the action of improvisation will take place. We use here the upper minor 3rd interval e4-g4 for the e4-f4-g4 part of the scale from the C major chord (I) and the lower major 3rd of G major g4-b4 for the g4-a4-b4 part of the scale. The 6th note c4 was an extension so as to be able to close either back to e4 (upper cycles generation of solos) or to the c5 (ascending generation of solos). This is the general scheme from intervals of 3rds to derive other such minimal subscales for other pairs of chords.

Inspired from similar Cretan music, we set here the Cretan default that the scale is defined by a minor interval of 6th of 8 semitones and 6 notes (b1,b2,b3,b4,b5,b6) in the following interval pattern of semitones 1-2-2-2-1, where, in  particular the b1 is the 3rd note of diatonic scale (e.g. in C4 major the e4) and the b6 is the 1st note of the next octave  (e.g. in C4 major, the C5 note , (b1,b2,b3,b4,b5,b6)=(e4,f4,g4,a4,b4, c5). It defines by its first note the Phrygian mode of the diatonic scale.  Notice that if we close it to become 6-notes scale it would be in intervals 1-2-2-2-1-4. It has 4 chords all of them major or minor. They are the C major (I) , F major (IV), Em (iii), Am (vi). Therefore it is a maximal harmonic 6-notes chord (see post 117) and can be called Cretan minor 6-notes scale as it is very often used in Cretan condillies.. To play it in an Irish whistle (or Cretan habioli) we close the lowest hole (d4 note) with a tape. When played starting from e4 and ending in e4 it is an upper cyclic generation of solos, and the 1-2-2 part at the end is a decelerating descending, while at the beginning is an accelerating ascending.
The choice of the subscale is to a minimal one which when playing almost randomly in it, starting and ending on the two notes a1, a2 will give melodies that fit to the two chosen chords of the improvisation. But it is known of course that all melodies in a diatonic scale can be covered with two only chords of it e.g. I and V.
MINIMAL SUBSCALES FOR TWO CHORDS: Here in our Cretan default choice (e4,f4,g4,a4,b4, c5) we used the upper minor 3rd interval e4-g4 for the e4-f4-g4 part of the scale from the C major chord (I) and the lower major 3rd of G major g4-b4 for the g4-a4-b4 part of the scale. The 6th note c4 was an extension so as to be able to close either back to e4 (upper cycles generation of solos) or to the c5 (ascending generation of solos). This is the general scheme from intervals of 3rds to derive other such minimal subscales for other pairs of chords.
Common pattern: As intervals of a scale they are in pitch order 1-2-2. In other words  the most common pattern of simplicial submelody is a descending tetrachord , in semitones and in temporal order it is 2-2-1. An example  the andalusian cadenza that in ordinal numbers of the diatonic scale it is 6-5-4-3. 
An alternative IRISH DEFAULT for the same chords I=C and V=G would be to use the lower major 3rd of G thus g4-a4-b4 and the lower major 3rd from C thus c5-d5-e5 in total g4-a4-b4-c5-d5-e5 or in another mode of it  c4-d4-e4-g4-a4-b4-c5 with interval structure in semitones 2-2-3-2-2-1  and is also known as a mode of the Celtic minor 6-notes scale (raised or not depending on which mode of it we are using see post 52, and 117) and exists also in hang recursion instruments. When played from c4 ascending it has an accelerating ascending because of the 2-3, while when ending back to c4 a decelerating descending.  As the 6-notes scale  is nothing else than the maximal harmonic scale of 6 notes as above and as in post 117. It has 5 chords: C major (I), Em (iii),  Am (vi) ,G (V), Bdim (vii). In order to have an ascending effect, we can start soloing from c4 and end soloing in e4, g4 or c5. To play it in an Irish whistle (or Cretan habioli) we close the 3rd hole (f4 note) with a tape.
This 2nd, raised Celtic Minor default c4-d4-e4-g4-a4-b4-c5 , compared to the 1st Cretan default (c4,e4,f4,g4,a4,b4, c5), it is more harmonic with stronger accelerations decelerations, while the 1st Cretan default is more chromatic with softer accelerations and decelerations. 
We could utilize therefore other small sub-scales e.g. another maximal harmonic 6-notes scale  1-2-2-3-2-2 or 2-2-1-2-2-3 , see post 117 called also (mode of) Celtic minor, c4-d4-e4-g4-a4-b4-c5. It has 5 chords one of which one is diminished but all the rest 4  major or minor. C major (I), Em (iii),  Am (vi) ,G (V), Bdim (vii). Another 3rd possibility is also  (c4,d4,e4,f4,g4, b4 c5) obtained by combining the upper minor 3rd interval of C major e4-f4-g4 and the upper  minor 3rd interval of G major b4-c5-d5. It has interval structure 2-2-1-2-4-1, again 4 chords but one is diminished. The chords are C major (I) ,E minor (iii) , G major (V) , Bdim (7dim). On an Irish whistle, it is played by covering with tape the 6th hole (note a4).  If we combine the major 3rd interval of c major c4-d4-e4 with the major 3rd interval of G major g4-a4-b4 we get the c4-d4-e4-g4-a4-b4-c5 which is again (a mode of ) the Celtic Minor above.
Finally, as 4th possibility: if we combine again simply the c4-e4-g4 C major with the G major g4-b4-d5, we get the c4-d4-e4-g4-b4-c5 with interval structure 2-2-3-4-1 which is (a mode of) the maximal harmonic 5-notes scale, that we may call Greek pentatonic scale of  post 117. It has the 3 chords C major G major E minor.  It is also directly derivable from the Celtic minor 6-note scale by converting one of the 2-2 to 4. It can be obtained also by combining the lower major 3rd part of the C major c4-d4-e4 with the upper minor 3rd part of the G major b4-c5-d5 and adding also the root g which is common to both chords. If we do not add the g   we get the c4-d4-e4-b4-c5 which is 4-note scale with interval structure 2-2-7-1. On an Irish whistle, it is played by covering with tape the3rd hole (note f4) and the5th hole (note a4)
A mode of the previous maximal harmonic 5-notes scale c4-d4-e4-g4-b4-c5  is the c4-e4-f4-g4-a4-c5 with semitones interval structure 4-1-2-2-3 and with chords F major and C major (I, IV). The  e4-f4-g4 is the upper minor 3rd of the C major and the f4-g4-a4 the lower major 3rd part of F major.    The last mode is also playable in a wind instrument like diatonic Irish whistles. The 1-2-2 interval is in the middle of the instrument and by closing permanently with tape, the first and last hole (in a 6 hole system) somehow no interaction occurs among the holes due to the geometry and so the  scale can be played directly on the whistle as if it was dedicated by construction to it.

Concluding: We can obtain the previous 6-notes 5-notes or 4 notes scales by combining one major or minor 3rd interval of each of two major chords (like C and G).
From the point, of view of chords that they contain the most harmonic is the Celtic minor 6-notes scale c4-d4-e4-g4-a4-b4-c5 with 5 chords 2 major 2 minor and one diminished. The 2nd best is the Cretan minor 6-notes scale e4,f4,g4,a4,b4, c5 with 4-chords 2 major 2 minor. Third, best is the 6-notes scale c4,d4,e4,f4,g4, b4 c5 with 4-chords 2 major one minor and one diminished. Then we get the  5-notes maximal harmonic Greek pentatonic scale c4-d4-e4-g4-b4-c5 with 3 chords 2 major and one minor. Finally, we get also a 4-notes scale c4-d4-e4-b4-c5, that can be considered to contain one 5-power chord e-b-e.

If the improvisational rotation in  the SUB-SCALE

starts from the lower end and ends in it it is called UPPER CYCLIC (NEUTRAL/SAD)
If it starts from the upper end and ends in it it is called LOWER CYCLIC (NEUTRAL  HAPPY)
If it starts from the upper end and ends at the lower end  it is called  DESCENDING (SAD)
If it starts from the lower end and ends at the upper end  it is called ASCENDING (HAPPY)

C) THE MELODY 
The melodies have one element of invariance and pre-determination which the beginning and ending notes, and the second element of arbitrariness which is what are the  intermediate notes of the scale and what are the involved durations and sequences or melodic shapes (ascending, descending , expansions, static rotations or oscillations, etc)

There are 4 generations of dactylades. 1) The Upper cycles 2) the Lower cycles 3) The ascending 4) the descending, The upper cycles melodies start from b1 and end  ( after 16 beats ) to b1 again. The lower cycles melodies start from b6 and end  ( after 32 beats ) to b6 again. 3)The ascending dactylades or trochaic  melodies start from b1 and end  ( after 32 beats ) to b6 . 4) The descending dactylades melodies  start from b6 and end  ( after 32 beats ) to b1

Common pattern: As intervals of a scale they are in pitch order 1-2-2. In other words  the most common pattern of simplicial submelody is a descending tetrachord , in semitones and in temporal order it is 2-2-1. An example  the andalusian cadenza that in ordinal numbers of the diatonic scale it is 6-5-4-3. 

The harmonic transition of the melodic theme when played on an overtone flute as in post 233,is just repeating the melody on the holes but on a higher harmonic. E.g. from the 2nd to 3rd harmonic will give a transition by a fifth.

In between the first and last note within the 32 beats (usually grouped in measures of 4 or 8 beats)

there are consecutive up or down moves (vectors) that are called petarismata or rotations (petarismata means in the Creek language, short flights or butterflying ). The specific combination pattern of such up and down moves is determined in the improvisation it is open and it is also the specific melodic-rhythmic personality of the dactylada (dactylic melody). For the simplicial sub-melody of the petarismata and bridges for the underlying chord-transitions see below in the rules of the harmony. If the scale is chosen as above to be supported from the 2 underlying chords, then almost anything that is statistically uniformly in time played on these subscales will sound to fit in harmony with the two accompanying chords as long as the dynamics of starting ending are as above Therefore as the correct harmony of the improvised melody is guaranteed the improvisation focus on creating rhythmic and melodic shapes that correspond to the requirements of our feelings.

When we are using 3-chords I, IV, V  (in sequence I-IV-V-I or I-V-IV-I) instead of two only  it is a bit mote complicated how to follow the underlying chords that have equal duration 4 beats each. But simple practice gives directly the way as it is direct in the human feeling how to improvise on a chord progression like I-IV-I-V.
A guide of course is  that we start from c4 as initial center for the I chord and then  the a melodic center (simplicial submelody) for the chord IV which is F major is the  f4 note (or a4) and then for the chord V  which is the G major is  the d4  note (or b4) then back to the end of the soloing which is the c4 or e4 or g4. 
We very often as in condillies may use the descending sequence of notes 1'-7-6-5-4-3 as steps of the diatonic scale (in semitones 1-2-2-2-1) in 3  descending waves, one descending and two cyclic :  1'-1'-7-6 the  5-7-7-6-5,  3-4-4-4-5-4-4-3 (chord progression of 5 steps  on 3 chords  I-IV-V-IV-I) Or it could be with three waves one   ascending and two  cyclic 3-4-5   6-7-6-6-5-5    3-4-4-4-5-4-4-3 and with chord progression of 5 steps on three chords  I-IV-I-V-I
As harmony it is usually a permutation of the the chords I, IV,V. But as melody it is usually three or four  melodic triads (vector intervals of 3rds see post  208) two minor and one or two major. 
The rhythm is from a 15-syllables poetry so the first two minor/major melodic triads count 8 syllables (beats) while the last melodic triad or last two melodic triads count  7 beats or syllables. Normally two triads are for the first poetic line (8 beats) and two more for the 2nd poetic line (7 syllables).Nevertheless the melody of the voice and the counter melody of the instrument  maybe different although on the same sub-scale (usually in semitones 1-2-2-2-1 or in steps of the scale 1'-7-6-5-4-3  )  and with the same chord progression on the I, IV V.

 In some cases the melody of the voice may use only 2 or only 1 of the  melodic triads with a sub-chord progression  , fewer chords , but from the same chord progression.

We may count each of the poetic lines, the 1st of 8 beats and syllables and the 2nd of 7 beats or syllables as 1) The Upper cycles 2) the Lower cycles 3) The ascending 4) the descending,
Obviously the most sad are the Descending-Descending and the most joyful the ascending ascending. While interpediateare e.g. Descending-upper cycle (sad) , or Upper-cycle-upper cycle (a little happy) or Ascending-upper-cycle (a bit more happy) , lower cycle - lower cycle ( a little happier) and ascending-lower cycle (much happier).

THE IMPROVISATION IS A SEQUENCE OF "ROTATIONS". EACH "ROTATION" HAS THE NEXT RHYTHMIC OR MORPHOLOGICAL STRUCTURE

THE 4 PARTS A1 A2 A3 B1 STRUCTURE 
This structure is rhythmic morphological and comes as a pattern from the 15-syllable poetry.
2 lines in a 15-syllables poetry are divided to 4 parts A1 A2 A3 B1, each of the Ai having 4 syllables and the B1 3 syllables. Similarly here in the melody the A1 A2 A3 have at least 4 beats and 2 measures and the B1 is 2 measures and at least 3 beats and a pause. Each of the A1 A2 A3 B1 contain at least one melodic theme. The melodic theme of A1 is translated or inverted to that of the A2 and that of the A2 to that of A2. Finally the melodic theme of A3 is mutated to that of B1.
A basic "signature" of the improvisation  is the simplicial submelody basic melodic theme as shape and pattern, which of course is parallel to the chord-progression pattern as rhythm and repetitions. 

D) THE HARMONY

The harmony of the dactylada (dactylic melody) is only two chords the 1st (I) and the 5th (V) of the major diatonic scale. The chord progression during a dactylada is I-V-I. E.g. in a C major scale it would be (Cmajor-Gmajor-Cmajor). Usually they are played 8 beats the I and 4 beats the V and so on.

As an alternative, we may have only one chord which is a power-5 chord 1-5-1' (with notes C4-G4-C5).
In some fast versions of this system we may use instead, the chord progression I-IV-V-I so that each chord lasts for 4 beats.  (We could as well chose I-V-IV-I). Nevertheless in such cases we will use not the above 6-notes scale but rather all the diatonic scale.

More generally see below about 2 or 3 only chords harmonization.
If we want to accompany such melodies  with  major or minor triads then they should be as few as possible e.g. 2 or 3. For happy melodies obviously, they are the I, IV, V. According to the degree of sadness we want to impose, we substitute any of the major chords with its lower minor relative. In other words  vi for I, ii for IV and iii for V. 

About the symbols: In a C major scale the symbols denote the next chords

I=1M=C
ii=2m=Dm
iii=3m=Em
IV=4M=F
V=5M=G
vi=6m=Am
vii=7d=Bdim

So the possible combinations are 

I, IV, V   or only I, V

vi , IV, V or only vi, V

I , ii, V 

I, IV, iii   or only I, iii

iv , ii, V or only iv, V

I , ii, iii or only I, iii

vi, IV, iii   or only I, iii

vi, ii, iii   or only vi, iii

vi-vii-iii or only  vi-iii

I -vii -V  or only I  V

In case we want toalter the natural minor ofthe scale to an harmonic minor or double harmonic minor the the usual changes of the harmonic personality as in post 158 apply.
In more detail: 

In general starting from a diatonic harmonic personality 

1M, 2m 3m 4M 5M 6m 7dim 1M

the next are the effects of turning the natural minor to harmonic minor or double harmonic minor.

The effect of the 1st blue note 5# of the harmonic minor on the harmonic personality is that 

the 3m  turns in to 3M and the 5M may turn  into  5b5  or better sounding  5#m or 5#dim or 5aug,  or  1dim  

Also the 7dim may turn in to 7m7b5 as 4 notes chord.

While the effect of  the 2nd blue note of the double harmonic minor 2# (or 3b) is that the 7dim turns in to 7M  or 7b5  and , the 1M may become 1aug and also the 2m may become 2#dimb3 or  better sounding 2#dim or 2#M. 

Further changes involve not only diminished chords but also augmented chords.

During the transition of two successive  chords Xi-Xi+1, we compose/improvise the melody within
1) a pentachord or tetrachord that starts at the middle note of Xi and ends at the middle note of Xi+1, if the Xi-Xi+1 transitions is harmonic with the two chords a 4th or 5th apart (obviously it contains two notes from each chord). The harmonic transition of the melodic theme when played on an overtone flute as in post 233,is just repeating the melody on the holes but on a higher harmonic. E.g. from the 2nd to 3rd harmonic will give a transition by a fifth.

2) a trichord that starts at the middle note of Xi and ends at the middle note of Xi+1, if the Xi-Xi+1 transitions is melodic with the two chords a minor of major 3rd apart (obviously it contains two notes from each chord) .
3) An interval of 2nd that starts at the middle note of Xi and ends at the middle note of Xi+1, if the Xi-Xi+1 transitions is chromatic with the two chords a minor of major 2nd apart (obviously it contains two notes from each chord) .
We may use of course variations of a melodic  theme by rotations, inversion, translations as arpeggios of the transitional trichord , tetrachord or pentachord .

We may conceive the improvised soloing from a1 to a2 as two bridges (as in posts 76, 72, 19, 65 ) for the chord transitions I->V  and V->I. We may also conceive the notes a1, as the melodic center of the simplicial sub-melody for the chord I in the chord transition I->V and the a2 as the melodic center and note of the simplicial sub-melody for the chord I again but for the chord transition V->I. The melodic centers and notes of the simplicial sub-melody for the chord V and chord transitions  I->V and V->I will be intermediate notes of the basic scale of the Trochada. In the default choice here where the scale is the notes 3-4-5-6-7  of a major diatonic scale (e.g. e4-f4-g4-a4-b4) then the melodic centers for the V chord will be the notes 5 or 7 (g4, b4). In a general case to have more degrees of freedom we select two notes for beginning and ending as notes of the simplicial sub-melody that belong to the one chord A1  and two notes as notes of the simplicial sub-melody that belong to the second intermediate chord A2 so as to have the improvised action that passes from the melodic centers x1-x2-x3 for the chords A1->A2->A1. In the default choice of the Cretan minor 6-notes subscale 3-4-5-6-7 that it is used here is such that the two melodic centers for the chord A2 are included and the almost-random playing in the subscale starting and ending in 3 or 1 gives melodies that fit the chords I and V.  In particular for upper cyclic or ascending  dactylades on Cretan minor scale, we start from c4 and end at e4 or g4 which are also the melodic centers corresponding to the chord C (I) . While the melodic centers corresponding to the chord G (V) are the d4 and b4. 
If we use an instrument like mandolin, mandocello, or tambouras and in general an instrument tuned by intervals of pure 5th, then we may use the isocratic method of accompanying with an interval of 5 which is the 1-5 notes of the underlying chord. Here for the I and V chord, the intervals of 5  will be two successive pairs of strings, with a common string. Then the melodic improvisation is played on the next higher string for each pair of strings that accompanies.
If it is used a Celtic harp the simultaneous playing of the solo with the right hand on higher strings and the two chords with the left hand on the lower strings is feasible.

E) THE LYRICS

Most of the dactylades during the improvisation do not have lyrics. But some of them, in a density determined by the feelings of the players and singer, does have. The Lyrics for a dactylada are two lines of 15-syllables poetry and as the last syllable is a pause in sound it is in total 16 syllables and as each dactylada is 32 beats and 8 measures , to every syllable corresponds 2 beats and to each measure 2 syllables. One dactylada corresponds to two lines of 8+7 syllables of lyrics. The first line has 8 syllables and the 2nd line only 7 syllables. If the poetry is free-15-syllables this is the only requirement. If the poetry is strictly traditional then it has to have an iambic or trochaic 4-measures poetic measure (-U) or (10) or loud volume-syllable-low volume syllable or (U-) or (0,1) at inverse order and odd lines must end to similar vowels (rhyme).
Notice also that the term trochaic measure in Greek means wheels measure or reels measure which coincides with the Irish term for such melodies

The lyrics are improvised as well as the melody of the dactylada or trochada , and the two lines of lyrics are called mantinada. 

Creatan condillies

https://www.youtube.com/watch?v=ejmMrb2r2ic

https://www.youtube.com/watch?v=VSERK1tCDBQ

https://www.youtube.com/watch?v=AjH68cAuoD8

Irish reels

https://www.youtube.com/watch?v=HcVD-6w4A8k

https://www.youtube.com/watch?v=njgAjaAGebw
https://www.youtube.com/watch?v=N2iHNSlJMfc


https://www.youtube.com/watch?v=mpN36I9xr-o

 REMARKS ABOUT EXTENSIONS
The previous simple system of improvisation is for two only chords. It may be considered as a simple system of improvisation for one chord transition only and its inverse. It utilizes two successive major/minor 3rd intervals of the two chords in harmonic relation. But it could be also between two relative chords or two chords in chromatic relation. Or we may utilize the triads of chords as above inside the diatonic scale to create a chord progression , Also altered triads of chords by shifting from the natural minor to the harmonic minor or double harmonic minor (with the two blue note 5#, 2#). See post 205. Once we master it, then we may add more chords for a longer chord progression and use it for all chord progressions. Of course, in that case, we will not spend so much time soloing on one only chord transition.