229. SIMPLE ORGANIZATION OF THE MELODY IN IMPROVISATION OR COMPOSITION OVER A CHORD PROGRESSION.

We have mentioned that the prefered way of composition in this book is as in improvisation, in other words first we define the simple and then the more complicated. In particular first we compose the harmony as a chord progression X1 X2 ,..., Xn over a scale-of-chords and then we compose the melody.  A very simple and happy case is that the chord progressions is only  3 different chords 1-4-5 over a diatonic scale.

The simplicity of triad of factors for the melodic action is  mainly the next three factors

1) The triad of polarity (qualitative) of a melodic move (ascending, descending, rotating stationarily or isocratic)

2) The  quantitative  triad of the character of the move :Chromatic, Melodic ,Harmonic

3) The rhythmic pattern of repetitions 

Here is where the trichords, tetrachord and pentachords are coming to make the organization simpler.



ALL 3 TRICHORDS  (also called vector intervals of  3rds)

All of them are of the DIATONIC FAMILY

1-2    Minor

2-1   Minor

2-2   Major 

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

DIATONIC FAMILY

(containing only 2 and 1)

2-2-1  syntono major  , Ionian/mixolydian

1-2-2  syntono minor  , Phrygian/Locrian

2-1-2   minor, Dorian/Aeolian

CHROMATIC FAMILY

(containing 3)

1-3-1   2nd chromatic

1-1-3    parachromatic tonal

3-1-1    1st chromatic 

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

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

DIATONIC FAMILY
(containing only 2, and 1)

2-2-2-1       Major Lydian    Contains a major chord (known also as Natzi/Zaouil)
2-2-1-2        Major Ionian/Mixolydian    Contains a major chord.(known also as Rast/Mahour)
2-1-2-2       Minor Dorian    Contains a minor chord (known also as Bousselik/Nichavent)
1-2-2-2       Minor Frygian/Aeolian    Contains a minor chord (known also as Qourdi)


CHROMATIC FAMILY
(containing  3 )

1-1-3-2
1-1-2-3
1-3-2-1   Contains a major chord and a diminished chord
1-2-3-1   Contains a minor chord and a diminished chord
1-2-1-3   Contains a minor chord and a diminished chord
1-3-1-2   Contains a major chord and a diminished chord (known also as Hijaz)
3-2-1-1    Contains  a diminished chord
2-3-1-1
3-1-2-1   Contains a major chord and a diminished chord
2-1-3-1   Contains a minor chord and a diminished chord (known also as Nevesser/Nikriz)
3-1-1-2   Contains a major chord (known also as Saz-kar)
2-1-1-3   Contains a minor chord (known also as Samba)


ENHARMONIAN FAMILY
(containing  4 )

1-1-1-4   Contains a minor chord
1-1-4-1
1-4-1-1
4-1-1-1   Contains a major chord

Now the organization has the next simple rules

RULE 1
During a chord, we compose/improvise the melody within a pentachord of the chord. That is a pentachord with ends the 1st and 5th of the chord (lowest highest note, therefore it contains the notes of the  chord) on normal position . We may use of course variations of a melodic  theme by rotations, inversion, translations as arpeggios of the pentachord of the chord. The average time duration of the notes is about equal or we make sure that the total duration of the notes of the cords is not less than half of the total duration of this part of the melody. This guarantees that this part of the melody fits harmonically to the chord. If we use an overtone whistle e.g. a diatonic or chromatic as in post 233, the 5-chord is just the range of the holes of the whistle.

RULE 2
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 use of course variations of a melodic  theme by rotations, inversion, translations as arpeggios of the pentachord of the chord.
The average time duration of the notes is about equal or we make sure that the total duration of the notes of the chords is not less than half of the total duration of this part of the melody. This guarantees that this part of the melody fits harmonically to the two chords ofthe transition.


If the improvisational rotation in  the SUB-SCALE of the holes of the overtone flute 

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)


If in the chord progression all the transitions are harmonic (intervals of 5th or 4th) then this organization method is simply a way to set intervals of 5ths vertically as chords and their pentachords and intervals of 5th or 4th horizontally as bridge-transitions between the chords.

HERE WE DESCRIBE A STANDARD 3-LAYERS STRUCTURE OF THE MELODY.

THE MELODIC 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).

Of course the above rule samy apply in the cases of improvisation as in the posts 214, 215 etc

Finally this method may also utilize simplicial sub melody composition at first, either the chromatic or the harmonic or the melodic as im post 104

As an improvisation rather than as composition the instruments of Celtic harp (appropriately tuned) , or chromatic pan-flute are the most convenient for such melodies