427. SIMPLICIAL SUBMELODY COMPOSITION METHOD AND ARPEGGIO-TAIL COMPOSITION METHOD OF THE MELODIES.

I have developed in previous posts the method of composing a melody over a chord progression based on the simplicial sub-melody , which has one note per chord.

On the other hand it is widely known in popular and folk music the structure of a melodic theme over a chord as having an arpeggio  (harmonic-melodic) part and a tail (chromatic) part (see e.g. post  421 )

The linking of thee two methods is the obvious that we substitute the one note of the simplicial sub-melody, with the arpeggio part of the melodic theme, and we leave the tail as the bridge of two notes of the simplicial submelody.

If we eliminate thus the tails (chromatic bridges) instead ofte simplicial submelody we get an arpeggio submelody . or harmonic submelody.

There is an issue of beats per minutes though. If we utilize the simplicial submelody method then there are one or few only notes per underlying chord while if we utilize the  arpeggio-tail method there are many notes per underlying chord. This suggests that the simplicial submelody method has double the number of beats per minute compared to the  alternative composition with the arpeggio-tail method. 

Obviously by letting more time  for each chord, the melodic theme will have larger part as arpeggio (e.g. 2/3 of it time) and less (e.g. 1/3) as tail. This is according to the older tradition in folk music.

E.g. a full 15 syllables poetic line (in 15-sylalble poetry) could be only two chords 5M7-> 1M or 

1M->5M7 etc. 

For a 15-sylalbes poetic lyrics, a full 15 syllables  poetic line of total syllables (4+4)+(4+3)=15 would correspond to a single melodic theme A1 , or B1 , C1, A2 etc. and thus here to 2 chords.  This is convenient for the arpeggio-tail method of composing melodies. While the simplicial sub-melody method would require 4 chords per 15-sylalbles poetic line. (see also post 428)

426. THE ORGANIZING RULE OF TRIADS OF CHORDS IN HARMONIC PROGRESSIONS OF CHORDS

See also posts 322,  205, 206, 215, 216 etc

An harmonic chord progression  X1 X2 X3 X4 .... is a progression of chords that are successive in the wheel by 4th, in other words, they are in harmonic relation (their roots are in intervals by 4ths)

This is general concept in the harmony  of songs, by far more powerful and simple that the concept of scale, as it involves 2, 3 or more scales.

The rule of triads refers in choosing the attribute of major or minor in triads Xn-> Xn+1->Xn+2 

E.g. Diatonic harmonic triads 

(Xn)m->(Xn+1)M->(Xn+2)M     (e.g. 2m7->5M->1M) Myxolidian  harmonic triad

(Xn)m->(Xn+1)m->(Xn+2)m   (e.g. 3m7->6m->2m) Aeolian harmonic triad

(Xn)M->(Xn+1)M->(Xn+2)M     (e.g. 5M7->1M->4M)  Ionian harmonic triad

All of them  are the next

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

Harmonic minor triads

(Xn)M7->(Xn+1)m->(Xn+2)m     (e.g. 3M7->6m->2m)

(They can be of course in all permutations e.g. 2m->3M7->6m )

Double harmonic minor triads

(Xn)M7->(Xn+1)M7->(Xn+2)m     (e.g. 7M7->3M7->6m)

Other non-singe-scale hybrid diatonic-harmonic minor ( harmonic  triads)

(Xn)m7->(Xn+1)M7->(Xn+2)m  (harmonic Xn+2 minor and diatonic Xn+2 major) 

(Xn)M7->(Xn+1)m7->(Xn+2)M   (harmonic Xn+1 minor and diatonic Xn+3 major) 

 Hybrid diatonic-harmonic minor (harmonic-melodic triads) 

1M->3M7->6m or  (harmonic 6m minor and diatonic 1M major, in other words in melodic relation) 

1M->6M7-2m or  (harmonic 2m minor and diatonic 1M major, in other words in chromatic relation) 

5M->7M7-3m or  (harmonic 3m minor and diatonic 1M major  in other words in melodic relation) 

5M->3M7->6m  (harmonic 6m minor and diatonic 1M major  in other words in melodic relation) 

So with these rules if we have a 6, 7,8 , 9 harmonic progression we split it in to successive triads that 

are of the above 3 kinds. so as to give a meaningful harmony to the harmonic progression based on the older concept and function of diatonic scales. 

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

A triad of chords is called HARMONIC TRIAD OF CHORDS iff the chords (as roots) are consecutive on the wheel by 4ths (either as major or minor) E.g. E Am Dm or G C F etc


A triad of chords is called MELODIC  TRIAD OF CHORDS iff the chords (as roots) are in consecutive melodic relation in other words iff they are consecutive on the wheel by 3rds E.g. Em C Am or  Am F Dm etc


A triad of chords is called CHROMATIC   TRIAD OF CHORDS iff the chords (as roots) are in consecutive chromatic  relation in other words iff they are consecutive as roots in (diatonic or not ) scale

E.g.  C Dm Em ,    or  Em  F  G  etc

Furthermore a triad of chords may have harmonic melodic or chromatic relation  with another triad of chords iff  the chords in sequence and 1-1 correspondence have this relation.

E.g. starting with the central major triad of a diatonic scale

5M-1M-4M the next triad is in chromatic relation with it  and chromatic parallel triad 

4#dim7-7dim7-3dim7 or also 4#M-7M-3M which is closer to the double harmonic minor  modulation of its natural minor with its standard chord covering.

Also the next triad is melodic relation with the original triad

3m-6m-2m 

ONCE IMPROVISATION OVER  A TRIAD OF CHORDS IS  MASTERED THEN THE NEXT STEP IS THE IMPROVISATION OF TWO OR MORE  TRIADS . ONE WITH MORE MINOR CHORDS AND ENDING WITH A  TRIAD WITH MORE (OR ALL) MAJOR CHORDS (IN THE EMOTIONAL INTENTION IS FROM SADNESS TO JOY).

This is done by combining successively the improvisations one two or more  triads of chords .


And here is  where  the relations of triads of chords becomes important.

Two triads of chords X1 X2 X3 and Y1 Y2 Y3 are  disjoint  iff  none of the X1 X2 X3 is identical with any of the Y1 Y2 Y3. 

Two disjoint triads of chords X1 X2 X3 and Y1 Y2 Y3  are in consecutive harmonic relation 
iff  the X3 is in harmonic relation with the Y1 (see also  post 30 on the harmonic melodic and chromatic relations of chords ) 

E.g.  X1=E X2=Am X3=Dm   and Y1=G Y2=C Y3=F 

Two disjoint triads of chords X1 X2 X3 and Y1 Y2 Y3  are in consecutive melodic relation 
iff  the X3 is in melodic relation with the Y1 (see also  post 30 on the harmonic melodic and chromatic relations of chords ) 

E.g.  X1=E X2=Am X3=Dm   and Y1=F Y2=Bb Y3=D# 

or E.g.  X1=B X2=Em X3=Am   and Y1=F Y2=Bb Y3=D# 

Two disjoint triads of chords X1 X2 X3 and Y1 Y2 Y3  are in consecutive chromatic  relation 
iff  the X3 is in chromatic relation with the Y1 (see also  post 30 on the harmonic melodic and chromatic relations of chords ) 

E.g.  X1=E X2=Am X3=Dm   and Y1=D#m Y2=G# Y3=C#    (Dm in chromatic relation with D#m)

or E.g. X1=G X2=C X3=F   and Y1=E Y2=Am Y3=Dm  (F in chromatic relation with E)

There are more relation when the 2 triads of chords X1 X2 X3 , and Y1 Y2 Y3 are not disjoint but have two consecutive chords common E.g.    X2=Y1 , X3=Y2  e.g.    (E Am Dm) and (Am Dm G) etc 

Here is an example of a quaternary of chords repeating in sequence as backtrack for melodic improvisation , which essentially originates from the triad of chords 1M-4M-5M or 2m-5M-1M.

The quaternary is 6m->2m->5M->1M

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

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

425. The major harmonic 5-cycle 6 (n or M) 2 (m or M) 5M 1M 4M and the minor harmonic 5-cycle 3(m or M) 6 (n or M) 2 (m or M) 5M 1M in composing songs.

In a diatonic scale we may have harmonic cycles of 5 chords e.g.

3m->6m->2m->5M->1M which has more  minor chords than major and may be called the minor harmonic 5-cycle and the

6m->2m->5M->1M->4M which has more major chords than minor chords and may be called the major harmonic 5-cycle.

Upon these cycles we may add the 5# blue note (from the harmonic minor Aeolian mode) or other blue notes by converting major chords to minor chords etc.

So when composing songs we may start the couple with the minor harmonic 5-cycle and end at the refrain with the major harmonic 5 cycle.

A characteristic example is the melody by Luiz Bonfa Black Orpheus, or Manha de Carnaval (Morning carnival) a melody from a film, composed by which nevertheless has an original version under the name samba de Orfeu, which is a bit different and more happy version of the melody.

E.g. see for the sad version Manha de Carnaval 

https://www.youtube.com/watch?v=nVkDfnGobmI&ab_channel=varadero1839

and the happy version samba de Orfeu

https://www.youtube.com/watch?v=LRhPocYpbYo&ab_channel=JanAdamec

or 

https://www.youtube.com/watch?v=zHo4dF5HyQ0&ab_channel=GunhildCarling

The sad version Manha de Carnaval is utilizing the minor harmonic 5-cycle of chords

3m->6m->2m->5M->1M . It alters also the 3m to 3M7

while the happy version is utilizing the major harmonic 5-cycle

6m->2m->5M->1M->4M . 

It alters also 6m to 6M7. I addition at a point it alters 5M to 5m and 4M to 4m !

424. How to remember melodies or play melodies by listening

There are 3 types of memory 

1) emotional-audible (emotional)

2) mobility of hand muscles (kineasthetic) 

3) optical-mental if it is from musical score. 

The strongest memory is 1). 

At the end of the repertory practice , we associate every melody name with its "fingerprint" which is only a few notes, enough to  let us  bring all of the melody it to our memory. 

Here in the next video the beatiful and clever girl she explains 3 steps from up to down 

from macroscopic perception to  microscopic perception

 1) Listen and analyze, find scales and chords.

2) Analysis of repetition  parts of the melody  

3) More analysis of each parts for patterns  like up-waving, down-waving , flat-waving, arpeggios, tails, straight up move, straight down move, highest and lowest notes of the parts . Also first notes of the parts or of all the melody etc  

 https://www.youtube.com/watch?v=T7c--Dh0po4

423. COMPOSITION OF SONGS BASED ON 4 CHORD PROGRESSIONS OF 4 CHORDS.

 See laso about the 12 bars blues post 396

The basic idea is to have a 3 part song with 2 couple and one refrain

And each couple and the refrain has as chord progression 4 chords  A1 B1 A2 B2

The primary choice is that the pairs (A1 B1) and (A2 , B2) are harmonic pairs

Then the relation of the paits may be chormatic , or melodic, or even all the 4 chords 

(A1 B1 A2 B2) may be in consecutive harmonic relation. 

Examples 

SONG A

REFRAIN=     1M7 4M  5M7 1M 

                         1M7 4M 4m 1M

COUPLE1= 6M7 2m 5m7 1M

COUPLE2= 3M7 6m 5M7 1M

SONG B

REFRAIN=      5M7 1M  1M7 4M 

COUPLE1= 6M7 2m 1M7 4M

COUPLE2= 3M7 6m 5M7 1M

SONG C

REFRAIN=      5M7 1M  4M 1M 

COUPLE1= 7M7 3m 6M7 2m

COUPLE2= 2M7 5m 1M7 4M

          

422. EASY IMPROVISATION OVER SYMMETRIC CHORD PROGRESSIONS THAT CREATE MELODY WITH SYMMETRIC THEMES MODULATIONS

 A chord progression A1 A2 A3,...,An is called symmetric if the relation oftwo succesive transitions Ai A(i+1) is of t he same type. Either harmonic, or melodic or chromatic. 

If a symmetric chord progression is such that the relation of the first A1 and last chord An is a chromatic transition, it is called symmetric cycle of chords. 

More generally a chord progression partitioned in pairs (A1 B1), (A2, B2),...,(An , Bn) is called pairs-symmetric, if all the transitions (Ai, Bi) are ofthe same type (harmonic, melodic or chromatic) e.g. harmonic and all the transition     (Ai, A(i+1)) are of thesame type e.g. chromatic. 

The advanage of such symmetric chord progresions is that when composing-improvisiong melody themes on its chord transtitions (e.g. on  (A1 A2)  or in  (A1,B1) for paits symmetric)  , by modulating them to the next chord transition we get a melody with symmetric modulations. 

But even if the chord progression is not symmetric or pair-symmetric, we may modulate the chord-internal and chord-external melody themes from chord transition to chord transition, with isomorphic ryhthm and ismorphic pitch order structure (topology). Still the melody will sound symmetric. Simply some steps ofthe melody will not always be the same type of intervals but will change from 3rds , to 2nds or 4ths/5ths while the number of notes rhythm and pitch order is preserved. 

An example is the song Thalassa platia (wide sea) by M. Hatzidakis where in the first part he is utilizing as symmetric chord progression the chromatic Analuzian cadenza Am->GM->FM->EM7

https://www.youtube.com/watch?v=08a20T78KiA&ab_channel=0204elleni

The refrain of  this songs is not a symmetric chord progression, but it could be adopted to have one E.g. melodyc symmetric or chromatic symmetric

E.g. a chromatic symmetric refrain could be   Em->Dm->CM->BM7

421. A SECRET KEY LINKING CHORD TRASITIONS AND MELODIC THEMES: THE TECHNIQUE OF COMPOSING MELODIC THEMS OVER A CHORD PROGRESSION, BY ALTERNATION OF 50% CHORD-INTERNAL MELODIC SCALE-50% CHORD-EXTERNAL CHROMATIC SCALE MELODIC THEMES DURING A CHORD AND CHORD TRANSITION.

A SECRET KEY LINKING CHORD TRASITIONS AND MELODIC THEMES

THE TECHNIQUE OF COMPOSING MELODIC THEMS OVER A CHORD PROGRESSION, BY the rule of " 50% vertical (arpeggio) 50% horizontal (tail)"ALTERNATION OF MELODIC SCALE (arpeggio)-CHROMATIC SCALE (tail) MELODIC THEMES DURING A CHORD AND CHORD TRANSITION.

What we mean with the above is that ifthe chord transition is chordA->chordB

We play alternating melodic theme M1  first "vertically" in the melodic version of the scale (arpeggio)  , in other words by alternating minor-major 3rds, which is easily within the chordA  (chordA internal theme or arpeggio) and then a 2nd melodic theme M2  about of equal time duration which is in the chromatic scale (tail) and is bridging to the next chordB (ChrodA external theme or tail) . Then we repeat at chordB etc. 

From the point of view of pitch-order topology and rhythms , the melodic themes M1 (arpeggio), M2 (tail) may be isomorphic or inverse isomorphic (which means an up move becomes a down move and vice versa). 

This is very common technique with the andaluzian cadenza (6m-> 5M-> 4M-> 3M7)  songs which is a chromatic chord progression. 

In this way at least 50% of the notes and time the melody is in the chord (rule of 50%) and also at least 50% of the steps are melodic intervals (3rds) as in beatiful Irish songs, which makes the melody more beatiful. Actually the full spectrum of choices in the melody would require not only the chromatic sequence or speed  of the notes of the diatonic scale and the melodic sequence by alternating major-minor thirds but also the harmonic sequence or speed by 4ths or 5ths. 

And the recipe of beauty would be 40% chromatic, 40% melodic , 20% harmonic densities in the melody. 

This tecnique explains the kind   of the chords transitions (harmonic-melodic-chromatic) with the corresond such  vertical-horizontal or chord-internal-external or melodic-chromatic melodic themes M1, M2 .  The chord transitions that are melodic or harmonic, have as the bridging melodic theme  the melodic theme M1 in the melodic scale, while the chromatic transitions have as bridging melodic theme the chromatic melodic theme M2. 

Example of a song with a melody with thsi structure

https://www.youtube.com/watch?v=rkermyl_JKw&t=2s&ab_channel=%CE%88%CE%BD%CE%B1%CF%82%CE%B1%CE%B3%CE%AD%CF%81%CE%B1%CF%82

How to remember melodies or play melodies by  listening:

3 types of memory 1) emotional-audible 2) mobility of hand muscles 3) optical-mental if it is from score. The strongest memory is 1). At the end of the repertory practice , we associate every melody name with its "fingerprint" which is only a few notes, enough to  let they bring it to our memory. 

Here in the next video she explains 3 steps from up to down from macroscopic perception to 

microscopic perception

 1) Listen and analyze, find scales and chords.

2) Analysis of repetition  parts of the melody  

3) More analysis of each parts for patterns  like up-waving, down-waving , flat-waving, arpeggios, tails, straight up move, straight down move, highest and lowest notes of the parts . Also first notes of the parts or of all the melody etc  

 https://www.youtube.com/watch?v=T7c--Dh0po4