433. A JOY-BASED PATTERN TO COMPOSE SONGS INSPIRED FROM THE EARLY NEW ORLEANS BLUES JAZZ SONGS.

A JOY-BASED PATTERN TO COMPOSE SONGS INSPIRED FROM THE EARLY NEW ORLEANS  BLUES JAZZ SONGS.

 See also post 430, 322, 426, 216. 215, 205

We remind also that the simplest and most effective way to compose songs (the music without  the words) is starting from the simplest and proceeding with the more complicated. Thus the order is

A) First the rhythm and morphological parts of the song

B) Then the harmony with the chord progression

C) Last the simplicial melody and the full melodic themes for each chord or chord transition of the chord progression (possibly with tail and arpeggio parts). 

The idea for this structure in composing soengs is from the new Orleans jazz songs. 

The joy of the composition of such songs is not only on he next below 

a) system of joyful  harmony and chord progression creation but also

 b) on the joy of the rhythm rhythm which is at least 180 bpm . Furthermore we may use fast notes double the main tempo for reasons of joy.  

c) joy from the melodic waving so that  if we label + and up-move in a waving and by - an equal time and interval down move of the waving the total waving score of the melody is plus. In simpler terms we may have melodic themes as waves that are by 2nds and start and end a 3rd lower or higher (higher is more joyful) thus withing a chord. Furthermore we may use fast notes double the main tempo for reasons of joy. Then chord changes are modulations of the melodic theme. 

Joy from the harmony: 

A1) The center of the songs is a joyful triplet of major chords in harmonic relation, in other words the

classical 5M, 1M , 4M. It is set in a sequence that corresponds to a rhythmic pattern. E.g. 

(1M, 4M, 1M 5M7)   with equal duration per chord. Thus a 4-fold rhythm. 

Usually, because the triplet of major chords has two harmonic relations (5M-1M) and (1M-4M) the rhythmic  pattern is divided in 2 , each part corresponding to one of the two harmonic relations. 

Simplistic counter-melody soloing could be on the 7-1-2 triad notes around the 1st semitone of the diatonic scale (1-2-1-7-1) or on the 2-3-4 triad notes around the 2nd semitone of the diatonic scale (3-4-3-2-3)

Or alternatively a 3-fold rhythm as follows  (1M, 4M, 1M, 5M7 , 1M) where the first 2 chords and the last chord have  double duration the time compared to the 3rd and 4th. So in rhythmic units it is (2, 2 1,1,2).

This initial harmonic and rhythmic center of the songs is repeated two times (at least) and corresponds to a joyful refrain, from which nevertheless the songs starts returns and ends.

Each time that we return to the central chord progression, it is not necessary to return with the same melodic theme. It can be different. 

A2) Then after each (1M, 4M, 1M, 5M7 , 1M) repeated twice we interpolate a less joyful rhythmically isomorphic pattern, derived with one of the 5 systems of substitutions of the major chords of the central part. (X1, X2, X3, X4 , X5) This may be called the couples of the song and have duration at least half of the duration of the central part, so as to guarantee that the joyful part has more duration than the possibly sad part. 

The system of substitutions are the next 5, which preserve the harmonic relations of the initial central chord progression. The substitutions are based on melodic (relative chords ,2 common notes) relations of the chords. That is why the 2m can also be substituted with 7bM and the 7d with the 2m, while the 7M7 with the 2#m and 5#m. 

Primary a, b substitutions

                                                      5M   1M   4M

substituted with                             3m    6m   2m (which 2m can again be substituted with 7bM)

or with                                          3M7   6M7 2M7

Primary c, d substitutions

                                                      5M   1M   4M

substituted with                             7d    3m   6m

or with                                          7M7   3M7 6M7

Secondary a, substitutions

                                                      5M   1M   4M

substituted with                             5m    1m   1m

A most intersecting is the double substitution e.g.  1M with (3M7 6m) with teh same duration

or  5M with (7M7, 3m)  or 4M with (6M7, 2m)  .

And also the transformation of the harmonic relation to chromatic with the substitution

of 5M7 resolving to 1M with  7m shifting to  1M or 1m

Of  1M resolving to 4M with   3m shifting to 4M or 2m.

We may extend the major harmonic triplet to a major harmonic 5 cycle as follows

in the 5M7 1M7 4M , if the 1M->4M is substituted by  6M7 -> 2M7 we resutlt in a 5 harmonic cycle 6M7-2M7 5M7 1M 4M

In general we have a Universal adequacy of the substitutions in the sense that if we have a melodic  theme within a chord and we want to have a

 a) harmonic (by 4ths or 5ths) modulation of it 

b) melodic (by 3rds) modulation of it 

c) Chromatic (by 2nds) modulation of it 

it is always possible with the above melodic substitutions of the chords. 

These substitutions introduce, blue notes outside the diatonic scale, that are included in the chords, and may define harmonic minor scales, double harmonic minor scales, blues scale etc. 

The preference order o introducing blue notes is the next

 Diatonic scales in harmonic relation with the focus diatonic scale

1.  7b                  (5m)

2. 4#                 (7M7, 2M7)

harmonic or double harmonic minors

3. 5#                (3M7, 4m)

4. 1#               (6M7)

Neapolitan , double harmonic minor) 

5.  2#   (7m7, 1m) 

So the chord progression of the whole song is a sequence of pairs of pieces as follows

(1M, 4M, 1M, 5M7 , 1M)

 (X1, X2, X3, X4 , X5)

The first corresponds to joy and lasts twice as the second which corresponds to degrees of sadness.

The joy of the composition of such songs is not only on he previous 

a) system of harmony and chord progression creation but also b) on the rhythm which is at least 180 bpm and 

c) melodic waving so that  if we label + and up-move in a waving and by - an equal time and interval down move of the waving the total waving score of the melody is plus 

432. A GENERAL HARMONY TYPE OF SONGS WHERE 3 SAD DIATONIC MODES AS HARMONIC TRIPLET OF CHORDS RESOLVE TO A HAPPY DIATONIC MODE AND HARMONIC TRIPLET OF CHORDS

 This type of harmony can be within a single diatonic scale e.g. C or 3 diatonic scales in harmonic relations e.g. G C F 

The harmonic triplets of chords per mode are the next

 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)

E.g. in a single diatonic scale

1) Phrygian, Aeolian Dorian resolving to Ionian 

2) Phrygian, Aeolian Dorian resolving to Mixolydian

3) Aeolina, Dorian Mixolydian resolving to Ionian

Or in 2 diatonic scales in harmonic relation e.g. G C F

1) Phrygian of G, Phrygian of C , Phrygian of F  resolving  to Ionian of C

2) Aeolian of G, Aeolina of C , Aeolina of F  resolving  to Ionian of C

3) Dorian of G, Dorian of C , Dorian of F  resolving  to Ionian of C

4) Mixolydian of G, Mixolydian of C , Mixolydianof F  resolving  to Ionian of C

431. THE METHOD OF CHORD-SCALES PROGRESSION AND ODD-EVEN RE-NUMBERING OF THE NOTES AS A TECHNIQUE TO COMPOSE AND IMPROVISE MELODIES AFTER A CHORD PROGRESSION.

 This method of composition of melodies has as sub-methods, the purely chromatic (tail)  method and the arpeggio-tail method to create melodies. 

Besides the re-numbering of the notes based on the underlying chord, we also re-number them as 0-1 notes (1 belongs to the chord, 0 does not belong) which is an even simpler numbering to compose the fitting to the chord melody. 

Of course the topology and the pitch waving of the melody is not derived from the chord progression and it is a more or less independent and important feature of the musical meaning of the melody. 

In order to compose-improvise  the melody we need to determine the next factors

1) The melody motive is over one, two or three chords?. Determine the melody motif (theme) which is 85% rhythm rather than pitch waving.

2) Determine the rule of arpeggio (3rds,4ths,5th, 6th ) and tail (steps by 2nd) pattern. E.g. The 3-notes chords that are inside the diatonic scale with arpeggio pattern, and the chromatic 4-notes chord with the blue notes outside the scale with tail step-wise by 2nds melodic theme.

3) We determine the pitch waving topology (dolphin word) across the chords. in other words up, down , stationary .  Cycles and balanced patterns are preferred. This factor is the closest to the ove all feeling ofthe melody together wit the chord-progression factor.

4) The rest of the melody is modulation over the chords (or chords pairs , or triads which is the melodic motif). Of course we do not follows strict modulation over the chords but we make asymmetric to signify start-end of melodic parts. This part is the repetition and variation part of the melody composition and includes the repetition and variation pattern of the chords in the chord progression.. 

The out-of-chord passing accented notes better be dealt as notes of extension of the chords. E.g. 2nds of the chord that would be it suspended chord.

Here a relevant video 

https://www.youtube.com/watch?v=jA7gdz56LtY&ab_channel=DavidBruceComposer

The anticipation passing notes resolving passing notes etc are minor techniques. 

https://www.youtube.com/watch?v=9LUQUk0hd10&t=704s&ab_channel=GuyMichelmore

430. TRIPLETS OF CHORDS FOR THE 7 DIATONIC MODES IN THE LATIN JAZZ STYLE HARMONIZATION.

 The standard chromatic pairs of chords for the 7 modes of a diatonic scale are (see post 215) the next

The chromatic pairs of chords in the diatonic scale  may get the the names ofthe modes of the scale too

1M-2m=IONIAN

2m-3m=DORIAN

3m-4M=FRYGIAN

4M-5M=LYDIAN

5M-6m=MYXOLYDIAN

6m-7d=AEOLIAN

7d-1M=LOCRIAN

Nevertheless in the Latin style jazz, instead of the 2m , 3m 6m we often use 2M7 , 3M7 and 6M7 , because we substitute the natural minor eolian mode with of the harmonic minor with 5# instead  and also harmonic double minor with 3b, etc Furthermore it may mean that instead of being in a single diatonic scale e.g. C we also utilize the previous or next in he Wheel by 4th (here F and G) 

So the Latin jazz style harmonization of the 7 diatonic modes ,where we add a 3rd chord to resolve to the first and have harmonic relation with the first, would become as follows

1M-2m=IONIAN-> 1M->2m-> 5M7  (Blues triplet)

2m-3m=DORIAN->  2m-> 3M7->6m (Harmonic minor triad)  or 2m-> 3M7->6M7 (Dbl Hminor)

3m-4M=FRYGIAN->3m->4M->7M7  (interesting triplet 1)

4M-5M=LYDIAN->  4M, 5M, 1M7  (major Harmonic triplet)

5M-6m=MYXOLYDIAN-> 5M-> 6m -2M7 (Blues triplet)

6m-7d=AEOLIAN->  6m-> 7m-> 3M7 (interesting triplet 2 )  or 6m-> 7M7->3M7 (DHminor)

7d-1M=LOCRIAN-> 7M7->1M -> 4#M7  (interesting triplet 3).

From these triplets we may extract harmonic pairs only

IONIAN-> 1M->2m-> 5M7  (Blues triplet) -> HPAIR=5M7->1m

DORIAN->  2m-> 3M7->6m (Harmonic minor triad) - > HPAIR=6m->2m

or 2m-> 3M7->6M7 (Dbl Hminor)  > HPAIR=6M7->2m

FRYGIAN->3m->4M->7M7  (interesting triplet 1)- > HPAIR=7M7->3m

LYDIAN->  4M, 5M, 1M7  (major Harmonic triplet) -> HPAIR=1M7->4M

MYXOLYDIAN-> 5M-> 6m -2M7 (Blues triplet) -> HPAIR=2M7->5M

AEOLIAN->  6m-> 7m-> 3M7 (interesting triplet 2 )- > HPAIR=3M7->6m 

 or 6m-> 7M7->3M7 (DHminor) - > HPAIR=3M7->6m 

7d-1M=LOCRIAN-> 7M7->1M -> 4#M7  (interesting triplet 3).- > HPAIR=4#M7->7M7 

In the next we may compose songs with first part (couple) a sad triplet or pair signifying a mode and resolving to the refrain to a happy triplet or pair (usually the Ionian or Mixolydian) 

Only the Ionian, Mixolydian, Dorian, Aeolian, Lydian, are triplets of chords that are exact harmonic triplets. The Frygian and Locrian are not exact harmonic triplets. 

Here are examples of chord progressions of at least 9 such songs

E. g. Dorian-> Ionian (Blues)

2m, 3M7

6m, 2m 

Resolving to

1M 2m

5M7 1M 

Dorian3-> Ionian2 (Blues)

2m, 3M7

6m, 2m 

Resolving to

1M 4M

5M7 1M 

Dorian2-> Ionian (Blues)

2m, 3M7

6M7 2m 

Resolving to

1M 2m

5M7 1M 

Frygian-> Ionian (Blues)

3m 4M

7M7 3m 

Resolving to

1M 2m

5M7 1M 

Frygian->Mixolydian (Blues)

3m 4M

7M7 3m 

Resolving to

5M 6m

2M7 5M 

Frygian3->Mixolydian3 (Blues)

3m 6m

7M7 3m 

Resolving to

5M 4M

2M7 5M 

Aeolian-> Ionian (Blues)

6m 7m

3M7 6m

Resolving to

1M 2m

5M7 1M

Aeolian2-> Ionian  (Blues)

6m 7M7

3M7 6m

Resolving to

1M 2m

5M7 1M

Aeolian3-> Ionian  (Blues)

6m 7M7

3m 6m

Resolving to

1M 2m

5M7 1M

Aeolian2-> Mixolydian (Blues) 

6m 7M7

3M7 6m

Resolving to

5M 6m

2M7 5M

Locrian-> Mixolydian  (Blues) 

7M7 1M

4#M7 7M7

Resolving to 

5M 6m

2M7 5M

Mixolydian 2 -> Ionian Blues

5m 6M7

2m 5m

Resolves to

1M 2m

5M7 1M 

Also  as an alternative from the chromatic pairs of the 7 modes we may create triplets wher he 3rd chord has harmonic relation with the 2nd part of the triplet and melodic relation with the 1st part

1M-2m=IONIAN=>  1M, 6M7, 2m

2m-3m=DORIAN=>  2m, 7M7, 3m

3m-4M=FRYGIAN=> 3m , 1M7, 4M

4M-5M=LYDIAN=> 4M, 2m7, 5M

5M-6m=MYXOLYDIAN=> 5M, 3M7, 6m

6m-7d=AEOLIAN=> 6m , 5bM7, 7d

7d-1M=LOCRIAN=> 7d, 5M7, 1M.

A nice chord cycle based on that would be

 1M, 6M7, 2m

 2m, 7M7, 3m

 3m , 1M7, 4M

4M, 2Μ7, 5m

5m  1M7 4M 

4M   4M7  7bM

7bM  5M7 1M

In the next we may compose songs with first part (couple) a sad triplet or pair signifying a mode and resolving to the refrain to a happy triplet or pair (usually the Ionian or Mixolydian) 

Only the Ionian, Mixolydian, Dorian, Aeolian, Lydian, are triplets of chords that are exact harmonic triplets. The Frygian and Locrian are not exact harmonic triplets. 

Here are examples of chord progressions 

E. g. Dorian-> Ionian (Blues)

2m, 7M7

3m, 3m 

Resolving to

5M7 1M 

4M , 1M

5M7, 1M

etc

Or

1M 

3M7  6m

7M7 3m

5M7 1M

4M , 1M

5M7, 1M

Also

1M 3M7 6m

1M 7M7 3m

4M  3M7 6m

4M 6M7 2m

5M  7M7 3m

5M  5bM7 7m

429. SIMPLICIAL SUBMELODY WITH ARPEGGIO INTERVAL PER CHORD INSTEAD OF ONE NOTE PER CHORD FOR COMPOSITION OF MELODIES

 Such simplicial sub-melodies  have much more information for melody composition, as they contain a pitch direction (up, down , steady) as pitch moves for each chord. They have also the advantage that they utilize the 66% of the chord, thus there is less indeterminacy in the relation melody-chord.

These pairs of notes are usually even number odd odd number notes of the full melody, in other words they need extension with interpolated notes. 

To compose the full melody we interpolate notes of the 6-notes scale Celtic minor between the notes of the simplicial sub-melody  so as to have intervals of 2nds, and so that the interpolated note (usually outside the chord) has duration 1/2. or 1/3 of the corresponding note of the simplicial submelody. In this way we are certain the the derived melody fits to the underlying chord. 

The pitch direction (up, dowm , steady) shows the topological pattern of the simplicial melodic themes. Of course a full melodic theme may involve more than one chord, e.g. 2 chords with the characterization of the transition relation as chromatic , melodic and harmonic. 

We give an example here with the Irish folk song Frost in Celtic minor (6 notes scale g,a,b,c,d,e)

The chord progression and structure of repetitions is  4 times the 

Am  Am 

Am  G

Am G

Am Am 

And then 2 times the 

Am G

Am G

Am G

Am Am 

G Am

Am G

Am G

Am Am 

And then all these 2 parts  3 times

The arpeggio interval simplicial submelody for the first part  and for each chord is the 

Am(e5->c5)   Am (c5->a4)

Am(a4->e4)  G(g4->b4)

Am(c5-c5) G(b4->e4)

Am(a4->c5)  Am (c5->e5) 

And for the 2nd part is 

Am(a4->c5) G(e5->b4)

Am(e5->a5) G(g5->d5)

Am(e5->a5)  G(b5->g5)

Am(a5->e5) Am(e5->a5) 

G(g5->d5) Am(c5->a4)

Am(e4->a4) G(b4->d5)

Am(a4->a4) G(d4->d4)

Am(a4->a4) Am(a4->a4) 

To compose the full melody we interpolate notes of the 6-notes scale Celtic minor between the notes of the simplicial sub-melody  so as to have intervals of 2nds, and so that the interpolated note (usually outside the chord) has duration 1/2. or 1/3 of the corresponding note of the simplicial submelody. 

428. THE THEMES VARIATION PATTERN METHOD OF COMPOSING MELODIES. E.G. ONE MELODIC THEME FOR EVERY 15-SYLLABLES POETIC LINE. CYCLES OF MELODIC THEMES.

 This method does not start from the chord progression pattern. Instead it starts from an equally simple pattern which is the pattern of variations of the melodic themes.

In other words if A1 , A2 are the basic melodic themes, and B1, C1, D1 , and B2, C2, D2 , are their variations correspondingly  (modulation-translations, transposition-translations , pitch inversions , rhythmic inversions etc)  then a pattern of the melodic themes variations could be

(A1 B1)  (A1 C1) 

(A2 B2)  (A2 C2) 

  ETC

E.g. this pattern  of melodic themes is of the folk Celtic song Donegal.

Under each melodic theme we put either 1) a single chord 2) a pair of chords 3) a triad of chords 4) four chords etc

Of course same melodic themes (and symbol) require same underlying chords. But the converse is not true. Different melodic themes may still have the same underlying chord. E.g. the mentioned folk celtic song Dionegal with the above melodic themes patterns utilizes only 2 chords D7 and G. 

A1(=G D7)         B1(=D7 G)               C1(=D7 G D7 G) 

A2(=G D7)         B2(=D7 G)               C2(=D7 G D7 G) 

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. But these 4 chords could as well be 2 only e.g. in the form 5M7  1M  1M 5M7

We may utilize for a full 15 syllables poetic line harmonic pairs of chords or chromatic pairs of chords that define the modes of a diatonic scale or even melodic pairs of chords

The chromatic airs of chords in the diatonic scale  may get the the names ofthe modes of the scale too

1M-2m=IONIAN

2m-3m=DORIAN

3m-4M=FRYGIAN

4M-5M=LYDIAN

5M-6m=MYXOLYDIAN

6m-7d=AEOLIAN

7d-1M=LOCRIAN

(see also post  364 , 225 and 325  )

It is important also to realize that these 7 pairs of chords in chromatic relation define not only tetrachords but also hexatonic scales (and corresponding harmonicas) as in the post 291.

We may extract pairs of chords that define modes as follows

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

Melodic pairs of chords would be

 1M-3m    IONIAN

2m-4M      DORIAN

3m-5M      FRYGIAN

4M-6m   LYDIAN

5M-7d  MYXOLYDIAN

6m-1M      AEOLIAN

7d-2m     LOCRIAN

The diatonic songs have a subtle balance of happy (major) and sad (minor) compared to chromatic tonality. A good example are the Irish folk songs

A good mix of modes for such songs is a moving melodic  5 cycle in the diatonic harmony. In other words an harmonic  triplet of chords that define the mode plus 2 more intermediate chords with melodic relation to the neighboring chords. E.g.  for the Ionian mode triplet  5M 1M 4M , we interpolate at melodic relations  the 3m (between 5M, 1M)  and 6m (between 1M and 4M) to get the melodic  5 cycle  5M 3m 1M 6m 4M. 

We may compare it with a moving harmonic 5-cycle e.g. 6m 2m 5M 1M 4M

or 3m 6m 2m 5M 1M etc

CYCLES OF MELODIC THEMES AND HAPPINESS.

Each melodic theme eventually is one of the 3 types (polarity). A pitch-vector going up, or going down or staying the same pitch. And one of the best  combination of such melodic themes  is the cycle, and

 1) especially the one that starts from a high pitch goes down and returns back to high pitch as the songs of the birds. 

2) In general up moves of pitch are happy, 

3) also melodic or harmonic intervals (large arpeggio part and small tail in he melodic theme) plus 4) large range melodic themes 

4) and most important  fast rhythm. 

 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)

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

420. FUGA AS PARALLEL MELODIES IN 4 MODES AT SUCCESSIVE MELODIC RELATIONS

 (where at each beat we are almost always about on the same step ofthe mode) 

419. A SYSTEMATIC WAY TO REHARMONIZE WITH MORE CHORDS A SONG IN THE STYLE OF GYPSY JAZZ . CHROMATIC MELODIC AND HARMONIC SPEED (DENSITY) IN CHANGING CHORDS.

 A SYSTEMATIC WAY TO REHARMONIZE WITH MORE CHORDS A SONG IN THE STYLE OF GYPSY JAZZ  BY USING INTERMEDIATE MELODIC OR CHROMATIC RELATIVES OF  THE INITIAL CHORDS AND NEIGHBORING DIMINISHED CHORDS. 

CHROMATIC MELODIC AND HARMONIC SPEED (DENSITY) IN CHANGING CHORDS.

418. The Upper and lower melodic transpositions reverse the triplet of majors to minors (the upper) and the triplet of minors to majors (lower).

417 . THE PARETO DISTRIBUTION IN THE DENSITY OF NOTES AND THE STEHANE GRAPPELLI MELODIC IMPROVISATIONS

416. ΤHE "INHALE" MIXOLYDIAN TETRACHORD AND THE "EXHALE" IONIAN PENTACHORD IN MELODIC IMPROVISATION

 One of the common secrets of an emotionally good melody is that it reflects the inhale-exhale cycle in the human emotional sensitivity. To give relaxation the exhaleing is longer than the inhaling

On the other hand a common harmic cycle in  simple improvisation is the 1M 4M 5M cycle (e.g. in Blues)

When we combine these two cycles at the context of melody, we may divide the 7 notes diatonic scale to the ionian 5-chord 1-2-3-4-5 and the mixolydian tetrachord 5-6-7-1'. As the Ionian is longer it may correspond to the exhaling while the mixolydian to the inhaling. My improvising melodies with this duality and over the chord triad 1M 4M 5M we get the emotional effect of inmhaling exhaling.

415 THE 7 MAIN SUBSTITUTIONS OF A MAJOR CHORD IN THE TRIPLET OF MAJORS 1M, 4M 5M IN IMPROVISATION AND COMPOSITION.

We are here in an assumed improvisatio which alternates the 3 major chords 1M 4M 5M of a diatonic scale, and thus if the melodic theme is within a single chord, we alternate the Ionian, Lydian and Mixolydian modes

The usual 1ST TYPE substitutions are the lower melodic relative chord or major with its major 6th

1M with 6m (Aeolian modulation) 

4M with 2m  (Dorian modulation) 

5M with 3m   (Frygian modulation) 

But it can as well be the 2ND TYPE upper melodic relative chord (substitutes with maj 7nth)

1M with 3m (Frygian modulation) 

4M with 6m  (Aeolian modulation) 

5M with  7d  (Locrian modulation) 

Beaitifull substitutions are THE 3RD TYPE with double relative to an harmonic minor will be

1M with 6M7 which contains the 3-note chord 1#dim

4M with 2M7 which contains the 3-note chord 4#dim

5M with 3M7 which contains the 3-note chord 5#dim

(example of such substitutions is in the famous by Bach prelude in C major  BWV 846 on which it was based also the Ave Maria) 

Or also the 4TH TYPE 

1M with 3M7  which contains the 3-note chord 5#dim

4M with 6M7  which contains the 3-note chord 1#dim

5M with  7M7 which contains the 3-note chord 2#dim

Also the 5TH TYPE 

1M with 1m 

4M with 4m 

5M with  5m 

Also the 6TH TYPE  (usual in Bach) 

1M with 1dim7 

4M with 4dim7

5M with  5dim7

Also the 7TH TYPE  (usual in Bach) 

1M with 1aug

4M with 4aug

5M with  5aug

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.

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.
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  :  HARMONIC TRIPLET (1M, 4M, 5M) 
2. DORIAN  : HARMONIC TRIPLET (2m, 5M, 6m) (Can be conceived as 5th type substitution) 
3. PHRYGIAN : HARMONIC TRIPLET (3m, 6m, 7d) (Can be conceived as 5th type substitution) 
4. LYDIAN: HARMONIC TRIPLET  (4M, 7d,1M) (Can be conceived as 5th type substitution) 
5. MIXOLYDIAN: HARMONIC TRIPLET  (5M, 1M,2m) (Can be conceived as 5th type substitution) 
6. AEOLIAN: HARMONIC TRIPLET (6m, 2m, 3m) (Can be conceived as 5th type substitution) 
7. LOCRIAN: HARMONIC TRIPLET  (7d, 3m, 4M) (Can be conceived as 5th type substitution) 

We may clasify them according the the major and minor chords

A.ALL 3 MAJOR CHORDS (ALL HAPPY) 

1. IONIAN  :  HARMONIC TRIPLET (1M, 4M, 5M)

B. 2 MAJORS AND ONE MINOR OR DIMINISHED CHORD (ALMOST HAPPY, ALMOST MAJOR)

4. LYDIAN: HARMONIC TRIPLET  (4M, 7d,1M)

5. MIXOLYDIAN: HARMONIC TRIPLET  (5M, 1M,2m)

C.  2 MINORS (OR DIMINISHED) AND ONE MAJOR  (LITTLE SAD,  ALMOST MINOR )

2. DORIAN  : HARMONIC TRIPLET (2m, 5M, 6m)

7. LOCRIAN: HARMONIC TRIPLET  (7d, 3m, 4M)

D. THREE MINORS OR DIMINISHED (ALL SAD) (ALL MINOR) 

3. PHRYGIAN : HARMONIC TRIPLET (3m, 6m, 7d)

6. AEOLIAN: HARMONIC TRIPLET (6m, 2m, 3m)

We may compare the basic harmonic triplets with the basic chromatic triplets (see also post 322)

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)



If we want an ordering of how much "minor" and "sad" or "anxious" is a mode and how much "major" and "happy" or "serene" is a mode based on the ordering d<m<M then we get the next partial ordering (non-linear ordering)

PHRYGIAN<AEOLIAN<DORIAN<MIXOLYDIAN<IONIAN

and

LOCRIAN<DORIAN

LYDIAN<MIXOLYDIAN

But the Locrian and Lydian are not comparable with all the others so as to put all of them in a linear order.

Here is a musicological old qualitative description of it, but the names are not the standard but an older version of them (e. mode V is referred in this table as Lydian , while nowadays is named Mixolydian). To realize about which mode is referenced we must look at the 2nd column with the latin numerals.

Based on this concept it is possible to define tunings  of an harmonica (see post 274 ) with these types of triads of chords so as to improvise with the corresponding harmony on each of the 7 modes!

 FOR STEPS IN CREATING A MELODY SEE THE 6 STEPS BELOW AND THE POST 402

1) CHOSE THE TYPE OF CHROMATIC-TONALITY HARMONY 

2) COMPOSE THE CHORD PROGRESSION AFTER THE CHOSEN CHROMATIC TONALITY

3) PARTITION THE CHORD PROGRESSION TO SINGLETS, PAIRS, TRIPLETS ETC OF CHORDS THAT  WOULD SUPPORT BRIDGING MELODIC THEMES

4) COMPOSE THE SIMPLICIAL SUBMELODY (A DEFAULT IS THE MIDLLE NOTES OF THE CHORDS) . For each partition segment of chords, the last note of the simplicial melody ofthe last chord is the main note of the simplicial submelody for this segment. 

5) COMPOSE THE MOVE OF THE BRIDGING MELODIC THEMES BY THE TRIAD UP-DOWN-STATIONARY BY FOLLOWING PRINCIPLES OF BALANCE AND THE EMOTIONS OF THE UNDERLYING PARTITIONED SEGMENT OF CHORDS. ONE POLARITY FOR EACH PARTITIONED SEGMENT OF CHORDS. E.g. partition segments ending in minor chord may be down-moves and those ending in major chord an up-move. If we assume the x-axis the time and the y-axis the pitch (the simplicial submelody set as basic pitch zero level) we may symbolize a rhythmic melodic bridge with a flag. Glag symmetric to a vertical axis are melodic bridges with inverse rhythmic pattrn. So such arrangments of the melody are like geometric frieze patterns and their 7 types of symmetry (see link below) . Of course most melodies are asymmetric

https://en.wikipedia.org/wiki/Frieze_group

6) COMPOSE THE RHYTHMIC PATTERN OF THE BRIDGING MELODIC THEMES AND THEMSELVES TOO.

414. HARMONIC TRANSPOSITIONS VERSUS HARMONIC MODULATIONS

 A transposition is to change the melody and harmony to another diatonic scale with a different root but same mode.

A modulation is to change the mode within the same diatonic scale (e.g. from Ionian to Aeolian, from Ionian to Dorian etc)

A transposition or modulation is called harmonic if the two roots differ by an interval of 5th or 4th

A transposition or modulation is called melodic if the two roots differ by an interval of  3rd

A transposition or modulation is called chromatic if the two roots differ by an interval of  2nd. 

We discuss in the next the advantage and disadvantages of an harmonic transposition versus an harmonic modulation. 

413. THE VERY SIMPLE CONCEPT OF CHORD-MODULATION OF A MELODIC THEME OVER 2 OR 3 CHORDS BY CHANGING THE UNDERLYING CHORDS

 This is a very simple and very usefull in improvisation and composition concept of chord-modulation , which is different from the concept of modulation by changinf the modes of the scale, and thus cahnging the melody.

E.g. Let a say that the melody are the notes x1, x2, x3 x4 x5 x6 over the chords A=(a1,a2,a3)  and B=(b1,b2b3)  with x1=a1, x3=a3, x4=b1, x6=b3. 

We changethe chords A , B to A'=(a'1,a'2,a'3) B'=(b'1,b'2,b'3) . Then modulating the same melodic theme over the new chords means that we keep the pitch order relations and rhythm of the new melodic theme but we change the notes so that now it fits the new chords. Most probaly the a1 to a'1 , a3 to a'3 , b1 to b'1 and b3 to b'3. 

This concepts allows to create nice melodies once a) the chord progression is predetermined b) an initial melodic theme has been created over a pair or triple of chords.

There are mainly 3 rules for the creation of melodic themes

1) Utlize 2 or 3 consecutive chords for none melodic theme

2) Make it connected by 2nds inside the main scale to give it naturality of singing

3) If one more of the 2 pr 3 chords are chromatic relative to the main scale make the melody pass from the external to the diatonic scale chromatic notes of the chords.

Here are 6 rules see also post 402 

1) CHOSE THE TYPE OF CHROMATIC-TONALITY HARMONY 

2) COMPOSE THE CHORD PROGRESSION AFTER THE CHOSEN CHROMATIC TONALITY

3) PARTITION THE CHORD PROGRESSION TO SINGLETS, PAIRS, TRIPLETS ETC OF CHORDS THAT  WOULD SUPPORT BRIDGING MELODIC THEMES

4) COMPOSE THE SIMPLICIAL SUBMELODY (A DEFAULT IS THE MIDLLE NOTES OF THE CHORDS) 

5) COMPOSE THE MOVE OF THE BRIDGING MELODIC THEMES BY THE TRIAD UP-DOWN-STATIONARY BY FOLLOWING PRINCIPLES OF BALANCE AND THE EMOTIONS OF THE UNDERLYING PARTITIONED SEGMENT OF CHORDS. ONE POLARITY FOR EACH PARTITIONED SEGMENT OF CHORDS. 

6) COMPOSE THE RHYTHMIC PATTERN OF THE BRIFGING MELODIC THEMES AND THEMSELVES TOO.

412 THE MOST COMMON IN BRAZIL FULL CHROMATIC TONALITY OF 12 NOTES THROUGH 3 DIATONIC SCALES IN HARMONIC RELATION

 3 Diatonic scales in harmonic relation e.g.

G, C F.

Chords from the 3 diatonic scales  the numbers are the notes of the middle diatonic scale

G      7m      2M                      4#M

C           1M 2m 3m (3M7) 4m 5M 6m 

F                                               5m     7b M

Thus 6 chromatic chords

3M7,  5m, 7b M, 7m,  2M 4#M

2 ofthem are with roots outside the middle diatonic scale.

There are mainly 3 rules for the creation of melodic themes

1) Utlize 2 or 3 consecutive chords for none melodic theme

2) Make it connected by 2nds inside the main scale to give it naturality of singing

3) If one more of the 2 pr 3 chords are chromatic relative to the main scale make the melody pass from the external to the diatonic scale chromatic notes of the chords.

Basic Jazz Chord Progressions

·        Major ii-V-I  (2m-5M-1M) . The major ii-V-I is easily the most important chord progression to get a handle on when it comes to jazz. ...

·        Minor ii-V-i. This chord progression has the same function as the previous major ii-V-I, but of course is in a minor key. ... (In 6 Aeolian mode would give the chords 7m 3M 6m  and in the Ionian mode it would be 2m  5M  1m )

·        Major I-vi-ii-V. ...(1M-4m-2m-5M)

·        Minor i-vi-ii-V. (In 6 Aeolian mode would give the chords 6m 2m 7m 3M and in the Ionan mode it would be 1m 4m 2m 5M)

The next is an example of a chord progression for a song with full chromatic harmony based on 3 diatonic scales in harmonic relation e.g. G major C major F major

Here is an example of a paritioned chord progression with chords from 3 tonalities related harmonically (this is common inthe harmony of brazilian songs) e.g. C-F-G.

I have improvised at first these chords inthe ukulele,soI that i like them and make the necesary corections

The melodic phrase chords are 3 , and I write the chord progression so that each line is a traid of melodic phrase chords. 

For simplicity all chords have the same duration

1st verse minor feeling, the translation of t he melodic theme is upwards. It is inthe tonalitis C and  F (with harmonic minors)

Dm      E7      Am

Gm      A7      Dm

1st chorus resolution to a major triad, which is alower shift ofthe melodic theme

Bb       C7       F

Here the next verse moves to the tonality G

E7       Am        Am

B7       E7          Am

Again a chorus resolution to major triads of the toanlity G

C        B7         G

Am   D7          G

Chromatic shift to the 7nth degree of the toanlity G as a new verse

F#7    Bm     Bm

B7     Em      Em

And a resolution to tonal of G tonality

D7      G        G

Now we add the simplicial submelody notes of the melody , one note per chord

We try it in a convenient instrument . I did so in the ukulelel and also on the digital ukulele (Geoshred) in the tablet.  I try to whistle also  threr simplicial submelody

1st verse minor feeling, the translation of t he melodic theme is upwards. It is inthe tonalitis C and  F (with harmonic minors)

Dm  (f5)     E7  (g#4)     Am (c5)

Gm   (Bb5)   A7  (c#5)    Dm  (f5)

1st chorus resolution to a major triad, which is alower shift ofthe melodic theme

Bb  (d5)     C7   (e5)    F (a4)

Here the next verse moves to the tonality G

E7  (e5)     Am    (a5)    Am  (a4)

B7   (f#5)    E7    (g#5)      Am  (e6)

Again a chorus resolution to major triads of the toanlity G

C   (e5)     B7    (d#5)     G  (b4)

Am  (c5)    D7   (f#5)       G  (g5)

Chromatic shift to the 7nth degree of the toanlity G as a new verse

F#7   (F#5)  Bm   (b4)   Bm  (b4)

B7    (f#5) Em   (b5)     Em  (B5) 

And a resolution to tonal of G tonality

D7  (d5)    G (g4)       G (g4)

Finally we write all these in a midi editor and and we enhance the simplicial submelody to an actually rhythmic melody with transition notes also outside the chords. 

In this way it is as if we write a text first fromthe verbs then the subject  and obkect ofthe verb and then the relations of the phrases. 

Here si another example

https://www.youtube.com/watch?v=4JHA1SIJkNM&ab_channel=DrKCostas

411. THE MOST COMMON FULL CHROMATIC TONALITY WITH ALL 12 NOTES AND 5 CHROMATIC CHORDS WITH ROOTS IN THE DIATONIC SCALE

 

6 Diatonic chards= 1M 2m 3m 4M 5M 6m

5 Chromatic chords=3M7 (from harmonic minor) 6M7 , 7M7 (from double harmonic minor)  5m

it contains all 5 blue or chromatic notes

 5# from the 3M7

2# from the 7M7

1# from the 6M

4# from 7M7 

7b= from 5m 

There are mainly 3 rules for the creation of melodic themes

1) Utlize 2 or 3 consecutive chords for none melodic theme

2) Make it connected by 2nds inside the main scale to give it naturality of singing

3) If one more of the 2 pr 3 chords are chromatic relative to the main scale make the melody pass from the external to the diatonic scale chromatic notes of the chords.

Basic Jazz Chord Progressions

·        Major ii-V-I  (2m-5M-1M) . The major ii-V-I is easily the most important chord progression to get a handle on when it comes to jazz. ...

·        Minor ii-V-i. This chord progression has the same function as the previous major ii-V-I, but of course is in a minor key. ... (In 6 Aeolian mode would give the chords 7m 3M 6m and in the Ionian mode it would be 2m  5M  1m )

·        Major I-vi-ii-V. ...(1M-4m-2m-5M)

·        Minor i-vi-ii-V. (In 6 Aeolian mode would give the chords 6m 2m 7m 3M and in the Ionan mode it would be 1m 4m 2m 5M)

An example of a  song chord progression with the simple full chromatic harmony is the next

3M7-> 6m

5M7-> 1M 

2m  6m

3M7 6m

5m 6M7

2m 2m 

7M7  3M7

6m 6m 

Here is another example 

https://www.youtube.com/watch?v=4YESQFQJR0Y&t=2s&ab_channel=DrKCostas