434. THE 1ST 2ND AND 3RD DENSITIES OF MELODIC THEME PER CHORD

 1ST DENSITY=ON NOTE PER CHORD

2ND DENSITY= 2-3 NOTES PER CHORD

3RD DENSITY = MULTIPLE VARIATIONS OF THE SAME MELODIC THEME PER CORD THUS                                  4 OR MORE NOTES PER CHORD

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)