439. RHYTHMIC LAYERS BY POWERS OF 2 OF A MELODIC THEME THAT CAN BE HARMONIC, MELODIC OR CHROMATIC.

 

Each melodic theme has temporal layers. E.g. its First layers is from equal duration say quarters. 

The 2nd layers is from eighths thus half the duration or double the speed

The 3rd layer is from 16nths thus again half the duration of the previous layers notes or double the speed of the previous layer.

Now at each layers we may have the attribute of harmonic, melodic chromatic iff  the corresponding intervals of consecutive notes are 4th or 5th, 3rds or 2nds correspondingly. 

1st, 2nd 3rds CHROMATIC VECTORS IN MELODIC AND HARMONIC RELATION AS STRUCTURE OF A TEMPORAL LAYER AS ABOVE PF THE THEMES OF A MELODY. 

1st, 2nd 3rds CHROMATIC VECTORS (denoted by e1,e2,e3)  are simply very short melodic themes that are chromatic move of a chromatic  internal of 2nd  and  of 1 ot 2 or 3 notes  either inside the 7-notes diatonic scale or  inside the chromatic 12-notes scale.They have a fixed rhythmic speed of quarters or eights of 16nths etc. 

Such melodic themes are the smallest and shortest span in the scale. Each such triplet melodic theme can substitute a note of the simplicial sub-melody.

But there are 2 more categories as follows which are essentially arpeggios!.

1st, 2nd 3rds MELODIC  VECTORS (denoted by m1,m2,m3)  are simply very short melodic themes that are melodic move of an internal of  3rd or 6th and of 1 ot 2 or 3 notes  either inside the 7-notes diatonic scale or  inside the chromatic 12-notes scale.

1st, 2nd 3rds HARMONIC   VECTORS (denoted by h1,h2,h3)  are simply very short melodic themes that are melodic move of an internal of  4th or 5th or 8th and of 1 ot 2 or 3 notes  either inside the 7-notes diatonic scale or  inside the chromatic 12-notes scale.

https://www.youtube.com/watch?v=ucNWbawSiZM&ab_channel=RyanLeach

438. TRIANGULATION OF CHROMATIC CHORD TRANSITIONS TO HARMONIC-MELODIC CHORD TRANSITIONS.

 The idea is based on the intervals relation  in diatonic steps  1=4-3 , or in words interval of 2nd=interval of 4th-interval of 3rd. 

Thus we substitute the next pairs of chords and chromatic transitions with melodic-harmonic transitions

1M->2m        =>  1M  4M 2m

2m->3m         =>   2m  5M  3m

3m -< 4M      =>   3m  1M 4M 

4M -> 5M    =>    4M 2m 5M

5M -> 6m    =>   5M  1M 6m

6m-> 7d      =>    6m 4M  7m  (7bM)

7d  -1M      =>     7m 5M 1M. 

Which by the way derives the next harmonic-melodic 16 cycle

1M  4M 2m 5M 3m 1M 4M 2m 5M7 1M 6m 4M 7M7 5M 5M7 1M 

437. CHROMATIC WAVES OVER A CHORD WITH WAVELENGTH INTERVALS OF 3RDS OR 4THS.

 Chromatic waves over a chord is a a nice concept to create continuously moving melodic themes with many notes over a chord. 

Such a chromatic wave is defined by an more or less ascending or descending chromatic sequence (in other words  by intervals of 2nds) of notes such that we stay longer time when we pass from a note of the underlying chord (thus creating waves by intervals of 3rds or 4ths defined by the underlying chord). The middle note (in normal position) of the underlying chord is the most characteristic note of the chord that defines if it is minor or major , blue note or not. Thus such chromatic waves wit wavelength intervals of 3rds move from middle note of a chord to the next middle note of the next chord. 

436. MELODIC PHRASES. CYCLES OF 4 DIFFERENT CHORDS WITH 3 HARMONIC TRANSITIONS VERSUS SUCH 4-CYCLES WITH 2 HARMONIC TRANSITIONS. THE TRANSITIONS SQUARE OF THE QUADRUPLE

This post is under the working hypotheses that a melodic phrase Ph (with a complete emotional meaning) has 2 parts and melodic themes symbolized by Mt1  Mt2  and usually  of opposite polarity (increasing -decreasing or vice versa)   such that Mt1 is over a chord transition C1->C2 and Mt2 over another chord transition C3->C4. The quadruplet C1 C2 C3 C4 is the harmony of the melodic phrase.  This quadruplet corresponds also to a pair of lines in 15-syllables poetry (8 syllables for Mt1 and 7 syllables for Mt2).

There are plenty many such quatruples inside a diatonic scale or diatonic chromatic tonality. E.g C1->C2 and C3->C4 may be both harmonic transitions , related by a melodic modulation. 

In such a the quadruple there are 4 direct transitions and  2 more indirect! 

We may prioritize them by the least number of chromatic transitions either direct or indirect. 

We classify such 4-cycles and discuss them below. 

435. THE "CHEMICAL FORMULAE" OF THE MELODIC THEMES: 1st, 2nd 3rds CHROMATIC VECTORS IN MELODIC AND HARMONIC RELATION AS STRUCTURE OF THE THEMES OF A MELODY.

 1st, 2nd 3rds CHROMATIC VECTORS IN MELODIC AND HARMONIC RELATION AS STRUCTURE OF THE THEMES OF A MELODY. 

1st, 2nd 3rds CHROMATIC VECTORS (denoted by e1,e2,e3)  are simply very short melodic themes that are achromatic move of a chromatic  internal of 2nd  and  of 1 ot 2 or 3 notes  either inside the 7-notes diatonic scale or  inside the chromatic 12-notes scale.They have a fixed rhythmic pattern  e.g. (a,a, g# a)

Such melodic themes are the smallest and shortest span in the scale. Each such triplet melodic theme can substitute a note of the simplicial sub-melody.

But there are 2 more categories as follows which are essentially arpeggios!.

1st, 2nd 3rds MELODIC  VECTORS (denoted by m1,m2,m3)  are simply very short melodic themes that are melodic move of an internal of  3rd or 6th and of 1 ot 2 or 3 notes  either inside the 7-notes diatonic scale or  inside the chromatic 12-notes scale.

1st, 2nd 3rds HARMONIC   VECTORS (denoted by h1,h2,h3)  are simply very short melodic themes that are melodic move of an internal of  4th or 5th or 8th and of 1 ot 2 or 3 notes  either inside the 7-notes diatonic scale or  inside the chromatic 12-notes scale.

Furthermore there are 3 more hybrid categories of up to  3-notes melodic themes which combine the chromatic with the melodic and harmonic

1st, 2nd 3rds CHROMATIC YODELING   VECTORS (denoted by cy1,cy2,cy3)  are simply very short melodic themes that are melodic move of an internal of  2nd and an interval 8th (octave) or higher   and of 1 ot 2 or 3 notes  either inside the 7-notes diatonic scale or  inside the chromatic 12-notes scale.

More general we may have 

1st, 2nd 3rds  CHROMATIC-MELODIC  OR  CHROMATIC-HARMONIC OR CHROMATIC YODELING VECTORS (denoted by cm1,cm2,cm3 and ch1,ch2,ch3 and cy1,cy2,cy3)    and are simply very short melodic themes that are chromatic-melodic moves or chromatic-harmonic moves or chromatic-yodeling of 1 or 2 or 3 notes  where the chromatic part are either inside the 7-notes diatonic scale or  inside the chromatic 12-notes scale.

The division of e1,e2,e3 versus (m1 m2 m3), (h1 h2 h3)   is also known in melodies are tail-arpeggio division of a melodic them.

Each such triplet melodic theme can substitute a note of the simplicial sub-melody or the 2 notes in a 2 notes per chord simplicial sub-melody

There is also one more hybrid combination of melodic-harmonic which is essentially an arpeggio.

When  the variation shift are melodic (intervals of 3rd or 6th) and harmonic (intervals of 4th or 5th) such shift-variations can be within a single chord or by chord transition. Thus we may have high density of melodic notes per chord or lowest density of melodic notes per chord. In other words the variational shifts that are optimal for more complicated melodies within a single chord is the melodic shift (by intervals of 3rds or 6ths) . In Greek folk Buzuki music this was repeatedly implemented by the Greek folk composer Zambetas. 

Musical instruments like the hang and steel pan or the African Kora  harp or the small Kalimba but also the harmonica and zamponia pan flute have such arrangements of the notes that favor triplet melodic themes as the latter CHROMATIC-MELODIC  OR  CHROMATIC-HARMONIC VECTORS cm1,cm2,cm3 and ch1,ch2,ch3 . 

It seems that the optimal number of (melodic ) variations of the small melodic theme within a chord is 2- or 3. 

This is a matter of combination of the combinatoric topology of a part of the  melody with the combinatoric topology of its underlying chord. A very important concept in the  composition of melodies and underlying harmony for which very little has been written! 

We may make the metaphor that the melodic triplets (e1, e2, e3)  (m1, m2, m3), (h1,h2,h3) , (cm1, cm2, cm3) , (ch1,ch2,ch3) are the electrons neutrons and protons or elements of a period system and that  chromatic , melodic harmonic relations are the 3 bonds that make them in to "chemical compounds" or final complex melodic themes or melodies.

E.g. Here 2nds chromatic vectors

In C major (a,a g#,a)->(harmonic transition by 5th)  (f,eeee)  chord a-c-e

Then again (a,a g#,a)-> (melodic transition by 6th) (g,f fff)  chord f-a-c

Or 

In C major (a,a g#,a)->(harmonic transition by 5th)  (f,eee)  chord a-c-e

Then  (b,b a#,b)-> (harmonic transition by 5th) (g,f fff)  chord b-d-f

A 3rds interval  chromatic vector can be half in the chromatic 12-notes scale an half in the diatonic scale and when shifted melodically or harmonically it can preserve its half-structure giving rise to simultaneous transposition and modulation. This adds blue-chromatic notes in the 7-notes diatonic scale.

Other types of melodic themes over 2 chords in the 15-syllables pattern  e.g.  G choprd 6 times d& 2 times and D7 6 times G 2 times

Are the next

1) Ascending or descending sequences with folding

2) Cycles of 4 or 5 notes part of the scale

3) Minimalist 2- o3 notes per chord in chromatic sequence

4) Minimalist Tail-arpeggio themes for ukulele, dobro guitar , trombone or overtone  tuned bowed strings.

5) super fast and complicated sequences retarded at the end or start and change of the chord. 

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