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
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.
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.
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.
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
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
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
