66. The 3 basic relations of the elementary melodic moves (themes). Chromatic, melodic, harmonic .

Here is a table of the analogy and correspondence of the levels of the musical language and Speaking languages

MUSICAL LANGUAGE	SPEAKING LANGUAGE
Note	Letter  of the alphabet
Interval (3 elementary melodic moves)	Syllables
Melodic moves or themes (5 basic  melodic patterns)	Words that make a simple proposition (subject verb object)
Chords duration may contain many musical themes	Sentences from a point to  a next point , that may contain many simple propositions

A theme melodic move, can easily have three factors that characterize it

1) If it is sad (-) or joyful (+) (we may call it minor or major  melodic move, although its underground chords sometimes , rarely  may be a  major or a minor chord respectively).

2) Its melodic density (see the 4 melodic speeds or densities, chromatic, diatonic, middle harmonic and high harmonic in post 68)

4) Its range as an interval (this is related somehow by inequality to the density as in 2). melodic theme-moves that their range is more than one octave are special in stressing the nature of being sad or joyful. 

These three parameters still do not define the melodic move-theme even if we know its first note. As we see melodic theme-moves are much more complicated than 3 or 4 notes chords! When creating a melody through melodic theme-moves, ideas similar to those that structure a good chord progression may apply.

We may device a symbolism for a melodic theme move based on the above three factors as follows An1Bn2(-) or An1Bn2(+) where An1 is the first note and Bn2 the last note of the move (n1 n2 denote the piano octave of it) and a minus - or plus + sign if its is sad (minor)  or joyful (major) e.g. G5A4(-). In this way we write the dynamics of he melody as a theme-progression ,much like a chord progression. 

What we do in this post is that we highlight and simplify the relations-transitions  of the musical moves (themes) to 3 only , with exactly the same names as the 3 basic Harmonic relations-transitions of chords for obvious reasons. (See post 30, but also post 61 and post 59). Nevertheless, in spite the fact that the name of the relations are the same, the interpretation is different when we are talking about chords compared to when we speak  about elementary melodic moves. There is an intended  similarity but the details are different. 

1) CHROMATIC or Connected-Complementary-sequential melodic moves (Wheel of 2nds)  (this is similar to complementary chords e.g. C->Dm Bdim->C etc)

Definition: Connected-Complementary melodic moves x-y  means that  their union contains a sequence of 3, 4 , 5 or more consecutive notes of the full chromatic 12-notes scale , or  a diatonic scale or in general a used scale at that time. And that this did not exist in each melodic move separately. Each of the x, y may be on notes of different chords, or tones of different   scales. Most often the y is the transpose or shifted morphological transformation  of x by 1-semitone or in general by one  step in a scale. 
Here is an example ofa  melody with themes that are mutaually Connected-Complementary
https://www.youtube.com/watch?v=PBAg10F7CPw
Some times a whole theme T over a chord or over a chord transition, consist of 3 or 4 melodic moves m1,m2,m3,m4  that are in sequence Connected-Complementary and then this theme is transformed in to T2, T3 , T4  so that in sequence these themes they are mutually relative which is the next relation!

As the relation of connected-sequential melodic moves requires one step in the scale we are interested in chord transitions x->y that the chords have notes at a distance of one step of the scale. a) For complementary chords transitions (see post 30) it would be at the roots b) For resolutional chords transitions  x->y , that is, y being a perfect 4th higher than x (5 semitones) such a "diode" it would be the 2nd-middle note   or the 3rd note of x and 1st-root note of y in normal position. Alternatively it could be the 1st root note of x and the 3rd note of y which are one octave apart but can become identical with an extension of x where it repeats its root one octave higher .  If x is a dominant 7nth chord with 4-notes such a "diode" it would also between the 4th note of x and the middle 2nd note of y. c) For relative chords transitions  x->y it would be the case y being y=Rmaj, x=Rmin or vice versa and the notes would be the middle 2nd notes of the chords (in normal position). Therefore this relation of the melodic move requires according to the underlying chord transition appropriate placement of the melodic move relative to the chords to utilize the previous"diodes" we described.

An example of this is the next melody. https://www.youtube.com/watch?v=M4OoR0g1FDo  

And another example is the next https://www.youtube.com/watch?v=Vf0x-kV7wqA

Melodic moves that are complementary create a very peculiar feeling, as the heart wants to contain everything! 

We give here two examples with the well known melodies of a) Resquesdos de L'Alhambra
b) Besame muschos.

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2) MELODIC or Relative melodic moves (Wheel of 3rds) (this is similar to relative  chords, e.g. C->Am , Em->G etc)

Two melodic moves x ,y are defined as relative if y is the shift of x higher or lower in the scale over another chord , or if y is a pitch or rhythmic inversion of x or y is a morphological variation of x (e.g. from wave to scale or spike or vice versa). Sometimes in this relation x->y we may shift from an emotion of joy to an emotion of sadness or vice versa , exactly as in the relative chords that we may move from minor to major chords or vice versa.

3) HARMONIC or Anxiety resolutional melodic moves (Wheel of 4ths) (this is similar to pairs of  chords, that the second resolves in serenity the anxiety first. E.g. G7->C, Bdim7->C etc)

Two melodic moves x ->y are defined as resolutional if y is a move on the notes of a chord (of the underlying chord progression) while  x is a move on notes  of 1 or 2 semitones distance between them and around notes of the chord , thus containing notes outside the chord and x->y is thus creating the emotional effect of resolving of anxiety to serenity and harmony. The order is sometimes reversed and from serenity we shift to anxiety. 

An obvious question is of course that if x->y melodic moves are in relation R(complementary, relative, resolutional) and their underlying chords are C(x)->C(y), would also these chords are in relation R((complementary, relative, resolutional) ? The answer is that in composition-improvisation we very often want it to be so, but in general it may not be so. 

We may find such very clear examples  e.g. in Paganini's caprice 24 (which has 12-broad themes ) https://www.youtube.com/watch?v=98y0Q7nLGWk  or the famous song tico-tico 

https://www.youtube.com/watch?v=B1i0dlegFJQ. 

We need to notice that these three types of relations of melodic moves correspond to the types of chord transitions and to the melodic speeds. 
(See also posts 30,68)

1) Connected-complementary melodic moves are usually covered and fit to complementary chords in chord transitions and to the chromatic/diatonic melodic speed.
2) Relative melodic moves are usually covered and fit to relative chords in chord transitions and to the middle harmonic  melodic speed.
3) Resolution melodic moves are usually covered and fit to successive resolution chords in chord transitions and to the high harmonic  melodic speed.

There is   correspondence to the 3-melodic densities or speeds  of the melodies that fit to such chord transitions of chord progressions. 

1) The complementary chords in a 2-chords transition corresponds to the chromatic/diatonic melodic speed or density. 

2) The relative chords in a 2-chords transition corresponds to the middle harmonic melodic speed or density. 

3) The successive resolutional  chords in a 2-chords transition corresponds to the high harmonic melodic speed or density. 

ANGLES IN FRETBOARD AND MELODIC SPEEDS

1) When playing the melodies on the fretboard in the guitar, the chromatic/diatonic speed is played mainly along the length of a string, so it is the zero angle.

2)  When playing the melodies on the fretboard in the guitar, the middle harmonic  speed is played mainly at an angle which relative to the horizontal is about 45 degrees and moves from the keys of the guitar to the sounding body as the melody descends in pitches! This is is because it consists of intervals of 3 or 4 semitones that in two successive strings is such an angle.

3)  When playing the melodies on the fretboard in the guitar, the high  harmonic  speed is played mainly at an vertical  angle  relative to the horizontal because the strings are tuned at intervals of 5 semitones (and one string in 4 semitones). Also the interval of 7 semitones (5th) when played in descending the pitches makes an angle  larger than vertical or 90 degrees (e.g. 135 degrees) and moves from  the the sounding body of the guitar to the keys of the guitar  as the melody descends in pitches!

PLAYING ONE MELODIC THEME PER ONE STRING:CORRESPONDING THE GEOMETRY OF THE STRINGS TO HARMONIC MODULATIONS OF THE MELODIC THEMES.
This technique of playing a melody,is particular easy and simple when creating by improvisation the melody. Since the string in the guitar and the other portable string instruments are tuned by 5 or 7 semitones apart ( intervals of pure 4th or 5th) then shifting  a melodic theme by a 4th up or down , which is also the distance of chords in the resolutions relations and cycle of 4ths, means that we should play the theme shifted almost in the same place of the fretboard but on string higher or lower. In other words the different strings symbolize the  steps of modulating or shifting the melodic theme along the wheel of 4ths, which is also a very common pattern of harmony. So the different strings are to be used for different modulations of the melodic theme. This simple idea  corresponds, the geometry of the strings on the fretboard to the harmony of modulations of the melodic theme. 

In the 4-double strings instruments (see post 67) the melodic themes modulations are as follows
1) Assume that we are playing a melodic theme on the highest pair of strings .
2) We utilize the 2nd lower pair of strings to shift the melodic theme a) one pure 4th (or 5 semitones) lower b) one pure 5th (or 7 semitones) lower c) to play the second voice which is a third lower.
3) We utilize the 3rd lower pair of strings to shift the melodic theme, 3 semitones  tome higher but also one octave lower from that (interval of 6th or 9 semitones=+3-12=-9)
4) We utilize the 4th lower pair of strings to shift the melodic theme, one   tome lower but also one octave lower from that (or 14 semitones=-2-12=-14)
5) Of course when shifting the melodic theme among the strings we change it also in the 
absolute distances among its notes, or its rhythm, or from ascending to descending and vice-versa etc.

We remind some observation is composing melodies

Summarizing in  simplistic way the correspondence of melodic pitch dynamics and the 4-basic emotions in music (joy, sadness, anxiety, serenity) we have 

1) Up pitch moves correspond to joy

2) Down pitch moves to sadness

3) Small pitch intervals of 1 or 2 semitones (chromatic or interval of 2nd) correspond to anxiety

4) Large pitch intervals (e.g. 4th, 5th octave etc) correspond to harmony and serenity. 

More instructive remarks in creating the final melody based on the chords are the next.

1) In the part of the chord progression with minor chords, utilize descending melodic moves so that sadness from melody and sadness from harmony fit. Similarly ascending melodic moves for  major chords.

2) In the sad melody parts of the melody (and minor chords) utilize rhythmic patterns that start with faster notes and end with slower notes, and the reverse for the happy part (and major chords).

3) In a triad or 7 nth 4-notes chord the most characteristic notes are the middle 2nd note (in 1-3-5 interval notation  is the 3) and the 7 nth (if it exists). So for the anxiety part of the melodic moves we may utilize 1-semitone trills around these two notes, or waving with 1 or 2 semitones steps and notes outside the chord in the interval of minor 3rd (3 semitones) of the chord. Alternatively instead of trill or small amplitude waves we may utilize chromatic monotone scaling by steps of 1 semitone , or scaling with steps by intervals of 2nd of the scale,  that go from these previous notes of the chord to the same such notes in the next octave. But always make sure that the notes of the chord sound in the average longer, than the notes of these anxiety transition moves with notes outside the chord. 

4) Alternate up (happy) and down (sad) pitch moves , or chromatic moves (anxiety), with harmonic (on chord notes) moves (serenity-harmony).

5) Utilize at least 2 octaves, or even 3 for the melodic moves repeating the notes of the underlying chord on the next octaves , so there is sufficient space for melodic moves, to express with sufficiency the emotions.

6) For the duality of emotions anxiety-serenity, it may be utilized also harmonic waves or monotone scaling over 2 octaves at least,  on the notes of the chord, but also chromatic trill wave over the notes of this wave or scaling (modulated wave on wave or move) and then return to the pure harmonic wave or scaling on the notes of the chord.

7) A chromatic wave by 1-semitones steps or all notes of the scale (steps by intervals of 2nd) that goes up and down at least 2 octaves, corresponds to a chord sub-progression of the song , of our choice that utilizes almost all the chords of the scale!

The next software called palette is a good attempt to help create melodies , but it is lacking the full concept of basic 3 relations of melodic moves (motives), although it utilizes what it calls motives, development (transformations) 

http://www.palette-mct.com/manual_eng/table_of_contents.html

DEFAULT MELODIES  FOR A CHORD PROGRESSION.
Given a  chord progression it is direct how to create a melody that fits the chords, with the following rules
1) During  each chord, the entry note of the simplicial submelody , is the middle note of the chord.
2) During  each chord, the exit note of the simplicial submelody (two notes per chord here), for major chords (including 7nth chords and extensions) is the upper note of the chord, for minor, diminished and augmented chords it is the lower note of the chord.
3) During the chord the melody follows an harmonic theme in one or more octaves span, in other words from notes of the chords, and is walking the chord by a spike, straight scaling or waving (these are parameters for the composer or improviser to choose) from middle and down to up (joy) if the chord is major, or from middle and upper to down (sadness) if it is minor, diminished or augmented. If the chord is simply major or minor we may enhance its harmony by extending it with its upper and lower relatives thus  by an interval of 3rd at the highest note and up , or at the lowest note and lower (in normal position). In other words making it a chord with 6th and/or 7nth.
4) At chord transitions x->y , the melody utilizes a dense melodic move (anxiety), with steps from 1 or 2 semitones, and within a scale (including the chromatic 12-notes scale) from the exit note of x of to the entry note of y , of the simplicial submelody.
5) The harmonic move   lasts longer than the transitional dense melodic move , as the latter  takes less than 30% of the duration of x, and y.

From the rule of local fitness of a melody to a  chord  progression , such a default melody will fit the chord progression.

(the post has not been written completely yet)