68. The 4 basic melodic speeds or densities: The chromatic (chromatic ripples), the diatonic ( ripples), the middle harmonic (waves), and the high harmonic(spikes). The melodic pitch accelerations. Fretboard angles and melodic densities

(this post has not been written completely yet)
We define and discuss in this post an important concept in composing beautiful melodies, that of the basic melodic speeds or densities.  This speed has nothing to do with the time speed of laying the melody. It only has to do with how large intervals is the steps of the melody, that is is called harmonic speed. 

1) The chromatic melodic speed or density (chromatic ripples) is melodic themes composed in such a way that successive notes are always in a distance of 1  semitone.
2) The diatonic speed or density (ripples)  is  melodic themes composed in such a way that successive notes are always in a distance of 1  step of the diatonic scale, thus 1 or 2 semitones.
3) The melodic or middle harmonic  speed or density (waves) is  melodic themes composed in such a way that successive notes are always in a distance of an interval of 3rd and alternating (major minor)  thus of 3 or 4 semitones. Any 3 successive notes define a major or minor chord.
4) The harmonic or high (maximum) harmonic  speed or density (spikes) is  melodic themes composed in such a way that successive notes are always in a distance of an interval of perfect 4th or 5th   thus of 5 or 7 semitones. 

Besides the 4 melodic speeds we have also the 2 melodic accelerations   which are sequential combination of acceleration=speed1+speed2 , where speed2>speed1 E.g.

1) Diatonic acceleration=chromatic speed+diatonic speed
2) Harmonic acceleration=diatonic or chromatic speed+harmonic speed (middle or high) 

Here the acceleration is not in the time but in the pitch change. 

Correspondence of chord transitions of chord progressions to the 3-melodic densities or speeds  of the melodies that fit to such chord progressions

(See also post 30)
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!

A characteristic of melodies of Andes ,Incas, Bolivia, Chile etc is that there is often the melodic pattern of non-waving ascension, which escalates from chromatic or diatonic melodic speed , to middle harmonic and then high harmonic , giving thus the feeling of acceleration of joy or sadness! 

The famous jazz violin player,  Stephan Grappelli soloing is utilizing the diatonic speed , with almost no (middle harmonic speed)  waving but approximation of continuous movements at diatonic speed together with occasional spike jump intervals  at high harmonic speed or even higher jumps. If waving are like dancing steps, the Grappelli soloing is like fast walking from point to point with rather small (diatonic) but not very small (Chromatic) steps. 

See e.g. https://www.youtube.com/watch?v=vi10rCh73j8

Another characteristic of the happy and joyful melodies of the Andes , is that the often may use almost exclusively  the maximum large intervals (within a scale) that exist in the chords of the song. And this would be intervals of 8th, 6th (for triad-chords) , 5th and 4th. In other words they use almost exclusively the maximum harmonic melodic  speed that the chords allow. 

This idea of maximum harmonic speed in melodies is also an idea that can give pretty directly improvisation melodies over a chord progression! This is good for happy melodies (like that of ethnic music of Andes). It directly defines improvisational beautiful melodies from the chord progression,  because the maximum intervals of a chord are unique or very few for each chord! In fact a single large such interval from each chord can define the melodic-rhythmic pattern for each chord! 

The standard preference is to use 

a1) For  a major chord x1-x2-x3, the 1st x1-3rd x2   notes interval of pure 5th (7 semitones), or the 1st nx1-2nd x2 notes interval of major 3rd (4 semitones)

a2) For  a minor chord x1-x2-x3, the 1st x1-3rd x2   notes interval of pure 5th (7 semitones), or the 1st x1-2nd x2 notes interval of minor 3rd (3 semitones)

a3) For  a dominant 7th and major 7th chord x1-x2-x3-x4, the 1st x1-3rd x2   notes interval of pure 5th (7 semitones), or  the 1st x1-4th x4   notes interval of minor 7th (8 semitones), or of  major 7th (9 semitones). 
An interesting case of simplicial submelody is  the first choice  always  (interval of 5th or 4th). 

Or we may allow this interval of 4th or 5h of each chord sound 2/3 of the time of the chord sounding and 1/3 of the time the other middle x2 note for minor or major  , or 7th note of the 7th chords.
 Still another case is the minimal harmonic simplicial submelody (but always with notes of the chords) where we take always the 2nd choice (the x1-x2 interval of 3rd, or x1-x4 interval of 7th) where this sounds 2/3 of the time and 1/3 of the time the 3rd note of the chord. This simplicial submelody gives emphasis to the character of each chord, that is being minor , major or 7th etc. 

But another more maximal  harmonic  method is based on the next rules

b1) For each chord the simplicial submelody consists of at least two notes one entry and one exit (that may though coincide)

b2) Complementary chords (e.g. Cmajor, Dminor) can transition with intervals of 5 or 7 semitones (e.g. exit note of Cmajor is the c, and entry note of Dminor is the f).

b3) Successive chords in the cycle of 4ths or 5ths, and relative chords have common notes, this the exit note of the first chord and the entry note of the 2nd chord are identical.

b4) If the entry note of the a chord and its exit  note is an interval of minor 3rd  (3 semitones) we may add two more notes during the chord which is twice the 3rd note of the chord, but at one octave distance, and convert the minor 3rd interval to major 3rd (4 semitones) which has higher harmonic score (see post 40). E.g. G7-->C-->E7 , entry of C=g3, exit of C=e2, so we add c2, c3, and the simplicial submelody goes like this g3-c2-c3-e2, duringthe chord C. We converted the minor 3rd interval g-e, to a major 3rd c-e. 

b5) Itis prefered that intervals of 1,2,3,4 semitones are converted to their complementary of 11,10,9,8 semitones, by changing octave.

The so derived simplicial submelody singles less melody than the chord progression itself!

E.g. for the Chord progression Am->F->G7->C->G7->C->G7->C->E7->Am, the sumplicial submelody with these rules would be a3-a2a2-f2f2-g3g3-g3g3-g3g3-g3g3-g3g3-c2c3e2e2-e3e3-a3.

This simplicial submelody can be the centers of  full melody over this chord progression


The next beautiful melody from Andes (La partida/Quiero ser tu sombra ) is an example of a a melody with all the 4 melodic speeds, chromatic, diatonic, mid and high harmonic

https://www.youtube.com/watch?v=MIgyAvDvoR0

In the harmonic method of composition,  after the determination of the chord-progression and then the simplicial submelody, the next step is to chose the melodic speed to fill the simplicial submelody to a full melody (see also post 9 for the harmonic method of composition). If it would be the chromatic speed, it would be an oriental-like melody. If it would be a diatonic speed, it would be a "lazy"  an easy to sing melody. If it would be the middle or high harmonic speed, it would be an exotic and beautiful but difficult to sing melody.