96. Organized symmetry and symmetric organization of a melody.

A fast and good melody requires appropriately organized symmetry and further organization patterns based on pitch-order emotions dynamics, rhythm, and harmony.

In order to understand better this rich concept, and separate it from the harmony, we will consider the part of the melody, which is parallel to a single chord, from all the chord progression of the song.

The organization of the symmetries of the melody is understood better over the "melodic corridor"
(See post 94 )

We have already mentioned types of symmetry for the melodic themes that are

0) An affine-topological pattern  of the melody which is independent of a realization in  a mode or in a scale (see post 97)

1) Reflection to a horizontal axis (time)

2) Reflection to a  vertical axis (pitch)

3) Point symmetry to a time point

4) Pitch translation

5) Recursive pitch waving ascending or descending.

6) Cyclic or balanced behavior   in ascending-descending.

7) Dilation on the size of intervals (waved changing of the 3 melodic densities or speeds). Usually the melody starts with low melodic speeds or densities , accelerates to higher speeds or densities and then decelerates again to lower speeds or densities, as is also the motion of bodies in dancing.

8) Statistical types of symmetries.

9) Furthermore, the melodic themes may be organized at small time level by the micro-rhythm of the "melodic words" e.g. 3:1 or 2:1 time duration ratio of the long-short notes, the long inside the underlying chord and the short possibly outside the chord. The melodic word is a basic micro-theme of 

the melody. The interval of the long-short notes is a basic step-interval of the melody and it is avoided to me an interval of 2nd , instead an interval of 3rd, 4ths/5th, 6th , 7th or 8th (see post  92 ). The next basic interval in the melody, is the pitch distance among two successive melodic words, which is usually  zero, an interval of 3rd, 4th, 5th etc.

10) or at a larger time scale, by the relevant poetic measure (11-syllables poetry, 15-syllables poetry, 17-syllables poetry) that determine the pattern of repetitions in the melodic themes E.g. 3 repetitions at 4th measure resolution-change or 4 repetitions and at he 5th resolution-change .

11) We may determine a statistical profile of statistical frequency of intervals in the melody such that the highest statistical  frequency of intervals of the melody are mainly the next intervals in the next preference order 5th, 4th, 8th, 6th, 3rd, 2nd. A happy melody tends to avoid sad and dissonant intervals and use instead happy harmonic intervals

12) As the micro-themes (melodic "words") develop over notes ascending and descending over even or odd number steps of the diatonic scale (as in such a way that chords are shaped) the total results, as intended,  is to use eventually all the notes of he diatonic scale, so that the melody has high scale-completeness measure (see post 86 about chromatic music ). This principles somehow determines the preferred chord progressions (E.g. I, IV, V7) .

13) Although we may focus in such an organized symmetry of the melody during a single underlying chord, the true harmony of the fast melody may use "ghost chords" around this single chord (see post 87 about ghost chords ).  

 E.g. if the chord progression is I, IV, V7 used where IV and V7 are ghost chords, then substituting IV with ii or vi and V7 with vii or iii, we get at least 9 more combinations and variations for the ghost-harmony of the melody , that essentially only the chord I is sounding. E.g. (I,ii,vii), (I,ii,V), (I,vi,V), (I,iv,vii) ,(I,ii, iii) ,(I,vi,iii), (I,vi,V), (I,IV,vii), (I,IV,iii).

14) A fast melody should balance properly repetition and  innovation during its development

It is obvious that a simple guitar harping is not a sufficient concept to grasp the required above high organization of the melody even during a single chord. The guitar has only 6-strings while to lay-out the previous organization structures may require many notes and the chord considered at two octaves rather than one only octave.

AN EXAMPLE OF A TYPE OF MELODIES THAT MAY EXHIBIT SUCH ORGANIZATION STRUCTURE AS ABOVE ARE THE CHORD-COURT MELODIES BASED ON "MUSICAL WORDS"

Here we concentrate one only simple organization structure which the closest corresponded in the poetic language and lyrics is the word. So we introduce a concept of micro-melodic theme, called

MUSICAL WORD that we may agree to symbolize say by w. It consists of a very small number of beats higher than 2 e.g.  3 or 4, and we may symbolize it with 0,s and 1,s , which means that at this beat if no sound is heard it is zero, while if a sound is heard it is 1. E.g. (0101) or (011) etc Now we divide the word in its LONG PART , that symbolize by L(w) , and SHORT PART . that we symbolize by S(w) and so that in time duration, or beats it holds that L(w)/S(w)>=2 (e.g. L(w)/S(w)=3 etc).

The musical-words or melodic micro-themes need not be by intervals of 2nds! They can be by intervals of 3rds and 5ths or 4ths! 

PITCH OSCILLATIONS AND THE MELODIC MICRO-RHYTHMIC-THEME
The musical-words or melodic micro-themes need not be by intervals of 2nds! They can be by intervals of 3rds and 5ths or 4ths! Actually as we shall see in the RULE OF OSCILLATION below its ends may be the required oscillation which most often is an interval of 5th or 4th. E.g.on of the most common such dancing pattern is the (1,1,1), where 2 of the 1's is the long part and 1 is the short part. It may start so  that these 3, 1's are the notes of the underlying chord a kind of harping) , but then it dances away so that only two of the 1's are eventually notes of the underlying chord. The number 3 here most often in dancing comes from the 3-like steps of the running horse. It corresponds also to the basic harping of a 3-notes chord.  It is also a micro-rhythmic pattern that repeat either inside or outside the chord. In this way by going up and down the diatonic scale,   this very micro-rhythmic structure of the melodic micro-theme, by odd and even steps creates chords and diatonic harmony. Of course the chord changes may be fast , so actually we are talking about ghost-chords! (see post 87 about ghost chords ). 
When playing or improvising  such melodies, with the vibraphone (metallophone) , the 2 , 3 or 4  mallets, correspond to this oscillating melodic micro-theme.

Such musical words may be ascending, descending or waving. Ascending as excitation may be small (intervals of 2nd) low middle (intervals of 3rds) or high middle (interval of 5th or 4th) or high (intervals of  8th or higher) Of course, as they are combined, they definitely create the effect of waving. BUT the waving is not the very standard by intervals by 2nds but a richer one, that involves many intervals of 3rds and even 5ths, and 8ths. The simplicial sub-melody of such melodies are movements mainly with intervals by 3rds and 5ths. There is also acceleration and deceleration as the melodic theme starts and ends.

E.g. we may descend with a chord say Am and its relative C (out of chords would be notes of G), and ascend with its chromatic-complementary thee G7 (out of chord notes would be those of Am or C ) etc. In other words, we ascend with even or odd notes and descend conversely. Here although we may utilize only 3 chords (Am, C, G) the alternating-changing may be fast covering practically all waving and melodies of the pentatonic or diatonic scale. The scale-completion of the melody (see post 86)  , may be at the next octave rather than in the same octave!
The rhythmic repetition 3 times then the 4th is different is more common than 2 times repeated then 2 times a different. The total range of waving say of the first 3 repetitions may be of size a 5th, while the 4th measure a range of size an 8th, or vice versa.

Let us also assume that the chord progression that underlines the melody is the X(1), X(2) ,...X(n).

As we wrote in previous posts, the melody consists by a progression of melodic themes, that are transformed, by the 4 main transformations or translation, inversion, dilation and rhythmic transformation. This is indeed happening in to the melodic micro-themes or melodic or musical words during the part of the melody that sounds during say the chord X(i) i=1,2...n, BUT we impose here a very important structure which is the key to the beautiful folk melodies, and makes them compatible with the chord progression that underlines, the melody. And this rule is a 

RULE1 OF TRANSIENT AND CHORD NOTES. Obligatory part: In simple words, each musical-word w , that has underlined chord X(i) has the notes of its long part L(w) , to be notes of the chord X(i), (which includes extended forms of X(i) like X(i)maj7 or X(i)7 or X(i)add9 or X(i)sus4 ) while , the notes of its short part S(w) to be transient and belonging to the notes of the neighboring chord that is X(i-1) or  X(i+1), (which includes extended forms of X(i+1) like X(i+1)maj7 or X(i+1)7 or X(i+1)add9 or or X(i+1)sus4) or and more rarely to the rest of the chords of the chord progression. And if so if it contains a note from a non-adjacent chord Y(j) of the progression, then usually somewhere in the progression there is a transition X(i)->Y(j) or Y(j)->X(i) . We keep the transient notes sound at most 1/3 of the time only and the notes of the chord at least 2/3 of the time, because of the rule of long and short parts of the musical word or micro-theme. No mentioning of any scale is necessary in this definition (as usually there are more than one) but only of the chord progression, which is compatible with our enhanced concept of modern harmony. Nevertheless the chord progression over which this technique produces fast melodies may contain very fast chord changes, and may not be identical with the actual chord progression that the instruments play as background to the melody. This is the concept of "ghost chords" in the melody as described in the post 87. E.g. The full ghost-chord progression may be D G D G D A D. While the chords really played is only D. 

RULE2 An alternative rule is that a musical-word w , that has underlined chord X(i) has the notes of its long part L(w) , to be notes of the chord X(i), (which includes extended forms of X(i) like X(i)maj7 or X(i)7 or X(i)add9 or X(i)sus4 ) while , the notes of its short part S(w) to be transient and is one only intermediate not between the notes of the  chord X(i) (usually a 2nd away from the notes of X(i) and preferably but not obligatory this additional note to be a note of the other chords of the progression, again preferably and if possible of the previous or next chord, rarely on  of other chords. And if so, if it contains a note from a non-adjacent chord Y(j) of the progression, then usually somewhere in the progression there is a transition X(i)->Y(j) or Y(j)->X(i) .In this way we keep the transient notes sound at most 1/3 of the time only and the notes of the chord at least 2/3 of the time, in addition to the rule of long and short parts of the musical word or micro-theme. Even if we did not have the structure of micro-themes as musical-words with long and short notes , and we are playing in a random way the three notes of the chord plus one transient, in equal time in the average, we are still in the harmony of this chord, because of the proportion 3:1. And this would still hold if we used 2 transient notes in which case we would have the time proportion 3:2.  But in addition to this rule if we want also the intervals of 3rds, 4ths, 5th and 8th to be more than 2/3 of all the intervals the way is to apply harping in a chord say with 6 or 8 steps on notes, where it is added only one intermediate note in the chord (e.g. 7nh, 6th, 4th or 2nd) and so that the created intervals of 2nd are only 2 in the 6 or 8 intervals. Then we shift to a relative chord an interval of  3rd away or to a resolution transition which is a chord in an interval  5th or 4th away , or we even shift to a chord a 2nd away in which case we do not use any additional note, and we continue so.  So finally %3rds+%4ths/5ths/8ths>=2*(% 2nds) . Again the chord progression over which this technique produces fast melodies may contain very fast chord changes, and may not be identical with the actual chord progression that the instruments play as background to the melody. This is the concept of "ghost chords" in the melody as described in the post 87. E.g. The full ghost chord progression may be D G D G D A D. While the chords really played is only D. 

THEREFORE EVERY CHORD PLAYS THE ROLE OF A MINI CENTRAL SUB-SCALE AROUND WHICH THE MELODY DANCES FOR A WHILE ALTHOUGH IT  IS STEPPING ON OTHER NOTES TOO BUT NOT FOR LONG, THAT ARE MAINLY THE NOTES OF THE NEXT CHORD-SUB-SCALE. 

RULE 3 OF OSCILLATION OR BALANCE
THE COURT-MELODY USUALLY  OSCILLATES INSIDE AN INTERVAL OF 5TH OR 8TH. AND IT MAY BE OF THE NOTES OF THE HARMONIC SIMPLICIAL SUBMELODY (oscillating link or bridge of chords) OR THE ROOR-DOMINANT OF THE CHORD, OR MIDDLE 3RD AND 6TH OR 7NTH OFTHE CHORD (internal bridge of a chord).

RULE 4 OF AFFINE STRUCTURE BALANCE
The melody if ir ascend then it descends and vice versa. The imblanace of thsi rather slight to indicate joy or sadness respectively. (For the Affine structure of a melody see post 97)

RULE 5 OF PITCH SCALE-COMPLENTESS
THE MELODY IS DESIRD TO USE AS EVENTUALLY MANY AS POSSIBLE OF ALL THE NOTES OF AN INTERVAL EITHER OF THE 12-TONES CHROMATI SCALE OR OF A 7 NOTES DIATONIC SCALE.


WE MAY CALL SUCH A CHATTY FAST MELODY THE CHORD-COURT MELODY OR SIMPLER THE CHATTY COURT MELODY OF THE CHORD PROGRESSION.
IT IS IMPORTANT TO REALIZE THAT THE COURT-CHATT MELODY MAY USE OSCILLATIONS BETWEEN THE NOTES OF THE HARMONIC SIMPLICIAL SUBMELODY THAT ARE MAILY INTERVALS OF 4TH, 5TH AND 8TH.  (SEE POST 9, 65, 72 )

GENERAL REMARKS ABOUT MELODY-CHORD CORRELATION 

0) When a melody is created without reference to any chord-progression (see e.g. post 82 about INDEPENDENT MELODIES ), then an statistical profile with high percentages of intervals of 5ths, 4ths, and 3rds compared to 2nds is sufficient to make it an beautiful harmonic melody. But if there is already a chord progression, and we improvise with a melody on it, 

1) then during the time interval that a chord is sounding, we may want to have notes of the melody that include at least one note of the chord and in overall the time that notes of the melody that belong to the chord ,sound, is longer that the total time that the rest of the notes not in the chord is sounding during the chord. This is a quite strong rule. 

2) A weaker rule is simply the requirement that the notes of the melody during the sounding of the chord, contain  notes of the sounding chord, and probably that compared to their neighboring notes, the notes in the melody of the chord, sound longer during the sounding of the underlying chord.

3) If we abolish even this rule then we have an independent melody parallel to an independent chord progression, which is entirely acceptable in Jazz. In an independent melody, from the chord progression, we feel the harmony of the chord progression, but we apply all , some or none of the previous rules to some or of the chords.

(This post has not been written completely yet)

95. SYMMETRIC SCALES OF MESSIAEN AND MORE

Although we have  classified in many ways many known and unknown scales, we mention here , the symmetric scales , without constraint if they are 4 notes 5 notes, 6 notes , 7 notes , 8 notes etc

As a start some already known symmetric scales, on the whole tone pan-flute. The musical composer Oliver Messiaen has enumerated the first 7 of them.

https://www.youtube.com/watch?v=VRO14-jiE0Y&t=82s

1) 2-2-2-2-2-2 (all chords augmented)
2) 2-1-2-1-2-1-2-1 (diminished scale ,all chords diminsihed,nice sounding to make a 8-notes  flute for it))
3) 2-1-1-2-1-1-2-1-1
4) 1-1-3-1-1-1-3-1 (nice sounding to make a 8-notes  flute for it)
5) 1-4-1-1-4-1 (nice sounding to makea  flute for it)
6) 2-2-1-1-2-2-1-1
7) 1-1-1-2-1-1-1-1-2-1
8) 3-1-3-1-3-1 (augmented scale. nice sounding to make a 6-notes  flute for it .E.G. D F F# A Bb C# D, which is a subscale of the 8-notes Samba scale D E F F# A Bb C C# D)
9) 5-1-5-1
10) 3-2-1-3-2-1 (nice sounding to make a 6-notes  flute for it)
11) 3-1-2-3-1-2 (nice sounding to make a 6-notes  flute for it)
12) 1-1-1-1-1-1-1-1-1-1-1-1

Some more are

13) 4-2-4-2
14) 3-3-3-3
16) 4-4-4


Semi-symmetric may be considered the next
The pentatonic may count also as one
1) 2-3-2-3-2
Also alternating 2nd 3rds

2) 2-3-2-4-1 or
3) 4-1-4-1-2 or
4) 1-4-2-3-2
etc



2-OCTAVES HARMONIC SCALES (NON-CHROMATIC) WITH MANY CHORDS

Notice that if we allow for range larger than an octave then as in the post 79, there are more symmetric scale e.g.

1) the -4-3-4-3-3-4-3-  which is the melodic minor scale when reduced to a single octave 
and other are the next


2) 3-3-4-4-3-3-4=24 This scale has obviously successive diminished minor , major and augmented chords.

3) 3-3-3-4-4-4-3=24

4) 3-5-3-5-3-5=24

5) 3-3-3-5-5-5=24

6) 3-4-3-4-7-7=24

7) 3-7-3-7-4=24

8) 3-3-7-7-4=24

9) 4-5-4-5-4-2=24

10) 4-5-4-5-4-2=24

11) 4-4-5-5-4-2=24

12) 4-4-4-5-5-5-2=24

13) 4-4-4-5-2-5=24

14) 5-7-5-7=24

15) 3-4-5-3-4-5=24

16) 3-4-3-4-5-5=24

17) 3-3-5-4-4=24

18) 4-5-7-4-4=24

19) 3-5-7-3-4-7=24

etc

Also in more than 2 octaves

3-octaves

5-5-5-5-5-5-6-=36

and 4-octaves

7-7-7-7-7-7-6-=48

The last one is close to how one can derive a diatonic scale by exact 5ths (Here the 5ths of 7-semitones are not exact, so the Pythagorean comma becomes a whole semitone)

etc.



(This post has not been completely yet) 

94. THE MIRACULOUS MELODIC CORRIDOR ,THE HARMONIC TABLE/SONOME AND THE LIPPENS /TERSPTRA KEYBOARD/ARRAY ORGAN.ISOMORPHIC 2-DIMENSIONAL LAYOUTS OF NOTES

I CONSIDER THE IDEA OF A 2-DIMENSIONAL RECTANGULAR OR HAXEGONAL LATTICE (THE LATTER IS MORE DENSE) AS KEYBOARD CONFIGIRATION OF NOTES AS BEST OPPORTUNITY OF TOUCHSCREEN SOFTWARE AND BEST WAY OF ARRANGING NOTES FOR PLAYING MUSIC ,IMPROVISING AND COMPOSING. 

THERE ARE MANY DIFFERENT WAYS THAT THE NOTES CAN CORRESPOND TO THE VERTICES OF A HEXAGONAL LATTICE.

ISOMPORPHIC 2-DIMENSIONAL LAYOUTS FOR KEYBARDS  STRING INSTRUMENTS  TUNINGS AND SOFTWARE PADS  FOR ARRANGING  THE MUSICAL NOTESAND THEIR IPORTANCE IN IMPROVISING.

THE TERM ISOMORPHIC REFERS TO THE CHORD-SHAPES THAT REMAIN THE SAME (ARE ISOMORPHIC) WHEN CHANGING THE ROOT NOTE AS LONG AS THE TYPE OF THE CHORD REMAINS THE SAME.

Isomorphic layouts: What they are and why they are awesome for your music

https://www.youtube.com/watch?v=ZczraF3dzU0&t=20s&fbclid=IwAR1bAiGG3HFPE9OciNXGPE5p_GD_L5AJaKXsabiypconKg_HYk_RAz5hR9s

https://www.youtube.com/watch?v=ZczraF3dzU0&t=96s

FOR CHORDS THE BEST WAY SEEMS TO BE THAT OF NAVICHORD,, IN OTHER WORDS ONE AXIS BY FITHS AND IN ANOTHER AXIS BY 3RDS. FOR MELODIC IMPROVISATIONS ITIS INONE AXIS BY 5THS AND IN ANOTHER AXIS BY 2NDS.

https://www.researchgate.net/publication/274567781_On_the_playing_of_monodic_pitch_in_digital_music_instruments

The Navichord (https://www.youtube.com/watch?v=xRdH_6cxLRg) is a wonderful application that sets the notes in 2-dimensional hexagonic arrangment as in the Serpstra keyboard. The major and minor chords are triangles of notes in it, and are played by pushing in the cenrer of the triangle. The 3 local relations ofthe chords (chromatic=no common notes, melodic=2 common notes and harmonic=1 common note) are immeditely seen.  The chord scales and chord progressions for  composition are realized by the chord sequencer .

An interesting question when designing settings for grid use of the fretboard in the Artiphon is "What is a geometric arrangement of notes of the 12-notes scale, that allows fast and easy “In the flow” playing and improvisation of melodies , especially tonal melodies with many intervals of 3rd 4th and 5th? (that is within the harmony of one scale) ?

The answer seems to have been given by the design of the next instruments

1. The Handpan and Hang
2. The thump piano
3. The double series of pipes zampona Pan-flutes.

Before this post the reader must study the posts 79 about the 2-octaves 7-note scale by alternating mainor and major 3rds (Small wheel of 3rds).

This scale is also the Harmonic tuning of the guitar (see post 1 and post 90 ) which is optimal when chord playing is mainly the target and not soloing so much

THE MELODIC CORRIDOR 

Constructing therapeutic harps, or similar instruments (e.g. thump  pianos https://en.wikipedia.org/wiki/Mbira or hang and handpans or zamponas diatonic double row pipes, pan-flutes  ) or such keyboards with this scale, has the property that almost what ever we play sounds harmonic as 3 or 4 notes in sequence are well known cords, and overlapping such triads , are relative chords. In fact we may design such an  harmonic diatonic  double row keyboard

 as follows 

  -D3-F3-A3-C3- E4-G4-B4-

-C4-E3-G3-B3-D4-F4-A4-C5- 

Similarly this can be a beautiful , practical and harmonic tuning for harmonicas.

The blue is blowing and the red is draw. Then with the key we may have the sharps too thus in total

-D3#-F3#-A3#-C3#- E4#-G4#-B4#-

 -D3-  F3- A3-   C3-  E4-  G4-   B4-

-C4-  E3-  G3-  B3  -D4  -F4-  A4-  C5- 
-C4#-E3#-G3#-B3#-D4#-F4#-A4#-C5#- 

OR 

-D3#-F3#-A3#-C3#- E4#-G4#-B4#-

 -D3-  F3- A3-   C3-  E4-  G4-   B4-

-C4#-E3#-G3#-B3#-D4#-F4#-A4#-C5#- 

-C4-  E3-  G3-  B3  -D4  -F4-  A4-  C5- 

This type of tuning can be applied also as setting to 4 strings  frets of  the fretboard of the artiphon the midi-controller, and give it sound of adouble diatonic harp or flute etc.

(for he artiphon see here https://artiphon.com/  )

THIS KIND OF KEYBOARD OR TUNING OF INSTRUMENTS (FLUTES, HARMONICA, ARTIPHON , KEYBOARD ETC)  ALLOWS FOR MELODIES IMPROVISATION IN A FAST  WAY EASILY WITHOUT COMPLICATED FINGERINGS OBSTRUCTIONS AS LONG AS THE MELODY IS A DIATONIC SCALE. IT IS A BIT BETTER THAN PIANO KEYBOARD AS IT FOLLOWS THE SHAPING OF CHORDS BY INTERVALS OF 3RDS. IT IS EVEN AEASIRT THAN SINGING OR WHISTLING FROM THE HARMONY POINT OF VIEW!

The advantages are

1. The steps of the melody by intervals of 3rds are successive frets
2. The steps of the melody by intervals of 2nd (one semitone or one tone) are zig-zag frets among the two central strings
3. Steps of the melody by intervals of 4th or 5th are frets in the two central strings that have distance two only frets

The 1) 2) 3) are particular usefull when one wnat to improvise melodies with steps mainly intervals of 3rds ths and 5ths and less by intervals of 2nds (As e.g. in the Folk Irish and Celtic music).

HAVE A LOOK ALSO ON THE HARMONIC TABLE OR SONOME

https://en.wikipedia.org/wiki/Harmonic_table_note_layout

AND THE WIKCI-HAYDEN LAYOUT

https://en.wikipedia.org/wiki/Wicki-Hayden_note_layout

more such hexagonal layouts can be designed e.g. binding intervals by 3rds alternating major minor and intervals of 2nds in a single diatonic scale like in the melodic corridor. Such a hexagonal layout of the MELODIC CORRIDOR could be called HEXAGONAL DIATONIC MELODIC LAYOUT

A simpler uniform version of the Melodic Corridor is the Lippens Keyboard, which is considered to be at least 20 times easier than the usual piano keyboard. It is based on the whole tones scale .

A pan-flute tuned to whole tones instead of a diatonic scale is already a simple Lippens Keyboard
Here are two relevant videos

https://youtu.be/MHfG20HvPHA?t=349

https://youtu.be/SGGpQoI01Wc?t=71

ALSO THE TERPSTRA KEYBOARD


https://www.youtube.com/watch?v=Nb_TQpwam54&t=464s

About the whole tone scales and similar symmetric scales (e.g. By O. Messiah and Jazz) on the whole tone panflute see the next

 https://www.youtube.com/watch?v=VRO14-jiE0Y&t=82s

The melodic corridor can be also be spotted  on the fretboard of the standard tuning 6-string guitar. It will also define an unusual shape  of the diatonic scale with 2 only notes per string. More on that on the post 94.

We give the diagram on the fretboard here of a the c-major melodic corridor in the 6-string standard guitar.

The melodic corridor can be used also to define both the harmonic simplicial andthe bridges between its notes that give the full melody

 Harmonic simplicial sub-melody. Probably best method of  creating first the simplicial sub-melody is based on preferring intervals distances of the notes of the simplicial sub-melody (opposite to the previous method) that are large intervals ,namely intervals of 5ths , 4th 6th or 8th.  . The simplicial sub-melody is somehow the centers of the final melody and most often it is one note per chord of the chord progression . It can also be considered as a very simple bass line parallel to the melody. So the rule to choose the simplicial sub-melody is the next

3.1) If we have two successive chords X(1) -> X(2) in the chord progression, and a is the note of the simplicial sub-melody belonging to chord X(1) , and b is the not of the simplicial sub-melody belonging to the chord X(2), then a->b is an interval in the following order of preference 5th, 4th, 8th, 6th. 

If the X(1) -> X(2) are in the relation of resolution (succesive in the wheel by 4ths) e.g. G->C then we have 3 choices for a->b, the g->c, or b->e, or d->g. If the X(1) -> X(2) are in the relation of relative chords (two common notes) e.g. C->Em then we have 2 choices for a->b,

c->g, or e->b. And if the X(1) -> X(2) are in the chromatic or complementary relation of  chords (roots that differ by one step of the scale) e.g. C->Dm, then we have one only choice or a->b, here the c->f. After we have defined the simplicial sub-melody then we create bridges between its notes by smaller intervals e.g. 3rds or 2nds. 

ARAY ORGAN (by  Bill Wesley)

This keyboard has horizontally from left to right (alternating in depth) the sequence by fths, horizontally at the same height sequency by tones and vertically sequence by octaves . More about it in the links  below  

The aray kalibra is essentially an Octaves x Fifths arrangement (Vertically X Horizontally) 

https://www.arraymbira.com/wp-content/uploads/2016/03/note-patterns.pdf

https://www.facebook.com/Arrayist/photos/rpp.1414742682076221/1669474799936340/?type=3&theater

https://www.youtube.com/watch?v=Fg5KWWouLxg&feature=youtu.be&t=895&fbclid=IwAR0E1c4JZs3DXAjBDJg0DkIUbb6fdzu2GojKrdzJcqQFCsTqjb5rm86Wyzo

https://www.youtube.com/watch?v=SU2JztST_TY&t=1094s

https://www.youtube.com/watch?v=nefHvt7cTw4

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

(This post has not been completely yet) 

93. THE HARMONIC STATISTICAL PROFILE OF A MELODY AND FAST ALMOST RANDOM IMPROVISATION BASED ON THAT. THE BEAUTY OF MELODIES THROUGH STATISTICS OF INTERVALS AS % OF 5THS/4THS/6THS or 8THS % 3RDS % 2NDS.

As we wrote in the post 40, the intervals of  5th/4ths have higher harmonic score than the intervals of 3rd which in their turn have higher harmonic score than the intervals of 2nd.

So many beautiful melodies have this distribution of  the percentage   of  intervals in them. In other words % of 5ths/4ths> % of 3rds % 2nds.

Some of the melodies of the music od Incas, Andes etc, but also of all over the world composers have this property.

The percentage of intervals of  % of 5ths/4ths>, % of 3rds or 6ths is called THE HARMONIC (STATISTICAL) PROFILE OF THE MELODY

We should notice also that although the diatonic 7-notes scale is closed to intervals of 2nd, 3rds and 5ths or 4ths (but not both) the standard pentatonic scale is  closed  to intervals by 5th and by 4ths .

We say that a scale is closed to  intervals by nth, if and only if starting from any note of it if we shift higher or lower by an interval by nth, we are again in a note of the scale.


Nevertheless , other proportions of  percentages of 5ths/4ths/8ths, of 3rds and of 2nd are known to give characteristic types of melodies among the different cultures.

Other observed HARMONIC PROFILES  of percentages are


%2nds> %3rds+%4ths/5ths/8ths 
(e.g. the 2nds double more than the rest of the intervals, ratio 3:1 ) :
Oriental and Arabic Music,  GypsyJazz, and Jazz Stephan Grappelli soloing

%3rds+%4ths/5ths/8ths>% 2nds :
(e.g. the 2nds less than half compared to the rest of the intervals,ratio 3:1 )
 Music of Incas, and countries of the Andes. Celtic music Ancient Egyptian  music

The way to create melodies with at least 2/3 of the intervals to by the larger intervals of 3rds , 5ths/4ths or 8ths, is to apply harping in a chord say with 6 or 8 steps on notes, where it is added only one intermediate note in the chord (e.g. 7nh, 6th, 4th or 2nd) and so that the created intervals of 2nd are only 2 in the 6 or 8 intervals. Then we shift to a relative chord an interval of  3rd away or to a resolution transition which is a chord in an interval  5th or 4th away , or we even shift to a chord a 2nd away in which case we do not use any additional note, and we continue so.  So finally %3rds+%4ths/5ths/8ths>=2*(% 2nds) .
A way to take short notes of such beautiful melodies is to write the chord progression, and then one note with small letters above or below the chord denoting which neighboring note (by interval of 2nd usually)  is the extension of the chord in the melody.

%4ths/5ths/8ths/6th>%3rds>% 2nds :
(e.g. the 2nds +3rds less than half compared to the rest of the intervals,ratio 3:1,  )
The way to create such melodies with at least 2/3 of the intervals to by the larger intervals of 5ths/4ths or 8ths, compared to 3rds ,  and 2nds is to apply the same technique as before, but when harping inside the chord we use the intervals of 4th and 5th and 8th of the  normal position and   2  inversions, instead of the 3rds in  the normal position! In this way in the fast soloing or harping on the notes of the the chord has more intervals of 4th, 5th and 8th than of 3rds!

Nevertheless the chord progression over which this technique produces fast melodies may contain very fast chord changes, and may not be identical with the actual chord progression that the instruments play as background to the melody. This is the concept of "ghost chords" in the melody as described in the post 87. E.g. The full ghost chord progression may be D G D G D A D. While the chords really played is only D. 


For independent from chord progression free improvised melodies a simple way to create melodies with number of 2nds intervals <=50% is to alternate intervals of 2nds with intervals of 3rds, 4ths, 5th,s and 6ths. Or a way to create melodies with number of 2nds intervals <=33% is
alternate for every one interval of 2nds two intervals of 3rds, 4ths, 5th,s and 6ths.

THEREFORE EVERY CHORD PLAYS THE ROLE OF A MINI CENTRAL SUB-SCALE AROUND WHICH THE MELODY DANCES FOR A WHILE ALTHOUGH IT  IS STEPPING ON OTHER NOTES TOO BUT NOT FOR LONG, THAT ARE MAINLY THE NOTES OF THE NEXT CHORD-SUB-SCALE. 

A simple and common way to create the right proportions of statistical frequencies of intervals as above is the next. Take for example a simple chord harping-waving that contains also with the  rules as in post 92, 103 , less than 50% of the time also notes outside the chord. And then half of this simple theme translate it one octave higher, and so oscillate between the two octaves. Normally the initial non-translated melody would have intervals of 2nd, 3rd, and 5th. The interval of 3rd will become 6th , the interval of 5th, a 4th and an interval of 2nd , will become 7nth. In this way also the statistical profile of such melodies will have more frequently high intervals  of 5th, 6th, 7nth and 8th compared to intervals of 2nds (see post 93 ) .g. the folk Irish melody Kerry Polka below

Within the current improvisation method of random melodies with high harmonic statistical profile, is the improvisation method for relaxing and meditation based of power-chords as in post 35. This is mainly alternating a power chord of interval of 5th/4th with a power chord of interval 3rd/6th, or in general alternating a power chord of interval 5th/4th with any 3 notes which are chords or not. The next videos describe it for the case of a Celtic harp.

https://www.youtube.com/watch?v=Z6JuEslUk_E

https://www.youtube.com/watch?v=aN-LFOZdqu4&t=33s

Another characteristic of such beautiful melodies with the "right harmonic proportions" is that they exhibit the effect of acceleration/deceleration in the movement exactly as the physical bodies. In other words, they start with slow speed (intervals of 2nds), accelerate (intervals of 3rds and then intervals of 5ths/4ths) and finally decelerate when reaching to the right center-note (from intervals of 5ths/4th to intervals of 3rds and then to intervals of 2nds), Of course there are many shortcuts where intermediate level of melodic-speed or melodic-density (see post 68 ) are omitted. 

ALTHOUGH THE DIATONIC SCALE REQUIRES MANY HARMONICS TO BE DEFINED, (within the first 27 harmonics see post 81) IT CAN BE PROVED THAT IT HAS THE LARGEST NUMBER OF MAJOR AND MINOR TRIADS COMPARED TO THE OTHER SCALES.

NEVERTHELESS THE STANDARD PENTATONIC SCALE IS THE MAXIMAL SUB-SCALE OF THE DIATONIC WHICH IS CLOSED TO INTERVALS BY 5TH (7 SEMITONES) IN OTHER WORDS STARTING FROM A NOTE OF THE SCALE BY GOING UP OR DOWN A 5THS (7 SEMITONES) WE ARE AGAIN BACK TO A NOTE OF THE SCALE. THE DIATONIC IS NOT CLOSED. IT IS CLOSED ONLY IF WE TOLERATE EITHER AN INTERVAL OF  5TH OR OF  4TH. EVEN WIT THIS RESTRICTION BY MAKING SUCH MELODIES AS ABOVE AROUND INTERLEAVS BY 5TH, AND MOVING UP AND DOWN CREATES BEAUTIFUL MELODIES

NOW FAST ALMOST RANDOM IMPROVISATION OF A MELODY CAN BE SO THAT SUCH A STATISTICAL PROFILE IS KEPT! THIS IS DONE IN A DIFFICULT WAY WITH THE GUITAR FRETBOARD OR CHROMATIC INSTRUMENTS , BUT WITH INSTRUMENTS THAT ARE OF DIATONIC TOPOLOGY LIKE PIANO-KEYBOARDS, ACCORDIONS, DIATONIC FLUTES, DIATONIC PAN-FLUTES , SAXOPHONES, CLARINETS, ZAMPONA FLUTES ETC  IT IS FEASIBLE AND MUCH EASIER. ONE HAS JUST TO REGULATE HIS HANDS MOVEMENTS E.G. ON THE PIANO KEYBOARD SO THAT THE SUCCESSIVE DISTANCES ON THE WHITE ONLY (OR BLACK-ONLY ) KEYS IS OF THE REQUIRED TYPE OF INTERVALS E.G. MAINLY >= OF 3RDS. SIMILARLY VERY HARMONIC SUCH RANDOM MOVEMENTS MELODIES CAN BE CONDUCTED ON ZAMPONA  PANFLUTES THAT PUT THE NOTES IN 2 ROWS IF  EVEN OR ODD ORDER IN THE DIATONIC SCALE. OFCOURSE ALL THIS IS EVEN MORE SMOOTH AND EASY OF IT IS DONE ON A MOBILE TOUCH-SCREEN APP OF SUCH INSTRUMENTS (ZAMPONA, PIANO, HANDPAN  ETC)

92. HOW TO CREATE MELODIES FROM A CHORD PROGRESSION 1/2: THE CHORD-COURTYARD MELODY: "MELODIC MICRO-RHYTHMIC-WORDS" PITCH HARMONY CREATED THROUGH RHYTHM: TRINARY HARPING COMBINATIONS MAINLY BY 3RDS

 HOW TO CREATE MELODIES FROM A CHORD PROGRESSION:  "MUSICAL WORDS" OR MELODIC MICRO-THEMES WITH SYLLABLES, LONG  IN THE CHORD AND SHORT OUT OF THE CHORD  PITCH HARMONY CREATED THROUGH RHYTHM: THE SMALL SECRET OF MAKING BEAUTIFUL FOLK MELODIES LIKE THOSE IN THE IRISH  CELTIC OR ANDEAN-INCAS FOLK MUSIC.

As we wrote in the past much of the beautiful folk melodies , come from ancient times that melodies where the mode of speaking and singing the poetry, was melody and which poetry already had organization levels in number of syllables, (e.g. 16-1=15 syllables , 12-1=11  syllables per poetic line) in long sounding and short sounding syllables of the words E.g. all words of ancient but also modern Greek language are divided to long and short according to the vowels although only in ancient times the speaking of the syllable was lasting longer when the syllable was long. Furthermost there was the organisation of the lines of poetry according to the rhyme, that together with all the above symmetries created multi-layer organisation in the rhythm (notice the similarity of the word rhyme with rhythm) , which is not existing in the writing of the music anymore. Normally we only have the concept of musical measure but not higher layer measures.

This post should be read, together with posts 103 and 104.

Here we concentrate one only simple organization structure which the closest corresponded in the poetic language and lyrics is the word. So we introduce a concept of micro-melodic theme, called

MUSICAL WORD that we may agree to symbolize say by w. It consists of a very small number of beats higher than 2 e.g.  3 or 4, and we may symbolize it with 0,s and 1,s , which means that at this beat if no sound is heard it is zero, while if a sound is heard it is 1. E.g. (0101) or (011) etc Now we divide the word in its LONG PART , that symbolize by L(w) , and SHORT PART . that we symbolize by S(w) and so that in time duration, or beats it holds that L(w)/S(w)>=2 (e.g. L(w)/S(w)=3 etc).
For example, we may compose the melody from 3-notes micro-themes, the first and last inside the chords and the middle possible outside the chords.

PITCH OSCILLATIONS AND THE MELODIC MICRO-RHYTHMIC-THEME
The musical-words or melodic micro-themes need not be by intervals of 2nds! They can be by intervals of 3rds and 5ths or 4ths! Actually as we shall see in the RULE OF OSCILLATION below its ends may be the required oscillation which most often is an interval of 5th or 4th. E.g.on of the most common such dancing pattern is the (1,1,1), where 2 of the 1's is the long part and 1 is the short part. It may start so  that these 3, 1's are the notes of the underlying chord a kind of harping) , but then it dances away so that only two of the 1's are eventually notes of the underlying chord. The number 3 here most often in dancing comes from the 3-like steps of the running horse. It corresponds also to the basic harping of a 3-notes chord.  It is also a micro-rhythmic pattern that repeat either inside or outside the chord. In this way by going up and down the diatonic scale,   this very micro-rhythmic structure of the melodic micro-theme, by odd and even steps creates chords and diatonic harmony. Of course the chord changes may be fast , so actually we are talking about ghost-chords! (see post 87 about ghost chords ). 
When playing or improvising  such melodies, with the vibraphone (metallophone) , the 2 , 3 or 4  mallets, correspond to this oscillating melodic micro-theme.

Such oscillating musical words may be ascending, descending or waving. Ascending as excitation may be small (intervals of 2nd) low middle (intervals of 3rds) or high middle (interval of 5th or 4th) or high (intervals of  8th or higher) Of course, as they are combined, they definitely create the effect of waving. BUT the waving is not the very standard by intervals by 2nds but a richer one, that involves many intervals of 3rds and even 5ths, and 8ths. The simplicial sub-melody of such melodies are movements mainly with intervals by 3rds and 5ths. There is also acceleration and deceleration as the melodic theme starts and ends.

E.g. we may descend with a chord say Am and its relative C (out of chords would be notes of G), and ascend with its chromatic-complementary thee G7 (out of chord notes would be those of Am or C ) etc. In other words, we ascend with even or odd notes and descend conversely. Here although we may utilize only 3 chords (Am, C, G) the alternating-changing may be fast covering practically all waving and melodies of the pentatonic or diatonic scale. The scale-completion of the melody (see post 86)  , may be at the next octave rather than in the same octave!
The rhythmic repetition 3 times then the 4th is different is more common than 2 times repeated then 2 times a different. The total range of waving say of the first 3 repetitions may be of size a 5th, while the 4th measure a range of size an 8th, or vice versa.

Let us also assume that the chord progression that underlines the melody is the X(1), X(2) ,...X(n).

As we wrote in previous posts, the melody consists by a progression of melodic themes, that are transformed, by the 4 main transformations or translation, inversion, dilation and rhythmic transformation. This is indeed happening in to the melodic micro-themes or melodic or musical words during the part of the melody that sounds during say the chord X(i) i=1,2...n, BUT we impose here a very important structure which is the key to the beautiful folk melodies, and makes them compatible with the chord progression that underlines, the melody. And this rule is a 

RULE 1 OF TRANSIENT AND CHORD NOTES. TRINARY HARPING COMBINATIONS. Obligatory part: In simple words, each musical-word w , that has underlined chord X(i) has the notes of its long part L(w) , to be notes of the chord X(i), (which includes extended forms of X(i) like X(i)maj7 or X(i)7 or X(i)add9 or X(i)sus4 ) while , the notes of its short part S(w) to be transient and belonging to the notes of the neighboring chord that is X(i-1) or  X(i+1), (which includes extended forms of X(i+1) like X(i+1)maj7 or X(i+1)7 or X(i+1)add9 or or X(i+1)sus4) or and more rarely to the rest of the chords of the chord progression. And if so if it contains a note from a non-adjacent chord Y(j) of the progression, then usually somewhere in the progression there is a transition X(i)->Y(j) or Y(j)->X(i) . We keep the transient notes sound at most 1/3 of the time only and the notes of the chord at least 2/3 of the time, because of the rule of long and short parts of the musical word or micro-theme. No mentioning of any scale is necessary in this definition (as usually there are more than one) but only of the chord progression, which is compatible with our enhanced concept of modern harmony. Nevertheless the chord progression over which this technique produces fast melodies may contain very fast chord changes, and may not be identical with the actual chord progression that the instruments play as background to the melody. This is the concept of "ghost chords" in the melody as described in the post 87. E.g. The full ghost-chord progression may be D G D G D A D. While the chords really played is only D. 
THE MICRO-RHYTHMIC DOLPHIN WORDS OF LONG-SHORT PART may have  the simplest order-topological pattern which  is an up , down or horizontal arrow. And a  long a note is inside the chord and short is  a note possible but not necessarily outside the chord. The distance of the long-short note is usually a 3rd, and the long is usually double duration from the short  We call such system of elementary Dolphin-words trinary harping combinations (by 3rds). If such micro-words are an up or own or horizontal arrow, then we prefer to have a balance of all proportions of up or down in any such subdivision. By choosing appropriately the proportions of up-down-horizontal any slope ,melody can be composed, that goes from anywhere to anywhere and at the same time being in harmonic-fitness with he underlying chords!

There are 3 reasons why the full melody might be in the mode of trinary harping combinations of Dolphin-words of long-short part.
a) It is an easy way to incorporate notes outside the chord in the melody while the melody is fitting to the chord, and at the same time have a rhythmic sounding
b) It gives fast melodies that for skilled instruments players gives an impressive listening 
c) It gives high harmonic statistical profile with high percentage f intervals of 3rds, if the internal distance of the notes in the elementary Dolphin-word is mainly intervals of 3rds

d) All of the above global properties of the melody are succeed from its very small building blocks. 

RULE 2 An alternative rule is that a musical-word w , that has underlined chord X(i) has the notes of its long part L(w) , to be notes of the chord X(i), (which includes extended forms of X(i) like X(i)maj7 or X(i)7 or X(i)add9 or X(i)sus4 ) while , the notes of its short part S(w) to be transient and is one only intermediate not between the notes of the  chord X(i) (usually a 2nd away from the notes of X(i) and preferably but not obligatory this additional note to be a note of the other chords of the progression, again preferably and if possible of the previous or next chord, rarely on  of other chords. And if so, if it contains a note from a non-adjacent chord Y(j) of the progression, then usually somewhere in the progression there is a transition X(i)->Y(j) or Y(j)->X(i) .In this way we keep the transient notes sound at most 1/3 of the time only and the notes of the chord at least 2/3 of the time, in addition to the rule of long and short parts of the musical word or micro-theme. Even if we did not have the structure of micro-themes as musical-words with long and short notes , and we are playing in a random way the three notes of the chord plus one transient, in equal time in the average, we are still in the harmony of this chord, because of the proportion 3:1. And this would still hold if we used 2 transient notes in which case we would have the time proportion 3:2.  But in addition to this rule if we want also the intervals of 3rds, 4ths, 5th and 8th to be more than 2/3 of all the intervals the way is to apply harping in a chord say with 6 or 8 steps on notes, where it is added only one intermediate note in the chord (e.g. 7nh, 6th, 4th or 2nd) and so that the created intervals of 2nd are only 2 in the 6 or 8 intervals. Then we shift to a relative chord an interval of  3rd away or to a resolution transition which is a chord in an interval  5th or 4th away , or we even shift to a chord a 2nd away in which case we do not use any additional note, and we continue so.  So finally %3rds+%4ths/5ths/8ths>=2*(% 2nds) . Again the chord progression over which this technique produces fast melodies may contain very fast chord changes, and may not be identical with the actual chord progression that the instruments play as background to the melody. This is the concept of "ghost chords" in the melody as described in the post 87. E.g. The full ghost chord progression may be D G D G D A D. While the chords really played is only D. 

THEREFORE EVERY CHORD PLAYS THE ROLE OF A MINI CENTRAL SUB-SCALE AROUND WHICH THE MELODY DANCES FOR A WHILE ALTHOUGH IT  IS STEPPING ON OTHER NOTES TOO BUT NOT FOR LONG, THAT ARE MAINLY THE NOTES OF THE NEXT CHORD-SUB-SCALE. 

RULE 3 OF OSCILLATION OR BALANCE BY TRINARY
THE COURTYARD-MELODY USUALLY  OSCILLATES INSIDE AN INTERVAL OF 5TH OR 8TH. AND IT MAY BE OF THE NOTES OF THE HARMONIC SIMPLICIAL SUBMELODY (oscillating link or bridge of chords) OR THE ROOR-DOMINANT OF THE CHORD, OR MIDDLE 3RD AND 6TH OR 7NTH OFTHE CHORD (internal bridge of a chord).A simple and common way to crate such an oscillations is to take for example a simple chord harping-waving that conatins also with the previous rules less than 50% of the time also notes outside the chord , and then half of this simple theme translate it one octave higher, and so oscillate between the two octaves. The interval of 3rd will become 6th , the interval of 5th, a 4th and an interval of 2nd , will become 7nth. 
THE MICRO-RHYTHMIC DOLPHIN WORDS OF LONG-SHORT PART may have  the simplest order-topological pattern which  is an up , down or horizontal arrow. And a  long a note is inside the chord and short is  a note possible but not necessarily outside the chord. The distance of the long-short note is usually a 3rd, and the long is usually double duration from the short  We call such system of elementary Dolphin-words trinary harping combinations (by 3rds). If such micro-words are an up or own or horizontal arrow, then we prefer to have a balance of all proportions of up or down in any such subdivision. By choosing appropriately the proportions of up-down-horizontal any slope ,melody can be composed, that goes from anywhere to anywhere and at the same time being in harmonic-fitness with he underlying chords!


See e.g. the folk Irish melody Kerry Polka below

d) 

See e.g. the Irish melody Blacksmith hornpipe

 http://ungaretti.racine.ra.it/ireland/music/blakhorn.mid

Another example is the Irish melody "The frost is all over"

http://www.contemplator.com/tunebook/midimusic/frost.mid

Here is also another example with the harp on the Dorian mode of the diatonic scale. 
Notice again that by the micro-words, with long-short parts the duration of the notes of the underlying chord (in C diatonic major and its Dorian mode it is the D minor chord) is double the duration of the notes outside the chord.
The whole of the improvisation has a single underlying chord the Dm.

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

RULE 4 OF AFFINE STRUCTURE BALANCE
The melody if ir ascend then it descends and vice versa. The imblanace of thsi rather slight to indicate joy or sadness respectively. (For the Affine structure of a melody see post 97)

RULE 5 OF PITCH SCALE-COMPLETENESS
THE MELODY IS DESIRD TO USE AS EVENTUALLY MANY AS POSSIBLE OF ALL THE NOTES OF AN INTERVAL EITHER OF THE 12-TONES CHROMATI SCALE OR OF A 7 NOTES DIATONIC SCALE.


WE MAY CALL SUCH A CHATTY FAST MELODY THE CHORD-COURTYARD MELODY OR SIMPLER THE CHATTY COURTYARD MELODY OF THE CHORD PROGRESSION.
IT IS IMPORTANT TO REALIZE THAT THE COURT-CHATT MELODY MAY USE OSCILLATIONS BETWEEN THE NOTES OF THE HARMONIC SIMPLICIAL SUBMELODY THAT ARE MAILY INTERVALS OF 4TH, 5TH AND 8TH.  (SEE POST 9, 65, 72 )


Here is one more example with vibraphone where we start and end the melodic themes on the notes of 4-notes chord of the scale (and as the full scale is 7-notes the passing or transient notes are only 3 less than the 4 of the chord therefore and such melodic theme, will be harmonized within the chord). 

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

GENERAL REMARKS ABOUT MELODY-CHORD CORRELATION 

0) When a melody is created without reference to any chord-progression (see e.g. post 82 about INDEPENDENT MELODIES ), then an statistical profile with high percentages of intervals of 5ths, 4ths, and 3rds compared to 2nds is sufficient to make it an beautiful harmonic melody. But if there is already a chord progression, and we improvise with a melody on it, 

1) then during the time interval that a chord is sounding, we may want to have notes of the melody that include at least one note of the chord and in overall the time that notes of the melody that belong to the chord ,sound, is longer that the total time that the rest of the notes not in the chord is sounding during the chord. This is a quite strong rule. 

2) A weaker rule is simply the requirement that the notes of the melody during the sounding of the chord, contain  notes of the sounding chord, and probably that compared to their neighboring notes, the notes in the melody of the chord, sound longer during the sounding of the underlying chord.

3) If we abolish even this rule then we have an independent melody parallel to an independent chord progression, which is entirely acceptable in Jazz. In an independent melody, from the chord progression, we feel the harmony of the chord progression, but we apply all , some or none of the previous rules to some or of the chords.

Here is the way to create melodies with at least 2/3 of the intervals that  are the larger intervals of 3rds , 5ths/4ths or 8ths. The way is to apply harping in a chord say with 6 or 8 steps on notes, where it is added only one intermediate note in the chord (e.g. 7nh, 6th, 4th or 2nd) and so that the created intervals of 2nd are only 2 in the 6 or 8 intervals. Then we shift to a relative chord an interval of  3rd away or to a resolution transition which is a chord in an interval  5th or 4th away , or we even shift to a chord a 2nd away in which case we do not use any additional note, and we continue so.  So finally %3rds+%4ths/5ths/8ths>=2*(% 2nds) 

A way to take short notes of such beautiful melodies is to write the chord progression, and then one note with small letters above or below the chord denoting which neighboring note (by interval of 2nd usually)  is the extension of the chord in the melody.

Usually the pattern of the melody e.g. in Celtic folk music is with underlying chords two successive in the wheel by 4ths, that is e.g. D7->G (actually the requirement is to cover the diatonic scale so it could also be D->A, D->Bm etc) . E.g. there is an ascending  excitation movement to the next octave, maybe also one more fifth higher (may be called upwards melodic movement) , during the D7, while there is descending waving return to G (maybe called downwards melodic movement) , which goes quite low so that finally the melody closes with waving ascending return to D from where it started. In general the repeated waving of the melody is large within an interval of 8th , or  large-medium within an interval of 5th or medium within an interval of 3rd.


Furthermore, the rule can be extended to the optional part    of the rule which is that we are at least 1/3  of the time (preferably more than 2/3 of the time) at intervals of 3rds in the 2-octave 7-notes scale by thirds, which is always chords, or higher intervals of 4ts and 5ths and the rest of the time with intervals of 2nds. If the chords are mainly in the resolution relation (4ths) or relatives (3rds) the faster the changes of the chords relative to the duration of the musical-words, that may be with intervals by 2nds, the more the higher intervals of 3rds, 4ths, 5ths are in the total melody. The shifting a musical-word or micro-theme which is based, say, in intervals by 3rds inside the underlying chord X(i), is already a translation of the theme by intervals of 3rds, 4ths or 5ths. And at the transition of the chords X(i)->X(i+1), we may consider that the musical-word micro-theme translates also by the interval of the roots of the chords (although this is not absolutely necessary always). Therefore if the chord transitions X(i)->X(i+1) are mainly in the relation of resolution (intervals by 4ths or 5ths) or relative chords (interval of 3rd) then transitioning in the next chord again translated the micro theme by intervals by 3rds 4th or 5ths. Therefore in total, we may have at least more than half of the successive intervals of the melody by intervals of 3rds , 4th, 5ths or 6ths. 
This works even better if for every resolution pair X(i)->X(i+1) we involve as parallel mirror of it its relative pair Y(i)->Y(i+1) where Y(i) relative chord to X(i) and Y(i+1) relative chord to X(i+1). (e.g. to the resolution pair Am->Dm the relative pair is the C->F In the language of intervals for the simplicial sub-melody, this means that we may descend with an interval of 4th (5 semitones) and ascend by a lower relative intervals of 4th again E.g. f4->c4-> e3->a3 ). 
When we solo around say a major chord e.g. C , that we may consider as root chord of a major diatonic scale , the out of chords notes are the 7th, 2nd, 4th, and 6th (b, d, f, a) . But the 2nd, 4th, 6th are the notes of the minor chord ii (Dm)  , which is the lower distant relative chord of the IV (F). Thus it also belong to the V6 (F6)  . While the 7nth (b) is in the V (G) or in the same chord C7. Also the 6th, may be considered as belonging to the I6 (C6). Therefore the sequence C7->F6 , or the G->C->F6, which is in the wheel by 4ths, covers such soloing. Different soloing is a permutation of such triads or pairs. We may also consider that it is covered in the wheel by 3rds, as the ascending sequence of 5 chords  with 3 minors 2 majors (minor oriented) Em->C->Am->F->Dm  or the 5 chords sequence with 2 minors and 3 majors (major oriented)  G->Em->C->Am->F. The latter consideration in the wheel by 3rds seems more natural. Therefore soloing around a chord like C,=(c,e,g) as interval of 7 notes b-c-d-e-f-g-a, is covered by an arc of 5 successive chords in the wheel by 3rds , and the soloing can be patterned by permutations of these chords, as fast-ghost chord progression (see post 87 ) while in reality we may play only 2 major or 3 major chords only.  The same method as we may continue further left or right in the wheel by 3rds defines also the modulations that lead us away from the initial diatonic scale.

For example, 
1) if X(i)->X(i+1) are two chords successive in the wheel by 4ths e.g. G->C, then the chord-pair sub-scale od join-arpeggio of the two successive chords is the pentatonic  scale (B,C,D,E,G) with interval structure 1-2-2-3-4.
2) if X(i)->X(i+1) are two chords successive in the wheel by 3rds e.g. C->Em then the chord-pair sub-scale of join-arpeggio of the two successive chords is the 4-notes scale (B,C,E,G) with interval structure 1-4-3-4. If it is the pair C->Am, then the chord-pair sub-scale of join-arpeggio of the two successive chords is the well known and standard  5-notes major pentatonic scale (C-D-E-G-A) with interval structure 2-2-3-2-3 

3) if  X(i)->X(i+1) are two chords successive in the wheel by 2nds e.g. Dm->Em then the chord-pair sub-scale of join-arpeggio of the two successive chords is the 6-notes scale (B,D,E,F,G,A)
with interval structure 3-2-1-2-2-2. Or if it is the pair F->G then it is the 6-notes scale (F,G,A,B,C,D) with interval structure 2-2-2-1-2-2. On the other hand if it the pair E->Am then it is a pentatonic  scale  (C,E,G#,A,B) with an interval structure 4-4-1-2-1. While if it is the pair Am->G it is the 6-notes scale (A,B,C,D,E,G). And if the G is with dominant seventh G7, so Am->G7, then it is all the 7-notes diatonic scale (A,B,C,D,E,F,G)! If it is the power chord Gpower, so Am->Gpower, then the chord-pair sub-scale of join-arpeggio of the two successive chords is the minor pentatonic scale (A, C, D, E, G)! 
The same if we have the chord progression 
Am->Gpower->C, again the chord-triad sub-scale of join-arpeggio of the three successive chords is the minor pentatonic scale (A, C, D, E, G)! Some beautiful folk songs have this chord progression, and melody in the corresponding pentatonic scale as above.
In the same way, the chord progression G->Am->C  would as join-arpeggio scale the 6-notes scale C-D-E-G-A-B, with internal structure (2-2-3-2-2-1)
Or the progression C-E7->Am the join arpeggio the 7-notes scale C,D,E,G,G#,A,B with interval structure 2-2-3-1-1-2-1.
And of course the join-arpeggio of the chords progression C-F-G or Em-Am-Dm is all the diatonic scale.


W e may strengthen the harmony of the melody by the following observations
THE BEAUTIFUL PROPORTIONS MELODY:  % of intervals of 5ths/4ths> % of intervals of 3rds>% % of intervals of 2nds.

The musical-words or melodic micro-themes need not be by intervals of 2nds! They can be by intervals of 3rds and 5ths or 4ths! 

As we wrote in the post 40, the intervals of  5th/4ths have higher harmonic score than the intervals of 3rd which in their turn have higher harmonic score than the intervals of 2nd.

So many beautiful melodies have this distribution of  the percentage   of  intervals in them. In other words % of 5ths/4ths> % of 3rds>% % 2nds.

Some of the melodies of the music of Incas, Andes etc, but also of all over the world composers have this property.

We should notice also that although the diatonic 7-notes scale is closed to intervals of 2nd, 3rds and 5ths or 4ths (but not both) the standard pentatonic scale is  closed  to intervals by 5th and by 4ths .

We say that a scale is closed to  intervals by nth, if and only if starting from any note of it if we shift higher or lower by an interval by nth, we are again in a note of the scale.


Nevertheless , other proportions of  percentages of 5ths/4ths/8ths, of 3rds and of 2nd are known to give characteristic types of melodies among the different cultures.

Other observed profiles of percentages are


%2nds> %3rds+%4ths/5ths/8ths 
(e.g. the 2nds double more than the rest of the intervals, ratio 3:1 ) :
Oriental and Arabic Music,  GypsyJazz, and Jazz Stephan Grappelli soloing

%3rds+%4ths/5ths/8ths>% 2nds :
(e.g. the 2nds less than half compared to the rest of the intervals,ratio 3:1 )
 Music of Incas, and countries of the Andes. Celtic music Ancient Egyptian  music

The way to create melodies with at least 2/3 of the intervals to by the larger intervals of 3rds , 5ths/4ths or 8ths, is to apply harping in a chord say with 6 or 8 steps on notes, where it is added only one intermediate note in the chord (e.g. 7nh, 6th, 4th or 2nd) and so that the created intervals of 2nd are only 2 in the 6 or 8 intervals. Then we shift to a relative chord an interval of  3rd away or to a resolution transition which is a chord in an interval  5th or 4th away , or we even shift to a chord a 2nd away in which case we do not use any additional note, and we continue so.  So finally %3rds+%4ths/5ths/8ths>=2*(% 2nds) 

%4ths/5ths/8ths/6th>%3rds>% 2nds :
(e.g. the 2nds +3rds less than half compared to the rest of the intervals,ratio 3:1,  )
The way to create such melodies with at least 2/3 of the intervals to by the larger intervals of 5ths/4ths or 8ths, compared to 3rds ,  and 2nds is to apply the same technique as before, but when harping inside the chord we use the intervals of 4th and 5th and 8th of the  normal position and   2  inversions, instead of the 3rds in  the normal position! In this way in the fast soloing or harping on the notes of the the chord has more intervals of 4th, 5th and 8th than of 3rds!

Another characteristic of such beautiful melodies with the "right harmonic proportions" is that the exhibit the effect of acceleration/deceleration in the movement exactly as the physical bodies. In other words, they start with slow speed (intervals of 2nds), accelerate (intervals of 3rds and then intervals of 5ths/4ths) and finally decelerate when reaching to the right center-note (from intervals of 5ths/4th to intervals of 3rds and then to intervals of 2nds), Of course there many shortcuts where intermediate level of melodic-speed or melodic-density (see post 68 ) are omitted.

The melody understands the chord sequentially rather than simultaneously, and therefore the chord is mainly two poles of notes roots and dominant that are 7 semitones or an intervals of 5th apart. So the melody waves between these two poles, utilizing the middle note but also another intermediate not in the chord, which creates also a few intervals of 2nd. This is normally the high-middle excitation in the waving. For high excitation we jump to intervals at an octave or higher.

ALTHOUGH THE DIATONIC SCALE REQUIRES MANY HARMONICS TO BE DEFINED, (within the first 27 harmonics see post 81) IT CAN BE PROVED THAT IT HAS THE LARGEST NUMBER OF MAJOR AND MINOR TRIADS COMPARED TO THE OTHER SCALES.

NEVERTHELESS THE STANDARD PENTATONIC SCALE IS THE MAXIMAL SUB-SCALE OF THE DIATONIC WHICH IS CLOSED TO INTERVALS BY 5TH (7 SEMITONES) IN OTHER WORDS STARTING FROM A NOTE OF THE SCALE BY GOING UP OR DOWN A 5THS (7 SEMITONES) WE ARE AGAIN BACK TO A NOTE OF THE SCALE. THE DIATONIC IS NOT CLOSED. IT IS CLOSED ONLY IF WE TOLERATE EITHER AN INTERVAL OF  5TH OR OF  4TH. EVEN WIT THIS RESTRICTION BY MAKING SUCH MELODIES AS ABOVE AROUND INTERLEAVS BY 5TH, AND MOVING UP AND DOWN CREATES BEAUTIFUL MELODIES

What ever it is improvised with the previous rules , and also follows a balance between repetition (3 times) and resolution (4th time) will result in to simple joyful and beautiful melodies. 

We remind also the concept of harmonic simplicial sub-melody of the full melody.(posts 9,63,65,72 


 Harmonic simplicial sub-melody. Probably best method of creating first the simplicial sub-melody is based on preferring intervals distances of the notes of the simplicial sub-melody (opposite to the previous method) that are large intervals ,namely intervals of 5ths , 4th 6th or 8th.  . The simplicial sub-melody is somehow the centers of the final melody and most often it is one note per chord of the chord progression . It can also be considered as a very simple bass line parallel to the melody. So the rule to choose the simplicial sub-melody is the next
3.1) If we have two successive chords X(1) -> X(2) in the chord progression, and a is the note of the simplicial sub-melody belonging to chord X(1) , and b is the not of the simplicial sub-melody belonging to the chord X(2), then a->b is an interval in the following order of preference 5th, 4th, 8th, 6th. 
If the X(1) -> X(2) are in a diatonic scale and in  the relation of resolution (succesive in the wheel by 4ths) e.g. G->C then we have 3 choices for a->b, the g->c, or b->e, or d->g. If the X(1) -> X(2) are in the relation of relative chords (two common notes) e.g. C->Em then we have 2 choices for a->b, c->g, or e->b. And if the X(1) -> X(2) are in the chromatic or complementary relation of  chords (roots that differ by one step of the scale) e.g. C->Dm, then we have one only choice or a->b, here the c->f. After we have defined the simplicial sub-melody then we create bridges between its notes by smaller intervals e.g. 3rds or 2nds.