Here is a table of the analogy and correspondence of the levels of the musical language and Speaking languages
In this post we go one step further, compared to the post 57, where we extrapolated a chord to a scale, and we create parallel to a chord the basic three melodic patterns as in the post 18 (morphological analysis of pitch patterns of melodies). Adding the direction up or down we get 4 melodic patterns
For this of course we need to remember that we have classified the intervals according to how far away is the next string to play them as harmonic intervals.
All of the above 3 types of melodic patterns should be played parallel and around the fingers and frets shape of a chord.
Now if we want to restrict to creating the 4 melodic moves with notes only from the chord, then the way is simple.
1) An iso-kratic (modal) pattern will be monotone repetition of one note of the chord, while strike the other notes too but we return always to the initial repeating note.
2) A waving (ascending or descending) melodic move is created in the obvious way from notes of the chord it has amplitude intervals of 3rd or 5th and their complementary 6th, 4th, if we ascend or descend to a next octave, always from notes of the chord.
3) A non-waving scaling pattern is essentially an arpeggio of the chord (chord-scale) , except it may go to the next octaves too.
4) A spike is a big interval from notes of the chord and the chord on next octaves. It is at minimum a 5th (7 semitones) or 6th (8 or 9 semitones) and higher (that is 7+n*12 or 8+n*12 , 9+n*12 )
It is important to realize though that a melodic move may be on the transition of two chords utilizing thus 2 chords instead of one!
The themes of a melody consist of a plot or sequence of the 4 basic moves (see post 59) which by itself says an emotional story without the help of the harmony. If we have (as here we assume we do) an underlying chord progression, then utilizing almost all the notes of the chords and one theme for each of the 3-harmonic-types of chord transitions , we may define the set of themes of the melody in easy way. Alternatively we may define a theme for each type of emotion, sad, joy, anxiety or serenity, or a theme for each type of chord respectively minor (sad) major (happy), 7nth or diminished or augmented (anxiety) and r5 (serenity.) The chord progression serves as a way to transform and make variations of the themes. The notes of the simplicial submelody are the centers of the melody that sound longer and are usually the tops and bottoms of the 4 basic melodic moves that create the themes of the melody but also the notes of the underlying chord.
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.
A melodic theme-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(-)(x) or An1Bn2(+)(x) 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) and (x)=1,2,3,4 denotes the dominating density of it is chromatic x=1, if it is diatonic x=2, if it is middle harmonic x=3 and high harmonic x=4 (see post 68) e.g. G5A4(-)(2) . In this way we write the dynamics of he melody as a theme-progression ,much like a chord progression.
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
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!
We summarize the basic concerns in the melodic improvisation
(similar to the syntax of phrase with subject verb and object etc).
1) Always use a finite set of melody motives , themes or moves. A theme may consists of the basic 4 melodic moves. (The theme entity for melodies is so important as the chord in harmony. A theme can be inside a chord or over a chord transition. Conversely any of the 3 types of chord transitions may define a theme for the melody, thus a finite set of themes for a chord progression)
2) Transform these melodic themes or moves which will be the invariant of their transformations. The simpler the themes the easier the transformations.
3) Close it by returning to the initial theme.
The ways to transform a theme are at least the next 5 and combinations of them
1) Translate it in different pitches (within a scale or not changing possibly the pitch distances )
2) Translate in time (repeat it)
3) Invert it in time or change its rhythm (if at the begging is slower and at the end faster it will be now the reverse etc)
4) Invert it or distort it in pitch (Create 1st 2nd 3rd or 4th voice versions, utilizing the chord progression as rules of transformation of the theme, or if it is ascending now it will be descending etc)
5) Change it as morphology (from a non-waving ascending it may become waving ascending or iso-kratic) . We prefer spikes and scaling as the main morphological types, while the waving and isokratic as intermediate bridges.
Here is an example involving these 4 melodic patterns.
If we start with a chord progression we may break the duration of each note of each chord to many times repeating same note and then create fast waving melodies from all these small notes that both make an trill harping of he chord and the same with the bridge to the next chord.Different variations of doing it create different voices but already harmonized due to the initial chord progression. (See e.g. https://www.youtube.com/watch?v=uoqFH-i7jYY )
We may connectthe previous with the next
LATIN JAZZ AND HARMONIC BUTTERFLYING
This butterflying is very often utilizing intervals of 3rds (3 or 4 semitones) and 4ths (5 semitones) and their complementary (6th, 8 and 9 semitones and 5th, 7 semitones when changing octave too), thus it is ascending or descending chords (chord-scales or chord-arpeggios , that is why it is called harmonic butterflying) and it is thus chord-harping too, but it involves also intervals of 2nd (1 or 2 semitones) which correspond to chord transitions. A hidden simplicity or invariant in this butterflying is obviously the underlying chord. This butterflying maybe of waving type of melodic move but the amplitudes of the waves may be intervals of 3rds (3 or 4 semitones) and 4ths (5 semitones), instead of intervals of 1 or 2 semitones as in eastern folk music butterflying. And it can be of course of non-waving and monotone scaling type of melodic move . Obviously this butterflying prefers changing strings tuned by 4ths, rather than moving along a single string as in the Greek Bouzouki butterflying.
See also Paganini solo https://www.youtube.com/watch?v=xhc1PsokFOw
The concept of the centers of a melody within a time interval , can be defined more precisely in mathematical-statistical way as follows: Divide all notes of the melody in to equal smaller ones (e.g. by the smallest duration note on the melody), and then create s a statistical histogram with statistical probabilities of how often the particular note and pitch occurs in the melody. The highest 3 peaks of this histogram define the top 3 centers of the melody within the particular time interval. This may be used to find a chord (according to the local criterion only see post 27) to much the melody in thsi time interval. If we utilize a moving time interval (e.g. of one or few measures) we may define the centers for all the melody. (See in post 27 also the scientific papers http://research.microsoft.com/en-us/um/redmond/projects/songsmith/ and http://research.microsoft.com/en-us/um/people/dan/mysong/ )
If the melody consists of a finite set of repeating themes, and each theme consists of one or more of the 4 basic melodic moves (see post 59 ), them the centers are most often the tops and bottoms of the 4 basic melodic moves but also the notes of the underlying chord. So they constitute what could be said as supper or resistance levels for the pitch to go up or down while waving.
In a triad or 4-notes with 7 nth 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) as the define their character as minor-major and 7nth or extended in general. Therefore these two notes have higher probability to be the notes of the simplicial submelody.
The themes of a melody consist of a plot or sequence of the 4 basic moves (see post 59) which by itself says an emotional story without the help of the harmony. If we have (as here we assume we do) an underlying chord progression, then utilizing almost all the notes of the chords and one theme for each of the 3-harmonic-types of chord transitions , we may define the set of themes of the melody in easy way. Alternatively we may define a theme for each type of emotion, sad, joy, anxiety or serenity, or a theme for each type of chord respectively minor (sad) major (happy), 7nth or diminished or augmented (anxiety) and r5 (serenity.) The chord progression serves as a way to transform and make variations of the themes. The notes of the simplicial submelody are the centers of the melody that sound longer and are usually the tops and bottoms of the 4 basic melodic moves that create the themes of the melody but also the notes of the underlying chord.
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
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!
After the chord progression and simplicial submelody we chose,
THE DEFINITION OF MELODIC BRIDGES THAN LINK TWO SUCCESSIVE CHORDS BETWEEN THEM AND START AND END AT THE NOTES OF THE SIMPLICIAL SUBMELODY.
1) WHICH CHORD-TRANSITIONS (PAIRS OF CHORDS) WILL HAVE A MELODIC BRIDGE! (Usually the chord-trasnitions that are in resolutional relation, or resolutional-like relation)
2) THEN WHICH BRIDGES WILL BE ISOMORPHIC IN PITCH AND RHYTHMIC DYNAMIC SHAPE AND WHICH DIFFERENT, DEFINING THEREFORE A PARTITIONING IN THE BRIDGES.
3) THEN IF IN EACH EQUIVALENCE CLASS OF ISOMORPHIC MELODIC BRIDGES IN THIS PARTITIONING, THE BRIDGES ARE EVENTUALLY ASCENDING OR DESCENDING (This besides the emotional significance, determines also where to play the chord in one of the 3 neighborhoods of the fretboard)
4) FINALLY HOW IN EACH EQUIVALENCE CLASS OF ISOMORPHIC MELODIC BRIDGES IN THE PARTITIONING, THE COMPLICATED PITCH DYNAMIC SHAPE OR WAVING AND RHYTHM WILL BE AS A REPETITION OF SUCH PATTERNS OF PREVIOUS ISOMORPHIC MELODIC BRIDGES, OR VARIATION OF SUCH PATTERNAS S SO NOT TO BE TOO BORING. (This pitch dynamic shape has again a significant emotional meaning)
We give an example of the simplicial sub-melody with the next melody of folk music with Cuatro https://www.youtube.com/watch?v=ob50UXyr1JE
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. Alternatively any descending , ascending or waving sequence of notes at diatonic speed such that the odd or even number of them is exactly the notes of the chord (extended probably by 7nth or 6th) and these motes sound e.g. 3 times more than the notes of the rest of the scaling is a melody that fits the particular chord! Irish melodies do it often. 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.
Another characteristic of the happy and joyful melodies is to define two notes (or interval) for the simplicial sub-melody for each chord so that in over all the melody is maximally harmonic (see post 40) and we 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 we use almost exclusively the maximum harmonic melodic speed that the chords allow (see post 68).
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. 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) It is prefered that intervals of 1,2,3,4 semitones are converted to their complemntary 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 sumblicial 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
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) As more general alternative to the above rules 1)-4) , we may define melodic moves not for each chord but for each chord-transition, and preferably for the X7-->x+1 type of transitions (see the symbolism of post 34) e.g. E7-->Am.
Then the chord X7 has only one note x1 for simplicial submelody the starting note of the melodic move, and the end note x2 of the melodic move is the next simlicial submelody note and one note of the chord x+1 not common with the chord X7. If the latter note x2 is not the root of x+1, it is created a tension that has to be resolved later where x2 would be the root of x+1. In between the x1 and x2, the rule is that at least 2/3 of the notes belong to the underlying chord, and this can be achieved by repeating notes of the underlying chord if necessary. The move x1->x2 may involve each of the chords X7, x+1 , twice in two octaves each instead of once in one octave only, which may create very impressive melodic effects. This gives an even better opportunity to use in the melodic move, intervals of 8th, 4th and 5th (high harmonic speed, see post 68) , that have higher harmonic score than the other intervals (see post 40). The at most 1/3 of the total duration of the move x1->x2 ,of notes that play with underlying the 1st chord but may be outside the starting chord, might be unusually at chromatic and diatonic speed (see post 68), and sometimes might belong to the next chord or even to none of the two chords. The melodic moves x1-->x2 can be called chord-transition melodic moves and must have an element of repetition in length and rhythm. In the transitional Irish melodies that utilize 2-3 only major chords, while the melodic moves are 4-5 or 6-7 , but also in the traditional Greek music of the Aegean Islands, the starting and ending point of the melodic move is during the duration of a single chord and are notes of the chord! But still the rule 2/3 -1/3 for notes internal and external to the chord still holds, and the starting and ending notes of the melodic move may define the simplicial submelody.
6) The harmonic move lasts longer than the transitional dense (chromatic or diatonic harmonic speed) melodic move , as the latter takes less than 30% of the duration of x, and y.
7) From the rule of local fitness of a melody to a chord progression , such a default melody will fit the chord progression.
In the example below the chord progression is Am E7 Am E7 Am E7 Am E7 Am A7 Dm G7 C F E7 Am and the centers of the melody are correspondingly for each of the above chords the E E E E E B A B A A F G E F D A . The melody-moves consist of 10 notes ,the first 9 belong to the first chord and the last 10th to the next. All the moves are on the chord transitions of the form X->(x+1) in the symbolism of the cycle of 24 chords (see post 34). E.g. E7->Am, or Am->E7, or A7->Dm, or G7->C. An exceptions is the transition F->E7. The notes that belong to the chord for each of these moves are 6 from the 9, that is 2/3 of the notes. They achieve it ,as we said , by repeating notes of the chord. And even in the transition F->E7 the notes hat do not belong to the chord F, while F sounds , do belong to the next chord E7 and so they prepare the ear for the next chord. The melody has all the 4 harmonic speeds (see post 68). They start (ignoring the repeating notes) from the root A of Am and end to the root E of E7,they go back and forth, then from the root A of Am go to the dominant B of E7 and back to the root A of Am. Then they repeat. Then from the root A of Am which is also of A7, they go to the middle note F of Dm. Then from the root G of G7 to the middle E of C. Then from the root of F to the chord F to the 4th note (7th) D of E7, and close back to the root A of Am. Starting from the root of X7 and ending in the middle (2nd note) or dominant (3rd note) of (x+1), (e.g. starting at a of A7 and ending at f of Dm) creates a tension, which resolves at the end of the cycle of 16 moves by ending at the root of minor chord (x+1) (here at a of Am).
Here is the result.
(The post has not been written yet completely)
