So far in post 9, we have developed the chord-progression first and afterwards the melodic themes, system of musical composition, which is mainly the pattern that takes place in improvisation , especially in jazz.
The main reason for this, is of course, because chord progressions is a simpler pattern than the melody. But what if the melodic themes is a simpler pattern than the chords progression?
We must remark here that there melodies that either
a) No single chord is best for accompany it all
b) or any chord can accompany it.
c) Too many chords fast changing (ghost chords) are appropriate to accompany it.
d) A small number of chords but only very fast changing (ghost chords) are appropriate to accompany it.
THE STATISTICAL TWO-NOTES HARMONY
What if the melodic theme is as here the simplicial melodic themes which is simple a melodic interval of two notes (actually melodic vectors as orientation does matter) which is simpler than the 3 notes of chord, and we start composing the melody with such melodic intervals? From this point of view there are only 3 types of such simplicial melodic themes: 1) Of intervals of 2nd and inverses (Chromatic transitions) 2) of intervals of 3rd and inverses (melodic transitions) 3) of intervals of 5th or 8ths and inversions (Harmonic transitions) .
These three types of transitions of notes , namely chromatic, melodic and harmonic are like the three basic relations of chords transitions (see post 30). So improvisation of a melody which is sounding alone without chords underlying it, but probably only some rhythmic percussion can be conducted solely by choosing each time how much melody, harmony or chrome we want!
See also post 68 about the 3 melodic densities or speeds (chromatic, melodic, harmonic)
In the context of 2-notes harmony or Interval harmony of melodies the closest counterpart of a chord is an interval of 5th or its inverae an interval of 4th. Oscillations between tow notes at an interval of 5th or 4th is the counterpart of the guitar harping within a chord.
Of course we can afterwards add 3-note or 4-notes chords and study such an harmony of the melody. But the visible and undisputed harmony of the melody is the two notes harmony, or the statistics and sequence of intervals of the melody.
If such a two-notes harmony was tried to be covert it to a 3-notes chords harmony, not only the extension would not be unique, but also it may be that a close fitted such extension might give a so much fast changing chord progression, that would rather be ghost-chords progression (see post 87 ).
For example let us assume that we improvise a melody that we ascend with such steps that would suggest chords at the odd steps of the diatonic scale (I, II, V) and the descend with steps that suggest the even chords (II, IV, VI). The change from odd to even and vice versa is done with intervals of 2nds, 7nths and 4ths.
Usually the melody would give so fast changing chords that would be classified as ghost chords (see post 87 ).
It is important of course to have here the simplest possible relation of the simplicial melodic themes with the chords , which is one note per chord or the melodic theme is the transition bridge between successive chords.
One of the best methods to choose relation of the notes of the simplicial submelody (one note per chord) and the chord progression, is so that the intervals between the notes are minimized (1 semitone) or maximized (interval of 5th or octave and inverses). For successive chords in the wheel of 4th both extremes are feasible. For chords that are relatives, intervals of 4ths are possible, while for chords with roots one tone apart, intervals of 5th are also possible. For chords with roots one semitone apart, obviously the minimum 1 semitone is feasible. Of course a meaningful (in respect to joy and sadness , anxiety and serenity) repetitive pattern must occur both in the simplicial melodic themes and in the chord progression.
The notes of the simplicial melodic themes (one for each chord at its simplest version) need not justify the chord progression. The justification will be with other embellishment notes that make the full melody as contrasted to the simplicial sub-melody. The initial justification of the chord progression is the feelings that it creates parallel to the simplicial sub-melody. The chord progression magnifies the attention and feelings of parts of the simplicial sub-melody and shrinks the feelings and roles of other parts of it. Of course both flows that of the simplicial melodic themes and of the chords progression must be harmonically compatible. In other words each note of he simplicial sub-melody must be also a note of the underlying chord.
As the wheel of 4ths is the basic tool to design chord progressions, so scales is the basic rule to design melodic vectors (simplicial melodic themes).
Diatonic instruments like Irish whistles, and flutes, diatonic panflutes etc are best for melodic improvisations with melodies with many intervals of 2nds. Intervals of 2nds provide the feeling of pitch continuation in the melody (chromaticity) but not of harmony.
The Zampona pan-flute and the melodic corridor arrangements of the notes of a diatonic scale (see post 94 ) are best for melodies with high harmonic profile that is % 2nds<=50%. or
% 2nds<=33%.
THE "CHORD-AND-TRANSITION MELODIC THEME" METHOD OF UNACCOMPANIED MELODIC IMPROVISATION.
Studying some of the musical pieces of Bach for solo instruments (e.g.
We remind the reader what we wrote in post 82, about creating melodies by melodic micro-themes. The reason we repeat the discussion here is that although this method initially was devised to compose melodies when already a chord progression is given, some of its aspects can apply also as a method to create chord-independent melodies without having in advance a chord progression, but creating the melody with sufficient hidden harmony in it. Here is what we wrote
We enlarge below more and we give an example.
We must remark here that there melodies that either
a) No single chord is best for accompany it all
b) or any chord can accompany it.
c) Too many chords fast changing (ghost chords) are appropriate to accompany it.
d) A small number of chords but only very fast changing (ghost chords) are appropriate to accompany it.
THE STATISTICAL TWO-NOTES HARMONY
What if the melodic theme is as here the simplicial melodic themes which is simple a melodic interval of two notes (actually melodic vectors as orientation does matter) which is simpler than the 3 notes of chord, and we start composing the melody with such melodic intervals? From this point of view there are only 3 types of such simplicial melodic themes: 1) Of intervals of 2nd and inverses (Chromatic transitions) 2) of intervals of 3rd and inverses (melodic transitions) 3) of intervals of 5th or 8ths and inversions (Harmonic transitions) .
These three types of transitions of notes , namely chromatic, melodic and harmonic are like the three basic relations of chords transitions (see post 30). So improvisation of a melody which is sounding alone without chords underlying it, but probably only some rhythmic percussion can be conducted solely by choosing each time how much melody, harmony or chrome we want!
See also post 68 about the 3 melodic densities or speeds (chromatic, melodic, harmonic)
In the context of 2-notes harmony or Interval harmony of melodies the closest counterpart of a chord is an interval of 5th or its inverae an interval of 4th. Oscillations between tow notes at an interval of 5th or 4th is the counterpart of the guitar harping within a chord.
Of course we can afterwards add 3-note or 4-notes chords and study such an harmony of the melody. But the visible and undisputed harmony of the melody is the two notes harmony, or the statistics and sequence of intervals of the melody.
If such a two-notes harmony was tried to be covert it to a 3-notes chords harmony, not only the extension would not be unique, but also it may be that a close fitted such extension might give a so much fast changing chord progression, that would rather be ghost-chords progression (see post 87 ).
For example let us assume that we improvise a melody that we ascend with such steps that would suggest chords at the odd steps of the diatonic scale (I, II, V) and the descend with steps that suggest the even chords (II, IV, VI). The change from odd to even and vice versa is done with intervals of 2nds, 7nths and 4ths.
Usually the melody would give so fast changing chords that would be classified as ghost chords (see post 87 ).
It is important of course to have here the simplest possible relation of the simplicial melodic themes with the chords , which is one note per chord or the melodic theme is the transition bridge between successive chords.
One of the best methods to choose relation of the notes of the simplicial submelody (one note per chord) and the chord progression, is so that the intervals between the notes are minimized (1 semitone) or maximized (interval of 5th or octave and inverses). For successive chords in the wheel of 4th both extremes are feasible. For chords that are relatives, intervals of 4ths are possible, while for chords with roots one tone apart, intervals of 5th are also possible. For chords with roots one semitone apart, obviously the minimum 1 semitone is feasible. Of course a meaningful (in respect to joy and sadness , anxiety and serenity) repetitive pattern must occur both in the simplicial melodic themes and in the chord progression.
The notes of the simplicial melodic themes (one for each chord at its simplest version) need not justify the chord progression. The justification will be with other embellishment notes that make the full melody as contrasted to the simplicial sub-melody. The initial justification of the chord progression is the feelings that it creates parallel to the simplicial sub-melody. The chord progression magnifies the attention and feelings of parts of the simplicial sub-melody and shrinks the feelings and roles of other parts of it. Of course both flows that of the simplicial melodic themes and of the chords progression must be harmonically compatible. In other words each note of he simplicial sub-melody must be also a note of the underlying chord.
As the wheel of 4ths is the basic tool to design chord progressions, so scales is the basic rule to design melodic vectors (simplicial melodic themes).
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.
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 : or % 2nds<=50%.:
(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
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.
We must remark here that there are melodies that either
a) No single chord is best for accompany it all
b) or any chord can accompany it.
c) Too many chords fast changing (ghost chords) are appropriate to accompany it.
d) A small number of chords but only very fast changing (ghost chords) are appropriate to accompany it.
1) Such melodies are e.g. fast sequential successive sounding by 2nds for 2 or 3 octaves
2) But very close to is also melodies with alternating 3rds or 6ths and 2nds in a diatonic scale
MELODIES WITH 100% INTERVALS OF 2NDS
Such melodies give the feeling of coherence in the melodic moves.
We must notice that even if we use, say 100%, intervals of 2nds in a scale, we may still create harmony. E.g. in such an extreme case of melody, the harmony is created by persisting and passing again and again from notes of an interval of the scale. E.g. if such an interval of successive notes of the scale is x(i), x(i+1), x(i+2) , or x(i), x(i+1), x(i+2), x(i+3), x(i+4) , and the time spend on each of these notes is in the average equal, then the harmony and underlying chord that is created is the x(i), x(i+2), x(i+4) because these are more than the x(i+1), x(i+3), and thus the melody spends more time in the chord x(i), x(i+2), x(i+4) among other chords for the time that is in the interval x(i), x(i+1), x(i+2), x(i+3), x(i+4).
SPENDING MORE TIME ON SPECIFIC NOTES:
Similarly if we take again the extreme and simplistic example of melodies with 100% intervals of 2nds, and we want for a time interval to have as harmony and underlying accompanying a chord X=(y1,y2,y3), then its about sufficient to spent about equal time to all other notes except in one or more of these notes y1,y2,y3, that we spent much more time (making theme temporary centers of the melody) creating thus the effect of this underlying chord harmony. Of course if we did not have the restriction of 100% intervals by 2nds, another method would be instead of spending more time to the notes of the chord , spending almost no time at all to notes not to the chord.
On the other hand if %3rds+%4ths/5ths/8ths>=2*(% 2nds) or number of 2nds intervals <=33% then essentially the melody is sequence of chords linked by intervals of 2nds.
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) .
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. Which of course usually mean of course in a diatonic scale that we arpeggio on chords successively one after the other in any order. But as we have said for god chord progressions, it is better to arpeggio i minor or major successive chords on the wheel by 4ths and 3rds
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.
String instruments, that the melody is played mainly along a string (e.g. Greek Bouzouki, sazi etc) the scales that are favored for melodies improvisation are ones with many 2nds and in particular scales with many occurrences of semitone intervals of 2nds (oriental type)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 : or % 2nds<=50%.:
(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
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.
We must remark here that there are melodies that either
a) No single chord is best for accompany it all
b) or any chord can accompany it.
c) Too many chords fast changing (ghost chords) are appropriate to accompany it.
d) A small number of chords but only very fast changing (ghost chords) are appropriate to accompany it.
1) Such melodies are e.g. fast sequential successive sounding by 2nds for 2 or 3 octaves
2) But very close to is also melodies with alternating 3rds or 6ths and 2nds in a diatonic scale
MELODIES WITH 100% INTERVALS OF 2NDS
Such melodies give the feeling of coherence in the melodic moves.
We must notice that even if we use, say 100%, intervals of 2nds in a scale, we may still create harmony. E.g. in such an extreme case of melody, the harmony is created by persisting and passing again and again from notes of an interval of the scale. E.g. if such an interval of successive notes of the scale is x(i), x(i+1), x(i+2) , or x(i), x(i+1), x(i+2), x(i+3), x(i+4) , and the time spend on each of these notes is in the average equal, then the harmony and underlying chord that is created is the x(i), x(i+2), x(i+4) because these are more than the x(i+1), x(i+3), and thus the melody spends more time in the chord x(i), x(i+2), x(i+4) among other chords for the time that is in the interval x(i), x(i+1), x(i+2), x(i+3), x(i+4).
SPENDING MORE TIME ON SPECIFIC NOTES:
Similarly if we take again the extreme and simplistic example of melodies with 100% intervals of 2nds, and we want for a time interval to have as harmony and underlying accompanying a chord X=(y1,y2,y3), then its about sufficient to spent about equal time to all other notes except in one or more of these notes y1,y2,y3, that we spent much more time (making theme temporary centers of the melody) creating thus the effect of this underlying chord harmony. Of course if we did not have the restriction of 100% intervals by 2nds, another method would be instead of spending more time to the notes of the chord , spending almost no time at all to notes not to the chord.
On the other hand if %3rds+%4ths/5ths/8ths>=2*(% 2nds) or number of 2nds intervals <=33% then essentially the melody is sequence of chords linked by intervals of 2nds.
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) .
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. Which of course usually mean of course in a diatonic scale that we arpeggio on chords successively one after the other in any order. But as we have said for god chord progressions, it is better to arpeggio i minor or major successive chords on the wheel by 4ths and 3rds
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.
Diatonic instruments like Irish whistles, and flutes, diatonic panflutes etc are best for melodic improvisations with melodies with many intervals of 2nds. Intervals of 2nds provide the feeling of pitch continuation in the melody (chromaticity) but not of harmony.
The Zampona pan-flute and the melodic corridor arrangements of the notes of a diatonic scale (see post 94 ) are best for melodies with high harmonic profile that is % 2nds<=50%. or
% 2nds<=33%.
THE "CHORD-AND-TRANSITION MELODIC THEME" METHOD OF UNACCOMPANIED MELODIC IMPROVISATION.
Studying some of the musical pieces of Bach for solo instruments (e.g.
BWV 1013 - Partita in A Minor for Solo Flute https://www.youtube.com/watch?v=Datoqxx-biw) we may inspired for the next method of unaccompanied improvised soloing:
The melody is like a man wandering-walking in a town, who spends much time at squares and garden of the town that his is exploring. The squares and garden are the chords, played in the solo , preferably a single chord spanned in two octaves, At this time of the soloing the emphasis is on the harmony. But when continuing till the next "garden or square" then the emphasis is on the melodic themes and their affine structure dynamics (see post 97 and 101). How much time is spend in "gardens" ( chords) or "street-walking" (transition melodic themes) is a matter of choice of the improviser. If the melody is unaccompanied, then at the same time the chord progressions is improvised in this way.
We remind the reader what we wrote in post 82, about creating melodies by melodic micro-themes. The reason we repeat the discussion here is that although this method initially was devised to compose melodies when already a chord progression is given, some of its aspects can apply also as a method to create chord-independent melodies without having in advance a chord progression, but creating the melody with sufficient hidden harmony in it. Here is what we wrote
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).
PITCH OSCILLATIONS AND THE MELODIC MICRO-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. In this way by going up and down the diatonic scale, this very 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 melodic micro-themes when improvised rhythmically (especially within a diatonic scale) , with statistically higher percentage of intervals of 3rds (4ths, 5ths also) compared to intervals of 2nds , will create chord-independent melodies with good harmony in them!
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.
PITCH OSCILLATIONS AND THE MELODIC MICRO-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. In this way by going up and down the diatonic scale, this very 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 melodic micro-themes when improvised rhythmically (especially within a diatonic scale) , with statistically higher percentage of intervals of 3rds (4ths, 5ths also) compared to intervals of 2nds , will create chord-independent melodies with good harmony in them!
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
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 )
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 statistically to all , some or none of the previous rules to some or of the chords.
We enlarge below more and we give an example.
