(This post has not been written completely yet)
This post should be read after reading post 92 and post 96.
As we shall see in the next, the Chord-local 7-notes scale should not be confused with the 7-notes arpeggio-scale of a chord , which requires 2-octaves.
As in general the current music is not restricted to the harmony and melody of only scale but of many scales diatonic or not (multi-tonal music) , we will describe the basic process, based only on the chord progression and not on a particular scale. We have wrote in the past that the chord progression (and also wheels of chords or scales of chords) is a substitute of the old concept of mono-tonal scale harmony.
So let as assume that we start with a cord progression CP=(X(1), X(2) ,...,X(n)) .
Then we will define a 7-notes scale S(i) for each chord X(i) , that it will be called Chord-local scale of the chord X(i).
We assume for simplicity that all chords X(i) are 3-note chords, with notes a(i),b(i) c(i).
Now we define also the set of all such notes a(i),b(i) c(i) for all chords X(i), as the note universe of the chord progression CP and we symbolize it with S(CP) .
For each chord X(i) ={ a(i),b(i) c(i)} we need to define intermediate notes y1(i), y2(i), y3(i) y4(i) so that y1(i)<a(i)<y2(i)<b(i)<y3(i)<c(i)<y4(i). In this way we may have notes to create 2nds 4ths, 6ths and 7nths extensions of the chord.
To discover such notes y1(i), y2(i), y3(i) y4(i), we use at first the previous chord X(i-1) , and next chord X(i+1) in the chord progression CP, and if they are not enough then from the set of notes S(CP) defined as above. If still the notes are not enough to define the y1(i), y2(i), y3(i) y4(i), then we choose ourselves notes that are most natural to do so.
Having defined the set of notes S(i)={y1(i)<a(i)<y2(i)<b(i)<y3(i)<c(i)<y4(i)} for the chord X(i), we notice that we already have a 3+4 notes or a 7-notes scale, which we denote by S(i). WE cal it chord-local 7 -notes scale or Chord-neighborhood 7-notes scale.
If the chord progression is e.g. all the chords of a diatonic scale, then for all chords the scales S(i) are the same diatonic scale (at different modes) and we have a mono-tonal harmony. But in general we may have more than one scale therefore modulations. The scales S(i) may be diatonic scales but maybe also other type of scales like Harmonic minor, or even scales without a particular known name.
Now once we have a chord-local scale for each chord of the chord progression, then a melodic theme created as in the post 92, will give a piece of melody that fits the chord X(i). It was called this this post the
Chord-courtyard melody (sub-melody here), denoted here by M(X(i)) or simply M(i). In total the duration of the sounding of the notes of the melody that belong also to the chord should be longer (preferable more than 2/3 of the total time) compared to the duration of the sounding of the notes ouside the chord and inside the chord-local 7-notes scale.
In addition all the basic
procedures of variation of this melodic theme, like
inner scale translation (see post 100) or
translation-modulation of the theme from scale S(i) to the scale S(i+1) etc are definable. Also
pitch inversions inside these scales,
rhythmic inversions and
dilation (contractions or expansions) or homemorphic variations ,etc as in the post 96, that we repeat here as a summary of the possible variations techniques.
Now as we move from chord to chord in the chord progression , then such 7-notes chord-local scales are defined, also chord-court pieces of the melody M(i) , that we apply variations to them as the scales change, to create finally the complete melody M(CP) of the chord-progression CP.
We repeat some of the discussion of the posts 92 and 96 here. First from, the post 92
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, or micro-rhythmic melodic theme, called MELODIC WORD (a concept from poetry) 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. but also of 8th E.g.one of the most common such dancing pattern (waltz) 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 or 8ths. There is also
acceleration and
deceleration as the melodic theme
starts and ends.
If one wants to use the calculated Harmonic simlicial sub-melody of the chord-progression as in post 104, then inner translation and oscillations that would be inside the chord-local 7-notes scale of the chord and aroundthe note of the harmonic simplicial submelody , then they are modulated when moving at the next chord-local 7-notes scale of the next chord and around the next note of the next chord of the harmonic simplicial sub-melody . Similar remarks apply for the chromatic simplicial sub-melody (see post 104) that usually has two notes per chord.
We remind the calculation of the harmonic simplicial submelody
1) Harmonic simplicial sub-melody. Probably the best method of creating the simplicial sub-melody which 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 or oscilaltion boundaries of the final melody and most often it is one note per chord of the chord progression . They may be also the start and end of the melodic themes. 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
1.1) 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.
1.2) After we have defined the simplicial sub-melody then we may create bridges between its notes by smaller intervals e.g. 3rds or 2nds for a full melody.
The notes of the harmonic submelody of a chord progression may be used to be somehow the centers or oscilaltion boundaries of a final melody and most often. They may be also be the start and end of the melodic themes. It depends if we create melodic themes inside the chord and around of a note of it which serves as it center or melodic themes linking two of them and their successive chords. For the first way , the melodic themes inside the chord and around the note of the harmonic simplicial submelody can be created as in the post 103 using the chord-local 7-notes scale for each one note of the harmonic simplicial submelody.
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, pitch inversion, dilation and rhythmic-inversion transformations. 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). 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. See e.g. the folk Irish melody Kerry Polka below
RULE 4 OF ORDER-TOPOLOGICAL STRUCTURE BALANCE
The melody if it ascend then it descends and vice versa. The imbalance of this rather slight to indicate joy or sadness respectively. (For the Affine or ordert-opolpgical 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 )
The order-topological theme (see post 101 about the Dolphin Language) may be a musical word or micro-rhythmic melodic theme as in post 92, or concatenations of them creating an order-topological shape (see post 101) so that in total the total time duration of notes of it that are notes also of the chord is longer and preferably >=2/3 of the total time compared to the total duration of the notes of it that are outside the chord and its arpeggio-scale (e.g. inside the chord-local 7-notes scale).
Chopin uses an beautiful technique (but also a technique in Greek folk melodies of Rebetika) where , the notes of the melody are most often pairs of simultaneous notes (harmonic intervals) of the arpeggio-scale, but also the notes outside the arpeggio scale are again pairs of simultaneous notes (in harmonic intervals of 3rds, 4ths, 5ths, 6ths, 8ths etc) that are borrowed from the next or previous (or in general any other) chord of the chord progression (or of the underlying 7-notes scale if there is one). In this way even the chromatic outside the chord parts of teh melody have harmony!
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.
And then the discussion from the post 96
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 or oscillations , ascending or descending.
6) Cyclic or balanced behavior in ascending-descending (standing oscillations).
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.
