As we wrote in the post 40, the intervals of 5th/4ths have higher harmonic score than the intervals of 3rd which in their turn have higher harmonic score than the intervals of 2nd.
So many beautiful melodies have this distribution of the percentage of intervals in them. In other words % of 5ths/4ths> % of 3rds % 2nds.
Some of the melodies of the music od Incas, Andes etc, but also of all over the world composers have this property.
The percentage of intervals of % of 5ths/4ths>, % of 3rds or 6ths is called THE HARMONIC (STATISTICAL) PROFILE OF THE MELODY
The percentage of intervals of % of 5ths/4ths>, % of 3rds or 6ths is called THE HARMONIC (STATISTICAL) PROFILE OF THE MELODY
We should notice also that although the diatonic 7-notes scale is closed to intervals of 2nd, 3rds and 5ths or 4ths (but not both) the standard pentatonic scale is closed to intervals by 5th and by 4ths .
We say that a scale is closed to intervals by nth, if and only if starting from any note of it if we shift higher or lower by an interval by nth, we are again in a note of the scale.
Nevertheless , other proportions of percentages of 5ths/4ths/8ths, of 3rds and of 2nd are known to give characteristic types of melodies among the different cultures.
Other observed HARMONIC PROFILES of percentages are
%2nds> %3rds+%4ths/5ths/8ths
(e.g. the 2nds double more than the rest of the intervals, ratio 3:1 ) :
Oriental and Arabic Music, GypsyJazz, and Jazz Stephan Grappelli soloing
%3rds+%4ths/5ths/8ths>% 2nds :
(e.g. the 2nds less than half compared to the rest of the intervals,ratio 3:1 )
Music of Incas, and countries of the Andes. Celtic music Ancient Egyptian music
The way to create melodies with at least 2/3 of the intervals to by the larger intervals of 3rds , 5ths/4ths or 8ths, is to apply harping in a chord say with 6 or 8 steps on notes, where it is added only one intermediate note in the chord (e.g. 7nh, 6th, 4th or 2nd) and so that the created intervals of 2nd are only 2 in the 6 or 8 intervals. Then we shift to a relative chord an interval of 3rd away or to a resolution transition which is a chord in an interval 5th or 4th away , or we even shift to a chord a 2nd away in which case we do not use any additional note, and we continue so. So finally %3rds+%4ths/5ths/8ths>=2*(% 2nds) .
A way to take short notes of such beautiful melodies is to write the chord progression, and then one note with small letters above or below the chord denoting which neighboring note (by interval of 2nd usually) is the extension of the chord in the melody.
%4ths/5ths/8ths/6th>%3rds>% 2nds :
(e.g. the 2nds +3rds less than half compared to the rest of the intervals,ratio 3:1, )
The way to create such melodies with at least 2/3 of the intervals to by the larger intervals of 5ths/4ths or 8ths, compared to 3rds , and 2nds is to apply the same technique as before, but when harping inside the chord we use the intervals of 4th and 5th and 8th of the normal position and 2 inversions, instead of the 3rds in the normal position! In this way in the fast soloing or harping on the notes of the the chord has more intervals of 4th, 5th and 8th than of 3rds!
Nevertheless the chord progression over which this technique produces fast melodies may contain very fast chord changes, and may not be identical with the actual chord progression that the instruments play as background to the melody. This is the concept of "ghost chords" in the melody as described in the post 87. E.g. The full ghost chord progression may be D G D G D A D. While the chords really played is only D.
For independent from chord progression free improvised melodies a simple way to create melodies with number of 2nds intervals <=50% is to alternate intervals of 2nds with intervals of 3rds, 4ths, 5th,s and 6ths. Or a way to create melodies with number of 2nds intervals <=33% is
alternate for every one interval of 2nds two intervals of 3rds, 4ths, 5th,s and 6ths.
THEREFORE EVERY CHORD PLAYS THE ROLE OF A MINI CENTRAL SUB-SCALE AROUND WHICH THE MELODY DANCES FOR A WHILE ALTHOUGH IT IS STEPPING ON OTHER NOTES TOO BUT NOT FOR LONG, THAT ARE MAINLY THE NOTES OF THE NEXT CHORD-SUB-SCALE.
Another characteristic of such beautiful melodies with the "right harmonic proportions" is that they exhibit the effect of acceleration/deceleration in the movement exactly as the physical bodies. In other words, they start with slow speed (intervals of 2nds), accelerate (intervals of 3rds and then intervals of 5ths/4ths) and finally decelerate when reaching to the right center-note (from intervals of 5ths/4th to intervals of 3rds and then to intervals of 2nds), Of course there are many shortcuts where intermediate level of melodic-speed or melodic-density (see post 68 ) are omitted.
Nevertheless , other proportions of percentages of 5ths/4ths/8ths, of 3rds and of 2nd are known to give characteristic types of melodies among the different cultures.
Other observed HARMONIC PROFILES of percentages are
%2nds> %3rds+%4ths/5ths/8ths
(e.g. the 2nds double more than the rest of the intervals, ratio 3:1 ) :
Oriental and Arabic Music, GypsyJazz, and Jazz Stephan Grappelli soloing
%3rds+%4ths/5ths/8ths>% 2nds :
(e.g. the 2nds less than half compared to the rest of the intervals,ratio 3:1 )
Music of Incas, and countries of the Andes. Celtic music Ancient Egyptian music
The way to create melodies with at least 2/3 of the intervals to by the larger intervals of 3rds , 5ths/4ths or 8ths, is to apply harping in a chord say with 6 or 8 steps on notes, where it is added only one intermediate note in the chord (e.g. 7nh, 6th, 4th or 2nd) and so that the created intervals of 2nd are only 2 in the 6 or 8 intervals. Then we shift to a relative chord an interval of 3rd away or to a resolution transition which is a chord in an interval 5th or 4th away , or we even shift to a chord a 2nd away in which case we do not use any additional note, and we continue so. So finally %3rds+%4ths/5ths/8ths>=2*(% 2nds) .
A way to take short notes of such beautiful melodies is to write the chord progression, and then one note with small letters above or below the chord denoting which neighboring note (by interval of 2nd usually) is the extension of the chord in the melody.
%4ths/5ths/8ths/6th>%3rds>% 2nds :
(e.g. the 2nds +3rds less than half compared to the rest of the intervals,ratio 3:1, )
The way to create such melodies with at least 2/3 of the intervals to by the larger intervals of 5ths/4ths or 8ths, compared to 3rds , and 2nds is to apply the same technique as before, but when harping inside the chord we use the intervals of 4th and 5th and 8th of the normal position and 2 inversions, instead of the 3rds in the normal position! In this way in the fast soloing or harping on the notes of the the chord has more intervals of 4th, 5th and 8th than of 3rds!
Nevertheless the chord progression over which this technique produces fast melodies may contain very fast chord changes, and may not be identical with the actual chord progression that the instruments play as background to the melody. This is the concept of "ghost chords" in the melody as described in the post 87. E.g. The full ghost chord progression may be D G D G D A D. While the chords really played is only D.
For independent from chord progression free improvised melodies a simple way to create melodies with number of 2nds intervals <=50% is to alternate intervals of 2nds with intervals of 3rds, 4ths, 5th,s and 6ths. Or a way to create melodies with number of 2nds intervals <=33% is
alternate for every one interval of 2nds two intervals of 3rds, 4ths, 5th,s and 6ths.
THEREFORE EVERY CHORD PLAYS THE ROLE OF A MINI CENTRAL SUB-SCALE AROUND WHICH THE MELODY DANCES FOR A WHILE ALTHOUGH IT IS STEPPING ON OTHER NOTES TOO BUT NOT FOR LONG, THAT ARE MAINLY THE NOTES OF THE NEXT CHORD-SUB-SCALE.
A simple and common way to create the right proportions of statistical frequencies of intervals as above is the next. Take for example a simple chord harping-waving that contains also with the rules as in post 92, 103 , less than 50% of the time also notes outside the chord. And then half of this simple theme translate it one octave higher, and so oscillate between the two octaves. Normally the initial non-translated melody would have intervals of 2nd, 3rd, and 5th. The interval of 3rd will become 6th , the interval of 5th, a 4th and an interval of 2nd , will become 7nth. In this way also the statistical profile of such melodies will have more frequently high intervals of 5th, 6th, 7nth and 8th compared to intervals of 2nds (see post 93 ) .g. the folk Irish melody Kerry Polka below
Within the current improvisation method of random melodies with high harmonic statistical profile, is the improvisation method for relaxing and meditation based of power-chords as in post 35. This is mainly alternating a power chord of interval of 5th/4th with a power chord of interval 3rd/6th, or in general alternating a power chord of interval 5th/4th with any 3 notes which are chords or not. The next videos describe it for the case of a Celtic harp.
Another characteristic of such beautiful melodies with the "right harmonic proportions" is that they exhibit the effect of acceleration/deceleration in the movement exactly as the physical bodies. In other words, they start with slow speed (intervals of 2nds), accelerate (intervals of 3rds and then intervals of 5ths/4ths) and finally decelerate when reaching to the right center-note (from intervals of 5ths/4th to intervals of 3rds and then to intervals of 2nds), Of course there are many shortcuts where intermediate level of melodic-speed or melodic-density (see post 68 ) are omitted.
ALTHOUGH THE DIATONIC SCALE REQUIRES MANY HARMONICS TO BE DEFINED, (within the first 27 harmonics see post 81) IT CAN BE PROVED THAT IT HAS THE LARGEST NUMBER OF MAJOR AND MINOR TRIADS COMPARED TO THE OTHER SCALES.
NEVERTHELESS THE STANDARD PENTATONIC SCALE IS THE MAXIMAL SUB-SCALE OF THE DIATONIC WHICH IS CLOSED TO INTERVALS BY 5TH (7 SEMITONES) IN OTHER WORDS STARTING FROM A NOTE OF THE SCALE BY GOING UP OR DOWN A 5THS (7 SEMITONES) WE ARE AGAIN BACK TO A NOTE OF THE SCALE. THE DIATONIC IS NOT CLOSED. IT IS CLOSED ONLY IF WE TOLERATE EITHER AN INTERVAL OF 5TH OR OF 4TH. EVEN WIT THIS RESTRICTION BY MAKING SUCH MELODIES AS ABOVE AROUND INTERLEAVS BY 5TH, AND MOVING UP AND DOWN CREATES BEAUTIFUL MELODIES
NOW FAST ALMOST RANDOM IMPROVISATION OF A MELODY CAN BE SO THAT SUCH A STATISTICAL PROFILE IS KEPT! THIS IS DONE IN A DIFFICULT WAY WITH THE GUITAR FRETBOARD OR CHROMATIC INSTRUMENTS , BUT WITH INSTRUMENTS THAT ARE OF DIATONIC TOPOLOGY LIKE PIANO-KEYBOARDS, ACCORDIONS, DIATONIC FLUTES, DIATONIC PAN-FLUTES , SAXOPHONES, CLARINETS, ZAMPONA FLUTES ETC IT IS FEASIBLE AND MUCH EASIER. ONE HAS JUST TO REGULATE HIS HANDS MOVEMENTS E.G. ON THE PIANO KEYBOARD SO THAT THE SUCCESSIVE DISTANCES ON THE WHITE ONLY (OR BLACK-ONLY ) KEYS IS OF THE REQUIRED TYPE OF INTERVALS E.G. MAINLY >= OF 3RDS. SIMILARLY VERY HARMONIC SUCH RANDOM MOVEMENTS MELODIES CAN BE CONDUCTED ON ZAMPONA PANFLUTES THAT PUT THE NOTES IN 2 ROWS IF EVEN OR ODD ORDER IN THE DIATONIC SCALE. OFCOURSE ALL THIS IS EVEN MORE SMOOTH AND EASY OF IT IS DONE ON A MOBILE TOUCH-SCREEN APP OF SUCH INSTRUMENTS (ZAMPONA, PIANO, HANDPAN ETC)
