We remind the reader that a simplicial countermelody is a counterpoint parallel melody (that by parts 2,3,or 1st voice) with much fewer notes that the original melody , about one or twonotes per underlying chord. If it willbe at the lowest octaves it would be simpli called a bass line .
The current suggested method is based one two factors
1) We may easily jump with the intsrument a melodic (3rds) or harmonic (4ths or 5ths) interval at any time. This is so e.g, with a trombone that we shift with the embouchure among the overtones, and as usually we are either in the harmonic intervals 2nd ovtave of the overtones, or the 2nd melodic intervalsovtace of overtones. If we are in a string intrsument tuned by a set of succesive overtones e.g. troll tuning then again by shifting to the neighboring string we have the same easy effect. It can be done also with digital guitars tablet applications tuned at overtones.
2) We may easily make small chromatic intervals (of 2nds) moves. With the trombone thsi is done with the slide for a range of a 4th , 5th or half octave. For a string intrsument tuned by a set of succesive overtones this is done again easily by shifting longitudinally onthe same string.
The improvisational method of creating such beautufull simplicial counter melodies is as follows.
Modt often a melody with many notes has the majority of its intervals as chromatic interavls of 2nds and maybe some melodic (3rds) or harmonic (4ths, 5ths) intervals. But the simplicial countermelody can be more beautiful by havin the minority of the intervals as chromatic and the resy as melodic and harmonic in a way that there is strict sepration.
1) The way to do is is that when the melody is moving we saty as much as possible on thesame note on the string onthe string instriment or on the same overtone across slide range in the trombone ,and if necessary we make a small shift by in interval of semitone or tone (2nds, chromatic intervals) .
2) If this is not possible so we have an harmonically fitting countermelody or when we fell that we want to shift up or down we shift at the trombone by one or two overones up or doen and we adjust the slide to have a note that fits. Similaly with the string instrument we shift by one or two strings and we adjust across the string to find a closest note that fits. E.g. at the lower harmonic octave of overtones of the trombone (Bb2-Bb3) the shifts by overtones are intervals of 4th or 5th, and as it is known a diatonic scale is closed to shifts by such intervals at all notes (except at 1 note) , thus no matter the diatonic scale we are and note on the slide of the trombone such an harmonic shift in 6 from the 7 cases it will lead again inside the scale. Furthermore all the interneduate notes in the 12-notes scale that sound when the slide is moving from one stable note to a next count for the beatiful result , as transitionalnotes and as including all the 12-notes thus giving a sense of completness o the melodic pitches. The same effect can be done with the digital instrument Geoshred pro in the tablet (https://www.youtube.com/watch?v=JTW3WUVDRhM&ab_channel=JordanRudess) where the slidibg of the finger across the digital string has the same effect as the slide of the trombone.It requires of course tohave tune the strings inthe geoshred pro as the overtones of a brass instrument,
If samone is well trained having assimilated the diatonic harmony, then by just listening to the one or to chords of the diatonic scale as background chord progression (e.g. 1M or 3m-4M or 5M7-1M or 5M7-1M-4M etc) he will imediately find with the overtone and the slide the diatonic scale interval by interval gradually without even knowning which diatonic scale it is. I assume it is the same with the cello and violin. We utilize only the emotional and kinesthetic nervous scenter without the optical center (as inharmonicas)
AS IN HARMONY THE BASIC CONCEPTIS THAT OF 3-NOTES CHORD, IN SIMPLICIAL COUNTERMELODIES THE BASIC CONCEPT IS A CHROMATIC TRIAD (TRICHORD) IN OTHER WORDS 3 SUCCESIVE NOTES SEPARATED BY INTERVALS OF 2NDS (CHROMATIC)
AS 3-NOTES CHORDS USUALLY EXTEND TO 4-NOTES CHORDS SIMILARLY THE CHROMATIC TRIADS (TETRACHORDS) ARE EXTENDED TO CHROMATIC TETRADS (TETRACHORDS) AND PENTACHORDS (CHROMATIC PENTATONICS) WITH TOTAL LENGTH A INTERVAL OF 4TH OR 5TH , WHICH WAS ALSO THE BASE HALF-OCTAVE SCALE IN ANCIENT TIMES.
SO FOR EACH CHORD THERE IS NOT MORE THAN A PARALLEL CHROMATIC TRIAD OR TETRACHORD OR CHROMATIC PENTATONIC AS SIMPLICIAL COUNTERMELODY
In over all a mathematical condition of the next type is required for the countermelody to be simplicial
GIVEN A MINIMUM LEAST NUMBER OF NOTES, AND STARTING FROM A NOTE FIND THE MINIMUM TOTAL LENGHT (IN SEMITONES) PATH OF NOTES THAT CONTAINS THEM AND THAT FITS THE HARMONY.
Of course the way to find such solutions of simplicial counter melodies, is e.g. by starting with a note and staying there as long as the harmony is fitting. When the harmony deviates (will deviate in general, that is why we need to know in advance the harmony of the song) for a long time, we chose to shift either up or down, which ever melodically feels better, and we slide till the first note that we find that it fits (will fit for long) the harmony. We stay there and repeat the procedure.
Obviously the result of it is a simplicial countermelody that separates the chromatic with the melodic and harmonic intervals, which is chromato-harmonic effect, like ho he ball moves ingolf: small moves and then very large moves.
We add here a simple technique to improvise over chords too with the trombone which emphasizes the glissando ability of the trombone..
We must notice that from any note we are in the diatonic scale during a chord there is always a note of the chord at most an interval of 3rd away!
1) So the method is tho start with an arbitrary note and correct it with the slide by at moist an interval of 3rd to a note that fits the chord
2) When we want to a much higher or lower note during the chord or because the chord changed we just blow harder or softer for a higher or lower overtone (partia) at the same position and then we correct it if necessary with the slide!
3) The whole process becomes easier if we are on the 3rd octave of overtones where the overtones form the major tonal chord (with a 7nth) . And for thsi the best idea is to utilize a french-horn mouthpiece for the tenor trombone!
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