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Sunday, June 16, 2019

234. THE MAGIC AEROPHONE TRUMPET FOR IMPROVISATIONAL MEDITATION. AEROPHONE DIDGERIDOOS(CHROMATIC/OVERTONES FUJARAS) WITH TRUMPET ACOUSTICS.

THE MAGIC AEROPHONE-FIPPLE TRUMPET. AEROPHONE DIDGERIDOOS(CHROMATIC/OVERTONES FUJARAS)  WITH TRUMPET ACOUSTICS.
LONG TUBE AEROPHONES (CHROMATIC/OVERTONES WINDS)  WITH FIPPLE ,SIMILAR TO FUJARAS/DIDGERIDOOS, TRUMPETS AND BRASS WINDS (ratio 80< Length/Bore and about equal 125 as in trumpets ) ?
It is known that many  long tube winds have been invented with cane reeds (like  coils either double reeds  e.g. the Rackett  https://www.youtube.com/watch?v=QwPgiVCVxEA  https://www.youtube.com/watch?v=d9_ma4ITRSc or single reed like Mr curly of Lindsay Polak https://www.youtube.com/watch?v=Iu60MwpMiow  https://www.youtube.com/watch?v=XNO97-mPP8U&t=14s) or lips-reeds in trumpets and other brasswinds. A trumpet that the sound is produced by the lips is a  lips-reed wind with closed-open acoustics that normally have only odd number harmonics (overtones) . Nevertheless because of the gradual cone at the end, as with the saxophone  eventually because of a complicated phenomenon of acoustics  both odd and even number of overtones. Still strictly speaking an aerophone is not producing the sound from a reed, but by a fipple or rim blowing. A modern trumpet at Bb was tube length of 1.482 m and is producing 8 overtones, the first is not possible to play so from 2nd to 8th are C4 G4 C5 E5 G5 A5 C6. These 7 notes are essentially part of an arpeggio of the C major chord with 7nth within 2 octaves. The keys-valves allow for 6 more series of such harmonics each one a semitone lower. 

So what if the same acoustics are derived as aerophone winds with fipples? Fujara and didgeridoos are simplistic  cases of them with close air acoustics at the side of the mouth but they can be rendered to open-open acoustics with fipples. Such winds have not been elaborated in the same way with valves etc as the brass lips-reeds winds.



The fujaras that are known if they have large bore inner diameter and thus length/bore ratio less than 80 will not belong to the acoustic and musical effect described here (sliding whistle over a dense scale of higher harmonics)
Examples of Fujaras
https://www.youtube.com/watch?v=y8Wzb3tLPCs

In the next we not only use the length to bore ratio between 80 and 125, 80< Length/Bore and about equal 125, but also to tune it to a particular note e.g. Bb we use as length the wavelength of the note two octaves lower. E.g. the wavelength of Bb3 is 148 cm (see http://pages.mtu.edu/~suits/notefreqs.html) but the root note will be by the 4th harmonic that is two octaves higher Bb5. Thus these open-open acoustics as far as Length/bore ratio and harmonics are closer to the french-horn rather than trumpet.

I made one such aerophone trumpet from a 97 cm long PVC pipe with inner diameter 12mm (thus Length/bore ratio= 970/12=80.83) and with a fipple from a Sweet tone Clarke whistle C5. I opened 4 holes above the middle of the tube (corresponding to the 2nd harmonic) that as in the trumpet keys give an increase of the tone by 1 semitone by 2 by 3 and by 4 semitones (one more key than trumpets) .The action is mainly on the 6th and 5th octave. The base not is F5.


As 2nd version o the holes we open a hole at the 2/3 of the length (corrected higher by above 80% of the more diameter) which corresponds the 3rd harmonic and two holes  that give sequentially 2 semitones above it. And we also we mark the middle of the tube (that would correspond to  thump hole giving the roo one octave higher, thus 2nd harmonic) but we do not open a hole there, we only open again 3 holes that give sequentially 1 tone  1  semitone and 1 semitone above it. In this setting of 5 holes (3+2) we incorporate almost the natural minor, the double harmonic minor and the harmonic minor in the main octave (which contains the 1-3-1 semitones pattern and has 5# and 2# in place of 5 and 2. The harmonic minor has only 5# in place of 5 and 2 while the natural minor has 5 and 2 ) which is chromatic feeling that complements the strongly harmonic feeling of the arpeggio of the major chord of each hole as higher harmonics). Strictly speaking the holes scale is the parachromatic Byzantine which is in semitones 1-2-3-2-1-1-3 (in steps of  F major it is 5, 5# 6, 1, 2, 2# 3 5).When we open all the lower 3 holes a major 3rd interval appears , while of we open only the upper two holes a minor 3rd interval appears. Alternating these two we get nice harmony.  In the modern trumpet the keys or valves add seven semitones within an interval of 5th thus  creating  in total 7 different series of overtones a semitone each away from the previous starting from the first one defined by the tube. In a guitar this would correspond to have 7 strings each one having pitch one semitone higher than the previous. Each string defines by its own a full sequence of harmonics. This is somehow what we could do here also except as it is not easy to reach the holes at the end of the tube we could open 4 above the  5th note and including 5th , 5 holes .  Thus as a scale it would be the chromatic (5, 5#, 6, 6#  7 )

Then I made a 2nd one which feels even better (because the ratio is higher 104 and the bore larger) without holes  . I made this 2nd   aerophone didgeridoo from a 172 cm long PVC pipe with inner diameter 16.5 mm (thus Length/bore ratio= 172/1,65=104.24) and with a fipple from a generation whistle at Bb . I did not opened holes as the variation of pitch was relatively easy and desne in the harmonics.The action is mainly on the 6th  and 5th octave. The base note is G5.



These winds should not be confused with the Mosenos that are similarly long and with a fipple but they still play at the 1st and 2 harmonics mainly with small Length/bore ratio (e.g. 20) compared to 80.

The most important characteristic of these aerophone trumpet, winds are

1) They need not be bass , but on octaves from 7nth to 4th etc
2) The sound is not really one note but rather like a chord with many hidden harmonics
3) They must have very high Length/bore ratio above 80 and preferably around 125
4) They behave in the pitch of the sound like sliding whistles with a continuum of pitches but not entirely on all frequencies but on a dense grid of harmonics (certainly more than 12 chromatic notes in the octave) 
5) They are very satisfying in playing like natural human whistling but unlike it or unlike the violin without frets, the harmonics give a natural scale of "frets"  that the pitch falls in it which is very harmonic to listen . It is so because the relative change o the pitch is determined always by harmonics.
6) The harmonics are very easy to obtain not by overblowing (as in standard overtone whistles)  but by simple blowing even under-blowing. 
7) Holes are not necessary for hem. Only if the Length/bore ratio is much less than 125, e.g. 80 then 4 choles (reachable by the hands) at equal pitch distances of one semitone are adequate to help small chromatic changes of 1, 2 3 or 4 semitones (in trumpets the 3 keys help for 1,2 and 3 semitones). The reason that 4 semitones is added is because  a  sequence of alternating minor-major thirds gives chords on every 3 notes.
8) Such winds are so much so as to read an existing  written melody from musical notes and play but a melody inside you to improvise and meditate .

When the L/B ratio is above 100 there is not even need for holes because the change of pitch by the change of blowing power is very sensitive and effective. But if one insists in making it easily chromatic then one hole close at the end of the tube at 0.9438 of the total length higher (plus about one inner diameter) will  give a hole of one semitone higher pitch. In the modern trumpet the keys or valves add seven semitones within an interval of 5th thus  creating  in total 7 different series of overtones a semitone each way from the previous starting from the first one defined by the tube.  Here in the picture below are two such aerophones with trumpets acoustics  one in G5 176.02 cm and one in Bb5 (like the lips-reed trumpet)  of 148.2 cm The length is more or less the theoretically expected by the wavelength at the 3rd octave  (G3 , Bb3)  e.g. here http://pages.mtu.edu/~suits/notefreqs.html The actually sound seems also as if having hidden root frequencies at the 2nd octave (G2 , Bb2 ) which makes it beautiful and harmonious. There is also a soft resistance in blowing which makes it satisfying.
The inner diameter of the bore is about 12mm and the tube I used is irrigation pipe. The pictures below for a first experimental assessment. As fipple I used that of generation whistles at Bb4. The feeling of the harmonics fixing your "whistling"at the right exact pitch is very satisfying, as well as the fiddling at any desired pitch like a violin with very dense frets on its  fingerboard, defined by the harmony of the overtones.  The sound is like that of waters, or the sound that often pigeons  make when they are flirting. Still it is harmonic like chord and whistling. The sound is not loud but that is exactly what sometimes needs in order not to disturb the neighbors, it is sweet and very appropriate for meditation. I prefer these aerophone trumpets for improvisational meditation compared the Shakuhachi flute and Nay flute that also serve for meditation



More experiments that are not irrelevant by Nikolas Brass



Saturday, June 15, 2019

233 . THE MAGIC OVERTONE WHISTLE FOR IMPROVISATIONAL MEDITATIVE CHEERING UP. : DIATONIC AND CHROMATIC OVERTONE WHISTLES WITH HALF OCTAVE ONLY HOLES (3 DIATONIC 5 CHROMATIC)


(see also post 199) 
THE ENCHANTED OVERTONE WHISTLE  THE  DIATONIC OVERTONE WHISTLES (48< Length / bore ID ratio<80  ) FOR CHORD ARPEGGIOS AT EACH HOLE.
These whistles are relatively unknown and i am not aware of any traditional flute in this category. The closest traditional flutes are the overtone flutes but they do not have usually but 1 or 2 only  holes to play a diatonic or other scale. The  flutes I suggest here have the peculiar characteristic that they are so long and with thin tupe (L/B ratio above 48) that when blowing or even under-blowing they cannot lay the 1str harmonic registry (octave). The only play with the 2nd or higher harmonics. They have more than 8 harmonics that sound easily with blowing softer or stronger. These flutes are a combination of the traditional overtone flutes and the standard diatonic flutes like irish whistlesAs far as it is  concerned the acoustics relevant to the L/B ratio (which is between 48 and 80  ) , they are in between the trumpet acoustics with ratio around 125 and classical flutes and whistles with ratio between 16 to 48.  They play with less than half action  "horizontally" with their holes as diatonic scale (e.g. 2 octaves) and more than half action  "vertically" at each hole more than 8 overtones (3 ,4 octaves) that are essentially arpeggios of major chords (up to the 7nth harmonic). Up to the 10 harmonic, the overtones of each hole belong to the scale (with the exception of the 7nth harmonic which makes the arpeggio , that of a major chord with  7nth). The playing is best when it is improvisational. It is nice to play a melodic theme and be able to play also over each note of it the arpeggio of  power-chord or major chord. The overall range of such flute is considerably larger than the standard whistles. The fipple sound hole is preferably smaller than the usual to help the higher overtones. Such winds are so much so as to read an existing  written melody from musical notes and play but a melody inside you to improvise and meditate .

The fujaras that are known if they have large bore inner diameter and thus length/bore ratio less than 80 will also belong to the acoustic and musical effect described here if made by smaller size bore and thus also shorter length (thus maybe not bass flutes). The fujaras use to have only 3 holes at the diatonic 4-chord in semitones 2-2-1. E.g. if the root is C3, then the holes give the notes D3-E3-F3 but at the 3rd harmonic G4 they will give the notes  A , B , C  thus eventually all the diatonic scale. Similarly if we open 5 holes chromatically in semitones 1-1-1-1 as in the style of valves of trumpet,  for the first harmonic it would be C#3-D3-D#3-E3-F3, the 3rd harmonic will give on the same holes G#, A , Bb, B, C , thus eventually all the 12-note chromatic scale
Examples of Fujaras
https://www.youtube.com/watch?v=y8Wzb3tLPCs

See also

https://www.youtube.com/watch?v=qzOLO5YHL9Q


If we want less than 7 notes "horizontally" for such an overtone flute, then the next best choice of the 7-notes diatonic scale is  the  is the maximal harmonic pentatonic scale (see post 117) I, iii, V, vi, vii 

The general rule to make an overtone whistle say in X base tone (e.g. C5, G4, D4, C4 etc) is to utilize the same bore inner diameter size with the ordinary whistle but about double the length. This is expected in general to give the Length/Bore ratio between 48 and 80. The resulting whistle is an overtone whistle that the basic tone (one octave lower than the corresponding whistle tone) cannot be played in the instrument , but the next octave (2nd Harmonic) is playable which is the original whistles root note.  Furthermore if we want a diatonic overtone whistle we utilize only 3 holes (the  lower pitch 3 holes if it would be an ordinary whistle) If the length is very long (for alto or low whistles) we "coil" the tube with turns and rounds as in t he brass wind instruments.  If we want a chromatic such overtone whistle we simple fill-up the gaps of the 3-holes of the diatonic overtones whistle as above with all their sharps or flats getting so 5 holes in the same area each one semitone away from the next , which is about the lower 1/3 of the tupe. In this way with the 2nd and 3rd overtones we have all the 7-notes diatonic scale or all the 12-notes chromatic scale. 

In the next picture I made from 16 mm bore  (inner diameter 12 mm) PVC and sweet tone Clarke whistles mouthpieces (fipples of D5 and C5 ) two such "magical" diatonic overtone whistles in D5 and C5 (although the length is as if of Low D4 and C4). The have respectively L/B ratios the D5 57/1.2=47.5 and the C5 64cm/1.2cm=53.33
They have 6+1 holes, but if we seal with a tape all except the highest 3, as in Fujara, we still have with the 1st and 3rd harmonic all the 7 notes of the diatonic scale.



In the next C5 and F5 overtone diatonic whistles only 3 holes are opened and suffice for a full 7-notes diatonic scale even only with the 2nd and 3rd harmonic.


Here is a bass in Bb3 diatonic from PVC of 32mm external diameter ,  of length about 148.2 cm (the same length with a Bb4 trumpet) , again with only 3 holes. In semitone intervals 2-2-1 or in notes Bb3 C4  D4 Eb4 . That is all it is necessary for a 7notes scale because it already starts with the 2n harmonic (due to the double than normal length)   and the 3rd harmonic gives in the same octave and on the same 3 holes  the the notes  F4-G4-A4-Bb4 thus all the Bb3 7-notes major scale. As it is a bass one, it falls in the category of Fujara. The high pitch ones I call overtone whistles. By changing the last part of the coil-tubes with another of appropriate length and holing we may have more roots on the same upper body.



In the next  photo we see a  C5 full chromatic overtone  whistle  that utilizes the 2nd and 3rd harmonic and with the 6 holes to give the chromatic half octave [C5]   C5# D5 D#5 E5 F5 F#5 with the 2nd harmonic and with the 3rd harmonic to give on the same holes the [G5]  G#5 A5 A#5 B5 C5 C#5 gives thus a full chromatic 12 notes octave. The 1s tharmonic  is not possible to play as it is an overtone whistle with Length/bore ratio L/B= 57  It is made again by PVC tube of external diameter 16 mm and internal 12 mm.  The idea is the same with the trumpet and the valves that produce 5 notes each a semitone away from the previous. Actually the whistle would be as well in Bb4 till F5 instead of C5 to G5  to be in accordance with the Bb scale of the trumpet.Or it could be in Eb5 to Bb5 .
We see 6 holes in the front (there is not thump hole) These 5 notes that divide a 5th (also a 4th) give the concept of ancient Greek 4-chords and 5-chords as basic building block for an octave scale. Compared to the full chromatic Ney in C5 in post 247, it has many more overtones than just the 2nd and 3rd because of the considerably larger Length/bore ratio. The chromatic Ney in post 247 is just an upper registry whistle while this here is a chromatic  overtone whistle. It has also an ordinary fipple (from a sweet tone clarke C5 whistle) and not a fipple with membrane as the Ney in post 257. 

Wednesday, June 12, 2019

232. ATTRACTOR AND REPULSOR NOTES IN A CHORD OF THE DIATONIC SCALE.. TRINITY VERSUS DUALITY IN THE DIATONIC SCALE

Let us assume that we are improvising a melody strictly inside the diatonic scale.

A general  trinity of the music in the diatonic scale is the triad of factors 

1) Chromatic dimension (intervals of 2nd/7nth, 1 or 2 semitones etc)

2) Melodic dimension (intervals of 3rd/6th , 3 or 4 semitones etc)

3) Harmonic dimension (intervals of 4th/5th or 8th , 5 or 7 semitones etc)

E.g. we ascend harmonically ,we descend melodically and we change triad of chords from minor or diminished to majors or vice versa chromatically  (from 7-3-6  to 1-4-5 chromatically at the chord relations 7-1 and 3-4 )

Let us also assume that when moving from not x1 to note x2 with a waving melodic vector (see post 231) we apply the expanding and contracting waving from the 7 independent melodic themes patterns as in post 231, that as picture are



and


Then we should start from a minimum possible amplitude and intervals (repulsor note ) and end in such one  (attractor note) . But in the diatonic scale the minimum interval is a semitone. There are two only poles and positions in the diatonic scale with semitones: The root pair b-c and the pair e-f
Therefor a note which is in one of the two semitones of the diatonic scale will be either the attractor or the repulsor of the melodic motion.

It happens that each of the chords of the diatonic scale has at least one attractor or repaslor which we will cal singular point of the chord. Here is the enumeration of them.

C major c-e-g has singular notes the e and c

D minor d-f-a has singular note the f

E minor e-g-b has singular note the e and b

F major f-a-c has singular notes the f and c

G major g-b-d has singular note the b

A minor a-c-e has singular notes the c and e

B diminished b-d-f has singular notes the b and f.

The above analysis and information helps someone to know where to start waving and were to end waving in melodic themes patters as above. 

It is well known that the two poles (duality) of the diatonic scale is the root and dominant. That are 5th apart. Utilizing twoocatvesa lso the duality we describe has the two poles a 5th apart.

Only two chords have only one pole: The Dm and the G. The major chords C and F have both poles and are consecutive in the cycle of 4ths. The same with the minor/diminished  chords Bd- Em and Am.

If we want to complement the described here chromatic duality of b-c and e-f in the diatonic scale , it is here where the dominant pair g-a enters. So the trinity are the next 3 pairs of notes and areas of the scale


b-c   / e-f /  g-a 

Of course this trinity in the diatonic scale is not much different than grasping the scale from the triad of major chords 1-4-5 (I-IV-V) or triad of minor chords 3-6-2 (iii-vi-ii).

Another general trinity of the music in the diatonic scale is the triad of factors 

Chromatic dimension (intervals of 2nd/7nth, 1 or 2 semitones etc)
Melodic dimension (intervals of 3rd/6th , 3 or 4 semitones etc)

Harmonic dimension (intervals of 4th/5th or 8th , 5 or 7 semitones etc)

Example of a nice melody which utilizes waving ending in such attractor and repulsor notes is the Irish St Anne's Reel

https://www.youtube.com/watch?v=lwllcWC_FL4



Monday, June 10, 2019

231. THE 3 CLASSES OF 7 VARIATIONAL INDEPENDENT MELODIC PATTERNS FROM THE COUPLING OF THE POSITIVE AND NEGATIVE EMOTIONS. THE 3 SIMPLICIAL DOLPHIN WORDS

THE 3 CLASSES AND 7  INDEPENDENT PATTERNS OF MELODIC THEMES FROM THE COUPLING OF POSITIVE AND NEGATIVE EMOTIONS.


WE MAY COMPARE THE NEXT PERCEPTIONS AND TECHNIQUES WITH THE 3 BASIC SOUNDS IN SOLOING 1) THE CHROMATIC (MAINLY INTERVALS OF 2NDS)  2) THE MELODIC (MAINLY INTERVALS OF 3RDS) 3) THE HARMONIC (MAINLY INTERVALS OF 4THS/5THS/8THS )


All the 3-classes of dynamic coupling of positive and negative emotions have been applied also in the psychology of social behaviour, and even in the psychology of behaviour of couples in the marriage 
(see "The mathematics of marriage" by Gottman, Murray, Swanson, Tyson, and Swanson, MIT press 2002. See also for the Voltera's equations "Models in Ecology" by J. Maynard Smith, Cambridge University press )
All of the above 3 classes of non-linear coupling have been solved and their solutions have been classified. 


The  3 classes of melodic patterns from the coupling of positive and negative emotions are


1) The ascending (or descending ) melodic pattern (3 patterns)


2) The stationary waving melodic pattern.  (3 patterns)



3) The isocratic note melodic pattern  (1 pattern)




The 1st class the ascending (or descending ) melodic pattern are subdivided by three  patterns

a) The straight stepwise ascending (or descending) melodic theme



b) The waving ascending (or descending) melodic theme



c)The abrupt jump (spike) interval ascending (or descending) by an interval larger than an octave without intermediate steps.






2) The The stationary waving melodic patterns are divided to 3 cases

a) The stable amplitude stationary waving pattern






b) The diminishing (contracting) amplitude stationary waving pattern









b) The expanding   amplitude stationary waving pattern






Obviously these patterns (and "Dolphin words" as defined e.g. in post 114 ) are variational independent, in the sense that no translation or inversion can produce one from another. On the other hand pitch translations within the scale or pitch inversion within the scale will not change the type and order-topological shape of the melodic theme pattern ( a straight ascension will remain such or a stationary waving will remain such etc)

On the other hand if we pass from one such pattern of the above  6 cases to another such pattern we have called this transition as mutation of the melodic theme.

Therefore the above 3 classes (and 6 cases of types which when including their inverses become 11 ) make  base of melodic themes for a melody or a melodic seed for a melody of a song.

Their nature in melodies is similar to the type of chords in chord progressions (major , minor, diminished, augmented,, seventh etc)


We may compose after these patterns melodies utilizing rules for the rhythm, scales, underlying harmony and musical morphology e.g. as in posts 229,221, 214, 203



THE MELODIC IMPROVISATION AS A SEQUENCE OF "ROTATIONS". EACH "ROTATION" HAS THE NEXT 3-LEVEL  RHYTHMIC OR MORPHOLOGICAL STRUCTURE

THE 4 PARTS A1 A2 A3 BI STRUCTURE 
This structure is rhythmic morphological and comes as a pattern from the 15-syllable poetry.
2 lines in a 15-syllables poetry are divided to 4 parts A1 A2 A3 B1, each of the Ai having 4 syllables and the B1 3 syllables. Similarly here in the melody the A1 A2 A3 , B1 are of 2 measures.  Each of the A1 A2 A3 B1 contain at least one melodic theme. If we put the restriction that both the melodic theme and its variations are consisting from intervals that are 2nds in less that 1/3 (=33%) of the cases, then we get an "Irish" but also "south american", melodic/harmonic sound in the melody. The melodic theme of A1 is translated or inverted to that of the A2 and that of the A2 to that of A2. Finally the melodic theme of A3 is mutated to that of B1. The simplicial sub-melody has one note in each measure therefore two notes in each of the A1 A2 A3 B. These two notes signify a MELODIC MOVEMENT (VECTOR) which is the basis of an emotion.  If we superimpose the melody at the first two levels, the detailed improvisational notes of the melodic theme (1st level) and the melodic move or vector of the simplicial submelody (2nd level) we get a new musical entity and concept that we may call WAVING MELODIC VECTOR. The wavings are as in the above 7 melodic themes patterns. Another classification of them is that they are of 3 classes a) Chromatic (of length an interval of 2nd) b) Melodic (of length an interval of 3rd) c) Harmonic (of length an interval of 5th). The choice in the improvisation of one of these 3 classes is similar to the choice in a chord progression if the chord-transition will me chromatic , melodic or harmonic.
Very often the wavings are of diminishing amplitude as we reach the melodic center-end note of it. This is very convenient to have in mind when we improvise because we think that we will move from a persisting note a (melodic center) to a persisting note b (melodic center ) in a scale but with improvisational waving way that we may change each time at willAll the melodic movements of the A1 A2 A3 B make a DOLPHIN WORD (as defined also in post 101, 114 ). Each part A (thus melodic move too) has an underlying chord. The chords of two parts like A1 A2 may be the same or different chords. The melodic move can be also a melodic triad (alternating major minor vector interval of 3rd as in post 208) . The Dolphin word of the "rotation" may be a closed polygon (e.g, triangle) of waving melodic vectors , so that the length of the melodic vector indicates also the length-interval of the waving melodic vector, which may also be the distance as musical interval of the middle notes of the underlying chords, of the melodic move. Each side of the polygon has its own waving melodic theme pattern as the above 7 .
This melodic polygon allows for simple and very concise, simple and visually beautiful  methods of writing the improvisation with not less information than the necessary but no more than a minimum too, so that each time we see the written paper and play the melody a different melody will emerge (mainly at the first layer/level of it) while still it will be "the same" song. 
When playing again such an improvisation the simplicial sub melody is repeated (thus the "rotation" A1 A2 A3 B or Dolphin word of it), but the other notes inside the measures that are embellishments may change. All together the "rotations" or Dolphin words make the total melodic phrases of the song. Therefore we have here at least a 3-level structures of the melody a) notes b) melodic moves c) "rotations" or Dolphin words,and in time it is 1, 2^3=8 (2 measures)  and 2^5=32 (A1A2A3B parts).


If we put the restriction that these patterns of  melodic theme and their variations are consisting from intervals that are 2nds in less that 1/3 (=33%) of the cases, then we get an "Irish" but also "south american", melodic/harmonic sound in the melody.

See also post 282


Examples of such progressions of simplicial melodic themes (or Dolphin words) are the next  (each vector-arrow is an oriented interval that fits to a single or more  underlying chord(s)).



Or


Or

Or




AS THE COMBINATION SIMPLICIAL MELODIC MOVES (ORIENTED INTERVALS SEE POST 282) CREATE PATTERNS THAT ARE CALLED "DOLPHIN WORDS" , WE MAYS AS WELL CLASSIFY THE "SIMPLICIAL DOLPHIN WORDS" . The simplest such patterns are of course the 3: 1) THE CYCLE 2) THE ASCENDING SEQUENCE 3) THE DESCENDING SEQUENCE.



230. CONTINUOUS NOTES OF REED-WINDS AND BOWED STRINGS VERSUS PLUCKED STRINGS NOTES. COUNTING THE RHYTHM WITH THE LEFT-RIGHT MOVES OF THE BOW

One may think that the musical notes of bowed string instruments like violin cello etc or of reed-winds like clarinet , saxophone , etc are of the same  description musical notes as the notes by plucking the strings of musical instruments like guitar, mandolin etc. This by far it is not so! If the mousical note by plucking the string of an instrument like guitar has 3 dimensions : 
1) Pitch, 
2) duration 
3) volume, 

the corresponding note of a bowed string instrument like violin or cello etc has 5 dimensions 

1) Pitch, 
2) Bows-speed/pressure  timbre (color)  and  reed-pressure or reed-length-in-the-mouth degree of winds.
3) Bow moving left-right direction changes and rhythmic pattern of it
4) duration 
5) volume.

By playing a single musical note of the latter type of fixed pitch and volume we may even conduct the rhythm on its continuous duration by changing the speed of the bow, thus by changing the Bows-speed timbre (color) which in spectral decomposition of the sound means changing the weight center of the harmonics of the sound higher or lower. Therefore somehow this Bows-speed timbre (color) is also one-dimensional quantity.  Similarly how much we put the reed in the mouth and how much we press it changes in a quantitative way the timbre of the note.


Here is ancient 2-voices music from the kazakhs violin which is called kobyz, which makes it more obvious



 COUNTING THE RHYTHM WITH THE LEFT-RIGHT MOVES OF THE BOW

THE RHYTHM IN IMPROVISATIONS REFLECTED ON THE BOW LEFT-RIGHT DIRECTION CHANGES REGARDLESS OF THE MELODY NOTES CHANGES:

In the bowed instruments when improvising we have a very simple and efficient way to reflect the rhythm and this is by making the bow left-right direction changes exactly at the rhythm of a measure in other words as the up or down measurements of the rhythm.
And we do so either if we play a single long lasting note (long note that nevertheless reflects the rhythm too) or when we play many notes, each note a single or an  integral number of bow right-left moves. (so we avoid many notes with the same  direction of the bow move and if necessary we jump to the next division of 2 in realizing the rhythm). In this way we shape the left-right moves of the  bow with a simple pattern that of the rhythm rather than random left-right moves which might feel more complicated in improvising. In this way a part of the melody with a more desne number of notes might still be played with the same density of  left-right moves of the bow. If necessary we may jump to the next division of 2 in realizing the rhythm, but always counting the rhythm.
Based on the above we may say that the bow has as modes of speeds of change of directions the powers of 2 of the written melody (integrals, halves, quarters, eighths, sixteenths, etc)


Thursday, May 30, 2019

229. SIMPLE ORGANIZATION OF THE MELODY IN IMPROVISATION OR COMPOSITION OVER A CHORD PROGRESSION.

We have mentioned that the prefered way of composition in this book is as in improvisation, in other words first we define the simple and then the more complicated. In particular first we compose the harmony as a chord progression X1 X2 ,..., Xn over a scale-of-chords and then we compose the melody.  A very simple and happy case is that the chord progressions is only  3 different chords 1-4-5 over a diatonic scale.

The simplicity of triad of factors for the melodic action is  mainly the next three factors

1) The triad of polarity (qualitative) of a melodic move (ascending, descending, rotating stationarily or isocratic)

2) The  quantitative  triad of the character of the move :Chromatic, Melodic ,Harmonic

3) The rhythmic pattern of repetitions 


Here is where the trichords, tetrachord and pentachords are coming to make the organization simpler.



ALL 3 TRICHORDS  (also called vector intervals of  3rds)



All of them are of the DIATONIC FAMILY

1-2    Minor

2-1   Minor

2-2   Major 

ALL 6 TETRACHORDS   (also called vector intervals of  4ths)


DIATONIC FAMILY
(containing only 2 and 1)
2-2-1  syntono major  , Ionian/mixolydian
1-2-2  syntono minor  , Phrygian/Locrian
2-1-2   minor, Dorian/Aeolian

CHROMATIC FAMILY
(containing 3)

1-3-1   2nd chromatic

1-1-3    parachromatic tonal

3-1-1    1st chromatic 

ALL 20 PENTACHORDS   (also called vector intervals of  5ths)

All pentachords contain a single power-5 chord that power-5 chord which is defined by the end-notes of the pentachord.

DIATONIC FAMILY
(containing only 2, and 1)

2-2-2-1       Major Lydian    Contains a major chord (known also as Natzi/Zaouil)
2-2-1-2        Major Ionian/Mixolydian    Contains a major chord.(known also as Rast/Mahour)
2-1-2-2       Minor Dorian    Contains a minor chord (known also as Bousselik/Nichavent)
1-2-2-2       Minor Frygian/Aeolian    Contains a minor chord (known also as Qourdi)


CHROMATIC FAMILY
(containing  3 )

1-1-3-2
1-1-2-3
1-3-2-1   Contains a major chord and a diminished chord
1-2-3-1   Contains a minor chord and a diminished chord
1-2-1-3   Contains a minor chord and a diminished chord
1-3-1-2   Contains a major chord and a diminished chord (known also as Hijaz)
3-2-1-1    Contains  a diminished chord
2-3-1-1
3-1-2-1   Contains a major chord and a diminished chord
2-1-3-1   Contains a minor chord and a diminished chord (known also as Nevesser/Nikriz)
3-1-1-2   Contains a major chord (known also as Saz-kar)
2-1-1-3   Contains a minor chord (known also as Samba)


ENHARMONIAN FAMILY
(containing  4 )

1-1-1-4   Contains a minor chord
1-1-4-1
1-4-1-1
4-1-1-1   Contains a major chord


Now the organization has the next simple rules

RULE 1
During a chord, we compose/improvise the melody within a pentachord of the chord. That is a pentachord with ends the 1st and 5th of the chord (lowest highest note, therefore it contains the notes of the  chord) on normal position . We may use of course variations of a melodic  theme by rotations, inversion, translations as arpeggios of the pentachord of the chord. The average time duration of the notes is about equal or we make sure that the total duration of the notes of the cords is not less than half of the total duration of this part of the melody. This guarantees that this part of the melody fits harmonically to the chord. If we use an overtone whistle e.g. a diatonic or chromatic as in post 233, the 5-chord is just the range of the holes of the whistle.

RULE 2
During the transition of two successive  chords Xi-Xi+1, we compose/improvise the melody within
1) a pentachord or tetrachord that starts at the middle note of Xi and ends at the middle note of Xi+1, if the Xi-Xi+1 transitions is harmonic with the two chords a 4th or 5th apart (obviously it contains two notes from each chord). The harmonic transition of the melodic theme when played on an overtone flute as in post 233,is just repeating the melody on the holes but on a higher harmonic. E.g. from the 2nd to 3rd harmonic will give a transition by a fifth.

2) a trichord that starts at the middle note of Xi and ends at the middle note of Xi+1, if the Xi-Xi+1 transitions is melodic with the two chords a minor of major 3rd apart (obviously it contains two notes from each chord) .
3) An interval of 2nd that starts at the middle note of Xi and ends at the middle note of Xi+1, if the Xi-Xi+1 transitions is chromatic with the two chords a minor of major 2nd apart (obviously it contains two notes from each chord) .
We may use of course variations of a melodic  theme by rotations, inversion, translations as arpeggios of the transitional trichord , tetrachord or pentachord .

We may use of course variations of a melodic  theme by rotations, inversion, translations as arpeggios of the pentachord of the chord.
The average time duration of the notes is about equal or we make sure that the total duration of the notes of the chords is not less than half of the total duration of this part of the melody. This guarantees that this part of the melody fits harmonically to the two chords ofthe transition.


If the improvisational rotation in  the SUB-SCALE of the holes of the overtone flute 

starts from the lower end and ends in it it is called UPPER CYCLIC (NEUTRAL/SAD)
If it starts from the upper end and ends in it it is called LOWER CYCLIC (NEUTRAL  HAPPY)
If it starts from the upper end and ends at the lower end  it is called  DESCENDING (SAD)
If it starts from the lower end and ends at the upper end  it is called ASCENDING (HAPPY)



If in the chord progression all the transitions are harmonic (intervals of 5th or 4th) then this organization method is simply a way to set intervals of 5ths vertically as chords and their pentachords and intervals of 5th or 4th horizontally as bridge-transitions between the chords.

HERE WE DESCRIBE A STANDARD 3-LAYERS STRUCTURE OF THE MELODY.

THE MELODIC IMPROVISATION IS A SEQUENCE OF "ROTATIONS". EACH "ROTATION" HAS THE NEXT 3-LEVEL  RHYTHMIC OR MORPHOLOGICAL STRUCTURE

THE 4 PARTS A1 A2 A3 BI STRUCTURE 
This structure is rhythmic morphological and comes as a pattern from the 15-syllable poetry.
2 lines in a 15-syllables poetry are divided to 4 parts A1 A2 A3 B1, each of the Ai having 4 syllables and the B1 3 syllables. Similarly here in the melody the A1 A2 A3 , B1 are of 2 measures.  Each of the A1 A2 A3 B1 contain at least one melodic theme. If we put the restriction that both the melodic theme and its variations are consisting from intervals that are 2nds in less that 1/3 (=33%) of the cases, then we get an "Irish" but also "south american", melodic/harmonic sound in the melody. The melodic theme of A1 is translated or inverted to that of the A2 and that of the A2 to that of A2. Finally the melodic theme of A3 is mutated to that of B1. The simplicial sub-melody has one note in each measure therefore two notes in each of the A1 A2 A3 B. These two notes signify a MELODIC MOVEMENT (VECTOR) which is the basis of an emotion.  If we superimpose the melody at the first two levels, the detailed improvisational notes of the melodic theme (1st level) and the melodic move or vector of the simplicial submelody (2nd level) we get a new musical entity and concept that we may call WAVING MELODIC VECTOR. The wavings are as in the 7 melodic themes patterns asin post 231. Another classification of them is that they are of 3 classes a) Chromatic (of length an interval of 2nd) b) Melodic (of length an interval of 3rd) c) Harmonic (of length an interval of 5th). The choice in the improvisation of one of these 3 classes is similar to the choice in a chord progression if the chord-transition will me chromatic , melodic or harmonic.Very often the wavings are of diminishing amplitude as we reach the melodic center-end note of it. This is very convenient to have in mind when we improvise because we think that we will move from a persisting note a (melodic center) to a persisting note b (melodic center ) in a scale but with improvisational waving way that we may change each time at willAll the melodic movements of the A1 A2 A3 B make a DOLPHIN WORD (as defined also in post 101, 114 ). Each part A (thus melodic move too) has an underlying chord. The chords of two parts like A1 A2 may be the same or different chords. The melodic move can be also a melodic triad (alternating major minor vector interval of 3rd as in post 208) . The Dolphin word of the "rotation" may be a closed polygon (e.g, triangle) of waving melodic vectors , so that the length of the melodic vector indicates also the length-interval of the waving melodic vector, which may also be the distance as musical interval of the middle notes of the underlying chords, of the melodic move.
This melodic polygone allows for simple and very concise, simple and visually beautiful  methods of writing the improvisation with not less information than the necessary but no more than a minimum too, so that each time we see the written paper and play the melody a different melody will emerge (mainly at the first layer/level of it) while still it will be "the same" song. 
When playing again such an improvisation the simplicial sub melody is repeated (thus the "rotation" A1 A2 A3 B or Dolphin word of it), but the other notes inside the measures that are embellishments may change. All together the "rotations" or Dolphin words make the total melodic phrases of the song. Therefore we have here at least a 3-level structures of the melody a) notes b) melodic moves c) "rotations" or Dolphin words,and in time it is 1, 2^3=8 (2 measures)  and 2^5=32 (A1A2A3B parts).

Of course the above rule samy apply in the cases of improvisation as in the posts 214, 215 etc

Finally this method may also utilize simplicial sub melody composition at first, either the chromatic or the harmonic or the melodic as im post 104

As an improvisation rather than as composition the instruments of Celtic harp (appropriately tuned) , or chromatic pan-flute are the most convenient for such melodies

Wednesday, May 29, 2019

228. MELODIC IMPROVISATIONAL ROTATIONS IN A PENTACHORD ON ONE OR 3 CHORDS AND AT LEAST TWO OCTAVES

When we say pentachords we mean the pentachords as defined in post 225 (see also post 203  and 214 and 262).

The pentachord is not considered restricted in a single octave, therefore power-5 chords, waves are created as defined in the post 217.

Although we mention here 3 chords (major minor or diminished mainly) as underlying chords, they can be substituted with a single power-5 chord that power-5 chord which is defined by the end-notes of the pentachord. In addition, if we apply the 3 chords mentioned as underlying chords, it need not be the chords contained in the pentachord, but the chords 1-4-5 of the diatonic scale that the (diatonic family) pentachord belongs. For the case of pentachord of the chromatic or enharmonian family more discussion is required.

If the improvisational rotation in  the pentachord

starts from the lower end and ends in it it is called UPPER CYCLIC (NEUTRAL/SAD)
If it starts from the upper end and ends in it it is called LOWER CYCLIC (NEUTRAL  HAPPY)
If it starts from the upper end and ends at the lower end  it is called  DESCENDING (SAD)
If it starts from the lower end and ends at the upper end  it is called ASCENDING (HAPPY)

For such rotational improvisations, string instruments tuned by octaves (strings at the same note but different octave see post 210 about octave tuning) are very convenient.


In addition for every such chord or chord transition we may have a morphological rhythmic pattern E.g. A1 B1 B2 B3 or A1 A2 A3 B1 , which shows how the melodic theme is repeated or varied by translation inversion and rotation-mutation.

We refresh here the enumeration of all 20 pentachords with their chords




ALL 20 PENTACHORDS   (also called vector intervals of  5ths)

All pentachords contain a single power-5 chord that power-5 chord which is defined by the end-notes of the pentachord.

DIATONIC FAMILY
(containing only 2, and 1)

2-2-2-1       Major Lydian    Contains a major chord (known also as Natzi/Zaouil)
2-2-1-2        Major Ionian/Mixolydian    Contains a major chord.(known also as Rast/Mahour)
2-1-2-2       Minor Dorian    Contains a minor chord (known also as Bousselik/Nichavent)
1-2-2-2       Minor Frygian/Aeolian    Contains a minor chord (known also as Qourdi)


CHROMATIC FAMILY
(containing  3 )

1-1-3-2
1-1-2-3
1-3-2-1   Contains a major chord and a diminished chord
1-2-3-1   Contains a minor chord and a diminished chord
1-2-1-3   Contains a minor chord and a diminished chord
1-3-1-2   Contains a major chord and a diminished chord (known also as Hijaz)
3-2-1-1    Contains  a diminished chord
2-3-1-1
3-1-2-1   Contains a major chord and a diminished chord
2-1-3-1   Contains a minor chord and a diminished chord (known also as Nevesser/Nikriz)
3-1-1-2   Contains a major chord (known also as Saz-kar)
2-1-1-3   Contains a minor chord (known also as Samba)


ENHARMONIAN FAMILY
(containing  4 )

1-1-1-4   Contains a minor chord
1-1-4-1
1-4-1-1
4-1-1-1   Contains a major chord