247. FROM THE NEY TO THE TROMBONE AND VALVED TRUMPETS: FULLY CHROMATIC OVERTONES FLUTES (NEY OR CHROMATIC FUJARA) FLUTE WITH FIPPLE WITH MEMBRANE OR SAX MOUTHPIECE. (FIPPLE OR REED VALVED-LIKE AEROPHONE TRUMPETSOR TROMBONES)

The Ney flute is very famous and loved my many, but also as it is rim-blowing and in a way different from the quena flutes or Chinese Xiao, or japanese Shakuhachi is considered quite difficult.

To make it more easy I designed and crafted one from PVC but not as rim-blowing flute but with fipple with membrane (see post  243) . This fipple with membrane gives to it almost the same breathy and harsh sound as the classical rim blowing Ney. But because we cannot create easily shifts of the pitch by one semitone with the mouth only as with the baspare (rim blowing mouthpiece) and in order to have the Ney fully chromatic (all 12 notes ogf the octave) with the 2nd and 3rd harmonic , I added one more hole one semitone away higher than the highest front hole of the classical Ney.

It is essentially an one octave , fully chromatic (all 12-notes of the octave) direct blowing flute.

In the next 2 photo we see a  C5 full chromatic upper  registry  whistle (see post 199 or 248)  that utilizes practically 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. It is the same  idea of the valves in a trumpet and slide of a trombone (and close to the main idea of a Ney). The 1s tharmonic  is hardly listened or of sound it is fused with the 2nd harmonic due to the membrane fipple (see post 243) and gives to this part of the 5th octave a more bass sound. It is made again by PVC tube of external diameter 25 mm. If we would utilize 20 mm or 12 mm tube so that it would become an overtone flute and it would be even better garanteed that the 1st harmonic is not playable as in the (valved) trumpet too. The length to bore ratio Length/bore=34 , thus strictly speaking an upper registry whistle (see post 199 ) rather than an overtone whistle . That is why it does not give practically more than the 3rd harmonic (quite large size bore). The idea is the same with the trumpet and the valves that produce 5 notes each a semitone away from the previous. We see 7 holes in the front (there is not thump hole) but the highest pitch hole is a tuning hole for C5, thus 6 holes covered 3+3 by the two hands. 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. If we close that tuning hole too it will give a Bb3 note as in a C4 Ney. The whistle has a breathy harsh sound due to the membrane fipple sounds almost exactly like a C4 Ney flute (which normally is rim blowing ) and if we exclude the 1st harmonic of the Ney it is identical with what the Ney is playing (of course the semitones are in the equal tempered scale rather than deviating oriental scale)

I remind the reader (see post 243)  that due to the same laws of acoustics we may use on the same body tube besides a  fipple also a quena rim with notch blowing mouthpiece and also a tenor sax or clarinet mouthpiece. Except that in the latter case we will have only the odd number overtones (1st 3rd, 5th etc)

A 2nd version of the Ney or chromatic fujara, or aerophine valved-like trumpet is the next in the picture at Eb4 root note, from PVC of 12mm external diameter, and mouthpiece from ordinary soprano whistles.

It has a  chromatic 6+1 fingering system as if of an ordinary whistle except  it is not in diatonic steps but steps of one semitone. The open hole of the tume gives  Eb when all else are closed , and the rest 6 front holes give correspondingly E4, F4, F#4 G4 G#4 A4 . There is also a 7nth hole and thump hole as in the 2nd photo, which is not really necessary but as in quenas it helps also by partial opening as registry key that helps triggering easier the 3rd overtone. It gives the note A4 (which also can be give if all front and thump hole are closed and we pass from the 2nd to the 3rd overtone). These holes when used for higher overtones are as correct as the valved in a trumpet or brass instrument.

No more not less correct.

The idea to derive a full chromatic scale with this 6+1 fingering system is excatly as the idea to derive all the chromatic scale with the 7 positions valves in a trumpet. Except that in the trumpet by each valve-step the pitch lowers by a semitone while here with each additional hole the pitch increases by one semitone. As with a  trombone or valved trumpet a fully chromatic non-repeating sequence of notes with the 1st 5 harmonics would require

2ND OVER TONE: ALL HOLES FROM TUBE BOTTOM HOLE   TILL  THE 6TH HIGHEST FRONT HOLE 

notes Eb4 E4 F4 Gb4 G4 Ab4 A4 . 

3RD OVERTONE: ALL HOLES FROM TUBE BOTTOM HOLE   TILL THE  5TH HIGHEST FRONT HOLE

notes Bb4 B4 C5 Db5 D5,

4TH OVERTONE: ALL HOLES FROM TUBE BOTTOM HOLE   TILL  THE  4TH HIGHEST FRONT HOLE

notes Eb5 E5 F5 Gb5 . 

5TH OVERTONE: ALL HOLES FROM TUBE BOTTOM HOLE   TILL  THE  3RD HIGHEST FRONT HOLE

notes G5 Ab5 A5 

As with a valved  trumpet or with the slided trombone, as we move from the 1st hole to the higher holes the required speed and pressure of  blowing increases, but when we reach at the  an appropriate higher  hole it is the same as with that of the next overtone at the bottom tube  hole of the fingering as above. If we layout the notes per overtone and hole it will be a triangular matrix over the 2 dimensions (overtones)x(holes)

At the end of the post is for comparison the essential rage of a valved trumpet

 I  have crafted one more such chromatic overtone flute at Bb4 with the 6+1 chromatic fingering system. It is in the range of the standard piccolo trumpet although it is about 7 cm long .

246. THE TRINITY OF GENDERS OF SCALES BASED ON OVERTONES, UNDERTONES, EQUAL TEMPERED (BACH) SCALE AND THE CORRESPONDING ANCIENT GREEK MUSICAL GENDERS : ENHARMONIC, CHROMATIC , DIATONIC.

SEE ALSO

http://barthopkin.com/otonuton-scales/

http://barthopkin.com/tangular-arc/

Bill Wesley -Arithmetic Array Mbira Jam

https://www.youtube.com/watch?v=nefHvt7cTw4

245. THE FIRST 4 BLUE NOTES OF THE DIATONIC SCALE , THE SERIES OF OVERTONES AND CELEBRATED IN VARIOUS CULTURES CHROMATIC MINOR SCALES FROM THEM.

We remind the reader that in the online notes here we call a sequence of 7 interval that sum-up to 12 semitones a mode and all cyclic permutations of it as the scale that the mode belongs.

As it was mentioned in post 40 the order of how much harmonic is  an interval (and interval is more harmonic than another means that the two notes have a  greater number of common harmonics or overtones) the order of "harmonicity" is

8th>5th>4th> major 3rd>minor  3rd

The first 4 blue notes of the diatonic scale are  by definition the neighboring by one semitone notes to the interval of 5th c-g thus g# f# around g and c# around c and the same with the best next interval of major 3rd c-e thus d# or c# again . This gives the maximum shift from an harmonic interval to one with dissonance thus chromaticity. 

It is important to realize that these blue notes of a diatonic scale are already suggested by the series of overtones, because the exact overtones have cases that are outside the equal tempered Bach scale. 

THE 9NTH HARMONIC SUGGESTS THE D#

THE 7NTH HARMONIC SUGGESTS THE  A#

THE 11TH HARMONIC SUGGESTS THE F#

THE 13NTH HARMONIC SUGGESTS THE G#

There cannot be other as first 4 notes other than the above 4 blue notes for the first 2 best intervals (5th and major 3rd) around the roor note .

Notice of course that all the 5 blue notes 2b 3b 5b 6b 7b make a major pentatonic scale with root 5b and main chords 5b major and 3b minor. 

Notice also the important fact that the 4 blue notes make the 4 non-major chords of the scale major chords!

7dim 3m , 6m, 2m to major chords!

The 5# makes the 3m to 3M , 
the 2# makes the 7dim to 7M, 
the 4# makes the 2m to 2M and 
the 1# makes the 6m to 6M 

On the other hand e.g. the 1st blue note (5#) may make also the 4M chord 4m, so making the basic triad 5N 1M 4M, to 5M 1M 4m. Also the 2nd blue note 2# allows, for a 1 minor chord too. making therefore the triad 5N 1M 4M to  5M 1m 4M  or   5M 1m 4 m.

Converselly when improvsing with the 3 basic major chords of diatinic scale 1M, 4M, 5M, then the most natural blue notes are those 3 blue notes that make them minor chords, thus

3b=2# which makes 1M to 1m
7b=6# which makes the 5M to 5m
6b=5# wchich makes the 4M to 4m


The scale 1,2,3,4,5#,6,7 is an harmonic minor scale. The scale 1,2,3,4,5,6#,7, is the Neapolitan scale (a permuted harmonic minor) The scale 1,2#,3,4,5,6, 7, is again the Neapolitan scale.
We may combine now the lue notes per two.

The scale 1,2#,3,4,5# 6, 7, is the double harmonic minor scale.
The scale 1,2,3,4,5#,6#,7, is the Mela Namanarayani, Raga Narmada, Pratapa, Harsh Major-Minor scale.
The scale  1,2#,3,4,5,6#,7 is the inverse double parachromatic Byzantine scale.


IN SUMMARY BOTH EARLY WESTERN AND EASTERN (GYPSY) JAZZ MAY MAKE THE NEXT 7 TEMPORARY CHANGES IN THE CHORDS OF THE DIATONIC SCALE DUE TO THE 5  BLUE NOTES 

3m becomes 3M
7dim becomes 7M
5M becomes 5#dim or 5m 
2m becomes 2M
6m becomes 6M
4M becomes 4m or 4dim
1M becomes 1m or 1#dim

Obviously not all of these changes occur necessarily simultaneously in a single song. maybe only few of them. And usually at least 50% of the time the chords are the normal of the diatonic scale. Other ways to organize them and perceive them are as triads of harmonic pairs of chords (see post 215  IMPROVISATION OVER A PAIR OF CHORDS . TRIADS OF HARMONIC PAIRS OF CHORDS. ). This awareness of these alterations of the normal chords of a diatonic scale (by blue notes) allows for a consistent and rich system of harmony for composing and improvising early jazz type of jazz.

AS WE MAY NOTICE THIS SYSTEM OF HARMONY WITH THE FIRST 4 BLUE NOTES (AND  5TH BLUE NOT 6#=7b  MAY BE ADDED) IS ESSENTIALLY A METHOD TO PLAY SOONER OR LATER IN THE MELODY ALL THE 12 NOTES OF THE FULL CHROMATIC SCALE STARTING FROM THE 7 NOTES OF THE DIATONIC SCALE AND RETURNING TO THEM AGAIN.

CONVERSELY ANY MELODY WHICH STARTS AS MELODY OF A DIATONIC SCALE AND THEN EVOLVES WITH ANY TURN AND ANY MOVE INSIDE THE 12-NOTES FULL CHROMATIC SCALE CAN BE COVERED OR ACCOMPANIED WITH THE NEXT ALTERNATIONS OF THE CHORDS OF THE DIATONIC SCALE. IN WESTERN JAZZ IT IS CONCEIVED AS ALTERATIONS DUE TO THE BLUE NOTES WHILE IN EASTERN JAZZ AS ALTERATIONS DUE TEMPORARY CHANGE OF THE NATURAL MINOR TO ONE OF THE CHROMATIC MINORS (HARMONIC, DOUBLE HARMONIC , NEAPOLITAN , PARACHROMATIC MINORS ETC)

As an harmonic personality as in post 36  with the chords that cover all notes of the 12-notes chromatic scale here si the table

Steps of the chromatic scale/Harmonic Personality

1

1#

2

2#

3

4

4#

5

5#

6

6#

7

JAZZ PERSONALITY

1M(ajor) or 1m

1#Dim or 6M

2m(inor) or 2M(ajor)7

7M

3m or 3M(ajor)7

4M or 4m or 4Dim

2M7

5M7 or 5m

5#Dim or 3M7

6m or 6M7

5m

7Dim or 7Major7

Now there are the next ways to chromatize these best two intervals of 5th and major 3rd

A) Chromatizing the 5th:

1) By using the 1s blue not 5# instead of g. 

This gives the harmonic minor  in steps  6-7-1-2-3-4-5#-6 or in c major a-b-c-d-e-f-g#-a and in semitone intervals 2-1-2-2-1-3-1

2) By using the 4#= f#=gb instead of g=5:

This gives   in steps  6-7-1-2-3-4-4#-6 or in c major a-b-c-d-e-f-f#--a and in semitone intervals 2-1-2-2-1-1-3 which may be called Byzantine simple parachromatic scale. It has as 6-notes subscale the  Blues scale 1-1-3-2-3-2.

3) By using the 4th blue note 1#=c#

This gives the melodic minor  in steps  6-7-1#-2-3-4-5-6 or in c major a-b-c#-d-e-f-g--a and in semitone intervals 2-2-1-2-1-2-2

B) Chromatizing the major 3rd

1) By using the 2nd blue note 2#=d#  which gives the Neapolitan scale in steps  6-7-1-2#-3-4-5-6 or in c major a-b-c-d#-e-f-g-a and in semitone intervals 2-1-3-1-1-2-2.

It contains the chromatic 5-chord 3-1-1-2  known also as Huzam

2) By using both the 1# and 5# 

in steps  6-7-1#-2-3-4-5#-6 or in c major a-b-c#-d-e-f-g#-a and in semitone intervals 2-2-1-2-1-3-1

which is again the inverse harmonic minor .


3) By using both the 1# and 4# and  keeping the 1

In steps 6-7-1-1#-2-3-4-4#-6 or in c major a-b-c-c#-d-e-f-f#-a and in semitone intervals 2-1-1-3-1-1-3  which is the Byzantine double parachromatic and has as 6-notes subscale the Blues scale 1-1-3-2-3-2.



C) Chromatizing both the 5th and major 3rd.

1) By using both the 1# and 4# and not keeping the 1

In steps 6-7-1#-2-3-4-4#-6 or in c major a-b-c#-d-e-f-f#-a and in semitone intervals 2-2-1-2-1-1-3  which has as 6-notes subscale the Blues scale 1-1-3-2-3-2.

It contains the chromatic 5-chord 2-1-1-3  known also as Samba

2) By using the 2# and the f# 

In steps 6-7-1-2#-3-4-4#-6 or in c major a-b-c-d#-e-f-f#-a and in semitone intervals 2-1-3-1-1-1-3  which is the Byzantine 2nd double parachromatic .

3) By using both the d# and g#
which gives the double harmonic minor 

In steps 6-7-1-2#-3-4-5#-6 or in c major a-b-c-d#-e-f-g#-a and in semitone intervals 2-1-3-1-1-3-1 .


We comment moreon the above:

 The Byzantine parachromatic minor utilizes the 3rd blue note f# if it would be a modification of the a natural minor In other words it would use f# instead of f and as a parachromatic minor it would be a b c db e f gb=f# a  or in semitone intervals 2-1-1-3-1-1-3 .   The 3rd blue note f# is utilized also in 6 notes  blues scales and country jazz music 2-1-1-3-2-3 or in notes a, b, c , c# , e , f# , a . The harmonic minor uses the 1st only Blue note that is g# instead of G in a natural minor and the double harmonic minor both 1st and 2nd blue notes the g# instead off g and D# instead of d. The Byzantine parachromatic minor scale is slightly less chromatic compared to the double harmonic minor and it was used in cosmic celebrations while the harmonic and double harmonic minor in Religious hymns. The scale that would use only the d# blue note therefore the a-b-c-d#-e-f-g-a,  in semitone intervals is the 2-1-3-1-1-2-2 is nothing else than the Mela Sulini, Raga Sailadesakshi, Raga Trishuli, Houzam: (Greece) or Neapolitan (Italy) scale. The scale that would use both the c# and d# blue notes would be the a-b-c#-d#-e-f-g-a,  in semitone intervals is the 2-2-2-1-1-2-2 which is the double melodic minor or Arabian scale also known as Kokilapriya, Raga Kokilaravam, or  Heptatonia tertia. The 7-notes scale as variation of the a natural minor that would use both the f# and d# blue notes would be the  a-b-c-d#-e-f#-g-a,  in semitone intervals is the 2-1-3-1-2-1-2 which is nothing else than the Bayat-e-Esfahan, Sultani Yakah, Zhalibny Minor, Armoniko minore: (Greece) or the 4th mode of the harmonic minor. The 7-notes scale that would use only the f# blue note is the  a-b-c-d-e-f#-g-a,  in semitone intervals is the 2-1-2-2-2-1-2 which is nothing else than the dorian mode of the G major scale. Notice also that the  Ney flute scale when converted to the equal tempered 12-notes scale would be an 8-note scale 2-1-1-2-1-1-3-1 or a-b-c-c#-d#-e-f-g#-a , and it contains the 3  blue notes c#, d#=eb and g# . The Ney 8-notes scale resembles a combination of the melodic minor and the harmonic minor.

We remind the reader that in the online notes here we call a sequence of 7 interval that sum-up to 12 semitones a mode and all cyclic permutations of it as the scale that the mode belongs. Thus any cyclic permutation of the 2-1-1-3-1-1-3  is considered again as the parachromatic Byzantine scale but at a different mode of it.

Other very well known 7-notes Byzantine scales but different from the parachromatic , also in  the chromatic family are the harmonic minor (https://en.wikipedia.org/wiki/Minor_scale#Harmonic_minor_scale ) and double harmonic minor (https://en.wikipedia.org/wiki/Double_harmonic_scale). 

244. LONG CHIMNEY (BRANCHE TUBE) IN LOW AND BASS WHISTLES TO LOWER THE TOTAL LENGTH AND MAKE THEM EASIER FOR FINGERING

 LONG CHIMNEY (BRANCHE TUBE) IN LOW AND BASS WHISTLES TO LOWER THE TOTAL LENGTH AND MAKE THEM EASIER  FOR FINGERING

The idea (and patent) of Yamaha with a long chimney or brach-tube just after the mouthpiece and of about 2/3 of bore size compared to main tube was so as to convert close-open acoustics (with odd only harmonics ) to open-open (with both odd and even harmonics). See e.g. https://www.youtube.com/watch?v=LzHasH3Acxw

But it has another effect too: It lowers the total length of the tube. This technique applied to low and bass whistles  makes them of considerably shorter length . This will make the covering of  the holes with the fingers a lot easier . Even the "pipers grip"might not be necessary now.

In  the next photo we see a  D4 clariphon (chalumeaux) with along chimney (about 1/3 of the sum-total length of both tubes . The brache has diameter about 2/3 of the diameter of the main tube) which converts it from closed-open acoustics to open-open acoustics. Nevertheless the same technique will make a Low D4 whistles with a fipple a lot shorter!

The next pictures are of corresponding Long Chimney soprano saxophones with cane reeds and sax mouthpieces as the Venova of Yamaha, or Cylisax of Linsey
https://www.youtube.com/watch?v=6wa0mPEmJI0
https://www.youtube.com/watch?v=J0Ka4M_CvVY
https://www.youtube.com/watch?v=1B5fTwSC4QQ

243. WHISTLES , QUENAS AND PANFLUTES WITH A MEMBRANE REED ON THE FIPPLE FOR LOW IMPEDANCE

WHISTLES AND QUENAS WITH A MEMBRANE  REED ON THE FIPPLE 

It is possible to have a reed on the soundhole of the fipple of a whistle! For this the sound hole must be larger, and then cover the extra part with a plastic or other material membrane reed. It could also be a cane reed. Or it could be a cooper foil  or aluminum foils,  of total thickness 0.08 mm .  Or it can be a double sheet of rubber surface from a balloon.  The vibration of the air which is vertical to the surface of the membrane will set in vibration the membrane-reed also which will influence the color and quality of the sound.  This idea exist also in the dizi chinese flutes, but they put the membrane not on the soundhole but on an extra hole just after the mouthpiece. It adds to the sound of the flute the sound of the membrane which vibrates as the air flows parallel to it. I used a membrane-reed from a (white) balloon, and actually I put it in double sheet as it was the balloon before inflating. It has to be well stretched and fixed on the fipple by tape. In the photo we see an example on a wooden-plastic Fipple of a Low D4 whistle with thin wall aluminum body of inner diameter 25 mm . The open sound hole that is left, has ratio of transverse to longitudinal sides 2:1.  The area that the membrane-reed covers is about double the uncovered one (Uncovered : 10mm*5mm Covered about 10mm*10mm ) Before the balloon reed, the fipple had large sound hole with very breathy sound and difficult 2nd octave. After the balloon reed the sound hole become 10mm*5mm and the low octave acquired very clear (not breathy) and soft sweet sound, while the 2nd octave acquired again very clear (not breathy) and loud melo sound,and somehow it is  more pleasant and easy to play in the higher octave than in the lower as is the case with the concert Bohm flute too.  This suggest happier melodies that star in the 2nd octave move in the low 1st octave and finally end again in the 2nd octave as in the upper registry whistles (see post 199 THE UPPER REGISTRY WHISTLES (28< Length / bore ID ratio  <48) FOR HAPPIER MELODIES ) .
The membrane on the fipple acts as intermediate impedance from that of the air vibration and the material of the tube at the sound-edge vibration. In total it lowers the impedance of initiating a vibration , especially on the 2nd octave.

 In winds there two types of impedance a) the vibration impedance responsible of propagating the vibration from the air column of the mouthpiece to the air column of the tube,and then outside the tube b) The air-flow impedance which is the resistance of the flow of the air. Large bore tubes have reverse effects on the two types of impedance: They increase the vibration impedance because a larger mass of air must vibrate , but they decrease the air-flow impedance because lower flow speeds are necessary to drive the blowing outside the tube compared to thin bore tubes. The air-flow impedance is by far of larger effect on the felt "resistance in playing and producing sound compared to the vibration impedance. The membrane on the fipple does not affect much the air-flow impedance but lessents the vibration impedance.

The overall result was a substantial improvement of the sound and easier playing response of the whistle. Somehow it has also the color of the sound of a quena.  Suddenly this cheap Low D4 whistle become the best sounding and playing Low D4 whistle among many other expensive ones that I have! The material of the reed influences the color of the sound. I did not try it but I assume that if I would put a cane reed from say an alto sax cane reed, the sound would be more woody. Obviously this can apply also to soprano C5 and D5 whistles and might allow rather wide bore such whistles (more than 14 mm)  to have easier , clear and loud 2nd octave, even if the Length/bore ratio is less than 20. This in particular gives very interesting applications on the native American  flutes , that traditional have Length/bore ratio<20 and do not have 2nd octave. With such membranes on the soundhole of the native American flutes they acquire easily 2nd octave  , but in order to be uniform in blowing it requires also a more appropriate hole sizing where the lower pitch holes are larger and the higher pitch holes smaller and not vice versa.

In the next 2 photos we see 6  whistles from PVC . An G4  an A4  and  a C4 (2nd  photo) with 20 mm inner diameter of the  bore and 25 mm external diameter and 3 a Bb3 , a C5 and and a D5 with 16.5 mm inner diameter of the bore and 20 mm external diameter . These whistles were initially crafted as tunable quenas , and they still have their quena mouthpieces. Their inner diameter of the bore gives Length/bore ratio less than 20 , thus normally they should not be able easily to have a 2nd octave with ordinary fipples. But with these membrane-reed fipples , they retain both the 1st octave full rich quena-like sound due to wide bore and big holes (for jazz partial holing) and also have a fine clear and loud 2nd octave because of the vibration of the membrane at higher pitches, which partially substitutes the adjustment in angle and air speed that we can do at the 2nd octave with the mouth and the quena rim-blowing mouthpieces. They are certainly easier to play and have more smooth and melo full  sound compared to them as quenas. 

In the next photo we see the originally crafted as tunable Bb4 quena , with its quena mouthpiece, but also with the membrane-fipple mouthpiece which makes it a whistle and an alto saxophone mouthpiece, that makes it also clariphon (chalumeaux) at Bb3 (one octave lower) and because of laws of acoustics capable of 1st only octave compared to quena and whistle that are capable of at least 2 octaves. In order  to have also the clariphon (chalumeaux) to play at least a 2nd octave too, either we should use a 8+1 holes system instead of 6+1 here,  or keep the 6+1 hole system and use (as in yamaha venova) a initial branche (chimney) as in post  244 that would make the close-open acoustics to open-open acoustics.

Obviously this idea of membrane that reduces the impedance and makes initiation of the sound easier but also vibration  self-maintenance shorter CAN APPLY TO QUENAS NOTCH AND TO PAN-FLUTE BLOWING HOLES!

242. HOW TO CONVERT A ROMANIAN CAVAL FLUTE TO PLAY THE HARMONIC MINOR DOUBLE HARMONIC MINOR , NEAPOLITAN MINOR ,AND NATURAL MINOR. THE CHROMATIC MINORS FLUTE

We remind the reader that in the online notes here we call a sequence of 7 interval that sum-up to 12 semitones a mode and all cyclic permutations of it as the scale that the mode belongs. Thus any cyclic permutation of the 2-1-1-3-1-1-3  is considered again as the parachromatic Byzantine scale but at a different mode of it.

See also the post about the parachromatic Byzantine flute (3rd chromatic Byzantine minor scale) post 235. 

Other very well known 7-notes Byzantine scales but different from the parachromatic or 3rd Byzantine chromatic minor , also in  the chromatic family are the harmonic minor or 1st Byzantine chromatic minor (https://en.wikipedia.org/wiki/Minor_scale#Harmonic_minor_scale ) and double harmonic minor or 2nd Byzantine chromatic minor (https://en.wikipedia.org/wiki/Double_harmonic_scale).

OF SCPECIAL INTEREST IS THAT INVERSE OF THE HARMONIC MINOR 2-2-1-2-1-3-1  IS DERIVED FROM THE FIRST 13 OVERTONES OR HARMONIC SERIES OF A STRING OR NATURAL TRUMPET IF  THE 7NTH HARMONIC (E.G.  C-D-E-F-G-G#-B-C )  if we perceive the 7nth overtone as B rather than Bb (in reality it is somewhere in the middle)  AND SO IT  is the inverse 7-notes scale of the first 13 overtones  ON THE OTHER HAND THE MELODIC MINOR OR THE 7-NOTE SCALE 2-2-1-2-1-2-2 E.G. C-D-E-F-G-G#-Bb-C WHICH IS DERIVED FROM THE FIRST 13 OVERTONES HARMONIC SERIES IN A NATURAL TRUMPET IF WE PERCEIVE THE 7NTH HARMONIC AS Bb rather than B.   BOTH SCALES  ARE   CONSTRUCTED FROM THE 4-CHORD 2-2-1 AND THE 5-CHORD. 


To convert a romanian 5-holes caval flute (see e.g. https://www.youtube.com/watch?v=p9j8DlakBuQ) to a 7 holes flute which can play both the harmonic minor and double harmonic minor we simply ad 4th hole to the upper 3 holes in the romanian caval between the upper 3 and lower two which is one semitone away from the last lower 3rd upper hole and also a thumb hole which is 3-semitones higher than the highest front hole and one semitone lower than the next 2nd harmonic root. Of course instead of a 4th upper front hole we may just make the lower of the upper 3 front holes of the caval larger and apply partial holing.

 Alternatively instead of a single large thump hole we may add a double thump hole (in vertical order not in horizontal order as in recorders double holes). Thus in a romanian caval flute rooted in A3 starting from the 5 holes that give  the notes A3-B3-C4-D#4-E4-F4 (in semitone intervals 2-1-3-1-1 which is a 6-notes scale sub-scale of the 7 notes double harmonic minor ) we will result in to the 7 holes  A3-B3-C4-D-D#4-E4-F4-G#4-A4 , (in semitone intervals 2-1-2-1-1-1-3-1 which is an 8 notes scale) and which will allow playing the 1st mode of the harmonic minor (1st Byzantine chromatic minor ) 2-1-2-2-1-3-1 or in notes A3-B3-C4-D4-E4-F4-G#4-A4, known to me as 1st mode of A3 harmonic minor and also the 1st mode of the double harmonic minor (2nd Byzantin chromatic minor scale) 2-1-3-1-1-3-1 or in notes A3-B3-C4-D#4-E4-F4-G#4-A4 known to me as 1st mode of A3 double harmonic minor. If we have double thump hole (or large size thump hole to apply partial holing) we have also the note G4 (in total A3-B3-C4-D#4-E4-F4-G4-G#4-A4 ) which allows also to play the natural (A4) minor.
In addition as the thump hole can play also the G, instead of G# ( e.g. A3-B3-C4-D#4-E4-F4-G4-A4) in semitones 2-1-3-1-1-2-2  then we get the 7-notes Neapolitan scale , instead of the double harmonic minor scale  2-1-3-1-1-3-1
See the photos below

The previous modification of the Romanian caval (which plays a 6-notes scale) so as to play both 7-notes scales , the harmonic minor and double harmonic minor was the minimal modification with 2 only additional holes.

Here are the photos of 2 soprano at B4 and D5  such modifications of a Caval flute with double thumb hole

WE SUMMARIZE:

We take now the example of D4-Caval Flute.

1) The Romanian Caval flute is a 6-notes scale 2-1-3-1-1-4 E.g. at D4 it is D4-E4-F4-G#4-A4-A#4 

This scale is one note less than a full 7-notes scale which is widely known among different cultures as double harmonic minor (see e.g. https://en.wikipedia.org/wiki/Double_harmonic_scale) When we say scale of notes , to differentiate it from a mode of a scale , we meana lso all 7 cyclic permutations of it as the same scale (all different 7 modes as modes of t he same scale)

So to make it a full double harmonic minor 2-1-3-1-1-3-1 or D4 it is D4-E4-F4-G#4-A4-A#4-C#5 you just have to open at hump hole  3-semitones higher than the highest front hole. And better be a large hole for partial holing for reasons that I will explain below. Or it can be a double hole but close together , by one semitone away so that with the thump we can cover one only or both. 

Now you already have the chords D minor , G minor , F minor , F major ,  A major , C# major  C#minor  C major With partial holing on the thump to give C5 we can play also the chord A minor

In addition we may play  the D-melodic minor  scale D4-E4-F4-G4-A4-B4-C#5-D5 with interval structure 2-1-2-2-2-2-1 (see e.g. https://www.basicmusictheory.com/d-melodic-minor-scale)

2) Many folk versions of Romanian Caval in Romania (as you can see in videos in youtube) add also a 4th hole to the upper group of 3 holes of the original caval and below the lower again one semitone apart, which gives the note G4. With this 8-notes scale D4-E4-F4-G4-G#4-A4-A#4-C#5, you can already play both the D4 double harmonic minor and also the D4 harmonic minor 2-1-2-1-1-3-1 or D4-E4-F4-G4-A4-A#4-C#5. (see e.g.https://en.wikipedia.org/wiki/Minor_scale#Harmonic_minor_scale  ) Plus you can play the natural D4 minor (with partial holing on the thump) that is D4-E4-F4-G4-A4-A#4-C5 with interval structure 2-1-2-2-1-2-2
And now the chords that you can play are the previous plus the  C minor .  

4) Sometimes some people add still another hole which is  the D#4 note. If you do so then  in addition you have the chord C minor so that all the minor triad of chords Dm-Gm-Cm is possible.
5) If on the otherhand we a the thump hole to a 5-hole caval  so that it is only one tone above the highest front hole, then we get the 7-notes Neapolitan scale (e.g. A B C D#, E, F, G, A) , instead of the double harmonic minor scale  (e.g. A B C D#, E, F, G#, A) .

VERSION OF THE FLUTE  IN  DOUBLE HARMONIC MINOR  WHICH IS CLOSED OR INVARIANT TO THE 3RD OVERTONE 

Nevertheless, the 3rd harmonic and on the same holes  in such a flute (and on the original 6-notes Romanian  Caval too) will not give nots inside the double harmonic minor as it does say in  a major mode flute . The simple harmonic minor with interval structure 2-1-2-1-1-1-3-1 is already non-symmetric in a shifting higher by an interval of 5th as does the 3rd overtone. Nevertheless the double harmonic minor has a mode the 5th mode which is symmetric to shift higher by an interval of 5th and in interval structure it is 1-3-1-2-1-3-1. Therefore if we open holes for this 5th mode of the double harmonic minor we will get again a flute in double harmonic minor which has the additional advantage that the 3rd overtones on the same holes gives again notes of the same scale.

E.g. if the flute starts again from g, the notes that we should open holes are the 

1st hole open gives g#4

2nd hole open gives b4

3rd hole open gives c5

4th hole open gives  d5

5th hole open gives  d#5

6th thumb hole gives f#5

This scale is the a mode of the c5 double harmonic minor . By partial holing on the 2nd hole and on the 6th hole we may play also the c5 simple harmonic minor and natural c5 minor .

A VERSION THAT INCLUDES THE BYZANTINE PARACHROMATIC SCALE 

If we add a 8th hole which is one semitone lower than the lowest hole of the current modified caval flute, then we get a flute  that includes the Romanian Caval, and the Byzantine parachromatic flute and can play a) The double harmonic minor b) the harmonic minor c) the byzantine parachromatic scale (see post 235)

A 8 HOLES VERSION WHICH IS UNIFORM IN THE SEMITONES AND CAN PLAY ALL THE ABOVE SCALES

Finally if we add still another holes in between the 1st front 2 and the upper front 4 , making thus in total 7 front holes in a row all one semitone away from its next we get a 9 notes scale 

2-1-1-1-1-1-1-3-1 that can play all the above scales a) double harmonic minor b) simple harmonic minor  c) parachromatic and much more while being uniform in semitones at the front 7 holes. 

We may compare it with some soprano (and not only) cavals that are about t he same except that the tump hole is only a semitone away from the highest front gibing the 9-notes scale 

2-1-1-1-1-1-1-1-3 . This arrangement though cannot play the double harmonic minor, although it seems more convenient at the fingers and in particular at the thump hole.

241. THE LOOSE CONCEPT OF DIATONIC SCALE TONALITY IN EARLY CLASSICAL JAZZ (NEW ORLEANS) : AT LEAST 50% OF THE TIME ONLY IN THE SCALE

As with almost all folk happy music, the early classical jazz of New Orleans had harmony in the songs was based initially on the simplicity of a triad of major chords and in particular of 1-4-5 (the 12-bars blues deviated later to 5-2-1, substituting 4 with its minor relative 2).

Nevertheless even early classical jazz is known for its reach chromatic harmony, and this seems as a contradiction but it is  not!

What happens here is what happens with a free accompanying of an improvisational melody with a chord. The chord fits as long as at least half of the the time that notes of the melody sound , are from notes that belong to the chord at various octaves.

Similarly an early classical jazz song is supposed to be on  diatonic scale (or mode of it) as long  as at least half of the the time that notes of the melody sound , are from notes that belong to the diatonic scale  at various octaves. 

Thus the triad 1-4-5 will work at least half of the time, with other chords either from this diatonic scale or from the chromatic 12-notes scale appearing if necessary as a closer follow-up of the melody! 

Here is an example of such early classical jazz songs played by the marvelous band Tuba Skinny:

https://www.youtube.com/watch?v=pZ7mg9Kl-RU

ACCOMPANYING WITH  SINGLE POWER CHORD:
And there is more on this!
The harmony of a jazz improvisation song can be simplified nor to three but to a single chord! 
E.g. If the improvisation song is in Bb, the single accompanying chord will be the power-5 chord on the root Bb3-F4-Bb4. Then two completely different melodies that are at least 50% in the scale and that follow the same rhythm, will very well be accepted as improvisational parallel countermelodies  within the base simple harmony.  (see also posts  71 ,126, 128, 135, 138, 141 )