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.