235. THE PARACHROMATIC BYZANTINE (BLUES WITH LEADING TONE) OVERTONE WHISTLE. HEXATONIC BLUES AS CHROMATIC 7-NOTES DIATONIC TONALITY

This whistle is like an overtone whistle with high Length/(inner_diameter_of_Bore) ratio (here it is 55.5cm/1cm=55.5 ) and it is based on the Byzantine (para)chromatic 7-notes scale in semitones 

2-1-1-3-1-1-3  (see post 227  and also https://books.google.gr/books?id=tvxMDwAAQBAJ&pg=PA281&lpg=PA281&dq=Byzantine+parachromatic+scale&source=bl&ots=CM8asY99sh&sig=ACfU3U2I6jjEtOsdTJhQYb1U3ygHl_yK7g&hl=el&sa=X&ved=2ahUKEwjB-9W1rfHiAhWq-ioKHfHMBDIQ6AEwC3oECAkQAQ#v=onepage&q=Byzantine%20parachromatic%20scale&f=false )

Here some modes and invere modes under various names of this scale. 

1 1 3 1 1 3 2	Chromatic Mixolydian
1 3 1 1 3 2 1	Chromatic Lydian, Raga Lalit, Bhankar
3 1 1 3 2 1 1	Chromatic Phrygian
1 1 3 2 1 1 3	Chromatic Dorian, Mela Kanakangi, Raga Kanakambari
1 3 2 1 1 3 1	Chromatic Hypolydian, Purvi That, Mela Kamavardhani, Raga Shri, Pantuvarali, Basant, Kasiramakriya, Suddharamakriya, Puriya Dhanashri, Dhipaka, Pireotikos: Greece
3 2 1 1 3 1 1	Chromatic Hypophrygian, Blues scale III
2 1 1 3 1 1 3	Chromatic Hypodorian, Relative Blues scale, Raga Dvigandharabushini
2 3 1 1 3 1 1	Chromatic Mixolydian inverse
1 1 2 3 1 1 3	Chromatic Phrygian inverse
1 1 3 1 1 2 3	Chromatic Hypophrygian inverse
3 1 1 3 1 1 2	Chromatic Hypodorian inverse

1 3 1 1 2 3 1

Raga Lalita, Persian, Chromatic Hypolydian inverse, Raga Suddha Pancama

Its characteristic tetrachord is the 1-1-3 (instead of the 1-3-1 in the harmonic minor and harmonic double minor).

Here also  as  Parachromatic, new genus 5 + 5 + 20 parts 7 in The mathematical theory of tone systems 

https://books.google.gr/books?id=o2K1DwAAQBAJ&pg=PA274&lpg=PA274&dq=Parachromatic,+new+genus+5+%2B+5+%2B+20+parts+7&source=bl&ots=bFLsv8tBf4&sig=ACfU3U3FRBsIjZd2OmwnlcZ8-tbr_FMPHQ&hl=en&sa=X&ved=2ahUKEwjkjrP_653zAhWNNOwKHSKJDhMQ6AF6BAgCEAM#v=onepage&q=Parachromatic%2C%20new%20genus%205%20%2B%205%20%2B%2020%20parts%207&f=false

The flute is of lowest note D4 and it is end-blowing (fipple) it is made from elder wood.

The Byzantine (para)chromatic 7-notes scale here is

D5, E5, F5, Gb5 ,A5, Bb5, B5 , D6

or as interval structure in semitones

2-1-1-3-1-1-3 . or of it assumed as the 5th mode of the  next version Gb3   parachropmatic= 5#-6#-7-1-2#-3-4-5# Thus like the double harmonic minor 1-2#-3-4-5#-6-7-1' but with an extra sharp at 6. It has also the chord 5#m. The Byznatine parachromatic flute in the photo is the 5th mode of it

It can be considered chromatic tonality of the B major diatonic scale in improvisation e.g. with 12-bars blues. 

The double harmonic minor would be on this flute as

D5, E5b, F5, Gb5 ,A5, Bb5, B5 , D6 or in semitones 1-2-1-3-1-1-3 in other words with flat on the 2nd note E4. 

While if we gave flat on the 5th note D5, E5, F5, Gb5 ,Ab5, Bb5, B5 , D6   it becomes in semitones

2-1-1-2-2-1-3  called  also Mela Namanarayani, Raga Narmada, Pratapa, Harsh Major-Minor (see post  227)

The Byzantine parachromatic flute is also the 2nd mode of the 7-notes Blues scale with  leading note. Here the first note of the Blues scale with leading note which would be the B4

The 7nth mode of the first version of the parachromatic in intervals is the 

3-2-1-1-3-1-1, is realized in a diatonic scale as

1-3b-4-5b-5-7b-7-1 

or 

1-2#-4-5b-5-7b-7-1 

or 

1-2#-3#-4#-5-6#-7-1  

The 5th mode of it is as follows

1-2#-3-4-5#-6#-7-1'  or insemotones 3-1-1-3-2-1-1 Thus like the double harmonic minor 1-2#-3-4-5#-6-7-1' but with an extra sharp at 6. It has also the chord 5#m. The Byznatine parachromatic flute inthe photo is the 5th mode of it. 

Compared to the diatonic scale 1-2-3-4-5-6-7 , the 1st mode it has the altered or chromatic tonality chords 7M, 2#m and 1m.

It is also called BLUES WITH LEADING TONE SCALE.

And by skipping the 7nth note we get the 6-tones blues scale 

1-3b-4-5b-5-7b-1 (1-2#-3#-4#-5-6#-1) or another mode (1-2#-4-5#-6#-7-1) ) and in semitones

 3-2-1-1-3-2.

An alternative Blues hexatonic would be 2-3-1-1-3-2. (e.g. 1-2-4-5b-5-7b-1  and it is known as Bebop hexatonic scale.  As  7-notes 1-2-4-5b-5-7b-7-1  in semitones 2-3-1-1-3-1-1 which is the inverse of  the Byzantine parachromatic ) and it can be as chromatic tonality over the same diatonic as in the standard blues hexatonic. 

An interseting 8-notes scale derived from it might be called parachromatic is the 

1-2#-3-4-4#-5-6#-7-1  or in semitones 3-1-1-1-1-3-1-1

7M, 2#m , 1M and  1m.

In other words if in the parachromatic 7-notes scale we start from the 7nth and we skip the 6th note we get the 6-notes blues scale. 

This scale is derived by combining the chromatic family pentachord 2-1-1-3 (which is also known as  Samba) with the chromatic family tetrachord 1-1-3 known also as parachromatic tonal tetrachord.

The Byzantine parachromatic scale is called also inverse Persian or  Purvi Theta scale.

If we want to tune a portable Celtic harp with levers for sharps it could be e.g. the next mode of it. 

c-d#-e-f-g#-a#-b-c

or  the 7nth mode of its (blues scale with leading note).

c-d#-e#-f#-g-a#-b-c

From the 4 "blue" notes of diatonic scale (e.g. at natural a minor a, b, c , d , e , f , g , a the 4 blue notes would be in this order g#, d# , f#, c# ). They 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# . There cannot be other as first 4 notes other than the above 4 blue notes.   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 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, 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. 

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). 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. Thus in a romanian caval flute rooted in C4 starting from the 5 holes that give  the notes C4-D4-Eb4-F#4-G4-Ab4 (in semitone intervals 2-1-3-1-1) we will result in to the 7 holes  C4-D4-Eb4-F4-F#4-G4-Ab4-B4-C5 , (in semitone intervals 2-1-2-1-1-1-3-1) which will allow playing the harmonic minor (1st Byzantine chromatic minor ) 2-1-2-2-1-3-1 or in notes C4-D4-Eb4-F4-G4-Ab4-B4-C5 , known to me as 1st mode of C4 harmonic minor and also the double harmonic minor (2nd Byzantin chromatic minor scale) 2-1-3-1-1-3-1 or in notes C4-D4-Eb4-F#4-G4-Ab4-B4-C5 known to me as 1st mode of C4 double harmonic minor. See the photo below

The whistle looks like a romanian caval flute too except the latter has not the lowest hole of the parachromatic byzanatine whistle (see e.g. https://www.youtube.com/watch?v=p9j8DlakBuQ) .  Thus a Romanian caval flute that we add a lowest hole one semitone lower than the lowest of the Caval becomes a Byzantine parachromatic flute.

The whistle looks also like the holes pattern of a Ney flute , and because of its high L/B ratio plays easier in  the 2nd octave than in the 1st octave. A Turkish Ney has also two groups of 3 holes with distances between each group of one semitone, but the distance between the two groups of 3 holes is almost a tone, while here it is a 3-semitones. If the scale of the Ney flute would be converted to the equal tempered 12-notes scale it would be the 8-notes scale 2-1-1-2-1-1-3-1 e.g. a-b-c-c#-d#-e-f-g#-a , which is obviously different from the parachromatic scale but also different from the neapolitan  or inverse of it and different from the harmonic minor or inverse of it. The Ney 8-notes scale resembles a combination of the melodic minor and the harmonic minor. A Ney is also rim-blowing wind while here it is with a fipple as it is usual with overtone winds. There is not thumb hole for the chromatic Byzantine whistle as it not necessary as overtone flute. But in Ney too that does exist a thumb hole it is mainly used in the first harmonic octave.

The Turkish caval seems  much closer to the Byzantine parachromatic flute than the Romanian caval.

Some how this Byzantine parachromatic scale whistle  resembles also a suling flute.

The tube is made from elder wood.

Here are two photos of it 

Finally if we add a 7nth hole between the 3rd and 4th of the current flute and one semitone lower than the 4th , and also a thumb hole which is 3 semitones higher than the highest front hole of the current flute we get a  7+1 holes 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.

I have ordered also in Seydel harmonica manifacturing company though their online customization in their site ,an harmonica tuned on the parachromatic Byzantine scale on the root D4.