HEXATONIC SCALES FOR THE HARMONICA
(see also post 215 and 364)
THESE 2-CHORD HEXATONIC HARMONICAS DESCRIBED HERE ARE NOT DESIGHNED SO MUCH TO PLAY ALL POSSIBLE MELODIES ON A SINGLE HARMONICA BY BENDING AND OVERBLOW BUT TO MAKE EASY IMPROVISATION ON HEXATONIC SUBSCALES OF THE SCALES DIATONIC, HARMONIC MINOR, 7-NOTES BLUES (INVERSE HARMONIC MINOR) , DOUBLE HARMONIC MINOR, MELODIC MINOR ETC SUCH 2-CHORDS IMPROVISATIONS ARE COMMON IN CUBA AND LATIN JAZZ FOLK MUSIC, GREEK ISLANDS MUSIC, IRISH MUSIC ETC
MOST OF THE HEXATONIC TUNINGS IN THIS DISCUSSION HAVE A SINGLE CHORD AT THE BLOW ROW AND ANOTHER SINGLE CHORD AT THE DRAW ROW.
ACTUALLY ANY TWO SUCCESIVE CHORDS IN THE DIATONIC SCALE (E.G. 7DIM-1M, OR 4M-5M, 3M-4M, 5M-6m , 6m-7dim) CAN BE USED FOR AN APPROPRIATE TWO-CHORD HEXATONIC TUNING HARMONICA.
THUS WE WILL HAVE THE NEXT 6 TYPES OF CHORD PAIRS IN THE HARMONICA WHICH ARE CHORDS IN DIATONIC CHROMATIC RELATION
M=MAJOR m=MIOR d=DIMINSIHED
n=number of semitones that the roots are apart
IONIAN/MYXOLYDIAN: M2m
DORIAN: m2m
FRYGIAN: m1M
LYDIAN: M2M
AEOLIAN: m2d
LOCRIAN:d1M
But we also present many other non-diatonic chromatic pairs that involve also augmented chords and a re met in the harmonic minor (which apears also in the overtone sequence) double harmonic minor, melodic minor (which apears also in the overtone sequence) etc
E.G.
m2M (Erik Satie hexatonic of the harmonic minor hptatonic)
M2dim (hexatonic from melodic minor)
m1m
M3m
M1M (Hexatonic from the harmonic minor)
aug2M
dim1m
m6m
aug3aug
dim1aug
etc
I have ordered in Seydel company and play all of the next harmonicas of diatonic gendre chromatic gendre and enharmonic gendre hexatonic sub scales of the diatonic scale of the harmonic minor scale and invererse harmonic minor scale (Blues 7-tonic scale ) and when I will find time I will upload sound files with improvisations of them. Of course I think it is much cheaper instead of ordering so many custom 2-chords hexatonic harmonicas as below, to just tune the digital harmonica Lekholm DM48 which I also have and it is fun to try these tunings and easy improvisations on them
ALL OF THE HEXATONIC TUNING IN THIS DISCUSSION HAVE A SINGLE CHORD AT THE BLOW ROW AND ANOTHER SINGLE CHORD AT THE DRAW ROW.
ACTUALLY ANY TWO SUCCESIVE CHORDS IN THE DIATONIC SCALE (E.G. 7DIM-1M, OR 4M-5M, 3M-4M, 5M-6m , 6m-7dim) CAN BE USED FOR AN APPROPRIATE TWO-CHORD HEXATONIC TUNING HARMONICA.
THUS WE WILL HAVE THE NEXT 6 TYPES OF CHORD PAIRS IN THE HARMONICA WHICH ARE CHORDS IN DIATONIC CHROMATIC RELATION (the roots are separated by an interval of 2nd)
e.g. if the 7-notes diatonicscale is the C-D-E-F-G-A-B-C in semitones 2-2-1-2-2-2-1 then
M=MAJOR m=MIOR d=DIMINSIHED
1,2,3 etc =number of semitones that the roots are apart
1) IONIAN/MYXOLYDIAN: M2m C-D-E-F-G-A-C in semitones 2-2-1-2-2-3 and over the Blow-draw 2 chords Cmajor Dminor
or G-A-B-C-D-E-G and over the Blow-Draw 2 chords Gmajor Aminor (also called Celtic minor hexatonic)
2) DORIAN: m2m D-E-F-G-A-B-D in semitones 2-1-2-2-2-3 and over the Blow-Draw 2 chords Dminor-Eminor (also called Celtic major hexatonic)
3) FRYGIAN: m1M E-F-G-A-B-C-E in semitones 1-2-2-2-1-4 and over the Blow-Draw 2 chords Fmajor-Eminor (also a hexatonic version of the
akebono 5-notes scale)
4) LYDIAN: M2M F-G-A-B-C-D-F in semitones 2-2-2-1-2-3 and over the Blow-Draw 2 chords Fmajor-Gmajor (also called an alternative
version of Celtic major scale)
5) AEOLIAN: m2d A-B-C-D-E-F-A in semitones 2-1-2-2-1-4 and over the Blow-Draw 2 chords Aminor-Bdim
6) LOCRIAN:d1M B-C-D-E-F-G-B in semitones 1-2-2-1-2-4 and over the Blow-Draw 2 chords Bdim-Cmajor (also called enharmonic major)
See also posts 274 and 225.
THE HEXATONIC SCALES DESCRIBED BELOW FOR THE HARMONICA THAT CREATE TWO ONLY CHORDS ARE AS WELL APPLICABLE FOR T HE CELTIC HARP WITH LEVERS. WE ONLY HAVETO REPEAT ONE NOTE ON THE NEXT STRING. AGAIN TWO ONLY CHORDS ARE CREATED (BU EVEN AND ODD STRINGS EXCEPTTHE REPETIONS) AND IMPROVISATIONS CAN BE CARRIED IN THE CELTIC HARP AS WELL.
In ancient Greece according to Aristoxenos, there were 3 musical gendres , the diatonic , the chromatic and enharmonic which were also tetrachords (total length an interval of 4th) and pentachords (total legth an interval of 5th and consisting from an initial or final tone and a tetrachord as before) and by combing a tetrachord with a pentachord they got various 7-notes scales inside an octave. In other words the 7-notes scale was of the form Tetrachord1+2+tetrachord2 , in which case it was called two "divorced" tercahords or Tetrachord1+tetrachord2+2 in which case it was called two adjoint tetrachords. 1) the Diatonic was balanced feelings (that eventually after more than 1 thousand years resulted to the 7-notes diatonic scale, and a simplified rounding of their tetrcahords to a single one was the 2-2-1 and most probably all permutations of it ) the 2) Chromatic was sad feelings (that eventually after more than 1 thousand years resulted to the 7-notes harmonic minor and double harmonic minor scales, blues scale etc , And a simplified rounding of their tetrachords to a single one was the 3-1-1 nd most probably all permutations of it ) and 3) the enharmonic was happy feelings (used major 3rd intervals and a simplified rounding to a single one was the 4-(1/2)-(1/2)) and most probably all permutations of it ) and has many similarities with the Japanese 5-notes scales like the Akebono with interval structure 4 - 2 - 1 - 4 - 1 e.g. at the mode 2-1-4-1-4 e.g. A B C E F A. (See e.g. the video https://www.youtube.com/watch?v=vv7CO-nVFj8 )
DIATONIC GENDRE: CIRCULAR TUNING FOR THE 6-NOTES CELTIC MINOR SCALE
We may also notice that the 6-notes scales are favored for a harmonica, as the periodicity in the circular tuning is per octave and not per 2 octaves as in 7-notes scales. A good example is the Celtic minor 6-notes scale ( in semitones 2-2-3-2-2-1). This scale is used also for the hundpans and hang drums. The example is in the next table of tunning for the case of D root. The blow row is only the chord I and the draw row only the chord ii. The Celtic minor is the maximal harmonic 6-notes scale, in the sense that it is a 6-notes scale with the maximum number of standard chords. In the same way that a 7-notes diatonic scale is a maximal harmonic 7-notes scale in the sense that it is a 7-notes scale with a maximum number of standard chords (see the article https://simplerguitarlearning.blogspot.com/2018/08/117-small-7-notes-diatonic-scale-and.html )
An example is in the next table of tunning for the case of D root.
MOST OF THE HEXATONIC TUNINGS IN THIS DISCUSSION HAVE A SINGLE CHORD AT THE BLOW ROW AND ANOTHER SINGLE CHORD AT THE DRAW ROW.
ACTUALLY ANY TWO SUCCESIVE CHORDS IN THE DIATONIC SCALE (E.G. 7DIM-1M, OR 4M-5M, 3M-4M, 5M-6m , 6m-7dim) CAN BE USED FOR AN APPROPRIATE TWO-CHORD HEXATONIC TUNING HARMONICA.
Stil another mode of it is the next where at blowing is the major chord and at draw is the minor. In the example table below we are in t he G major scale.
On the other hand the sequence 2-3-2-2-2-1 (e.g. C-D-F-G-A-B) IS NOT A CYCLIC PERMUTATION of the 2-2-3-2-2-1 or 1-2-2-3-2-2 or 3-2-2-1-2-2 and it should be considered a different scale than the Celtic 6-notes (minor) not a different mode of it. It could be called maybe Celtic 6-notes major, because both the blow-row chord and the draw-row chord are major chords! But it can also be considered a Hexatonic version of the melodic minor 2-1-2-2-2-2-1. It may be also called 1st harmonic hexatonic as it appears as the notes of the first 11 overtone harmonics. The indication 1st is becaouse the 7nth harmonic e.g. at root C is between Bb and B , so the first choice gives this hexatonic while the 2nd choice the 2nd harmonic hexatonic which is the 2-2-1-2-4-1 as we shall see later in the enharmonic gendre.
MOST OF THE HEXATONIC TUNINGS IN THIS DISCUSSION HAVE A SINGLE CHORD AT THE BLOW ROW AND ANOTHER SINGLE CHORD AT THE DRAW ROW. Below is the table of such a tuning for a harmonica starting from D, and not C but with the same interval structure 2-3-2-2-2-1. And there is alo the inverse of this scale with interval structure 2-1-2-2-2-3 E.g. again derivable from the 7-notes C major mode of the diatonic scale , but now we omit C. Thus D-E-F-G-A-B-D . I believe the previous discussion completely clarifies the distiction between a scale and its modes.
The Byzantine culture absorbed the musical culture of Ancient Greece, that used mainly not 7-notes scales but 4 and 5 notes scales of total length an interval of 4th or 5th (called tetrachorda). The names of the modes Ionian, Dorian, Phrygian , Lydian etc were originally different 7-notes scales in the Byzantine empire relevant to the places in Greece that were mostly used, that when the European culture after Bach absorbed them in the 12-notes equal tempered system, thet altered them, and they ended to become different modes of the one diatonic scale and not different scales.
Hexatonic scales as the above at various modes of them are used not only at modern handpans but also at chinese Bahu flutes.
CHROMATIC GENDRE: BLUES - COUNTRY 6-NOTES MAJOR SCALE AND THE 7-NOTES BYZANTINE PARACHROMATIC SCALE.
According to the wikipedia (https://en.wikipedia.org/wiki/Blues_scale), a 6-notes version of the major country-blues scale is e.g. the
C, D, D♯/E♭, E, G, A, with interval structure 2-1-1-3-2-3. Or if we prefer a root at D, then D-E-F-F#-A-B-D. While if we prefer the root A it will be A-B-C-Db-E-Gb-A or 6-7-1-2b-3-5b-6 We notice that we utilize the 2b and 5b blue notes of the diatonic scale only in place of the 2 and 5 and we omit the 4 note. Below is the table for a harmonica with such a tuning.
On the other hand historically the Byzantine emptire was utilizing many 7-notes scales, not possible to include in the Bach equal tempered 12-notes chromatic scale. But 3 chromatic sacles of them are possible more or less to include, Two of the chromatic such scales are the harmonic minor (e.g. from the A natural minor we derive the harmonic minor by giving a sharp at G, thus A B C D E F G# A , with interval structure 2-1-2-2-1-3-1) and the double harmonic minor (an additional sharp to d thus A B C D# E F G# A , with interval structure 2-1-3-1-1-3-1). They where used mainly in religious hymns in the Churchs. But the 3rd such chromatic scale was used mainly in the Emperors palace and other cosmic events and was called parachromatic (see e.g. http://www.huygens-fokker.org/docs/modename.html http://www.huygens-fokker.org/scala/ ). The Byzantine parachromatic scale is called also inverse Persian or Purvi Theta scale. The part 2-1-1-3 is also known as samba pentachord in arabian culture, while the part 1-1-3 is known since ancient Greece time as the tonal tetrachord of the chromatic family. The interval structure of the parachromatic Byzantine scale is 2-1-1-3-1-1-3 . When assumed to start from the 6th note (Aelolian mode), 6-7-1-2-3-4-5-6 , to derive the Byzantine parachromatic we only need to convert 2 to 2b and 5 to 5b which means 6-7-1-2b-3-4-5b-6 .Thus starting from D , it would be D, E, F, Gb ,A, Bb, B , D While if we prefer the root A it will be A-B-C-Db-E-F-Gb-A or 6-7-1-2b-3-4-5b-6. We notice that we utilize the 2b and 5b blue notes of the diatonic scale only in place of the 2 and 5 . We may observe that it is a 7-notes version of the Blues scale, and a tuning table for a harmonicas at the D4- major 6-notes Blues-country scale and a D4- parachromatic 7-notes scales are given below. (see also article https://simplerguitarlearning.blogspot.com/2019/06/235-parachromatic-byzantine-overtone.html ) The blues major scale is derived from the Byzantine parachromatic 6-7-1-2b-3-4-5b-6. by omitting the 4 note , thus 6-7-1-2b-3-5b-6 with interval structure 2-1-1-3-2.
On the other hand if we assume the Byzantine parachromatic to be a major scale and we start from the ionian mode of a diatonic scale 1-2-3-4-5-6-7-1, or A, B, C♯, D, E, F♯, and G♯. then the Byzantine parachromatic would be 1-2-3b-4b-5-6b-7bb-1' or A-B-C-Db-E-F-Gb-A. And to derive the major blues scale we simply omitt the 6b, or A-B-C-Db-E-Gb-A (in semitones 2-1-1-3-2-3).
The major blues scale e.g. D major Blues scale might be supposed to be used for improvisations of 12-bars blues on the D major scale, as it can also be also derived from the major D pentatonic by adding a blue note 3b which will make it 6-notes scale. E.g. the blues major D scale D, E, F, Gb ,A, B , D, (in semitones 2-1-1-3-2-3) whould play over the chords Dmajor D-F#-A, (D-Gb-A), A major A-C#-E, or A major with 6th A-C#-E-Gb and G major G-B-D. Obviously some notes would creare a dissonance, but it may be considered part of the chromaticity of the Blues major scale improvisation. Similarly the D major blues could be used to improvise over the C major and G major 12-bars blues.
CHROMATIC GENDRE: MORE 6-NOTES SCALES THAT ARE BEAUTIFUL FOR HARMONICAS. COMBINING PARTS OF THE PENTATONIC WITH CHROMATIC PARTS.
MOST OF THE HEXATONIC TUNINGS IN THIS DISCUSSION HAVE A SINGLE CHORD AT THE BLOW ROW AND ANOTHER SINGLE CHORD AT THE DRAW ROW.
ACTUALLY ANY TWO SUCCESIVE CHORDS IN THE DIATONIC SCALE (E.G. 7DIM-1M, OR 4M-5M, 3M-4M, 5M-6m , 6m-7dim) CAN BE USED FOR AN APPROPRIATE TWO-CHORD HEXATONIC TUNING HARMONICA.
We noticed in the previous post that the Blues-country scale with interval structure 2-1-1-3-2-3, (and any cyclic permutation of it, is still the same scale although a different mode of it) sounds partially as the pentatonic scale 2-2-3-2-3 and partially with chromatic part 1-1-3 which was identified as the ancient Greek tonal tetrachord of the chromatic family. By writting the Blues scale in a different 5th mode of it (cyclic permutation) makes it more clear: 2-3-2-1-1-3 . The 2-3-2 part is inherited from the pentatonic scale 2-2-3-2-3 and the 1-1-3 is the ancient Greel tonal tetrachord of the chromatic family (that exist also in the Byzantine emperor parachromatic 7-notes scale). Such scales may be obviously be used in Gypsy jazz, but in ordinary western jazz too.
Other parts of the pentatonic sacle are also the 2-2-3,
1) Thus we may discover the next hexatonic scale that should sound similarly 2-2-3-1-1-3 and it is not a different mode of the Blues-country scale. In the tables below we show this tuning , when starting from the root D . Thus D-E-F#-A-Bb-B-D. It is still a 6-notes version of the Byzantine parachromatic scale of the previous post but different from the Blues-country scale, still sounding in a similar way.
2) There are the invesres of course of the previous hexatonic scales a) the inverse ofthe Blues-country in the mode 2-3-2-1-1-3, which is the 2-3-2-3-1-1 (after inverting and taking a cyclic permutation of it). b) The inverse of the 2-2-3-1-1-3, which is the 3-2-2-1-1-3 ((after inverting and taking a cyclic permutation of it). We write them always so as to separate the pentatonic part, and the chromatic part.
3) If we combine now the pentatonic part 2-3-2 (of the Blues scale) with the chromatic part 1-3-1 (which exists in the harmonic minor) we get a hexatonic scale 2-3-2-1-3-1, that sounds partially as pentatonic and partially as chromatic (harmonic minor). It is a 6-notes version of the harmonic minor scale,perfect for harmonicas that favor in the cyclic tuningthe heaxtonic scales. Some times it is also called the Erik Satie hexatonic scale. (See e.g. the video https://www.youtube.com/watch?v=okU96j6ThIM&t=8s )We give below the tuning table when starting from the root D. And of course there is the inverse of it again which is not a different mode of it. D-E-G-A-Bb-C#-D.
4) If we combine now the pentatonic scale part 3-2-2 with the chromatic part 1-3-1 (which exists in the harmonic minor) we get a hexatonic scale
3-2-2-1-3-1, or at a different mode as 2-1-3-1-3-2 that sounds partially as pentatonic and partially as chromatic (harmonic minor). It is a 6-notes version of the Neapolitan scale 2-1-3-1-1-2-2 (e.g. from D it would be D-E-F-G#-A-Bb-C-D), perfect for harmonicas that favor in the cyclic tuning the hexatonic scales. We give below the tuning table when starting from the roor D thus D-E-F-G#-A-C-D , with interval structure at the mode 2-1-3-1-3-2 . It is over the chords Dm-Caug. This 6-tonic scale is also a hexatonic scale of the 7-notes extension of the Blues scale 3-2-1-1-3-2 which in semitones it is the 2-1-2-1-1-3-2 e.g. C-D-Eb-F-Gb-G-Bb-C. And of course there is the inverse of this neapolitan again which is not a different mode of it and in semitones it is the 2-3-1-3-1-2 and it is also a hexatonic version of the 7-notes scale 2-2-1-1-3-1-2 (e.g. C-D-E-F-Gb-A-Bb-C). This hexatonic scale e.g. C-D-F-Gb-A-Bb-C is over the chords Fmajor and Gb augmented. On the other hand what is considered a 7-notes blues scale (see e.g. https://en.wikipedia.org/wiki/Blues_scale ) the 2-1-2-1-3-1-2 (which is actually the inverse harmonic minor scale) e.g. C-D-Eb-F-Gb-A-Bb-C , has a 6-notes version 1-2-1-3-1-4 or in adifferent mode the 2-1-3-1-4-1 e.g. Eb-F-Gb-A-Bb-D-Eb which is over the chords Ebm and Dm. Similarly an alternative 6-notes version of the latter 7-notes blues scale (and also inverse harmonic minor) is the C-D-Eb-F-Gb-A-C or in semitones 2-1-2-1-3-3 and over the chords Cdim and Dminor.
ALL 7 HEXATONIC SCALES FROM THE 7 MODES OF THE 7-NOTES BLUES SCALE (OR INVERSE HARMONIC MINOR SCALE)
Some og these hexatonic scales of the inverse harmonic minor are also hexatonic scales of the diatonic scale or the melodic minor or the double harmonic minor!
7-NOTES BLUES SCALE C-D-Eb-F-Gb-A-Bb (or in semitones 2-1-2-1-3-1-2) also inverse harmonic minor scale, with chords
Cdim, Dminor, Ebminor, FMajor, Gb augmented , A diminished , Bb major
4.1) 1st mode C-D-Eb-F-Gb-A-C (or in semitones 2-1-2-1-3-3) based on the 2 chords Cdim-Dm
4.2) 2nd mode D-Eb-F-Gb-A-Bb-D (or in semitones 1-2-1-3-1-4) based on the 2 chords
Dmin-Ebmin (hexatonic caval double harmonic minor too)
4.3) 3rd mode Eb-F-Gb-A-Bb-C (or in semitones 2-1-3-1-2-3) based on the 2 chords Ebmin-Fmajor (Erik Satie hexatonic scale)
4.4) 4th mode F-Gb-A-Bb -C-D-F (or in semitones 1-3-1-2-2-3) based on the 2 chords
Fmajor-Gbaug ( inverse hexatonic neapolitan )
4.5) 5th mode Gb-A-Bb-C-D-Eb-Gb (or in semitones 3-1-2-2-1-3) based on the 2 chords
Gbaug-Adim
4.6) 6th mode A-Bb-C-D-Eb-F-A (or in semitones 1-2-2-1-2-4) based on the 2 chords Adim-Bbmajor (hexatonic enharmonic major, or hexatonic Locrian mode)
4.7) 7th mode Bb-C-D-Eb-F-Gb-Bb (or in semitones 2-2-1-2-1-4) based on the 2 chords
Bbmajor-Cdim (Hexatonic melodic minor too)
ALL 7 HEXATONIC SCALES FROM THE 7 MODES OF THE 7-NOTES HARMONIC MINOR SCALE .
Some og these hexatonic scales of the inverse harmonic minor are also hexatonic scales of the diatonic scale or the melodic minor or the double harmonic minor!
7-NOTES HARMONIC MINOR SCALE A-B-C-D-E-F-G#-A (or in semitones 2-1-2-2-1-3-1) with chords Aminor-Bdim-Caug-Dminor-EMajor-FMajor-G#dim-Aminor
4.1) 1st mode A-B-C-D-E-F-A in semitones 2-1-2-2-1-4 based on the 2 chords
Amin-Bdim (Aelian diatonic too)
4.2) 2nd mode B-C-D-E-F-G#-B in semitones 1-2-2-1-3-3 based on the 2 chords Bdim-Caug
4.3) 3rd mode C-D-E-F-G#-A -C in semitones 2-2-1-3-1-3 based on the 2 chords Caug-Dminor (Neapolitan Hexatonic too)
4.4) 4th mode D-E-F-G#-A-B-D in semitones 2-1-3-1-2-3 based on the 2 chords Dminor-Emajor (Erik Satie hexatonic)
4.5) 5th mode E-F-G#-A-B-C-E in semitones 1-3-1-2-1-4 based on the 2 chords
Emajor-Fmajor
4.6) 6th mode F-G#-A-B-C-D-E-F in semitones 3-1-2-1-2-3 based on the 2 chords
Fmajor-G#dim
4.7) 7th mode in semitones 1-2-1-2-2-4 based on the 2 chords
G#dim-Amin (hexatonic enharmonic minor)
FROM THE 7-NOTES MELODIC MINOR THE HEXATONIC SUBSCALES NOT COVERED BY THE PREVIOUS ARE THE NEXT
E.g. let the 7-notes melodic minor A-B-C-D-E-F#-G#-A in semitones 2-1-2-2-2-2-1 and chords
m-m-aug-M-M-m-d the next are additional hexatonics
C-D-E-F#-G#-A-B-D in semitones 2-2-2-2-1-3 and 2 chords Caug-Dmajor
B-C-D-E-F#-G#-B in semitones 1-2-2-2-2-3 and 2 chords Bminor-Caug
F-G#-A-B-C-D-F# in semitones 2-1-2-1-2-4 and 2 chords F#minor-G#dim
5) If we start with the double harmonic minor, e.g. from A, it is A-B-C-D#-E-F-G#-A which has interval structure 2-1-3-1-1-3-1 , we may derive an appropriate hexatonic which contains a part ofthe pentatonic scale ,which here is the 3-2-3. The resulting scale is the 3-2-3-1-2-1, or in a different mode the 2-1-3-2-3-1. Starting from the root D it is D-E-F-G#-Bb-C#-D. At Blow it is Bb major and at Draw it is C#minor
The mode 1-2-1-3-2-3 e.g. F# G ABb C# D# would give at the Blow row a single minor chord F# and at the Drow row a major chord D# .
Again we may discover different hexatonic scales from the double harmonic minor like the
2-1-3-1-4-1 E.g. E-Gb-G-Bb-B-Eb-E , which as harmonica has at Blow a minor chord (here Eminor) and the draw again a minor chord one semitone lower (here Ebminor). Again because of the two minor chords one semitone apart the sound is with tesmion and neither the blow chord neither the draw chord resolves it better.
For Gm -F#m the scale would be G-A-Bb-C#-D-F#-G and for Dm-C#m it would be D-E-F-G#-A-C#-D.
There are also similar hexatonic scales that are symmetric like 3-2-1-3-2-1 or 3-1-2-3-1-2 or 1-2-3-1-2-3. The latter when placed to an harmonica tuning it gives at the blow row a single chord and at the draw row again a single chord E.g. A-Bb-C-D#-E-F#-A.
ENHARMONIC GENDRE: MORE HEXATONIC SCALES FOR HARMONICAS : UTILISING AKEBONO 5-NOTES SCALE
MOST OF THE HEXATONIC TUNINGS IN THIS DISCUSSION HAVE A SINGLE CHORD AT THE BLOW ROW AND ANOTHER SINGLE CHORD AT THE DRAW ROW.
ACTUALLY ANY TWO SUCCESIVE CHORDS IN THE DIATONIC SCALE (E.G. 7DIM-1M, OR 4M-5M, 3M-4M, 5M-6m , 6m-7dim) CAN BE USED FOR AN APPROPRIATE TWO-CHORD HEXATONIC TUNING HARMONICA.
In ancient Greece according to Aristoxenos, there were 3 musical gendres , the diatonic , the chromatic and enharmonic which were also tetrachords (total length an interval of 4th) and pentachords (total legth an interval of 5th and consisting from an initial or final tone and a tetrachord as before) and by combing a tetrachord with a pentachord they got various 7-notes scales inside an octave . In other words the 7-notes scale was of the form Tetrachord1+2+tetrachord2 , in which case it was called two "divorced" tercahords or Tetrachord1+tetrachord2+2 in which case it was called two adjoint tetrachords. 1) the Diatonic was balanced feelings (that eventually after more than 1 thousand years resulted to the 7-notes diatonic scale, and a simplified rounding of their tetrcahords to a single one was the 2-2-1 and most probably all permutations of it ) the 2) Chromatic was sad feelings (that eventually after more than 1 thousand years resulted to the 7-notes harmonic minor and double harmonic minor scales, blues scale etc , And a simplified rounding of their tetrachords to a single one was the 3-1-1 nd most probably all permutations of it ) and 3) the enharmonic was happy feelings (all possible major 3rd intervals were usually more than all possible minor 3rd intervals and a simplified rounding to a single one was the 4-(1/2)-(1/2)) and most probably all permutations of it ) and has many similarities with the Japanese 5-notes scales like the Akebono with interval structure 4 - 2 - 1 - 4 - 1 e.g. at the mode 2-1-4-1-4 e.g. A B C E F A. (See e.g. the video https://www.youtube.com/watch?v=vv7CO-nVFj8 )
One natural way to derive a hexatonic scale is to require that part ofthe hexatonic scale is either in the pentatonic or in the 7-notes diatonic. Thus here the two versions 2-2-2-1-4-1 and 2-2-2-4-1-1 may be obtained. In notes relevant to the D major scale at appropriate modes are 1) 4-1-2-2-2-1 as D-F#-G-A-B-C#-D and 2) 1-2-2-2-4-1 as A-B-C#-F-F#-G-A
Below are tables of tuning for such harmonicas. The first of them has been called in post 204 the Cretan hexatonic
Still one more hexatonic with rather familiar sound is the 2-2-1-2-4-1, which can be obtained my omiting a note from the 7-notes diatonic scale E.g. C D E F G B C. For the D major scale it would be D E F# G A C# D.
It may be also called 2nd harmonic hexatonic as it appears as the notes of the first 11 overtone harmonics. The indication 2nd is becaouse the 7nth harmonic e.g. at root C is between Bb and B , so the 2nd choice gives this hexatonic while the 1st choice the 1st harmonic hexatonic which is the 2-2-1-2-3-2, or Celtic maor that we discussed earlier.
Its table is shown below when starting from C3. It is not harmonic not to play all possible songs in it (such would be a cyclic tuning one) but to play melodies that are easily accompanied by two only chords the I=1Major, and viidim=7diminished (which sounds like the V7) as all the blow row is the 1major and all the draw ros is the 7diminshed.
THE CASE OF 2-2-1-2-4-1 OR 2ND HARMONIC HEXATONIC IS OF EXTREME IMPORTANCE AS IT PRODUCES HAPPY MUSIC
E.G. FOR C MAJOR IT IS C MAJOR-Bdiminished AND IN NOTES C-D-E-F-G-B-C AS IN THE TABLE BELOW.
And there is also the very beatiful 2-2-1-4-2-1 that when tuned at an harmonic gives the Blow-row a minor chord and the draw-row a dimished chord.Similarly the 2-2-1-2-1-4 or D E F# G A Bb D which can be considered a hexatonic version of the G melodic minor.
Other beatiful such scales that combine the Chromatic with the enharmonic gendre are the
2-1-4-1-3-1. The Blow-row is a major chord and the draw-row another major chord one semitone apart. We give the tuning table below when starting from G3 as Hexatonic _enharmonic_harmonic_minor. The two major chords are D# and D. Because of the two minor chords one semitone apart the sound is with tesmion and neither the blow chord neither the draw chord resolves it better. We met the inerse of thsi scale in the prevous discussion ofthe chromatic gendre andthe double harmonic minor.
More examples are symmetric hexatonic scales like the 1-1-4-1-1-4, or non-cyclic permutations of them like 4-1-4-1-1-1, and 4-4-1-1-1-1.
Another case is the pair of chords Blow=6m draw=5#dim E.g. in the G minor it is
Blow=G Bb D and Draw=A C F#, thus the hexatonic of the enharmonic gendre 2-1-2-2-4-1.
G A Bb C D F# with the tuning table below. It is a hexatonic version of both the harmonic minor and the melodic minor.
It can be
More such scales are the
4-3-1-2-1-1
4-3-1-1-2-1
4-3-1-1-2-1
3-4-1-1-2-1
3-4-1-2-1-1
And even more of them in post 225.
