145. THE SCALE OF NOTES AS INADEQUATE CONCEPT FOR BEAUTIFUL MELODIES COMPOSITION. BEAUTY OF MELODIES BASED ON SCALES OF CHORDS AND PITCH DYNAMICS OF THEIR MELODIC THEMES (TRANSLATION, INVERSION, EXPANSION/CONTRACTION , ROTATION ,MUTATION OR HOMEOMORPHISM)

(This post has not been written completely yet)

THE KEY-WORD HERE INTHE 4TH GENERATION DIGITAL MUSIC FOR THE MUSICAL-THEORETIC IDEAS OF THIS   POST (AS FAR AS MORDEN SOFTWARE FOR MUSIC MAKING IS ) IS CHORD-SEQUENCERS AND BACKING-TRACK BUILDERS.

THE TERM  SEQUENCER MEANS HERE A LOOP OR RHYTHMIC CYCLE OF ACHORD PROGRESSION (LIKE  AMELODIC THEME THAT VARIES IN A MELODIC SEQUENCER).

THERE MANY GOOD SOFTWARE PROGRAMS FOR THIS LIKE CHORDBOT, NAVICHORD , ETC

In post 83 we mentioned that in musical practice a more general approach is taken that improvising within a single scale, which involves more than one scale and relevant modulations.  This is determined from the harmony rather than from the melody. We mentioned also the concept a set of chords as scale of chords rather than a particular chord progression, which is different in the same way that a scale differs from a melody in it.

Usually, the improvisation in Jazz, is melody-oriented in the sense, that it usually has a predetermined chord progression and based on that many melodies are improvised. We described in detail the composition and improvisation method that starts with the chord progression at first and then composes the melody in post 9. 

We will develop here a second level of the improvisation where we improvise at first on the chord progression and parallel to it, based on the melodic centers we improvise on melodies. The melodic centers (simplicial sub-melody)  are not too much more complicated than the chord progression.

For this end, we describe in post 83  the 3 wheels of chords, the chromatic, the one by intervals of 3rds and the one by intervals of 4ths, and 3 types of chord cycles from them, the short (3-chords), the middle (6-8 chords) and the full cycle (12-15 chords). In the wheel by 3rds there are 2 medium size sub-cycles (See below)    These subcycles of chords, for the chord progressions improvisation, play the roles that scales play for the solo improvisations!
(see also post 17 and post 32)

The most common scale of chords is a connected arc of chords in the wheel by 4ths. That is 3 or 4 or 5 or 6 chords , that each is a pure 4th (or pure 5th) away from the previous and it  is either major or minor chord. Two such successive chords have one end-note in common. This is the equivalent of  the traditional scale, and because the chords may turn from minor to major and vice versa, it is in fact a bundle of different scales with modulations between them. A simple way to improvise over such a "scale" of chords is to play the melody, go up and down according to the demands of the emotions, and then use the chords as areas around the main and more permanent notes of the melody (simplicial sub-melody or centers of the melody) , but putting these centers of the melody as middle notes usually (but not only) of the chords of the chord-scale. To be more certain for the good result we may alternate the melody with the chords, but use only chords of the predetermined scale of chords. (See also post 147 for combining melodic themes with chords).

One of the simplest scale of chords is 3 consecutive chords in the cycles of 4ths.

E.g. in the C major diatonic scale

Dm->G->C  (Western Jazz)  (m-M-M) (happy)

G->C->F  (Irish folk)  (M- M- M) (happy)

Em->Am->Dm (Eastern folk)  (m-m-m)  (sad)

Bdim->Em->Am  (Eastern Jazz) (d-m-m)  (sad)

other combinations of major M, minor m, diminished d and augmented aug are

d-M-M  (happy)

aug-M-M  (happy)

aug-m-M  (sad)

aug-m-m  (sad)

M-m-m  (sad)

d-m-M (sad)

d-d-M (sad)

d-d-m (sad)

aug-aug-M (sad)

aug-aug-m (sad)

d-aug-M (sad)

d-aug-m (sad)

d-aug-d (sad)

aug-aug-d (sad)

etc

We may start with a sad triad of chords and end with a happy one shifting by an interval of 3rd or even with the same roots but changing the type of the chord.

Other example is the next scale of chords

 Bdim->Em->Am->Dm->G->C->F 

is a scale of chords of the simple type, that is a connected arc in the wheel of chords by 4ths, and the specifications of diminueta, minor or major are set so that the particular scale of chords is also the chords of the major diatonic scale of notes!

Nevertheless we can alter that specification of the chords in which case more than one scale are produced:

B7->Em->A7->Dm->G7->Cm->F  or 

Bm7->E7->Am7->D7->Gm7->C7->Fm or 

B7->E->A7->Dm->Gm7->Cm->F  etc

Or 

B7->E(m)->A(m)->D(m)->G(m)->C->F

The E(m) means either major chord E or minor chord Em etc

The next scales of 7-chords have only two minor chords which complies with a desired ratio of minor chords not more than 1/3 of all chords

B7->E(m)->A(m)->D->G->C->F

B(m)7->E(m)->A->D->G->C->F

B7->E->A(m)->D(m)->G->C->F

B7->E->A->D(m)->G(m)->C->F

B7->E->A->D->G(m)->C(m)->F

B7->E->A->D->G->C(m)->F(m)


Or we may alternate minor major once at odd chords and once at even chords e.g.

B7->Em->A->Dm->G7->C->F->Bb->B7->E->Am->D7->Gm->C7->F->Bb->B7->E 
Larger scales are from 12-chords 

G#->C#->F#->B->E->A->D->G->C->F->Bb->Eb

or 


G#->C#->F#->B->Em->Am->Dm->G->C->F->Bb->Eb



Other simpler scales from chords are of 4 only chords e.g.


G->C->F ->Bdim7 etc

or 

G->C->F ->Caug(or G#aug) etc

or they can be based on wheel by 3rds and alternating minor major relative chords 
e.g. 

G->Em->C->Am->F >Dm->G etc

THE GENERAL PATTERN OF PROGRESSIONS WITH ALTERNATING CHORD-RELATIONS OF 
CHROMATIC-MELODIC ,CHROMATIC-HARMONIC , HARMONIC-MELODIC , HARMONIC-HARMONIC, MELODIC-MELODIC, CHROMATIC-CHROMATIC CHORD-TRANSITIONS.

This is a progressions X1->X2->X3->...->Xn  where the Xi->Xi+1  and Xi+1->Xi+2 is an alternation of chord relation and  transitions of the chromatic-melodic   , chromatic-harmonic,  melodic-harmonic,  chromatic-chromatic, melodic-melodic or harmonic-harmonic relations. 
Such constant alternating patterns of chord relations somehow determine also that the melodic themes (either within a single chord or within a chord transition), are structured and translated or inverted or expanded with similarly alternating intervals of 2nd, 3rd or 4th/5th. 

THE GENERAL PATTERN OF A CHROMATIC DOUBLE SCALE OF CHORDS 

Here is an alternative way to produce not harmonic scales of chords (based on the harmonic relation of chords) but chromatic scales of chords based on the harmonic relation of chords but which still involve the other two chord relations the melodic and the harmonic 


WE START WITH A CHROMATIC CADENZA OR ASCENZA  in semitones 2->2->1  or 1-3-1 or 1-3-1-1-3-1 in harmonic and double harmonic minor scales,   and we paralel chords rooted on such notes X1->X2->X3->X4 with chords 

Y1->Y2->Y3->Y4, such that the relation of Xi with Yi is either in a relation of being  relative chords (melodic relation of chords) or a 4th apart (harmonic relation of chords) 

Of course the less total number of different chords that we may use is better and it sounds more familiar if such chords belong to an harmonic personality (diatonic or harmonic minor or double harmonic minor etc).We may use either minor or major chords. 

TRIPLE ALTERNATION OF CHORD-TRANSITIONS

More generally   and we paralel chords  X1->X2->X3->...->Xn  that are in  one of the relations chromatic, melodic harmonic , with chords X1->X2->X3->...->Xn so that the relation of Xi with Yi is always constantly in one of the 3 basic relations  relative chords (melodic relation of chords) or a 4th apart (harmonic relation of chords) .

When playing the scale as progression X1->Y1->X2->Y2->... it is equivalent with having a triple alternation of chord relation and  transitions of the chromatic-melodic   , chromatic-harmonic,  melodic-harmonic,  chromatic-chromatic, melodic-melodic or harmonic-harmonic relations and a third which is variable. 

Such constant alternating patterns of chord relations somehow determine also that the melodic themes (either within a single chord or within a chord transition), are structured and translated or inverted or expanded with similarly alternating intervals of 2nd, 3rd or 4th/5th. 

PRODUCING CHORD PROGRESSIONS FROM CHORD-SCALES

Now when we want to improvise based on such a scale of chords (harmony first), we may start with one such chord from this scale and play a melodic theme that fits it. Then we move to the next melodic theme, with all the know so far rules of good melody composition (e.g. variations of translation, inversion, homeomorphism) and try to fit it also to one of the chords of the previous scale of chords. If we succeed in this we repeat it , with the next melodic theme, and appropriate chord from this set of chords or scale of chords, and so on. In this way we have an inter play with harmony and melody at the very process of improvisation or composition. 

This method of composing a melody, is more general and more comprehensive than composing a melody within a single scale of notes. It results composing melodies in many different scales and modulations between them, but the simplicity is still kept as set of chords (scale of chords) rather than scale of notes.

Here is a way when the scale of chords is identical with the chords of diatonic scale of notes.


An relatively easy and safe way to produce such  mesmerizing  monotone but beautiful flows of improvisation , is to use scale of chords as in post 148. And in particular a very familiar  scale of chords that are the chords of diatonic scale:

I , ii, ii, IV, V vi, vii, I' (=1M, 2m, 3m, 4M, 5M, 6m, 7dim 1'M)

and in addition to an instrument tuned by the harmonic tuning (see post 90) so that there is a densest possible opportunity of major or minor chords per number of frets.

Some of the variation techniques to walk this scale of chords are

1) Walk in the chromatic order up and down (all then only odds then only even) 

2) Walk in the relative chords order up and down

3) Walk in the resolution or harmonic order by 4ths or 5th order up and down

4) Walk only the minor chords first descending and then the major chords ascending 

5) Walk in the 4-notes chords (major 7nth extension of the chords) up and down, all then only even then only odd

6) Walk in a half scale (in the chromatic order) up down then other half  up and down.


7) Walk in a random way either 3-note chords or 4 notes chords

8) Alter some chords to include the 5#, or 2# of the harmonic minor or double harmonic minor, or other like 6#. E.g. alter the 3m to 3M7 or 3dim etc

144. Melodic Repetition, Variation, Contrast , as special cases of pitch or rhythmic translation or expansion, pitch or rhythmic inversion and pitch or rhythmic mutation.

(This post has not been written completely yet)

https://www.youtube.com/watch?v=rl-V2IsUprQ


https://www.youtube.com/watch?v=I2Ej4Jpquas

143. THE MOST POPULAR CHORD PROGRESSION IN WESTERN SONGS, AS DERIVED FROM MAXIMAL HARMONIC 5-NOTES SUB-SCALE.

(This post has not been written completely yet)

We have mentioned in previous posts in this book, that the diatonic scale has the optimal mathematical property of being the only 7-notes scale (within the chromatic Bach 12-notes scale) with he maximum number of major and minor chord-triads.

An interesting next question is what are the corresponding such scales with the same maximal property but with a smaller number of notes? E.g. 4,6, or 6 notes?

The answer was given in post 117 where the maximal such harmonic sb-scales are enumerated.

We highlight only the maximal harmonic 5-notes and 6-notes subscales as giving rise to the most popular in western songs chord progressions.

5-notes maximal harmonic pentatonic 

intervals patterns 4-3-2-2-1 e.g. c4-e4-g4-a4-b4-c5

(It is essentially A chord with 7nth and with 6th)

Notice that this scale suggests the chord progression by taking chords of the full 7-notes diatonic scale based on the above notes of the maximal harmonic 5-notes scale which has the highest statistical frequency in popular songs:  1(7)  4 5 6m E.g. in C major scale it would be C7, F , G Am (=I7, IV, V, vi )=(1(7), 4, 5, 6m).

6-notes maximal harmonic  

intervals patterns 2-2-3-2-2-1 e.g. c4-d4-e4-g4-a4-b4-c5

(It is essentially a chord with 7nth, 6th and 2nd. A mode of it  is known also the raised Celtic minor scale of the hang-drums )

Notice that this scale also  suggests a  chord progression by taking chords of the full 7-notes diatonic scale based on the above notes of the maximal harmonic 5-notes scale which has  highest statistical frequency in popular songs:  1(7) , 2m,  4 ,5, 6m E.g. in C major scale it would be C7,Dm, F , G Am. This progression includes both the Blues progression 1 2m 5 (=I , ii, V) , and the most popular 1,4,5,6m (=I, IV, V, vi) .

For the F major scale, which is common in Eastern Europe folk music , such a scale of chords would be

F7, Gm, Bb, C, Dm,

While for the Bb major scale , which is very common in Greek folk music, such a scale of chords would be

Bb, Cm, Eb , F , Gm.

This most popular chord progression has a variation:

Instead of 1M, 4M, 5M 6m , the 1M, 2m, 5M 6m  (6m->2m->5M ->1M)

Or sometimes

5M->1M->4M->2m->5M


E.g. of (6m->2m->5M ->1M)

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

142. MELODIC IMPROVISATION WITH SIMPLISTIC SUB-MELODY OVER INTERVALS OF 5THS (cycle of 5ths) OR 4THS (cycle of 4ths).

(This post has not being written completely yet)

One of the simplest and oldest techniques of melodic improvisation is the create melodic themes that start and end at intervals of 5ths (cycle of 5ths) or 4ths (cycle of 4ths).

We have already met a similar chord-progression based improvisation (in post 17 at the end   and  post 34 ) based on the cycle of 5ths or 4ths, and the two methods are definitely related.

This is also used in the method of complementary melodic themes improvisation in post 140.

141. ONE ONLY ACCOMPANYING CHORD MELODIC IMPROVISATION

(This post has not been written completely yet)

After the very basic meditative improvisation with one only note (the root of a scale) as accompanying harmony, the next step of simplicity is the single accompanying chord melodic improvisation.

Here the technique of the CHORD-LOCAL 7-NOTES SCALE OF A CHORD (chord-courtyard scale ) applies. See post 102, 103  and 110, 159

When spending time with the melody with an underlying chord the best idea is to have the chord in 4-notes form e.g. like a with 7nth or with 6th, and in the current octave or in the next. Then start the melody at a note of the chord and end it again at a note of a chord in this or the next octave. For example, we may compose the melody from 3-notes micro-themes, the first and last inside the chords and the middle possible outside the chords. Since the chord has 4-notes and the scale  7 notes the passing or transient notes are only 3, less than the 4 of the chord, therefore, any such melodic theme fits harmonically to this chord.

Here is an example :

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

But also this can be elaborated to a double chord triad method. In other words, we may use two triads of two chords the one is the underlying e.g. X and the second Y has one or two common notes with X7 (or Xmaj7 or X6) and we alternate the two triads as successive notes of a melody. The result is a sequence of notes that more than 50% or 66% notes belonging to the chord X7 or X6. Thus the method of long-short parts melodic and rhythmic micro-themes of post 77 applies.



Here is an example  https://www.youtube.com/watch?v=ZDuegoLXaR0&t=241s

The single accompanying chord can be a power chord X5, e.g. C5=(c, g) that the root and dominant only of a diatonic scale. Then As Y can be any chord of the diatonic scale except the minor chord on the 2nd note (Dm in C major diatonic scale) And in general the melodic improvisation can be the arpeggios of a chord progression! 

Here is an example 

https://www.youtube.com/watch?v=VtVFWOBH2tI

More ideas here

https://www.youtube.com/watch?v=qKVp44tAZQ0&pbjreload=10


Here are one chord backtracks for practice.

https://www.youtube.com/watch?v=NasVe9Q04_M

https://www.youtube.com/watch?v=e3ciXPKqq0w&t=632s 

https://www.youtube.com/watch?v=xMNcv-i7Ado

https://www.youtube.com/watch?v=2NJOidKkzHo

etc.

140. COMPLEMENTARY THEMES IMPROVISATION. Melody driven improvisation within a scale.

(This post has not been written completely yet)

COMPLEMENTARY THEMES IMPROVISATION. Melody driven improvisation within a scale.

This method of improvisation is melody-driven within a scale or composite scale (like Bebop Scales of post 139). Its main idea is the statistical action-reaction principle or principle of complementarity of melodic themes as a kind of dialogue question-answer or proposal-answer   Its rules are the next

1) The melody is within a scale S (which can be also composite of  8-notes , 9-notes or more) E.g. The Bobop dominant 8-notes scale of post 139 or 8-notes maximal harmonic of post 117, C D E F F# G A B C`

and is subdivided into pairs of melodic themes A-B so that A and B are in some sense harmonic or melodic complementary. The themes A and B may be subdivided into 1 or 2 sub-themes A1 A2 or B1 B2.

2) HARMONIC COMPLEMENTARITY:  The total theme A+B covers as much as possible of the scale given the length of A and B. E.g. the A is mainly over even (or odd) notes of the scale and B is mainly over odd (or even) notes of the scale. Usually, the endnotes of A and B are either a) identical b) differ by an interval of 5th/4th c) differ by an octave. From this point of view we may perceive the scale as double layered: 1) A scale by intervals of fifths or 4ths 2) The full scale. Then the simplicial sub-melody is only on the first coarse sub-scale scale while the full melody is on the fine full scale. The structure of these two layers 1) 2)  reflects the structure of the sequence of pairs (A, B) of complementary melodic themes.

3) MELODIC COMPLEMENTARITY: The themes A and B have complementary dynamics as Dolphin Words (see post 114) E.g. A is ascending and B is descending or A is expansive and B is contracting etc.

4) The rhythm is rather fast e.g. 110-120 beats/min

5) The chords that accompany may follow the melody and are chords of the scale. If we want as few chords as possible and the scale is e.g. diatonic, then it could be only 2 or 3 chords e.g. I ii, V . But it can be in general a sequence of chords of the scale. If e.g. the improvisation is on a Celtic levered harp them we may alternate chords with pairs of such melodic themes A+B so that each chord has mediant the last bote of each theme.


The above method can be combined with the melodic improvisation within the harmony of a chord each time, as in post 141.

When spending time within the harmony of a chord the best idea is to have the chord in 4-notes form e.g. like a with 7nth or with 6th, and in the current octave or in the next. Then start the melody at a note of the chord and end it again at a note of a chord in this or the next octave. For example we may compose the melody from 3-notes micro-themes, the first and last inside the  chords and the middle possible outside the chords. Since the chord has 4-notes and the scale  7 notes the passing or transient notes are only 3, less than the 4 of the chord, therefore, any such melodic theme fits harmonically to this chord.

Here is an example :

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

139. SCALES THAT ARE UNION OF OTHER KNOWN SCALES. BEBOP 8-NOTES SCALES, 9-NOTES EASTERN AND WESTERN CHROMATIC SCALES

(This post has not been written completely yet)

We describe scales that are the union of other known scales. They are somehow 2-layered or n-layered scales.

1) Examples are the Bobop 8-notes scales in Jazz, that try to make 8-notes scales that can play simultaneously two other known scales. E.g. Diantonic+melodic minor, or Diatonic+harmonic minor or Diatonic+harmonic double minor, or melodic minor+harmonic minor  or Diatonic+blues 6-notes=8-notes Bebop dominant=8-notes maximal harmonic scale of post 117  etc

From Wikipedia: https://en.wikipedia.org/wiki/Bebop_scale

The bebop scales are frequently used in jazz improvisation and are derived from the modes of the major scale, the melodic minor scale, and the harmonic minor scale. According to Corey Christiansen, "David Baker, one of the world's finest jazz educators, named these scales the 'bebop scales' because they were used so often by jazz artists from the Bebop Era. These artists include Charlie Christian, Charlie Parker, Lester Young, and Dizzy Gillespie, to name a few."^[1]

There are five types of frequently used bebop scales:

1. the bebop dominant scale
2. the bebop Dorian scale
3. the bebop major scale
4. the bebop melodic minor scale
5. the bebop harmonic minor scale

Each of these scales has an extra chromatic passing tone. In general, bebop scales consist of traditional scales with an added passing tone placed such that when the scale is begun on a chord tone and on the downbeat, all other chord tones will also fall on downbeats, with the remaining tones in the scale occurring on the upbeat (given that the scale is played ascending or descending; i.e., no intervallic skips are played).

As such, many heptatonic scales may be modified by the addition of an eighth passing tone to accomplish this same effect; however, the modifier "bebop" is reserved to indicate those scales most frequently used—and popularized—during the bebop era (and/or by modern practitioners of the bebop genre).

Bebop dominant scale[edit]

The bebop dominant scale is derived from the Mixolydian mode and has a chromatic passing tone between the 7th and the root.

0:00

It has all the notes in both the major scale and the Mixolydian scale of the same root. This scale is often used over dominant seventh chords and all extended dominant chords,^[2] and the II-V chord progressions. According to Michael Miller, "[w]hen someone says they're playing 'the bebop scale,' this is the one they're talking about." The interval structure in semitones is 

2-2-1-2-2-1-1-1

Bebop Dorian scale[edit]

The bebop Dorian scale (also known as the bebop minor scale^[3][4]) is derived from the Dorian mode and has a chromatic passing tone between the minor 3rd and the perfect 4th.

0:00

It has all the notes in both the Dorian scale and the Mixolydian scale of the same root. It is the 5th mode of the bebop dominant scale.

A second form of the bebop Dorian scale features a major seventh bebop note between the dominant seventh and the tonic.

0:00

The second style, featuring the major seventh, is generally used by guitar players for its accessibility when applied to traditional minor scale shapes (that is, it is simply easier for guitarists to play). However, many players and resources adhere to the traditional spelling of the scale.

Bebop major scale[edit]

The bebop major scale is derived from the Ionian mode (major scale) and has a chromatic passing tone between the 5th and 6th notes.

0:00

This scale is often used over major sixth chords and major seventh chords.

Bebop melodic minor scale[edit]

The bebop melodic minor scale is derived from the ascending form of the melodic minor scale (jazz minor scale) and has a chromatic passing tone between the 5th and 6th notes.

0:00

It has all the notes of both the ascending form of the melodic minor scale and the harmonic minor scale of the same root. This scale is often used over minor sixth chords.

(Melodic minor=6,7,1,2,3,4#,5#,6'=(in semitones) (2-1)-(2-2)-(2-2-1))

These scales are listed in David N. Baker's books on bebop. They are also included, with the exception of the Dorian bebop scale, in Roni Ben-Hur's book Talk Jazz: A Comprehensive Collection of Bebop Studies, which is derived from the work of Barry Harris. Ben-Hur further elaborates on the concept of placing additional chromatic passing tones between other notes in the scales.

Bebop harmonic minor scale[edit]

The bebop harmonic minor scale (or bebop natural minor scale, as listed in Mark Levine's The Drop 2 Book) is derived from the harmonic minor scale and has a chromatic passing tone (an additional ♭7) between the 6th and the 7th notes.

0:00

It contains all of the notes of both the harmonic minor scale and the natural minor scale (Aeolian mode) of the same root. It can be used on all three chords of a minor II-V-I progression. It is a mode of the bebop major scale: for instance, the C bebop harmonic minor scale has the same pitches as the E♭ bebop major scale.

2) We introduce the Eastern chromatic 9-notes triple scale which is the union of a  harmonic minor a harmonic double minor with the same root and their relative diatonic major scale (or natural aeolian mode minor with the same root). Its internal structure is    2-1-2-1-1-1-2-1-1 (E.g. D-E-F-G-G#-A-Bb-C-C#-D)

I have constructed (handmade) some quenas, quenillas and quenachos (direct blowing winds) with this 9-notes scale (3 minor scales together, natural minor, harmonic minor, and harmonic double minor) and I call them, the Byzantine chromatic minors flutes. They can easily be modified from a harmonic double minor flute by adding two sharp-2nd-holes at the 3rd and 6th hole. They have  7 front holes in two groups two lower one semitone apart, 4 upper again with one semitone apart between them,and a double thumb with one semitone away the two holes in the thump.  (It can be played though from an Ionian mode diatonic flute e,g, C4 major, by adding sharps-2nd holes  at the 2nd hole, D4#, and 5th hole G4#) They are used also in Gypsy jazz, folk Romanian melodies and Greek folk melodies of Rebetika music.

Some romanian caval flutes have the 9-notes scale 2-1-1-1-1-1-1-1-3.


3) We introduce the Western chromatic 9-notes triple scale which is the union of 3 major diatonic scales consecutive in the circle of 4ths E.g. G-C-F , or C-F-Bb etc It coincides with the maximal harmonic 9-notes scale of the post 117. Its interval structure is 2-2-1-1-1-2-1-1-1. E.g, C-D-E-F-F#-G-A-Bb-B-C We may notice that it can also be obtained from the standard pentatonic scale 2-2-3-2-3 by analyzing the two 3 into semitones 1-1-1. It can be played from an Ionian mode diatonic flute e,g, at C4 major, by adding sharps-2nd holes at the 4th hole, F4#, and 6th hole A#=Bb.
I have a bass wind with clarinet mouthpiece from Armenia with this 9-notes scale.

4) The next 10 notes scale 2-1-1-1-1-1-2-1-1-1, which can be made on a flute with 7 front holes a double thumphole is also invariant in playing by the 3rd overtone, In other words the 3rd overtone will give notes on the same holes again inside the scale.