508. THE COUNTERPOINT CONTINUOUS BASS THEOREM OF 3 CONSECUTIVE NOTES OF THE DIATONIC AND PENTATONIC SCALE.

 FOR THE DIATONIC SCALE

 Let su take for example, the C major scale.

If we use only 3 notes classical chords

C= C E G 

Dm=  D F A 

Em=  E G B 

F= F A C 

G= G B D 

Am= A C E 

Bdim= B D F 

The next triads of notes exist on all 7 chords WITH AT LEAST ONE NOTE!

C-D-E or B-C-D

D-E-F

E-F-G

G-A-B or F-G-A

A-B-C

In other words these are ALL consecutive 3-notes of the scale.

ANY OF THE 7 CHORD OF THE SCALE HAS AT LEAST ONE POINT IN SUCH A TRIAD!

AND THE TRIADS ARE THE  MINIMAL NUMBER FOR CLASSICAL CHORDS, WITH THIS PROPERTY FOR ALL 7 CHORDS (ANY CHORD PROGRESSION). 

FOR JAZZ 4-NOTES CHORDS, THE MINIMAL NUMBER IS ONLY 2 CONSECUTIVE NOTES. 

(Of course particular chord progressions may require only 2 or only 1 notes) 

Thus by choosing any of these  chromatic CONSECUTIVE TRIADS , and alternating the notes so that at the time of any chord, the drone notes exist in the underlying chord, we can drone (COUNTERPOINT MELODY) any melody of the diatonic scale.

For each song , it does not matter which triad we use, and each triad can be used for all songs. 

Of course, when we have transposition to another scale, still another pair is needed.

Or if instead of A natural minor, we transpose to A harmonic minor (g# ) or double harmonic minor (d#, g#) , then a 3rd or a forth note is needed. E.g, (G, G#, A) fo A harmonic minor

or ( D, D#, E) also. 

FOR THE PENTATONIC SCALE

 Let us take e.g. the A minor pentatonic

A-C-D-E-G-A , this is actually 2 3-notes parts in semitones 3-2 (A-C-D, and E-G-A) "divorced" or in conjunction by a whole tone D-E.

so (3-2)-2-(3-2). 

Then any melody will be harmonized by Am or C major CP, GP. 

The 4 chords of the pentatonic scale are shaped by the 1st 2nd and 3rd voice of any melody and are the chords

 Am, C, CP, GP, where CP =(C,G,C) and GP=(G,D,G) 

2nd voice=C,  E, G,  G,  C

1st voice = A, C,  D, E, G 

3rd voice= E,  A,  G, C,  C

If we look at any 3 consecutive notes of the pentatonic, then ANY such triad will work for isokratic continuous bass! Because at least one not of any such triad exist in the 4 chords of the pentatonic.  This verifies the counterpoint melodies theorem of the 3 consecutive notes also for the pentatonic scale.

Thus by choosing any of these  chromatic CONSECUTIVE TRIADS , and alternating the notes so that at the time of any chord, the drone notes exist in the underlying chord, we can drone (COUNTERPOINT MELODY) any melody of the PENTATONIC scale.

For each song , it does not matter which TRIAD  we use, and each TRIAD can be used for all songs. 

ANY OF THE 4 CHORD OF THE SCALE HAS AT LEAST ONE POINT IN SUCH A TRIAD!

AND THE TRIADS ARE THE  MINIMAL NUMBER FOR CLASSICAL AND POWER CHORDS, WITH THIS PROPERTY FOR ALL CHORDS. 

(Of course particular chord progressions may require only 2 or only 1 notes) 

507: WHY ANY PAIR OF NOTES OF A DIATONIC SCALE AT A DISTANCE OF A WHOLE TONE CAN BE USED AS ALTERNATING DRONES FOR ANY MELODY OF THE SCALE.

 Let su take for example, the C major scale.

Then all teh 4-voices chords are the next

Cmaj7= C E G B

Dm7=  D F A C 

Em7=  E G B D

Fmaj7= F A C E

Gmaj7= G B D F

Am7= A C E G

Bdim7= B D F A

we notice that any of the 7 chromatic pairs (all pairs of distance of a 2nd) 

C-D

D-E

F-G

G-A

A-B

B-C  (semitone)

E-F  (semitone) 

exist in ALL OF THE 7 CHORDS!

Thus by choosing any of these 4 chromatic pairs, and alternating the notes so that at the time of any chord, the drone notes exist in the underlying chord, we can drone any melody of the diatonic scale.

For each song , it does not matter which pair we use, and each pair can be used for all songs. 

Of course, when we have transposition to another scale, still another pair is needed.

Or if instead of A natural minor, we transpose to A harmonic minor (g# ) or double harmonic minor (d#, g#) , then a 3rd or a forth note is needed. E.g, (G, G#, A) fo A harmonic minor

or ( D, D#, E) also. 

If we use only 3 notes classical chords

C= C E G 

Dm=  D F A 

Em=  E G B 

F= F A C 

G= G B D 

Am= A C E 

Bdim= B D F 

We notice that all the same  pairs exist in all chords except one. 

C-D

D-E

F-G

G-A

A-B

Nevertheless, the next triads of notes exist on all 7 chords

C-D-E or B-C-D

D-E-F

E-F-G

G-A-B or F-G-A

A-B-C

In other words ALL consecutive 3-notes of the scale.

506. HOW TO CREATE DRONE HARMONY OF ONLY 2 NOTES DIFFERING BY A WHLE TONE ONLY ON ANY MELODY IN A PENTATONIC SCALE.

 Let us take e.g. the A minor pentatonic

A-C-D-E-G-A , this is actually 2 3-notes parts in semitones 3-2 (A-C-D, and E-G-A) "divorced" or in conjunction by a whole tone D-E.

so (3-2)-2-(3-2). 

Then any melody will be harmonized by Am or C major. 

The two possibilities give drones A and G, which is exactly what we require. 

The 2nd possibility is the pair of notes C and D because they also exist in all 4 chords of the pentatonic scale.

The 4 chords of the pentatonic scale are shaped by the 1st 2nd and 3rd voice of any melody and are the chords

 Am, C, CP, GP, where CP =(C,G,C) and GP=(G,D,G) 

2nd voice=C,  E, G,  G,  C

1st voice = A, C,  D, E, G 

3rd voice= E,  A,  G, C,  C

NEVERTHELESS if we extend to 3 consecutive notes of the pentatonic, then ANY such triad will work for isokratic continuous bass!  This verifies the counterpoint melodies theorem of the 3 consecutive notes also for the pentatonic scale.

505. HOW TO PROJECT A CHORD PROGRESSION AND CHORD TRANSITIONS TO A DRONE COUNTER-MELODY WITH LESS NOTE CHANGES AND PAIRS OF ONE TONE DISTANCE.

Obviously, there are many methods for this. But here is one simple method of minimalistic distances among the notes and of not more notes than chords (simplicial counter melody).

We partiction the chord progressin in to pairs , so each pair will be a chromatic, melodic, or harmonic transition

1) If we have a harmonic chord transition e.g. G7->C, then we correspond to notes, the 3rd of the G, which is d, and the 1st of the C which is c. This G7->C will project to  d->c . This is a 1 tone distance of notes or a chromatic pair of notes (distance of 2nds)

2) If we have a chromatic chord transition, e.g. C->Dm, then simply we project to the roots c->d. An even more minimal pait would be e->f which is a minor 2nd or 1 semitone! 

3) If we have a melodic transition e.g. G-> Em, then we simply project to the root of the minor here E and to the 5th of the major here D  again D->e, which is a 2nd distance, thus a melodic pair of notes. 

504. HOW TO CREATE A MELODIC RIFF STRUCTURE WHICH IS MORE STABLE AND LOOPING (OSTINATO) THAN THE CHORD PROGRESSION CHANGES.

 This method usually requires , that the song be played at a single diatonic scale (tone)

The idea is to create a stable simplicity, much more stable than the chord progression of the song. It is a similar idea with the simplicity of the triangulation improvisation discussed in post 498. But here the elements of simplicity are not power chords (no 3rds) of tonal, subdominant, and dominant, but only a riff of 2-3 or 4 notes of the scale, that repeats in a monotone way as bridges between chords. It is the chords that modulate the last 4th or 5th note of the riff, so the riff gives the illusion that it changes. But it does not change. We only change it when we transpose to another diatonic scale. 

Examples by an unknown to me guitarist 

https://www.facebook.com/groups/592068997525110/permalink/28697706473201319/

https://www.facebook.com/groups/592068997525110/permalink/28697408299897803/

https://www.facebook.com/groups/592068997525110/permalink/28694027193569247/

https://www.facebook.com/groups/592068997525110/permalink/28686143641024269/

503. 8-NOTES BEBOP SCALES AS HARMONICAS, WITH ONLY ONE BLOW AND ONLY ONE DRAW 4-NOTES CHORD. (DUAL BLOW-DRAW AUTOMATIC HARMONIZATION)

 

There are 8 notes scales-modes called Bebop , in Jazz. E.g. major, minor, dominant , subdominant etc. We want to order cyclically tuned harmonicas in them, so that all blow 4 notes chords, are the same (including inversions) and all drow 4 notes chords the same. In other words an automatic Dual Blow-Drow harmonization of what ever we play in this 8 notes harmonica. If we restrict to the 6 jazz chords types, Xmaj7, Xm7, X7, Xhalfdim, Xdim7 Xaug, which bebop 8 notes scales have this property?

Answer verified by AI.

Yep — you’re talking about the 8-note Bebop scales. The trick is: add 1 chromatic "passing tone" to a 7-note diatonic scale so that chord tones fall on downbeats.

For harmonicas: "Blow = one 4-note chord, Draw = another 4-note chord, and all inversions of each are ok".

This is only possible if the 8-note scale splits perfectly into 2 disjoint tetrachords.

1. The 4 Bebop scales used in Jazz

Scale	8 Notes	Formula	Why it exists
Bebop Major	C D E F G G# A B	1 2 3 4 5 #5 6 7	Add #5 to Major. Makes chord tones on beats
Bebop Dominant	C D E F G A Bb B	1 2 3 4 5 6 b7 7	Add 7 to Mixolydian
Bebop Dorian/Minor	C D Eb E F G A Bb	1 2 b3 3 4 5 6 b7	Add 3 to Dorian
Bebop Melodic Minor	C D Eb E F G Ab A B	1 2 b3 3 4 5 b6 6 7	Actually 9 notes, so we use "Bebop Harmonic Minor": C D Eb F G Ab A B

The "Bebop Harmonic Minor" is the standard 8-note one: 1 2 b3 4 5 b6 6 7

2. The condition: Split into 2 disjoint 4-note chords

We need: Scale = Blow4 ∪ Draw4 and Blow4 ∩ Draw4 = ∅
And each 4-note set must be one of: Xmaj7, Xm7, X7, Xø, X°7, X+

Let’s test each:

A. Bebop Major: C D E F G G# A B

Can we split? Yes:
Blow = C E G B = Cmaj7
Draw = D F G# A = Dø7 = B half-diminished in 1st inv = D F Ab A

Check: Both are in your 6 jazz types. And they use all 8 notes, no overlap.
Result: WORKS Blow = Imaj7, Draw = iiø7

B. Bebop Dominant: C D E F G A Bb B

Split:
Blow = C E G Bb = C7
Draw = D F A B = Dm6 but Dm6 = D F A B = Bm7b5 in 3rd inv = B D F A = Bø7

Both are valid: X7 and Xø7
Result: WORKS Blow = I7, Draw = iiø7

C. Bebop Dorian: C D Eb E F G A Bb

Split:
Blow = C Eb G Bb = Cm7
Draw = D E F A = D7sus? No. D F A C would be Dm7 but we have E not C.
D E G# A no. D F Ab A = Dø but we don’t have Ab.
Best split: Blow = C Eb G A = Caug(add6) not in list. Draw = D E F Bb = D7b9 no5

This fails to give 2 of the 6 types cleanly.
Result: NO CLEAN SPLIT

D. Bebop Harmonic Minor: C D Eb F G Ab A B

Split:
Blow = C Eb G B = Cm(maj7) Not in your 6 types.
Blow = C E G# B = Caug(maj7) No.
Blow = C Eb G Ab = Cm b6 No.

Best split: Blow = C E G# = Caug but need 4 notes. C Eb G B = CmMaj7
Draw = D F Ab A = Dø7
CmMaj7 is not in your list of 6.
Result: NO, unless you add mMaj7

3. Final Answer

Only 2 of the standard Bebop 8-note scales give you perfect Dual Blow-Draw harmonization with your 6 chord types:

1. Bebop Major Scale
   Blow = Imaj7 Draw = iiø7
   Example in C: Blow C E G B, Draw D F G# A
2. Bebop Dominant Scale
   Blow = I7 Draw = iiø7
   Example in C: Blow C E G Bb, Draw D F A B

Both use the "iiø7" on draw. That’s why bebop dominant is so common on harmonica — you get I7 and iiø7 automatically.

The Bebop Dorian and Bebop Harmonic Minor don’t split cleanly into your 6 chord types without adding mMaj7.

For ordering harmonicas

If you want every key to work the same way: order a set of "Bebop Major" or "Bebop Dominant" tuned harps. Then any key you play, Blow is always the Tonic 7th chord and Draw is always the iiø7.

 

What about the Bebop minor (nor dorian, neither melodic minor) e.g. Bebop Cminor: c d eflat f g a bflat , b , c. ?

Ah yes — that’s the Bebop Minor aka Bebop Aeolian
1 2 b3 4 5 6 b7 7

So in C: C D Eb F G A Bb B C
You add the major 7th as the passing tone to natural minor.

Let’s test it for your harmonica condition.

1. The scale and the 8 notes

C D Eb F G A Bb B

We need to split into 2 groups of 4, disjoint, each = one of: Xmaj7, Xm7, X7, Xø, X°7, X+

2. Check all possible splits

The only clean split is:
Blow = C Eb G Bb = Cm7
Draw = D F A B = Dm6

Now check if Dm6 is in your list:
Dm6 = D F A B
Pitch classes: {2,5,9,11}
Re-order to 7th chord: B D F A = Bm7b5 = Bø7

Yes! Bø7 is in your list as "Xhalfdim".

So:

javascript

Blow = i m7      = Cm7  
Draw = ii ø7     = Bø7  [which is Dm6 in 3rd inversion]

All 8 notes used, no overlap. And any inversion of each 4-note set is still the same chord type.

3. Result

Bebop Minor DOES work ✅

Scale	Blow 4 notes	Draw 4 notes
Bebop Minor	i m7	ii ø7

Example C Bebop Minor:
Blow: C Eb G Bb
Draw: D F A B

4. Summary of all 3 that work

Bebop Scale	Blow Chord	Draw Chord	Vibe
Bebop Major	Imaj7	iiø7	Bright, C maj
Bebop Dominant	I7	iiø7	Bluesy, C7
Bebop Minor	im7	iiø7	Dark, C minor

Notice the pattern: Draw is always iiø7. Blow changes with the quality.

Bebop Dorian 1 2 b3 3 4 5 6 b7 and Bebop Harmonic Minor fail because you can’t get 2 chords from your list of 6 without overlap or needing mMaj7.

So for a harmonica set you’d want 3 tunings: Bebop Major, Bebop Dominant, Bebop Minor. Then every key gives you automatic "tonic chord on blow, iiø on draw".

502. ADVANTAGES OF THE TROLL MINOR TUNING. ERGONOMIC PLAYING SIMULTANEOUSLY OF ANCIENT AND MODERN CHORDS.

 TROLL MINOR E.G. IN D: D-A-D-F (5TH, 4TH, MINOR 3RD)