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)