430. TRIPLETS OF CHORDS FOR THE 7 DIATONIC MODES IN THE LATIN JAZZ STYLE HARMONIZATION.

 The standard chromatic pairs of chords for the 7 modes of a diatonic scale are (see post 215) the next

The chromatic pairs of chords in the diatonic scale  may get the the names ofthe modes of the scale too

1M-2m=IONIAN

2m-3m=DORIAN

3m-4M=FRYGIAN

4M-5M=LYDIAN

5M-6m=MYXOLYDIAN

6m-7d=AEOLIAN

7d-1M=LOCRIAN

Nevertheless in the Latin style jazz, instead of the 2m , 3m 6m we often use 2M7 , 3M7 and 6M7 , because we substitute the natural minor eolian mode with of the harmonic minor with 5# instead  and also harmonic double minor with 3b, etc Furthermore it may mean that instead of being in a single diatonic scale e.g. C we also utilize the previous or next in he Wheel by 4th (here F and G) 

So the Latin jazz style harmonization of the 7 diatonic modes ,where we add a 3rd chord to resolve to the first and have harmonic relation with the first, would become as follows

1M-2m=IONIAN-> 1M->2m-> 5M7  (Blues triplet)

2m-3m=DORIAN->  2m-> 3M7->6m (Harmonic minor triad)  or 2m-> 3M7->6M7 (Dbl Hminor)

3m-4M=FRYGIAN->3m->4M->7M7  (interesting triplet 1)

4M-5M=LYDIAN->  4M, 5M, 1M7  (major Harmonic triplet)

5M-6m=MYXOLYDIAN-> 5M-> 6m -2M7 (Blues triplet)

6m-7d=AEOLIAN->  6m-> 7m-> 3M7 (interesting triplet 2 )  or 6m-> 7M7->3M7 (DHminor)

7d-1M=LOCRIAN-> 7M7->1M -> 4#M7  (interesting triplet 3).

From these triplets we may extract harmonic pairs only

IONIAN-> 1M->2m-> 5M7  (Blues triplet) -> HPAIR=5M7->1m

DORIAN->  2m-> 3M7->6m (Harmonic minor triad) - > HPAIR=6m->2m

or 2m-> 3M7->6M7 (Dbl Hminor)  > HPAIR=6M7->2m

FRYGIAN->3m->4M->7M7  (interesting triplet 1)- > HPAIR=7M7->3m

LYDIAN->  4M, 5M, 1M7  (major Harmonic triplet) -> HPAIR=1M7->4M

MYXOLYDIAN-> 5M-> 6m -2M7 (Blues triplet) -> HPAIR=2M7->5M

AEOLIAN->  6m-> 7m-> 3M7 (interesting triplet 2 )- > HPAIR=3M7->6m 

 or 6m-> 7M7->3M7 (DHminor) - > HPAIR=3M7->6m 

7d-1M=LOCRIAN-> 7M7->1M -> 4#M7  (interesting triplet 3).- > HPAIR=4#M7->7M7 

In the next we may compose songs with first part (couple) a sad triplet or pair signifying a mode and resolving to the refrain to a happy triplet or pair (usually the Ionian or Mixolydian) 

Only the Ionian, Mixolydian, Dorian, Aeolian, Lydian, are triplets of chords that are exact harmonic triplets. The Frygian and Locrian are not exact harmonic triplets. 

Here are examples of chord progressions of at least 9 such songs

E. g. Dorian-> Ionian (Blues)

2m, 3M7

6m, 2m 

Resolving to

1M 2m

5M7 1M 

Dorian3-> Ionian2 (Blues)

2m, 3M7

6m, 2m 

Resolving to

1M 4M

5M7 1M 

Dorian2-> Ionian (Blues)

2m, 3M7

6M7 2m 

Resolving to

1M 2m

5M7 1M 

Frygian-> Ionian (Blues)

3m 4M

7M7 3m 

Resolving to

1M 2m

5M7 1M 

Frygian->Mixolydian (Blues)

3m 4M

7M7 3m 

Resolving to

5M 6m

2M7 5M 

Frygian3->Mixolydian3 (Blues)

3m 6m

7M7 3m 

Resolving to

5M 4M

2M7 5M 

Aeolian-> Ionian (Blues)

6m 7m

3M7 6m

Resolving to

1M 2m

5M7 1M

Aeolian2-> Ionian  (Blues)

6m 7M7

3M7 6m

Resolving to

1M 2m

5M7 1M

Aeolian3-> Ionian  (Blues)

6m 7M7

3m 6m

Resolving to

1M 2m

5M7 1M

Aeolian2-> Mixolydian (Blues) 

6m 7M7

3M7 6m

Resolving to

5M 6m

2M7 5M

Locrian-> Mixolydian  (Blues) 

7M7 1M

4#M7 7M7

Resolving to 

5M 6m

2M7 5M

Mixolydian 2 -> Ionian Blues

5m 6M7

2m 5m

Resolves to

1M 2m

5M7 1M 

Also  as an alternative from the chromatic pairs of the 7 modes we may create triplets wher he 3rd chord has harmonic relation with the 2nd part of the triplet and melodic relation with the 1st part

1M-2m=IONIAN=>  1M, 6M7, 2m

2m-3m=DORIAN=>  2m, 7M7, 3m

3m-4M=FRYGIAN=> 3m , 1M7, 4M

4M-5M=LYDIAN=> 4M, 2m7, 5M

5M-6m=MYXOLYDIAN=> 5M, 3M7, 6m

6m-7d=AEOLIAN=> 6m , 5bM7, 7d

7d-1M=LOCRIAN=> 7d, 5M7, 1M.

A nice chord cycle based on that would be

 1M, 6M7, 2m

 2m, 7M7, 3m

 3m , 1M7, 4M

4M, 2Μ7, 5m

5m  1M7 4M 

4M   4M7  7bM

7bM  5M7 1M

In the next we may compose songs with first part (couple) a sad triplet or pair signifying a mode and resolving to the refrain to a happy triplet or pair (usually the Ionian or Mixolydian) 

Only the Ionian, Mixolydian, Dorian, Aeolian, Lydian, are triplets of chords that are exact harmonic triplets. The Frygian and Locrian are not exact harmonic triplets. 

Here are examples of chord progressions 

E. g. Dorian-> Ionian (Blues)

2m, 7M7

3m, 3m 

Resolving to

5M7 1M 

4M , 1M

5M7, 1M

etc

Or

1M 

3M7  6m

7M7 3m

5M7 1M

4M , 1M

5M7, 1M

Also

1M 3M7 6m

1M 7M7 3m

4M  3M7 6m

4M 6M7 2m

5M  7M7 3m

5M  5bM7 7m

429. SIMPLICIAL SUBMELODY WITH ARPEGGIO INTERVAL PER CHORD INSTEAD OF ONE NOTE PER CHORD FOR COMPOSITION OF MELODIES

 Such simplicial sub-melodies  have much more information for melody composition, as they contain a pitch direction (up, down , steady) as pitch moves for each chord. They have also the advantage that they utilize the 66% of the chord, thus there is less indeterminacy in the relation melody-chord.

These pairs of notes are usually even number odd odd number notes of the full melody, in other words they need extension with interpolated notes. 

To compose the full melody we interpolate notes of the 6-notes scale Celtic minor between the notes of the simplicial sub-melody  so as to have intervals of 2nds, and so that the interpolated note (usually outside the chord) has duration 1/2. or 1/3 of the corresponding note of the simplicial submelody. In this way we are certain the the derived melody fits to the underlying chord. 

The pitch direction (up, dowm , steady) shows the topological pattern of the simplicial melodic themes. Of course a full melodic theme may involve more than one chord, e.g. 2 chords with the characterization of the transition relation as chromatic , melodic and harmonic. 

We give an example here with the Irish folk song Frost in Celtic minor (6 notes scale g,a,b,c,d,e)

The chord progression and structure of repetitions is  4 times the 

Am  Am 

Am  G

Am G

Am Am 

And then 2 times the 

Am G

Am G

Am G

Am Am 

G Am

Am G

Am G

Am Am 

And then all these 2 parts  3 times

The arpeggio interval simplicial submelody for the first part  and for each chord is the 

Am(e5->c5)   Am (c5->a4)

Am(a4->e4)  G(g4->b4)

Am(c5-c5) G(b4->e4)

Am(a4->c5)  Am (c5->e5) 

And for the 2nd part is 

Am(a4->c5) G(e5->b4)

Am(e5->a5) G(g5->d5)

Am(e5->a5)  G(b5->g5)

Am(a5->e5) Am(e5->a5) 

G(g5->d5) Am(c5->a4)

Am(e4->a4) G(b4->d5)

Am(a4->a4) G(d4->d4)

Am(a4->a4) Am(a4->a4) 

To compose the full melody we interpolate notes of the 6-notes scale Celtic minor between the notes of the simplicial sub-melody  so as to have intervals of 2nds, and so that the interpolated note (usually outside the chord) has duration 1/2. or 1/3 of the corresponding note of the simplicial submelody.