223. MINORIZATION-MAJORIZATION AS A UNIQUE HARMONIC TRANSFORMATION (NEGATIVE--POSITIVE HARMONY) MODULATIONS VERSUS TRANSPOSITIONS OF MELODIES AND HARMONIES

Here it is described why and how the transformation of a song from a major mode diatonic scale to a minor mode diatonic scale (and vice versa) is not just an ordinary change of mode among the 7 possible modes of the diatonic scale (e.g. from the ionina to the aeolian) but a  unique harmonic and melodic transformation.

In the nxt video this transformation from a  major mode to the minor mode (but also as scale modulation) is described under the term negative harmonics.

Do you know beautiful songs written in a Aeolian or minor mode of a diatonic scale? Then try the positive harmony, in other words transform them melodically and harmonically to a major mode and make them happier.

https://www.youtube.com/watch?v=qHH8siNm3ts&t=168s


TRANSCRIPTIONS:
We must discriminate between the concept of transposition transcription  of the  melody and harmony of a song from that of modulation transcription .  A transposition transcription preserves the intervals among the notes of the melody and types of chords and it is played on higher or lower pitch. But a modulation transcription does not preserves the intervals among the notes of the melody neither the types of the underlying chords as it is "translating within the scale" and not within the 12-notes chromatic scale, the melody and its chords starting from a different note of the scale (different mode). Both though require that all the melody (or song) is written in a single scale (or mode) and the transcription is another scale or mode of equal number of notes. 

222. THE 7 MODES OF A DIATONIC SCALE AS TRIADS OF CHORDS

We cannot stress much the importance of triads of chords (but also of notes intervals and scales) in improvisation.

A good application is to realize that as a diatonic scale is characterized as chords on the wheel by 4ths by its 3 chords on the steps 1M, 4M , 5M  (harmonic triplet of chords) ,  OR 7d 1M 2m (chromatic tripler of chords) the same can apply for the modes of the diatonic scale.

The chords of a mode of a diatonic scale at the steps 1,4,5 (or 7,1, 2) of it characterize its mood.

For example for the mixolydian mode of the diatonic scale from C ,(G, A, B , C, D, E, F, G) the chords at the steps 1,4 ,5 are the G, C, Dm) thus the 1, 2, 5 or I, ii, V of the original ionian and are the base of blues jazz.


Based on this perception, the 7 modes of the diatonic scale have the following chord triads:

(that is chords on their 1st 4th and 5th step, and we symbolize by m=minor M=major d=diminsihed.
Based on this perception, the 7 modes of the diatonic scale have the following chord triads:

(that is chords on their 1st 4th and 5th step, and we symbolize by m=minor M=major d=diminsihed.



1. IONIAN  :  HARMONIC TRIPLET (1M, 4M, 5M)
2. DORIAN  : HARMONIC TRIPLET (2m, 5M, 6m)
3. PHRYGIAN : HARMONIC TRIPLET (3m, 6m, 7d)
4. LYDIAN: HARMONIC TRIPLET  (4M, 7d,1M)
5. MIXOLYDIAN: HARMONIC TRIPLET  (5M, 1M,2m)
6. AEOLIAN: HARMONIC TRIPLET (6m, 2m, 3m)
7. LOCRIAN: HARMONIC TRIPLET  (7d, 3m, 4M)

We may clasify them according the the major and minor chords

A.ALL 3 MAJOR CHORDS (ALL HAPPY) 

1. IONIAN  :  HARMONIC TRIPLET (1M, 4M, 5M)

B. 2 MAJORS AND ONE MINOR OR DIMINISHED CHORD (ALMOST HAPPY, ALMOST MAJOR)

4. LYDIAN: HARMONIC TRIPLET  (4M, 7d,1M)

5. MIXOLYDIAN: HARMONIC TRIPLET  (5M, 1M,2m)

C.  2 MINORS (OR DIMINISHED) AND ONE MAJOR  (LITTLE SAD,  ALMOST MINOR )

2. DORIAN  : HARMONIC TRIPLET (2m, 5M, 6m)

7. LOCRIAN: HARMONIC TRIPLET  (7d, 3m, 4M)

D. THREE MINORS OR DIMINISHED (ALL SAD) (ALL MINOR) 

3. PHRYGIAN : HARMONIC TRIPLET (3m, 6m, 7d)

6. AEOLIAN: HARMONIC TRIPLET (6m, 2m, 3m)

We may compare the basic harmonic triplets with the basic chromatic triplets (see also post 322)

1. IONIAN  :  CHROMATIC TRIPLET (7d, 1M, 2m)
2. DORIAN  :  CHROMATIC TRIPLET (1M, 2m, 3m )
3. PHRYGIAN : CHROMATIC TRIPLET(2m,3m, 4M)
4. LYDIAN:  CHROMATIC TRIPLET(3m, 4M, 5M)
5. MIXOLYDIAN: CHROMATIC TRIPLET (4M, 5M, 6m)
6. AEOLIAN:  CHROMATIC TRIPLET (5M, 6m, 7d)
7. LOCRIAN:  CHROMATIC TRIPLET (6m, 7d, 1M)



If we want an ordering of how much "minor" and "sad" or "anxious" is a mode and how much "major" and "happy" or "serene" is a mode based on the ordering d<m<M then we get the next partial ordering (non-linear ordering)

PHRYGIAN<AEOLIAN<DORIAN<MIXOLYDIAN<IONIAN

and

LOCRIAN<DORIAN

LYDIAN<MIXOLYDIAN

But the Locrian and Lydian are not comparable with all the others so as to put all of them in a linear order.

Here is a musicological old qualitative description of it, but the names are not the standard but an older version of them (e. mode V is referred in this table as Lydian , while nowadays is named Mixolydian). To realize about which mode is referenced we must look at the 2nd column with the latin numerals.

Based on this concept it is possible to define tunings  of an harmonica (see post 274 ) with these types of triads of chords so as to improvise with the corresponding harmony on each of the 7 modes!

221. UNLOCKING THE MELODIC AND HARMONIC IMPROVISATION BY UTILIZING TRIADS OF NOTES , INTERVALS , CHORDS AND 3-LEVELS STRUCTURE OF A MELODY

See also posts 217, 216, 214, 208 etc

We enlarge more on it below. It is a generalization of the concept of scale, as a diatonic scale can also be defined by a triad of major (or minor) chords consecutive on the wheel by 4ths.

The triads is the golden middle ground between the extreme simplicity of the one  note ,interval or chord and the more complex combinations of 5 or more notes , intervals or chords.

The simplicity of triad of factors for the melodic action is  mainly the next three factors

1) The triad of polarity (qualitative) of a melodic move (ascending, descending, rotating stationarily or isocratic)

2) The  quantitative  triad of the character of the move :Chromatic, Melodic ,Harmonic

3) The rhythmic pattern of repetitions (e.g. A1 A2 A3 B1)

We remind the reader that in posts 203 and 214 we described a 3-levels structure of melodies which we refresh here:

THE MELODIC IMPROVISATION IS A SEQUENCE OF "ROTATIONS". EACH "ROTATION" HAS THE NEXT 3-LEVEL  RHYTHMIC OR MORPHOLOGICAL STRUCTURE

THE 4 PARTS A1 A2 A3 BI STRUCTURE 

This structure is rhythmic morphological and comes as a pattern from the 15-syllable poetry.

2 lines in a 15-syllables poetry are divided to 4 parts A1 A2 A3 B1, each of the Ai having 4 syllables and the B1 3 syllables. Similarly here in the melody the A1 A2 A3 , B1 are of 2 measures.  Each of the A1 A2 A3 B1 contain at least one melodic theme. If we put the restriction that both the melodic theme and its variations are consisting from intervals that are 2nds in less that 1/3 (=33%) of the cases, then we get an "Irish" but also "south american", melodic/harmonic sound in the melody. The melodic theme of A1 is translated or inverted to that of the A2 and that of the A2 to that of A2. Finally the melodic theme of A3 is mutated to that of B1. The simplicial sub-melody has one note in each measure therefore two notes in each of the A1 A2 A3 B. These two notes signify a MELODIC MOVEMENT (VECTOR) which is the basis of an emotion.  If we superimpose the melody at the first two levels, the detailed improvisational notes of the melodic theme (1st level) and the melodic move or vector of the simplicial submelody (2nd level) we get a new musical entity and concept that we may call WAVING MELODIC VECTOR. The wavings are as in the 7 melodic themes patterns asin post 231. Another classification of them is that they are of 3 classes a) Chromatic (of length an interval of 2nd) b) Melodic (of length an interval of 3rd) c) Harmonic (of length an interval of 5th). The choice in the improvisation of one of these 3 classes is similar to the choice in a chord progression if the chord-transition will me chromatic , melodic or harmonic. Very often the wavings are of diminishing amplitude as we reach the melodic center-end note of it. This is very convenient to have in mind when we improvise because we think that we will move from a persisting note a (melodic center) to a persisting note b (melodic center ) in a scale but with improvisational waving way that we may change each time at willAll the melodic movements of the A1 A2 A3 B make a DOLPHIN WORD (as defined also in post 101, 114 ). Each part A (thus melodic move too) has an underlying chord. The chords of two parts like A1 A2 may be the same or different chords. The melodic move can be also a melodic triad (alternating major minor vector interval of 3rd as in post 208) . The Dolphin word of the "rotation" may be a closed polygon (e.g, triangle) of waving melodic vectors , so that the length of the melodic vector indicates also the length-interval of the waving melodic vector, which may also be the distance as musical interval of the middle notes of the underlying chords, of the melodic move.
This melodic polygone allows for simple and very concise, simple and visually beautiful  methods of writing the improvisation with not less information than the necessary but no more than a minimum too, so that each time we see the written paper and play the melody a different melody will emerge (mainly at the first layer/level of it) while still it will be "the same" song. 

When playing again such an improvisation the simplicial sub melody is repeated (thus the "rotation" A1 A2 A3 B or Dolphin word of it), but the other notes inside the measures that are embellishments may change. All together the "rotations" or Dolphin words make the total melodic phrases of the song. Therefore we have here at least a 3-level structures of the melody a) notes b) melodic moves c) "rotations" or Dolphin words,and in time it is 1, 2^3=8 (2 measures)  and 2^5=32 (A1A2A3B parts).

220. THE DOUBLE 4-STRINGS GREEK BOUZOUKI F2-bB2-D3-G3-B3-E4 (4-3M-4-3M-4) TUNING OF THE 6-STRING GUITAR OR OUD

See also post  and 200

The standard tuning of the guitar comes from a scale LIKE :

F2-Bb2-D3-G3-B3-E4-G#4-C#5-F5

So we may repeat the pattern 4-3M-4  D3-G3-B3-E4 of the standard tuning of the guitar to the

4-3M-4-3M-4  or F2-Bb2-D3-G3-B3-E4

We play this tuning as two 4-strings Greek bouzouki

The high  D3-G3-B3-E4  (4-3M-4) in G major

The low  F2-Bb2-D3-G3  (4-3M-4) in Bb major

219. A REMARKABLE IMPROVEMENT OF THE STANDARD 6-STRINGS TUNING OF THE GUITAR . C2-G2-D3-G3-B3-E4 (5-5-4-3M-4) 4 INSTRUMENTS IN ONE TUNING

As alternative we may apply the 5-5-4-3M-4  E.g.  C2-G2-D3-G3-B3-E4  of the 6-string guitar or  1+6 courses oud.

It can be considered a type of modification of the overtones tuning 

1-1'-5'-1''-3''-7'' C₂-C₃-G₃-C₄-E₄-G₄                 
to the 
1-5-2'-5'-7'-3''

The D3-G3-B3-E4  part is a 4-string Greek Bouzouki in G major

The G2-D3-G3 part is a 3-string Greek Bouzouki in Bb major or G major

The C2-G2-D3-G3 is a bass Irish 4-string Bouzouki

The C2-G2-D3 is a low tambouras or saz with privileged scale the C major.


AS AN ALTERNATIVE INSTEAD OF UTLIZINGTHE G MAJOR (E MINOR)  AS PRIVILEDGED SCALE WE COULD UTILIZE THE Bb MAJOR (G MINOR) AS PRIVILEDGED SCALE WITH THE TUNING

The F3-Bb3-D3-G4  part is a 4-string Greek Bouzouki in Bb major

The Bb2-F3-Bb3 part is a 3-string Greek Bouzouki in Bb major

The Eb2-Bb2-F3-Bb3 is a bass Irish 4-string Bouzouki

The Eb2-Bb2-F3 is a low tambouras or saz with privileged scale the Eb major.

The highest 3 strings (1st 2nd 3rd) give in the 2-frets triad chords  the Aeolian (6th step) mode of the privileged scale (e.g. Bb)

The 2nd 3rd 4th strings give in the 2-frets triad chords the Ionian (1st step) mode of the privileged scale (e.g. Bb)

The 6th, 5th, 4th strings in the 2-frets triad chords give the Lydian (4ths step) mode of the privileged scale (e.g. Bb) 

As a contrast, the standard 6-string guitar tuning in the same sets of strings and on 2-frets triad chords give only the Aeolian and the Ionian mode!

Some further advantages of this guitar tuning are 

1) It  goes lower than a standard  guitar and as low as the cello

2) Still at the 4 higher strings all the chord-shapes and chords of the standard guitar can be played without any note missing. Thus we reduce all well known guitar chord playing in the higher 4-strings

3) Nevertheless in the lower 3 strings it plays also the triad-chords of 3 strings of an octave mandolin or mandocello! 

4) It plays all the tunes of Irish bouzouki on the lower  4 strings and all tunes of the Greek 4-strings Bouzouki in the higher 4 strings.  Including the isocratic melodies with two strings playing as drone an interval of 5th

5) In the 3rd 4th 5th strings it plays all the tunes of a Greek 3-strong bouzouki, including the isocratic with two strings playing as drone an interval of 5th

6)Thus it combines playing with ancient tunings that require strings tuned at  intervals of 5th (melodies orientation) and more modern tunings like that of the standard guitar or 4-strings Greek Bouzouki (chords or harmonic orientation)

7) The simplest patterns of 2-frets triad (3-strings) chords have 3 modes of the privileged scale in this tuning (Ionian, Aeolian, Lydian) compared to the 2 only modes (Aeolian , Ionian) in  the standard tuning of the 6-strings guitar

218 . THE CONCEPT OF SIMPLICIAL SUB-PROGRESSION OF CHORDS IN IMPROVISATION.

This concept of simplicial sub-progression of chords is entirely analogous to the concept of simplicial sub-melody of a melody. The basic application is of course that we try to find simplicial sub-progression of chords that are triads of chords where the subconscious feeling of the improvisation is very familiar and easier.

We enlarge more on this concept

217. POWER-CHORD OF 3RD OR 5TH AS WAVES OF A SIMPLICIAL SUB-MELODY

For the concept of simplicial sub-melody see e.g. post 104

This simplicial sub-melody is a bit different than the other types of simplicial sub-melodies , as it
utilizes 3 notes (a1, a2 a3) per chord X(i) , and they are the notes of power-chord of interval of 3rd or 5th which exist in the chord X(i). E.g. if  X(i)=C4 major then the (a1, a2 a3) could be (c4-e4-c5) or (c4-g4-c5) or (e4-g4-e5) etc.

As example of folk song with such power chord of 3rd waves is the Bearcice Reel

https://www.youtube.com/watch?v=E9D7RqdmV7U