209. MELODIC TETRA (4) OR PENTA (5) -CHORDS: SOLO COMPOSITION AND IMPROVISATIONS BASED ON ALTERNATING MELODIC QUARTETS OR QUINTETS OF INTERVALS OF 4TH AND 5TH.

THE ANCIENT MUSICAL THEORY SIMPLE DESCRIPTION OF RAPSODY MUSIC STIL LIVING IN THE AEGEAN ISLANDS LIKE THAN OF CRETE IN GREECE :

Such music was created in ancient times it  is mesmerizing with complicated melodic lines but in reality very simple musical description.

For these Aegean islands (Greece) improvisational folk melodies with violin or Lyra, the next factors prevail.

1) "Poetic meters" over the same note sometimes note up to 8 notes

3) Straight vectors ascending or descending usually of 4 or 5 notes so as to reach a new chord neighborhood.

2) Mainly waves by intervals of 2nds (chromatic) inside intervals of 3rds (melodic, either standing or ascending descending, and usually inside a chord  so as to reach the neighborhood of a new chord.

A) THE UNDERLYNG CHORD OF THE SONG IS ONLY ONE AND IS A POWER  CHORD AT ROOT POSITION OF SAY A DIATONIC SCALE (ALTHOUGH IN ANCIENT TIMES THEY DID NOT HAVE THE CONCEPT OF A  7-NOTES SCALE BUT ONLY OF A 4-NOTES SCALE THE  TETRACHORD WHICH WAS A SCALE SPANING ONLY AN INTERVAL OF 4TH INSTEAD OF AN INTERVAL OF 8TH, THUS POWER CHORD WOULD BE THE ROOT POSITION ON THE TETRACHORD). 

B) THE SOLOING IS ANY REPEATING PROGRESSION OF SHORT RYTHMIC MELODIC THEMES WITHIN A TETRACHORD WHICH  IS USUALLY  THE 1-2-2 IN SEMITONES THUS THE FRYGIAN TETRACHORD AT THE 3RD POSITION OF A  DIATONIC SCALE WITH UNDERLYING POWER CHORD AT THE ROOT POSITION OF THE TETRACHORD OR THE 3RD POSITIONOF A MODERN 7-NOTES DIATONIC SCALE. (SOMETIMES ALTERNATING WITH ANOTHER TETRACHORD E.G. THE IONIAN TETARCHORD AT ROOT POSITION OF THE 7-NOTES DIATONIC SCALE , AND IN ANY CASE THE ACCOMPANYING CAN BE ALSO BY THE POWER CHORD AT THE ROOT POSITION OF THE 7-NOTES DIATONIC SCALE IN INSTEAD OF THE 3RD POSITION OF THE DIATONIC SCALE)

THE MORE COMPLICATED BUT NOT  ALWAYS MORE ENLIGHTENING DESCRIPTION WITH MODERN SCALES AND CHORDS: 

MELODIC TETRA (4) OR PENTA (5) -CHORDS: SOLO COMPOSITION AND IMPROVISATIONS BASED ON ALTERNATING MELODIC QUARTETS OR QUINTETS OF INTERVALS OF 4TH AND 5TH.

(This post has not been written completely yet)

In post 208 we discussed a similar idea but with alternating major/minor 3rds creating thus underlying harmony of major /minor chords of diatonic scale. The optimal tuning for this is string instruments  tuned uniformly by intervals of 5ths.

Here the idea is the same but we alternate intervals of 4th-5th to create power-5 chords. The optimal tuning here is the octaves tuning of post 210.

When improvising is a solo in an almost random way but which tries to listen also to the inner emotions, a good path is to walk by intervals of 2nd small distances of total length and interval of alternating intervals of 4th (5 semitones) and 5th  (7 semitones) exactly as it happens in a power-5 chords of diatonic scale, as this also creates an underlying  simple and string harmony. 

This type of walking vector-intervals (see also post 183 1nd 159) in other words intervals closed together with all the intermediate notes of diatonic scale that it belongs to it we have called previous post as vector-chord improvisation as contrasted to arpeggio improvisations.

Therefore instead of the concept of scale (and as here we do not assume a chord progression or scale of chords) we have the concept of tetra-chords and penta-chords   as vector intervals of  4th and 5th respectively.
In ancient Greece the dominant concept was not the 7-notes scale but the tetra-chord and penta-chord. By combing two such we get 7-notes scales  

Of course here also a 4-chord and a 5-chord (or vice versa) of length an interval of 4th and an interval of 5th create a 7 -notes scale . Some of them are modes of the diatonic scale, the harmonic minor  the double harmonic minor and the melodic minor.

Of course we add wavings by intervals of 2nd and we go up or down according to the alternation of sad and happy changes of the emotions. 

The 4th/th  alternation also corresponds to alternation of sad and happy emotions. 

If we are on string instruments tuned by octaves (see post 210), then we can also accompany this solo with the interval of 8th of the two immediately lower strings as a kind of drone power-8 chord. The melodic themes created in one or two consecutive such (vector) intervals of 4th-5th can be varied of course with translations, inversions, rotations (including expansions)  and mutations. In an octaves tuning this can be done by shifting octaves which means shifting among the strings.
Normally two tetra-chords/pentachords  are for the first poetic line (8 beats) and two more for the 2nd poetic line (7 syllables) in lyrics of 15-syllables poetry.

ALL 6 TETRACHORDS   (also called vector intervals of  4ths)

DIATONIC FAMILY

(containing only 2 and 1)

2-2-1  syntono major  , Ionian/mixolydian

1-2-2  syntono minor  , Phrygian/Locrian

2-1-2   minor, Dorian/Aeolian

CHROMATIC FAMILY

(containing 3)

1-3-1   2nd chromatic

1-1-3    parachromatic tonal

3-1-1    1st chromatic 

ALL 20 PENTACHORDS   (also called vector intervals of  5ths)

All pentachords contain a single power-5 chord that power-5 chord which is defined by the end-notes of the pentachord.

DIATONIC FAMILY

(containing only 2, and 1)

2-2-2-1       Major Lydian    Contains a major chord (known also as Natzi/Zaouil)

2-2-1-2        Major Ionian/Mixolydian    Contains a major chord.(known also as Rast/Mahour)

2-1-2-2       Minor Dorian    Contains a minor chord (known also as Bousselik/Nichavent)

1-2-2-2       Minor Frygian/Aeolian    Contains a minor chord (known also as Qourdi)

CHROMATIC FAMILY

(containing  3 )

1-1-3-2

1-1-2-3

1-3-2-1   Contains a major chord and a diminished chord

1-2-3-1   Contains a minor chord and a diminished chord

1-2-1-3   Contains a minor chord and a diminished chord

1-3-1-2   Contains a major chord and a diminished chord (known also as Hijaz)

3-2-1-1    Contains  a diminished chord

2-3-1-1

3-1-2-1   Contains a major chord and a diminished chord

2-1-3-1   Contains a minor chord and a diminished chord (known also as Nevesser/Nikriz)

3-1-1-2   Contains a major chord (known also as Saz-kar)

2-1-1-3   Contains a minor chord (known also as Samba)

ENHARMONIAN FAMILY

(containing  4 )

1-1-1-4   Contains a minor chord

1-1-4-1

1-4-1-1

4-1-1-1   Contains a major chord

Of course a 4-chord and a 5-chord (or vice versa) of length an interval of 4th and an interval of 5th create a 7 -notes scale . Some of them are modes of the diatonic scale, the harmonic minor  the double harmonic minor and the melodic minor.

In composing melodic themes based on melodic tetra-chords/penta-chords  we should use also the concept and technique  of  variational  independent base of melodic shapes or melodic seed (see post 106). I other words the melodic themes shapes that are mutually variational independent, in other words neither translation neither , inversion, neither rotation can derive any one of them from the others , and in addition all other melodic themes of  the song can be derived with variations from them.

208. MELODIC TRIADS: SOLO COMPOSITION AND IMPROVISATIONS BASED ON ALTERNATING (MELODIC TRIADS AS VECTOR) INTERVALS OF MAJOR(HAPPY) /MINOR(SAD) 3RD:RECIPES OF HAPPINESS AND SADNESS

(This post has not been written completely yet)

MELODIC TRIADS: SOLO COMPOSITION AND IMPROVISATIONS BASED ON ALTERNATING (MELODIC TRIADS AS  VECTOR) INTERVALS OF MAJOR(HAPPY) /MINOR(SAD) 3RD:RECIPES OF HAPPINESS AND SADNESS

HERE IS EXAMPLE OF SUCH  IMPROVISATION

https://www.youtube.com/watch?v=Hxym5yTmdC8&t=1420s

When improvising is a solo in an almost random way but which tries to listen also to the inner emotions, a good path is to walk by intervals of 2nd small distances of total length an interval of 3rd and alternate  major (4 semitones happiness ) and minor (3 semitones, sadness ) exactly as it happens in a diatonic scale, as this also creates an underlying  major or minor chord. If on the other hand it is two consecutive intervals of minor 3rd it would create an underlying diminished chord and if consecutive major intervals of 3rd an augmented chords (that occur in the harmonic and double harmonic minor) , both more  rare compared to major and minor chords. 

This does not mean that we create a specific diatonic scale or mode of it but rather pieces of diatonic scales, therefore it is more probable that we are in a bebop scale (union of two diatonic scales).

This type of walking vector-intervals (see also post 183 1nd 159) in other words intervals closed together with all the intermediate notes of diatonic scale that it belongs to it we have called previous post as vector-chord improvisation as contrasted to arpeggio improvisations.

Therefore instead of the concept of scale (and as here we do not assume a chord progression or scale of chords) we have the concept of TRIAD  as vector interval of 3rd MINOR (SAD) OR MAJOR (HAPPY) . By composing triads we get various types of scales known or unknown but with recognizable hidden harmony.
OF COURSE WE MAY VERY WELL WALK BY TRIADS A DIATONIC SCALE GIVING SEQUENCES OF MAJOR (HAPPINESS) AND MINORS (SADNESS) 3RDS IN THE PROPORTION AND COMBINATION WE WANT.
KNOWING THIS IN MAJOR-MINOR 3RDS WE ALWAYS KNOW WHERE TO FIND HAPPINESS AND MORE HAPPINESS AND SADNESS AND MORE SADNESS.
Inharmony a chord is a triad, and triads of chords define usually in  a minimal way the harmony of a scale. Similarly here in melodic composition, the basic composition element is a melodic triad as above, and and triads of melodic triads define somehow an scale of an octave.

The usual  triads  are the next 3 in semitones

1-2
2-1
2-2
  giving in total  semitones 3 or 4 or an interval of  3rd

Of course we add wavings by intervals of 2nd and we go up or down according to the alternation of sad and happy changes of the emotions. The major/minor 3rds alternation also corresponds to alternation of sad and happy emotions. We may of course alternate to the solo also triad chords. If we are on string instruments tuned by 5ths, then we can also accompany this solo with the interval of 5th of the two immediately lower strings as a kind of power-5 chord. The melodic themes created in one or two consecutive such (vector) intervals of 3rd can be varied of course with translations, inversions, rotations (including expansions)  and mutations.
Normally two triads are for the first poetic line (8 beats) and two more for the 2nd poetic line (7 syllables).

If we do not walk the intermediate notes of the vector interval of 3rd and we just jump-play it, alternating major minor such intervals of 3rd we are simply in t what we have called in post 94 the melodic corridor, which e.g. how the siku pan-fludes and pan--flutes with double rows of pipes are designed in the folk music of andes.

In composing  melodic themes based on melodic triads we should use also the concept and technique  of  variational  independent base of melodic shapes or melodic seed (see post 106). I other words the melodic themes shapes that are mutually variational independent, in other words neither translation neither , inversion, neither rotation can derive any one of them from the others , and in addition all other melodic themes oft he song can be derived with variations from them.

We should not confuse the melodic triads, which is a concept similar to that of  a scale of notes with the shapes of melodies in a melodic triad (as e.g. in post 100-106).

207. CHORDS MIDDLE NOTES SIMPLICIAL SUB-MELODY AND IMPROVISATION BASED ON THEM

See also posts 65, 72, 92, 103, 104 (concepts of chord-local 7-notes scale and chord-courtyard)

The chord-middle note simplicial sub-melody (CMNSS) this is one of the most simple tupes and most characteristic sub-melodies for the chord progression. The reason is that the middle note characterises a chord of it is major or minor, and thus this sub-melody involves notes that sometimes are the critical notes of modulations e.g. from the natural minor o the harmonic minor or double harmonic minor

In post 104 we have described more types of simplicial sub-melodies.

Here we describe a basic technique of the composition method that starts first from the chord progression and then the melody introduced in post 9  (as in jazz improvisation).

A simplicial (or simplistic) sub-melody is a bit more varying than a drone (isocratic)  melody, and is also the  source  of the bass lines. 

1) Chromatic simplicial sub-melody (CSS , minimum distance notes) .  The simplicial submelody is defined by the next rules. 

 When two successive chords of the chord progression have notes that are one semitone distance only, we chose these two notes as notes of the simplicial sub-melody. For reasons of flexibility we allow two notes per chord if necessary. This happens for all cases that the two consecutive chords in a diatonic scale that are at roots distance of an interval of pure 4th (5 semitones) or pure 5th (7 semitones) or if they are mutually complementary chords (with roots of one step of  the scale apart). In general it is a good idea to chose as notes of the simplicial submelody for two successive chords in the chord progression, two notes, one from each chord with the minimum distance in semitones from the notes of the two chords. E.g. if the chords are , the first chord is the C major=(c4,e4,g4) and the 2nd chord is the F major=(f4,a4,c5), then the notes are e4-f4 that is 3rd-1st. If the chords are the first chord is the C major=(c4,e4,g4) and the 2nd chord is the D minor=(d4,f4,a4), then the notes are e4-f3 that is 3rd-3rd. 

 If the two consecutive chords are mutually relative with two common notes, the notes of the simplicial submelody for each chord are either a common note or the note that the other chord does not contain! That is the 1st-5th order notes. E.g. If the first chord is the C major=(c4,e4,g4) and the 2nd chord is the E minor=(e4,g4,b4) then the notes are b4-c5, that is 5th, and higher 1st. But if the chords are  C major=(c4,e4,g4) and the 2nd chord is the A minor=(a3,c4,e4), then the notes are a4-g4  , that is the higher 1st. and the 5th. If the chords are major-minor relatives : C major=(c4,e4,g4) and the 2nd chord is the C minor=(c4,eb4,g4), then the notes are eb4-e4 , that is 3rd-3rd. 

1.3) Chromatic links simplicial submelody (also bass lines) In general we may have the next rule. If X1, X2 are two succesive chords of the chord progression, and we are at X1, a chromatic link or chromatic bridge  is defined by finding two notes a1 in X1, a2 in X2, so that a1-a2 is at the minimum interval distance among all other chord notes of X1 , X2. Then the chromatic link starts with a1, b1,b2....,bn,a2 , and ends with a2 and all the intermediate steps are one semitone distance. 

1.3) Minimal chromatic drone sub-melody (MCD sub-melody).
This simplicial sub-melody is like the chromatic sub-melody, except that we utilize preferably the common notes of the chords, and we require it  
1.3.1) of as few notes as possible and
1..3.2)  of as little distance as possible. 
The rules are the next

Rule 1: We start from the chord and we find a common note with its next chord. If there are two common notes, we look at the next 3rd chord and chose this that is also either a note of the 3rd--next chord or minimal distance of a note of it. We proceed in this way till the last chord of the underlying chord progression. 
It can be proved that if the chord progression are chords of a diatonic scale, then the minimal  chromatic drone melody, can have only some or all of the first 3 notes of the scale (e.g. in a C major mode diatonic scale the c, d, e)  
This is very useful in double flutes or whistles or double reed-winds playing where in the first it is played a minimal chromatic drone sub-melody, and in the 2nd a full melody.

A minimal chromatic drone sub-melody need not be a kind of bass-line! It very well be a kind of very high register or octave simple melodic line. Personally I prefer the latter.

2) Harmonic simplicial sub-melody (HSS, maximum distance notes) . Probably the best method of creating  the simplicial sub-melody which is based on preferring intervals distances of the notes of the simplicial sub-melody (opposite to the previous method) that are large intervals ,namely intervals of 5ths , 4th 6th or 8th.  . The simplicial sub-melody is somehow the centers or oscilaltion boundaries of the final melody and most often it is one note per chord of the chord progression . They may be also the start and end of the melodic themes. Or they can be just centers that the melodic theme must pass from them. It can also be considered as a very simple bass line parallel to the melody. So the rule to choose the simplicial sub-melody is the next

2.1) If we have two successive chords X(1) -> X(2) in the chord progression, and a is the note of the simplicial sub-melody belonging to chord X(1) , and b is the note of the simplicial sub-melody belonging to the chord X(2), then a->b is an interval of maximum distance and the preference in intervals is in the following order of preference 5th, 4th, 8th, 6th. 
For the notes of maximum distance between successive chords we have the next choices : 

If the X(1) -> X(2) are in the relation of resolution (succesive in the wheel by 4ths) e.g. G->C then we have 3 choices for a->b, the g->c, or b->e, or d->g. If the X(1) -> X(2) are in the relation of relative chords (two common notes) e.g. C->Em then we have 2 choices for a->b,

c->g, or e->b. And if the X(1) -> X(2) are in the chromatic or complementary relation of  chords (roots that differ by one step of the scale) e.g. C->Dm, then we have one only best choice of a->b, here the c-> f, and a 2nd best choice the c-> which is an interval of 6th.
The notes of maximum distance would be two notes per chord. The 1st would be the maximum distance from the previous chord and the 2nd the maximum distance from the next chord. We prefer usually to simplify it it in to one only note but either two or one only note  if necessary we shift to the next octave so as to have the rule that two successive notes of two successive chords of the harmonic simplicial sub-melody have always distance large intervals of  5th, 4th, 8th, 6th. 
2.2) After we have defined the simplicial harmonic and the chromatic sub-melody then we may create bridges between its notes by smaller intervals e.g. 3rds or 2nds for a  full melody. The best ways is to start from the first note of the Chromatic Simplicial submelody (CSS) of the chord relevant to the previous chord, pass from the unique note of the Harmonic simplicial submelody (HSS)  of the chord and end at the 2nd note of the chromatic simplicial submelody (CSS) of the chord relevant to the next chord. (See post 109).
The notes of the harmonic submelody of a chord progression may be used to be  somehow the centers or oscilaltion boundaries of a final melody and most often.  They may be also be the start and end of the melodic themes. It depends if we create melodic themes inside the chord and around of a note of it which serves as it center or melodic themes linking two of them  and their successive chords. For the first way , the melodic themes inside the chord and around the note of the harmonic simplicial submelody can be created as in the post 103 using the chord-local 7-notes scale for each one note of the harmonic simplicial submelody.


There are also the 


3) CHORD-PROGRESSION SIMPLICIAL SUB-MELODIES (CPSS) 
 This is defined in the most easy way as consisting from one note per chord of the chord progression and always at the same degree (1st or 3rd or 5th, or 6th, or 7nth or 9nth or 2nd etc) 
Here is relevant video that by extrapolating  this simplicial sub-melody , we get an improvisational melody, an idea of Jerry Bergonzy

https://www.youtube.com/watch?v=2X-WsnWCAaA&t=21s


4) The chord-middle note simplicial sub-melody (CMNSS) this is one of the most simple tupes and most characteristic sub-melodies for the chord progression. The reason is that the middle note characterises a chord of it is major or minor, and thus this sub-melody involves notes that sometimes are the critical notes of modulations e.g. from the natural minor o the harmonic minor or double harmonic minor 
IN THE NEXT WE DESCRIBE HOW TO CALCULATE THE SIMPLICIAL SUB-MELODY OF THE MELODIC CENTERS OF A MELODY

For improvisation in general over a known  or unknown a tune we need two types of concepts 
1) Simplifying to the melody concepts like chord-progression, simplicial sub-melody , bas etc
2) Enhancing to the melody concepts like counter-melody on the vector-chord underlying at that time the melody etc From the chord the middle (3rd note together with the root 1st note) is considered tobe the most characteristic from the chord as it differentiates it from major and minor.
Because 5 notes are played statistically almost equally in time and 3 are inside the chord while 2 only outside the overall result is harmonic with the chord. taking the middle note (3rd) ofthe chord as it its geometric center rather than its root, we have that this soloings is a kind of  almost random "dancing" around the geometric center of the chordand inside the underlying scale. Since for each chord there is usually one note of a simplicial submelod, and we may take as note of the simplicial sub melody the geometric center (3rd in1-3-5) we may alsos say that this way of improvising is a "dancing" around the notes of this (middle note) simplicial submelody

The chord-closure or vector-chord as defined in post 159 is only for the normal position of a chord.

The random playing of the notes at an equal time each, or "rotations" or permutations of a vector-chord (or chromatic and diatonic neighborhood of  a chord) ,  leads to a melody that the chord that fits to it harmonically to accompany it, is the chord of the vector-chord. In this way, a pre-defined chord progression visualized as a progression of vector chords, defines almost completely an improvisational melody. 

2ND LAYER FASTS HARMONIZATIONS OF VECTOR-CHORDS IMPROVISATIONS

Furthermore, when improvising by "waving" or "rotating" inside the vector chord, we may also add some harmony by playing the improvisational solo as 1st-2nd voice or doubles by intervals of 3 and of course changing them to major minor 3rds so that it belongs to the scale if the roots are in  the scale or keeping it the same to the closest such that is in the scale. It can be with doubles or even triads (3-notes chords) which of course will create a fast-changing harmony which is reasonable to accompany with only stable power chord of 5 (interval of  5). Usually, the fast changing of the chords is of the chords I, IV, V (or  substituting any one of them with its lower relative minor chord. see also post 159)

E.g. here is a good example of such melodic wavings in the next midi file. It can be considered as chromatic or diatonic waving around each note of the chord but in addition, harmonized with doubles by intervals of 3rds http://www.greeksongs.gr/midis/arampasperna.mid 

Because 5 notes are played statistically almost equally in time and 3 are inside the chord while 2 only outside the overall result is harmonic with the chord. taking the middle note (3rd) ofthe chord as it its geometric center rather than its root, we have that this soloings is a kind of  almost random "dancing" around the geometric center of the chordand inside the underlying scale.

We should notice that besides such "chromatic waving" or "rotating" within the closure of a triad chord in the normal position, we may have also waving ascending and waving descending or translating, if we expand the chord in two or 3 octaves. And this may be done again with fast-changing harmonization (I, IV, V)  with doubles or triads , as long as the duration of the notes outside the chords (the initial and maybe two more within the pattern I, IV, V) are less than the duration of the notes inside the chords or as long as the intervals created by the notes of the melody and the notes of the chords have more 3rds 4ths and 5ths compared to intervals of  2nds.

We must remark here that if there is a melody in the song which is say using the chords X1, X2 X3,...Xn , the melodic improvisational fillings parallel and in between the parts of the melody with instruments like Bouzouki or mandolin or violin or lyre etc , need not keep the same chord-progression X1,...Xn but a permutation of it as well ,although in general, it will use the same chords and rarely more chords but of the same notes-scale or same scale of chords  (chord-scale). 

In all cases, a variational chord progression X(a1), ...,  X(ak)  will determine as above after determining the vector-chord wavings an improvisational solo.

If we are composing e.g. in a midi editor the above perceptions are adequate for easy composition of melodies. But if we are playing an instrument and we want to improvise, then instead of having as center the arpeggio of a chord to improvise diatonically or chromatically around it it ir ending at it it  is easier to think of waving around or ending at centers that are not chords but notes that are away by intervals of 3rd, 4th, 5th 8th (e.g. the notes of a simplistic sub-melody).

See also post 159

206. HOW TO CREATE LONG SYMMETRIC CHORD PROGRESSIONS AND THEIR SIMPLICIAL SUB-MELODY FOR BEAUTIFUL SONGS FROM THE 7 CHORDS OF A DIATONIC SCALE.

AN EXCELLENT SOFTWARE TOOL TO UNDERSTAND THE BASIC 3 CHORD REATIONS IS THE SOFTWARE NAVICHORD (FOR IOS). IT HAS A HEXAGONIC TOUCH-SCREEN KEYBORD OF THE NOTES WHERE THE CHORDS ARE TRIAGNGLES AND ARE PLAYED BY TOUCHING THE CENTER OFTHE TRIANGLE

SUCH HEXAGONIC KEYBOARDS HAVE BEEN PATENTED ALSO IN THE TERPSTRA KEYBOARD.    THE 3 BASIC LOCAL RELATIONS OF THE CHORDS (NO-COMMON NOTE OR CHROMATIC RELATION, ONE COMMON NOTE OR HARMONIC RELATION AND TWO COMMON  NOTES OR MELODIC RELATION) ARE IMMEDIATELY VISIBLE.

THE NAVICHORD IS  ALSO A CHORD LOOP SEQUENCER WHICH PRODUCES CHORD PROGRESSIONS AND BACKTRACKS.

WE DESCRIBE TWO METHODS , ONE WITH TRIANGLES OF CHORDS AND ONE WITH PARALLELOGRAMS OF CHORDS.

The two methods to create chord progressions from the 7 chords of a diatonic scale are like creating words of a language which has as alphabet the 7 chords of the diatonic scale. It allows of unlimited combinations with varying degrees of symmetries.Of course always of a diatonic scale. we include also modulations of a certain type which are change of the natural minor of the diatonic scale to a same root harmonic minor or double harmonic minor.

A) THE CHORD PROGRESSION IS A CYCLE OR SEQUENCE OF TRIADS (TRIANGLES) OF CHORDS AS BELOW.

For happy melodies obviously, the triad is  the I, IV, V. According to the degree of sadness we want to impose, we substitute any of the major chords with its lower minor relative. In other words  vi for I, ii for IV and iii for V. 

About the symbols: In a C major scale the symbols denote the next chords

I=1M=C

ii=2m=Dm

iii=3m=Em

IV=4M=F

V=5M=G

vi=6m=Am

vii=7d=Bdim

So the possible combinations are 

I, IV, V   (1M, 4M,5M majors harmonic triad)

vi , IV, V  (4M, 5M , 5m,  chromatic triad, e.g, part of the Andalusian cadenza when reversed) 

I , ii, V    ( 2m, 5M ,1M harmonic triad)

I, IV, iii   (3m 1M, 4M,   melodic-harmonic triad)

IV , ii, V   ( 1M, 4M, 2m, harmonic-melodic triad)  

I , ii, iii  (3m, 1M, 2m, melodic chromatic or only chromatic triad)

vi, IV, iii   (3m, 6m, 4M, harmonic-melodic triad)

vi, ii, iii   (3m, 6m, 2m, harmonic triad)

vi-vii-iii (7d, 3m, 6m, harmonic triad)

I -vii -V  (5M, 1M , 7d, harmonic-chromatic triad)

In case we want to alter the natural minor ofthe scale to an harmonic minor or double harmonic minor the the usual changes of the harmonic personality as in post 158 apply.

In more detail: 

In general starting from a diatonic harmonic personality 

1M, 2m 3m 4M 5M 6m 7dim 1M

the next are the effects of turning the natural minor to harmonic minor or double harmonic minor.

The effect of the 1st blue note 5# of the harmonic minor on the harmonic personality is that 

the 3m  turns in to 3M and the 5M may turn  into  5b5  or better sounding  5#m or 5#dim or 5aug,  or  1dim  

Also the 7dim may turn in to 7m7b5 as 4 notes chord.

While the effect of  the 2nd blue note of the double harmonic minor 2# (or 3b) is that the 7dim turns in to 7M  or 7b5  and , the 1M may become 1aug and also the 2m may become 2#dimb3 or  better sounding 2#dim or 2#M. 

Further changes with augmented chords because of the harmonic and double harmonic minor we involve not only diminished chords but also augmented chords.

E.g.

In C major

Am  Bdim E  Am (repeated many times)  then

C Bd  G C  (repeated many times)  then

Am Dm E Am (repeated many times)  then again

Am  Bdim E  Am (repeated many times)  etc

Listen also to

https://www.youtube.com/watch?v=NwIw2BQW_jE

and to

https://www.youtube.com/watch?v=HcVD-6w4A8k

Of course the next critical issue is to determine the simplicial sub-melody that goes parallel to the chord progression. This determines also the chord progression as triads of notes and the correct voicing of the chord progression, so as to play directly also the simplicial submelody through the correct voicing of chord progression as triads of notes only. In other words

THE SIMPLICIAL SUBMELODY IS OF EQUIVALENT DETERMINATION WITH THE VOICING OF THE CHORD PROGRESSION AS TRIADS OF NOTES. 

Triads of chords with minor chords in them most often are correlated with straight descending shape of the theme of the simplicial sub-melody. While triads of chords with all three chords major chords are correlated with straight ascending shape of the theme of the simplicial sub-melody. Usually we prefer the middle note (3 from 1-3-5) of the chord for the note of the simplicial sub-melody. But we should study also the harmonic, chromatic and default  simplicial sub melodies discussed in posts 66, 109. 

Then we proceed with the embellishments and waving around the simplicial submelody to derive a full dense and even fast melody.

For example if we chose the next two triads of chords for te chord progression in a song in the C major scale 

(Am ,Bdim, E)  and (C Bdim G7) then the chord progression is 

Am-> Bdim-> E-> Am  repeated 4 times and 

C-> Bdim->G7->C  repeated 4 times and   

and all together repeated 3 times.

Then the first triad of chords  which has the minor chord Am signifies sadness and the simplicial submelody is chosen descending with a middle waving . So it is the a5->d5->e5->a4 . One note for each occurence of a chord which belongs to the chord . And the triads of chords C-> Bdim->G7->C has more major chords which signifies happiness so the simplicial submelody is defined as straight ascending . So corresponding one note (which belongs to the chord) to each chord it may be the c4->d4->g4->c5 .  We may also create an introductory part A of the song which is both parts B , C of the simplicial submelody with the necessary waving embellishments around it c4->d4->g4->c5->a5->d5->e5->a4 which we repeat two times each time we repeat the parts B and C above   of the two triads of chords.

The two methods to create chord progressions from the 7 chords of a diatonic scale the one here with triads (triangles) if chords and the one in post 148 with parallelogram diagrams of chords are like creating a language which has as alphabet the 7 chords of the diatonic scale. It allows of unlimited combinations with varying degrees of symmetries.

The next  Irish reel example is made more or less with thsi way.

https://www.youtube.com/watch?v=NwIw2BQW_jE

B) THE GENERAL PARALLELOGRAM 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 PARALLELOGRAM 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

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.

Besides the basic harmonic triplets (in other words a sequence of 3 chords X1,X2,X3 so that X1-X2 , X2-X3 are harmonic relations od chords, in other words chords that their roots differ by an interval of 4th (5th)) , there are also the chromatic triplets (in other words a sequence of 3 chords X1,X2,X3 so that X1-X2 , X2-X3 are chromatic relations od chords, in other words chords that their roots differ by an interval of 2nd). BOTH  ARE BASIC TYPES OF TRIPLETS. In other words with the 3 CHORDS OF THE TRIPLET WE CAN ACCOMPANY ANY MELODY IN THE DIATONIC SCALE. WE CANNOT HAVE THIS PROPERTY OF BEING HARMONICALLY A BASE OF 3 CHORDS FOR MELODIC TRIPLETs (in other words a sequence of 3 chords X1,X2,X3 so that X1-X2 , X2-X3 are melodic relations of chords, in other words chords that their roots differ by an interval of 3rd) 

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.

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)

We may compare the basic chromatic triplets with the basic harmonic triplets (see also post 222)

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)


Besides these 2 types of basic triplets we have also a 3rd type X1 X2 X3 , where X1-X2 is a chromatic relation and the X2-X3 is an harmonic relation or vice versa. We may call them the mixed
basic chromatic-harmonic triplets. E.g.  the basic triplet that is used sometimes in blues 1M 2m, 5M , is such as 1M-2m have chromatic relation while 1M-5M harmonic relation.

To convert a basic harmonic triplet to another chromatic or mixed basi triplet we utilize correspondences where we correspond each of the 3 main major chords of the diatonic scale with their lower minor relative and the 5M7 with the 7d. Therefore

2m<->4M
3m<->5M
6m<->1M
7d<-> 5M7

The same arguments may apply for the chromatic tonality where some of the mnor chords become major and some of the major chords minor. E.g. We have the harmonic triplet (3M7, 6m ,2m ) of the frygian mode and the harmonic triplet (7M7-3M7-6m) of the Locrian mode which are combined with the more standard harmonic triplets of the diatonic tonality of the dorian mode (2m-5M7-1M) or the myxolydian mode (5M7-1M7-4M) .

For  alternative basic chromatic triplets of the chromatic tonality (that corresponds to the harmonic minor and double harmonic minor) we have the triplets (we notice that thsi type of chromatic tonality gives for the basic chromatic triplets, cases of 2 major chords and one minor, thus the major chords are dominating!)


IONIAN MODE: 7M-1M-2m
DORIAN MODE: 1M-2m-3M
FRYGIAN MODE: 2m-3M7-4M
LYDIAN MODE: 3M-4M-5M
AEOLIAN MODE: 5M-6m-7M
LOCRIAN MODE: 6m-7M-1M

205. HOW TO CREATE CHORD PROGRESSIONS AND A SIMPLISTIC SUB-MELODY FROM TRIADS OF CHORDS OF THE DIATONIC SCALE AND ALSO ALTER THEM FOR THE HARMONIC AND DOUBLE HARMONIC MINOR MODULATIONS OF ITS NATURAL MINOR

THE CHORD PROGRESSION IS A CYCLE OR SEQUENCE OF TRIADS OF CHORDS AS BELOW.

(we contrast this method with the alternation of pairs in harmonic-chromatic-melodic relations as inpost 148 at the end of it. Here we use triads of chords instead of pairs of chords  and the symmetry is different.
The two methods to create chord progressions from the 7 chords of a diatonic scale the one here with triads (triangles) if chords and the one in post 148 with parallelogram diagrams of chords are like creating a language which has as alphabet the 7 chords of the diatonic scale. It allows of unlimited combinations with varying degrees of symmetries.)

For happy melodies obviously, the triad is  the I, IV, V. According to the degree of sadness we want to impose, we substitute any of the major chords with its lower minor relative. In other words  vi for I, ii for IV and iii for V. 

About the symbols: In a C major scale the symbols denote the next chords

I=1M=C

ii=2m=Dm

iii=3m=Em

IV=4M=F

V=5M=G

vi=6m=Am

vii=7d=Bdim

So the possible combinations are 

I, IV, V   (1M, 4M,5M majors harmonic triad)

vi , IV, V  (4M, 5M , 5m,  chromatic triad, e.g, part of the Andalusian cadenza when reversed) 

I , ii, V    ( 2m, 5M ,1M harmonic triad)

I, IV, iii   (3m 1M, 4M,   melodic-harmonic triad)

IV , ii, V   ( 1M, 4M, 2m, harmonic-melodic triad)  

I , ii, iii  (3m, 1M, 2m, melodic chromatic or only chromatic triad)

vi, IV, iii   (3m, 6m, 4M, harmonic-melodic triad)

vi, ii, iii   (3m, 6m, 2m, harmonic triad)

vi-vii-iii (7d, 3m, 6m, harmonic triad)

I -vii -V  (5M, 1M , 7d, harmonic-chromatic triad)

In case we want to alter the natural minor ofthe scale to an harmonic minor or double harmonic minor the the usual changes of the harmonic personality as in post 158 apply.

In more detail: 

In general starting from a diatonic harmonic personality 

1M, 2m 3m 4M 5M 6m 7dim 1M

the next are the effects of turning the natural minor to harmonic minor or double harmonic minor.

The effect of the 1st blue note 5# of the harmonic minor on the harmonic personality is that 

the 3m  turns in to 3M and the 5M may turn  into  5b5  or better sounding  5#m or 5#dim or 5aug,  or  1dim  

Also the 7dim may turn in to 7m7b5 as 4 notes chord.

While the effect of  the 2nd blue note of the double harmonic minor 2# (or 3b) is that the 7dim turns in to 7M  or 7b5  and , the 1M may become 1aug and also the 2m may become 2#dimb3 or  better sounding 2#dim or 2#M. 

Further changes with augmented chords because of the harmonic and double harmonic minor we involve not only diminished chords but also augmented chords.

E.g.

In C major

Am  Bdim E  Am (repeated many times)  then
C Bd  G C  (repeated many times)  then
Am Dm E Am (repeated many times)  then again
Am  Bdim E  Am (repeated many times)  etc

Listen also to

https://www.youtube.com/watch?v=NwIw2BQW_jE

and to

https://www.youtube.com/watch?v=HcVD-6w4A8k

Of course the next critical issue is to determine the simplicial sub-melody that goes parallel to the chord progression. This determines also the chord progression as triads of notes and the correct voicing of the chord progression, so as to play directly also the simplicial submelody through the correct voicing of chord progression as triads of notes only. In other words

THE SIMPLICIAL SUBMELODY IS OF EQUIVALENT DETERMINATION WITH THE VOICING OF THE CHORD PROGRESSION AS TRIADS OF NOTES. 

Triads of chords with minor chords in them most often are correlated with straight descending shape of the theme of the simplicial sub-melody. While triads of chords with all three chords major chords are correlated with straight ascending shape of the theme of the simplicial sub-melody.

Then we proceed with the embellishments and waving around the simplicial submelody to derive a full dense and even fast melody.

For example if we chose the next two triads of chords for te chord progression in a song in the C major scale 

(Am ,Bdim, E)  and (C Bdim G7) then the chord progression is 

Am-> Bdim-> E-> Am  repeated 4 times and 
C-> Bdim->G7->C  repeated 4 times and   
and all together repeated 3 times.

Then the first triad of chords  which has the minor chord Am signifies sadness and the simplicial submelody is chosed descending with a middle waving . So it is the a5->d5->e5->a4 . One note for each occurence of a chord which belongs to the chord . And the triads of chords C-> Bdim->G7->C has more major chords which signfies happiness so the simplicial submelody is defined as straight ascending . So correpsonding one note (which belongs to the chord) to each chord it may be the c4->d4->g4->c5 .  We may also creare an introductory part A of the song which is both parts B , C of the simplicial submelody with the necessary waving ebelishments around it c4->d4->g4->c5->a5->d5->e5->a4 which we repeat two times each time we repeat the parts B and C above   of the two triads of chords.

The two methods to create chord progressions from the 7 chords of a diatonic scale the one here with triads (triangles) if chords and the one in post 148 with parallelogram diagrams of chords are like creating a language which has as alphabet the 7 chords of the diatonic scale. It allows of unlimited combinations with varying degrees of symmetries.

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.

Besides the basic harmonic triplets (in other words a sequence of 3 chords X1,X2,X3 so that X1-X2 , X2-X3 are harmonic relations od chords, in other words chords that their roots differ by an interval of 4th (5th)) , there are also the chromatic triplets (in other words a sequence of 3 chords X1,X2,X3 so that X1-X2 , X2-X3 are chromatic relations od chords, in other words chords that their roots differ by an interval of 2nd). BOTH  ARE BASIC TYPES OF TRIPLETS. In other words with the 3 CHORDS OF THE TRIPLET WE CAN ACCOMPANY ANY MELODY IN THE DIATONIC SCALE. WE CANNOT HAVE THIS PROPERTY OF BEING HARMONICALLY A BASE OF 3 CHORDS FOR MELODIC TRIPLETs (in other words a sequence of 3 chords X1,X2,X3 so that X1-X2 , X2-X3 are melodic relations of chords, in other words chords that their roots differ by an interval of 3rd) 

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.

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)

We may compare the basic chromatic triplets with the basic harmonic triplets (see also post 222)

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)


Besides these 2 types of basic triplets we have also a 3rd type X1 X2 X3 , where X1-X2 is a chromatic relation and the X2-X3 is an harmonic relation or vice versa. We may call them the mixed
basic chromatic-harmonic triplets. E.g.  the basic triplet that is used sometimes in blues 1M 2m, 5M , is such as 1M-2m have chromatic relation while 1M-5M harmonic relation.

To convert a basic harmonic triplet to another chromatic or mixed basi triplet we utilize correspondences where we correspond each of the 3 main major chords of the diatonic scale with their lower minor relative and the 5M7 with the 7d. Therefore

2m<->4M
3m<->5M
6m<->1M
7d<-> 5M7

The same arguments may apply for the chromatic tonality where some of the mnor chords become major and some of the major chords minor. E.g. We have the harmonic triplet (3M7, 6m ,2m ) of the frygian mode and the harmonic triplet (7M7-3M7-6m) of the Locrian mode which are combined with the more standard harmonic triplets of the diatonic tonality of the dorian mode (2m-5M7-1M) or the myxolydian mode (5M7-1M7-4M) .

For  alternative basic chromatic triplets of the chromatic tonality (that corresponds to the harmonic minor and double harmonic minor) we have the triplets (we notice that thsi type of chromatic tonality gives for the basic chromatic triplets, cases of 2 major chords and one minor, thus the major chords are dominating!)


IONIAN MODE: 7M-1M-2m
DORIAN MODE: 1M-2m-3M
FRYGIAN MODE: 2m-3M7-4M
LYDIAN MODE: 3M-4M-5M
AEOLIAN MODE: 5M-6m-7M
LOCRIAN MODE: 6m-7M-1M

204. THE CELTIC HEXATONIC MINOR THE CRETAN HEXATONIC AND THE GREEK PENTATONIC SCALES

Studying the Celtic fast dancing melodies (reels) and the Cretan fast dancing melodies (condilies) we find particular scales that are 6-notes and 5-notes (pentatonic).

The Celtic minor is a well-known scale (with various modes) that has also been used to tune hang percussion instruments. In these notes in music here, we have adopted the definition of a scale as a sequence of notes that give one or more octaves and also all cyclic permutations of them. In this way starting from a different note of the scale gives only a different mode, not a different scale.

The Celtic minor 6-notes scale has the next interval pattern in semitones 

2-2-3-2-2-1 

or
3-2-2-1-2-2

Thus as C major scale we just omit the f 4th note

E.g.

c4-d4-e4-g4-a4-b4-c5

 It has 5 chords: C major (I), Em (iii),  Am (vi) ,G (V), Bdim (vii). 


As an alternative at its mode 2-2-1-2-2-3, it is again just the 7-notes diatonic scale 2-2-1-2-2-2-1 where we omit the 7nth note and it becomes 2-2-1-2-2-3.

As alternative if we omit the 3rd note in major mode diatonic scale we get the 6-notes scale 

2-3-2-2-2-1 and its 6 modes. (e.g. 2-2-1-2-3-2 or 3-2-2-2-1-2 etc) We could call it 2nd celtic 6-tonic scale.

It is a 6-notes scale with a maximal number of major/minor chords (See post 117)

The chinese Bawu direct blowing or transverse blowing flutes, and the hulusi flutes as well utilize a celtic minor scale in the mode (starting from the lowest note ) 2-2-1-2-2-3. They name the Bawu or Hulusi tuning of the flute by the 4th note. The Bawu and Hulusi flutes are free-reed winds as the Crumhorn, the Schalmei, the harmonica and the Accordeon. I call them here free-reeds not mainly because they do not touch a surface when they vibrate (the Slamei does touch a surface) but because the lips do not touch the reed.

THE HAPPY ENHARMONIC MAJOR  6-NOTES SCALE

In a diatonic scale there are 3 intervals of major 3rd 1-3, 4-6 , 5-7 (e.g. in C major C-E, F-A , G-B) and 4 minor 2-4, 3-5, 6-1, 7-2. If we want a  scale with more happy intervals of 3rd (major) than sad (minor) then should start with the 3 major 3rds 1-3, 4-6 , 5-7, and create the 6-notes enharmonic generation scale 

1-3-4-5-6-7-1 (e.g. in C major C-E-F-G-A-B-C) with interval structure

4-1-2-2-2-1  

WE may call it the happy enharmonic  MAJOR 6-notes scale

Also in Japanese folk music are used a few enharmonic gendre 5-notes scales with more intervals of major 3rd than minor 3rd. See also post 274 where harmonicas are tuned in this hexatonic scale.

In  the Celtic Minor scale which can be derived by the 3 minor 3rd intervals of the diatonic scale 2-4, 3-5, 6-1 or in C major

C-D-E-F-G-A-C with interval structure 2-2-1-2-2-3 (see also post  276)

The Cretan  6-notes scale is identical with this enharmonic gendre hexatonic scale and it has the next interval pattern in semitones 

4-1-2-2-2-1

It is derived from taking the major 3rd 1-3 of a root chord 1-3-5 and inverting it to be from 3 to next root 1'

Thus as C major scale we just omit the d 2nd note

E.g.

c4-e4-f4-g4-a4-b4-c5

 It has 4 chords all of them major or minor. They are the C major (I) , F major (IV), Em (iii), Am (vi). 

It is met most often in "condilies" with 2-3 cadenzas in the part 1-2-2-2-1.

We may compare it with the Hexatonic scale

3-2-2-1-2-2.  (Celtic minor)

which  can also be  derived by  taking the minor 3rd 3-5 of a root chord 1-3-5 and inverting it to be from 5 to next octave  3'.

Both  scales occur in the Cretan mantinodies or kondilies.

The hexatonic scale is most often an embelishment extension ofthe stanrd diatonic tetrachord 1-2-2.
Common pattern of simplicial submelody of Cretan folk rapsody music: : As intervals of a scale they are in pitch order 1-2-2. In other words  the most common pattern of simplicial submelody is a descending tetrachord , in semitones and in temporal order it is 2-2-1. An example  the andalusian cadenza that in ordinal numbers of the diatonic scale it is 6-5-4-3. 

The Greek pentatonic (5-notes) scale has the next interval pattern in semitones 

2-2-3-4-1 

Thus as C major scale we just omit the f 4th note and the  6th note

E.g.

c4-d4-e4-g4-b4-c5

It has the 3 chords C major G major E minor.  
It appears also in the Richter Tuning of the harmonica at the first octave andthe Chords 1M-5M.

The Greek pentatonic scale is a pentatonic scale with maximum number of major and minor chords. We must not be confused with the standard pentatonic scale (Egyptian, Mongolic, Western Indian  etc of interval structure  2 2 3 2 3.  (1st mode of the pentatonic minor. The 5th mode  3-2-2-3-2 is  also the pentatonic minor, and there is also  the 2nd mode or Egyptian scale 2-3-2-3-2 and the 
3-2-2-2-3 pentatonic which is not a different mode of it )

The greek pentatonic (5-notes) scale  is a subscale of the Celtic 6-notes  minor scale.

But also the India or Egyptian pentatonic scale 2-2-3-2-3 is also a a subscale of  the 6-notes celtic minor

This allows for interesting improvisations shifting from 

1) Ionian more of diatonic 2-2-1-2-2-2-1

2) Celtic minor  2-2-3-2-2-1

3) Greek pentatonic 2-2-3-4-1 (known also as Raga Chitthakarshini)

4) Indian pentatonic 2-2-3-2-3

where in all cases the 3 first notes and interval structure in semitones 2-2 remain stable 

The way that these scales derive from folk fast solos over two only chords (I-V-I) is as  in the  post 203.