143. THE MOST POPULAR CHORD PROGRESSION IN WESTERN SONGS, AS DERIVED FROM MAXIMAL HARMONIC 5-NOTES SUB-SCALE.

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We have mentioned in previous posts in this book, that the diatonic scale has the optimal mathematical property of being the only 7-notes scale (within the chromatic Bach 12-notes scale) with he maximum number of major and minor chord-triads.

An interesting next question is what are the corresponding such scales with the same maximal property but with a smaller number of notes? E.g. 4,6, or 6 notes?

The answer was given in post 117 where the maximal such harmonic sb-scales are enumerated.

We highlight only the maximal harmonic 5-notes and 6-notes subscales as giving rise to the most popular in western songs chord progressions.

5-notes maximal harmonic pentatonic 

intervals patterns 4-3-2-2-1 e.g. c4-e4-g4-a4-b4-c5

(It is essentially A chord with 7nth and with 6th)

Notice that this scale suggests the chord progression by taking chords of the full 7-notes diatonic scale based on the above notes of the maximal harmonic 5-notes scale which has the highest statistical frequency in popular songs:  1(7)  4 5 6m E.g. in C major scale it would be C7, F , G Am (=I7, IV, V, vi )=(1(7), 4, 5, 6m).

6-notes maximal harmonic  

intervals patterns 2-2-3-2-2-1 e.g. c4-d4-e4-g4-a4-b4-c5

(It is essentially a chord with 7nth, 6th and 2nd. A mode of it  is known also the raised Celtic minor scale of the hang-drums )

Notice that this scale also  suggests a  chord progression by taking chords of the full 7-notes diatonic scale based on the above notes of the maximal harmonic 5-notes scale which has  highest statistical frequency in popular songs:  1(7) , 2m,  4 ,5, 6m E.g. in C major scale it would be C7,Dm, F , G Am. This progression includes both the Blues progression 1 2m 5 (=I , ii, V) , and the most popular 1,4,5,6m (=I, IV, V, vi) .

For the F major scale, which is common in Eastern Europe folk music , such a scale of chords would be

F7, Gm, Bb, C, Dm,

While for the Bb major scale , which is very common in Greek folk music, such a scale of chords would be

Bb, Cm, Eb , F , Gm.

This most popular chord progression has a variation:

Instead of 1M, 4M, 5M 6m , the 1M, 2m, 5M 6m  (6m->2m->5M ->1M)

Or sometimes

5M->1M->4M->2m->5M


E.g. of (6m->2m->5M ->1M)

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

142. MELODIC IMPROVISATION WITH SIMPLISTIC SUB-MELODY OVER INTERVALS OF 5THS (cycle of 5ths) OR 4THS (cycle of 4ths).

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One of the simplest and oldest techniques of melodic improvisation is the create melodic themes that start and end at intervals of 5ths (cycle of 5ths) or 4ths (cycle of 4ths).

We have already met a similar chord-progression based improvisation (in post 17 at the end   and  post 34 ) based on the cycle of 5ths or 4ths, and the two methods are definitely related.

This is also used in the method of complementary melodic themes improvisation in post 140.

141. ONE ONLY ACCOMPANYING CHORD MELODIC IMPROVISATION

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After the very basic meditative improvisation with one only note (the root of a scale) as accompanying harmony, the next step of simplicity is the single accompanying chord melodic improvisation.

Here the technique of the CHORD-LOCAL 7-NOTES SCALE OF A CHORD (chord-courtyard scale ) applies. See post 102, 103  and 110, 159

When spending time with the melody with an underlying chord the best idea is to have the chord in 4-notes form e.g. like a with 7nth or with 6th, and in the current octave or in the next. Then start the melody at a note of the chord and end it again at a note of a chord in this or the next octave. For example, we may compose the melody from 3-notes micro-themes, the first and last inside the chords and the middle possible outside the chords. Since the chord has 4-notes and the scale  7 notes the passing or transient notes are only 3, less than the 4 of the chord, therefore, any such melodic theme fits harmonically to this chord.

Here is an example :

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

But also this can be elaborated to a double chord triad method. In other words, we may use two triads of two chords the one is the underlying e.g. X and the second Y has one or two common notes with X7 (or Xmaj7 or X6) and we alternate the two triads as successive notes of a melody. The result is a sequence of notes that more than 50% or 66% notes belonging to the chord X7 or X6. Thus the method of long-short parts melodic and rhythmic micro-themes of post 77 applies.



Here is an example  https://www.youtube.com/watch?v=ZDuegoLXaR0&t=241s

The single accompanying chord can be a power chord X5, e.g. C5=(c, g) that the root and dominant only of a diatonic scale. Then As Y can be any chord of the diatonic scale except the minor chord on the 2nd note (Dm in C major diatonic scale) And in general the melodic improvisation can be the arpeggios of a chord progression! 

Here is an example 

https://www.youtube.com/watch?v=VtVFWOBH2tI

More ideas here

https://www.youtube.com/watch?v=qKVp44tAZQ0&pbjreload=10


Here are one chord backtracks for practice.

https://www.youtube.com/watch?v=NasVe9Q04_M

https://www.youtube.com/watch?v=e3ciXPKqq0w&t=632s 

https://www.youtube.com/watch?v=xMNcv-i7Ado

https://www.youtube.com/watch?v=2NJOidKkzHo

etc.

140. COMPLEMENTARY THEMES IMPROVISATION. Melody driven improvisation within a scale.

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COMPLEMENTARY THEMES IMPROVISATION. Melody driven improvisation within a scale.

This method of improvisation is melody-driven within a scale or composite scale (like Bebop Scales of post 139). Its main idea is the statistical action-reaction principle or principle of complementarity of melodic themes as a kind of dialogue question-answer or proposal-answer   Its rules are the next

1) The melody is within a scale S (which can be also composite of  8-notes , 9-notes or more) E.g. The Bobop dominant 8-notes scale of post 139 or 8-notes maximal harmonic of post 117, C D E F F# G A B C`

and is subdivided into pairs of melodic themes A-B so that A and B are in some sense harmonic or melodic complementary. The themes A and B may be subdivided into 1 or 2 sub-themes A1 A2 or B1 B2.

2) HARMONIC COMPLEMENTARITY:  The total theme A+B covers as much as possible of the scale given the length of A and B. E.g. the A is mainly over even (or odd) notes of the scale and B is mainly over odd (or even) notes of the scale. Usually, the endnotes of A and B are either a) identical b) differ by an interval of 5th/4th c) differ by an octave. From this point of view we may perceive the scale as double layered: 1) A scale by intervals of fifths or 4ths 2) The full scale. Then the simplicial sub-melody is only on the first coarse sub-scale scale while the full melody is on the fine full scale. The structure of these two layers 1) 2)  reflects the structure of the sequence of pairs (A, B) of complementary melodic themes.

3) MELODIC COMPLEMENTARITY: The themes A and B have complementary dynamics as Dolphin Words (see post 114) E.g. A is ascending and B is descending or A is expansive and B is contracting etc.

4) The rhythm is rather fast e.g. 110-120 beats/min

5) The chords that accompany may follow the melody and are chords of the scale. If we want as few chords as possible and the scale is e.g. diatonic, then it could be only 2 or 3 chords e.g. I ii, V . But it can be in general a sequence of chords of the scale. If e.g. the improvisation is on a Celtic levered harp them we may alternate chords with pairs of such melodic themes A+B so that each chord has mediant the last bote of each theme.


The above method can be combined with the melodic improvisation within the harmony of a chord each time, as in post 141.

When spending time within the harmony of a chord the best idea is to have the chord in 4-notes form e.g. like a with 7nth or with 6th, and in the current octave or in the next. Then start the melody at a note of the chord and end it again at a note of a chord in this or the next octave. For example we may compose the melody from 3-notes micro-themes, the first and last inside the  chords and the middle possible outside the chords. Since the chord has 4-notes and the scale  7 notes the passing or transient notes are only 3, less than the 4 of the chord, therefore, any such melodic theme fits harmonically to this chord.

Here is an example :

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

139. SCALES THAT ARE UNION OF OTHER KNOWN SCALES. BEBOP 8-NOTES SCALES, 9-NOTES EASTERN AND WESTERN CHROMATIC SCALES

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We describe scales that are the union of other known scales. They are somehow 2-layered or n-layered scales.

1) Examples are the Bobop 8-notes scales in Jazz, that try to make 8-notes scales that can play simultaneously two other known scales. E.g. Diantonic+melodic minor, or Diatonic+harmonic minor or Diatonic+harmonic double minor, or melodic minor+harmonic minor  or Diatonic+blues 6-notes=8-notes Bebop dominant=8-notes maximal harmonic scale of post 117  etc

From Wikipedia: https://en.wikipedia.org/wiki/Bebop_scale

The bebop scales are frequently used in jazz improvisation and are derived from the modes of the major scale, the melodic minor scale, and the harmonic minor scale. According to Corey Christiansen, "David Baker, one of the world's finest jazz educators, named these scales the 'bebop scales' because they were used so often by jazz artists from the Bebop Era. These artists include Charlie Christian, Charlie Parker, Lester Young, and Dizzy Gillespie, to name a few."^[1]

There are five types of frequently used bebop scales:

1. the bebop dominant scale
2. the bebop Dorian scale
3. the bebop major scale
4. the bebop melodic minor scale
5. the bebop harmonic minor scale

Each of these scales has an extra chromatic passing tone. In general, bebop scales consist of traditional scales with an added passing tone placed such that when the scale is begun on a chord tone and on the downbeat, all other chord tones will also fall on downbeats, with the remaining tones in the scale occurring on the upbeat (given that the scale is played ascending or descending; i.e., no intervallic skips are played).

As such, many heptatonic scales may be modified by the addition of an eighth passing tone to accomplish this same effect; however, the modifier "bebop" is reserved to indicate those scales most frequently used—and popularized—during the bebop era (and/or by modern practitioners of the bebop genre).

Bebop dominant scale[edit]

The bebop dominant scale is derived from the Mixolydian mode and has a chromatic passing tone between the 7th and the root.

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It has all the notes in both the major scale and the Mixolydian scale of the same root. This scale is often used over dominant seventh chords and all extended dominant chords,^[2] and the II-V chord progressions. According to Michael Miller, "[w]hen someone says they're playing 'the bebop scale,' this is the one they're talking about." The interval structure in semitones is 

2-2-1-2-2-1-1-1

Bebop Dorian scale[edit]

The bebop Dorian scale (also known as the bebop minor scale^[3][4]) is derived from the Dorian mode and has a chromatic passing tone between the minor 3rd and the perfect 4th.

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It has all the notes in both the Dorian scale and the Mixolydian scale of the same root. It is the 5th mode of the bebop dominant scale.

A second form of the bebop Dorian scale features a major seventh bebop note between the dominant seventh and the tonic.

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The second style, featuring the major seventh, is generally used by guitar players for its accessibility when applied to traditional minor scale shapes (that is, it is simply easier for guitarists to play). However, many players and resources adhere to the traditional spelling of the scale.

Bebop major scale[edit]

The bebop major scale is derived from the Ionian mode (major scale) and has a chromatic passing tone between the 5th and 6th notes.

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This scale is often used over major sixth chords and major seventh chords.

Bebop melodic minor scale[edit]

The bebop melodic minor scale is derived from the ascending form of the melodic minor scale (jazz minor scale) and has a chromatic passing tone between the 5th and 6th notes.

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It has all the notes of both the ascending form of the melodic minor scale and the harmonic minor scale of the same root. This scale is often used over minor sixth chords.

(Melodic minor=6,7,1,2,3,4#,5#,6'=(in semitones) (2-1)-(2-2)-(2-2-1))

These scales are listed in David N. Baker's books on bebop. They are also included, with the exception of the Dorian bebop scale, in Roni Ben-Hur's book Talk Jazz: A Comprehensive Collection of Bebop Studies, which is derived from the work of Barry Harris. Ben-Hur further elaborates on the concept of placing additional chromatic passing tones between other notes in the scales.

Bebop harmonic minor scale[edit]

The bebop harmonic minor scale (or bebop natural minor scale, as listed in Mark Levine's The Drop 2 Book) is derived from the harmonic minor scale and has a chromatic passing tone (an additional ♭7) between the 6th and the 7th notes.

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It contains all of the notes of both the harmonic minor scale and the natural minor scale (Aeolian mode) of the same root. It can be used on all three chords of a minor II-V-I progression. It is a mode of the bebop major scale: for instance, the C bebop harmonic minor scale has the same pitches as the E♭ bebop major scale.

2) We introduce the Eastern chromatic 9-notes triple scale which is the union of a  harmonic minor a harmonic double minor with the same root and their relative diatonic major scale (or natural aeolian mode minor with the same root). Its internal structure is    2-1-2-1-1-1-2-1-1 (E.g. D-E-F-G-G#-A-Bb-C-C#-D)

I have constructed (handmade) some quenas, quenillas and quenachos (direct blowing winds) with this 9-notes scale (3 minor scales together, natural minor, harmonic minor, and harmonic double minor) and I call them, the Byzantine chromatic minors flutes. They can easily be modified from a harmonic double minor flute by adding two sharp-2nd-holes at the 3rd and 6th hole. They have  7 front holes in two groups two lower one semitone apart, 4 upper again with one semitone apart between them,and a double thumb with one semitone away the two holes in the thump.  (It can be played though from an Ionian mode diatonic flute e,g, C4 major, by adding sharps-2nd holes  at the 2nd hole, D4#, and 5th hole G4#) They are used also in Gypsy jazz, folk Romanian melodies and Greek folk melodies of Rebetika music.

Some romanian caval flutes have the 9-notes scale 2-1-1-1-1-1-1-1-3.


3) We introduce the Western chromatic 9-notes triple scale which is the union of 3 major diatonic scales consecutive in the circle of 4ths E.g. G-C-F , or C-F-Bb etc It coincides with the maximal harmonic 9-notes scale of the post 117. Its interval structure is 2-2-1-1-1-2-1-1-1. E.g, C-D-E-F-F#-G-A-Bb-B-C We may notice that it can also be obtained from the standard pentatonic scale 2-2-3-2-3 by analyzing the two 3 into semitones 1-1-1. It can be played from an Ionian mode diatonic flute e,g, at C4 major, by adding sharps-2nd holes at the 4th hole, F4#, and 6th hole A#=Bb.
I have a bass wind with clarinet mouthpiece from Armenia with this 9-notes scale.

4) The next 10 notes scale 2-1-1-1-1-1-2-1-1-1, which can be made on a flute with 7 front holes a double thumphole is also invariant in playing by the 3rd overtone, In other words the 3rd overtone will give notes on the same holes again inside the scale. 

138. IMPROVISATION FOR MEDITATION WITH A MELODY IN A SCALE ACCOMPANIED WITH THE ROOT OR SINGLE NOTE OF THE SCALE

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This type of improvisation is of the simplest and beautiful ones. Practically no chord accompanying of the melody is used. The only simple harmony is the continuous sounding of a single note which is usually the root of the scale. For this single not accompanying is used usually a monochord string instrument, but it could be used a guitar and other instrument making a conscious trill or repetitive hitting of one note.

Here are examples of it by Shastro with bansuri flute

 https://www.youtube.com/watch?v=i7YsFn22F1g

https://www.youtube.com/watch?v=mi2WtNfmfJI&list=PLV1q2ZPK3-lCbyLxCrLC3v8HmBB3B8s8o

https://www.youtube.com/watch?v=bjLZujyt-Dw&t=542s
etc

The characteristics of this type of improvisation are:

1) The monotone continuous background sounding of the root of a single (diatonic) scale

2) Rather slow e.g. 58 beats/min (like whales or dolphin whistles) suggesting an ocean feeling.

3)  Melodic themes, of this single diatonic scale that are mainly independent and integrate their meaning by themselves and not by the plot and combination of them.

4) The beauty of the total melody is the statistics of its "Dolphin words" (order-topological shapes of melodic themes) 

Extensions of this type of improvisation are if instead of a single note we repeat a single interval of pure 5th or single triad chord.



 If one wants to add more clear harmony inside the scale, he could "walk" all the sequence of chords by 4ths"  iii7->iv7->ii7->V7->I7->IV7->iii7 etc

ONCE ONE HAS MASTERED THSI SIMPLE FORM OF IMPROVISATION HE WILL PROCEED TO THE MORE GENERAL METHOD AS IN POST 296 ABOUT MODES AND LONGITUDINAL CHORDS.

137. 5-notes /4-notes sub-scales improvisation on any 7-notes scale. Pentatonic scales contained in the diatonic , the harmonic minor (1st Byzantine minor) and harmonic double minor (2nd Byzantine minor) 7-notes scales.

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One of the most beautiful melodies improvisations is to go up and down in a 7-notes scale but only with 5 steps (5-notes sub-scales) or 4-steps (4-notes subscales or chords). We do not need to go up and down with the same 5-notes/4-notes  sub-scale, but we need to go up or down from root to higher or lower octave next root,  with only 5-steps or 4-steps (creating thus a 5-notes/4-notes  subscale).  The reason, of course, is that in this way we increase the percentage of intervals of 3rds and even we might make them more than intervals of 2nds in the melody, thus we increase the harmony in the melody. Beautiful melodies are created especially if the underlying 7-notes scale is the harmonic double minor (2nd Byzantine minor) scale.

In a 7-notes scale flute, this is done by keeping 2-times or 3-times during ascending or descending the scale, two fingers as if tight together. We change each time which of these fingers would be.

We show in this post that the well known Japanese pentatonic scales like Akebono, Insen etc of Koto music and many more unknown but beautiful pentatonic scales are contained in the Harmonic minor (1st Byzantine minor) and harmonic double minor (2nd Byzantine minor, or Gypsy minor or Hungarian minor ) scale.

We list 5 more,  and beautiful, 5-notes scales of the 7-notes harmonic double minor scale