The western major and minor scales (they are the same scale but different modes or cyclic permutations), historically is known also as the Egyptian /Mongolian scale)
The 1st mode of the pentatonic scale is the major mode 2-2-3-2-3
The Egyptian mode of the pentatonic scale (2 3 2 3 2 ) which is the 2nd mode of the pemtatonic scale, the Mongolian or standard 1st or major mode (2 2 3 2 3) , The American Indian Pentatonic scale and the minor Pentatonic (3 2 2 3 2) which is the 5th mode of the pentatonic scale and it exists in the Shakuhachi flutes and Native American flutes are different cyclic permutations or modes of the same scale. There is also a northern American Indian scale (3 2 2 2 3) which is not a mode of the standard pentatonic scale, but a permutation of its intervals.
It seems nevertheless that the Indian music as well as the folk Irish music in the Celtic harp use often also the next mode of the pentatonic 2-3-2-2-3 E.g. in C major scale it would be C-D-F-G-A-C, (because this is easy to tune by levers in a C major scale tuned Celtic harp). We might call it Celtic mode of the pentatonic.
Finally there is also the next mode of the pentatonic : 3-2-3-2-2 , which It does not happen to know if it has a name, but it could be called 2nd minor mode of the pentatonic as it starts with the 3 semitones as the minor mode
The minor mode of the pentatonic can be obtained by starting the scale at the 5th step
Conversely to obtain the major mode of the pentatonic we must start the scale at the 2nd step.
E.g. The C major pentatonic C-D-E-G-A-C has as minor mode pentatonic the relative scale
A-C-D-E-G
The Egyptian mode of the pentatonic is if we start the major mode pentatonic scale at the 2nd step. E.g. from the C-D-E-G-A-C we get the D-E-G-A-C-D. And from the Egyptian mode to obtain the major mode we must start from the 5th step.
The Celtic mode of the pentatonic is if we start the major mode of the pentatonic at the 4th step
E.g. from the C-D-E-G-A-C we get the G-A-C-D-E-G. While from the Celtic mode of the pentatonic to obtain the major mode we must start from the 3rd step.
Finally the 2nd minor mode of the pentatonic can be obtained from the major mode by starting at the 3rd step. E.g. from the C-D-E-G-A-C we get the E-G-A-C-D-E. Conversely to obtain the major mode of the pentatonic from the 2nd minor mode we must start at the 4th step.
A c major pentatonic scale can be considered also as the C major chord with 6th and 2nd notes
Again if we include only minor major and R5 chords the chords of the minor pentatonic starting from C would be
Cm, D#, F5, A#5
A minor pentatonic
B minor pentatonic
D minor pentatonic
And the same patterns are for the minor pentatonic as it is a cyclic permutation (mode) of the major pentatonic. Among them the pattern 4 seems attractive due to its simplicity
BUT it is interesting to try a non-cyclic permutation of the western pentatonic scale like
2-2-2-3-3 !! This is called dominant pentatonic=2-2-3-3-2
E.G. C-D-E-F#-A-C
It is also called Northern America Indian Scale
http://www.flutopedia.com/scale_Northern.htm
We may try to find all 5-notes scales containing semitones, tones and 3-tones.
It seems that there are exist only these two!
1) Western/Mongolic pentatonic 2-2-3-2-3 (self-inverse)
2) Dominant western pentatonic 2-2-2-3-3 (self-inverse)
Notice also that an extrapolation of the western pentatonic are the 7-notes and 8-notes scales that contain twice the tetra-chord 1-3-1, 1-3-1 separately
2-(1-1)-3-(1-1)-3 (Romani or Harmonic double minor )
(1-1)-(1-1)-3-(1-1)-3
This also shows a way of chord progressions, where one starts with the diatonic scale, 2-2-1-2-2-2-1, then interpolates (simplifies) to the pentatonic 2-2-3-2-3 then extrapolates to the harmonic double minor 2-1-1-3-1-1-3 and then backwards again.
We may make a classification also of 4-notes scales made from intervals of semitone 1, tone 2, 3-semitones 3 and 2-tones 4. Such 4-scales are essentially chords arpeggios of 4-notes chords (see post 28) There are 7 of them
1) 4-3-3-2
2) 4-3-4-1
3) 3-4-3-2
4) 3-3-3-3
5) 3-3-4-2
6) 3-4-4-1
7) 4-4-3-1
In addition if in these arpeggios of the 4-notes chords, by doubling the lowest note one octave higher make 5-notes pentatonic scales. And if the intervals of 4 are extrapolated to 2-2 or 1-3, 3-1, and intervals of 3 to 1-2 , 2-1, then are shaped 6-notes scales,in soloing.
A celebrated example of 6-notes scale derived from the major pentatonic scale C; D; E; G; A; C; (interval structure 2-2-3-2-3 )is the
MAJOR BLUES SCALE (ALSO CALLED COUNTRY SCALE) C; D; Eb;E; G; A; C with interval structure 2-1-1-3-2-3.
The major blues scale e.g. D major Blues scale might be supposed to be used for improvisations of 12-bars blues on the D major scale, as it can also be also derived from the major D pentatonic by adding a blue note 3b which will make it 6-notes scale. E.g. the blues major D scale D, E, F, Gb ,A, B , D, whould play over the chords Dmajor D-F#-A, (D-Gb-A), A major A-C#-E, or A major with 6th A-C#-E-Gb and G major G-B-D. Obviously some notes would creare a dissonance, but it may be considered part of the chromaticity of the Blues major scale improvisation. Similarly the D major blues could be used to improvise over the C major and G major 12-bars blues.
Notice that the 3-notes 2-1-1 in the major blues scale exist also in the double minor scale or Arabic scale. Also notice that the blue note here the D#=Eb is also the 2nd "blue" note of the double harmonic A minor scale which has 2 blue notes the d# =3b=2# and the g#=5# . This suggest also the 7-notes scale C D# E F G A B C with interval structure 3-1-1-2-2-2-1 which is nothing else than the Neapolitan scale with harmonic personality 1M 2#m 3m 4M 5M 6m 7M 1M!
There are two other ways to extend the major blues scale 2-1-1-3-2-3 to a 7-notes scale and come from breaking the 3nd 3 to 2-1 or 1-2, giving
2-1-1-3-2-1-2 or 2-1-1-3-2-2-1 . Both sound a bit softer than the Byzantine parachromatic (see post 235 ) and have been classified in post 21. It can be conceived as combination of 3 notes of the 7-notes melodic double minor scale with interval structure (2-1-1-2-2-2-2) , with the major pentatonic scale to give the 6-notes 2-1-1-3-2-3 ). Other refinement of the pentatonic scale to a 6-tone scale is the next: 2-2-3-1-1-3 ! E.g.
C-D-E-G-G#-A-C This scale like the standard major blue scale is a minimal chromatic variation of the pentatonic scale.It can be called DOUBLE MINOR BLUES SCALE
On the other hand if we add to the major pentatonic scale C D E G A C the 1st blue note of the harmonic minor that is the g#, it becomes the next 6-notes scale
C D E G G# A C with interval structure 2-2-3-1-1-3 .
If on the other hand we add the G#, but substitute the G with F it becomes the
C D E F G# A C with interval structure 2-2-1-3-1-3 which is an Erik Satie-like scale as it is a slight variation of the Erik Satie 6-notes scale (see also post 21, the Erik Satie scale has structure 2-1-3-1-2-3 or e.g. D E F G# A B D )
Similarly, the MINOR BLUES SCALE is derived from the minor pentatonic scale
C; D#/Eb; F; G; A#/Bb; C;,(interval structure 3-2-2-3-2 ) to give the 6-notes scale C; Eb; F; F# G; Bb; C; with interval structure 3-2-1-1-3-2, which is cyclic permutation of the major blue scale. (notice that the 3-notes 2-1-1 exist also in the double minor scale or Arabic scale. That is why it can be conceived as combination of 3 notes of the 7-notes melodic double minor scale with interval structure (2-1-1-2-2-2-2) , with the minor pentatonic scale to give the the 6-notes 3-2-1-1-3-2).`
We may compare these 6-tone scales with the raised Celtic minor scale
2-3-2-2-1-2, which is used in the hang drums. e.g. C-D-F-G-A-Bb-C
It is a mode of the maximal harmonic 6-notes scale (see post 117)
Here is a nice video about soul and blue scales
https://www.youtube.com/watch?v=mjttaiOq-8Q
Here is more about the C minor blue scale
In fact, a blue arpeggio of a 7nth chord with the interval structure
3-1-3-4-1 (called here blue pentatonic scale of a chord)
may be considered a pentatonic scale corresponding exclusively to that chord!
https://www.youtube.com/watch?v=y-gV5RGJbLo
Other such derived 6-notes scales of blue arpeggios over 2 chords of the triple min-maj-min chord is the 3-1-2-1-3-2
And from blue arpeggios over 2 chords of the triple maj-min-maj chord is the 3-1-3-1-3-1
Still another interesting 6-notes scale which has less minor chords and is an alternative extension of the major pentatonic which could be called half-pentatonic is this
2-1-2-3-2-2 (half diatonic +half pentatonic)
Also still alternative 7-notes extension of the pentatonic and the major Blue too, is the
1-1-1-1-3-2-3 (Chromatic+pentatonic, which is the no 13, 7-notes scale of post 52)
Or the 7-notes extension of the major blue
2-1-1-3-1-1-3 (which is the no 4 7-notes ,inverse Persian scale or Purvi Theta scale of post 54)
Or classify all 4-notes scales that contain steps by 2,3, 5 semitones, where again cyclic permutations and inverses do not count as different. There are only two of them!
1) 3-2-5-2 e.g. B-D-E-A-B
which is also a chord arpeggio of Asus2sus4 or E7sus4 or D6add9(no 3rd)
2) 3-5-2-2 e.g. B-D-G-A-B
which is also a chord arpeggio of Bm7#5 or Gadd9
Such scales as the two above , sometimes are used by Bobby McFerrin
See e.g. https://www.youtube.com/watch?v=BmXsA-siNvo
It is easy to realize that both are interpolations of the diatonic scale
3-2-5-2 --> (1-2)-2-(1-2-2)-2
3-5-2-2 --> (1-2)-(2-1-2)-2-2
In general, any 4-note chord, by doubling the lowest note one octave higher makes 5-notes pentatonic scale. E.g. the chord R7b5 makes the 4-notes scale (arpeggio)
4-2-4-2 .
We may also try to find all 6-notes scales containing 3 3-semitones. There seem to be 4 of them
1) 3-3-3-1-1-1 (self-inverse)
2) 3-3-1-3-1-1 and its inverse
3) 1-1-3-1-3-3
4) 3-1-3-1-3-1 (self-inverse)
Or compare them with other 4-notes scales like 3-3-3-3 and
6-tonic scales can be derived from the Harmonic minor with the known interval structure
2-2-1-3-1-2-1
the
2-2-1-3-1-3 which is by adding to the major chord the 2nd, the 4th, the 5# and the 6th
or also
2-3-3-1-3.
Pentatonic scales can be derived also from the harmonic minor with the known interval structure 2-2-1-3-1-2-1
Then we may derive the two pentatonic scales
4-1-3-1-3
or the
2-2-4-1-3
From which we may derive the next two 4-notes scales
2-2-4-4
and
5-3-1-3
Or the Chinese-Japanese 5-notes scale that have 2-tones steps , in other words interval structure
Interval from the root : 1, 3, 4#, 5, 7
Intervals in steps: 4 - 2 - 1 - 4 - 1 (the tetra-chord 1-4-1 is used instead of the oriental
1-3-1) It is called also the AKEBONO SCALE (some say that it is also the indian scale Raga Katyayani ) (Usually as A B C E F A) It can be obtained e.g. by the major pentatonic scale C D E G A C by making flat the 3rd E, and the 5th A (or 6th A in the diatonic scale). Some call it the double minor pentatonic.
(listen to it here https://www.youtube.com/watch?v=gsBbWXD1NNI or
here https://www.youtube.com/watch?v=aSQg-ff5exE
https://www.youtube.com/watch?v=GcSDv7Bfabw
)
Formula: Quadra-step, Whole, Half, Quadra-step, Half
See e.g.
http://www.pianoscales.org/chinese.html
C: C, E, F#, G, B, C (we notice that it is a sub-scale of the F-major 7-notes scale)
For example if we take the mode of the diatonic scale starting from F
F G A B C D E F , a Chinese scale will be shaped by keeping the semitones B C,, E, F, but eliminating the notes G, D , Thus it will be
F, A, B, C, E,
This scale in an inverse mode can also be obtained from the
C double harmonic minor (2nd minor Byzantine) scale
C Db E F G Ab B C by eliminating the notes with flats, that is the Db and Ab obtainingt hsu the pentatonic scale
C E F G B C with interval structure 4-1-2-4-1
In the Shakuhachi flutes in D4 pentatonic minor or D4 Native American flute this scale can be payed by substituting the 1st and 4th hole with its 2/3 open version
An inverse mode of the AKEBONO scale called also Pelog scale
In other words both the western and Chinese pentatonic scales can be shaped by eliminating two notes (interpolating) of the diatonic 7-notes scale
We notice that there is a complementarity with the western pentatonic , in the sense that the western pentatonic skips the 1-semitone intervals of the 7-note diatonic while the chinese , keeps them and skips 2 in between notes.
The 1st mode of the pentatonic scale is the major mode 2-2-3-2-3
The Egyptian mode of the pentatonic scale (2 3 2 3 2 ) which is the 2nd mode of the pemtatonic scale, the Mongolian or standard 1st or major mode (2 2 3 2 3) , The American Indian Pentatonic scale and the minor Pentatonic (3 2 2 3 2) which is the 5th mode of the pentatonic scale and it exists in the Shakuhachi flutes and Native American flutes are different cyclic permutations or modes of the same scale. There is also a northern American Indian scale (3 2 2 2 3) which is not a mode of the standard pentatonic scale, but a permutation of its intervals.
It seems nevertheless that the Indian music as well as the folk Irish music in the Celtic harp use often also the next mode of the pentatonic 2-3-2-2-3 E.g. in C major scale it would be C-D-F-G-A-C, (because this is easy to tune by levers in a C major scale tuned Celtic harp). We might call it Celtic mode of the pentatonic.
Finally there is also the next mode of the pentatonic : 3-2-3-2-2 , which It does not happen to know if it has a name, but it could be called 2nd minor mode of the pentatonic as it starts with the 3 semitones as the minor mode
The minor mode of the pentatonic can be obtained by starting the scale at the 5th step
Conversely to obtain the major mode of the pentatonic we must start the scale at the 2nd step.
E.g. The C major pentatonic C-D-E-G-A-C has as minor mode pentatonic the relative scale
A-C-D-E-G
The Egyptian mode of the pentatonic is if we start the major mode pentatonic scale at the 2nd step. E.g. from the C-D-E-G-A-C we get the D-E-G-A-C-D. And from the Egyptian mode to obtain the major mode we must start from the 5th step.
The Celtic mode of the pentatonic is if we start the major mode of the pentatonic at the 4th step
E.g. from the C-D-E-G-A-C we get the G-A-C-D-E-G. While from the Celtic mode of the pentatonic to obtain the major mode we must start from the 3rd step.
Finally the 2nd minor mode of the pentatonic can be obtained from the major mode by starting at the 3rd step. E.g. from the C-D-E-G-A-C we get the E-G-A-C-D-E. Conversely to obtain the major mode of the pentatonic from the 2nd minor mode we must start at the 4th step.
The way to get the standard (Mongolian) major mode of the pentatonic scale 2-2-3-2-3 from a 7-notes diatonic scale in major mode is to eliminate the 2nd note of the 1st semitone interval and the 1st note of the 2nd semitone interval .
The way to get the Celtic mode of the pentatonic scale 2-3-2-2-3 from a 7-notes diatonic scale in major mode is to eliminate the 1st notes or the 2nd notes of the two semitone intervals.
The way to get the minor mode of the pentatonic scale 3-2-2-3-2 from a 7-notes diatonic scale in major mode is to eliminate the 1st notes of the two semitone intervals and shift one step forward.
A c major pentatonic scale can be considered also as the C major chord with 6th and 2nd notes
C major pentatonic
The pentatonic scale is supposed to be obtained by the first 9 harmonics when reduced to the first octave with frequencies based on a fundamental, given by the harmonic order (numerator) and power of 2 which is the reduction in the first octave
C, D, E, G, A, C'
1, 9/8 , 5/4 , 3/2 , 7/4.
Similarly the 7-notes diatonic scale
C, D, E, G, A, C'
1, 9/8 , 5/4 , 3/2 , 7/4.
Similarly the 7-notes diatonic scale
C---1 harmonic
D---9
E---5
F---11
G---3
A---7
B---15
C---2
| Notes of this scale: |
| C; D; E; G; A; C; |
| Interval structure of this scale: |
| 2-2-3-2-3 |
| Chords that fit in this scale: |
| Normal Triads: we may start with the G power chord=(G,D,G) and also the C Am Other Triads: Csus2 Dsus4 Dsus2 Gsus4 Gsus2 Asus4 4 Notes Chords: C6 D7sus4 D7sus2 Am7 A7sus4 C\E C\G |
We notice that the minor pentatonic is actually a mode of the major pentatonic, that is a cyclic permutation of it.
Also the Egyptian scale is a mode of this scale with semitone patterns
2-3-2-3-2 (e.g. D, E, G, A, C, D)
If we include only minor major and R5 chords the chords of the pentatonic would be
C, D5, G5, Am
Here is a video of the use of pentatonic scale as soloing around any chord!
(actually, the pentatonic scale can be considered the arpeggio of the chord with 2nd and 6th notes too or 6th and added 9th C6add9 )
https://www.youtube.com/watch?v=MVSzSVYqjbU
Also the Egyptian scale is a mode of this scale with semitone patterns
2-3-2-3-2 (e.g. D, E, G, A, C, D)
If we include only minor major and R5 chords the chords of the pentatonic would be
C, D5, G5, Am
Here is a video of the use of pentatonic scale as soloing around any chord!
(actually, the pentatonic scale can be considered the arpeggio of the chord with 2nd and 6th notes too or 6th and added 9th C6add9 )
https://www.youtube.com/watch?v=MVSzSVYqjbU
C minor pentatonic
| Notes of this scale: |
| C; D#/Eb; F; G; A#/Bb; C; |
| Interval structure of this scale: |
| 3-2-2-3-2 |
| Chords that fit in this scale: |
| Normal Triads: Cm D# Other Triads: Csus4 D#sus2 Fsus4 Fsus2 A#sus4 A#sus2 4 Notes Chords: Cm7 C7sus4 D#6 F7sus4 F7sus2 Csus4\F Csus4\G Cm\D# Cm\G Cm\Eb |
Again if we include only minor major and R5 chords the chords of the minor pentatonic starting from C would be
Cm, D#, F5, A#5
Some standard ways to play the pentatonic scale , where the rule here is 2 notes per string, are the next :
A minor pentatonic
| Notes of this scale: |
| A C D E G |
| Interval structure of this scale: |
| (W+h) W W (W+h) W (W: Whole tone, h: half tone) |
| Scale structure: |
| 1 b3 4 5 b7 |
| Chords that fit in this scale: |
| Normal Triads: C Am Other Triads: Csus2 Dsus4 Dsus2 Gsus4 Gsus2 Asus4 4 Notes Chords: C6 D7sus4 D7sus2 Am7 A7sus4 C\E C\G 5 and 6 Note Chords: C6/9 D9sus4 D9sus2 Am11 C6\G C6/9\E C6/9\G |
| Scales Equivalent to A minor pentatonic : |
| C major pentatonic; |
| Scales wich notes are within A minor pentatonic: |
B minor pentatonic
| Notes of this scale: |
| B D E F# A |
| Interval structure of this scale: |
| (W+h) W W (W+h) W (W: Whole tone, h: half tone) |
| Scale structure: |
| 1 b3 4 5 b7 |
| Chords that fit in this scale: |
| Normal Triads: D Bm Other Triads: Dsus2 Esus4 Esus2 Asus4 Asus2 Bsus4 4 Notes Chords: D6 E7sus4 E7sus2 Bm7 B7sus4 5 and 6 Note Chords: D6/9 E9sus4 E9sus2 Bm11 |
|
D minor pentatonic
| Notes of this scale: |
| D F G A C |
| Interval structure of this scale: |
| (W+h) W W (W+h) W (W: Whole tone, h: half tone) |
| Scale structure: |
| 1 b3 4 5 b7 |
| Chords that fit in this scale: |
| Normal Triads: Dm F Other Triads: Csus4 Csus2 Dsus4 Fsus2 Gsus4 Gsus2 4 Notes Chords: Dm7 D7sus4 F6 G7sus4 G7sus2 Csus4\F Csus4\G 5 and 6 Note Chords: Dm11 F6/9 G9sus4 G9sus2 |
| Scales Equivalent to D minor pentatonic : |
| F major pentatonic; |
And the same patterns are for the minor pentatonic as it is a cyclic permutation (mode) of the major pentatonic. Among them the pattern 4 seems attractive due to its simplicity
BUT it is interesting to try a non-cyclic permutation of the western pentatonic scale like
2-2-2-3-3 !! This is called dominant pentatonic=2-2-3-3-2
E.G. C-D-E-F#-A-C
It is also called Northern America Indian Scale
http://www.flutopedia.com/scale_Northern.htm
We may try to find all 5-notes scales containing semitones, tones and 3-tones.
It seems that there are exist only these two!
1) Western/Mongolic pentatonic 2-2-3-2-3 (self-inverse)
2) Dominant western pentatonic 2-2-2-3-3 (self-inverse)
Notice also that an extrapolation of the western pentatonic are the 7-notes and 8-notes scales that contain twice the tetra-chord 1-3-1, 1-3-1 separately
2-(1-1)-3-(1-1)-3 (Romani or Harmonic double minor )
(1-1)-(1-1)-3-(1-1)-3
This also shows a way of chord progressions, where one starts with the diatonic scale, 2-2-1-2-2-2-1, then interpolates (simplifies) to the pentatonic 2-2-3-2-3 then extrapolates to the harmonic double minor 2-1-1-3-1-1-3 and then backwards again.
We may make a classification also of 4-notes scales made from intervals of semitone 1, tone 2, 3-semitones 3 and 2-tones 4. Such 4-scales are essentially chords arpeggios of 4-notes chords (see post 28) There are 7 of them
1) 4-3-3-2
2) 4-3-4-1
3) 3-4-3-2
4) 3-3-3-3
5) 3-3-4-2
6) 3-4-4-1
7) 4-4-3-1
In addition if in these arpeggios of the 4-notes chords, by doubling the lowest note one octave higher make 5-notes pentatonic scales. And if the intervals of 4 are extrapolated to 2-2 or 1-3, 3-1, and intervals of 3 to 1-2 , 2-1, then are shaped 6-notes scales,in soloing.
A celebrated example of 6-notes scale derived from the major pentatonic scale C; D; E; G; A; C; (interval structure 2-2-3-2-3 )is the
MAJOR BLUES SCALE (ALSO CALLED COUNTRY SCALE) C; D; Eb;E; G; A; C with interval structure 2-1-1-3-2-3.
The major blues scale e.g. D major Blues scale might be supposed to be used for improvisations of 12-bars blues on the D major scale, as it can also be also derived from the major D pentatonic by adding a blue note 3b which will make it 6-notes scale. E.g. the blues major D scale D, E, F, Gb ,A, B , D, whould play over the chords Dmajor D-F#-A, (D-Gb-A), A major A-C#-E, or A major with 6th A-C#-E-Gb and G major G-B-D. Obviously some notes would creare a dissonance, but it may be considered part of the chromaticity of the Blues major scale improvisation. Similarly the D major blues could be used to improvise over the C major and G major 12-bars blues.
Notice that the 3-notes 2-1-1 in the major blues scale exist also in the double minor scale or Arabic scale. Also notice that the blue note here the D#=Eb is also the 2nd "blue" note of the double harmonic A minor scale which has 2 blue notes the d# =3b=2# and the g#=5# . This suggest also the 7-notes scale C D# E F G A B C with interval structure 3-1-1-2-2-2-1 which is nothing else than the Neapolitan scale with harmonic personality 1M 2#m 3m 4M 5M 6m 7M 1M!
Furthermore we may notice that the 1-1-3 tetrachord of the blues scale is the chromatic tetrachord of Ancient Greek music, that exists also in the parachromatic Byzantine scale (see post 235 ) which was played in the Emperor's palace , but not in the church (In the church was played the harmonic minor and double harmonic minor scale).
There are two other ways to extend the major blues scale 2-1-1-3-2-3 to a 7-notes scale and come from breaking the 3nd 3 to 2-1 or 1-2, giving
2-1-1-3-2-1-2 or 2-1-1-3-2-2-1 . Both sound a bit softer than the Byzantine parachromatic (see post 235 ) and have been classified in post 21. It can be conceived as combination of 3 notes of the 7-notes melodic double minor scale with interval structure (2-1-1-2-2-2-2) , with the major pentatonic scale to give the 6-notes 2-1-1-3-2-3 ). Other refinement of the pentatonic scale to a 6-tone scale is the next: 2-2-3-1-1-3 ! E.g.
C-D-E-G-G#-A-C This scale like the standard major blue scale is a minimal chromatic variation of the pentatonic scale.It can be called DOUBLE MINOR BLUES SCALE
On the other hand if we add to the major pentatonic scale C D E G A C the 1st blue note of the harmonic minor that is the g#, it becomes the next 6-notes scale
C D E G G# A C with interval structure 2-2-3-1-1-3 .
If on the other hand we add the G#, but substitute the G with F it becomes the
C D E F G# A C with interval structure 2-2-1-3-1-3 which is an Erik Satie-like scale as it is a slight variation of the Erik Satie 6-notes scale (see also post 21, the Erik Satie scale has structure 2-1-3-1-2-3 or e.g. D E F G# A B D )
Similarly, the MINOR BLUES SCALE is derived from the minor pentatonic scale
C; D#/Eb; F; G; A#/Bb; C;,(interval structure 3-2-2-3-2 ) to give the 6-notes scale C; Eb; F; F# G; Bb; C; with interval structure 3-2-1-1-3-2, which is cyclic permutation of the major blue scale. (notice that the 3-notes 2-1-1 exist also in the double minor scale or Arabic scale. That is why it can be conceived as combination of 3 notes of the 7-notes melodic double minor scale with interval structure (2-1-1-2-2-2-2) , with the minor pentatonic scale to give the the 6-notes 3-2-1-1-3-2).`
We may compare these 6-tone scales with the raised Celtic minor scale
2-3-2-2-1-2, which is used in the hang drums. e.g. C-D-F-G-A-Bb-C
It is a mode of the maximal harmonic 6-notes scale (see post 117)
Here is a nice video about soul and blue scales
https://www.youtube.com/watch?v=mjttaiOq-8Q
Here is more about the C minor blue scale
In fact, a blue arpeggio of a 7nth chord with the interval structure
3-1-3-4-1 (called here blue pentatonic scale of a chord)
may be considered a pentatonic scale corresponding exclusively to that chord!
https://www.youtube.com/watch?v=y-gV5RGJbLo
Other such derived 6-notes scales of blue arpeggios over 2 chords of the triple min-maj-min chord is the 3-1-2-1-3-2
And from blue arpeggios over 2 chords of the triple maj-min-maj chord is the 3-1-3-1-3-1
Musical Scale Info: C minor blues
| Notes of this scale: |
| C; D#/Eb; F; F#/Gb; G; A#/Bb; C; |
| Interval structure of this scale: |
| (W+h) W h h (W+h) W or 3-2-1-1-3-2 |
| Chords that fit in this scale: |
| Normal Triads: Cm Cdim D# D#m Other Triads: Csus4 D#sus2 Fsus4 Fsus2 A#sus4 A#sus2 4 Notes Chords: Cm7 Cm7b5 C7sus4 D#6 D#m6 F7sus4 F7sus2 Csus4\F Csus4\G Cm\D# Cm\G Cm\Eb 5 and 6 Note Chords: Cm11 D#6/9 F9sus4 F9sus2 Cm7\D# C7sus4\G Cm7\Eb |
| Scales Equivalent to C blues : |
| ; |
| Scales whose notes are within C blues: |
| D#/Eb major pentatonic; C minor pentatonic; |
Still another interesting 6-notes scale which has less minor chords and is an alternative extension of the major pentatonic which could be called half-pentatonic is this
2-1-2-3-2-2 (half diatonic +half pentatonic)
Also still alternative 7-notes extension of the pentatonic and the major Blue too, is the
1-1-1-1-3-2-3 (Chromatic+pentatonic, which is the no 13, 7-notes scale of post 52)
Or the 7-notes extension of the major blue
2-1-1-3-1-1-3 (which is the no 4 7-notes ,inverse Persian scale or Purvi Theta scale of post 54)
Or classify all 4-notes scales that contain steps by 2,3, 5 semitones, where again cyclic permutations and inverses do not count as different. There are only two of them!
1) 3-2-5-2 e.g. B-D-E-A-B
which is also a chord arpeggio of Asus2sus4 or E7sus4 or D6add9(no 3rd)
2) 3-5-2-2 e.g. B-D-G-A-B
which is also a chord arpeggio of Bm7#5 or Gadd9
Such scales as the two above , sometimes are used by Bobby McFerrin
See e.g. https://www.youtube.com/watch?v=BmXsA-siNvo
It is easy to realize that both are interpolations of the diatonic scale
3-2-5-2 --> (1-2)-2-(1-2-2)-2
3-5-2-2 --> (1-2)-(2-1-2)-2-2
In general, any 4-note chord, by doubling the lowest note one octave higher makes 5-notes pentatonic scale. E.g. the chord R7b5 makes the 4-notes scale (arpeggio)
4-2-4-2 .
We may also try to find all 6-notes scales containing 3 3-semitones. There seem to be 4 of them
1) 3-3-3-1-1-1 (self-inverse)
2) 3-3-1-3-1-1 and its inverse
3) 1-1-3-1-3-3
4) 3-1-3-1-3-1 (self-inverse)
The next 6-tone scale is an interpolation of the diatonic, and is used in Jazz soloing
1-2-2-2-1-4
1-2-2-2-1-4
Or compare them with other 4-notes scales like 3-3-3-3 and
6-tonic scales can be derived from the Harmonic minor with the known interval structure
2-2-1-3-1-2-1
the
2-2-1-3-1-3 which is by adding to the major chord the 2nd, the 4th, the 5# and the 6th
or also
2-3-3-1-3.
Pentatonic scales can be derived also from the harmonic minor with the known interval structure 2-2-1-3-1-2-1
Then we may derive the two pentatonic scales
4-1-3-1-3
or the
2-2-4-1-3
From which we may derive the next two 4-notes scales
2-2-4-4
and
5-3-1-3
Or the Chinese-Japanese 5-notes scale that have 2-tones steps , in other words interval structure
Interval from the root : 1, 3, 4#, 5, 7
Intervals in steps: 4 - 2 - 1 - 4 - 1 (the tetra-chord 1-4-1 is used instead of the oriental
1-3-1) It is called also the AKEBONO SCALE (some say that it is also the indian scale Raga Katyayani ) (Usually as A B C E F A) It can be obtained e.g. by the major pentatonic scale C D E G A C by making flat the 3rd E, and the 5th A (or 6th A in the diatonic scale). Some call it the double minor pentatonic.
(listen to it here https://www.youtube.com/watch?v=gsBbWXD1NNI or
here https://www.youtube.com/watch?v=aSQg-ff5exE
https://www.youtube.com/watch?v=GcSDv7Bfabw
)
Formula: Quadra-step, Whole, Half, Quadra-step, Half
See e.g.
http://www.pianoscales.org/chinese.html
C: C, E, F#, G, B, C (we notice that it is a sub-scale of the F-major 7-notes scale)
For example if we take the mode of the diatonic scale starting from F
F G A B C D E F , a Chinese scale will be shaped by keeping the semitones B C,, E, F, but eliminating the notes G, D , Thus it will be
F, A, B, C, E,
This scale in an inverse mode can also be obtained from the
C double harmonic minor (2nd minor Byzantine) scale
C Db E F G Ab B C by eliminating the notes with flats, that is the Db and Ab obtainingt hsu the pentatonic scale
C E F G B C with interval structure 4-1-2-4-1
In the Shakuhachi flutes in D4 pentatonic minor or D4 Native American flute this scale can be payed by substituting the 1st and 4th hole with its 2/3 open version
An inverse mode of the AKEBONO scale called also Pelog scale
In other words both the western and Chinese pentatonic scales can be shaped by eliminating two notes (interpolating) of the diatonic 7-notes scale
We notice that there is a complementarity with the western pentatonic , in the sense that the western pentatonic skips the 1-semitone intervals of the 7-note diatonic while the chinese , keeps them and skips 2 in between notes.
`
The inverse order of the Chinese pentatonic is called Pelog scale in other words the
Pelog scale=(1-2-4-1-4)
It is interesting also to try non-cyclic permutations of the Chinese pentatonic scale like
4-2-4-1-1
and the inverse 1-1-4-2-4
There is also the japanese pentatonic scale Insen with interval structure
1-4-2-3-2
All 5-notes scales containing the intervals 1,2,4 are the next (not including their cyclic permutations, that is their modes)
1) 4-1-4-2-1
2) 1-2-4-1-4
3) 4-2-4-1-1
4) 1-1-4-2-4
5) 4-4-1-1-2
6) 2-1-1-4-4
7) 4-4-1-2-1
Here are all 5-notes scales containing 4, 1, 3:
1) 1-3-1-4-3
2) 3-1-3-4-1 (blue pentatonic arpeggio of major 7th chord)
3) 1-3-4-2-2
4) 1-4-3-2-2
5) 3-1-4-2-2
6) 3-4-1-2-2 (this scale is the join arpeggio of two major chhords that are succesive in the wheel by 4ths e.g. G-C, see also post 92)
7) 4-3-1-2-2
8) 4-1-3-2-2
9) 4-1-2-3-2
10) 1-4-2-3-2 (mode of the Japanese Insen scale)
11) 1-3-1-3-4
The next pentatonic does not contain the 4 but the 5 (interval of 4th)
10) 1-3-1-2-5 E.g. (E F G# A B E)
I have found improvisation solos in Gypsy Jazz climbing an octave by the steps of the previous scales (1-1-4-2-4)! (e.g Bossa Dorado song) which is of course an interpolation to 5-notes scale of the Arabic 7-notes scale (1-1-2-2-2-2-2).
In jazz often 5-notes (pentatonic) scales are shaped by extrapolating the 4-notes arpeggios of a 4-notes chords (as those in post 28). E.g. an interval of 3 is extrapolated to 2-1, and an interval of 4 to 2-2 or 3-1.
Or combinations of the tetra-chords 1-3-1 and 1-4-1 like 6-notes scales
1-3-1-4-1-2
The 4-notes sub-scale or tetra-chord
1-1-4
was called in ancient Greece Enharmonio (actually instead of 1 semitone it was only 1/4 of the semitone)
The inverse order of the Chinese pentatonic is called Pelog scale in other words the
Pelog scale=(1-2-4-1-4)
It is interesting also to try non-cyclic permutations of the Chinese pentatonic scale like
4-2-4-1-1
and the inverse 1-1-4-2-4
There is also the japanese pentatonic scale Insen with interval structure
1-4-2-3-2
All 5-notes scales containing the intervals 1,2,4 are the next (not including their cyclic permutations, that is their modes)
1) 4-1-4-2-1
2) 1-2-4-1-4
3) 4-2-4-1-1
4) 1-1-4-2-4
5) 4-4-1-1-2
6) 2-1-1-4-4
7) 4-4-1-2-1
Here are all 5-notes scales containing 4, 1, 3:
1) 1-3-1-4-3
2) 3-1-3-4-1 (blue pentatonic arpeggio of major 7th chord)
3) 1-3-4-2-2
4) 1-4-3-2-2
5) 3-1-4-2-2
6) 3-4-1-2-2 (this scale is the join arpeggio of two major chhords that are succesive in the wheel by 4ths e.g. G-C, see also post 92)
7) 4-3-1-2-2
8) 4-1-3-2-2
9) 4-1-2-3-2
10) 1-4-2-3-2 (mode of the Japanese Insen scale)
11) 1-3-1-3-4
The next pentatonic does not contain the 4 but the 5 (interval of 4th)
10) 1-3-1-2-5 E.g. (E F G# A B E)
I have found improvisation solos in Gypsy Jazz climbing an octave by the steps of the previous scales (1-1-4-2-4)! (e.g Bossa Dorado song) which is of course an interpolation to 5-notes scale of the Arabic 7-notes scale (1-1-2-2-2-2-2).
In jazz often 5-notes (pentatonic) scales are shaped by extrapolating the 4-notes arpeggios of a 4-notes chords (as those in post 28). E.g. an interval of 3 is extrapolated to 2-1, and an interval of 4 to 2-2 or 3-1.
Or combinations of the tetra-chords 1-3-1 and 1-4-1 like 6-notes scales
1-3-1-4-1-2
The 4-notes sub-scale or tetra-chord
1-1-4
was called in ancient Greece Enharmonio (actually instead of 1 semitone it was only 1/4 of the semitone)
