47. The Harmonic or Byzantine or Romani or Hungarian or Ukrainian or Flamenco or Mohammedan minor and double minor scale, (also mode of Arabic Niavent scale)

The Byzantine double minor (or harmonic double minor scale )  scale is 1-3-1-2-1-3-1 in semitones, In other words it is the know oriental folk tetra-chord
1-3-1 doubled and linked in the middle with its repetition with a whole tone. It is also a mode of the Arabic-like scale Niavent in the Greek folk music (Niavent=2-1-3-1-1-3-1 )

Some times as Byzantine scale is mentioned the 7 notes scale, which is also called Harmonic double minor


 1-3 - 1 - 2 - 1 - 3 - 1 

Of course the Byzantine scales were many and were 7-notes but with frequencies not possible to play in our western 12-notes Bach scale.

The chords that fit to  the Byzantine or Romani or Hungarian double minor scale ,( we take here as an example the D Romani or Hungarian double  minor) are the next:

Notes of this scale:

D; E; F; G#/Ab; A; A#/Bb; C#/Db; D;

Interval structure of this scale:

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

Chords that fit in this scale:

Normal Triads: C#     C#m     C#aug     Dm     Ddim     Faug     A     Aaug     A#     A#m     A#dim  Other Triads: Dsus2     Asus4  4 Notes Chords: C#6     C#m6     Dm(maj7)     E7b5     Amaj7     A#maj7     A#7     A#7b5     A#m7     A#m(maj7)     A#m7b5

Two nice positions of the  Romani (Gypsy)  double minor scale are the next. The first is the shape of major7 chord together with its shift by one semitone! The rule of this shape is 2 notes per string.

Other positions are the next 

The Byzantine or Romani (Gyspy)  or Mohammedan non-double  minor  scale is essentially (a cyclic permutation of )  the harmonic minor scale

1) Harmonic minor (called also mode of Hijazz ) = (1-3-1)-2-(-1-2-2),


A mode (cyclic permutation) of the harmonic minor is called  also 7-tone Blue-scale in American folk music.

Chords of the harmonic minor (intervals 2-1-2-2-1-3-1):



Triads:           min              dim aug         min           maj         maj       dim
Extended
4-notes chord: min/maj7    m7b5 maj7#5 min7 dom7 maj7     dim7

For example for the A harmonic minor(A,B,C,D,E,F,G#) (intervals 2-1-2-2-1-3-1) the chords are

i	iidim	III	iv	V	VI	VII
Amin	Bdim	Caug	Dmin	Emaj	Fmaj	G#dim
Aminmaj7	Bm7b5	Cmaj7#5	Dmin7	E7	Fmaj7	G#dim7

Typical progression

Typical chord progressions in A harmonic minor
i - iv - V7	Am - Dm - E7
ii - V7 - i	Bm7b5 - E7 - Am

More general the chords that fit to the harmonic minor (not taking necessarily the notes in alternating order , that is take one leave one  or 1-3-5  etc) are the next

Notes of this scale:

A; B; C; D; E; F; G#/Ab; A;

Interval structure of this scale:

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

Chords that fit in this scale:

Normal Triads: Caug     Dm     Ddim     E     Eaug     F     Fm     Fdim     G#aug     G#dim     Am     Bdim  Other Triads: Dsus2     Esus4     Asus4     Asus2  4 Notes Chords: Dm6     Dm7     Dm7b5     Dº7     D7sus2     E7     E7#5     E7sus4     F6     Fm6     Fmaj7     Fm(maj7)     Fº7     G#º7     Am(maj7)     Bm7b5     Bº7

Again a nice way to play the Harmonic minor on the fretboard with the rule of this shape is 2 notes per string, is the next

5 other ways to play this scale on the guitar fretboard are the next 

Two variations of the Byzantine double minor scale are the Persian and inverse Persian scales or

Persian scale or todi theta scale=(1-3-1-1-2-3-1) 
E.g. starting from C

Notes of this scale:

C; C#/Db; E; F; F#/Gb; G#/Ab; B; C;

Interval structure of this scale:

h (W+h) h h W (W+h) h

Chords that fit in this scale:

Normal Triads: C#     C#m     Caug     E     Eaug     Fm     Fdim     G#aug  Other Triads: C#sus4     Esus2     F#sus4     F#sus2     Bsus4     Bsus2  4 Notes Chords: C#maj7     C#7     C#m7     C#m(maj7)     C#7sus4     E6     Fm(maj7)     F#7sus4     F#7sus2     G#7#5

Inverse Persian scale or Purvi Theta scale= (3-1-1-3-2-1-1) 

E.g. starting from C

Notes of this scale:

C; C#/Db; E; F#/Gb; G; G#/Ab; B; C;

Interval structure of this scale:

h (W+h) W h h (W+h) h

Chords that fit in this scale:

Normal Triads: C     C#m     Caug     C#dim     E     Em     Eaug     G#aug  Other Triads: C#sus4     Esus2     F#sus4     F#sus2     Bsus4     Bsus2  4 Notes Chords: Cmaj7     C#m7     C#m(maj7)     C#m7b5     C#7sus4     E6     Em6     F#7sus4     F#7sus2     G#7#5     C\E     C\G

And a simple video comparing the chords in natural and harmonic minor

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

46. The 7, maj7, 6, m6, dim, and aug versions of the open chords.

(This post has not been written completely yet)

In this post we list the shapes of the maj7, 6, m6, dim, and aug versions of the open chords.

45. Relations of classical diatonic scales defined by common notes ,chords, triads and tetra-chords.

44. Placing the harmonic structure of 24-cycle of chords by 4ths and relatives, on the fretboard by the DAE system.

Here we will show how the relative chords appear by the DAE system on the guitar fretboard. Inother words how by looking at the fretboard we may find the harmonic structure of relaltive chords of a chord, directly on the fretboard. Also how the resolution of chords by intervals of 4ths (dominant7th-root) also appear in the guitar fretboard, using the DAE system. Again this is very susefull as we "see" the structure of harmony directly on the chord patterns on the fretboard. As the 24 cycle of chords (see post 32) is also a rule of modulations, we will have how such a rule of modulations appears on the guitar fretboard. Tonality then will be simple an arc of 6-chord on this 24 cycle. As the above method is beyond tonality , the concept of tonality and modulation will not block  us much when we play the chord progressions and think the harmony we are playing.

The most direct representation of the 24-cycle of all chords is on the fretboard of  6-string bass or 6-string guitar which is tuned at all strings by pure 4ths.
Then this pattern of the chords appears naturally on the fretboard of a bass or guitar tuned on all chords by pure 4ths!  In the next image we see only the positions or arpeggio of the Cmaj chord, and we can easily add the lower relative Am.Then put the same for all other positions of the other chords. The vertical direction from lower to higher notes is the same as the direction of the 24-cycle of chords. Every vertical path inside a fret, spans with 3 of the positions of the major chords a diatonic scale.

THE USUAL 4 WAYS TO WALK INSIDE THE FRETBOARD ARE

1) By knowing patterns of scales

2) By known the shapes of chords, and then walk around the chord shapes

3) By knowing all the names of the notes of all the frets of the fretboard

4) Without any mental image, but simply by the feeling of the desired note, and the feeling-familiarization of the fretboard.

E.g. see https://www.youtube.com/watch?v=d7-ZnzAqt0A

The 5 -triads in successive resolution harmonic relation on the fretboard.

The best way to learn the fretboard is without mental images but only the feeling of the notes at each fret.But this takes too much practice and familiarization with the fretboard.

On the other hand the best way to learn all the fretboard through mental images,rather than feeling,is not by patterns of scales, neither by the names of all the notes of the frets, but rather with sufficient many chord-shapes that almost cover all the fretboard. And even better  if these chords are organized in to easy repeating patterns. Here we describe a method, based on the triads of chords in shapes of E, A, D, so that each is relative to its previous, at the harmonic relation of successive resolution in the cycle of 4ths (see also post 30, 23).

Here we list the chords of shapes E, A, D,on the notes of the e4-string

e4, g4, a4, b4, d5, 

For the symbolism of chords placed on the fretboard, see post 23

chords (E- shape)	chords (A- shape)	chords (D- shape)
e4  (0E)E	(0A)A	(0D)D
g4 (3E)A	(3A)C	(3D)F
a4 (5E)A	(5A)D	(5D)G
b4 (7E)B	(7A)E	(7D)A
d5 (10E)D	(10A)G	(10D)C

When adding the minor chords of the diatonic scale, if the roots is an A-shape we have the following positions

With A-shape as root,  where the I, and V are on the same fret. In the symbolism of post 23 the  (nA)X means at n-th fret play the shape A and it sounds as chord X. Here instead of X we will utilize the Latin symbols of the steps in a major scale, as it is standard in Jazz with small if the chord is minor and capital if the chord is major

So the chords I, ii, iii, IV, V, vi, vii, are played on the fretboard only as shapes A and E as follows

I=(nA)I, ii=((n+2)Am)ii , iii= ((n-1)D)iii,  (nD)IV,  V=(nE)V,  vi=((n+2)Em)vi  

vii=((n-1)dim7)vii.

In short the three main major chords I, IV, V are the 

I=(nA)I, IV=((n)D)IV, V=(nE)V. 

As for the equivalence of chords in different positions and shapes on the fretboard for the  shapes D, A and E hold the rules

1)The D shape sounds as the same chord with A shape 5 frets higher , In symbols e.g. (1D)D=(5A)D and in general (nD)X=((n+5)A)X

2) The A shape sounds as the same chord with E shape 5 frets higher , In symbols e.g. (1A)A=(5E)A and in general (nA)X=((n+5)E)X

3) The E shape sounds as the same chord with D shape 2 frets higher , In symbols e.g. (1E)E=(2D)E and in general (nE)X=((n+2)D)X

In relation with the 24-chords cycle of chords by intervals of 4ths  the DAE system has the next keys and correspondences (with the symbolism of chords on the fretboard as in post 23 ).

 The sequence  X=(nE)Y1, X+1=((n)A)Y2, X+2=((n)D)Y3 is of course a vertical sequenceof chords in thefretbaird and a sequence of 3 successive chords in the cycle of 4ths and symbols of post 34. Now after the X+2=((n)D)Y3, the cycle of 4ths continues either lower in the fretboard or higher in the fretboard

1) Lower in the fretboard is X+3=((n-2)A)Y4

2) Higher in the fretboard is X+3=((n+3)E)Y4

From this point of view, the area of the open chords of the guitar, is simply two such vertical 3-sequences of chords on the cycle of 4ths, as the C-shape is essentially a ((n-3)D)Y chord and D-shape and the G-shape is a ((n-2)A)Y chord and A-shape. 

43. The pitch geometry of the parallel strings , and alternative rules to distribute melodies among the strings .

We are used to the visible geometry of the fretboard. But what our imagination needs is a simpler pattern which is the pitch geometry of the parallel strings , so as to guide the fingers how to play, when the sound feeling of the fretboard is not yet adequate, or when it is adequate but we want an innovative kind of sound, that we have not practiced so far.

The pitch geometry of the parallel  strings is  created by taking an horizontal line of all pitches by semitones, and putting the strings as parallel straight line segments on this line and each one according to their pitch range. So in this way each of the pairs 6-5, 5-4 , 4-3 ,2-1 strings are positioned so that the second starts 5 semitone steps after the start of the first, while for the exception pair 3-2, the second starts 4 semitone steps after the start of the first 

In the pitch geometry, any scale has one only horizontal pattern according to their intervals, but different verical pattern according to the string transition rules or realizations among the strings. 

There are some useful observations about alternative rules to play melodies and improvisations on the parallel strings. Normally one has to play from 5 to 9 notes per string before moving to the next string, This comes by assuming that in the average ones utilizes 3.5 octaves that is 3.5*12 semitones=42 semitones, and then if we divide them by the 6 strings 42/6=7 semitones. IN this way the timbre or color of the sound changes from deep bass and hard on the lower strings and close to the upper end of the strings to soprano and vivid-soft of higher strings and in the middle of the fretboard.

Nevertheless of one is using in the melody say only 2.5 octaves, then this would be 2.5*12=30 semitones, and 30/6=5 semitones, thus 3-7 semitones per string. 

The reason one would prefer only 1-3 notes per string, which means fast way to change strings, is when this melody is anchored to one only position of  a chord (e.g. the particular inversion and position of the chord has a better voicing and sound) and thus the melody has to be also around the finger pattern of the chord. 

Here are some rules of distributing a melody or solo among strings together with their logic. Such rules  can be used also when in exercises  improvisation as in post 11, of the 1st  that is when we want to link the inner feeling of the sound of notes with frets of the guitar fretboard.

1) We play a solo on one only  particular string because 

a) we prefer the sound of the particular string among the other strings

b) We want to utilize another neighborhood  string as repeating root (isokratis)

c) It is easier to visualize the solo there, and its range is small covered by one string. e.g. we want to play on D minor scale, and it is convenient to do it on the string D, or on the E major scale, and it is convenient  to do it on the strings E etc. 
e) We want to move with sufficient speed from one position of a chord to another of the other 3 of its positions
f) We want to make waving od amplitude 1 or 2 semitones only

g) Other reasons

2) We play a solo on n only consecutive strings (e.g. n=2,3,4 and e.g. highest 4 strings 4th, 3rd 2nd 1st or lowest 4-strings 6th,5th,4th,3rd) . Possible reasons: 

a) The sound of the strings e.g. being highest or lowest 

b) being the highest 3, or 4 strings because the easier DAE pattern of the chords 

c) n=2 and because solo on one string is easier to visualize and the range of the melody is about 2 octaves requiring thus  only 2 strings. 

d) n=4 and it is the strings 6th 5th, 4th, 3rd because the mutual tuning is uniform (distance by intervals of 4th) which makes string transitions of the solo uniformly easy

e) Other reasons.

3) We play the solo on only  5 frets, with 1 or 2 or 3,rarely 4 notes per string , thus changing often the string, because 
a) we want to stay close to a single chord pattern and position, and not move the hand, that can control easily about 4 frets 

b) we want to stay on a particular area of the fretboard where the sound is soft (middle of the fretboard) or hard (beginning of the fretboard). See also the two almost mirror images of the fretboard each by about 5-frets in post 5.

c) We want to utilize only open chords, so we want to play the melody together with chord-harping (finger-picking) , only on the first 4-5 frets of the fretboard
e) We want to make melodic butterflying with intervals greater than 4 or 5  semitones (intervals of pure 4th or 5th) (e.g 1 or even two octaves) so we want to shift 1 or 2 strings but close to the frets we are. 

f) Other reasons

4) We play the solo with a rule of n-notes per string. 

Reasons

a) We want a particular type of scale patterns among the strings

b)  We want a particular rule to move the left hand as a whole along the fretboard
c) We want a particular speed to move along the fretboard, so as to change the color and softness-hardness of the sound in a regulated way. 
e) Other reasons

5) We play a solo with  sub-scales 1)  v-vi-vii-i and 2) ii-iii-iv in different strings (the Latin numerals are order of steps in a diatonic scale)

a) because the semitones (vii-i) , (iii-iv) in the diatonic scale  have a distance  of exactly a pure 4th (5 semitones), so they are parallel and in the same fret  in two recessive strings tuned by a pure 4th

b) In general we take as  advantage that strings are tuned by  interval of 5 semitones (pure 4th) to translate melodic themes exactly by 5 semitones to the next string with the same shape on the frets.

6) We take as advantage that 3rd and 2nd strings are tuned by a major 3rd, to play parallel second voices on these two strings.


The panacea rule of successive strings transition in improvisation:

We assume here that improvisation along a single string is easier, and we have to talk a bit about a universal rule of transition from one string to another. We  also assume that the two successive strings are tuned in relative pitch of a perfect 4th (5 semitones). Then a universal rule of  transition to the next string is to do it with an interval of minor or major 3rd (3 or 4 semitones) which is for the two strings  a distance of 2 or 1 frets! The reason is that intervals of 3rd are the distance from a first to a second voice, and so when improvising within a diatonic scale, it is true always that a step of either 3 or 4 semitones will be again inside the diatonic scale! We may even try arbitrary one of the two  and if it sounds wrong we slide it quickly to one semitone left or right which will be the correct, while at the same time we create a nice sound shift to a right interval.

A second even more simple and certain  panacea rule of successive strings transition in improvisation is the next. The idea behind it is to play the diatonic scale along a single string , till the step which is of one semitone (e.g. E-F in the C major diatonic) , and then as the next step is for certain one tone we shift to the next string which will be 3 frets behind. Thus the transition to the next string is only once and always of one tone or 3 frets.

This can be generalized by playing the diatonic scale along a single string, and always we chose to shift to the next string only if he step is of one tone,  which will be 3 frets behind.

Again we do not mention the standard rule, of shifting the left hand one fret to higher notes at the 2nd string. 

THE USUAL 4 WAYS TO WALK INSIDE THE FRETBOARD ARE

1) By knowing patterns of scales

2) By known the shapes of chords, and then walk around the chord shapes

3) By knowing all the names of the notes of all the frets of the fretboard

4) Without any mental image, but simply by the feeling of the desired note, and the feeling-familiarization of the fretboard.

E.g. see https://www.youtube.com/watch?v=d7-ZnzAqt0A

A very useful remark for improvisation of melody within a particular chord is the next.
Suppose we are at a note y1 of the melody which fits the underlying chord with notes x1x2x3 (whatever that may mean), then depending on the particular position of y1 relative to the x1x2x3, a shift by an interval of 3rd, 4th, 5th, and 6th wil lead to a note y2 that will again fit the chord!. This is because the relative positions of the notes x1x2x3 of the chord are intervals of major, minor 3rd and pure 5th, and their complementary intervals relative to the octave are minor or major 6th, and pure 4th 

We may apply the previous to the next

LATIN JAZZ AND HARMONIC BUTTERFLYING 

This butterflying is very often utilizing intervals of 3rds (3 or 4 semitones) and 4ths (5 semitones) and their complementary (6th,  8 and 9 semitones and 5th, 7 semitones when changing octave too),   thus it is ascending or descending chords (chord-scales or chord-arpeggios  , that is why it is called harmonic butterflying) and it is thus chord-harping too, but it involves also intervals of 2nd (1 or 2 semitones) which correspond to chord transitions. A hidden simplicity or invariant in this  butterflying is obviously the underlying chord.  This butterflying maybe of  waving type of melodic move but the amplitudes of the waves may be intervals of 3rds (3 or 4 semitones) and 4ths (5 semitones), instead of intervals of 1 or 2 semitones as in eastern folk music butterflying. And it can be of course of non-waving and monotone scaling type of melodic move . Obviously this butterflying prefers changing strings tuned by 4ths, rather than moving along a single string as in the Greek Bouzouki butterflying.

(The post has not been written yet completely)