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)