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 3 basic harmonic relations of two successive chords are described as types of chord transitions below and are based on the 3 types of intervals 1) 4th as inverted perfect 5th 2) 3rd (either major or minor) 3) 2nd (either major or minor).
AND OBVIOUSLY, SINCE THIS IS THE ORDER OF WHICH TYPE OF INTERVALS IS MORE HARMONIC (SEE POST 40 ) THE SAME APPLIES TO THE CORD RELATIONS: RESOLUTIONAL RELATION IS MORE HARMONIC COMPARED TO RELATIVES RELATION WHICH IN ITS TURN IS MORE HARMONIC COMPARED TO DIATONIC OR COMPLEMENTARY RELATION!
The most common transitions of chords in the songs are the next 3
1) HARMONIC RELATION Successive resolutional relation of chords (Wheel of 4ths)
R1(x)-->R2(y) where R2 is a perfect forth higher than R2, and x, y define the quality of the chord as major, minor, dim, 7th etc. Of course even more often x contains a qualification as 7th chord resolving to a non-7th chord R2(y). E.g. G7-->C, or A7-->Dm etc
MAIN UTILITY: The main advantage of this chord transition is that with just the two chords we practically cover all the notes (except one) of a diatonic scale, and both the chords can be major or both can minor or alternating. We cover with such chord transitions melodies that may aextend a whole octave or more. By extending the first to dominant 7th chords we get also the emotion of anxiety resolution to serenity.
MELODIC MEANING : When such a pair of chords accompanies a melody then taking the themes of this melody either the theme is inside the chords is or is a bridge theme relating the two chords. This means that either the interval of 5 (4th) or 7 semitones (5th) appears as a shift or translation of the theme (chord-theme) or exists inside the theme (bridge-theme).
EMOTIONAL TRANSITION: The emotional impact is as it is very well known the resolution from anxiety to serenity (e.g. E7->Α). The reverse order has reverse emotional impact , but here enter the ingenious tricks of harmonic resolutions inversions (see post 29)
RELEVANT MELODIC DENSITY OR SPEED: The relevant melodies are the high harmonic density or high harmonic melodic speed (see post 68 ). Usually the notes x1,x2 of the simplicial submelody (see posts 9, 72 ) that correspond to the two chords of this transition are either an interval of 4th (5 semitones) apart or 1 semitone apart.
In the symbolism of the post 23 of the chords as positioned by shape on the fretboard,
the next are in the resolutional relation relation
The (nE)X major chord (which means the chord of E shape at the nth fret, and that sounds like X) resolves to the major chord ((n)A)Y while the relative to the same corresponding relative.
The (nA)X major chord (which means the chord of A shape at the nth fret, and that sounds like X) resolves to the major chord ((n)D)Y while the relative to the same corresponding relative.
The (nD)X major chord (which means the chord of D shape at the nth fret, and that sounds like X) resolves to the major chord ((n+2)E)Y while the relative to the same corresponding relative.
Obviously the sequence of the letters in the term DAE system, is the reverse order of the successive resolutions relations (E->A->D)
R1(x)-->R2(y) where R2 is a perfect forth higher than R2, and x, y define the quality of the chord as major, minor, dim, 7th etc. Of course even more often x contains a qualification as 7th chord resolving to a non-7th chord R2(y). E.g. G7-->C, or A7-->Dm etc
MAIN UTILITY: The main advantage of this chord transition is that with just the two chords we practically cover all the notes (except one) of a diatonic scale, and both the chords can be major or both can minor or alternating. We cover with such chord transitions melodies that may aextend a whole octave or more. By extending the first to dominant 7th chords we get also the emotion of anxiety resolution to serenity.
MELODIC MEANING : When such a pair of chords accompanies a melody then taking the themes of this melody either the theme is inside the chords is or is a bridge theme relating the two chords. This means that either the interval of 5 (4th) or 7 semitones (5th) appears as a shift or translation of the theme (chord-theme) or exists inside the theme (bridge-theme).
EMOTIONAL TRANSITION: The emotional impact is as it is very well known the resolution from anxiety to serenity (e.g. E7->Α). The reverse order has reverse emotional impact , but here enter the ingenious tricks of harmonic resolutions inversions (see post 29)
RELEVANT MELODIC DENSITY OR SPEED: The relevant melodies are the high harmonic density or high harmonic melodic speed (see post 68 ). Usually the notes x1,x2 of the simplicial submelody (see posts 9, 72 ) that correspond to the two chords of this transition are either an interval of 4th (5 semitones) apart or 1 semitone apart.
In the symbolism of the post 23 of the chords as positioned by shape on the fretboard,
the next are in the resolutional relation relation
The (nE)X major chord (which means the chord of E shape at the nth fret, and that sounds like X) resolves to the major chord ((n)A)Y while the relative to the same corresponding relative.
The (nA)X major chord (which means the chord of A shape at the nth fret, and that sounds like X) resolves to the major chord ((n)D)Y while the relative to the same corresponding relative.
The (nD)X major chord (which means the chord of D shape at the nth fret, and that sounds like X) resolves to the major chord ((n+2)E)Y while the relative to the same corresponding relative.
Obviously the sequence of the letters in the term DAE system, is the reverse order of the successive resolutions relations (E->A->D)
2) MELODIC RELATION Relative chords (Wheel of 3rds)
R1(x)-->R2(y) where R2 is a minor or major one interval of 3rd lower than R1, or a major or minor 3rd higher than R1, defining thus that the two chords are relatives (normally with two common notes) . Or R1=R2 but R1(x) is major and R2(y) is minor or versa,in other words relative chords with the same root. . Most often of course normally, the first is major and the second minor and vice versa. E.g. C-->Am or
R1(x)-->R2(y) where R2 is a minor or major one interval of 3rd lower than R1, or a major or minor 3rd higher than R1, defining thus that the two chords are relatives (normally with two common notes) . Or R1=R2 but R1(x) is major and R2(y) is minor or versa,in other words relative chords with the same root. . Most often of course normally, the first is major and the second minor and vice versa. E.g. C-->Am or
C-->Em, or Em-->G.
MAIN UTILITY: The main advantage of this chord transition is that we may pass from a minor to a major or vice-versa, thus change from sadness to joy or vice-versa with slight only change of the notes of the melody and the chord!
MELODIC MEANING: When such a pair of chords accompanies a melody then taking the themes of this melody either the theme is inside the chords is or is a bridge theme relating the two chords. This means that either the interval of 3 (minor 3rd) or 4 semitones (major 3rd) appears as a shift or translation of the theme (chord-theme) or exists inside the theme (bridge-theme).
EMOTIONAL TRANSITION: The emotional impact depends to if we pass from a major to minor or from minor to major. When we pass from major to one of its three relative minors is a transition from joy to sadness and vice versa when we pass from a minor to one of its three relative majors.
RELEVANT MELODIC DENSITY OR SPEED: The relevant melodies are the middle harmonic density or middle harmonic melodic speed (see post 68 ).Usually the notes x1,x2 of the simplicial submelody (see posts 9, 72 ) that correspond to the two chords of this transition are either an interval of 3rd (3 or 4 semitones) apart, and at least one of them is a non-common note.
All the above three relations support the declaration of melodic bridge from harmonic speed to diatonic speed.Often melodic bridges from a chord to the next, may start with harmonic speed or density covering the first chord A and then decelerate to diatonic speed or density when reaching to the next chord B.
ONLY TWO RELATIONS FOR THE HAND:
From the point of view of the hand on the fret-board and not of the ear, the relations of two chords can be simplified to only 2: 1) The resolutional (Shape E -> to shape A-> to shape D etc) and 2) The shift of the chord by a tone or semitone on the fretboard. The reason is that the 3rd relation of relative chords can be derived by combining the resolutional backwards or forwards and then shifting forwards or backwards by a tone or semitone!
This gives a practical "rule of thump" way to find chords in melody, by experimenting proceeds in the resolutional wheel of 4ths together shifts back or forth by tones or semitones to chords, and making it as local as possible if the melody has also similar local (small distance) changes.
ONLY ONE RELATIONS (the resolution or wheel of 4ths) FOR THE EAR:
From the point of view of the ear recognizes harmonically the resolution relation, that is the wheel of 4ths The reason is that the 2nd relation of complememtary can be considered as x+3 in the wheel of 4ths while 3rd relation of relative chords can be considered as the x-4 and x-5 in the wheel of 4ths. Thus all the relations translate to the resolution relation.
In the symbolism of the post 23 of the chords as positioned by shape on the fretboard,
the next are in the upper and lower relatives relation :
For the relative chords of major chords the rules are :
The (nE)X chord (which means the chord of E shape at the nth fret, and that sounds like X) has as minor lower relative chord the ((n-1)Dm)Ym (e.g. F with Dm) (or ((n+4)Am)Ym) and as upper relative chord the ((n-3)Am)Zm (or ((n+4)Em)Ym)
The (nA)X chord (which means the chord of A shape at the nth fret, and that sounds like X) has as minor lower relative chord the ((n+2)Em)Ym (e.g. A with F#m) and as upper relative chord the
((n-1)ADm)Zm
The (nD)X chord (which means the chord of D shape at the nth fret, and that sounds like X) has as minor lower relative chord the ((n+2)Am)Ym (e.g. D with Bm) and as upper relative chord the ((n+2)Em)Zm
It is easy to see that the shape of lower relative minor chord of major chord, compared to the shape of the major chord is simply the cycle of letters of the DAE system (D->A->E->D), which is the reverse order of the successive irresolution relations which is E->A->D->E . That is the lower relative minor of major D shape chord is a minor A shape chord, the lower relative minor of major A shape chord is a minor E shape chord, the lower relative minor of major E shape chord is a minor D shape chord!!! Notice also that to find the lower relatives of the vertical sequence of successive resolutional chords E,A,D on the fretboard, we only need to go either 1 step lower in the fretboard (n-1) or 2 steps higher in the fretboard (n+2).
One step lower for E and 2 steps higher for A and D, while always the shape of the relative is in the reverse order of the resolutional order E->A->D->E.
While the shape of upper relative minor chord of major chord, compared to the shape of the major chord is simply the reverse order of cycle of letters of the DAE system (D->E->A->D) exactly as in the relation of successive resolutions . That is the upper relative minor of major D shape chord is a minor E shape chord, the upper relative minor of major A shape chord is a minor D shape chord, and the upper relative minor of major E shape chord is a minor A shape chord!!!
For the relative chords of minor chords:
The (nEm)Xm chord (which means the chord of E shape at the nth fret, and that sounds like X) has as minor lower relative chord the ((n-2)D)Y and as upper relative chord the ((n-2)A)Z
The (nAm)Xm chord (which means the chord of A shape at the nth fret, and that sounds like X) has as minor lower relative chord the ((n+1)E)Y and as upper relative chord the ((n-2)D)Z
The (nDm)Xm chord (which means the chord of D shape at the nth fret, and that sounds like X) has as minor lower relative chord the ((n+1)A)Y and as upper relative chord the ((n+1)E)Z
MAIN UTILITY: The main advantage of this chord transition is that we may pass from a minor to a major or vice-versa, thus change from sadness to joy or vice-versa with slight only change of the notes of the melody and the chord!
MELODIC MEANING: When such a pair of chords accompanies a melody then taking the themes of this melody either the theme is inside the chords is or is a bridge theme relating the two chords. This means that either the interval of 3 (minor 3rd) or 4 semitones (major 3rd) appears as a shift or translation of the theme (chord-theme) or exists inside the theme (bridge-theme).
EMOTIONAL TRANSITION: The emotional impact depends to if we pass from a major to minor or from minor to major. When we pass from major to one of its three relative minors is a transition from joy to sadness and vice versa when we pass from a minor to one of its three relative majors.
RELEVANT MELODIC DENSITY OR SPEED: The relevant melodies are the middle harmonic density or middle harmonic melodic speed (see post 68 ).Usually the notes x1,x2 of the simplicial submelody (see posts 9, 72 ) that correspond to the two chords of this transition are either an interval of 3rd (3 or 4 semitones) apart, and at least one of them is a non-common note.
All the above three relations support the declaration of melodic bridge from harmonic speed to diatonic speed.Often melodic bridges from a chord to the next, may start with harmonic speed or density covering the first chord A and then decelerate to diatonic speed or density when reaching to the next chord B.
ONLY TWO RELATIONS FOR THE HAND:
From the point of view of the hand on the fret-board and not of the ear, the relations of two chords can be simplified to only 2: 1) The resolutional (Shape E -> to shape A-> to shape D etc) and 2) The shift of the chord by a tone or semitone on the fretboard. The reason is that the 3rd relation of relative chords can be derived by combining the resolutional backwards or forwards and then shifting forwards or backwards by a tone or semitone!
This gives a practical "rule of thump" way to find chords in melody, by experimenting proceeds in the resolutional wheel of 4ths together shifts back or forth by tones or semitones to chords, and making it as local as possible if the melody has also similar local (small distance) changes.
ONLY ONE RELATIONS (the resolution or wheel of 4ths) FOR THE EAR:
From the point of view of the ear recognizes harmonically the resolution relation, that is the wheel of 4ths The reason is that the 2nd relation of complememtary can be considered as x+3 in the wheel of 4ths while 3rd relation of relative chords can be considered as the x-4 and x-5 in the wheel of 4ths. Thus all the relations translate to the resolution relation.
In the symbolism of the post 23 of the chords as positioned by shape on the fretboard,
the next are in the upper and lower relatives relation :
For the relative chords of major chords the rules are :
The (nE)X chord (which means the chord of E shape at the nth fret, and that sounds like X) has as minor lower relative chord the ((n-1)Dm)Ym (e.g. F with Dm) (or ((n+4)Am)Ym) and as upper relative chord the ((n-3)Am)Zm (or ((n+4)Em)Ym)
The (nA)X chord (which means the chord of A shape at the nth fret, and that sounds like X) has as minor lower relative chord the ((n+2)Em)Ym (e.g. A with F#m) and as upper relative chord the
((n-1)ADm)Zm
The (nD)X chord (which means the chord of D shape at the nth fret, and that sounds like X) has as minor lower relative chord the ((n+2)Am)Ym (e.g. D with Bm) and as upper relative chord the ((n+2)Em)Zm
It is easy to see that the shape of lower relative minor chord of major chord, compared to the shape of the major chord is simply the cycle of letters of the DAE system (D->A->E->D), which is the reverse order of the successive irresolution relations which is E->A->D->E . That is the lower relative minor of major D shape chord is a minor A shape chord, the lower relative minor of major A shape chord is a minor E shape chord, the lower relative minor of major E shape chord is a minor D shape chord!!! Notice also that to find the lower relatives of the vertical sequence of successive resolutional chords E,A,D on the fretboard, we only need to go either 1 step lower in the fretboard (n-1) or 2 steps higher in the fretboard (n+2).
One step lower for E and 2 steps higher for A and D, while always the shape of the relative is in the reverse order of the resolutional order E->A->D->E.
While the shape of upper relative minor chord of major chord, compared to the shape of the major chord is simply the reverse order of cycle of letters of the DAE system (D->E->A->D) exactly as in the relation of successive resolutions . That is the upper relative minor of major D shape chord is a minor E shape chord, the upper relative minor of major A shape chord is a minor D shape chord, and the upper relative minor of major E shape chord is a minor A shape chord!!!
For the relative chords of minor chords:
The (nEm)Xm chord (which means the chord of E shape at the nth fret, and that sounds like X) has as minor lower relative chord the ((n-2)D)Y and as upper relative chord the ((n-2)A)Z
The (nAm)Xm chord (which means the chord of A shape at the nth fret, and that sounds like X) has as minor lower relative chord the ((n+1)E)Y and as upper relative chord the ((n-2)D)Z
The (nDm)Xm chord (which means the chord of D shape at the nth fret, and that sounds like X) has as minor lower relative chord the ((n+1)A)Y and as upper relative chord the ((n+1)E)Z
Of course the in-place change of a chord from minor or major or vice-versa is also a relation of middle relative chords.
3) CHROMATIC RELATION Complementary chords or chromatic relation of chords (Wheel of 2nds)
R1(x)-->R2(y) where R1(x) and R2(y) are of the same type,in other words both major or both minor and R1, R2 are one tone apart. If R2=R1# or R2=R1b , then we classify this relation as complementary-resolutional rather than simply complementary. In other words the chord is shifted by one semitone higher or lower, and of course most often it retains its quality as major or minor (x=y). In the rare case of the Andaluzian cadenza, the R2 is one tone lower than R1. If R2 and R1 are one step difference in a diatonic scale we say also that the R1(x), R2(y) are complementary chords as all the notes of the two chords make 6 notes all the notes of the scale except one.
MAIN UTILITY: The main advantage of this chord transition is that with just the two chords we practically cover all the notes (except one) of a diatonic scale, and we may pass from a major to a minor chord or vice versa or remain to major or minor and cover with such chord transitions melodies that may extend less than whole octave .
MELODIC MEANING: When such a pair of chords accompanies a melody then taking the themes of this melody either the theme is inside the chords is or is a bridge theme relating the two chords. This means that either the interval of 1 (minor 2nd) or 2 semitones (major 2nd) appears as a shift or translation of the theme (chord-theme) or exists inside the theme (bridge-theme).
EMOTIONAL TRANSITION: The emotional impact depends to if we pass from a major to minor and if we step one tone higher or one tone lower. When we pass from major to a minor one step lower or one step higher, it is a transition from joy to sadness. When we pass from minor to a major one step higher, it is a transition from sadness to joy.
RELEVANT MELODIC DENSITY OR SPEED: The relevant melodies are the chromatic/diatonic harmonic density or chromatic/diatonic melodic speed (see post 68 ).Usually the notes x1,x2 of the simplicial submelody (see posts 9, 72 ) that correspond to the two chords of this transition are either an interval of 2nd (1 or 2 semitones) apart.
In the symbolism of the post 23 of the chords as positioned by shape on the fretboard,
the next are in the complementary by one tone relation relation :
R1(x)-->R2(y) where R1(x) and R2(y) are of the same type,in other words both major or both minor and R1, R2 are one tone apart. If R2=R1# or R2=R1b , then we classify this relation as complementary-resolutional rather than simply complementary. In other words the chord is shifted by one semitone higher or lower, and of course most often it retains its quality as major or minor (x=y). In the rare case of the Andaluzian cadenza, the R2 is one tone lower than R1. If R2 and R1 are one step difference in a diatonic scale we say also that the R1(x), R2(y) are complementary chords as all the notes of the two chords make 6 notes all the notes of the scale except one.
MAIN UTILITY: The main advantage of this chord transition is that with just the two chords we practically cover all the notes (except one) of a diatonic scale, and we may pass from a major to a minor chord or vice versa or remain to major or minor and cover with such chord transitions melodies that may extend less than whole octave .
MELODIC MEANING: When such a pair of chords accompanies a melody then taking the themes of this melody either the theme is inside the chords is or is a bridge theme relating the two chords. This means that either the interval of 1 (minor 2nd) or 2 semitones (major 2nd) appears as a shift or translation of the theme (chord-theme) or exists inside the theme (bridge-theme).
EMOTIONAL TRANSITION: The emotional impact depends to if we pass from a major to minor and if we step one tone higher or one tone lower. When we pass from major to a minor one step lower or one step higher, it is a transition from joy to sadness. When we pass from minor to a major one step higher, it is a transition from sadness to joy.
In the symbolism of the post 23 of the chords as positioned by shape on the fretboard,
the next are in the complementary by one tone relation relation :
The (nE)X chord (which means the chord of E shape at the nth fret, and that sounds like X) has as lower tone complementary chord the ((n-2)E)Y and as upper tone complementary chord the ((n+2)E)Z
The (nA)X chord (which means the chord of A shape at the nth fret, and that sounds like X) has as lower tone complementary chord the ((n-2)A)Y and as upper tone complementary chord the ((n+2)A)Z
The (nD)X chord (which means the chord of D shape at the nth fret, and that sounds like X) has as lower tone complementary chord the ((n-2)D)Y and as upper tone complementary chord the ((n+2)D)Z
MORE ONCHORD RELATIONS AND THEIR PSYCHOLOGICAL MEANING HERE
M symbolizes major chord m the minor chord and the number in between the distance of their roots in semitones
https://www.youtube.com/watch?v=YSKAt3pmYBs
HARMONIC POLES AND HARMONIC WAVING IN THE CHORD PROGRESSION AND STRUCTURE OF THEMES IN THE MELODY:
The emotional parallel of the harmony of intervals, suggests that the chord progression and harmonic structure of the themes of the melody, waves (Harmonic waves) between the emotion of stress,intervals of 1 or 2 semitones to the pole of harmonic serenity ,intervals of 5 (4th) , 7 (5th) or 12 (octave) semitones.
Conversely any sequence of chords with the above rules defines an harmonically meaningful chord pattern for a nice song or improvisation.
The order of the "average disance" of the chords in the above 3 harmonic relations are
complementary chords< Relative chords < Successive resolutional chords
This also corresponds to the 3-melodic densities or speeds of the melodies that fit to such chord transitions of chord progressions.
1) The complementary chords in a 2-chords transition corresponds to the chromatic/diatonic melodic speed or density.
2) The relative chords in a 2-chords transition corresponds to the middle harmonic melodic speed or density.
3) The successive resolutional chords in a 2-chords transition corresponds to the high harmonic melodic speed or density.
Based on the idea of the three relations of the chords, we may compose beautiful chord progressions. Two general rules are the next:
E.g. B7->Em->Am->D7->G->Bm-> etc
E.g. The well known song of Frank Sinatra "Fly me to the moon" is using this technique in its sequence of chords
Another example is the song of Nat King Cole L.O.V.E.
(main arc is the (Em or E7)->A7->D7->G(or Bm or Gm7) ->E7 etc with backwards retraces by one chord)
E.g. D7->G ,(1 semitone apart) Db7->Fm
or D7->G, (2 semitones apart) E7->Am
or Am->D7->G, (1 semitone apart) F#7->B7->Em
1) When playing the melodies on the fretboard in the guitar, the chromatic/diatonic speed is played mainly along the length of a string, so it is the zero angle.
2) When playing the melodies on the fretboard in the guitar, the middle harmonic speed is played mainly at an angle which relative to the horizontal is about 45 degrees and moves from the keys of the guitar to the sounding body as the melody descends in pitches! This is is because it consists of intervals of 3 or 4 semitones that in two successive strings is such an angle.
3) When playing the melodies on the fretboard in the guitar, the high harmonic speed is played mainly at an vertical angle relative to the horizontal because the strings are tuned at intervals of 5 semitones (and one string in 4 semitones). Also the interval of 7 semitones (5th) when played in descending the pitches makes an angle larger than vertical or 90 degrees (e.g. 135 degrees) and moves from the the sounding body of the guitar to the keys of the guitar as the melody descends in pitches!
Nevertheless from the point of view of common notes, the relative chords have 2 common notes, then the successive resolution chords have one common note and the complementary chords none common note.
The 3 harmonic relations of chords, with of course the chord-shapes is also a method of walking inside the fretboard.
The order of the "average disance" of the chords in the above 3 harmonic relations are
complementary chords< Relative chords < Successive resolutional chords
This also corresponds to the 3-melodic densities or speeds of the melodies that fit to such chord transitions of chord progressions.
1) The complementary chords in a 2-chords transition corresponds to the chromatic/diatonic melodic speed or density.
2) The relative chords in a 2-chords transition corresponds to the middle harmonic melodic speed or density.
3) The successive resolutional chords in a 2-chords transition corresponds to the high harmonic melodic speed or density.
Based on the idea of the three relations of the chords, we may compose beautiful chord progressions. Two general rules are the next:
A11 . 1st general rule for harmonic chord progressions: Progressions by arcs in the 12-chord cycle by intervals of 4th
This cycle defines by every connected arc of it a chord progression , where a chord may be substituted with its same root relative major or minor chord , or its lower or upper minor relative chord. Of course as they are an arc of the above 12-cycle they are successive chords or in the harmonic relation of resolution.
E.g. B7->Em->Am->D7->G->Bm-> etc
Or B7->Em->Am->D7->G->C->(Am orA7)->D7 etc
E.g. The well known song of Frank Sinatra "Fly me to the moon" is using this technique in its sequence of chords
Another example is the song of Nat King Cole L.O.V.E.
(main arc is the (Em or E7)->A7->D7->G(or Bm or Gm7) ->E7 etc with backwards retraces by one chord)
A12 . 2nd general rule for harmonic chord progressions: Two arcs in the 12-chord cycle by intervals of 4th (substituting any of the chords with its minor if it is major or vice versa) that have distance at the closest ends either 1 , or 2 or 3 or 4 semitones!
E.g. D7->G ,(1 semitone apart) Db7->Fm
or D7->G, (2 semitones apart) E7->Am
or D7->G , (3 semitones apart) B7-> Em
or Am->D7->G, (1 semitone apart) F#7->B7->Em
ANGLES IN FRETBOARD AND MELODIC SPEEDS
2) When playing the melodies on the fretboard in the guitar, the middle harmonic speed is played mainly at an angle which relative to the horizontal is about 45 degrees and moves from the keys of the guitar to the sounding body as the melody descends in pitches! This is is because it consists of intervals of 3 or 4 semitones that in two successive strings is such an angle.
3) When playing the melodies on the fretboard in the guitar, the high harmonic speed is played mainly at an vertical angle relative to the horizontal because the strings are tuned at intervals of 5 semitones (and one string in 4 semitones). Also the interval of 7 semitones (5th) when played in descending the pitches makes an angle larger than vertical or 90 degrees (e.g. 135 degrees) and moves from the the sounding body of the guitar to the keys of the guitar as the melody descends in pitches!
Nevertheless from the point of view of common notes, the relative chords have 2 common notes, then the successive resolution chords have one common note and the complementary chords none common note.
The 3 harmonic relations of chords, with of course the chord-shapes is also a method of walking inside the fretboard.
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, and utilizing the 3 fretboard-neighborhoods.
4) Without any mental image, but simply by the feeling of the desired note, and the feeling-familiarization of the fretboard. At this it must be made the use of the belief that one "knows" simply by the feeling which fret sounds which note !
E.g. see https://www.youtube.com/watch?v=d7-ZnzAqt0A
The meaning of course of these 3 types of transitions is that when listening to the harmony and melody of the song, the melodically connecting element when the chord changes is 1) either a resolution in the cycle of 4ths, or 2) a relation of relatives of the chords (common notes of the chords), or 3) a small move of the root of the chord, complementary chords. Or in other words that the parallel melody during the transition of the chord most often is also doing one of the next correspondingly to the above 3 transition types 1) Moves by one semitone (resolution in the cycle of 4ths) 2) Remains the same note or moves by a 3rd (transition to a relative chord) 3) Moves by 1 semitone or by 1 tone (shift of the root of the chord by 1 semitone or 1 tone).
For the correlation of melodies with chords that fit to them, or conversely , melodies that can be improvised over a chord progression the next local concept is very significant: The melodic closure of a chord: This is defined as the closed interval of notes from all the 12-tone (chromatic) scale) with lower end the lowest note of the chord, and highest end the highest note of the chord. The chord is assumed within an octave, and normal positions, 1st inversion, and 2nd inversion have different closures. The melodic closure is also conceivable as transportable in all octaves, and not only where the chord is It holds the next interesting theorem. If we define randomly a melody within a the closure of a chord in normal position and no other note outside it, with uniform probability of occurrence of any of the notes of the closure, then according to the local condition of fit of a piece of melody with a chord the only chord in normal position that would fit this melody is the one with this as its closure!. Or more generally of we define as probabilities of sounding a note on all the octave an equal value for all notes except at the notes of the chord X where we have as probability the double this value (e.g. sound each note of the octave once but the notes of the chord twice) then any such random melody with this probability structure will have as its fitting underlying chord the chord X.
For the correlation of melodies with chords that fit to them, or conversely , melodies that can be improvised over a chord progression the next local concept is very significant: The melodic closure of a chord: This is defined as the closed interval of notes from all the 12-tone (chromatic) scale) with lower end the lowest note of the chord, and highest end the highest note of the chord. The chord is assumed within an octave, and normal positions, 1st inversion, and 2nd inversion have different closures. The melodic closure is also conceivable as transportable in all octaves, and not only where the chord is It holds the next interesting theorem. If we define randomly a melody within a the closure of a chord in normal position and no other note outside it, with uniform probability of occurrence of any of the notes of the closure, then according to the local condition of fit of a piece of melody with a chord the only chord in normal position that would fit this melody is the one with this as its closure!. Or more generally of we define as probabilities of sounding a note on all the octave an equal value for all notes except at the notes of the chord X where we have as probability the double this value (e.g. sound each note of the octave once but the notes of the chord twice) then any such random melody with this probability structure will have as its fitting underlying chord the chord X.
