29. Other types of anxiety-serenity resolutions not based on diminished (and 7ths) or augmented chords, parallel resolutions and inversions of resolutions.

We had Summarized in  a simplistic way the correspondence of melodic pitch dynamics and the 4-basic emotions in music (joy, sadness, anxiety, serenity) we have 

1) Up pitch moves correspond to joy

2) Down pitch moves to sadness

3) Small pitch intervals of 1 or 2 semitones (chromatic or interval of 2nd) correspond to anxiety

4) Large pitch intervals (e.g. 4th, 5th octave etc) correspond to harmony and serenity. 

Some instructive remarks in the composition of the melody based on the chord progression

1) In the part of the chord progression with minor chords, utilize descending melodic moves so that sadness from melody and sadness from harmony fit

2) In the sad melody parts of the melody (and minor chords) utilize rhythmic patterns that start with faster notes and end with slower notes, and the reverse for the happy part (and major chords).

3) In a triad or 7 nth 4-notes chord the most characteristic notes are the middle 2nd note (in 1-3-5 interval notation  is the 3) and the 7 nth (if it exists). So for the anxiety part of the melodic moves we may utilize 1-semitone trills around these two notes, or waving with 1 or 2 semitones steps and notes outside the chord in the interval of minor 3rd (3 semitones) of the chord. Alternatively instead of trill or small amplitude waves we may utilize chromatic monotone scaling by steps of 1 semitone , or scaling with steps by intervals of 2nd of the scale,  that go from these previous notes of the chord to the same such notes in the next octave. But always make sure that the notes of the chord sound in the average longer, than the notes of these anxiety transition moves with notes outside the chord. 

4) Alternate up (happy) and down (sad) pitch moves , or chromatic moves (anxiety), with harmonic (on chord notes) moves (serenity-harmony).

5) Utilize at least 2 octaves, or even 3 for the melodic moves repeating the notes of the underlying chord on the next octaves , so there is sufficient space for melodic moves, to express with sufficiency the emotions.

6) For the duality of emotions anxiety-serenity, it may be utilized also harmonic waves or monotone scaling over 2 octaves at least,  on the notes of the chord, but also chromatic trill wave over the notes of this wave or scaling (modulated wave on wave or move) and then return to the pure harmonic wave or scaling on the notes of the chord.

7) A chromatic wave by 1-semitones steps or all notes of the scale (steps by intervals of 2nd) that goes up and down at least 2 octaves, corresponds to a chord sub-progression of the song , of our choice that utilizes almost all the chords of the scale!

But in this post we shall talk about correlations of these emotions with the harmony not the melody of chord transitions!

Parallel or alternative resolutions: For example if G->G7 resolves to --> C, then a parallel resolution is a sequence of chords R1,R2,...Rn, with the same feeling of resolution and R1=G7, Rn=C.

The I-V-IV-V-I triple majors paralel resolution 

(1M->4M->5M->1M)

e.g. D->A->G->A->D 
this progression is also created when we descend or ascend by 2nds a melody (waving or not) with 2nd voice which can be extended with 3-notes or a major chord instead of 2 voices, in a diatonic scale.

Such sequences come  initially from the natural progression by 2nds of the chords

e.g. I-ii-iii-IV-V-I , that by substituting minors with their relative majors becomes 

I-IV-V-IV-V-I

or  I-ii-iii-IV-V-vi-vii-I    
I-IV-V-IV-V-IV-V-I

 E.g.The aug parallel resolution  R1=G R2=Gaug R3=C.  

Or R1=Bb, Rn=A in the Andaluzian Cadenza Dm, C, Bb A.
or 1M7->1M then 5M->5aug->1M

There are plenty many chord progressions that are parallel resolutions.

E.g. The parallel to major-major resolution the relative minor-chromatic a parallel to the G7->C is the G7->Em->B7->C  or if it is the A7->D, then A7->F#m->C#7 ->D
Similarly, the parallel to a minor-minor resolution is the relative major-major resolution
E.g. parallel to the Am->Dm is the major-major resolution C->F, so in total

Am->F->C->Dm notice that we set the inverse of the relative resolution. 

or if it is the major-major G->C, the relative resolution is the Am->Dm or  Bm->Em, so the total will be G->Dm->Am->C or  G->Em->Bm->C. 

The parallel to major-minor resolution chromatic- chromatic, a parallel e.g. to the resolution A7->Dm is the sequence  A7->D#7->A#->Dm or A7->A#->D#7->Dm

The 1st dim7 simple chromatic parallel resolution e.g. 

Instead of A7->Dm, the Edim7->Dm. Or e.g. instead of 

E7->Am the Bdim7->Am.

The 2nd dim7 simple chromatic parallel resolution e.g. 

Instead of A7->Dm  , the Ddim7->Dm. Or e.g. instead of 

E7->Am the Adim7->Am.
The 3rd dim7 simple chromatic parallel resolution
Instead of E7->A the Edim7->A (that is also why some times D#7 is considered to resolve to A, and D#7 is almost identical with the Edim7) or instead of A7->Dm the Adim7->Dm.
The 3 dim7 simple chromatic parallel resolution are not of equal intensity. Their intensity of resolutions is the order with which are presented.

The dim7 enhanced chromatic  parallel resolution e.g. Ddim7->A7->Dm  

The Xm6  . minor 6th resolution:
This is a resolution with chord transition in the relation of complementary chords. In other words, the first chord is a minor and resolves to  a major one tone lower, if the minor is a minor 6th: E.g. Am6->G, or Em6->D, or Dm6->C , or Gm6->F etc. This is so because the minor 6th contains already part of the 7nth of the previous chord in the wheel by 4ths e.g. D7->G, becomes Am6->G etc.



This resolutions can resolve to the relative so instead Am6->G the Am6->Em, thus it is an inversion of the Em->Am, that is mentioned below:

The extended Xm6 minor 6th resolution
This is the same as the previous but , we interpolate one more major chord at first with root one tome higher than the minor 6th and then end with the major with root one tome lower than the minor 6th e.g. Am6->B7->G, or Em6->F7->D, or Dm6->E7-C , or Gm6->A7->F , Fm6->G->Db  etc.

Since the Xm6 chord is identical with the Ym7b5 chord (half diminished 7th chord)  where Y is one minor 3rd lower than X, (e.g Fm6=Dm7b5) there is a natural resolution of Ym7b5 one 4th higher e.g. Dm7b5-> G, which is the interpolated chord in the extended Fm6 resolution Dm7b5=Fm6->G->Db. 

The minor 6th parallel resolution with the common relative minor at 6th.

This is a resolution with chord transition in the relation one 4th back to the wheel of 4ths, thus inversion of standard resolution to minor. chords.  E.g. Am6->Em, or Em6->Bm, or Dm6->Am , or Gm6->Dm etc.

The common minor as 6th parallel resolution. This is the standard resolution in the wheel by 4ths, e.g. C->F where we interpolate rge common minor relative chord when we do not want to use the first chord with 7nth, so it becomes e.g. C->Am->F or C6->F.

  The #7 enhanced chromatic  parallel resolution e.g. 

A#7->A7->Dm.  (4M7->3M7->6m)

The #7 simple chromatic  parallel resolution e.g. 

Instead of A7->Dm the D#7->Dm, Or instead of E7->Am, the A#7->Am 
or instead of 3M7->6m the 7b7->6m

The relatives-sharp/flat parallel resolutions.

1) The logic of this resolution is the following: Since the major relative chord of say a minor chord has two notes in common with the minor chord, then the dominant seventh of this major  relative one semitone higher or lower will have two notes, one semitone apart creating the effect of resolution.

E.g. F is relative to Dm, thus F#7->Dm and E7->Dm (4#7->2m) )will be parallel resolutions. Similarly the Bb is relative major of Dm, thus  B7->Dm are a parallel resolutions. Thus we notice that not only with one step back in the cycle of 4th we have a resolution (that is A7->Dm) but also with two or three steps back we have resolutions (that is E7->Dm, B7->Dm)! And again as D is relative to Dm, then also Db7=C#7->Dm and D#7=Eb7->Dm are resolutions. Similar observations can be made with the minor relatives of major chord.

Again  we may have parallel resolutions of two major chords of shift their relative minor chord by one semitone up or down. E.g. F7->D#m, F7->Dbm , Bb7->D#m, Bb7->Dbm.

As another example from the major relatives C and G of Em, we may derive the parallel resolutions C7->Fm, G7->Fm, 

C7->Ebm, G7->Ebm.

2) 2nd times relatives parallel resolution: Similar to this parallel resolution is the next case  . Instead of 
E7->Am the E7->G->Gmaj7->G7->C->Am  Or also E7->G->Gmaj7->Dm7->C->Am 
Or E7->G->Gmaj7->F->C->Am. Notice that here we shift to the 2nd times relative (E7->Em->G) and we also go one step ahead in the wheel of 4ths that is to Dm7 before we return to Am. In soloing on it from the g#4 during E7 we move chromatically g#4->g4->f#4->f4->a3. 
Similarly instead of D7->Gm the D7->F->Fmaj7->F7->Bb->Gm (D7->F->Fmaj7->Cm7->Gm)
Or instead of  A7->Dm the A7->C->Cmaj7->C7->F->Dm (A7->C->Cmaj7->Gm7->Dm)

The two steps forward in  the wheel of 4th  parallel resolution
Another way to grasp the previous parallel resolution chromatic soloing g#4->g4->f#4->f4->a3. from E7 to Am , and also modify it is , to perceive it as moving two steps forward in the wheel of 4ths and move back to the resolving chord.
Thus to move from E7 to Am, we go two steps foprward in the wheel of 4ths that is (here we prefer minor) Dm, Gm , and trace it backwards Thus instead of E7->Am the E7-> Gm->Dm7->Am . Or instead of A7->Dm the A7->Cm->Gm->Dm. Instead of B7->Em the B7->Dm->Am->Em etc

The sharp/flat parallel resolution.

This is a simple logic: Instead of resolving e.g. G7->C we shift by semitone up or down the first or second chord. Thus

G#7->G7 or F#7->G7 or C#->C or B->C etc.

This can apply to 3-chord double resolutions E.g. from the standard resolution B7->E7->Am, we may derive the parallel resolution B7->F7->Am, where the last two chords happen to be relative chords too in the case of this example. Or the parallel resolution C->E7->Am, where the first and last chords in this example are relative chords. 

The complementary chord parallel resolution

In this case instead e.g. resolving D7->G we utilize the upper minor complementary chord of G, here the Am instead of the D7, so the parallel resolutions is Am->G ! Notice that the Am is relative to the D7 as it has two common notes the c and a, although it is not relative to the D chord. Alternatively we may pass from the minor Am two steps back in the wheel of 4ths in other words to B7 and then to G so in total Am->B7->G. 

The double major-minor enhanced resolution

e.g. instead of B7-Em, the F#7->B7-Em,or instead of 

A7->Dm, the E7->A7->Dm (It is interesting to compare this also with the retraced double resolution below in other words the Gm7->A7->Dm)

The chromatic-chromatic  ancenza parallel  resolution. This instead of simple resolving e.g. G to C (G7->C) it starts and ends the same but as chromatic ascenza (=increasing pitch) as follows G(7)->G#(7)->B(7)->C Or instead of only D7->G, the progression  D7->D#7->F#->G. This of course is the same as when we inverse he resolution So instead of G->D7, we enhance to G->F#->D#->D7. 

The chromatic-diatonic ancenza parallel  resolution. This instead of simple resolving e.g. G to C (G7->C) it starts and ends the same but as chromatic-diatononic  ascenza (=increasing pitch AND accelerating intervals) as follows 

G->G#->A#->C . Or instead of only D7->G, the progression  D->D#->F->G.

Interval explanation by notes in one semitone distance

This is called the standard Dominant resolution e.g. G7->C  , D7->G, C7->F etc The key to explain of this anxiety-serenity resolutions is that the dominant 7th chord e.g. G7 is the superposition of the Gmajor+Bdiminished, and the diminished chord is by itself a bit sad with anxiety, which is correlated with the Cmajor chord which has serenity because it contains at least one notes of one semitone distance of notes of the C major. These are the notes B, with one semitone distance from the C of Cmajor. The  same is the explanation why the  Cdim7 below resolves to G, because it has the notes D# and F# with one semitone distance from the notes D, G of Gmajor. Sometimes even Cm will be considered resolving to G, because of the D# note at one semitne distance from the D note of G, and the major chord sounds with more serenity than the minor chord!

And the same is the explanation why in the Andalusian Cadenza  Dm, C, Bb A. , the Bb resolves to A, because it has 3 notes one semitone distance apart from corresponding notes of A.

Similarly as the E7 resolves to A so the Em7b5 resolves to A too because it has the 3 notes D, F , G# one semitone apart from the C#, E , A of A chord. And similarly the Edim7 resolves to A as it has the notes D, F one semitone apart from the C#, E  of A

For the same reason if D7 resolves to G, then also Daug resolves to G because Daug has the notes  F#, C# at one semitone distance from the notes G, D of G major chord and Daug sounds in anxiety.

Retraced double resolution. Such a phenomenon of 1-semitone apart notes we have also, if a simple resolution e.g. like A7-->Dm is enhanced to the Gm7-->A7-->Dm, or in the symbolism of the 24-cycles of chords (see post 34) in general the resolution 

X7-->(x+1), is enhanced to the (x+2)7-->X7-->(x+1). 

The reasons is that the (x+2)7 and X7 are complementary chords and have at least 3 notes 1-semitone apart. E.g. the Gm7, and A7 have the 3 notes (f, a#, d) of Gm 1-semitone apart of the notes (e, a, c#) of A7. 

Double resolution to a minor. This is 2 major chords resolving to a minor, and the first major chord is  dominant 7nth resolving to the second major chord which is also dominant seventh which in its turn resolves to the 3rd minor chord the 1st 2nd 3rd have in sequence a distance of pure forth E.g. F#7-->B7-->Em, or  B7-->E7-->Am , or E7-->A7-->Dm etc

1st type of two relative resolutions

This is the case of two relative chords one minor one major, and then resolutions ending on them E.g. Em is relative to G, and we get the 1st relative resolutions B7->Em and then D7->G. For reasons of balance instead of 3 major and one minor chord we may use 2 major and 2 minor chords , thus 

B7->Em, Dm7->G

2nd type of two relative resolutions

This is the case again of two relative chords one minor one major, and then resolutions on them but the first is from the first and the second resolution ends to the seconf chord E.g. Em is relative to G, and we get the 2nd relative resolutions  D7->G and then Em->A. For reasons of balance instead of 3 major and one minor chord we may use 2 major and 2 minor chords, thus  Dm7->G and then Em(7)->A(7)

Chromatic double minor or major resolution 

This is like e.g. the B7-->E7-->A but the intermediate E7 is substituted with the chromatic in between

 Bb7, so in total it is  B7->Bb7->A7 and similarly for minors

instead of Bm7-->Em7-->Am , the Bm7->Bbm7->Am7

Or e.g. instead of Em7-->Am7-->Dm7, the 

Em7-->D#m7-->Dm7  etc

The chord progression can be reversed too!

Resolution cycle.

This is repeated cycle of chords that at each step or piecewise at arcs it is a resolution!

E.g. G->G7->Gaug->C(1st resolution)->Cdim7->G(2nd resolution and back to the same chord)

Here a geometric representation would lead to a paradox like in a well known optical illusion as below (but here it is an emotional illusion of resolutions)

Inverse resolution= It is a sequence R1,R2,...Rn with the same feeling of resolution (from anxiety to serenity) and R1=C, Rn=G.

For example 

The minor relative inversion : To inverse e.g. G-->C here are two ways

 R1=C R2=Cm R3=G, or 

C->Cm->C#maj7->G 
or  5M7->1M inverts by 1M->1m->5M

or  1M->4M->4m->1M   or    

2m->5M inverts by 5M->5m->6M->2m

This minor inversion of a resolution introduces the minors of the triad of major 1M, 4M, 5M

(introduces the 1m,4m,5m) which is very important in the chromatic tonality and in particular the

full chromatic tonality. The introduction of the corresponding major chords of the 3 minor chords 3m,6m,2m (to 3M,6M,2M) is  done mainly by the harmonic minor and double harmonic minor instead of the natural minor in the diatonicc scale. 

THSU THIS MINOR RELATIVE INVESION IS A BASIC WAY 

IN CROMATIC TONALITY TO CHANGE THE 1M, 4M, 5M O MINOR CHORSD

1m-4m-5m. 

The dim7 inversion of major-major e.g.  R1=C R2=Cdim7 R3=G. Or

The aug inversion  of major-major e.g. R1=C, R2= Gaug R3=G  

The maj7 inversion of major-minor  e.g. to inverse the A7->Dm , here is a way 

Dm->A#maj7->A7    (6M7->2m inverted by 2m->4maj7->3M7)

The dim7 inversion of major-minor e.g. Dm->A#dim7->A7 (6m->4dim7->3M7)

The aug inversion  of major-minor e.g. Dm->Aaug->A7 
The minor 6th resolution inversion as alternative resolution
This is a resolution with chord transition in the relation one 4th back to the wheel of 4ths, thus inversion of standard resolution to minor. chords.  E.g. Am6->Em, or Em6->Bm, or Dm6->Am , or Gm6->Dm etc.

The common minor relative chord ,inversion e.g. C->Em->G.
The relative-complementary chord inverse resolution
In this, we want e.g. to pass to inverse G7->C, so we pass to the lower relative minor of C that is to Am, then two steps back in the wheel of 4ths that is to B7 and then to G. In total
C->Am->B7->G.  

The 1st inverse resolution of minor-minor  To inverse e.g. the minors Am->Dm here is a way Dm->Bb->E7->Am (the Dm and Bb are relative chords). 
The 2nd (semitone shift) inverse resolution of minor-minor 
Let us say that we want to invert the Am->Dm. We start with Dm and then we pass to the major relative F, then one semitone lower E7 and resolve to Am. In total
Dm->F->E7-Am. Other example:   Gm->Bb->A7->Dm

The inverse resolution of major-minor. To inverse e.g. the E7->Am here is a way

Am->C->B7->E7 or e.g. to inverse the A7->Dm , the Dm->F->E7->A7 

The dim7 inverse resolution of major-minor e.g. to inverse the E7->Am the sequence is  Am->C->Adim7->E7

or the short relative-chromatic inversion of major-minor e.g. to inverse the E7->Am, 

the  sequence Am-> F7->E7 (where the Am is relative to the F7, which is chromatic by a semitone to the E7) or to inverse the A7->Dm , the sequence Dm->A#->A7

 The long relative-chromatic inversion of major-minor. E.g. to inverse the A7->Dm, the sequence Dm->A#->E7->A7. Or to inverse the E7->Am the sequence Am->F->B7->E7

The relative and double resolution inversion of a classical major-major resolution. To inverse e.g., the G7->C here is a way

C->A7->D7->G (Here the A7 is relative of Am which is a relative of C!) 

Or C->Am7->D7->G7 or C->Am->Dm->G7

E.g, if it is to inverse E7->A, we go as follows from A we go to its relative F#m  then resolve to Bm and then rrsolve to E7. So in total A->F#m->Bm->E7

or The bridge inversion C7->F-Dm7->G7 (here the C7 resolves to F which is relative to Dm7, which is relative to D7 which resolves to G7) 

The short bridge inversion e.g. C7->F->G7

The long bridge inversion e.g. C->Gm->F->Dm7-G7

And to inverse e.g. the E7-->Am , the Andalusian cadenza may be used with R1=Am, R2=G, R3=F, R4=E7. 

The Bulerias  inversion

E.g. to invert B7->Em

Em->Em7->A->A7->D->D7->G->G7->C->C7->B->B7

The minor-minor 7-chords Gypsy inversion

To invert the Bm->Em as follows:
Em->A7->D->G->C#7->F#7->Bm

E.g. in D major:  3m->6m is inverted by 6m->5M7->1M->4M->7M7th->3M7->6m

which is essentiall completingthe 7-chords cycle of the chords ofthe diatoninc scale.


or to invert Em->Am as follows

Am->D7->G->C->F#7->B7->Em



or to invert Am-> as follows

Dm->G7->C->F->B7->E7->Am

or 

Dm->G7->C->F->Bb->E7->Am

notice that it is a 7-cycle of 4ths (except one) starting and ending with minor and all in between by majors but somewhere in the 5th or 6th chord there is shift by a semitone thus not pure 4th.

 There are more ways to do so!

E.g. 

The relative-chromatic inversion of major-major To inverse the D7-->G we may use the progression G-->Bm-->Bbm-->(Am7)->D7 over the notes d, c#, c. The idea is to start with the G and then pass to its minor upper relative Bm and then by  semitone shift to Bbm and one more semitone back  to Am , but instead of Am we play   D7 which is  also a relative also of Am as it has the two common notes a and c !. ( Or to reverse G7-->C, use the sequence C-->Em-->D#m-->(Dm7->)->G7 over the notes g, f#, f)

in abstract symbols

to invert 5M7->1M as follows 1M->3m->2#m->2m7->5M7

We discuss in the next some ways to have  inversion of  resolutions and parallel resolutions.

We have met also the chromatic-chromatic inversion  So instead of G->D7, we enhance to G->F#->D#->D7. The idea is to shift by a semitone both chords. 

The relative -chromatic inversion of major-minor 

E.g. To inverse the B7->Em we go from Em  to the major relative G7 then shift chromatically to the F#7 and resolve to B7 so it is  the sequence         Em->G7->F#7->B7

Reverse of a resolution. This is just the reverse of the resolution , which of course is not a resolution but leads from serenity to anxiety e.g. Em-->B7, Some chord progressions, utilize 1,2, or even 4 Reverses of resolutions and then an final straight resolution which resolves the tension of all the previous reverses of resolutions E.g. C--->G7--->D7--->B7---Em. (We use here the similarity of the sound, because of common notes of the B7 and D7)

Resolutions based on relative chords

Since two relative chords have two notes on common (e.g. Am=(a,c,e), C=(c,e,g)) , if one of the two is one semitone away, then the two chords will have two notes one semitone apart E.g. in the previous example A#m=(a#, c#, e#)-->C, or Abm=(ab, cb, eb)--->C, or C#=(c#,e#, g#)-->Am=(a,c.e). Still another way for the relative chords Am-->C is to change the Am to a major chord A=(a,c#,e)-->C=(c,e,g) that will have one note , in 1-semitone apart.

Relatives-indirect resolution. These resolution are derive from ordinary by substituting the second final chord with its relative. E.g. from the standard resolution to a minor B7-->Em we may derive the relatives-indirect B7-->C or B7-->G resolving to major ,as C and G are major relative chords of Bm. The most common use of such substitutions is to pass from minor chords to relative chords. Of course there is the opposite, where  a major is substituted by its relative minor e.g. from the standard resolution D7-->G we may derive the relatives-indirect D7-->Em or D7-->Bm. 

The chromatic transition to a relative chord. This is the passage to a relative chord semitone by semitone in other words in a chromatic way. E.g. To go from G to Em (or E) we do the sequence G->Gb->F->E7.

The chromatic transition to a complementary chord

E. to go from A to G, we go A(or Am)->Ab->G. Or to go from

C to D, C->C#->D (Dm)

For example the famous song Dream a little dream of me, has 1) Chromatic-chromatic inversion of a resolution 2) Chromatic transition to a relative chord 3) Chromatic transition to a complementary chord

https://www.youtube.com/watch?v=socgaSO4Ngs&spfreload=1

PAGANINI-LIZT RESOLUTION IN CAMBANELA

In the above famous musical piece we have a persisting pair of chords that comes from that harmonic minor 3M7->6m and this melodic theme at the end of the musical piece resolves not the 6M7->2m as it would be expected but the relative (in F major) of 2m, the  Bb , thus 6M7 ->Bb.   Similarly if it was 7M7->3m, it would resolve to the 3M7->4M. 

Some rules for passing from sadness to joy in the harmony of the chord progressions.

1) Pass and close from minor chords to major chords as relative chords (e.g. as relative chords Em-->C , or Am--A7

2) Or from the triangle minor chords to the triangle of the major chords of the diatonic scale through the diatonic bridge. E.g. Em-->Am-->Dm (Dm7 bridge, or D7) --->G--->C--->G. (1st majorization)

3) Pass from the triangle minor chords to the corresponding same root  triangle of  major chords 

E.g.  Em-->Am-->Dm  then E7-->A7-->D.(2nd majorization)

4) Use a reverse resolution with minor chord , and then resolve to a straight resolution with major chords E.g. Em-->B7-->D7--G (we use here the similarity of the sound because of common notes of the B7 and D7). 

5) Inverse a major-minor resolution (e.g. B7-->Em) to its major chord (here B) by utilizing the major Andalusian cadenza (Em-->D-->C-->B).(3rd majorization)

6) Pass from a resolution of one ot two minor chords e.g.  X7-->(x+1), to one with both major chords  Y7-->Y+1 E.g. From B7-->Em to D7-->G as in the progression B7-->Em-->C-->D7-->G. 

7) Even for sad melodies do not use more than 1/3 of the total number of chord-instances as minor chords. The rest 2/3 should be with major chords. But for highly joyous songs use only major chords and rather few (2-3) than many. 

The diatonic progressions is the sequence (iii->vi->ii->V->I->IV->VII->iii), e.g. in C major scale the sequence Em->Am->Dm->G->C->F->Em (Here the symbolism of Roman numerals as it is standard in jazz, it  refers to the order of the root of the chord in the scale, and it is capital if it is major and small if it s minor) This progression leads from sadness to joy, from the triad of minor chords to the triad of major chords. 

In a diatonic scale, the triad of minor chords (sad triad) is the (iii->vi->ii) where the (iii, vi) and (vi,ii) are consecutive in the cycle of pure 4ths, with standard resolutions (iii7-> vi) , (vi7->ii) and the 

(ii, iii) are complementary chords, in other words all of their notes give all the notes of the scale except one. 

The triad of joy or triad of major chords  is the (V, I, IV) , where the (V, I) and (I,IV) are consecutive in the cycle of pure 4ths, with standard resolutions (V7-> I) , (I7->IV) and the  (IV, V) are complementary chords, in other words all of their notes give all the notes of the scale except one. 

The bridge between these two triads is the well known jazz progression (ii7, V7, I) , where again  the (ii, V) and (V,I) are consecutive in the cycle of pure 4ths, with standard resolutions (ii7-> V) , (V7->I), and  the  (ii, I) are complementary chords, in other words all of their notes give all the notes of the scale except one. 

The diatonic progression closes also to a cycle by utilizing the triad progressions 

(IV->IV#7->VII7->iii) or (IV7->VIIb->vi). E.g. in C major scale, F->F#7->B7->Em