HARMONY

In this section we will learn some simple classical harmony which also applies to western folk music, or rock music, or simple jazz.

Index

Major scale

Classical harmony is based on two scales. The major and the (harmonic) minor scale. Let us begin with the major scale. C major scale: 
          W   W   H   W   W   W   H
        c   d   e   f   g   a   b   c'
        i  ii  iii  iv  v   vi vii
All the notes in the scale have a name: 
        i   : tonic
        ii  : supertonic
        iii : mediant
        iv  : subdominant
        v   : dominant
        vi  : submediant
        vii : leading tone
For the moment memorize the tonic (i), subdominant (iv), dominant (v) and leading tone (vii).

Triads

The following three triads are the most important chords in classical harmony: tonic, dominant, subdominant.

Tonic

The triad over the tonic note (in C major the C major chord : c e g) is also called tonic. We will note the tonic as I. A piece (written in the C major) usually begins with the tonic (C major) tonic and almost always ends with the tonic tone.

Dominant

The triad over the dominant note (in C major the G major chord : g b d) is also called dominant and is noted as V. The dominant chord contains the leading tone which tends to resolve to the tonic.

Subdominant

The triad over the subdominant note (in C major the F major chord : f a c) is also called subdominant and is noted as IV.

Note that the notes in these three chords cover the whole scale: 

               IV 
          +-----+---+
          |     |   |
          c d e f g a b 
          | | |   |   |
          +---+---+   |
          I |     |   |
            +-----+---+
                  V
Also note that all of them are major triads.

The most important seventh is the dominant seventh:

Dominant seventh

If we build the seventh on the fifth degree of the scale then we get a dominant seventh chord (that's why this kind of seventh is called dominant) (in C major the G7 : g b d f) and is noted as V7. The dominant seventh contains a diminished fifth (b - f) which is considered as dissonance and must be resolved. In the classical resolution the leading tone (b) goes to the tonic (c) and the seventh of V7 (f) goes to the third of I (e): 
            Resolution
            ----------
         *   f  --> e
             d  --> c (or e)
         *   b  --> c
             g  --> g
V7 forces I to come. Try playing C | G | C and then C | G7 | C to note the difference. How does C | G7 | F sounds? The tonic I, the subdominant IV and the dominant (seventh) V7 are the main chords for (all the) songs of western music. Some songs do not have any other chords. I will list these chords for the more important keys: 
              Key | I   IV  V7  |     notes of the diatonic
              ----+-------------+---------------------------
              Eb  | Eb  Ab  Bb7 |   !e  f  g !a !b  c  d !e
              Bb  | Bb  Eb  F7  |   !b  c  d !e  f  g  a !b
              F   | F   Bb  C7  |    f  g  a !b  c  d  e  f
        -     C   | C   F   G7  |    c  d  e  f  g  a  b  c
              G   | G   C   D7  |    g  a  b  c  d  e #f  g
              D   | D   G   A7  |    d  e #f  g  a  b #c  d
              A   | A   D   E7  |    a  b #c  d  e #f #g  a   
              E   | E   A   B7  |    e #f #g  a  b #c #d  e
              B   | B   E   F#7 |    b #c #d  e #f #g #a  b
Check out some popular songs you know and watch out for the presence and use of these chords.

Subdominant sixth

Another fairly often used chord is the major sixth on the 4th degree, the subdominant sixth (f a c d) which is noted as IV6 when the fifth is not present and as IV56 (5 below 6) if the fifth is present. [Note that it is the same chord with a minor seventh on the second degree]. From now on we will only note it as IV6 and enclose the fifth in parenthesis if optional.

ii-V-I progression

With the use of tonic, subdominant sixth and dominant seventh we can play the most played progression in the world of modern music, the so called ii7-V7-I progression, which is actually a IV6-V7-I progression. Why don't we call it then IV-V-I progression? A lot do. We saw that IV6 is the same with the seventh on the second degree. People like ii-V-I more because sevenths are more common than sixths and moreover the movement in the bass is better because of the fourth fall: d falls to g and g falls to c.

The other degrees

We introduced chords on the 1st, 4th and 5th degree of the diatonic scale. We can do the same with the rest notes of the scale. Before we do so we introduce the notion of parallel chords.

Parallels

A chord is parallel to another chord if it is a third away. For example Am is the parallel minor of C. The same way C is the parallel major of Am.

Tonic parallel

On the sixth degree of the scale is the parallel minor of the tonic. This is noted as Ip or simply vi. (Am in C major). I is capital because the tonic is major and p is small because the parallel is minor.

Dominant parallel

On the third degree of the scale is the parallel minor of the dominant. This is noted as Vp or simply iii. (Em in C major)

Subdominant parallel

On the second degree of the scale is the parallel minor of the subdominant. This is noted as IVp or simply ii. (Dm in C major)

Dominant seventh without root

On the seventh degree of the scale one finds the diminished triad which is a part of the dominant seventh. Therefore we denote the chord on this degree as V/7 or vii (The slash should come over V but that's not possible in ASCII). This chord relatively often replaces the V7 chord.

Now we have triads on all degrees of the diatonic major scale: 

              (c)         (d)   (f)
         g     a     b     c     d     e     f
         e     f     g     a     b     c     d
         c     d     e     f     g     a     b  
         --------------------------------------
         C   Dm(7)  Em    F(6)  G(7)   Am   Bmb5
         I   ii(7)  iii  IV(6)  V(7)   vi   vii-
[Note that the parentheses are not part of the notation. They should be erased if the optional note is present.] The dominant seventh V7 has the property that it establishes the key. One can find a (unaltered) G7 only in the key of C major, a C7 only in the key of F major, a D7 only in the key of G major and so on.

Secondary dominants

Each chord can be reinforced by playing its dominant seventh before it. A commonly used chord is the double dominant which is the dominant of the dominant. In C major, G is the dominant so D7 is the double dominant seventh. A double dominant coincides with II7, ie with the major second degree (Notice that normally the second degree is minor). Play: 
            chords :      C   D7   G7  C  (in C major)
        or  chords :      F   G7   C7  F  (in F major)
            -----------------------------
            harmony:      I   II7  V7  I
to get an idea of how it sounds. Note that a double dominant contains notes which are not in the scale. For example D7 is d #f a c, whereas #f is not in the C major scale.

Dominants of the rest of the chords are called simply secondary dominants. In the following we give all the secondary dominants of the C major scale. Secondary dominants are noted with a V in parentheses before the chord. 

          A7  Dm  ,  B7  Em  ,  C7  F  ,  E7  Am
         (V7) ii  , (V7) iii , (V7) IV , (V7) vi

As secondary dominants we can also have secondary subdominants. They are noted as (IV) before the chord. Double subdominant is the subdominant of the subdominant. In C major, F is the dominant and Bb is the double dominant. A double subdominant coincides with bVII, i.e with the major lowered seventh degree.

Indeed any degree can appear as secondary. As we said a common progression is the ii-V-I progression. This progression can be played before any minor or major chord in a scale: 

          Dm7 G7 C  ,  Am7 D7  G  
          ii7 V7 I  , (ii7 V7) V 

          Em7 A7  Dm  ,  F#m7 B7  Em  ,  Gm7 C7  F  ,  Bm7 E7  Am
         (ii7 V7) ii  , (ii7  V7) iii , (ii7 V7) IV , (ii7 V7) vi

Minor scales

If we now take the natural minor scale: 
          W   H   W   W   H   W   W
        a   b   c   d   e   f   g   a
        i  ii  iii  iv  v  vi  vii
then we notice that
  1. the tonic (a c e) is a minor chord and is noted as i.
  2. the subdominant (d f a) is also a minor chord and is noted as iv.
  3. the dominant (e g b) is also a minor chord and is noted as v.
The natural minor scale has no leading tone. Therefore it has no dominant seventh. The seventh in the fifth degree is a minor seventh. In order to restore this scale harmonically we raise the seventh (g -> #g); then we get a scale with a leading tone: 
      
          W   H   W   W   H   WH   H
        a   b   c   d   e   f    #g  a
        i  ii  iii  iv  v   vi  #vii
this is called the "harmonic" minor. That's why the name. We can now build a major dominant (e #g b) which is noted as V. The seventh on the fifth degree is also a dominant seventh (e #g b d) and noted as V7. With the help of the V7 we can establish the tonic t. The invented harmonic minor has an augmented second interval (WH) between the sixth and the seventh note. This does not sound melodically correct (I find it good sounding :-) so the sixth is raised too. Then we get the following scale: 
          W   H   W   W   W   W   H
        a   b   c   d   e   #f  #g  a
        i  ii  iii  iv  v  #vi #vii
which is called (guess why) "melodic" minor. Notice that within this scale we have a major subdominant too. Chords on all degrees of the diatonic natural minor scale: 
                     
         e     f     g     a     b     c     d
         c     d     e     f     g     a     b
         a     b     c     d     e     f     g  
         --------------------------------------
         Am   Bmb5   C     Dm    Em    F     G
         i    ii-   III    iv    v     VI   VII
Note that all the chords are the same with those of C major scale. But their function is different. Here is Dm iv, in C major it was ii and so on. Chords on all degrees of the diatonic harmonic minor scale: 
                      (b)   (d)
     e     f    #g    (a)    b     c     d
     c     d     e     f    #g     a     b
     a     b     c     d     e     f    #g 
     --------------------------------------
     Am   Bmb5  C+   Dm(6)  E(7)   F   G#mb5
     i    ii-  III+  iv(6)  V(7)   VI  #vii-
Chords on all degrees of the diatonic melodic minor scale: 
          (a)         (b)   (d)
     e    #f    #g    (a)    b     c     d
     c     d     e    #f    #g     a     b
     a     b     c     d     e    #f    #g 
     --------------------------------------
     Am    Bm   C+    D(6) E(7) F#mb5 G#mb5
     i    ii(7) III+ IV(6) V(7)  #vi-  #vii-
The minor scales offer a big repertoire of chords to play.

Other chords

The dominant ninth on the V degree. Noted as V9. In C major : G9 (g b d f a), in A melodic minor : E9 (e #g b d #f).

The half-diminished seventh on the vii degree. Noted as V/9 or vii7-5. It is a dominant ninth with no root. In C major : B7b5 (b d f a). In A melodic minor : G#7b5 (#g b d #f).

The (full) diminished seventh on the vii degree of the harmonic minor. Noted as V/b9 because of the lowered (minor) ninth wrt to the dominant or viio (The circle o denotes a full diminished seventh). In A harmonic minor : G#dim (#g b d f)

Altered chords

The following chords are called altered because not all of their notes belong to the scale they appear.

Neapolitan sixth

The lowered subdominant sixth of the (harmonic) minor scale. Noted as iv-6 or N6. In Am : Dm-6 (d f !b) is the same chord with Bb. Note that we don't include the fifth (a) in the Dm-6. As a seventh chord the neapolitan appears as a dominant seventh, i.e. Bb7 (!b r f !a), which means that the fifth of subdominant Dm is altered too.

Note that one can have a neapolitan sixth in a major scale. In this case one has to take the lowered sixth of the minor subdominant. For example in C major, iv-6 : Fm-6 (f !a !d) same with Db. The seventh Db7 is used too.

The neapolitan sixth can be noted as bII or bII7. This chord is a substitute for the dominant V7 both in major and minor mode. It is called the tritone substitution since the roots of bII7 and V7 are a tritone (diminished 5th) away from each other. Actually the chords V7b5 and bII7b5 are identical to each other.

Example: G7b5 : g b !d f and Db7b5 : !d f !!a !c. Check this out!

Altered dominants

The notes that should be raised or lowered are noted with # or b, or sometimes with + or - respectively. Examples: D7#5 or D7+5, D7b9 or D7-9, ....

The symbol "alt" is used to notate a dominant seventh with both altered fifth and ninth: Galt = G7b5b9 or G7#5#9.

Modulation

Sometimes a piece written in the key of C major modulates in the key of its relative minor Am or dominant G major or subdominant F major or whatever key you want. We say that a piece modulates in another key when it has changed the tonic to another key for some relatively long part of the piece. However changes of keys can be short too. A short change is noted with parenthesis when it ends to the tonic and with angle parenthesis when it does not end to the tonic (though excepted). Examples (these are right out of my head, I didn't even play them; who knows? they may sound good :-) : 
             D7  Gm (Em7 A7) D7) G7 C.
        C: ((V7) iv (ii7 V7) V7) V7 I

            [Bb Gm F7]  F C G7 C.
        C:  [I  vi V7] IV I G7 I.          
                     ^ here is Bb excepted
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