Harmony Workbook 1

Harmony workbook 1. Nomenclatura 2. Diatonic chords in relation to the tonal center 3. Diatonic cadence in relation to the harmonic rhythm 4. Secondary dominants 5. Tritone substitution 6. Diminished chords 7. Chord scales 8. Modal interchange 9. Subdominant minor cadence 10.Modulation

2. Diatonic chords are triads or four note chords which contain only notes of the major or minor scale.

Ex.2.1: The diatonic triads in the scale of the C melodic major scale ( also known as Sankarabharanam in south-, Bilaval in north Indian music)

C Dmin Emin F G Amin Bdim w w & w w w w w w w wI wIImin wIIImin wIV V VImin VIIdim S R3 min G3 min M1 P D2 N3 dim Triads are common in classical harmony and folk- and pop music

Ex.2.1.1 In functional jazz harmony (Bebop & Hardbop) four note chords are prefered, because they give a more distinctive dominant chord (V7)

7 7 7 7 7 7 7b5 Cmaj Dmin Emin Fmaj G Amin Bmin w w w w & w w w w w w w Imaj7w IImin7w IIImin7w IVmajw 7 V7 VImin7 VIImin7b5 S maj7 R3 min7 G3 min7 M1 maj7 P 7 D2 min7 N3 min7b5

Ex.2.2: the diatonic four note chords in the scale of the C harmonic major scale (Sarasangi in south Indian music)

7 9b5 7 (maj7) 7b9 13 7#9 7b5 Cmaj Dmin Emin Fmin G A maj Bmin b bw w w w w w w & w bw w bw w bw w Imaj7w IImin7b5w IIImin7w IVmin(maj7) V7b9 13 bVImaj7#9 VIImin7b5 ©Rainer Pusch

Ex.2.3: the diatonic triads in the scale of the C harmonic major scale

C Ddim Emin Fmin G A aug Bdim b w w w bw & w bw w bw w bw w I w IIdimw IIIminw IVminw V bVIaug VIIdim

3. Diatonic cadence in relation to the harmonic rhythm Two notes of a scale seperated by a half step create a melodic energy. The less stabel note (less related to the tonal center) wants to resolve to the other. In the major scale in tertian harmony the 4th resolve to the 3 and the ♮7 to the 1. For that reason chords of the scale which contain 1 or both notes want to resolve . Chords which contain the 4th note only we call subdominant and chords which both notes dominant.

3.1 harmonic functions of diatonic chords:

tonic subdominant dominant Imaj7 IVmaj7 V7 strong VImin7 V7sus4 ↨ IIImin7 IImin7 VIImin7b5 weak strong ←—————→ weak

3.2 harmonic rhythm

In a 4/4measure the 1st and 3rd quater note are strong the 2nd and 4th note are weak.

strong weak strong weak

& œ œ œ œ

In 2 4/4 measures the 1st and 3rd half note are strong the 2nd and 4th note are weak. strong weak strong weak

& ˙ ˙ ˙ ˙

in 4 4/4 measures, the first and the third one is strong and the second and fourth one is weak

©Rainer Pusch strong weak strong weak

in superposing a strong chord on a strong time unit and a relatively weak chord on a weak time unit we get a balanced cadence

Ex.: Turnaround strong weak strong weak Imaj7 VImin7 IImin7 V7 Ex. 2.2 Mack the Knife strong weak strong weak strong Imaj6 IImin7 IImin7 V7 Imaj6 VImin7 IImin7 IImin7 V7 Imaj6

3. Secondary dominants

Secondary dominants are dominants which resolve into diatonic chords and are named in relation to their specific diatonic resolution: V/II, V/III, V/IV, V/V, V/VI, V/VII i.e.: five of two, five of three, etc. In general they are placed on weak time units. All dominants are often prepared by their related IImin7 chord.

Ex. 3.1 : the first 8 bars of "You are the sunshine of my life"

I IVmaj7 #11 IIImin7 V7b9b13/II C G/F Emin7 └─── ───┘ A7b9b13 IImin7 V7 Imaj7 IImin7 V7 Dmin7 └─── ───┘ G7 Cmaj7 Dmin7└‒┘ G7

4. Chord scales *)

If you build chords with diatonic thirds up to the 13th degree, you get seven part harmony. If one of he notes is an avoid note (x) the resultant chord will sound very dissonant, because the avoid note creates a b9 interval with one of the other notes and/or destroys the harmonic function. The only exception for chords in thirds is the V7b9 chord, where you look for dissonance to get more kinetic energy. Now we transpose the upper 3 notes (so called tensions) down an octave and we receive the ©Rainer Pusch correspondingchord scale. All notes of this scale besides the avoid note can be played on any time unit, while the chord sounds. The avoid note should be treated like all other notes as a passing note, i.e. in general on a weak time unit which resolves to the nearest scale note on a strong time unit. If the melody ends on a weak time unit this unit becomes an anticipation of the strong one and you have to treat it like that. Keep in mind that the high notes are weaker in the bottom of the structure and vice versa. So they become in these positions very useful diatonic passing notes. *) For other chord scales check out the “chord scale relation chart”

! Ex.:2.5: the diatonic four note chords in the scale of the C harmonic major scale

Ex.1.2: la gamme C-majeure harmonique

Ex. 1.3: la gamme C-eolienne

Ex.1.4: la gamme C-mineure harmonique

Ex.1.5: la gamme C-mineure mélodique

©Rainer Pusch

5. Modal interchange

If you borrow a harmonic function from another scale with the same root you get a so called modal interchange.

Ex.: The first 2 bars of "Night and Day"

IImin7b5 V7b9b13 Imaj7 Dmin7b5 └─── ───┘G7b9b13 Cmaj7 (C-harmonic minor) (C-ionian)

Ex. 5.1: the 9th bar of the B part of "You are the sunshine of my life"

VImaj7 V/VI VImin VImin(maj7) VImin7 └──────┘ Amaj7 Amin Amin(maj7) Amin7 Bmin7 E7b9b13 (A ionian) (A aeolian \ harmonic minor \ aolien ou dorian)

5.2 Subdominant minor cadence

This is a special modal interchange used in a lot of standard songs. The Vimin7 bVII7 progression is borrowed from the corresponding aeolian mode. It resolves most of the time into the tonic.

Ex.: The first 8 bars of "Misty"

Imaj7 V/VI IV IVmin7 bVII7 └──────┘ └──────┘ Ebmaj7 Abmaj7 Bbmin7 Eb7 Abmin7 Db7 (Eb ionian) (Eb aolien)

©Rainer Pusch Imaj7 Vimin7 IImin7 V7 IIImin7 V7/II IImin7 V7 └──────┘ └──────┘ └──────┘ Ebmaj7 Cmin7 Fmin7 Bb7 Gmin7 C7 Fmin7 Bb7 (Eb ionian)

6. Triton substitution

If you substitute a V7 chord wth a V7 chord a triton (#4) away you get a “chromatic dominant” or the triton substitute dominant (subV7) The harmonic function is the same because the guide tones, which line out the function, are the same. The b7 becomes the 3rd and the 3rd becomes the b7. The corresponding IImin7 chord can be substituted the same way. I n doing this you get 4 cadences, which sound differently, but their harmonic function is the same.

IImin7 V7 I └──────┘ ⎯⎯→ C Dmin7 G7 IImin7 subV7 I └─ ── ─┘ ⎯ → Dmin7 Db7 C subV7 I └──────┘ ⎯ → Abmin7 Db7 C V7 I └─ ── ─┘ ⎯⎯→ C Abmin7 G7

Ex.: the first 4 bars of "One Note Samba" IIImin7 subV/V IImin7 subV7 └─ ── ── ─┘ ⎯ → └─ ── ── ─┘ Dmin7 Db7 Cmin7 B7

7. Diminished chords

7.1 In chromatic upward movements the dim chords are dominat chords without root. (C7 9 = C E G bB D / E07 = EdMin7 = E G bB D)

Ex.: First 2 bars of "It Could Happen To You"

©Rainer Pusch Imaj7 V7/II IImin7 V/III ⎯⎯→ Ebmaj7 C7 Fmin7 D7 Imaj7 #Idim7 IImin7 #IIdm7

Ebmaj7 Edim7 Fmin7 F#dim7

2. In chromatic downward movements the reharmonisation with a secondary dominant or subV7 is possible. But the sound is different.

IIImin7 bIIIdim7 IImin7 Emin7 Ebdim7 Dmin7 IIImin7 V7/II IImin7 └─── ───┘ ⎯⎯→ Emin7 A7 Dim7 IIImin7 subV7/II IImin7 Emin7 Eb7 Dmin7

7.3. Remplacement of the diatonic function

Ex.: "Spring is here"

Idim7 Imaj7 Idim7 Imaj7 Abdim(maj7) Abmaj7 Abdim(maj7) Abmaj7 Reharm: VII7 Imaj7 VII7 Imaj7

G7b9 Abmaj7 G7b9 Abmaj7

7.4. #IVdim7 resolves to the V or often into the I chord with the 5th in the base.

Ex.: 4th bar of "Hard Times" IVmaj7 #IVdim7 I/5 Abmaj7 Adim7 Eb/Bb

You just have to fill the wholes between the minor thirds of the dim chord with notes of the scale of the tonal center in which you analyse the dim chord

Ex.: #IIdim7 in the tonal centre of C

The half notes are the notes of #IIdim7 = Ebdim7. The quarter notes are the notes of the C melodic major (Ionian) scale. The resulting scale in this case is mode 7 of E harmonic minor. If you prefer the note F instead of E, go for it! Your ear is the judge

8. Modal cadences

The chords of a scale which contain not the characteristic note (avoid not) of the scale become tonic function (strong) The chords of of a scale which contain the characteristic note (avoid not) of the scale become dominant function (weak) Be careful with chords (specially in tonic function) which contain a triton, because they have a strong tendency to function as normal V7 chords. Now you just have to place these chords on strong or weak time units depending on their function and you got a cadence, which produces the sound of your scale.

Ex.: "My Favorite Thing" Imin7 IImin7 Imin7 IImin7 Emin7 F#min7 Emin7 F#min7 strong weak strong weak The characteristic note in E dorian is the 6 = C# n

9. Mediant cadences are movements in the cycle of thirds (small or large). They replace often diatonic II-V-I cadences or turnarounds

Ex.: "Countdown"

©Rainer Pusch IImin7 V7/bVI bVImaj7 V7/III IIImaj7 V7 Imaj7 ⎯⎯→ ⎯⎯→ ⎯⎯→ Emin7 F7 Bbmaj7 Db7 Gbmaj7 A7 Dmaj7 IImin7 V7 Imaj7 Imaj7 └───────── ─┘ ⎯⎯→ ────────── Dmaj7 Dmaj7 A7 Emin7

Ex.: The last 2 bars of "Isotope"

I7 VI7 #IV7 bIII C7 A7 F#7 Eb7

10. Constant structures are chord progressions with only one chord quality

Ex.: The last 2 bars of "Lady Bird"

Imaj7 bIIImaj7 bVImaj7 bIImaj7 Cmaj7 Ebmaj7 Abmaj7 Dbmaj7

Ex.: "Maiden Voyage" I7sus4 D7sus4 bIII7sus4 F7sus4 I7sus4 D7sus4 bIII7sus4 F7sus4 bII7sus4 Eb7sus4 VII7sus4 C#7sus4 I7sus4 D7sus4 bIII7sus4 F7sus4