Sat Jun 19 19:44:53 CEST 2010

Jazz & 7th chords

Some of the things I learned about scales and chords recently.  

1. Where do the basic chords come from?  From the diatonic scale:

     T T s T T T s
    C D E F G A B C'
    1 2 3 4 5 6 7 8

It's simplest to do this on the (piano) keyboard, using the white keys
only (key of C major).  Transposition to other keys give rise to more
sharp/flat (black) notes in the scale.  This is largely a technical
issue (and imho a disadvantage of music notation when equal
temperament is used..)

Western music is largely based on these 12 tone intervals.  Here they
are annotated with their occurence in the diatonic scale:

m2  Semitone       s
M2  Whole tone     T
m3  Minor third    Ts, sT
M3  Major third    TT
4   Perfect forth  TTs, TsT, sTT
b5  Tritone        TTT, sTTs
5   Perfect fifth  TTTs, TTsT, TsTT, sTTT
m6  Minor sixth
M6  Major sixth
m7  Minor seventh
M7  Major seventh  

One of the most remarkable properties of the diatonic scale is that it
contains a large number of perfect fifths: only the one starting at
the 7th contains a flat fifth (B-F' or 7-11).  The same goes for their
inversions the perfect forths.

Chords can now be built by stacking two major and minor 3rds (= third
and fifth) Building them directly from the diatonic scale gives:

 C Dm Em F G Am Bdim

Three major/minor chords containing a major/minor third, and one chord
with a minor third and a flat fifth: a diminished triad.

Triads      stack    root + interval
Major       M3 m3    M3, 5
Minor       m3 M3    m3, 5
Diminished  m3 m3    m3, b5

2.  What about jazz?  Use quads by adding a 7th.

7th chords are 3 3rd intervals on top of each other, or a 3, 5 and 7
from the root.  The most important components in a 7th chord are the 3
and 7, which are called the color tones.  They are a 5th apart.  

It's often OK to leave out the 1 or 5 if the harmonic context is clear
enough.  A 7th chord can also be though of as a triad extended with a
bass note.  I.e. with a clear bass note C context, an Em chord sounds
like a Cmaj7 chord.  ( Music is inherently ambiguous! )

There are more possible combinations for 7th chords.  There are 5 with
perfect fifths:

  root intervals  ex     third stack  name
  1 3  5 7        Cmaj7  M3 m3 M3     Major seventh
  1 b3 5 b7       Cm7    m3 M3 m3     Minor seventh
  1 3  5 b7       C7     M3 m3 m3     Dominant seventh

Lowering the 5th and 7th gives 3 more with flat fifths:

  1 b3 b5 b7      Cm7b5  m3 m3 M3     Half diminished seventh
  1 b3 b5 bb7            m3 m3 m3
  1 3  b5 b7             M3 2  M3

The first 4 come from the diatonic scale by stacking thirds:
   Cmaj7 Dm7 Em7 Fmaj7 G7 Am7 Bm7b5

The other 2 do not occur on the diatonic scale.  

So, a 7th chord is:

  - bass note + 5th (color interval), stacked at 3rd
  - stack of 4 3rds
  - two thirds, separated by a fifth

3.  Progressions

In western music the cadence V-I is an important base for many chord
progressions.  The II-V-I in jazz is two 5ths down (4th up = 5th

I don't have a very clear picture here, but it seems to boil down to
progressions within a key (i.e. that stay in the same scale) and those
that modulate to a different key.

[1] http://en.wikipedia.org/wiki/Musical_mode