From: dranidis@informatik.uni-muenchen.de (Dimitris Dranidis)
Subject: THEORY: About the sixth chords, cadences, and so on.....
Date: Thu, 26 May 1994 10:35:53 GMT


    This is a post about sixth chords.
    Someone has mentioned that sixth chords as for example F6,
    are not technically a part of traditional harmony. Well I 
    disagree.......

    NOTE:
    You should not read this if you are not interested in theory.
    It became longer than I thought....
    
    -- 
    
    A (major) sixth chord is almost so old as a seventh chord.
    The whole story begins with the creation of cadences....
    
    Cadences are chord progressions which establish a scale.
    Let's take the major C scale (which else?)
    
    C D E F G A B 
    
    A chord you can begin with is the C major chord, i.e.the I: 

    C D E F G A B 
    |   |   |
    +---+---+
    I
    
    So three notes of the seven are established.
    The second chord you will probably use is the dominant V. Why? Because
    its interval from the root is a perfect fifth, which was (and is)
    considered a very consonant interval. 

    C D E F G A B 
    | | |   |   |
    +---+---+   |
    I |     |   |
      +-----+---+
            V
    
    So, now two notes (F and A) remain unestablished (they did not sound yet).
    F and A build a major third. You can stack a minor third above them 
    to build the F major chord (F A C), the IV:

          IV
    +-----+---+
    |     |   |
    C D E F G A B 
    | | |   |   |
    +---+---+   |
    I |     |   |
      +-----+---+
            V

    Or, you can stack a minor third below them to build the 
    D minor chord (D F A), the ii:
    
      ii   
      +---+---+
      |   |   |
    C D E F G A B 
    | | |   |   |
    +---+---+   |
    I |     |   |
      +-----+---+
            V
            
    Both choices complete the scale.  You have certainly heard a lot of people
    talking about IV-V-I or ii-V-I progressions. These are also called 
    cadences.

    In classic harmony the first choice won, that is the I-IV-V cadence. Why?
    For the same reason that we started with the I-V scheme. The IV degree of
    the scale falls a perfect fifth below the first degree. 

    +---+---+       
    |       |        
    F G A B C D E F G  
            |       |
            +---+---+

    In classic harmony one ususally speaks about functions. There are three 
    main functions: 
        a) Tonic, the I (C major), 
           ...thats home....
        b) Dominant, the V (G major), a fifth above the Tonic, 
           ...the way towards home...
        c) Subdominant, the IV (F major), a fifth below the Tonic, 
           ...the way away from home...

    (Now we are approaching the sixth....patience....)
    
    Two of the first chords used except the three above, were the:
        a) Dominant seventh (G7), [flat seventh]
        b) The Subdominant sixth (F6), [major sixth]
    We all know and are familiar with the dominant seventh: (G B D F).

    Lets take a look at the subdominant sixth: F6 (F A C D). Well you'll say
    thats a Dm7, and I'll say you're right. However in this context it has 
    the function of a subdominant, thats why we call it F6 and not Dm7.
    Take also a look at the diagram:
    
          IV
    +-----+---+
    | ii  |   |
    | +---+---+
    | |   |   |
    C D E F G A B 
    | | |   |   |
    +---+---+   |
    I |     |   |
      +-----+---+
            V
    
    As you can notice, F6 (or Dm7) is simply a combination of the IV and 
    the ii, and it solves the problem of deciding which chord to choose
    in order to complete the I-V cadence.  You have certainly heard of
    the ii7-V-I progression (people playing jazz always refer to this
    progression). Well people with a classical background may call 
    this progression a IV6-V-I progression.
    
    Thats the story about the major sixth...
    
    ---
   `&'
    #    e-mail: dranidis@informatik.uni-muenchen.de   Dimitris Dranidis    
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