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Practising with Dominant seventh Chords.
It is time now, that one tries to understand the circle of fifths concept. We have seen before, that the function of the dominant chord is to "smoothly land" on the tonic chord by an opposite motion from its seventh and third degree going upwards and downwards to the tonic chord. (See Chord II). The example below starts from C and leaps counterclockwise to all the Circle of Fifths chords. (See picture).

Note that:

  • C chord (I degree) is the starting  Tonic.
  • C7 then belongs to F Key or tonality and the last two measures.
  • C7, (B flat, seventh) and (E, third) resolve respectively to (A, third, and (F, tonic) note.  
  • F becoming then the New tonic. (and so on until one reaches C again) 
  • This technique is called, modulating to the dominant.
    • Remark: C7, can not be compared to a pivot chord, although it is placed in the middle of C and F.  A Pivot chord belongs to the previous and next tonality, whereas C7 , here, belongs uniquely to F key.

The Circle of Fifths scales practice will give an example of using a scale with its relevant chord, following the Circle of Fifths counterclockwise. Another point here to mention, is, tritone sharing.  G7 and Db7 share the same tritone. See the picture below. 

The Dominant Substitutes.

Another point here to mention is Tritone substitution. The tritone substitution can be performed by exchanging a dominant 7th chord for another dominant 7th chord placed in the opposite position. See below. G7 -- D flat7.  See Circle of Fifths. It is then possible, to use chord substitution (SubV7) to improvise in G7 under a D flat7 chord.

Tritone Sharing exemple: in red, F note, in G7 and Db7 chords. In brown, B note in G7 and Db7 chord.  

The Dominant Seventh (V7) chords and The Substitute Dominant Chords (Sub V7) Table: 
On the extremity of the table, one has, on the left row, dominant (V7) chords, and Subdominant chords (SubV7) on the right row. See Tritone in the middle of the table. Notice, that C7 and F#7 share the same triton, not matter if they are in a reverse position.

In the video below, and for reading convenience, Tritones in all Dominant 7th chords are always placed at the same place.