Learn to improvise. 2003-2004. Lesson 05: related keys, 2nd dominant.

We know the keys C and Am. Now we will discuss the keys G and F.
C and G are related keys as their distance is a fifth (5 keysteps). The same holds for the keys C and F. Related keys are special as they differ in only one note.
By simply counting keysteps, the key of G can be derived from the key of C.
The chords of G are C, G and D7 (notes d-f#-a-c or f#-a-c-d).
The notes of these chords in a row give the scale of G: g a b c d e f#.
The note f# is the only one which differs from the scale of C.
As C and G differ in only one note, these keys are related in the 1st degree.
The key of F consists of the chords C, F and Bb (notes b b, d, f).
The scale of F is f g a bb c d e. Only note bb differs from the scale of C.
The dominant in the key of F is C, which usually is replaced by C7 (notes g-bb-c-e), as is common use for dominant chords.
The principle of playing in a different key is simply counting of keysteps, but in practice it is hard due to a complete different image of keyposition.
The limitation of the difference to only one note brings about a frequent use of related keys in a song. The initial key is e.g. C, but a little further D7 may appear (in folksongs), which means that at that moment the key is G, as D7 does not belong to C but to G.
The valid key (G) at that moment is a different one than the initial key (C).
(Who is used to sheetmusic might be inclined to think that the key can be obtained from the key signature. The composer however has put at the beginning only those sharps and flats which appear mostly in order to simplify writing and reading. He also leaves out the key signature for g# for the key of Am.)
So, as long as D7 is present we are in the key of G, and consequently, the note f is not belonging to the scale, is 'scale alien', or plainly false. You have to take this into account when making a melody.
Click here to hear an example.
The chord D7 usually is followed by the chord G. After all that's the key we are in; so it is a natural continuation.
The use of D7 has a fresh effect.
E.g. C D7 G C
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If we let chord G be followed by G7, the note f is present again, forcing the key to C. By bringing out this note f, especially when playing slowly, the changeover to another key is emphesized, which may be captivating.
E.g. C D7 G G7 C
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When playing fast G7 is hit right away.
E.g. C D7 G7 C
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In these cases of temporary modulation the initial key is kept in mind all the time.
As g is the dominant of c and d is the dominant of g, you could say: d is the dominant of the dominant of c. In other words: d is the 2nd dominant of c.
This can be extended: 3rd, 4th, 5th dominant.
E.g. (Mister Sandman) C B7 E7 A7 D7 G7 C ...
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The related key F of C can be seen in: C C7 F C
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An example where both the related keys (G and F) of C can be heard is:
C C7 F C   C D7 G G7   C C7 F C  C G7 C C
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HOMEWORK: Learn also the chords D7 and C7 and improvise on the following scheme:
C G7 C C   C D7 G G7   C E7 F C   C G7 C C
C7 C7 F F   D7 D7 G G7   C G7 C F   C G7 C C
Click here to hear an example.
Don't try to play my melody; make your own, but stick to the scheme; this example is only meant to explain my intention. Before being able to make a melody to a given scheme, you will first have to play the scheme without melody, in order to sense its possibilities.
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