Learn to improvise. 2004-2005. Lesson 11: leading tones and chords.

What is the temporary key (C or F) if you are playing in key C and are going from chord C to chord F via C7? The answer is in key F, as note b clearly does not belong to the scale during C7.

A similar function has Caug. It contains a note (g#) leading from C to F. Caug is the third degree of Am, so you could say you are in de key of Am during Caug. Note g indeed does not sound to belong to the scale.

However... the notes b-flat and g# are so temporary in these cases that their leading function is much more pronounced than the temporary key. I consider them as leading notes and the chords C7 and Caug in these cases as leading chords. Also dim chords are used as leading chords.
C7 Caug C#dim7 Cdim7 with leading notes b-flat, g#, c#, d#+f#

Actually the feeling is ambiguous because you keep on asking whether you are modulating or using a leading note. Perhaps a blues captivates by this feeling during C7. A melody note b-flat (in C) asks for a solution. Think also of the enthralling seventh note in the Rumanian music. Unmistakably a seventh note gives an expectation.
Expectation by seventh note

There are more leading notes than the above ones.
Em with leading note b.

But especially the seventh note has always had the special attention of the researchers. The problem is the definition of the whole step (2 key steps), e.g. the proportion between c and b-flat.
Point of departure always is the frequency ratio 3/2 of the perfect fifth (7 key steps, e.g. c-g). E.g. if c would have 100 vibrations per second than g would have 150. The next higher c would have 200 vibrations per second. The ratio between that high c and the g is 200/150 = 4/3. That is a perfect fourth (5 key steps). A whole step (2 key steps) can be obtained by the difference of the fifth and the fourth (g-f). Actually it is no difference but a ratio, so we will have to divide in stead of subtract. So if c = 100 per second, than f = 4/3x100 per second, g = 3/2x100 per second and the result is a whole step = (100x3/2) divided by (100x4/3) = 3/2x3/4 = 9/8 = 1,125. So the note g vibrates 1.125 times faster than the neighboring note f. This definition is especially suited for the function of leading note from C to F.

But other definitions are possible. If you consider the major third (4 key steps, e.g. c-e) as the 5th overtone divided by 2 octaves, so 5/4 and you make the whole step (d-c) from fourths and thirds (c-f-b-flat-d), then you get fourth-fourth-major triad and divided by 2 to end up in the right octave, you will get a whole step = (4/3x4/3x5/4)/2 = 10/9 = 1.111

But a major third (c-e) also may be seen as the 5th overtone consisting of 2 whole steps. Then a whole step is the root from 5/4 = 1,118.

If you consider b-flat as the 7th overtone of c, shifted 3 octaves backward, then a whole step is 2x2x2/7 = 8/7 = 1,143

A piano has the equal temperament with a whole step being 2 to the power of 1/6 = 1,122 (This is fairly good to be used as a leading note as 1.125 differs less than 0.2% from 1,122).
All these seventh notes have their own atmosphere and might be used by the improviser who is not restricted to the piano (e.g. a singer). It also explains the charm of a detuned piano for special cases.
HOMEWORK: Use leading notes. Use the seventh note not only as a leading note, but also as a melodic element or in a mixolydian environment.
Seventh note as melody note.

Use it in a blues.
Seventh note in a blues.

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