### Learn to improvise. 2004-2005. Lesson 05: relationship between keys in degrees.

Sheet music has sharps and flats only for the initial major key. For improvisation we need to know that for the minor keys as well. The tabel shows the degrees of relationship between the keys.

major key C G D A E B F# F Bb Eb Ab Db Gb
number of sharps 0 1 2 3 4 5 5(6) 0 0 0 0 0 0
number of flats 0 0 0 0 0 0 0 1 2 3 4 5 5(6)

minor key Am Em Bm F#m C#m Abm Ebm Dm Gm Cm Fm Bbm D#m
number of sharps 1 2 3 3 3 4 0 1 1 0 0 0 5(6)
number of flats 0 0 0 0 0 0 4(5) 1 2 2 3 4 0

The system of sharps and flats is not nice for the following scales:
F# = f# g# a# b c# d# e# and Gb = gb ab bb c-flat db eb f
D#m = d# e# f# g# a# b c## and Ebm = eb f gb ab bb c-flat d
It is more practical to name the underlined notes inconsequently f, b en d.

From the initial key C music often modulates to the keys G, F or Am, as their scales differ from C in only one note (see tabel). If two notes differ the modulation is more striking. This is the case for the modulation from C to D, Bb, Em, Dm, or Cm (see tabel).
A clear way to confirm a modulation is to start the new key with a note that belongs to it but not to the old key. As an example we will look at 8 keys, at the most being different from C in 2 notes. See next tabel. The first column contains the name of the keys, the second one the number of sharps and flats (black keys) and in the next three columns the main chords with their notes (together making the scale). In the columns 'notes different in scales' one can see which notes does not belong to the scale of C (black keys).

key number of # b root dom.7 chord subd.chord notes different in scales
C none C=c+e+g G7=g+b+d+f F=f+a+c a b c d e f g
Am 1 # Am=a+c+e E7=e+g#+b+d Dm=d+f+a a b c d e f g#
G 1 # G=g+b+d D7=d+f#+a+c C=c+e+g a b c d e f# g
F 1 b F=f+a+c C7=c+e+g+bb Bb=bb+d+f a bb c d e f g
Dm 1# 1b Dm=d+f+a A7=a+c#+e+g Gm=g+bb+d a bb c# d e f g
D 2# D=d+f#+a A7=a+c#+e+g G=g+b+d a b c# d e f# g
Cm 2b Cm=c+eb+g G7=g+b+d+f Fm=f+ab+c ab b c d eb f g
Em 2# Em=e+g+b B7=b+d#+f#+a Am=a+c+e a b c d# e f# g

E.g. modulating from C to Am the note being different is g#. E7 contains it.
For C to G it is f#. D7 contains that one.
For C to F it is b-flat. Both C7 and the chord B-flat contain that one.
For C to Dm there are two notes being different. The one is c#, belonging to A7, the other is b-flat, belonging to Gm.

The thumb rule to enter a key is obviously the dominant seventh chord.
In a case as the modulation from C to Dm, also the subdominant chord (Gm) may be used as it contains the note b-flat being the different one.

C and Cm have the same dominant seventh chord, so this modulation does not follow the thumb rule. In this case first chords may be Cm and Fm as both have a note being different from C (e-flat and a-flat).
HOMEWORK: Start practising a key only after you can work with the previous one! An order of study may be: C, Am, G, F, Dm, D, Cm, Em ...
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