Recently one of my friends who plays guitar said he wants to learn music theory, because he learned that if the major key of a song is known, several chords in related keys can be expected. For example, a C major chord usually comes with an A minor chord. This is useful when he accompanies a song, or improvise. I was immediately shocked that this relationship is already written in Hanon's The Virtuoso Pianist in 60 Exercises in the scales exercises, which I started to play a long while ago, but no one told me the use of it. Instead, my dear friend who knew nothing about Hanon, or piano scales, already knows these chord relationships.
In The Virtuoso Pianist in 60 Exercises, there are 12 sets of scales, each of which presents one major and two minors (harmonic and melodic minors). Thus totally there are 36 different kinds of scales. If we relate two different scales when there is only one note, out of the 7 notes, to be changed to become another scale, we can generate a network of scale relationship. For example, C-major can easily turn into A minor (harmonic) by changing G to G#. I wrote a program to search for all pairs that have this relationship (only need to match 36x36 times), and got the image above. It can be seen that C major can turn into two different majors (C and G) and three minors (C-melo, A-har, and D-mel). What may be less known is that C is closely related to D-mel, which means that a C tone can turn into a D tone smoothly, by firstly turning into D-mel. This finding, with the network, may be useful in composing...hopefully someone who knows composing can tell me whether it is useful. At least, there is already a simple chart in Wikipedia:
PS.
In my scale relationship chart, the melodic minor represents the ascending part. The descending part is the nature minor, which has the same key signature of the related major scale. Therefore we don't have to duplicate the scales.
The scale relationship chart is made of the little interactive widget below. (Please use your browser to zoom in to have a bigger image.)
