The Great Sphere I have been working on is made up of many circles. As part of an investigation into the relationship between colour and the 12 notes of the Western chromatic scale I have found some interesting patterns. One of the patterns is from the relationship between the notes in western music. The major and minor scales have seven notes. The start of each cycle is called an octave. Today I will look at the C major scale. Here is a representation of the scale:
I have started at C at the top and threaded across the ring jumping thirds each time. From the tonic (C) we go to the major third (E), to the fifth (G), to the seventh (B), to the second (D), to the fourth (F), to the sixth (A) and finally back to the tonic again. One of the reasons I have chosen the C major scale is because it has no sharps or flats, and like a piano layout we can easily spot the groupings. Notice the two pairs of points that are close together, B & C, and E & F. Also where there are dark spaces are the 2 black keys, Db & Eb, and 3 black keys, Gb, Ab and Bb.
For a minor scale all you need to do is turn this asymmetrical seven pointed star 90 degrees:
Getting back to the C major scale, let’s plot the C major chord that has the notes C, E and G:
What first struck me when I drew up these lines is something that I had never noticed in my whole life of studying music. Because we are taught to think of the tonic triad as first, third and fifth, that is, two notes up the scale each time, I had not thought about how many chromatic notes there were between them. From the tonic (C) to the major third (E) are 4 chromatic notes, from the major third to fifth are 3, and from the fifth to the tonic are 5.
Is this something to do with Pythagoras’ Theorem? No, the numbers do not represent the lengths of the lines but the distance in notes and the angle at the E note is not a right angle. However the numbers 3,4 and 5 are the same and it is this relationship between the notes that we find pleasing. And it is not just the major chord it is also happening in the minor:
It is something that has sparked some interest for me to investigate Pythagoras a little more and in particular the Music of the Spheres.
The final picture today is of the common chords I, IV, V and VI – C major, F major, G major and A minor. The triangle shaped chords are coloured by the colour of the tonic of that chord. The paths that cross are then blended.
So there are quite a few interesting developments so far. The imagery of colours, rings and lines connecting points is inspired from astrology charts and dream catchers. This is the direction of my current study. For the previous post about the Great Sphere click here.
UPDATE: I have just uploaded this video