Introduction to the Chromatic Spiral

The 12 music notes (including sharps and flats) are displayed like a clock. As the notes rise in pitch they move around the clock. When they are back at 12 they are they same note only up an octave. (At this stage the soundwave is twice as fast.) This video plays with this idea.

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Chromatic Spiral ~ Harmonic Series 3D

In previous versions of the Chromatic Circle I have introduced depth as a way of portraying pitch of notes but I’ve found it cumbersome. In researching for the Great Sphere I have come across the work of Marysol Gonzallez Sterling and her Biosonic webpage. There I saw the musical spiral amongst other things and it struck me as the obvious answer.

Here is the current version of the Chromatic Scale Spiral 3D as at 2013-05-23. The Spiral will be part of the Great Sphere.

Chromatic Spiral 2

The Spiral is displaying the Harmonic Series here. You can get more details on the Harmonic Series at the Wikipedia page but briefly it is a series of pitches present in all notes and the physics foundation for Western harmonic structure.

First_eight_harmonics_vertical 3D

Each note is another fraction along from the note before. If the low C pictured above is this first line (0-1) then the next C above that is the next line below (1/2). That’s an octave. The next note up is a 1/3 harmonic and lands on the G – the perfect fifth. The 1/4 gives an interval of a perfect fourth which brings us back to C. 1/5 makes a major third taking us to E, 1/6 is a minor third to get us to G and 1/7 is a subminor third to give us Bb. Next, the 1/8 gives us a supermajor second to get us back to C for the fourth time covering three octaves. And it doesn’t stop there.

Anyone with some musical theory knowledge will see that these notes make your standard chord. Although , the further along the series the less standard it is.

693px-Harmonic_partials_on_strings 3D

Music in the Great Sphere

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:

C-Major Scale

C-Major 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:

C-Major Scale with C-Minor Scale underplayed

C-Major Scale with C-Minor Scale underlayed

C-Minor Scale

C-Minor Scale

Getting back to the C major scale, let’s plot the C major chord that has the notes C, E and G:

C-Major chord: C,E and G

C-Major chord: 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.

Pythagoras was here

Pythagoras was here

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:

Pythagoras minor

Pythagoras 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.

The common chords I, IV, V and VI - C major, F major, G major and A minor

The common chords I, IV, V and VI – C major, F major, G major and A minor

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