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.
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.
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.