New Musical Theory Model Based on the Dodecahedron. We know about the circle of fifths. A quick review: In music theory, the circle of fifths (or circle of fourths) is the relationship among the 12 tones of the chromatic scale. It shows their corresponding key signatures. Also found arethe associated major and minor keys. Musical tones use 7 letters of the alphabet. They are A-B-C-D-E-F-G. These letters repeat over and over to encompass the full key signature span.
At the top of the circle, the key of C Major has no sharps or flats. Starting from the apex and proceed clockwise by ascending fifths. The key of G has one sharp. The key of D has 2 sharps….. Proceed counterclockwise from the apex by descending fifths: The key of F has one flat. The key of B♭ has 2 flats…… At the bottom of the circle, the sharp and flat keys overlap, showing pairs of enharmonically equivalent key signatures.
Click on the above internal link. It offers background on the 5 Platonic solids. The Platonic Solid we are concerned with here is the dodecahedron. In antiquity it symbolized the overall shape of the Universe. By this rational,we live in a musical Universe. As for the featured picture, note: The major keys are written in the center of each pentagon. Start in consecutive order (from C major) from its lower left point. The tone on the lower right completes the 5 tones. In the case of “C” major, it is the tone “G”. This lower right begins the next pentagon. It is completed at “D” …
Ascend 5 consecutive tones with each pentagon.
The fifth tone on the lower right of each pentagon defines the key signature name of the next pentagon. This goes for the complete cycle: “G major, D major, A major…”
The 12 pentagons make the complete cycle at F major. “F” major’s lower right hand tone is “C”. The outline of the dodecahedron is complete at this point.