The Secret Pattern of Music: The chromatic scale wound into a six-pointed star

If the twelve notes of the chromatic scale are written one after another on a hexagonal grid, in rings that grow by twelve cells each turn, the rings take the shape of a six-pointed star. This paper describes that construction, the Star of the Secret Pattern of Music, and the basic musical structure that follows from it with no choice other than the starting note. Twelve straight rays, the mother sequences, leave the centre; each one is the cycle of a single interval. The rays of fourths and fifths are one road travelled in both directions, and every ring read through its tips and joints spells an interval cycle, so ring 5 is the cycle of fourths and ring 7 the cycle of fifths. Three cells in line across the fifths ray form the twelve major triads in the order of sharps, and their mirror images across the fourths ray form the twelve minor triads in the order of flats. In one wedge of the star, every chord has a fixed shape, and a single eight-cell figure always produces a major scale. Translated step by step, the figure chains the twelve major scales around the circle of fifths, each one sharing four cells (a tetrachord) with the next. The supplementary script verify_star.py reproduces every verified result. System conceived by Áureo Puerta Carreño in 2016; earliest public record 21 April 2017 (Instagram @aureoguitar).