An example of the use of the Golden Ratio (or Golden Section) by Eric Satie. The Golden Ratio is a mathematical equation Satie kept in mind while creating the proportions of each section in this third movement of "Sonneries de la Rose + Croix".
Notice the A section is composed of the harmony by itself, melody by itself, and then harmony and melody but up an octave. The B section brings the melody and harmony together in the original octave before concluding with the harmony by itself. The ratio between the length of the A section and B section gives us the Golden Ratio.
Also listen for the harmonic emphasis on B Major and F Major (on complete opposite ends of the circle of 5ths), especially B Major in the transition and F Major cadencing at the end of the sections with harmony alone.
While the original work may have been for trumpets and harp, this interpretation focuses on the bell-like "Sonneries" or "Ringing" heard at the opening and closing of the work.
#Sonneries #Rose+Croix #SatieAnalysis