Phi Pi melody

Phi and Pi in the melody Phi= (golden ratio) Pi= (Pi number) a=1, b=a/Phi, c=b/Phi (durations of notes) E = 8a 12b 4c (duration of the melody) E/ = Phi*Pi The melody has an interesting feature: if you take any pair of notes, then the durations of these notes will be in proportion to the golden ratio (Phi = ). Durations of notes: a = 1 second b = a / Phi () c = b / Phi () There are 8, 12 and 4 such notes in the melody. The total duration of the melody is seconds. If you divide the sum by 4, you get . This is the golden ratio in the third degree. Any 6 notes of the melody that sound one after the other add up to the Phi cubed. The degrees of the golden ratio The first 2 notes are Phi. The first 3 notes are Phi squared. The first 6 notes are Phi cubed. The first 9 notes are Phi to the 4th degree. The first 15 notes are Phi to the 5th degree. The first 25 notes are Phi to the 6th degree. The first 41 notes are 7th degree Phi. Symmetry If the melody is repeated several times and the second note is played in the middle of the repetition in any measure, then the durations to the left and right of the selected note will be symmetrical to each other. The same goes for the fifth note. If the duration of the second note is sequentially multiplied by Phi, then the obtained values ​​will be left and right, symmetrically to the selected note. The fifth note is the same. There is another kind of symmetry in the melody. Take any couple of notes. The durations of the notes equidistant from this pair will be in proportion to the golden ratio. Pi number and If the duration of the melody is divided by , then we get the product of the golden ratio and the number Pi (Phi * Pi = ).