Jean Grand-Maitre and I are creating a 30 minute ballet inspired by the wonderful magic of Phi. It has long been used overtly as a device, used most notably my Bartok, Webern, Nono, and even Debussy. Most uses I have observed and read about use phi as a formal or rhythmic device. I myself have used phi as a catalyst and inspiration, in my doctoral thesis St Croix, and in Talking Down the Tiger. In this piece, I wanted to explore phi melodically and harmonically. After several weeks of research, I was very pleased with the results:
This is a matrix I created using phi. It is the amalgam of 2 smaller melodies (AKA hexachords), shown here.
Interesting facts on PHI: any 10 consecutive fibonacci numbers added up will give a sum which is divisible by 11 (and the 7th number of any 10 consecutive numbers, if multiplied by 11, will give the sum of those same 10 numbers!). I Thank Mario Livio for this insight, in his wonderful book “The Golden Ratio”
This is particularly interesting to me as I had inadvertently created an 11 note ‘row’ (much like a 12 tone row used by serialists). Interestingly, the missing pitch is the tritone, the most dissonant interval. This happened quite by chance. Using 1 and the pitch C, Db is 2, D is 3, and so on. As one proceeds this way in either an upward or downward direction, the pitch F# does not appear for quite some time (at least until the 30th number in the series. Eventually it probably appears, but I have yet to test it beyond the 1st 30 numbers).
Here is the melody derived using Fibonacci numbers, going up and down in alternation: