Why 109?
Firstly, I divided the first notes of the Iannix Xenakis work ‘Pshappha’ into 6 groups with 12 intervals (dodecaphonic system).
In this way, there are 109 musical notes into these 6 groups.
Group I, 16
notes; group II, 16 notes; group III, 16 notes; group IV, 16 notes; group V,
16(+25)notes and the group VI, 14 notes.
Next, I considered double notes as a single one (because I belive the silence between notes is important).
Although ‘Pshappha’ are made for percussion solo, I traslated it into a different notation, slowly and calmly. It has been made with the keyboard of the synthesizer ‘Dexed’ that is closely modeled on the Yamaha DX7. All in all, the work lasts 7 minuts 54 seconds (7+5+4=16, wich refers to 1.6, the beginning of the Fibonacci’s sequence). The entire 109 project is more or less free but the selected Xenaki’s score appears from 0.00.00 to 0.04.54. From then until the end, part of the first cycle is repeated.
I belive there’s a secret under the number 109:
The number 109 is related to the Fibonacci sequence (particularly with the number 89) https://www.goldennumber.net/89-and-109/
If we divide 1/89, the result is 0,0112359550561798... (+44
characters!) and the first six numbers belong to the Fibonacci sequence.
Then, if we divide each number of the sequence between 10 (1+0+9=10) raised to the power of his position in the Fibonacci sequence then...
- 1/89 = 0,0112359550561798..
- 0/101 = 0
- 1/102 = 0,01
- 1/103 = 0,001
- 2/104 = 0,0002
- 3/105 = 0,00003
- 5/106 = 0,000005
- (...)
Of couse,the Fibonacci’s sequence (11235) is repeated in the beginning and end.
And, if we divide 1/109 we have a decimal with 108 characters: 0,0091743119266055(...)53211. The last 5 numbers are the Fibonacci sequence in reverse order.
And, if you take each number and divide it by 10 (1+0+9=10) raised to the power of 109 minus its position in the Fibonacci sequence, then:
- 0/10109 = (...)0
- 1/10108 = (...)1
- 1/10107 = (...)1
- 2/10106 = (...)2
- 3/10105 = (...)3
- 5/10104 = (...)5
- (...)
Again the Fibonacci’s sequence (11235) with the number
109.
Note: The diameter of the sun is 109 times wider than Earth https://spaceplace.nasa.gov/sun-compare/en/
Microstructures by a confined present. Music: inèrcies, based on the work psappha, Iannis Xenakis. Words, inèrcies 2021.