Convergence to the Golden Ratio no. 5
Casey Mongoven
May 16, 2005
description of
piece: Fibonacci sequence used on both speakers; right
speaker trails the left by 1 member of the sequence, showing how adjacent
members of the Fibonacci sequence converge to the golden ratio interval in the
harmonic series
number of
members in Fibonacci sequence used: 14
number of
intervals used: 13
temperament: series
of harmonic partials
lowest
frequency: 8.0796 Hertz
highest
frequency: 3046.0092 Hertz
length: 51.61
seconds
note value:
3.97 seconds
waveform: square
0°
pan: see
sequence values
dynamic value: mp
throughout
attack: .005
seconds
release: .008
seconds
pitches used:
# frequency in Hertz
1 8.0796
2 16.1592
3 24.2388
5 40.398
8 64.6368
13 105.0348
21 169.6716
34 274.7064
55 444.378
89 719.0844
144 1163.4624
233 1882.5468
377 3046.0092
sequence values
(harmonic partials used):
LEFT SPEAKER (-30°)
1 1 2 3 5 8 13 21 34 55 89
144 233
RIGHT SPEAKER (30°)
1 2 3 5 8 13 21 34 55 89 144 233 377
graph:
