Convergence to the Golden Ratio no. 1
Casey Mongoven
March 23, 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: 9
number of
intervals used: 8
temperament: series
of harmonic partials
lowest
frequency: 0 Hertz
highest
frequency: 898.8 Hertz
length: 21.2
seconds
note value:
2.65 seconds
waveform: square
0°
pan: see
sequence values
dynamic value: fff throughout
attack: .005
seconds
release: .008
seconds
pitches used:
# frequency in Hertz
0
0
1 42.8
2 85.6
3 128.4
5 214
8
342.4
13
556.4
21
898.8
sequence values
(harmonic partials used):
LEFT SPEAKER (-30°)
1 1 2 3 5 8 13 21
RIGHT SPEAKER (30°)
0 1 1 2 3 5 8 13
graph:
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