Convergence to the Golden Ratio no. 2
Casey Mongoven
March 24, 2005
description of
piece: a series of intervals derived from the ratios between
consecutive Fibonacci numbers (0/1, 1/1, 1/2, 2/3, 3/5, 5/8, …) showing
convergence to the golden ratio
number of
members in Fibonacci sequence used: 22
number of
intervals used: 21
lowest
frequency: 0 Hertz
highest
frequency: 413 Hertz
length: 54.6
seconds
note value:
2.6 seconds
waveform, pan: fixed
tone: sine 0°, -30°; moving tone: sine 180°, 30°
dynamic value: p
throughout
attack: .005
seconds
release: .008
seconds
pitches used:
decimal
frequency in Hertz
0
0.000000000
1
206.5000000
2
413.0000000
1.5
309.7500000
1.666666667 344.1666667
1.6
330.4000000
1.625
335.5625000
1.615384615 333.5769231
1.619047619 334.3333333
1.617647059 334.0441176
1.618181818 334.1545455
1.617977528 334.1123596
1.618055556 334.1284722
1.618025751 334.1223176
1.618037135 334.1246684
1.618032787 334.1237705
1.618034448 334.1241135
1.618033813 334.1239825
1.618034056 334.1240325
1.618033963 334.1240134
1.618033999 334.1240207
sequence
values:
LEFT SPEAKER (-30°)
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
RIGHT SPEAKER (30°)
0 1 2 1.5 1.666666667 1.6 1.625 1.615384615 1.619047619 1.617647059 1.618181818 1.617977528 1.618055556 1.618025751 1.618037135 1.618032787 1.618034448 1.618033813 1.618034056
1.618033963 1.618033999 1.618033985
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