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%matplotlib inline
import librosa, librosa.display, numpy, scipy.signal, matplotlib.pyplot as plt, IPython.display as ipd
THX Logo Theme¶
Just released today, 25 May 2018. I'll refine this notebook later.
Today, THX posted the score of the original logo theme on Twitter.
Following the instructions in the score, here is my version of the THX logo theme. It may not be exactly the same, but it comes close.
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f_sustain = [450*x for x in [1/8, 1/6, 1/4, 1/3, 1/2, 2/3, 1, 4/3, 2, 8/3, 4, 16/3]] * 1
num_voices = len(f_sustain)
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f = [200*2**numpy.random.rand() for _ in range(num_voices)]
f_middle = [200*2**numpy.random.rand() for _ in range(num_voices)]
For this notebook, I will not use a typical vector broadcasting method that is typical in NumPy or Matlab. Rather, I will address each sample one by one. This strategy can reduce space requirements and ensure continuity of the signal.
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sr = 22050
t_incr = 1.0/sr
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t_start = 4
t_middle = 10
t_sustain = 14
t_end = 16
N = t_end*sr
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f_coef_start = [(f_middle[voice]/f[voice])**(t_incr/t_start) for voice in range(num_voices)]
f_coef_middle = [(f_sustain[voice]/f_middle[voice])**(t_incr/(t_middle-t_start)) for voice in range(num_voices)]
Amplitude coefficients.
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A_coef_up = 10**(t_incr/100)
A_coef_down = 10**(-t_incr/100)
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out_signal = numpy.zeros(N)
theta = [0] * num_voices
t = 0
A = 0.01
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for n in range(1, N):
for voice in range(num_voices):
out_signal[n] += numpy.sin(2*numpy.pi*theta[voice])
if t < t_start:
f[voice] *= f_coef_start[voice]
A *= A_coef_up
elif t < t_middle:
f[voice] *= f_coef_middle[voice]
A *= A_coef_up
elif t < t_sustain:
pass
else:
A *= A_coef_down
theta[voice] += f[voice]*t_incr
t += t_incr
out_signal[n] *= A
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out_signal /= out_signal.max()
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ipd.Audio(out_signal, rate=sr)
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C = librosa.cqt(out_signal, sr=sr, fmin=10, n_bins=100, hop_length=256)
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logC = librosa.amplitude_to_db(numpy.abs(C))
plt.figure(figsize=(15, 8))
librosa.display.specshow(logC, sr=sr, x_axis='time', y_axis='cqt_note', fmin=12, cmap='coolwarm')
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How does it compare to the original?¶
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original, sr = librosa.load('audio/thx_original.mp3')
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ipd.Audio(original, rate=sr)
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C = librosa.cqt(original, sr=sr, fmin=10, n_bins=100, hop_length=256)
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logC = librosa.amplitude_to_db(numpy.abs(C))
plt.figure(figsize=(15, 8))
librosa.display.specshow(logC, sr=sr, x_axis='time', y_axis='cqt_note', fmin=12, cmap='coolwarm')
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