102 lines
2.7 KiB
Python
102 lines
2.7 KiB
Python
import bisect
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import math
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import struct
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import sys
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# Number of times to sample each second
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bitrate = 44100
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music = []
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def saw(x):
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"""
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Sawtooth wave
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"""
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return x / 2 / math.pi % 1
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def freq(octave, step):
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"""
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Returns the frequency of a note
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"""
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return 55 * 2 ** (octave + step / 12 - 1)
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def droplet(f, t):
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"""
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Returns the intensity of the "droplet" waveform of frequency f sampled at time t
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https://dsp.stackexchange.com/questions/46598/mathematical-equation-for-the-sound-wave-that-a-piano-makes
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https://youtu.be/ogFAHvYatWs?t=254
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"""
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w = 2 * math.pi * f
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Y = 0.6 * math.sin(w * t) * math.exp(-0.001 * w * t)
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Y += 0.2 * math.sin(2 * w * t) * math.exp(-0.001 * w * t)
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Y += 0.05 * math.sin(3 * w * t) * math.exp(-0.001 * w * t)
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Y += Y * Y * Y
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Y *= 1 + 16 * t * math.exp(-6 * t)
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return Y
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def seething(f, t):
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"""
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Returns the intensity of the "seething" waveform of frequency f sampled at time t
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"""
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w = 2 * math.pi * f
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Y = 0.6 * math.sin(w * t) * math.exp(-0.0005 * w * t)
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Y += 0.1 * math.sin(0.99 * w * t) * math.exp(-0.0005 * w * t)
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Y += 0.1 * math.sin(1.01 * w * t) * math.exp(-0.0005 * w * t)
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Y += 0.2 * math.sin(2 * w * t) * math.exp(-0.0005 * w * t)
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Y += math.copysign(Y * Y, Y)
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Y *= 1 + 16 * t * math.exp(-6 * t)
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Y *= 0.5 * min(24 * t, 1)
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return Y
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def honk(f, t):
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"""
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Returns the intensity of the "honk" waveform of frequency f sampled at time t
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"""
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w = 2 * math.pi * f
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Y = sum([(saw(i * w * t) / 3 + math.sin(i * w * t)) * math.exp(-0.002 * w * t) for i in range(1, 6)]) / 2
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Y = math.copysign(abs(Y) ** (1 / 2), Y)
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return Y
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def at(t):
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"""
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Returns the total intensity of music sampled at time t
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This is actually pretty efficient ngl
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Because people usually don't have that many overlapping notes
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"""
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i = bisect.bisect(music, (t, 2**31))
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ret = 0
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for j in range(max(i - 32, 0), i):
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m = music[j]
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if m[1] > t and m[2] > 0:
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ret += m[4] * m[5](freq(m[2], m[3]), t - m[0])
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return int(2**28 * ret)
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def process(notes, start, speed=1, gain=1, blend=0, waveform=droplet):
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"""
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Adds a list of notes to the music list
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"""
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t = start
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for note in notes:
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vol = 1
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if len(note) == 4:
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vol = note[3]
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start = min(t, t + note[0] / speed)
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end = max(t, t + note[0] / speed)
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music.append((start, end + 16 * int(blend), note[1], note[2], vol * gain, waveform))
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t = end
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def play(start, end):
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"""
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Print music from the start time to end time encoded in s32 to standard output
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"""
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music.sort()
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for i in range(start * bitrate, end * bitrate):
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sys.stdout.buffer.write(struct.pack("i", at(i / bitrate)))
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