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import bisect
import math
import struct
import sys
# Number of times to sample each second
bitrate = 44100
intro = [
(1, 3, 3),
(1, 3, 7),
(1, 3, 10),
(3, 4, 2),
(1, 3, 1),
(1, 3, 5),
(1, 3, 8),
(3, 4, 0),
(1, 2, 11),
(1, 3, 3),
(1, 3, 6),
(2, 3, 10),
(1 / 2, 3, 9, 1 / 2),
(1 / 2, 3, 8, 1 / 2),
(6, 3, 7, 1 / 2),
]
melody = [
(3, 3, 7),
(3, 3, 3),
(3, 3, 8),
(2, 3, 7),
(2, 3, 5),
(3, 3, 7),
(2, 3, 3),
(2, 2, 10),
(2, 3, 0),
(6, 3, 3),
]
bass = [
(1, 0, 7),
(1, 2, 7),
(1, 2, 7),
(1, 0, 7),
(1, 2, 3),
(1, 2, 3),
(1, 0, 7),
(1, 2, 8),
(1, 2, 8),
(1, 0, 7),
(1, 2, 7),
(1, 0, 7),
(1, 2, 5),
(1, 0, 7),
(1, 2, 7),
(1, 2, 7),
(1, 0, 7),
(1, 2, 3),
(1, 0, 7),
(1, 1, 10),
(1, 0, 7),
(1, 2, 0),
(1, 0, 7),
(1, 2, 3),
(1, 2, 3),
(1, 0, 7),
(1, 2, 3),
(1, 2, 3),
]
music = []
def process(notes, start, speed=1, gain=1):
"""
Adds a list of notes to the music list
"""
t = start
for note in notes:
vol = 1
if len(note) == 4:
vol = note[3]
music.append((t, t + note[0] / speed, note[1], note[2], vol * gain))
t += note[0] / speed
# Process all lists of notes
process(intro, 0, 3)
process(melody, 8, 3)
process(bass, 8, 3, 1 / 2)
# And sort them
music.sort()
def freq(octave, step):
"""
Returns the frequency of a note
"""
return 55 * 2 ** (octave + step / 12 - 1)
def tone(f, t):
"""
Returns the intensity of a tone of frequency f sampled at time t
"""
# https://dsp.stackexchange.com/questions/46598/mathematical-equation-for-the-sound-wave-that-a-piano-makes
# https://youtu.be/ogFAHvYatWs?t=254
# return int(2**13*(1+square(t, 440*2**(math.floor(5*t)/12))))
# Y = sum([math.sin(2 * i * math.pi * t * f) * math.exp(-0.0004 * 2 * math.pi * t * f) / 2**i for i in range(1, 4)])
# Y += Y * Y * Y
# Y *= 1 + 16 * t * math.exp(-6 * t)
w = 2 * math.pi * f
Y = 0.6 * math.sin(w * t) * math.exp(-0.0015 * w * t)
Y += 0.4 * math.sin(2 * w * t) * math.exp(-0.0015 * w * t)
Y += Y * Y * Y
Y *= 1 + 16 * t * math.exp(-6 * t)
return Y
def at(t):
"""
Returns the total intensity of music sampled at time t
"""
i = bisect.bisect(music, (t, 10**9))
# This is actually pretty efficient ngl
# Because people usually don't have that many overlapping notes
ret = 0
for j in range(max(i - 20, 0), i):
m = music[j]
if m[0] + m[1] >= t:
ret += m[4] * tone(freq(m[2], m[3]), t - m[0])
return int(2**12 * ret)
# Print out music encoded in s16 to standard output
for i in range(0 * bitrate, 16 * bitrate):
sys.stdout.buffer.write(struct.pack("h", at(i / bitrate)))
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