Implement different waveforms

blend.py

@@ -250,11 +250,11 @@ yue.process(melody, 24, 4, blend=1)
 yue.process(bass, 24, gain=1.5, blend=1)
 yue.process(bass, 32, gain=1.5, blend=1)
 yue.process(melody, 40, 4, blend=1)
-yue.process(melody2, 40, 4, blend=1)
+yue.process(melody2, 40, 4, blend=1, waveform=yue.seething)
 yue.process(bass, 40, gain=1.5, blend=1)
 yue.process(bass, 48, gain=1.5, blend=1)
 yue.process(melody, 56, 4, blend=1)
-yue.process(melody3, 56, 4, blend=1)
+yue.process(melody3, 56, 4, blend=1, waveform=yue.seething)
 yue.process(bass, 56, gain=1.5, blend=1)
 yue.process(bass, 64, gain=1.5, blend=1)
 yue.process(outro, 72, 4, blend=1)

yue.py

@@ -8,21 +8,6 @@ bitrate = 44100
 music = []
 
 
-def process(notes, start, speed=1, gain=1, blend=0):
-    """
-    Adds a list of notes to the music list
-    """
-    t = start
-    for note in notes:
-        vol = 1
-        if len(note) == 4:
-            vol = note[3]
-        start = min(t, t + note[0] / speed)
-        end = max(t, t + note[0] / speed)
-        music.append((start, end + 16 * int(blend), note[1], note[2], vol * gain))
-        t = end
-
-
 def freq(octave, step):
     """
     Returns the frequency of a note
@@ -30,9 +15,9 @@ def freq(octave, step):
     return 55 * 2 ** (octave + step / 12 - 1)
 
 
-def tone(f, t):
+def droplet(f, t):
     """
-    Returns the intensity of a tone of frequency f sampled at time t
+    Returns the intensity of the "droplet" waveform 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
     """
@@ -45,6 +30,21 @@ def tone(f, t):
     return Y
 
 
+def seething(f, t):
+    """
+    Returns the intensity of the "seething" waveform of frequency f sampled at time t
+    """
+    w = 2 * math.pi * f
+    Y = 0.6 * math.sin(w * t) * math.exp(-0.0005 * w * t)
+    Y += 0.1 * math.sin(0.99 * w * t) * math.exp(-0.0005 * w * t)
+    Y += 0.1 * math.sin(1.01 * w * t) * math.exp(-0.0005 * w * t)
+    Y += 0.2 * math.sin(2 * w * t) * math.exp(-0.0005 * w * t)
+    Y += math.copysign(Y * Y, Y)
+    Y *= 1 + 16 * t * math.exp(-6 * t)
+    Y *= 0.5 * min(24 * t, 1)
+    return Y
+
+
 def at(t):
     """
     Returns the total intensity of music sampled at time t
@@ -56,10 +56,25 @@ def at(t):
     for j in range(max(i - 32, 0), i):
         m = music[j]
         if m[1] > t:
-            ret += m[4] * tone(freq(m[2], m[3]), t - m[0])
+            ret += m[4] * m[5](freq(m[2], m[3]), t - m[0])
     return int(2**28 * ret)
 
 
+def process(notes, start, speed=1, gain=1, blend=0, waveform=droplet):
+    """
+    Adds a list of notes to the music list
+    """
+    t = start
+    for note in notes:
+        vol = 1
+        if len(note) == 4:
+            vol = note[3]
+        start = min(t, t + note[0] / speed)
+        end = max(t, t + note[0] / speed)
+        music.append((start, end + 16 * int(blend), note[1], note[2], vol * gain, waveform))
+        t = end
+
+
 def play(start, end):
     """
     Print music from the start time to end time encoded in s32 to standard output