Implement saw wave and honk waveform

keyboard.py

@@ -10,7 +10,7 @@ bitrate = 44100
 
 note = []
 for i in range(0, 24):
-    note.append([yue.tone(yue.freq(3, i), j / bitrate) / 4 for j in range(0, 3 * bitrate)])
+    note.append([yue.seething(yue.freq(4, i), j / bitrate) / 4 for j in range(0, 3 * bitrate)])
 
 sd.default.samplerate = bitrate
 print("READY")

yue.py

@@ -8,6 +8,13 @@ bitrate = 44100
 music = []
 
 
+def saw(x):
+    """
+    Sawtooth wave
+    """
+    return x / 2 / math.pi % 1
+
+
 def freq(octave, step):
     """
     Returns the frequency of a note
@@ -45,6 +52,16 @@ def seething(f, t):
     return Y
 
 
+def honk(f, t):
+    """
+    Returns the intensity of the "honk" waveform of frequency f sampled at time t
+    """
+    w = 2 * math.pi * f
+    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
+    Y = math.copysign(abs(Y) ** (1 / 2), Y)
+    return Y
+
+
 def at(t):
     """
     Returns the total intensity of music sampled at time t