Add OSC with dubious construction

2 files changed, 292 insertions, 261 deletions

diff --git a/music.nim b/music.nim
index 24c01ca..2ad0e3f 100644
--- a/music.nim
+++ b/music.nim
@@ -3,291 +3,315 @@ import musiclib, std/[math, sugar]
 # Number of times to sample each second
 const bitrate = 44100
 
+func osc_weird_pluck*(f, t: float): float =
+  # I got this as a bug
+  let w = 2 * PI * f
+  let wxt = w * t
+  let exp_swxt = math.exp(-0.001 * wxt)
+  let y0 = 0.6 * math.sin(wxt)
+  let y1 = 0.2 * math.sin(2 * wxt)
+  let y2 = 0.05 * math.sin(3 * wxt)
+  let y3 = (y0 + y1 + y2) * exp_swxt
+  let y4 = (1+y3)*y3*y3 # this line is different
+  y4 * (1 + 16 * t * math.exp(-6 * t))
+
 func osc_piano*(f, t: float): float =
-    ## Returns the intensity of a tone of frequency f sampled at time t
-    ## t starts at 0 (note start)
-    # 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)
-    let w = 2 * PI * f
-    var Y = 0.6 * math.sin(w * t) * math.exp(-0.001 * w * t)
-    Y += 0.2 * math.sin(2 * w * t) * math.exp(-0.001 * w * t)
-    Y += 0.05 * math.sin(3 * w * t) * math.exp(-0.001 * w * t)
-    Y += Y * Y * Y
-    Y *= 1 + 16 * t * math.exp(-6 * t)
-    Y
-
-func osc_pulse*(f,t:float):float =
-    let width = (1.0 / f) / 2
-    let phase: float = t mod (width * 2)
-    if phase < width: 1.0 else: -1.0
+  ## Returns the intensity of a tone of frequency f sampled at time t
+  ## t starts at 0 (note start)
+  # 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)
+  let w = 2 * PI * f
+  let ewt = math.exp(-0.001 * w * t)
+  var Y = 0.6 * math.sin(w * t) * ewt +
+        0.2 * math.sin(2 * w * t) * ewt +
+        0.05 * math.sin(3 * w * t) * ewt
+  
+  let Y2 = Y * (Y * Y + 1)
+  Y2 * (1 + 16 * t * math.exp(-6 * t))
+
+func osc_pulse*(f, t: float, phasedrift: float = 0.0): float =
+  let doublewidth = 1.0 / f
+  let width = doublewidth / 2
+  let phase: float = (t + doublewidth * phasedrift) mod doublewidth
+  if phase < width: 1.0 else: -1.0
+
+func osc_saw*(f,t:float, phasedrift: float = 0.0):float =
+  let doublewidth = 1.0 / f
+  let width = doublewidth / 2
+  let phase: float = (t + doublewidth * phasedrift) mod doublewidth
+  if phase < width:
+    -1.0 + 2.0 * phase / width
+  else:
+    1.0 - 2.0 * (phase - width) / (1.0 - width)
 
 func freq*(octave, step: float): float =
-    ## Returns the frequency of a note
-    55 * pow(2, (octave + step / 12 - 1))
+  ## Returns the frequency of a note
+  55 * pow(2, (octave + step / 12 - 1))
 
 var osc: OscFn = (f, t: float) => 0.0
 
 proc p*(len, octave, step, vol: float = 1): Note =
-    ## Note helper constructor
-    (len, freq(octave, step), vol, osc)
-
+  ## Note helper constructor
+  (len, freq(octave, step), vol, osc)
 
 #------- song region -------
 
-const GAIN_NORMAL = 0.24
+const GAIN_NORMAL = 0.22
 
 osc = (f, t: float) => osc_piano(f, t) * GAIN_NORMAL
 
 let intro = [
-    p(1,3,3),
-    p(1,3,7),
-    p(1,3,10),
-    p(6,4,2),
-
-    p(1,3,1),
-    p(1,3,5),
-    p(1,3,8),
-    p(3,4,0),
-
-    p(1,2,11),
-    p(1,3,3),
-    p(1,3,6),
-    p(3,3,10),
-
-    p(1,2,8),
-    p(1,3,0),
-    p(1,3,3),
-    p(8,3,7),
+    p(1, 3, 3),
+    p(1, 3, 7),
+    p(1, 3, 10),
+    p(6, 4, 2),
+
+    p(1, 3, 1),
+    p(1, 3, 5),
+    p(1, 3, 8),
+    p(3, 4, 0),
+
+    p(1, 2, 11),
+    p(1, 3, 3),
+    p(1, 3, 6),
+    p(3, 3, 10),
+
+    p(1, 2, 8),
+    p(1, 3, 0),
+    p(1, 3, 3),
+    p(8, 3, 7),
 ]
 
-# osc = osc_pulse
+let outro = [
+    p(1, 3, 3),
+    p(1, 3, 7),
+    p(1, 3, 10),
+    p(1, 4, 2),
+    p(1, 4, 3),
+    p(1, 4, 7),
+    p(2, 4, 8),
+
+    p(1, 3, 1),
+    p(1, 3, 5),
+    p(1, 3, 8),
+    p(1, 4, 0),
+    p(1, 4, 1),
+    p(1, 4, 5),
+    p(2, 4, 8),
+
+    p(1, 2, 11),
+    p(1, 3, 3),
+    p(1, 3, 6),
+    p(1, 3, 10),
+    p(1.5, 3, 11),
+    p(1.5, 4, 3),
+    p(3, 4, 8),
+
+    p(1.5, 2, 8),
+    p(1.5, 3, 0),
+    p(2, 3, 3),
+    p(16, 3, 7, 2),
+]
 
 let melody = [
-    p(1,3,3),
-    p(1,3,7),
-    p(1,3,10),
-    p(1,4,2),
-    p(1,4,3),
-    p(1,4,7),
-    p(2,4,8),
-
-    p(1,3,1),
-    p(1,3,5),
-    p(1,3,8),
-    p(1,4,0),
-    p(1,4,1),
-    p(1,4,5),
-    p(2,4,8),
-
-    p(1,3,3),
-    p(1,3,7),
-    p(1,3,10),
-    p(1,4,2),
-    p(1,4,3),
-    p(1,4,10),
-    p(2,4,3),
-
-    p(1,3,1),
-    p(1,3,5),
-    p(1,3,8),
-    p(1,4,0),
-    p(1,4,10),
-    p(1,4,8),
-    p(2,4,10),
-
-
-    p(1,3,3),
-    p(1,3,7),
-    p(1,3,10),
-    p(1,4,2),
-    p(1,4,3),
-    p(1,4,7),
-    p(2,4,8),
-
-    p(1,3,1),
-    p(1,3,5),
-    p(1,3,8),
-    p(1,4,0),
-    p(1,4,1),
-    p(1,4,5),
-    p(2,4,1),
-
-    p(1,3,3),
-    p(1,3,7),
-    p(1,3,10),
-    p(1,4,2),
-    p(1,4,3),
-    p(1,4,10),
-    p(1,4,8),
-    p(1,4,7),
-
-    p(1,3,1),
-    p(1,3,5),
-    p(1,3,8),
-    p(1,4,0),
-    p(1,4,10),
-    p(1,4,8),
-    p(2,4,10),
+    p(1, 3, 3),
+    p(1, 3, 7),
+    p(1, 3, 10),
+    p(1, 4, 2),
+    p(1, 4, 3),
+    p(1, 4, 7),
+    p(2, 4, 8),
+
+    p(1, 3, 1),
+    p(1, 3, 5),
+    p(1, 3, 8),
+    p(1, 4, 0),
+    p(1, 4, 1),
+    p(1, 4, 5),
+    p(2, 4, 8),
+
+    p(1, 3, 3),
+    p(1, 3, 7),
+    p(1, 3, 10),
+    p(1, 4, 2),
+    p(1, 4, 3),
+    p(1, 4, 10),
+    p(2, 4, 3),
+
+    p(1, 3, 1),
+    p(1, 3, 5),
+    p(1, 3, 8),
+    p(1, 4, 0),
+    p(1, 4, 10),
+    p(1, 4, 8),
+    p(2, 4, 10),
+
+
+    p(1, 3, 3),
+    p(1, 3, 7),
+    p(1, 3, 10),
+    p(1, 4, 2),
+    p(1, 4, 3),
+    p(1, 4, 7),
+    p(2, 4, 8),
+
+    p(1, 3, 1),
+    p(1, 3, 5),
+    p(1, 3, 8),
+    p(1, 4, 0),
+    p(1, 4, 1),
+    p(1, 4, 5),
+    p(2, 4, 1),
+
+    p(1, 3, 3),
+    p(1, 3, 7),
+    p(1, 3, 10),
+    p(1, 4, 2),
+    p(1, 4, 3),
+    p(1, 4, 10),
+    p(1, 4, 8),
+    p(1, 4, 7),
+
+    p(1, 3, 1),
+    p(1, 3, 5),
+    p(1, 3, 8),
+    p(1, 4, 0),
+    p(1, 4, 10),
+    p(1, 4, 8),
+    p(2, 4, 10),
 ]
 
+osc = (f, t: float) => osc_weird_pluck(f, t) * GAIN_NORMAL
+
 let melody2 = [
-    p(1,0,0),
-    p(1,5,10),
-    p(1,5,8),
-    p(1,5,7),
-    p(1,5,8),
-    p(3,5,7,2),
-
-    p(1,5,3),
-    p(1,4,10),
-    p(6,5,1,2),
-
-    p(1/2,5,0,2),
-    p(1/2,5,1,2),
-    p(3,5,3,2),
-    p(1/2,5,10,2),
-    p(7/2,5,3,2),
-
-    p(8,0,0),
-
-    p(1,0,0),
-    p(1,5,3),
-    p(1,5,10),
-    p(1,5,10),
-    p(4/3,5,10),
-    p(4/3,5,8),
-    p(4/3,5,7),
-
-    p(1,0,0),
-    p(1,5,1),
-    p(1,5,8),
-    p(1,5,8),
-    p(4/3,5,8),
-    p(4/3,5,8),
-    p(4/3,5,10),
-
-    p(8,0,0),
-
-    p(1,0,0),
-    p(5,5,3,2),
-    p(2,5,10,2),
+    p(1, 0, 0),
+    p(1, 5, 10),
+    p(1, 5, 8),
+    p(1, 5, 7),
+    p(1, 5, 8),
+    p(3, 5, 7, 2),
+
+    p(1, 5, 3),
+    p(1, 4, 10),
+    p(6, 5, 1, 2),
+
+    p(1/2, 5, 0, 2),
+    p(1/2, 5, 1, 2),
+    p(3, 5, 3, 2),
+    p(1/2, 5, 10, 2),
+    p(7/2, 5, 3, 2),
+
+    p(8, 0, 0),
+
+    p(1, 0, 0),
+    p(1, 5, 3),
+    p(1, 5, 10),
+    p(1, 5, 10),
+    p(4/3, 5, 10),
+    p(4/3, 5, 8),
+    p(4/3, 5, 7),
+
+    p(1, 0, 0),
+    p(1, 5, 1),
+    p(1, 5, 8),
+    p(1, 5, 8),
+    p(4/3, 5, 8),
+    p(4/3, 5, 8),
+    p(4/3, 5, 10),
+
+    p(8, 0, 0),
+
+    p(1, 0, 0),
+    p(5, 5, 3, 2),
+    p(2, 5, 10, 2),
 ]
 
 let melody3 = [
-    p(1,0,0),
-    p(1,5,10),
-    p(1/2,5,8,2/3),
-    p(1/2,5,7,2/3),
-    p(1/4,5,8,1/2),
-    p(1/4,5,7,1/2),
-    p(1/4,5,8,1/2),
-    p(1/4,5,7,1/2),
-    p(1,5,8),
-    p(3,5,7,2),
-
-    p(1,5,3),
-    p(1,4,10),
-    p(1,5,1),
-    p(5,5,7,2),
-
-    p(1/2,5,7),
-    p(1/2,5,10),
-    p(1/4,5,7),
-    p(1/4,5,10),
-    p(1/4,5,7),
-    p(1/4,5,10),
-    p(1,6,3),
-    p(2,5,3,2),
-    p(1/2,6,3),
-    p(5/2,5,3,2),
-
-    p(1/2,5,10),
-    p(1/2,5,8),
-    p(1/2,5,7),
-    p(1/2,5,8),
-    p(1/2,5,7),
-    p(1/2,5,3),
-    p(1/2,4,10),
-    p(1/2,5,1),
-    p(1/2,5,0),
-    p(1/2,4,10),
-    p(1/2,4,8),
-    p(1/2,4,10),
-    p(1/2,5,3),
-    p(1/2,5,7),
-    p(1/2,5,3),
-    p(1/2,5,10),
-
-    p(4/3,5,7),
-    p(4/3,6,3),
-    p(4/3,6,3),
-    p(4/3,6,2),
-    p(4/3,5,10),
-    p(4/3,5,7),
-
-    p(3,5,5),
-    p(2,5,7),
-    p(2,5,8),
-    p(1,6,1),
-
-    p(1,5,3),
-    p(1,5,5),
-    p(2,5,7),
-    p(1,5,3),
-    p(1,5,8),
-    p(2,5,10),
-
-    p(3/2,6,0),
-    p(3/2,6,1),
-    p(5,6,3,2),
-]
-
-let outro = [
-    p(1,3,3),
-    p(1,3,7),
-    p(1,3,10),
-    p(1,4,2),
-    p(1,4,3),
-    p(1,4,7),
-    p(2,4,8),
-
-    p(1,3,1),
-    p(1,3,5),
-    p(1,3,8),
-    p(1,4,0),
-    p(1,4,1),
-    p(1,4,5),
-    p(2,4,8),
-
-    p(1,2,11),
-    p(1,3,3),
-    p(1,3,6),
-    p(1,3,10),
-    p(1.5,3,11),
-    p(1.5,4,3),
-    p(3,4,8),
-
-    p(1.5,2,8),
-    p(1.5,3,0),
-    p(2,3,3),
-    p(16,3,7,2),
+    p(1, 0, 0),
+    p(1, 5, 10),
+    p(1/2, 5, 8, 2/3),
+    p(1/2, 5, 7, 2/3),
+    p(1/4, 5, 8, 1/2),
+    p(1/4, 5, 7, 1/2),
+    p(1/4, 5, 8, 1/2),
+    p(1/4, 5, 7, 1/2),
+    p(1, 5, 8),
+    p(3, 5, 7, 2),
+
+    p(1, 5, 3),
+    p(1, 4, 10),
+    p(1, 5, 1),
+    p(5, 5, 7, 2),
+
+    p(1/2, 5, 7),
+    p(1/2, 5, 10),
+    p(1/4, 5, 7),
+    p(1/4, 5, 10),
+    p(1/4, 5, 7),
+    p(1/4, 5, 10),
+    p(1, 6, 3),
+    p(2, 5, 3, 2),
+    p(1/2, 6, 3),
+    p(5/2, 5, 3, 2),
+
+    p(1/2, 5, 10),
+    p(1/2, 5, 8),
+    p(1/2, 5, 7),
+    p(1/2, 5, 8),
+    p(1/2, 5, 7),
+    p(1/2, 5, 3),
+    p(1/2, 4, 10),
+    p(1/2, 5, 1),
+    p(1/2, 5, 0),
+    p(1/2, 4, 10),
+    p(1/2, 4, 8),
+    p(1/2, 4, 10),
+    p(1/2, 5, 3),
+    p(1/2, 5, 7),
+    p(1/2, 5, 3),
+    p(1/2, 5, 10),
+
+    p(4/3, 5, 7),
+    p(4/3, 6, 3),
+    p(4/3, 6, 3),
+    p(4/3, 6, 2),
+    p(4/3, 5, 10),
+    p(4/3, 5, 7),
+
+    p(3, 5, 5),
+    p(2, 5, 7),
+    p(2, 5, 8),
+    p(1, 6, 1),
+
+    p(1, 5, 3),
+    p(1, 5, 5),
+    p(2, 5, 7),
+    p(1, 5, 3),
+    p(1, 5, 8),
+    p(2, 5, 10),
+
+    p(3/2, 6, 0),
+    p(3/2, 6, 1),
+    p(5, 6, 3, 2),
 ]
 
-osc = (f, t: float) => osc_piano(f, t) * GAIN_NORMAL * 1.5
+# clip length to 1 second
+osc = (f, t: float) => (if t > 1: 0.0 else:
+  (osc_saw(f, t) * GAIN_NORMAL * 0.06) + (osc_pulse(f, t) * GAIN_NORMAL * 0.3))
 
 let bass = [
-    p(1,1,3),
-    p(1,1,10),
-    p(1,1,1),
-    p(1,1,8),
-    p(1,1,3),
-    p(1,2,3),
-    p(1,1,1),
-    p(1,1,10),
+    p(1, 1, 3),
+    p(1, 1, 10),
+    p(1, 1, 1),
+    p(1, 1, 8),
+    p(1, 1, 3),
+    p(1, 2, 3),
+    p(1, 1, 1),
+    p(1, 1, 10),
 ]
 
 from std/algorithm import sort
@@ -312,5 +336,5 @@ music.sortByStart()
 
 # Print out music encoded in s16 to standard output
 for i in (0 * bitrate ..< 84 * bitrate):
-    let bytes = cast[array[4, uint8]](music.at(i / bitrate))
-    doAssert 4 == stdout.writeBytes(bytes, 0, 4)
+  let bytes = cast[array[4, uint8]](music.at(i / bitrate))
+  doAssert 4 == stdout.writeBytes(bytes, 0, 4)
diff --git a/musiclib.nim b/musiclib.nim
index 91e63c4..c21cb95 100644
--- a/musiclib.nim
+++ b/musiclib.nim
@@ -1,4 +1,4 @@
-import std/[algorithm, math, sugar, strformat]
+import std/[algorithm, math, sugar, strformat, logging]
 
 type
     OscFn* = proc (f: float, t: float): float
@@ -65,4 +65,11 @@ proc at*(music: openArray[ProcessedNote], t: float): int32 =
     ret *= GAIN_BIAS
     
     # clip sample
-    clamp(ret, int32.low.float..int32.high.float).int32
+    if ret >= int32.high.float:
+        warn(&"audio clipping at t={t}")
+        int32.high
+    elif ret <= int32.low.float:
+        warn(&"audio clipping at t={t}")
+        int32.low
+    else:
+        int32(ret)