Refactor more

Changes

3 changed files (+282/-255)

• .gitignore
  • @@ -1,1 +1,2 @@
    - /music + /music + /music.s32
• music.nim
  • @@ -1,250 +1,276 @@
    - import musiclib + import musiclib, std/math # Number of times to sample each second let bitrate = 44100 + 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 freq*(octave, step: float): float = + ## Returns the frequency of a note + 55 * pow(2, (octave + step / 12 - 1)) + + func p*(len, octave, step, vol: float = 1): Note = + ## Note helper constructor + let osc: OscFn = osc_piano + (len, freq(octave, step), vol, osc) + let intro = [ - n(1,3,3), - n(1,3,7), - n(1,3,10), - n(6,4,2), + p(1,3,3), + p(1,3,7), + p(1,3,10), + p(6,4,2), - n(1,3,1), - n(1,3,5), - n(1,3,8), - n(3,4,0), + p(1,3,1), + p(1,3,5), + p(1,3,8), + p(3,4,0), - n(1,2,11), - n(1,3,3), - n(1,3,6), - n(3,3,10), + p(1,2,11), + p(1,3,3), + p(1,3,6), + p(3,3,10), - n(1,2,8), - n(1,3,0), - n(1,3,3), - n(8,3,7), + p(1,2,8), + p(1,3,0), + p(1,3,3), + p(8,3,7), ] let melody = [ - n(1,3,3), - n(1,3,7), - n(1,3,10), - n(1,4,2), - n(1,4,3), - n(1,4,7), - n(2,4,8), + p(1,3,3), + p(1,3,7), + p(1,3,10), + p(1,4,2), + p(1,4,3), + p(1,4,7), + p(2,4,8), - n(1,3,1), - n(1,3,5), - n(1,3,8), - n(1,4,0), - n(1,4,1), - n(1,4,5), - n(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), - n(1,3,3), - n(1,3,7), - n(1,3,10), - n(1,4,2), - n(1,4,3), - n(1,4,10), - n(2,4,3), + 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), - n(1,3,1), - n(1,3,5), - n(1,3,8), - n(1,4,0), - n(1,4,10), - n(1,4,8), - n(2,4,10), + 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), - n(1,3,3), - n(1,3,7), - n(1,3,10), - n(1,4,2), - n(1,4,3), - n(1,4,7), - n(2,4,8), + p(1,3,3), + p(1,3,7), + p(1,3,10), + p(1,4,2), + p(1,4,3), + p(1,4,7), + p(2,4,8), - n(1,3,1), - n(1,3,5), - n(1,3,8), - n(1,4,0), - n(1,4,1), - n(1,4,5), - n(2,4,1), + 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), - n(1,3,3), - n(1,3,7), - n(1,3,10), - n(1,4,2), - n(1,4,3), - n(1,4,10), - n(1,4,8), - n(1,4,7), + 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), - n(1,3,1), - n(1,3,5), - n(1,3,8), - n(1,4,0), - n(1,4,10), - n(1,4,8), - n(2,4,10), + 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), ] let bass = [ - n(1,1,3), - n(1,1,10), - n(1,1,1), - n(1,1,8), - n(1,1,3), - n(1,2,3), - n(1,1,1), - n(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), ] let melody2 = [ - n(1,0,0), - n(1,5,10), - n(1,5,8), - n(1,5,7), - n(1,5,8), - n(3,5,7,2), + 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), - n(1,5,3), - n(1,4,10), - n(6,5,1,2), + p(1,5,3), + p(1,4,10), + p(6,5,1,2), - n(1/2,5,0,2), - n(1/2,5,1,2), - n(3,5,3,2), - n(1/2,5,10,2), - n(7/2,5,3,2), + 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), - n(8,0,0), + p(8,0,0), - n(1,0,0), - n(1,5,3), - n(1,5,10), - n(1,5,10), - n(4/3,5,10), - n(4/3,5,8), - n(4/3,5,7), + 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), - n(1,0,0), - n(1,5,1), - n(1,5,8), - n(1,5,8), - n(4/3,5,8), - n(4/3,5,8), - n(4/3,5,10), + 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), - n(8,0,0), + p(8,0,0), - n(1,0,0), - n(5,5,3,2), - n(2,5,10,2), + p(1,0,0), + p(5,5,3,2), + p(2,5,10,2), ] let melody3 = [ - n(1,0,0), - n(1,5,10), - n(1/2,5,8,2/3), - n(1/2,5,7,2/3), - n(1/4,5,8,1/2), - n(1/4,5,7,1/2), - n(1/4,5,8,1/2), - n(1/4,5,7,1/2), - n(1,5,8), - n(3,5,7,2), + 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), - n(1,5,3), - n(1,4,10), - n(1,5,1), - n(5,5,7,2), + p(1,5,3), + p(1,4,10), + p(1,5,1), + p(5,5,7,2), - n(1/2,5,7), - n(1/2,5,10), - n(1/4,5,7), - n(1/4,5,10), - n(1/4,5,7), - n(1/4,5,10), - n(1,6,3), - n(2,5,3,2), - n(1/2,6,3), - n(5/2,5,3,2), + 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), - n(1/2,5,10), - n(1/2,5,8), - n(1/2,5,7), - n(1/2,5,8), - n(1/2,5,7), - n(1/2,5,3), - n(1/2,4,10), - n(1/2,5,1), - n(1/2,5,0), - n(1/2,4,10), - n(1/2,4,8), - n(1/2,4,10), - n(1/2,5,3), - n(1/2,5,7), - n(1/2,5,3), - n(1/2,5,10), + 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), - n(4/3,5,7), - n(4/3,6,3), - n(4/3,6,3), - n(4/3,6,2), - n(4/3,5,10), - n(4/3,5,7), + 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), - n(3,5,5), - n(2,5,7), - n(2,5,8), - n(1,6,1), + p(3,5,5), + p(2,5,7), + p(2,5,8), + p(1,6,1), - n(1,5,3), - n(1,5,5), - n(2,5,7), - n(1,5,3), - n(1,5,8), - n(2,5,10), + p(1,5,3), + p(1,5,5), + p(2,5,7), + p(1,5,3), + p(1,5,8), + p(2,5,10), - n(3/2,6,0), - n(3/2,6,1), - n(5,6,3,2), + p(3/2,6,0), + p(3/2,6,1), + p(5,6,3,2), ] let outro = [ - n(1,3,3), - n(1,3,7), - n(1,3,10), - n(1,4,2), - n(1,4,3), - n(1,4,7), - n(2,4,8), + p(1,3,3), + p(1,3,7), + p(1,3,10), + p(1,4,2), + p(1,4,3), + p(1,4,7), + p(2,4,8), - n(1,3,1), - n(1,3,5), - n(1,3,8), - n(1,4,0), - n(1,4,1), - n(1,4,5), - n(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), - n(1,2,11), - n(1,3,3), - n(1,3,6), - n(1,3,10), - n(1.5,3,11), - n(1.5,4,3), - n(3,4,8), + 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), - n(1.5,2,8), - n(1.5,3,0), - n(2,3,3), - n(16,3,7,2), + p(1.5,2,8), + p(1.5,3,0), + p(2,3,3), + p(16,3,7,2), ] from std/algorithm import sort
  • @@ -265,7 +291,7 @@ music.process(melody3, 56, 4)
    music.process(bass, 56, gain=1.5) music.process(bass, 64, gain=1.5) music.process(outro, 72, 4) - music.sort() + music.sortByStart() # Print out music encoded in s16 to standard output for i in (0 * bitrate ..< 84 * bitrate):
• musiclib.nim
  • @@ -1,68 +1,68 @@
    - import std/[algorithm, math, sugar] + import std/[algorithm, math, sugar, strformat] - type Note* = tuple - len: float - octave: float - step: float - vol: float + type + OscFn* = proc (f: float, t: float): float - func n*(a, b, c, d: float = 1): Note = - (a, b, c, d) + Note* = tuple + len: float ## seconds + freq: float + vol: float + osc: OscFn - type ProcessedNote* = tuple - start: float - `end`: float - octave: float - step: float - vol: float + ProcessedNote* = tuple + start: float ## absolute time in seconds + stop: float ## absolute time in seconds + freq: float + vol: float + osc: OscFn + + ## give some seconds for the note to fade out + const HACK_DROPOFF_DELAY = 2.0 - func process*(music: var seq[ProcessedNote], notes: openArray[Note]; m_start: float, speed: float=1, gain:float = 1) = + const HACK_LONGEST_NOTE = 16.0 + + func process*(music: var seq[ProcessedNote], notes: openArray[Note]; start_init: float, speed: float=1, gain:float = 1) = ## Adds a list of notes to the music list - var start = m_start + ## + ## `notes` sequence of notes with no rests in between + var start = start_init var t = start for note in notes: - let vol = note[3] - start = min(t, t + note[0] / speed) - let `end` = max(t, t + note[0] / speed) - music &= ((start, `end`, note[1], note[2], vol * gain)) - t = `end` + assert note.len >= 0.0 + assert note.len <= HACK_LONGEST_NOTE, &"note too long: {note.len}" + start = t + let stop = t + note.len / speed + music &= (start, stop, note.freq, note.vol * gain, note.osc) + t = stop - func bisect(music: openArray[ProcessedNote], x: (float, float)): int = - ## Return the index where to insert item `x` in list `music`, assuming `music` is sorted. - music.lowerBound(x, (m, key) => cmp((m[0], m[1]), key)) + func sortByStart*(music: var seq[ProcessedNote]) = + music.sort((a, b) => cmp(a.start, b.start)) + func bisect(music: openArray[ProcessedNote], x: float): int = + ## Return the index where to insert item `x` in list `music` + ## + ## assumes `music` is sorted by `.start` - func freq(octave, step: float): float = - ## Returns the frequency of a note - 55 * pow(2, (octave + step / 12 - 1)) + music.lowerBound(x, (m, key) => cmp(m.start, key)) - func tone(f, t: float): float = - ## 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) - 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 + const GAIN_BIAS: float = pow(2.0, 28.0) - const bias: float = pow(2.0, 28.0) - func at*(music: openArray[ProcessedNote], t: float): int32 = + proc at*(music: openArray[ProcessedNote], t: float): int32 = ## Returns the total intensity of music sampled at time t - let i: int = music.bisect((t, pow(2.0, 31.0))) - # This is actually pretty efficient ngl - # Because people usually don't have that many overlapping notes + ## + ## assumes `music` is sorted by `.start` + + var i: int = music.bisect(t) - 1 + var ret: float = 0 - # this `32` is flaky - # maybe some notes are longer? - for j in (max(i - 32, 0) ..< i): - let m = music[j] - if m[0] + m[1] > t: - ret += m[4] * tone(freq(m[2], m[3]), t - m[0]) - int32(ret * bias) + + while i >= 0: + let m = music[i] + assert m.start <= t + if m.stop + HACK_DROPOFF_DELAY >= t: + ret += m.vol * m.osc(m.freq, t - m.start) + if m.start + HACK_LONGEST_NOTE + HACK_DROPOFF_DELAY < t: + break + i -= 1 + + int32(ret * GAIN_BIAS)