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--
-- adapted from ChucK's shepard.ck (Ge Wang, 2016)
--
local min, max, exp = math.min, math.max, math.exp
local function dbtorms(f)
f = min(max(f, 0), 485)
return exp((2.302585092994 * 0.05) * (f-100))
end
local SQRT_PI2 = math.sqrt(2*math.pi)
local function gauss(x, mu, sd)
return (1.0 / (sd*SQRT_PI2)) * exp(-(x-mu)^2 / (2*sd^2))
end
-- built-in mtof() caches all 128 MIDI notes
local function mtof_raw(note)
return 440 * 2^((note - 69)/12)
end
-- mean for normal intensity curve
local MU = 66
-- standard deviation for normal intensity curve
local SIGMA = 42
-- normalize to 1.0 at x==MU
local SCALE = 1 / gauss(MU, MU, SIGMA)
-- increment per sample (use negative for descending)
--local INC = tostream(.004 / msec(1))
local INC = EvdevStream("TrackPoint"):evrel('REL_X'):scale(-0.008, 0.008):div(msec(1)):cache()
-- starting pitches (in MIDI note numbers, octaves apart)
local pitches = {12, 24, 36, 48, 60, 72, 84, 96, 108}
local function mtoamp(note)
-- compute loundess for each tone
local intensity = gauss(note, MU, SIGMA)*SCALE
-- map intensity to amplitude
return dbtorms(intensity*96)
end
tostream(pitches):map(function(m)
local tone = INC:scan(function(last, inc)
local next = (last or m)+inc
if next > 120 then
next = next - 108
elseif next < 12 then
next = next + 108
end
return next
end):cache()
return tone:map(mtof_raw):TriOsc() * tone:map(mtoamp)
end):fold(function(a, b) return a+b end):ravel():gain(1/#pitches):play()
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