// Für Elise | Piano Contest
// Grand Piano
// by srtuss 2022/12/7
//
// In this implementation, we attempt a piano sound in a purely and simply subtractive-synthesis manner.
// We want to keep synthesis as simple and fast as possible, because we will end up playing LOTS of synth voices simultaneously (strings
// may keep vibrating for several seconds).
// It is based around a synthesizer preset in FL Studio called "Grand piano", by Dave Hughes
//
// After listening to some piano sounds in our DAW, and looking at some waveforms and spectrograms, we can make the following basic observations:
// * Keys sound very different at different octaves. Low keys have a harsh, metallic timbre. High keys become smooth like a sinusoid.
// * The waveforms produced are not merely pure tones, but have a shimmering quality, like subtle slow frequency modulation.
// * The hammering action produces a brief amplitude spike, followed by a gradual decay.
// * The vibration of low keys fades slower than high keys.
//
// HOW IT WORKS
// We use a total of 4 wavetable oscillators per "key press".
// Each wavetable holds a timbre related to a pitch-range on the piano (taken from sampled piano sounds).
// The intensity/contribution of each oscillator varies depending on the note that is pressed.
// Each oscillator has it's own gentle frequency modulation which creates a shimmering quality when mixed together with the other oscillators.
// The output of the oscillators is mixed and fed through a lowpass filter.
// The lowpass cutoff and amplitude are modulate to mimic the piano hammering action.
// The oscillator for the highest pitches receives a burst of FM to further mimic the piano hammering action.
// Finally the sound passes through effect processors:
// * A chorus to increase the amount of shimmer, and to add stereo qualities. A chorus effect creates detuned copies of the
// input signal. This is the same as multiplying the total number of oscillators, but without additional computational cost.
// * A reverb to give the impression of a large space around the piano.
//
//
// Forked from "Für Elise | Piano Contest" by reinder
// https://dittytoy.net/ditty/cb751b4b3b
ditty.bpm = 60;
// Simple allpass reverberator, based on this article by Spin Semiconductor:
// http://www.spinsemi.com/knowledge_base/effects.html
const reverb = filter.def(class {
constructor(opt) {
this.lastReturn = 0;
this.krt = .4;
this.delaylines = [];
this.flt = new SVF({fc:.001, q:.5, num:1, mode: 'hp'});
this.pred = new Delayline(4000);
[263, 863, 1319, 1433, 439, 359, 887, 1399, 233, 1367, 4253, 2903].forEach((dl) => this.delaylines.push(new Delayline(dl)));
}
allpass(delayline, x, k) {
var delayin = x - delayline.lastOut * k;
var y = delayline.lastOut + k * delayin;
delayline.clock(delayin);
return y;
}
process(input, opt) {
var inv = input[0];
var dls = this.delaylines;
inv = this.flt.process(this.pred.clock(inv));
var v = this.lastReturn;
// Let the signal pass through the loop of delay lines. Inject input signal at multiple locations.
v = this.allpass(dls[0], v + inv, .5);
v = this.allpass(dls[1], v, .5);
dls[2].clock(v);
v = dls[2].lastOut * this.krt;
v = this.allpass(dls[3], v + inv, .5);
v = this.allpass(dls[4], v, .5);
dls[5].clock(v);
v = dls[5].lastOut * this.krt;
v = this.allpass(dls[6], v + inv, .5);
v = this.allpass(dls[7], v, .5);
dls[8].clock(v);
v = dls[8].lastOut * this.krt;
v = this.allpass(dls[9], v + inv, .5);
v = this.allpass(dls[10], v, .5);
dls[11].clock(v);
v = dls[11].lastOut * this.krt;
this.lastReturn = v;
// Tap the delay lines at randomized locations and accumulate the output signal.
var ret = [0, 0];
ret[0] += dls[2].tap(111);
ret[1] += dls[2].tap(2250);
ret[0] += dls[5].tap(311);
ret[1] += dls[5].tap(1150);
ret[0] += dls[8].tap(511);
ret[1] += dls[8].tap(50);
ret[0] += dls[11].tap(4411);
ret[1] += dls[11].tap(540);
// Mix wet + dry signal.
ret[0] = ret[0] * opt.wet + input[0] * opt.dry;
ret[1] = ret[1] * opt.wet + input[1] * opt.dry;
var m = (ret[0] + ret[1])*.5;
var s = (ret[0] - ret[1])*.5;
s *= 2;
return [m+s, m-s];
}
});
const chorus = filter.def(class {
constructor(options) {
this.lastOutput = [0, 0];
var time = 60 / ditty.bpm;
//time *= 3 / 4;
time /= 2;
var n = Math.floor(time / ditty.dt);
this.delay = new Delayline(5000);
this.ops = [];
for(var i = 0; i < 9; ++i) {
var t = i/9;
this.ops.push({p:t, f: 1, fl: t, fr: 1-t});
}
}
process(inp, options) {
this.delay.clock(inp[0]);
var vl = 0, vr = 0;
for(var i = 0; i < this.ops.length; ++i) {
var op = this.ops[i];
var p = (Math.sin(op.p*Math.PI*2)*.5+.5)*40;
var pi = ~~p;
var v = lerp(this.delay.tap(pi), this.delay.tap(pi+1), p-pi);
vl += v * op.fl;
vr += v * op.fr;
op.p += ditty.dt * op.f;
}
inp[0] = inp[0] * .5 + vl * .1;
inp[1] = inp[1] * .5 + vr * .1;
return inp;
}
});
const series = (n, lambda) => {
var r = [];
for(var i = 0; i < n; ++i)
r.push(lambda(i));
return r;
}
const spectral = (amps, phas, length) => {
var sum = 0;
for(var i = 0; i < amps.length; ++i)
sum += Math.abs(amps[i]);
for(var i = 0; i < amps.length; ++i)
amps[i] /= sum;
var res = new Float32Array(length);
for(var i = 0; i < amps.length; ++i) {
var f = (i + 1) * Math.PI * 2;
var amp = amps[i];
var ph = phas[i];
for(var j = 0; j < length; ++j) {
var x = j / length;
res[j] += Math.sin(x * f + ph) * amp;
}
}
return res;
}
// Wavetable data, encoded as amplitudes and phases of each harmonic
var op1 = {a:[2,0,2,3,4,12,4,6,8,7,21,6,13,8,25,17,13,9,17,20,7,14,19,17,12,31,12,13,20,10,29,9,12,15,14,9,22,27,19,13,26,12,
27,14,11,23,21,17,17,14,34,16,31,11,15,26,34,20,23,27,26,26,14,17,30,20,25,27,10,15,14,12,20,29,26,21,37,21,24,23,19,28,37,16,
26,39,26,19,31,36,22,24,27,33,31,30,32,35,21,31,28,25,28,30,24,33,35,26,37,36,43,29,39,45,34,36,42,33,37,45,45,31,34,51,37,37,
38,31],p:[186,220,171,225,174,196,224,242,168,228,135,98,218,143,203,-45,120,224,117,-22,142,163,241,-14,170,125,194,115,28,
-51,77,220,49,77,122,222,87,135,171,-40,120,129,90,-20,203,171,-87,204,44,103,157,266,192,167,-40,18,20,120,193,261,142,171,
151,-64,95,220,101,151,141,23,140,-78,136,138,167,172,150,250,77,28,173,89,60,248,35,-66,93,139,218,195,-83,84,192,-45,263,140,
203,-65,145,32,258,146,251,-14,161,-36,222,104,-90,162,257,95,-34,150,201,20,102,120,251,255,33,121,133,39,-23,190,146,-13]};
var op2 = {a:[1,0,3,4,11,5,6,5,9,7,14,7,19,8,12,10,16,13,17,9,10,16,22,15,13,15,10,13,15,9,22,13,13,28,16,20,20,22,19,14,18,
15,27,15,17,18,24,17,20,19,29,25,27,22,16,20,30,23,24,19,22,24,22,22,25,24,23,21,10,15,20,19,26,26,36,25,28,21,33,24,26,26,35,
30,23,28,26,21,26,34,27,23,41,30,25,26,34,33,31,35,28,29,29,35,25,39,27,35,37,42,32,31,29,43,28,27,32,42,41,29,32,38,42,41,42,
30,48,38],p:[213,204,195,204,67,206,117,-58,183,-54,103,9,-54,121,-68,22,245,259,240,35,155,189,188,-2,142,161,-76,118,60,-61,
103,-28,-17,37,32,236,74,85,97,-17,4,119,169,47,-51,167,261,157,-43,3,159,255,253,125,-1,-22,99,35,251,206,36,94,90,-67,205,
181,115,145,80,39,58,-90,153,119,96,94,40,-79,81,101,62,57,39,255,12,230,8,124,-18,-84,-47,114,204,54,-48,142,232,-78,75,-29,
-79,97,265,35,66,268,243,65,5,120,-68,121,23,126,260,91,69,94,-74,-76,111,119,102,-9,-3,237,198,10]};
var op3 = {a:[0,8,13,22,14,21,20,19,23,21,28,31,29,30,28,26,36,38,35,35,35,44,39,41,39,45,34,39,40,37,42,43,47,40,52,35,51,39,
47,36,45,41,51,38,44,47,56,45,48,45,55,48,51,48,44,36,46,54,48,42,51,62,47,52,48,46,52,76,49,41,53,47,59,51,46,52,45,45,50,46,
48,77,58,41,50,54,59,54,62,54,47,55,63,59,50,42,72,47,47,45,57,52,59,51,50,77,55,45,66,46,57,49,53,49,66,55,45,68,50,43,57,62,
57,67,56,47,62,53],p:[0,0,0,30,38,98,243,-84,-29,-59,-42,29,183,21,115,124,209,-30,187,97,218,-6,128,-11,264,259,152,226,217,
246,7,19,191,228,223,253,42,-81,1,27,208,219,175,193,128,53,-28,-11,-75,169,131,-56,-36,-64,219,202,209,-66,1,75,-83,133,74,
17,122,168,-63,134,-62,-39,32,208,86,171,-2,207,179,204,209,-47,127,255,102,-13,-83,-85,177,-39,32,-7,-78,17,198,254,169,220,
-30,-87,143,85,106,250,59,-69,152,151,62,155,-10,-27,72,-17,246,32,148,245,124,-63,-14,45,-20,6,229,-40,192,-4,69,12]};
var op4 = {a:[0,14,15,22,21,25,29,31,45,44,41,36,53,48,50,53,62,48,53,52,68,60,60,57,59,47,74,50,63,50,60,56,66,61,62,67,69,
74,58,67,70,63,84,71,57,81,78,74,74,73,73,61,71,71,80,57,88,71,69,59,73,68,77,63,60,81,71,77,77,62,78,76,72,105,60,79,77,66,
79,69,77,94,80,63,84,79,83,89,76,64,72,73,94,89,78,72,96,76,81,89,89,90,81,80,72,80,103,88,87,85,97,86,86,103,93,87,97,100,96,
86,89,97,87,96,93,85,91,84],p:[180,203,193,176,185,187,183,214,174,221,210,164,-67,-86,-29,-68,-57,253,178,258,234,268,-14,
209,58,192,236,195,-15,200,-11,192,253,190,176,-26,-29,265,4,246,197,-9,259,-19,-2,32,-53,125,196,184,-11,184,5,184,253,178,
52,186,-18,184,-10,196,-49,183,-5,242,-24,29,221,3,206,-27,10,99,2,202,-11,172,29,-1,26,127,11,179,58,168,11,239,1,175,5,173,
195,154,-14,180,64,-9,179,154,13,-39,1,161,-8,178,-32,19,6,-11,-57,6,175,265,169,15,55,56,154,180,167,163,17,-15,2,140,180,174]};
const wtables = (wf) => {
var r = [];
for(var j = 0; j < 4; ++j) {
r.push(spectral(
series(128 >> j, (i) => 10**(wf.a[i]/-20)),
series(128 >> j, (i) => wf.p[i]*Math.PI/180),
512));
}
return r;
};
var wfOp1 = wtables(op1);
var wfOp2 = wtables(op2);
var wfOp3 = wtables(op3);
var wfOp4 = wtables(op4);
const ilerp = (a, b, x) => clamp01((x-a) / (b-a))
const piano = synth.def(class {
constructor(opt) {
this.ops = [];
var f = midi_to_hz(opt.note);
var wti = Math.log2(f * 512 * ditty.dt);
wti = ~~clamp(wti, 0, 3);
this.ops.push({p: Math.random(), f: f, wt: wfOp1[wti], pmod: -.01, pmods: 3, amp: ilerp(c7, d2, opt.note)*.5});
this.ops.push({p: Math.random(), f: f, wt: wfOp2[wti], pmod: .01, pmods: 4, amp: ilerp(c7, d2, opt.note)*.5});
this.ops.push({p: Math.random(), f: f, wt: wfOp3[wti], pmod: .03, pmods: 3.2222, amp: ilerp(c0, c3, opt.note)*ilerp(c6, f4, opt.note)});
this.ops.push({p: Math.random(), f: f, wt: wfOp4[wti], pmod: -.03, pmods: 2.99, amp: ilerp(f4, c6, opt.note)+ilerp(c2, c1, opt.note)*.7});
this.flt = new SVF({mode:'lp', num: 3, q: 1});
this.cutoff = .3 + Math.random() * .02;
this.t = 0;
}
process(note, env, tick, opt) {
var v = 0;
for(var i = 0; i < this.ops.length; ++i) {
var op = this.ops[i];
if(i == 3)
op.p += op.f * ditty.dt * (2**(Math.sin(Math.min(this.t*900,2.5)*Math.PI*2) * 1));
else
op.p += op.f * ditty.dt;
while(op.p >= 1)
op.p -= 1;
var ph = op.p + Math.sin(tick*op.pmods) * op.pmod;
var w = (ph*512) & 511;
var opv = lerp(op.wt[w], op.wt[(w+1)&511], ph*512-~~(ph*512));
var vol = 1;
if(i == 3) {
vol = Math.exp(this.t * -10) * .5 + .5;
}
v += opv * vol * op.amp;
}
this.flt.q = lerp(.5,1,Math.exp(this.t * -2.));
if(this.cutoff > .1)
this.cutoff *= .99994;
else
this.cutoff *= .999995;
this.flt.fc = this.cutoff;
v = this.flt.process(v);
v *= (1-clamp01((this.t - .022)*1000)*.33);
this.t += ditty.dt;
return v * env.value;
}
}, { release: 1});
const numWorkers = 2; // increase number of workers when performance is low
const fürEliseData = fürElise();
for (let i=0; i<numWorkers; i++) {
loop( () => {
fürEliseData.notes.forEach( (n, index) => {
sleep(second_to_tick(n.dt));
if (index % numWorkers === i % numWorkers) {
const duration = n.sustain ? Math.max(n.duration, Math.min(n.duration + 0.5, n.sustainMaxDuration)) : n.duration;
piano.play(n.midi, {
amp: n.velocity,
duration: second_to_tick(duration),
pan: (n.midi-50)/50 - .5
});
}
});
}, { name: `Piano ${i}`, sync: fürEliseData.duration, amp: 1.5 })
.connect(chorus.create())
.connect(reverb.create({wet:.1, dry:.8}));;
}
const applause = synth.def(class {
constructor(opt) {
this.l = 1;
this.t = 0;
this.fo = 60;
this.flt = new SVF({mode:"bp", fc:.04, num: 2, q: 1.3});
this.flt2 = new SVF({mode:"bp", fc:.08, num: 2, q: 1.3});
}
process(note, env, tick, opt) {
var v = (Math.random()-.5) * Math.exp(this.t * -this.fo);
this.t += ditty.dt;
if(this.t > this.l) {
this.t = 0;
this.l = lerp(.05 + Math.random() * .05, lerp(.01, .04, Math.random()), env.value);
this.fo = lerp(50, 100, Math.random());
this.flt2.fc = lerp(.08, .1, Math.random());
}
return (this.flt.process(v) + this.flt2.process(v) * 0.2) * env.value;
}
});
loop(() => {
sleep(145);
applause.play(c3, { attack: 2, release: 4, duration: 10, pan: -1 });
applause.play(c3, { attack: 2, release: 4, duration: 10, pan: 1 });
sleep(20);
}, { name: '...', sync: fürEliseData.duration, amp: 1.5 }).connect(reverb.create({wet:.5,dry:.5}));
//
// Use this data. The data contains each note's velocity, duration, and time and whether the sustain pedal is active.
// The data is based on a midi file by: https://www.patreon.com/rousseau
// You can find the recording of the midi file here: https://youtu.be/wfF0zHeU3Zs
//
function fürElise() {
const data = 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const ret = { notes: [], duration: 160 };
for (let i=0, ip=0, n=data.notes, p=data.sustainPedal, sustain=false; i<n.length; i+=4) {
if (n[i+2] > p[ip]) ip++, sustain=!sustain;
ret.notes.push({
midi: n[i+0],
duration: n[i+1],
time: n[i+2],
dt: i>0?n[i+2]-n[i-2]:n[i+2],
velocity: n[i+3],
sustain,
sustainMaxDuration: p[ip]-n[i+2],
});
}
return ret;
}
class Delayline {
constructor(n) {
this.n = ~~n;
this.p = 0;
this.lastOut = 0;
this.data = new Float32Array(n);
}
clock(input) {
this.lastOut = this.data[this.p];
this.data[this.p] = input;
if(++this.p >= this.n) {
this.p = 0;
}
return this.lastOut;
}
tap(offset) {
var x = this.p - offset - 1;
x %= this.n;
if(x < 0) {
x += this.n;
}
return this.data[x];
}
}
// State Variable Filter based on an article by cytomic Sound Music Software
// https://cytomic.com/files/dsp/SvfLinearTrapOptimised2.pdf
function processSVF(s, input, a1, a2, a3, k) {
var v1, v2, v3;
v3 = input - s.ic2eq;
v1 = a1 * s.ic1eq + a2 * v3;
v2 = s.ic2eq + a2 * s.ic1eq + a3 * v3;
s.ic1eq = 2 * v1 - s.ic1eq;
s.ic2eq = 2 * v2 - s.ic2eq;
s.lp = v2;
s.bp = v1;
s.hp = input - k * v1 - v2;
s.ap = s.lp + s.hp - k * s.bp;
}
class SVF {
constructor(opt)
{
this.stages = [];
this.mode = opt ? opt.mode || 'lp' : 'lp';
this.fc = 0;
this.q = 1;
this.num = opt ? opt.num || 1 : 1;
// g parameter determines cutoff
// k parameter = 1/Q
for(var i = 0; i < this.num; ++i) {
this.stages.push({lp:0, bp:0, hp:0, ap:0, ic1eq:0, ic2eq:0});
}
this.q = opt && isFinite(opt.q) ? opt.q : 1;
this.fc = opt && isFinite(opt.fc) ? opt.fc : .25;
}
process(input)
{
if(this.fc != this._fc) {
this._fc = this.fc;
this._q = this.q;
var fc = this.fc * .5;
if (fc >= 0 && fc < .5) {
this.g = Math.tan(Math.PI * fc);
this.k = 1 / this.q;
this.a1 = 1 / (1 + this.g * (this.g + this.k));
this.a2 = this.g * this.a1;
this.a3 = this.g * this.a2;
}
}
if(this.q != this._q) {
this._q = this.q;
this.k = 1 / this.q;
this.a1 = 1 / (1 + this.g * (this.g + this.k));
this.a2 = this.g * this.a1;
this.a3 = this.g * this.a2;
}
for(var i = 0; i < this.num; ++i) {
processSVF(this.stages[i], input, this.a1, this.a2, this.a3, this.k);
processSVF(this.stages[i], input, this.a1, this.a2, this.a3, this.k);
input = this.stages[i][this.mode];
}
return input;
}
}
