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CZ oscillators: refactor and add phase aligned versions
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@magnetophon
magnetophon committed Jul 3, 2020
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Expand Up @@ -986,7 +986,19 @@ released under LGPL, STK-4.3, MIT, BSD, or a similar FOSS license.
************************************************************************/

//===================== Casio CZ Oscillators ==========================
// Oscillators that mimics some of the Casio CZ oscillators.
// Oscillators that mimic some of the Casio CZ oscillators.
//
// There are two sets:
// - A set with an index parameter
// - A set with a res parameter
//
// The "index oscillators" outputs a sine wave at index=0 and gets brighter with a higher index.
// There are two versions of the "index oscillators":
// - with P appended to the name: is phase aligned with 'fund:sin'
// - without P appended to the name: has the phase of the original CZ oscillators
//
// The "res oscillators" have a resonant frequency.
// "res" is the frequency of resonance as a factor of the fundamental pitch.
//=====================================================================

//----------`(os.)CZsaw`----------
Expand All @@ -1006,12 +1018,35 @@ released under LGPL, STK-4.3, MIT, BSD, or a similar FOSS license.
//------------------------------------------------------------
// Author: Bart Brouns
// License: GPLv3
// CZ oscilators by Mike Moser-Booth. ported from pd to Faust by Bart Brouns
// CZ oscillators by Mike Moser-Booth:
// https://forum.pdpatchrepo.info/topic/5992/casio-cz-oscillators
// Ported from pd to Faust by Bart Brouns

CZsaw(fund, index) = (((fund*((.5-tmp)/tmp)),(-1*fund+1)*((.5-tmp)/(1-tmp))):min+fund)*2*ma.PI:cos
with {
tmp = (.5-(index*.5)):max(0.01):min(0.5);
};
CZsaw(fund, index) = CZ.sawChooseP(fund, index, 0);

//----------`(os.)CZsawP`----------
// Oscillator that mimics the Casio CZ saw oscillator,
// with it's phase aligned to `fund:sin`.
// `CZsawP` is a standard Faust function.
//
// #### Usage
//
// ```
// CZsawP(fund,index) : _
// ```
//
// Where:
//
// * `fund`: a saw-tooth waveform between 0 and 1 that the oscillator slaves to
// * `index`: the brightness of the oscillator, 0 to 1. 0 = sine-wave, 1 = saw-wave
//------------------------------------------------------------
// Author: Bart Brouns
// License: GPLv3
// CZ oscillators by Mike Moser-Booth:
// https://forum.pdpatchrepo.info/topic/5992/casio-cz-oscillators
// Ported from pd to Faust by Bart Brouns

CZsawP(fund, index) = CZ.sawChooseP(fund, index, 1);

//----------`(os.)CZsquare`----------
// Oscillator that mimics the Casio CZ square oscillator
Expand All @@ -1030,12 +1065,35 @@ with {
//------------------------------------------------------------
// Author: Bart Brouns
// License: GPLv3
// CZ oscilators by Mike Moser-Booth. ported from pd to Faust by Bart Brouns
// CZ oscillators by Mike Moser-Booth:
// https://forum.pdpatchrepo.info/topic/5992/casio-cz-oscillators
// Ported from pd to Faust by Bart Brouns

CZsquare(fund, index) = (fund>=0.5), (ma.decimal((fund*2)+1)<:_-min(_,(-1*_+1)*((INDEX)/(1-INDEX)))) :+ *ma.PI:cos*0.5
with {
INDEX = (index:pow(0.25)) * 0.98;
};
CZsquare(fund, index) = CZ.squareChooseP(fund, index, 0);

//----------`(os.)CZsquareP`----------
// Oscillator that mimics the Casio CZ square oscillator,
// with it's phase aligned to `fund:sin`.
// `CZsquareP` is a standard Faust function.
//
// #### Usage
//
// ```
// CZsquareP(fund,index) : _
// ```
//
// Where:
//
// * `fund`: a saw-tooth waveform between 0 and 1 that the oscillator slaves to
// * `index`: the brightness of the oscillator, 0 to 1. 0 = sine-wave, 1 = square-wave
//------------------------------------------------------------
// Author: Bart Brouns
// License: GPLv3
// CZ oscillators by Mike Moser-Booth:
// https://forum.pdpatchrepo.info/topic/5992/casio-cz-oscillators
// Ported from pd to Faust by Bart Brouns

CZsquareP(fund, index) = CZ.squareChooseP(fund, index, 1);

//----------`(os.)CZpulse`----------
// Oscillator that mimics the Casio CZ pulse oscillator
Expand All @@ -1054,12 +1112,35 @@ with {
//------------------------------------------------------------
// Author: Bart Brouns
// License: GPLv3
// CZ oscilators by Mike Moser-Booth. ported from pd to Faust by Bart Brouns
// CZ oscillators by Mike Moser-Booth:
// https://forum.pdpatchrepo.info/topic/5992/casio-cz-oscillators
// Ported from pd to Faust by Bart Brouns

CZpulse(fund, index) = ((fund-min(fund,((-1*fund+1)*(INDEX/(1-INDEX)))))*2*ma.PI):cos
with {
INDEX = index:min(0.99):max(0);
};
CZpulse(fund, index) = CZ.pulseChooseP(fund, index, 0);

//----------`(os.)CZpulseP`----------
// Oscillator that mimics the Casio CZ pulse oscillator,
// with it's phase aligned to `fund:sin`.
// `CZpulseP` is a standard Faust function.
//
// #### Usage
//
// ```
// CZpulseP(fund,index) : _
// ```
//
// Where:
//
// * `fund`: a saw-tooth waveform between 0 and 1 that the oscillator slaves to
// * `index`: the brightness of the oscillator, 0 gives a sine-wave, 1 is closer to a pulse
//------------------------------------------------------------
// Author: Bart Brouns
// License: GPLv3
// CZ oscillators by Mike Moser-Booth:
// https://forum.pdpatchrepo.info/topic/5992/casio-cz-oscillators
// Ported from pd to Faust by Bart Brouns

CZpulseP(fund, index) = CZ.pulseChooseP(fund, index, 1);

//----------`(os.)CZsinePulse`----------
// Oscillator that mimics the Casio CZ sine/pulse oscillator
Expand All @@ -1078,12 +1159,35 @@ with {
//------------------------------------------------------------
// Author: Bart Brouns
// License: GPLv3
// CZ oscilators by Mike Moser-Booth. ported from pd to Faust by Bart Brouns
// CZ oscillators by Mike Moser-Booth:
// https://forum.pdpatchrepo.info/topic/5992/casio-cz-oscillators
// Ported from pd to Faust by Bart Brouns

CZsinePulse(fund, index) = (min(fund*((0.5-INDEX)/INDEX),(-1*fund+1)*((.5-INDEX)/(1-INDEX)))+fund)*4*ma.PI:cos
with {
INDEX = ((index*-0.49)+0.5);
};
CZsinePulse(fund, index) = CZ.sinePulseChooseP(fund, index, 0);

//----------`(os.)CZsinePulseP`----------
// Oscillator that mimics the Casio CZ sine/pulse oscillator,
// with it's phase aligned to `fund:sin`.
// `CZsinePulseP` is a standard Faust function.
//
// #### Usage
//
// ```
// CZsinePulseP(fund,index) : _
// ```
//
// Where:
//
// * `fund`: a saw-tooth waveform between 0 and 1 that the oscillator slaves to
// * `index`: the brightness of the oscillator, 0 gives a sine-wave, 1 is a sine minus a pulse
//------------------------------------------------------------
// Author: Bart Brouns
// License: GPLv3
// CZ oscillators by Mike Moser-Booth:
// https://forum.pdpatchrepo.info/topic/5992/casio-cz-oscillators
// Ported from pd to Faust by Bart Brouns

CZsinePulseP(fund, index) = CZ.sinePulseChooseP(fund, index, 1);

//----------`(os.)CZhalfSine`----------
// Oscillator that mimics the Casio CZ half sine oscillator
Expand All @@ -1102,12 +1206,35 @@ with {
//------------------------------------------------------------
// Author: Bart Brouns
// License: GPLv3
// CZ oscilators by Mike Moser-Booth. ported from pd to Faust by Bart Brouns
// CZ oscillators by Mike Moser-Booth:
// https://forum.pdpatchrepo.info/topic/5992/casio-cz-oscillators
// Ported from pd to Faust by Bart Brouns

CZhalfSine(fund, index) = (select2(fund<.5, .5*(fund-.5)/INDEX+.5, fund):min(1))*2*ma.PI:cos
with {
INDEX = (.5-(index*0.5)):min(.5):max(.01);
};
CZhalfSine(fund, index) = CZ.halfSineChooseP(fund, index, 0);

//----------`(os.)CZhalfSineP`----------
// Oscillator that mimics the Casio CZ half sine oscillator,
// with it's phase aligned to `fund:sin`.
// `CZhalfSineP` is a standard Faust function.
//
// #### Usage
//
// ```
// CZhalfSineP(fund,index) : _
// ```
//
// Where:
//
// * `fund`: a saw-tooth waveform between 0 and 1 that the oscillator slaves to
// * `index`: the brightness of the oscillator, 0 gives a sine-wave, 1 is somewhere between a saw and a square
//------------------------------------------------------------
// Author: Bart Brouns
// License: GPLv3
// CZ oscillators by Mike Moser-Booth:
// https://forum.pdpatchrepo.info/topic/5992/casio-cz-oscillators
// Ported from pd to Faust by Bart Brouns

CZhalfSineP(fund, index) = CZ.halfSineChooseP(fund, index, 1);

//----------`(os.)CZresSaw`----------
// Oscillator that mimics the Casio CZ resonant saw-tooth oscillator
Expand All @@ -1126,9 +1253,11 @@ with {
//------------------------------------------------------------
// Author: Bart Brouns
// License: GPLv3
// CZ oscilators by Mike Moser-Booth. ported from pd to Faust by Bart Brouns
// CZ oscillators by Mike Moser-Booth:
// https://forum.pdpatchrepo.info/topic/5992/casio-cz-oscillators
// Ported from pd to Faust by Bart Brouns

CZresSaw(fund,res) = (((-1*(1-fund))*((cos((ma.decimal((max(1,res)*fund)+1))*2*ma.PI)*-.5)+.5))*2)+1;
CZresSaw(fund,res) = CZ.resSaw(fund,res);

//----------`(os.)CZresTriangle`----------
// Oscillator that mimics the Casio CZ resonant triangle oscillator
Expand All @@ -1147,12 +1276,11 @@ CZresSaw(fund,res) = (((-1*(1-fund))*((cos((ma.decimal((max(1,res)*fund)+1))*2*m
//------------------------------------------------------------
// Author: Bart Brouns
// License: GPLv3
// CZ oscilators by Mike Moser-Booth. ported from pd to Faust by Bart Brouns
// CZ oscillators by Mike Moser-Booth:
// https://forum.pdpatchrepo.info/topic/5992/casio-cz-oscillators
// Ported from pd to Faust by Bart Brouns

CZresTriangle(fund,res) = select2(fund<.5, 2-(fund*2), fund*2)*tmp*2-1
with {
tmp = ((fund*(res:max(1)))+1:ma.decimal)*2*ma.PI:cos*.5+.5;
};
CZresTriangle(fund,res) = CZ.resTriangle(fund,res);

//----------`(os.)CZresTrap`----------
// Oscillator that mimics the Casio CZ resonant trapeze oscillator
Expand All @@ -1171,9 +1299,65 @@ with {
//------------------------------------------------------------
// Author: Bart Brouns
// License: GPLv3
// CZ oscilators by Mike Moser-Booth. ported from pd to Faust by Bart Brouns

CZresTrap(fund, res) = (((1-fund)*2):min(1)*sin(ma.decimal(fund*(res:max(1)))*2*ma.PI));
// CZ oscillators by Mike Moser-Booth:
// https://forum.pdpatchrepo.info/topic/5992/casio-cz-oscillators
// Ported from pd to Faust by Bart Brouns

CZresTrap(fund, res) = CZ.resTrap(fund, res);

CZ =
environment {
saw(fund, index) = sawChooseP(fund, index, 0);
sawP(fund, index) = sawChooseP(fund, index, 1);
sawChooseP(fund, index, p) =
(((FUND(fund,allign,p)*((.5-INDEX)/INDEX)),(-1*FUND(fund,allign,p)+1)*((.5-INDEX)/(1-INDEX))):min+FUND(fund,allign,p))*2*ma.PI:cos
with {
INDEX = (.5-(index*.5)):max(0.01):min(0.5);
allign = si.interpolate(index, 0.75, 0.5);
};
square(fund, index) = squareChooseP(fund, index, 0);
squareP(fund, index) = squareChooseP(fund, index, 1);
squareChooseP(fund, index, p) = (FUND(fund,allign,p)>=0.5), (ma.decimal((FUND(fund,allign,p)*2)+1)<:_-min(_,(-1*_+1)*((INDEX)/(1-INDEX)))) :+ *ma.PI:cos
with {
INDEX = (index:pow(0.25)):max(0):min(1);
allign = si.interpolate(INDEX, -0.25, 0);
};

pulse(fund, index) = pulseChooseP(fund, index, 0);
pulseP(fund, index) = pulseChooseP(fund, index, 1);
pulseChooseP(fund, index, p) = ((FUND(fund,allign,p)-min(FUND(fund,allign,p),((-1*FUND(fund,allign,p)+1)*(INDEX/(1-INDEX)))))*2*ma.PI):cos
with {
INDEX = index:min(0.99):max(0);
allign = si.interpolate(index, -0.25, 0.0);
};

sinePulse(fund, index) = sinePulseChooseP(fund, index, 0);
sinePulseP(fund, index) = sinePulseChooseP(fund, index, 1);
sinePulseChooseP(fund, index, p) = (min(FUND(fund,allign,p)*((0.5-INDEX)/INDEX),(-1*FUND(fund,allign,p)+1)*((.5-INDEX)/(1-INDEX)))+FUND(fund,allign,p))*4*ma.PI:cos
with {
INDEX = ((index*-0.49)+0.5);
allign = si.interpolate(index, -0.125, -0.25);
};

halfSine(fund, index) = halfSineChooseP(fund, index, 0);
halfSineP(fund, index) = halfSineChooseP(fund, index, 1);
halfSineChooseP(fund, index, p) = (select2(FUND(fund,allign,p)<.5, .5*(FUND(fund,allign,p)-.5)/INDEX+.5, FUND(fund,allign,p)):min(1))*2*ma.PI:cos
with {
INDEX = (.5-(index*0.5)):min(.5):max(.01);
allign = si.interpolate(index:min(0.975), -0.25, -0.5);
};
FUND =
case {
(fund,allign,0) => fund;
(fund,allign,1) => (fund+allign) : ma.frac; // allign phase with fund
};
resSaw(fund,res) = (((-1*(1-fund))*((cos((ma.decimal((max(1,res)*fund)+1))*2*ma.PI)*-.5)+.5))*2)+1;
resTriangle(fund,res) = select2(fund<.5, 2-(fund*2), fund*2)*INDEX*2-1
with {
INDEX = ((fund*(res:max(1)))+1:ma.decimal)*2*ma.PI:cos*.5+.5;
};
resTrap(fund, res) = (((1-fund)*2):min(1)*sin(ma.decimal(fund*(res:max(1)))*2*ma.PI));
};

//===============================PolyBLEP-Based Oscillators=================================

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