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physmodels.lib
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//##################################### physmodels.lib ###################################
// Faust physical modeling library. Its official prefix is `pm`.
//
// This library provides an environment to facilitate physical modeling of musical
// instruments. It contains dozens of functions implementing low and high level
// elements going from a simple waveguide to fully operational models with
// built-in UI, etc.
//
// It is organized as follows:
//
// * [Global Variables](#global-variables): useful pre-defined variables for
// physical modeling (e.g., speed of sound, etc.).
// * [Conversion Tools](#conversion-tools-1): conversion functions specific
// to physical modeling (e.g., length to frequency, etc.).
// * [Bidirectional Utilities](#bidirectional-utilities): functions to create
// bidirectional block diagrams for physical modeling.
// * [Basic Elements](#basic-elements-1): waveguides, specific types of filters, etc.
// * [String Instruments](#string-instruments): various types of strings
// (e.g., steel, nylon, etc.), bridges, guitars, etc.
// * [Bowed String Instruments](#bowed-string-instruments): parts and models
// specific to bowed string instruments (e.g., bows, bridges, violins, etc.).
// * [Wind Instrument](#wind-instruments): parts and models specific to wind
// instruments (e.g., reeds, mouthpieces, flutes, clarinets, etc.).
// * [Exciters](#exciters): pluck generators, "blowers", etc.
// * [Modal Percussions](#modal-percussions): percussion instruments based on
// modal models.
// * [Vocal Synthesis](#vocal-synthesis): functions for various vocal synthesis
// techniques (e.g., fof, source/filter, etc.) and vocal synthesizers.
// * [Misc Functions](#misc-functions): any other functions that don't fit in
// the previous category (e.g., nonlinear filters, etc.).
//
// This library is part of the Faust Physical Modeling ToolKit.
// More information on how to use this library can be found on this [page](https://ccrma.stanford.edu/~rmichon/pmFaust) or this [video](https://faust.grame.fr/community/events/#introduction-to-the-faust-physical-modeling-toolkit-romain-michon). Tutorials on how to make
// physical models of musical instruments using Faust can be found
// [here](https://ccrma.stanford.edu/~rmichon/faustTutorials/#making-physical-models-of-musical-instruments-with-faust) as well.
//
// #### References
// * <https://github.com/grame-cncm/faustlibraries/blob/master/physmodels.lib>
//########################################################################################
// Authors: Romain Michon, Pierre-Amaury Grumiaux, and Yann Orlarey
import("stdfaust.lib");
declare name "Faust Physical Models Library";
declare version "1.1.0";
/*
TODO:
- It'd be cool to have a version of the block diagram generator that automatically flips
things based on the use of chains, etc.
- When setting pole of filters by hand (e.g. smooth, should adjust pole in function of SR)
- Probably need a single resonator function / see how to integrate that with "mode"
- Need a non-linear function and see how this can be integrated with modal synthesis
- See how bowed modal models could be integrated to this
- Currently still missing keyboard instruments
- Currently still missing vocal synth: easy to fix (create a formant filter function)
- Real polyphonic instruments should be designated with some kind of prefix (e.g.,
full)
*/
//=============================Global Variables===========================================
// Useful pre-defined variables for physical modeling.
//========================================================================================
//--------------`(pm.)speedOfSound`----------
// Speed of sound in meters per second (340m/s).
//--------------------------------------
speedOfSound = 340;
//--------------`(pm.)maxLength`----------
// The default maximum length (3) in meters of strings and tubes used in this
// library. This variable should be overriden to allow longer strings or tubes.
//--------------------------------------
maxLength = 3;
//================================Conversion Tools=======================================
// Useful conversion tools for physical modeling.
//========================================================================================
//--------------`(pm.)f2l`----------
// Frequency to length in meters.
//
// #### Usage
//
// ```
// f2l(freq) : distanceInMeters
// ```
//
// Where:
//
// * `freq`: the frequency
//-------------------------------
f2l(freq) = speedOfSound/freq;
//--------------`(pm.)l2f`----------
// Length in meters to frequency.
//
// #### Usage
//
// ```
// l2f(length) : freq
// ```
//
// Where:
//
// * `length`: length/distance in meters
//-------------------------------
l2f(length) = speedOfSound/length;
//--------------`(pm.)l2s`----------
// Length in meters to number of samples.
//
// #### Usage
//
// ```
// l2s(l) : numberOfSamples
// ```
//
// Where:
//
// * `l`: length in meters
//-------------------------------
l2s(l) = l*ma.SR/speedOfSound;
//=============================Bidirectional Utilities====================================
// Set of fundamental functions to create bi-directional block diagrams in Faust.
// These elements are used as the basis of this library to connect high level
// elements (e.g., mouthpieces, strings, bridge, instrument body, etc.). Each
// block has 3 inputs and 3 outputs. The first input/output carry left going
// waves, the second input/output carry right going waves, and the third
// input/output is used to carry any potential output signal to the end of the
// algorithm.
//========================================================================================
//--------------`(pm.)basicBlock`----------
// Empty bidirectional block to be used with [`chain`](#chain): 3 signals ins
// and 3 signals out.
//
// #### Usage
//
// ```
// chain(basicBlock : basicBlock : etc.)
// ```
//-------------------------------
basicBlock = _,_,_;
//-------`(pm.)chain`----------
// Creates a chain of bidirectional blocks.
// Blocks must have 3 inputs and outputs. The first input/output carry left
// going waves, the second input/output carry right going waves, and the third
// input/output is used to carry any potential output signal to the end of the
// algorithm. The implied one sample delay created by the `~` operator is
// generalized to the left and right going waves. Thus, `n` blocks in `chain()`
// will add an `n` samples delay to both left and right going waves.
//
// #### Usage
//
// ```
// leftGoingWaves,rightGoingWaves,mixedOutput : chain( A : B ) : leftGoingWaves,rightGoingWaves,mixedOutput
// with{
// A = _,_,_;
// B = _,_,_;
// };
// ```
//-----------------------------
chain(A:As) = ((ro.crossnn(1),_',_ : _,A : ro.crossnn(1),_,_ : _,chain(As) : ro.crossnn(1),_,_)) ~ _ : !,_,_,_;
chain(A) = A;
//-------`(pm.)inLeftWave`--------------
// Adds a signal to left going waves anywhere in a [`chain`](#chain) of blocks.
//
// #### Usage
//
// ```
// model(x) = chain(A : inLeftWave(x) : B)
// ```
//
// Where `A` and `B` are bidirectional blocks and `x` is the signal added to left
// going waves in that chain.
//--------------------------------
inLeftWave(x) = +(x),_,_;
//-------`(pm.)inRightWave`--------------
// Adds a signal to right going waves anywhere in a [`chain`](#chain) of blocks.
//
// #### Usage
//
// ```
// model(x) = chain(A : inRightWave(x) : B)
// ```
//
// Where `A` and `B` are bidirectional blocks and `x` is the signal added to right
// going waves in that chain.
//--------------------------------
inRightWave(x) = _,+(x),_;
//-------`(pm.)in`--------------
// Adds a signal to left and right going waves anywhere in a [`chain`](#chain)
// of blocks.
//
// #### Usage
//
// ```
// model(x) = chain(A : in(x) : B)
// ```
//
// Where `A` and `B` are bidirectional blocks and `x` is the signal added to
// left and right going waves in that chain.
//--------------------------------
in(x) = +(x),+(x),_;
//-------`(pm.)outLeftWave`--------------
// Sends the signal of left going waves to the output channel of the [`chain`](#chain).
//
// #### Usage
//
// ```
// chain(A : outLeftWave : B)
// ```
//
// Where `A` and `B` are bidirectional blocks.
//--------------------------------
outLeftWave(x,y,s) = x,y,x+s;
//-------`(pm.)outRightWave`--------------
// Sends the signal of right going waves to the output channel of the [`chain`](#chain).
//
// #### Usage
//
// ```
// chain(A : outRightWave : B)
// ```
//
// Where `A` and `B` are bidirectional blocks.
//--------------------------------
outRightWave(x,y,s) = x,y,y+s;
//-------`(pm.)out`--------------
// Sends the signal of right and left going waves to the output channel of the
// [`chain`](#chain).
//
// #### Usage
//
// ```
// chain(A : out : B)
// ```
//
// Where `A` and `B` are bidirectional blocks.
//--------------------------------
out(x,y,s) = x,y,x+y+s;
//-------`(pm.)terminations`--------------
// Creates terminations on both sides of a [`chain`](#chain) without closing
// the inputs and outputs of the bidirectional signals chain. As for
// [`chain`](#chain), this function adds a 1 sample delay to the bidirectional
// signal, both ways. Of course, this function can be nested within a
// [`chain`](#chain).
//
// #### Usage
//
// ```
// terminations(a,b,c)
// with{
// a = *(-1); // left termination
// b = chain(D : E : F); // bidirectional chain of blocks (D, E, F, etc.)
// c = *(-1); // right termination
// };
// ```
//----------------------------------------
terminations(a,b,c) = (_,ro.crossnn(1),_,_ : +,+,_ : b) ~ (a,c : ro.crossnn(1));
//-------`(pm.)lTermination`----------
// Creates a termination on the left side of a [`chain`](#chain) without
// closing the inputs and outputs of the bidirectional signals chain. This
// function adds a 1 sample delay near the termination and can be nested
// within another [`chain`](#chain).
//
// #### Usage
//
// ```
// lTerminations(a,b)
// with{
// a = *(-1); // left termination
// b = chain(D : E : F); // bidirectional chain of blocks (D, E, F, etc.)
// };
// ```
//----------------------------------------
lTermination(a,b) = (ro.crossnn(1),_,_ : _,+,_ : b) ~ a;
//-------`(pm.)rTermination`----------
// Creates a termination on the right side of a [`chain`](#chain) without
// closing the inputs and outputs of the bidirectional signals chain. This
// function adds a 1 sample delay near the termination and can be nested
// within another [`chain`](#chain).
//
// #### Usage
//
// ```
// rTerminations(b,c)
// with{
// b = chain(D : E : F); // bidirectional chain of blocks (D, E, F, etc.)
// c = *(-1); // right termination
// };
// ```
//----------------------------------------
rTermination(b,c) = (_,_,_,_ : +,_,_ : b) ~ (!,c);
//-------`(pm.)closeIns`----------
// Closes the inputs of a bidirectional chain in all directions.
//
// #### Usage
//
// ```
// closeIns : chain(...) : _,_,_
// ```
//----------------------------------------
closeIns = 0,0,0;
//-------`(pm.)closeOuts`----------
// Closes the outputs of a bidirectional chain in all directions except for the
// main signal output (3d output).
//
// #### Usage
//
// ```
// _,_,_ : chain(...) : _
// ```
//----------------------------------------
closeOuts = !,!,_;
//-------`(pm.)endChain`----------
// Closes the inputs and outputs of a bidirectional chain in all directions
// except for the main signal output (3d output).
//
// #### Usage
//
// ```
// endChain(chain(...)) : _
// ```
//----------------------------------------
endChain(b) = closeIns : b : closeOuts;
//==================================Basic Elements========================================
// Basic elements for physical modeling (e.g., waveguides, specific filters,
// etc.).
//========================================================================================
//-------`(pm.)waveguideN`----------
// A series of waveguide functions based on various types of delays (see
// [`fdelay[n]`](#fdelayn)).
//
// #### List of functions
//
// * `waveguideUd`: unit delay waveguide
// * `waveguideFd`: fractional delay waveguide
// * `waveguideFd2`: second order fractional delay waveguide
// * `waveguideFd4`: fourth order fractional delay waveguide
//
// #### Usage
//
// ```
// chain(A : waveguideUd(nMax,n) : B)
// ```
//
// Where:
//
// * `nMax`: the maximum length of the delays in the waveguide
// * `n`: the length of the delay lines in samples.
//----------------------------------
waveguideUd(nMax,n) = par(i,2,de.delay(nMax,n)),_;
waveguideFd(nMax,n) = par(i,2,de.fdelay(nMax,n)),_;
waveguideFd2(nMax,n) = par(i,2,de.fdelay2(nMax,n)),_;
waveguideFd4(nMax,n) = par(i,2,de.fdelay4(nMax,n)),_;
//-------`(pm.)waveguide`----------
// Standard `pm.lib` waveguide (based on [`waveguideFd4`](#waveguiden)).
//
// #### Usage
//
// ```
// chain(A : waveguide(nMax,n) : B)
// ```
//
// Where:
//
// * `nMax`: the maximum length of the delays in the waveguide
// * `n`: the length of the delay lines in samples.
//----------------------------------
waveguide(nMax,n) = waveguideFd4(nMax,n);
//-------`(pm.)bridgeFilter`----------
// Generic two zeros bridge FIR filter (as implemented in the
// [STK](https://ccrma.stanford.edu/software/stk/)) that can be used to
// implement the reflectance violin, guitar, etc. bridges.
//
// #### Usage
//
// ```
// _ : bridge(brightness,absorption) : _
// ```
//
// Where:
//
// * `brightness`: controls the damping of high frequencies (0-1)
// * `absorption`: controls the absorption of the brige and thus the t60 of
// the string plugged to it (0-1) (1 = 20 seconds)
//----------------------------------
// TODO: perhaps, the coefs of this filter should be adapted in function of SR
bridgeFilter(brightness,absorption,x) = rho * (h0 * x' + h1*(x+x''))
with{
freq = 320;
t60 = (1-absorption)*20;
h0 = (1.0 + brightness)/2;
h1 = (1.0 - brightness)/4;
rho = pow(0.001,1.0/(freq*t60));
};
//-------`(pm.)modeFilter`----------
// Resonant bandpass filter that can be used to implement a single resonance
// (mode).
//
// #### Usage
//
// ```
// _ : modeFilter(freq,t60,gain) : _
// ```
//
// Where:
//
// * `freq`: mode frequency
// * `t60`: mode resonance duration (in seconds)
// * `gain`: mode gain (0-1)
//----------------------------------
modeFilter(freq,t60,gain) = fi.tf2(b0,b1,b2,a1,a2)*gain
with{
b0 = 1;
b1 = 0;
b2 = -1;
w = 2*ma.PI*freq/ma.SR;
r = pow(0.001,1/float(t60*ma.SR));
a1 = -2*r*cos(w);
a2 = r^2;
};
//================================String Instruments======================================
// Low and high level string instruments parts. Most of the elements in
// this section can be used in a bidirectional chain.
//========================================================================================
//-------`(pm.)stringSegment`----------
// A string segment without terminations (just a simple waveguide).
//
// #### Usage
//
// ```
// chain(A : stringSegment(maxLength,length) : B)
// ```
//
// Where:
//
// * `maxLength`: the maximum length of the string in meters (should be static)
// * `length`: the length of the string in meters
//----------------------------------
stringSegment(maxLength,length) = waveguide(nMax,n)
with{
nMax = maxLength : l2s;
n = length : l2s/2;
};
//-------`(pm.)openString`----------
// A bidirectional block implementing a basic "generic" string with a
// selectable excitation position. Lowpass filters are built-in and
// allow to simulate the effect of dispersion on the sound and thus
// to change the "stiffness" of the string.
//
// #### Usage
//
// ```
// chain(... : openString(length,stiffness,pluckPosition,excitation) : ...)
// ```
//
// Where:
//
// * `length`: the length of the string in meters
// * `stiffness`: the stiffness of the string (0-1) (1 for max stiffness)
// * `pluckPosition`: excitation position (0-1) (1 is bottom)
// * `excitation`: the excitation signal
//----------------------------------
openString(length,stiffness,pluckPosition,excitation) = chain(stringSegment(maxStringLength,ntbd) : in(excitation) : dispersionFilters : stringSegment(maxStringLength,btbd))
with{
dispersionFilters = par(i,2,si.smooth(stiffness)),_; // one pole filters
maxStringLength = maxLength;
ntbd = length*pluckPosition; // length of the upper portion of the string
btbd = length*(1-pluckPosition); // length of the lower portion of the string
};
//-------`(pm.)nylonString`----------
// A bidirectional block implementing a basic nylon string with selectable
// excitation position. This element is based on [`openString`](#openstring)
// and has a fix stiffness corresponding to that of a nylon string.
//
// #### Usage
//
// ```
// chain(... : nylonString(length,pluckPosition,excitation) : ...)
// ```
//
// Where:
//
// * `length`: the length of the string in meters
// * `pluckPosition`: excitation position (0-1) (1 is bottom)
// * `excitation`: the excitation signal
//----------------------------------
nylonString(length,pluckPosition,excitation) =
openString(length,stiffness,pluckPosition,excitation)
with{
stiffness = 0.4; // empirically set but it sounds good ;)
};
//-------`(pm.)steelString`----------
// A bidirectional block implementing a basic steel string with selectable
// excitation position. This element is based on [`openString`](#openstring)
// and has a fix stiffness corresponding to that of a steel string.
//
// #### Usage
//
// ```
// chain(... : steelString(length,pluckPosition,excitation) : ...)
// ```
//
// Where:
//
// * `length`: the length of the string in meters
// * `pluckPosition`: excitation position (0-1) (1 is bottom)
// * `excitation`: the excitation signal
//----------------------------------
steelString(length,pluckPosition,excitation) =
openString(length,stiffness,pluckPosition,excitation)
with{
stiffness = 0.05; // empirically set but it sounds good ;)
// in fact, we could almost get rid of the filters in that case,
// but I think it's good to keep them for consistency
};
//-------`(pm.)openStringPick`----------
// A bidirectional block implementing a "generic" string with selectable
// excitation position. It also has a built-in pickup whose position is the
// same as the excitation position. Thus, moving the excitation position
// will also move the pickup.
//
// #### Usage
//
// ```
// chain(... : openStringPick(length,stiffness,pluckPosition,excitation) : ...)
// ```
//
// Where:
//
// * `length`: the length of the string in meters
// * `stiffness`: the stiffness of the string (0-1) (1 for max stiffness)
// * `pluckPosition`: excitation position (0-1) (1 is bottom)
// * `excitation`: the excitation signal
//----------------------------------
openStringPick(length,stiffness,pluckPosition,excitation) = strChain
with{
dispersionFilters = par(i,2,si.smooth(stiffness)),_;
maxStringLength = maxLength;
nti = length*pluckPosition; // length of the upper portion of the string
itb = length*(1-pluckPosition); // length of the lower portion of the string
strChain = chain(stringSegment(maxStringLength,nti) : in(excitation) : out :
dispersionFilters : stringSegment(maxStringLength,itb));
};
//-------`(pm.)openStringPickUp`----------
// A bidirectional block implementing a "generic" string with selectable
// excitation position and stiffness. It also has a built-in pickup whose
// position can be independenly selected. The only constraint is that the
// pickup has to be placed after the excitation position.
//
// #### Usage
//
// ```
// chain(... : openStringPickUp(length,stiffness,pluckPosition,excitation) : ...)
// ```
//
// Where:
//
// * `length`: the length of the string in meters
// * `stiffness`: the stiffness of the string (0-1) (1 for max stiffness)
// * `pluckPosition`: pluck position between the top of the string and the
// pickup (0-1) (1 for same as pickup position)
// * `pickupPosition`: position of the pickup on the string (0-1) (1 is bottom)
// * `excitation`: the excitation signal
//----------------------------------
openStringPickUp(length,stiffness,pluckPosition,pickupPosition,excitation) = strChain
with{
dispersionFilters = par(i,2,si.smooth(stiffness)),_;
maxStringLength = maxLength;
nti = length*pluckPosition; // top to excitation length
nto = nti*pickupPosition; // nuts to pickup length
oti = nti*(1-pickupPosition); // pickup to excitation length
itb = length*(1-pluckPosition); // pickup to bottom length
strChain = chain(stringSegment(maxStringLength,nto) : out :
stringSegment(maxStringLength,oti) : in(excitation) : dispersionFilters :
stringSegment(maxStringLength,itb));
};
//-------`(pm.)openStringPickDown`----------
// A bidirectional block implementing a "generic" string with selectable
// excitation position and stiffness. It also has a built-in pickup whose
// position can be independenly selected. The only constraint is that the
// pickup has to be placed before the excitation position.
//
// #### Usage
//
// ```
// chain(... : openStringPickDown(length,stiffness,pluckPosition,excitation) : ...)
// ```
//
// Where:
//
// * `length`: the length of the string in meters
// * `stiffness`: the stiffness of the string (0-1) (1 for max stiffness)
// * `pluckPosition`: pluck position on the string (0-1) (1 is bottom)
// * `pickupPosition`: position of the pickup between the top of the string
// and the excitation position (0-1) (1 is excitation position)
// * `excitation`: the excitation signal
//----------------------------------
openStringPickDown(length,stiffness,pluckPosition,pickupPosition,excitation) =
strChain
with{
dispersionFilters = par(i,2,si.smooth(stiffness)),_;
maxStringLength = maxLength;
nto = length*pickupPosition; // top to pickup length
nti = nto*pluckPosition; // top to excitation length
ito = nto*(1-pluckPosition); // excitation to pickup length
otb = length*(1-pickupPosition); // pickup to bottom length
strChain = chain(stringSegment(maxStringLength,nti) : in(excitation) :
stringSegment(maxStringLength,ito) : out : dispersionFilters :
stringSegment(maxStringLength,otb));
};
// TODO: eventually, we'd want to implement a generic function here that
// automatically switches the position of elements in the algorithm
// depending on the position of the pick. Even though this is currently
// possible, it will pose optimization issues (we'd want the new mute
// feature of Faust to be generalized in order to do that)
//-------`(pm.)ksReflexionFilter`----------
// The "typical" one-zero Karplus-strong feedforward reflexion filter. This
// filter will be typically used in a termination (see below).
//
// #### Usage
//
// ```
// terminations(_,chain(...),ksReflexionFilter)
// ```
//----------------------------------
ksReflexionFilter = _ <: (_+_')/2;
//-------`(pm.)rStringRigidTermination`----------
// Bidirectional block implementing a right rigid string termination (no damping,
// just phase inversion).
//
// #### Usage
//
// ```
// chain(rStringRigidTermination : stringSegment : ...)
// ```
//----------------------------------
rStringRigidTermination = rTermination(basicBlock,*(-1));
//-------`(pm.)lStringRigidTermination`----------
// Bidirectional block implementing a left rigid string termination (no damping,
// just phase inversion).
//
// #### Usage
//
// ```
// chain(... : stringSegment : lStringRigidTermination)
// ```
//----------------------------------
lStringRigidTermination = lTermination(*(-1),basicBlock);
//-------`(pm.)elecGuitarBridge`----------
// Bidirectional block implementing a simple electric guitar bridge. This
// block is based on [`bridgeFilter`](#bridgeFilter). The bridge doesn't
// implement transmittance since it is not meant to be connected to a
// body (unlike acoustic guitar). It also partially sets the resonance
// duration of the string with the nuts used on the other side.
//
// #### Usage
//
// ```
// chain(... : stringSegment : elecGuitarBridge)
// ```
//----------------------------------
elecGuitarBridge = rTermination(basicBlock,-bridgeFilter(0.8,0.6));
//-------`(pm.)elecGuitarNuts`----------
// Bidirectional block implementing a simple electric guitar nuts. This
// block is based on [`bridgeFilter`](#bridgeFilter) and does essentially
// the same thing as [`elecGuitarBridge`](#elecguitarbridge), but on the
// other side of the chain. It also partially sets the resonance duration of
// the string with the bridge used on the other side.
//
// #### Usage
//
// ```
// chain(elecGuitarNuts : stringSegment : ...)
// ```
//----------------------------------
elecGuitarNuts = lTermination(-bridgeFilter(0.8,0.6),basicBlock);
//-------`(pm.)guitarBridge`----------
// Bidirectional block implementing a simple acoustic guitar bridge. This
// bridge damps more hight frequencies than
// [`elecGuitarBridge`](#elecguitarbridge) and implements a transmittance
// filter. It also partially sets the resonance duration of the string with
// the nuts used on the other side.
//
// #### Usage
//
// ```
// chain(... : stringSegment : guitarBridge)
// ```
//----------------------------------
guitarBridge = rTermination(basicBlock,reflectance) : _,transmittance,_
with{
reflectance = -bridgeFilter(0.4,0.5);
transmittance = _; // TODO
};
//-------`(pm.)guitarNuts`----------
// Bidirectional block implementing a simple acoustic guitar nuts. This
// nuts damps more hight frequencies than
// [`elecGuitarNuts`](#elecguitarnuts) and implements a transmittance
// filter. It also partially sets the resonance duration of the string with
// the bridge used on the other side.
//
// #### Usage
//
// ```
// chain(guitarNuts : stringSegment : ...)
// ```
//----------------------------------
guitarNuts = lTermination(-bridgeFilter(0.4,0.5),basicBlock);
//-------`(pm.)idealString`----------
// An "ideal" string with rigid terminations and where the plucking position
// and the pick-up position are the same. Since terminations are rigid, this
// string will ring forever.
//
// #### Usage
//
// ```
// 1-1' : idealString(length,reflexion,xPosition,excitation)
// ```
//
// With:
// * `length`: the length of the string in meters
// * `pluckPosition`: the plucking position (0.001-0.999)
// * `excitation`: the input signal for the excitation.
//----------------------------------------------------------
idealString(length,pluckPosition,excitation) = wg
with{
maxStringLength = maxLength;
lengthTuning = 0.08; // tuned "by hand"
tunedLength = length-lengthTuning;
nUp = tunedLength*pluckPosition; // upper string segment length
nDown = tunedLength*(1-pluckPosition); // lower string segment length
wg = chain(lStringRigidTermination : stringSegment(maxStringLength,nUp) :
in(excitation) : out : stringSegment(maxStringLength,nDown) :
rStringRigidTermination); // waveguide chain
};
//-------`(pm.)ks`----------
// A Karplus-Strong string (in that case, the string is implemented as a
// one dimension waveguide).
//
// #### Usage
//
// ```
// ks(length,damping,excitation) : _
// ```
//
// Where:
//
// * `length`: the length of the string in meters
// * `damping`: string damping (0-1)
// * `excitation`: excitation signal
//----------------------------------
ks(length,damping,excitation) = endChain(ksChain)
with{
maxStringLength = maxLength;
lengthTuning = 0.05; // tuned "by hand"
tunedLength = length-lengthTuning;
refCoef = (1-damping)*0.2+0.8;
refFilter = ksReflexionFilter*refCoef;
ksChain = terminations(_,chain(in(excitation) :
stringSegment(maxStringLength,tunedLength) : out),refFilter);
};
//-------`(pm.)ks_ui_MIDI`----------
// Ready-to-use, MIDI-enabled Karplus-Strong string with buil-in UI.
//
// #### Usage
//
// ```
// ks_ui_MIDI : _
// ```
//----------------------------------
ks_ui_MIDI = gate : impulseExcitation*gain : ks( (freq : f2l), damping )
with{
f = hslider("v:karplus/h:[0]params/[0]freq[style:knob]",440,50,1000,0.01);
bend = ba.semi2ratio(hslider("v:karplus/h:[0]params/[1]bend[style:knob][hidden:1][midi:pitchwheel]"
,0,-2,2,0.01)) : si.polySmooth(gate,0.999,1);
gain = hslider("v:karplus/h:[0]params/[2]gain[style:knob]",0.8,0,1,0.01);
s = hslider("v:karplus/h:[0]params/[3]sustain[hidden:1][midi:ctrl 64][style:knob]"
,0,0,1,1);
damping = hslider("v:karplus/h:[0]params/[1]damping[midi:ctrl 1][style:knob]"
,0.01,0,1,0.01) : si.smoo;
t = button("v:karplus/[1]gate");
gate = t+s : min(1);
freq = f*bend;
};
//-------`(pm.)elecGuitarModel`----------
// A simple electric guitar model (without audio effects, of course) with
// selectable pluck position.
// This model implements a single string. Additional strings should be created
// by making a polyphonic application out of this function. Pitch is changed by
// changing the length of the string and not through a finger model.
//
// #### Usage
//
// ```
// elecGuitarModel(length,pluckPosition,mute,excitation) : _
// ```
//
// Where:
//
// * `length`: the length of the string in meters
// * `pluckPosition`: pluck position (0-1) (1 is on the bridge)
// * `mute`: mute coefficient (1 for no mute and 0 for instant mute)
// * `excitation`: excitation signal
//----------------------------------
elecGuitarModel(length,pluckPosition,mute,excitation) = endChain(egChain)
with{
maxStringLength = maxLength;
lengthTuning = 0.11; // tuned "by hand"
stringL = length-lengthTuning;
muteBlock = *(mute),*(mute),_;
egChain = chain(
elecGuitarNuts :
openStringPick(stringL,0.05,pluckPosition,excitation) :
muteBlock :
elecGuitarBridge);
};
//-------`(pm.)elecGuitar`----------
// A simple electric guitar model with steel strings (based on
// [`elecGuitarModel`](#elecguitarmodel)) implementing an excitation
// model.
// This model implements a single string. Additional strings should be created
// by making a polyphonic application out of this function.
//
// #### Usage
//
// ```
// elecGuitar(length,pluckPosition,trigger) : _
// ```
//
// Where:
//
// * `length`: the length of the string in meters
// * `pluckPosition`: pluck position (0-1) (1 is on the bridge)
// * `mute`: mute coefficient (1 for no mute and 0 for instant mute)
// * `gain`: gain of the pluck (0-1)
// * `trigger`: trigger signal (1 for on, 0 for off)
//----------------------------------
elecGuitar(stringLength,pluckPosition,mute,gain,trigger) =
pluckString(stringLength,1,1,1,gain,trigger) :
elecGuitarModel(stringLength,pluckPosition,mute);
//-------`(pm.)elecGuitar_ui_MIDI`----------
// Ready-to-use MIDI-enabled electric guitar physical model with built-in UI.
//
// #### Usage
//
// ```
// elecGuitar_ui_MIDI : _
// ```
//----------------------------------
elecGuitar_ui_MIDI = elecGuitar(stringLength,pluckPosition,1,gain,gate)*outGain
with{
f = hslider("v:elecGuitar/h:[0]midi/[0]freq[style:knob]",440,50,1000,0.01);
bend = ba.semi2ratio(hslider("v:elecGuitar/h:[0]midi/[1]bend[hidden:1][midi:pitchwheel][style:knob]"
,0,-2,2,0.01)) : si.polySmooth(gate,0.999,1);
gain = hslider("v:elecGuitar/h:[0]midi/[2]gain[style:knob]",0.8,0,1,0.01);
s = hslider("v:elecGuitar/h:[0]midi/[3]sustain[hidden:1]
[midi:ctrl 64][style:knob]",0,0,1,1);
pluckPosition = hslider("v:elecGuitar/[1]pluckPosition[midi:ctrl 1]",0.8,0,1,0.01) : si.smoo;
outGain = hslider("v:elecGuitar/[2]outGain",0.5,0,1,0.01);
t = button("v:elecGuitar/[3]gate");
gate = t+s : min(1);
freq = f*bend;
stringLength = freq : f2l;
};
//-------`(pm.)guitarBody`----------
// WARNING: not implemented yet!
// Bidirectional block implementing a simple acoustic guitar body.
//
// #### Usage
//
// ```
// chain(... : guitarBody)
// ```
//----------------------------------
// TODO: not implemented yet
guitarBody = reflectance,transmittance,_
with{
transmittance = _;
reflectance = _;
};
//-------`(pm.)guitarModel`----------
// A simple acoustic guitar model with steel strings and selectable excitation
// position. This model implements a single string. Additional strings should be created
// by making a polyphonic application out of this function. Pitch is changed by
// changing the length of the string and not through a finger model.
// WARNING: this function doesn't currently implement a body (just strings and
// bridge).
//
// #### Usage
//
// ```
// guitarModel(length,pluckPosition,excitation) : _
// ```
//
// Where:
//
// * `length`: the length of the string in meters
// * `pluckPosition`: pluck position (0-1) (1 is on the bridge)
// * `excitation`: excitation signal
//----------------------------------
guitarModel(length,pluckPosition,excitation) = endChain(egChain)
with{
maxStringLength = maxLength;
lengthTuning = 0.1; // tuned "by hand"
stringL = length-lengthTuning;
egChain = chain(guitarNuts : steelString(stringL,pluckPosition,excitation) :
guitarBridge : guitarBody : out);
};
//-------`(pm.)guitar`----------
// A simple acoustic guitar model with steel strings (based on
// [`guitarModel`](#guitarmodel)) implementing an excitation model.
// This model implements a single string. Additional strings should be created
// by making a polyphonic application out of this function.
//
// #### Usage
//
// ```
// guitar(length,pluckPosition,trigger) : _
// ```
//
// Where:
//
// * `length`: the length of the string in meters
// * `pluckPosition`: pluck position (0-1) (1 is on the bridge)