# 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: useful pre-defined variables for physical modeling (e.g., speed of sound, etc.).
• Conversion Tools: conversion functions specific to physical modeling (e.g., length to frequency, etc.).
• Bidirectional Utilities: functions to create bidirectional block diagrams for physical modeling.
• Basic Elements: waveguides, specific types of filters, etc.
• String Instruments: various types of strings (e.g., steel, nylon, etc.), bridges, guitars, etc.
• Bowed String Instruments: parts and models specific to bowed string instruments (e.g., bows, bridges, violins, etc.).
• Wind Instrument: parts and models specific to wind string instruments (e.g., reeds, mouthpieces, flutes, clarinets, etc.).
• Exciters: pluck generators, "blowers", etc.
• Modal Percussions: percussion instruments based on modal models.
• Vocal Synthesis: functions for various vocal synthesis techniques (e.g., fof, source/filter, etc.) and vocal synthesizers.
• 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. Tutorials on how to make physical models of musical instruments using Faust can be found here as well.

## Global Variables

Useful pre-defined variables for physical modeling.

### (pm.)speedOfSound

Speed of sound in meters per second (340m/s).

### (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.

## Conversion Tools

Useful conversion tools for physical modeling.

### (pm.)f2l

Frequency to length in meters.

#### Usage

f2l(freq) : distanceInMeters


Where:

• freq: the frequency

### (pm.)l2f

Length in meters to frequency.

#### Usage

l2f(length) : freq


Where:

• length: length/distance in meters

### (pm.)l2s

Length in meters to number of samples.

#### Usage

l2s(l) : numberOfSamples


Where:

• l: length in meters

## 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: 3 signals ins and 3 signals out.

#### Usage

chain(basicBlock : basicBlock : etc.)


### (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 = _,_,_;
};


### (pm.)inLeftWave

Adds a signal to left going waves anywhere in a 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.

### (pm.)inRightWave

Adds a signal to right going waves anywhere in a 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.

### (pm.)in

Adds a signal to left and right going waves anywhere in a 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.

### (pm.)outLeftWave

Sends the signal of left going waves to the output channel of the chain.

#### Usage

chain(A : outLeftWave : B)


Where A and B are bidirectional blocks.

### (pm.)outRightWave

Sends the signal of right going waves to the output channel of the chain.

#### Usage

chain(A : outRightWave : B)


Where A and B are bidirectional blocks.

### (pm.)out

Sends the signal of right and left going waves to the output channel of the chain.

#### Usage

chain(A : out : B)


Where A and B are bidirectional blocks.

### (pm.)terminations

Creates terminations on both sides of a chain without closing the inputs and outputs of the bidirectional signals chain. As for chain, this function adds a 1 sample delay to the bidirectional signal, both ways. Of course, this function can be nested within a chain.

#### Usage

terminations(a,b,c)
with{
};


### (pm.)lTermination

Creates a termination on the left side of a 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.

#### Usage

lTerminations(a,b)
with{
};


### (pm.)rTermination

Creates a termination on the right side of a 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.

#### Usage

rTerminations(b,c)
with{
};


### (pm.)closeIns

Closes the inputs of a bidirectional chain in all directions.

#### Usage

closeIns : chain(...) :     _,_,_


### (pm.)closeOuts

Closes the outputs of a bidirectional chain in all directions except for the main signal output (3d output).

#### Usage

_,_,_ : chain(...) : _


### (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(...)) : _


## 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]).

#### 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.

### (pm.)waveguide

Standard pm.lib waveguide (based on waveguideFd4).

#### 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.

### (pm.)bridgeFilter

Generic two zeros bridge FIR filter (as implemented in the 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)

### (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)

## 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

### (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

### (pm.)nylonString

A bidirectional block implementing a basic nylon string with selectable excitation position. This element is based on 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

### (pm.)steelString

A bidirectional block implementing a basic steel string with selectable excitation position. This element is based on 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

### (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

### (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

### (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

### (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)


### (pm.)rStringRigidTermination

Bidirectional block implementing a right rigid string termination (no damping, just phase inversion).

#### Usage

chain(rStringRigidTermination : stringSegment : ...)


### (pm.)lStringRigidTermination

Bidirectional block implementing a left rigid string termination (no damping, just phase inversion).

#### Usage

chain(... : stringSegment : lStringRigidTermination)


### (pm.)elecGuitarBridge

Bidirectional block implementing a simple electric guitar bridge. This block is based on 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)


### (pm.)elecGuitarNuts

Bidirectional block implementing a simple electric guitar nuts. This block is based on bridgeFilter and does essentially the same thing as 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 : ...)


### (pm.)guitarBridge

Bidirectional block implementing a simple acoustic guitar bridge. This bridge damps more hight frequencies than 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)


### (pm.)guitarNuts

Bidirectional block implementing a simple acoustic guitar nuts. This nuts damps more hight frequencies than 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 : ...)


### (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.

### (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

### (pm.)ks_ui_MIDI

Ready-to-use, MIDI-enabled Karplus-Strong string with buil-in UI.

#### Usage

ks_ui_MIDI : _


### (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 applications 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

### (pm.)elecGuitar

A simple electric guitar model with steel strings (based on elecGuitarModel) implementing an excitation model. This model implements a single string. Additional strings should be created by making a polyphonic applications 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)

### (pm.)elecGuitar_ui_MIDI

Ready-to-use MIDI-enabled electric guitar physical model with built-in UI.

#### Usage

elecGuitar_ui_MIDI : _


### (pm.)guitarBody

WARNING: not implemented yet! Bidirectional block implementing a simple acoustic guitar body.

#### Usage

chain(... : guitarBody)


### (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 applications 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

### (pm.)guitar

A simple acoustic guitar model with steel strings (based on guitarModel) implementing an excitation model. This model implements a single string. Additional strings should be created by making a polyphonic applications 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)
• gain: gain of the excitation
• trigger: trigger signal (1 for on, 0 for off)

### (pm.)guitar_ui_MIDI

Ready-to-use MIDI-enabled steel strings acoustic guitar physical model with built-in UI.

#### Usage

guitar_ui_MIDI : _


### (pm.)nylonGuitarModel

A simple acoustic guitar model with nylon strings and selectable excitation position. This model implements a single string. Additional strings should be created by making a polyphonic applications 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

nylonGuitarModel(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

### (pm.)nylonGuitar

A simple acoustic guitar model with nylon strings (based on nylonGuitarModel) implementing an excitation model. This model implements a single string. Additional strings should be created by making a polyphonic applications out of this function.

#### Usage

nylonGuitar(length,pluckPosition,trigger) : _


Where:

• length: the length of the string in meters
• pluckPosition: pluck position (0-1) (1 is on the bridge)
• gain: gain of the excitation (0-1)
• trigger: trigger signal (1 for on, 0 for off)

### (pm.)nylonGuitar_ui_MIDI

Ready-to-use MIDI-enabled nylon strings acoustic guitar physical model with built-in UI.

#### Usage

nylonGuitar_ui_MIDI : _


### (pm.)modeInterpRes

Modular string instrument resonator based on IR measurements made on 3D printed models. The 2D space allowing for the control of the shape and the scale of the model is enabled by interpolating between modes parameters. More information about this technique/project can be found here: * https://ccrma.stanford.edu/~rmichon/3dPrintingModeling/.

#### Usage

_ : modeInterpRes(nModes,x,y) : _


Where:

• nModes: number of modeled modes (40 max)
• x: shape of the resonator (0: square, 1: square with rounded corners, 2: round)
• y: scale of the resonator (0: small, 1: medium, 2: large)

### (pm.)modularInterpBody

Bidirectional block implementing a modular string instrument resonator (see modeInterpRes).

#### Usage

chain(... : modularInterpBody(nModes,shape,scale) : ...)


Where:

• nModes: number of modeled modes (40 max)
• shape: shape of the resonator (0: square, 1: square with rounded corners, 2: round)
• scale: scale of the resonator (0: small, 1: medium, 2: large)

### (pm.)modularInterpStringModel

String instrument model with a modular body (see modeInterpRes and * https://ccrma.stanford.edu/~rmichon/3dPrintingModeling/).

#### Usage

modularInterpStringModel(length,pluckPosition,shape,scale,bodyExcitation,stringExcitation) : _


Where:

• stringLength: the length of the string in meters
• pluckPosition: pluck position (0-1) (1 is on the bridge)
• shape: shape of the resonator (0: square, 1: square with rounded corners, 2: round)
• scale: scale of the resonator (0: small, 1: medium, 2: large)
• bodyExcitation: excitation signal for the body
• stringExcitation: excitation signal for the string

### (pm.)modularInterpInstr

String instrument with a modular body (see modeInterpRes and * https://ccrma.stanford.edu/~rmichon/3dPrintingModeling/).

#### Usage

modularInterpInstr(stringLength,pluckPosition,shape,scale,gain,tapBody,triggerString) : _


Where:

• stringLength: the length of the string in meters
• pluckPosition: pluck position (0-1) (1 is on the bridge)
• shape: shape of the resonator (0: square, 1: square with rounded corners, 2: round)
• scale: scale of the resonator (0: small, 1: medium, 2: large)
• gain: of the string excitation
• tapBody: send an impulse in the body of the instrument where the string is connected (1 for on, 0 for off)
• triggerString: trigger signal for the string (1 for on, 0 for off)

### (pm.)modularInterpInstr_ui_MIDI

Ready-to-use MIDI-enabled string instrument with a modular body (see modeInterpRes and * https://ccrma.stanford.edu/~rmichon/3dPrintingModeling/) with built-in UI.

#### Usage

modularInterpInstr_ui_MIDI : _


## Bowed String Instruments

Low and high level basic string instruments parts. Most of the elements in this section can be used in a bidirectional chain.

### (pm.)bowTable

Extremely basic bow table that can be used to implement a wide range of bow types for many different bowed string instruments (violin, cello, etc.).

#### Usage

excitation : bowTable(offeset,slope) : _


Where:

• excitation: an excitation signal
• offset: table offset
• slope: table slope

### (pm.)violinBowTable

Violin bow table based on bowTable.

#### Usage

bowVelocity : violinBowTable(bowPressure) : _


Where:

• bowVelocity: velocity of the bow/excitation signal (0-1)
• bowPressure: bow pressure on the string (0-1)

### (pm.)bowInteraction

Bidirectional block implementing the interaction of a bow in a chain.

#### Usage

chain(... : stringSegment : bowInteraction(bowTable) : stringSegment : ...)


Where:

• bowTable: the bow table

### (pm.)violinBow

Bidirectional block implementing a violin bow and its interaction with a string.

#### Usage

chain(... : stringSegment : violinBow(bowPressure,bowVelocity) : stringSegment : ...)


Where:

• bowVelocity: velocity of the bow / excitation signal (0-1)
• bowPressure: bow pressure on the string (0-1)

### (pm.)violinBowedString

Violin bowed string bidirectional block with controllable bow position. Terminations are not implemented in this model.

#### Usage

chain(nuts : violinBowedString(stringLength,bowPressure,bowVelocity,bowPosition) : bridge)


Where:

• stringLength: the length of the string in meters
• bowVelocity: velocity of the bow / excitation signal (0-1)
• bowPressure: bow pressure on the string (0-1)
• bowPosition: the position of the bow on the string (0-1)

### (pm.)violinNuts

Bidirectional block implementing simple violin nuts. This function is based on bridgeFilter.

#### Usage

chain(violinNuts : stringSegment : ...)


### (pm.)violinBridge

Bidirectional block implementing a simple violin bridge. This function is based on bridgeFilter.

#### Usage

chain(... : stringSegment : violinBridge


### (pm.)violinBody

Bidirectional block implementing a simple violin body (just a simple resonant lowpass filter).

#### Usage

chain(... : stringSegment : violinBridge : violinBody)


### (pm.)violinModel

Ready-to-use simple violin physical model. This model implements a single string. Additional strings should be created by making a polyphonic applications out of this function. Pitch is changed by changing the length of the string (and not through a finger model).

#### Usage

violinModel(stringLength,bowPressure,bowVelocity,bridgeReflexion,
bridgeAbsorption,bowPosition) : _


Where:

• stringLength: the length of the string in meters
• bowVelocity: velocity of the bow / excitation signal (0-1)
• bowPressure: bow pressure on the string (0-1))
• bowPosition: the position of the bow on the string (0-1)

### (pm.)violin_ui

Ready-to-use violin physical model with built-in UI.

#### Usage

violinModel_ui : _


### (pm.)violin_ui_MIDI

Ready-to-use MIDI-enabled violin physical model with built-in UI.

#### Usage

violin_ui_MIDI : _


## Wind Instruments

Low and high level basic wind instruments parts. Most of the elements in this section can be used in a bidirectional chain.

### (pm.)openTube

A tube segment without terminations (same as stringSegment).

#### Usage

chain(A : openTube(maxLength,length) : B)


Where:

• maxLength: the maximum length of the tube in meters (should be static)
• length: the length of the tube in meters

### (pm.)reedTable

Extremely basic reed table that can be used to implement a wide range of single reed types for many different instruments (saxophone, clarinet, etc.).

#### Usage

excitation : reedTable(offeset,slope) : _


Where:

• excitation: an excitation signal
• offset: table offset
• slope: table slope

### (pm.)fluteJetTable

Extremely basic flute jet table.

#### Usage

excitation : fluteJetTable : _


Where:

• excitation: an excitation signal

### (pm.)brassLipsTable

Simple brass lips/mouthpiece table. Since this implementation is very basic and that the lips and tube of the instrument are coupled to each other, the length of that tube must be provided here.

#### Usage

excitation : brassLipsTable(tubeLength,lipsTension) : _


Where:

• excitation: an excitation signal (can be DC)
• tubeLength: length in meters of the tube connected to the mouthpiece
• lipsTension: tension of the lips (0-1) (default: 0.5)

### (pm.)clarinetReed

Clarinet reed based on reedTable with controllable stiffness.

#### Usage

excitation : clarinetReed(stiffness) : _


Where:

• excitation: an excitation signal
• stiffness: reed stiffness (0-1)

### (pm.)clarinetMouthPiece

Bidirectional block implementing a clarinet mouthpiece as well as the various interactions happening with traveling waves. This element is ready to be plugged to a tube...

#### Usage

chain(clarinetMouthPiece(reedStiffness,pressure) : tube : etc.)


Where:

• pressure: the pressure of the air flow (DC) created by the virtual performer (0-1). This can also be any kind of signal that will directly injected in the mouthpiece (e.g., breath noise, etc.).
• reedStiffness: reed stiffness (0-1)

### (pm.)brassLips

Bidirectional block implementing a brass mouthpiece as well as the various interactions happening with traveling waves. This element is ready to be plugged to a tube...

#### Usage

chain(brassLips(tubeLength,lipsTension,pressure) : tube : etc.)


Where:

• tubeLength: length in meters of the tube connected to the mouthpiece
• lipsTension: tension of the lips (0-1) (default: 0.5)
• pressure: the pressure of the air flow (DC) created by the virtual performer (0-1). This can also be any kind of signal that will directly injected in the mouthpiece (e.g., breath noise, etc.).

### (pm.)fluteEmbouchure

Bidirectional block implementing a flute embouchure as well as the various interactions happening with traveling waves. This element is ready to be plugged between tubes segments...

#### Usage

chain(... : tube : fluteEmbouchure(pressure) : tube : etc.)


Where:

• pressure: the pressure of the air flow (DC) created by the virtual performer (0-1). This can also be any kind of signal that will directly injected in the mouthpiece (e.g., breath noise, etc.).

### (pm.)wBell

Generic wind instrument bell bidirectional block that should be placed at the end of a chain.

#### Usage

chain(... : wBell(opening))


Where:

• opening: the "opening" of bell (0-1)

### (pm.)fluteHead

Simple flute head implementing waves reflexion.

#### Usage

chain(fluteHead : tube : ...)


### (pm.)fluteFoot

Simple flute foot implementing waves reflexion and dispersion.

#### Usage

chain(... : tube : fluteFoot)


### (pm.)clarinetModel

A simple clarinet physical model without tone holes (pitch is changed by changing the length of the tube of the instrument).

#### Usage

clarinetModel(length,pressure,reedStiffness,bellOpening) : _


Where:

• tubeLength: the length of the tube in meters
• pressure: the pressure of the air flow created by the virtual performer (0-1). This can also be any kind of signal that will directly injected in the mouthpiece (e.g., breath noise, etc.).
• reedStiffness: reed stiffness (0-1)
• bellOpening: the opening of bell (0-1)

### (pm.)clarinetModel_ui

Same as clarinetModel but with a built-in UI. This function doesn't implement a virtual "blower", thus pressure remains an argument here.

#### Usage

clarinetModel_ui(pressure) : _


Where:

• pressure: the pressure of the air flow created by the virtual performer (0-1). This can also be any kind of signal that will be directly injected in the mouthpiece (e.g., breath noise, etc.).

### (pm.)clarinet_ui

Ready-to-use clarinet physical model with built-in UI based on clarinetModel.

#### Usage

clarinet_ui : _


### (pm.)clarinet_ui_MIDI

Ready-to-use MIDI compliant clarinet physical model with built-in UI.

#### Usage

clarinet_ui_MIDI : _


### (pm.)brassModel

A simple generic brass instrument physical model without pistons (pitch is changed by changing the length of the tube of the instrument). This model is kind of hard to control and might not sound very good if bad parameters are given to it...

#### Usage

brassModel(tubeLength,lipsTension,mute,pressure) : _


Where:

• tubeLength: the length of the tube in meters
• lipsTension: tension of the lips (0-1) (default: 0.5)
• mute: mute opening at the end of the instrument (0-1) (default: 0.5)
• pressure: the pressure of the air flow created by the virtual performer (0-1). This can also be any kind of signal that will directly injected in the mouthpiece (e.g., breath noise, etc.).

### (pm.)brassModel_ui

Same as brassModel but with a built-in UI. This function doesn't implement a virtual "blower", thus pressure remains an argument here.

#### Usage

brassModel_ui(pressure) : _


Where:

• pressure: the pressure of the air flow created by the virtual performer (0-1). This can also be any kind of signal that will be directly injected in the mouthpiece (e.g., breath noise, etc.).

### (pm.)brass_ui

Ready-to-use brass instrument physical model with built-in UI based on brassModel.

#### Usage

brass_ui : _


### (pm.)brass_ui_MIDI

Ready-to-use MIDI-controllable brass instrument physical model with built-in UI.

#### Usage

brass_ui_MIDI : _


### (pm.)fluteModel

A simple generic flute instrument physical model without tone holes (pitch is changed by changing the length of the tube of the instrument).

#### Usage

fluteModel(tubeLength,mouthPosition,pressure) : _


Where:

• tubeLength: the length of the tube in meters
• mouthPosition: position of the mouth on the embouchure (0-1) (default: 0.5)
• pressure: the pressure of the air flow created by the virtual performer (0-1). This can also be any kind of signal that will directly injected in the mouthpiece (e.g., breath noise, etc.).

### (pm.)fluteModel_ui

Same as fluteModel but with a built-in UI. This function doesn't implement a virtual "blower", thus pressure remains an argument here.

#### Usage

fluteModel_ui(pressure) : _


Where:

• pressure: the pressure of the air flow created by the virtual performer (0-1). This can also be any kind of signal that will be directly injected in the mouthpiece (e.g., breath noise, etc.).

### (pm.)flute_ui

Ready-to-use flute physical model with built-in UI based on fluteModel.

#### Usage

flute_ui : _


### (pm.)flute_ui_MIDI

Ready-to-use MIDI-controllable flute physical model with built-in UI.

#### Usage

flute_ui_MIDI : _


## Exciters

Various kind of excitation signal generators.

### (pm.)impulseExcitation

Creates an impulse excitation of one sample.

#### Usage

gate = button('gate');
impulseExcitation(gate) : chain;


Where:

• gate: a gate button

### (pm.)strikeModel

Creates a filtered noise excitation.

#### Usage

gate = button('gate');
strikeModel(LPcutoff,HPcutoff,sharpness,gain,gate) : chain;


Where:

• HPcutoff: highpass cutoff frequency
• LPcutoff: lowpass cutoff frequency
• sharpness: sharpness of the attack and release (0-1)
• gain: gain of the excitation
• gate: a gate button/trigger signal (0/1)

### (pm.)strike

Strikes generator with controllable excitation position.

#### Usage

gate = button('gate');
strike(exPos,sharpness,gain,gate) : chain;


Where:

• exPos: excitation position wiht 0: for max low freqs and 1: for max high freqs. So, on membrane for example, 0 would be the middle and 1 the edge
• sharpness: sharpness of the attack and release (0-1)
• gain: gain of the excitation
• gate: a gate button/trigger signal (0/1)

### (pm.)pluckString

Creates a plucking excitation signal.

#### Usage

trigger = button('gate');
pluckString(stringLength,cutoff,maxFreq,sharpness,trigger)


Where:

• stringLength: length of the string to pluck
• cutoff: cutoff ratio (1 for default)
• maxFreq: max frequency ratio (1 for default)
• sharpness: sharpness of the attack and release (1 for default)
• gain: gain of the excitation (0-1)
• trigger: trigger signal (1 for on, 0 for off)

### (pm.)blower

A virtual blower creating a DC signal with some breath noise in it.

#### Usage

blower(pressure,breathGain,breathCutoff) : _


Where:

• pressure: pressure (0-1)
• breathGain: breath noise gain (0-1) (recommended: 0.005)
• breathCutoff: breath cuttoff frequency (Hz) (recommended: 2000)

### (pm.)blower_ui

Same as blower but with a built-in UI.

#### Usage

blower : somethingToBeBlown


High and low level functions for modal synthesis of percussion instruments.

### (pm.)djembeModel

Dirt-simple djembe modal physical model. Mode parameters are empirically calculated and don't correspond to any measurements or 3D model. They kind of sound good though :).

#### Usage

excitation : djembeModel(freq)


Where:

• excitation: excitation signal
• freq: fundamental frequency of the bar

### (pm.)djembe

Dirt-simple djembe modal physical model. Mode parameters are empirically calculated and don't correspond to any measurements or 3D model. They kind of sound good though :).

This model also implements a virtual "exciter".

#### Usage

djembe(freq,strikePosition,strikeSharpness,gain,trigger)


Where:

• freq: fundamental frequency of the model
• strikePosition: strike position (0 for the middle of the membrane and 1 for the edge)
• strikeSharpness: sharpness of the strike (0-1, default: 0.5)
• gain: gain of the strike
• trigger: trigger signal (0: off, 1: on)

### (pm.)djembe_ui_MIDI

Simple MIDI controllable djembe physical model with built-in UI.

#### Usage

djembe_ui_MIDI : _


### (pm.)marimbaBarModel

Generic marimba tone bar modal model.

This model was generated using mesh2faust from a 3D CAD model of a marimba tone bar (libraries/modalmodels/marimbaBar). The corresponding CAD model is that of a C2 tone bar (original fundamental frequency: ~65Hz). While marimbaBarModel allows to translate the harmonic content of the generated sound by providing a frequency (freq), mode transposition has limits and the model will sound less and less like a marimba tone bar as it diverges from C2. To make an accurate model of a marimba, we'd want to have an independent model for each bar...

This model contains 5 excitation positions going linearly from the center bottom to the center top of the bar. Obviously, a model with more excitation position could be regenerated using mesh2faust.

#### Usage

excitation : marimbaBarModel(freq,exPos,t60,t60DecayRatio,t60DecaySlope)


Where:

• excitation: excitation signal
• freq: fundamental frequency of the bar
• exPos: excitation position (0-4)
• t60: T60 in seconds (recommended value: 0.1)
• t60DecayRatio: T60 decay ratio (recommended value: 1)
• t60DecaySlope: T60 decay slope (recommended value: 5)

### (pm.)marimbaResTube

Simple marimba resonance tube.

#### Usage

marimbaResTube(tubeLength,excitation)


Where:

• tubeLength: the length of the tube in meters
• excitation: the excitation signal (audio in)

### (pm.)marimbaModel

Simple marimba physical model implementing a single tone bar connected to tube. This model is scalable and can be adapted to any size of bar/tube (see marimbaBarModel to know more about the limitations of this type of system).

#### Usage

excitation : marimbaModel(freq,exPos) : _


Where:

• freq: the frequency of the bar/tube couple
• exPos: excitation position (0-4)

### (pm.)marimba

Simple marimba physical model implementing a single tone bar connected to tube. This model is scalable and can be adapted to any size of bar/tube (see marimbaBarModel to know more about the limitations of this type of system).

This function also implement a virtual exciter to drive the model.

#### Usage

excitation : marimba(freq,strikePosition,strikeCutoff,strikeSharpness,gain,trigger) : _


Where:

• excitation: the excitation signal
• freq: the frequency of the bar/tube couple
• strikePosition: strike position (0-4)
• strikeCutoff: cuttoff frequency of the strike genarator (recommended: ~7000Hz)
• strikeSharpness: shaarpness of the strike (recommened: ~0.25)
• gain: gain of the strike (0-1)
• trigger signal (0: off, 1: on)

### (pm.)marimba_ui_MIDI

Simple MIDI controllable marimba physical model with built-in UI implementing a single tone bar connected to tube. This model is scalable and can be adapted to any size of bar/tube (see marimbaBarModel to know more about the limitations of this type of system).

#### Usage

marimba_ui_MIDI : _


### (pm.)churchBellModel

Generic church bell modal model generated by mesh2faust from libraries/modalmodels/churchBell.

Modeled after T. Rossing and R. Perrin, Vibrations of Bells, Applied Acoustics 2, 1987.

Model height is 301 mm.

This model contains 7 excitation positions going linearly from the bottom to the top of the bell. Obviously, a model with more excitation position could be regenerated using mesh2faust.

#### Usage

excitation : churchBellModel(nModes,exPos,t60,t60DecayRatio,t60DecaySlope)


Where:

• excitation: the excitation signal
• nModes: number of synthesized modes (max: 50)
• exPos: excitation position (0-6)
• t60: T60 in seconds (recommended value: 0.1)
• t60DecayRatio: T60 decay ratio (recommended value: 1)
• t60DecaySlope: T60 decay slope (recommended value: 5)

### (pm.)churchBell

Generic church bell modal model.

Modeled after T. Rossing and R. Perrin, Vibrations of Bells, Applied Acoustics 2, 1987.

Model height is 301 mm.

This model contains 7 excitation positions going linearly from the bottom to the top of the bell. Obviously, a model with more excitation position could be regenerated using mesh2faust.

This function also implement a virtual exciter to drive the model.

#### Usage

excitation : churchBell(strikePosition,strikeCutoff,strikeSharpness,gain,trigger) : _


Where:

• excitation: the excitation signal
• strikePosition: strike position (0-6)
• strikeCutoff: cuttoff frequency of the strike genarator (recommended: ~7000Hz)
• strikeSharpness: shaarpness of the strike (recommened: ~0.25)
• gain: gain of the strike (0-1)
• trigger signal (0: off, 1: on)

### (pm.)churchBell_ui

Church bell physical model based on churchBell with built-in UI.

#### Usage

churchBell_ui : _


### (pm.)englishBellModel

English church bell modal model generated by mesh2faust from libraries/modalmodels/englishBell.

Modeled after D. Bartocha and . Baron, Influence of Tin Bronze Melting and Pouring Parameters on Its Properties and Bell' Tone, Archives of Foundry Engineering, 2016.

Model height is 1 m.

This model contains 7 excitation positions going linearly from the bottom to the top of the bell. Obviously, a model with more excitation position could be regenerated using mesh2faust.

#### Usage

excitation : englishBellModel(nModes,exPos,t60,t60DecayRatio,t60DecaySlope)


Where:

• excitation: the excitation signal
• nModes: number of synthesized modes (max: 50)
• exPos: excitation position (0-6)
• t60: T60 in seconds (recommended value: 0.1)
• t60DecayRatio: T60 decay ratio (recommended value: 1)
• t60DecaySlope: T60 decay slope (recommended value: 5)

### (pm.)englishBell

English church bell modal model.

Modeled after D. Bartocha and . Baron, Influence of Tin Bronze Melting and Pouring Parameters on Its Properties and Bell' Tone, Archives of Foundry Engineering, 2016.

Model height is 1 m.

This model contains 7 excitation positions going linearly from the bottom to the top of the bell. Obviously, a model with more excitation position could be regenerated using mesh2faust.

This function also implement a virtual exciter to drive the model.

#### Usage

excitation : englishBell(strikePosition,strikeCutoff,strikeSharpness,gain,trigger) : _


Where:

• excitation: the excitation signal
• strikePosition: strike position (0-6)
• strikeCutoff: cuttoff frequency of the strike genarator (recommended: ~7000Hz)
• strikeSharpness: shaarpness of the strike (recommened: ~0.25)
• gain: gain of the strike (0-1)
• trigger signal (0: off, 1: on)

### (pm.)englishBell_ui

English church bell physical model based on englishBell with built-in UI.

#### Usage

englishBell_ui : _


### (pm.)frenchBellModel

French church bell modal model generated by mesh2faust from libraries/modalmodels/frenchBell.

Modeled after D. Bartocha and . Baron, Influence of Tin Bronze Melting and Pouring Parameters on Its Properties and Bell' Tone, Archives of Foundry Engineering, 2016.

Model height is 1 m.

This model contains 7 excitation positions going linearly from the bottom to the top of the bell. Obviously, a model with more excitation position could be regenerated using mesh2faust.

#### Usage

excitation : frenchBellModel(nModes,exPos,t60,t60DecayRatio,t60DecaySlope)


Where:

• excitation: the excitation signal
• nModes: number of synthesized modes (max: 50)
• exPos: excitation position (0-6)
• t60: T60 in seconds (recommended value: 0.1)
• t60DecayRatio: T60 decay ratio (recommended value: 1)
• t60DecaySlope: T60 decay slope (recommended value: 5)

### (pm.)frenchBell

French church bell modal model.

Modeled after D. Bartocha and . Baron, Influence of Tin Bronze Melting and Pouring Parameters on Its Properties and Bell' Tone, Archives of Foundry Engineering, 2016.

Model height is 1 m.

This model contains 7 excitation positions going linearly from the bottom to the top of the bell. Obviously, a model with more excitation position could be regenerated using mesh2faust.

This function also implement a virtual exciter to drive the model.

#### Usage

excitation : frenchBell(strikePosition,strikeCutoff,strikeSharpness,gain,trigger) : _


Where:

• excitation: the excitation signal
• strikePosition: strike position (0-6)
• strikeCutoff: cuttoff frequency of the strike genarator (recommended: ~7000Hz)
• strikeSharpness: shaarpness of the strike (recommened: ~0.25)
• gain: gain of the strike (0-1)
• trigger signal (0: off, 1: on)

### (pm.)frenchBell_ui

French church bell physical model based on frenchBell with built-in UI.

#### Usage

frenchBell_ui : _


### (pm.)germanBellModel

German church bell modal model generated by mesh2faust from libraries/modalmodels/germanBell.

Modeled after D. Bartocha and . Baron, Influence of Tin Bronze Melting and Pouring Parameters on Its Properties and Bell' Tone, Archives of Foundry Engineering, 2016.

Model height is 1 m.

This model contains 7 excitation positions going linearly from the bottom to the top of the bell. Obviously, a model with more excitation position could be regenerated using mesh2faust.

#### Usage

excitation : germanBellModel(nModes,exPos,t60,t60DecayRatio,t60DecaySlope)


Where:

• excitation: the excitation signal
• nModes: number of synthesized modes (max: 50)
• exPos: excitation position (0-6)
• t60: T60 in seconds (recommended value: 0.1)
• t60DecayRatio: T60 decay ratio (recommended value: 1)
• t60DecaySlope: T60 decay slope (recommended value: 5)

### (pm.)germanBell

German church bell modal model.

Modeled after D. Bartocha and . Baron, Influence of Tin Bronze Melting and Pouring Parameters on Its Properties and Bell' Tone, Archives of Foundry Engineering, 2016.

Model height is 1 m.

This model contains 7 excitation positions going linearly from the bottom to the top of the bell. Obviously, a model with more excitation position could be regenerated using mesh2faust.

This function also implement a virtual exciter to drive the model.

#### Usage

excitation : germanBell(strikePosition,strikeCutoff,strikeSharpness,gain,trigger) : _


Where:

• excitation: the excitation signal
• strikePosition: strike position (0-6)
• strikeCutoff: cuttoff frequency of the strike genarator (recommended: ~7000Hz)
• strikeSharpness: shaarpness of the strike (recommened: ~0.25)
• gain: gain of the strike (0-1)
• trigger signal (0: off, 1: on)

### (pm.)germanBell_ui

German church bell physical model based on germanBell with built-in UI.

#### Usage

germanBell_ui : _


### (pm.)russianBellModel

Russian church bell modal model generated by mesh2faust from libraries/modalmodels/russianBell.

Modeled after D. Bartocha and . Baron, Influence of Tin Bronze Melting and Pouring Parameters on Its Properties and Bell' Tone, Archives of Foundry Engineering, 2016.

Model height is 2 m.

This model contains 7 excitation positions going linearly from the bottom to the top of the bell. Obviously, a model with more excitation position could be regenerated using mesh2faust.

#### Usage

excitation : russianBellModel(nModes,exPos,t60,t60DecayRatio,t60DecaySlope)


Where:

• excitation: the excitation signal
• nModes: number of synthesized modes (max: 50)
• exPos: excitation position (0-6)
• t60: T60 in seconds (recommended value: 0.1)
• t60DecayRatio: T60 decay ratio (recommended value: 1)
• t60DecaySlope: T60 decay slope (recommended value: 5)

### (pm.)russianBell

Russian church bell modal model.

Modeled after D. Bartocha and . Baron, Influence of Tin Bronze Melting and Pouring Parameters on Its Properties and Bell' Tone, Archives of Foundry Engineering, 2016.

Model height is 2 m.

This model contains 7 excitation positions going linearly from the bottom to the top of the bell. Obviously, a model with more excitation position could be regenerated using mesh2faust.

This function also implement a virtual exciter to drive the model.

#### Usage

excitation : russianBell(strikePosition,strikeCutoff,strikeSharpness,gain,trigger) : _


Where:

• excitation: the excitation signal
• strikePosition: strike position (0-6)
• strikeCutoff: cuttoff frequency of the strike genarator (recommended: ~7000Hz)
• strikeSharpness: shaarpness of the strike (recommened: ~0.25)
• gain: gain of the strike (0-1)
• trigger signal (0: off, 1: on)

### (pm.)russianBell_ui

Russian church bell physical model based on russianBell with built-in UI.

#### Usage

russianBell_ui : _


### (pm.)standardBellModel

Standard church bell modal model generated by mesh2faust from libraries/modalmodels/standardBell.

Modeled after T. Rossing and R. Perrin, Vibrations of Bells, Applied Acoustics 2, 1987.

Model height is 1.8 m.

This model contains 7 excitation positions going linearly from the bottom to the top of the bell. Obviously, a model with more excitation position could be regenerated using mesh2faust.

#### Usage

excitation : standardBellModel(nModes,exPos,t60,t60DecayRatio,t60DecaySlope)


Where:

• excitation: the excitation signal
• nModes: number of synthesized modes (max: 50)
• exPos: excitation position (0-6)
• t60: T60 in seconds (recommended value: 0.1)
• t60DecayRatio: T60 decay ratio (recommended value: 1)
• t60DecaySlope: T60 decay slope (recommended value: 5)

### (pm.)standardBell

Standard church bell modal model.

Modeled after T. Rossing and R. Perrin, Vibrations of Bells, Applied Acoustics 2, 1987.

Model height is 1.8 m.

This model contains 7 excitation positions going linearly from the bottom to the top of the bell. Obviously, a model with more excitation position could be regenerated using mesh2faust.

This function also implement a virtual exciter to drive the model.

#### Usage

excitation : standardBell(strikePosition,strikeCutoff,strikeSharpness,gain,trigger) : _


Where:

• excitation: the excitation signal
• strikePosition: strike position (0-6)
• strikeCutoff: cuttoff frequency of the strike genarator (recommended: ~7000Hz)
• strikeSharpness: shaarpness of the strike (recommened: ~0.25)
• gain: gain of the strike (0-1)
• trigger signal (0: off, 1: on)

### (pm.)standardBell_ui

Standard church bell physical model based on standardBell with built-in UI.

#### Usage

standardBell_ui : _


## Vocal Synthesis

Vocal synthesizer functions (source/filter, fof, etc.).

### (pm.)formantValues

Formant data values.

The formant data used here come from the CSOUND manual * http://www.csounds.com/manual/html/.

#### Usage

ba.take(j+1,formantValues.f(i)) : _
ba.take(j+1,formantValues.g(i)) : _
ba.take(j+1,formantValues.bw(i)) : _


Where:

• i: formant number
• j: (voiceType*nFormants)+vowel
• voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)
• vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u)

### (pm.)voiceGender

Calculate the gender for the provided voiceType value. (0: male, 1: female)

#### Usage

voiceGender(voiceType) : _


Where:

• voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)

### (pm.)skirtWidthMultiplier

Calculates value to multiply bandwidth to obtain skirtwidth for a Fof filter.

#### Usage

skirtWidthMultiplier(vowel,freq,gender) : _


Where:

• vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u)
• freq: the fundamental frequency of the excitation signal
• gender: gender of the voice used in the fof filter (0: male, 1: female)

### (pm.)autobendFreq

Autobends the center frequencies of formants 1 and 2 based on the fundamental frequency of the excitation signal and leaves all other formant frequencies unchanged. Ported from chant-lib. * Reference: https://ccrma.stanford.edu/~rmichon/chantLib/.

#### Usage

_ : autobendFreq(n,freq,voiceType) : _


Where:

• n: formant index
• freq: the fundamental frequency of the excitation signal
• voiceType: the voice type (0: alto, 1: bass, 2: countertenor,
• input is the center frequency of the corresponding formant

### (pm.)vocalEffort

Changes the gains of the formants based on the fundamental frequency of the excitation signal. Higher formants are reinforced for higher fundamental frequencies. Ported from chant-lib. * Reference: https://ccrma.stanford.edu/~rmichon/chantLib/.

#### Usage

_ : vocalEffort(freq,gender) : _


Where:

• freq: the fundamental frequency of the excitation signal
• gender: the gender of the voice type (0: male, 1: female)
• input is the linear amplitude of the formant

### (pm.)fof

Function to generate a single Formant-Wave-Function. * Reference: https://ccrma.stanford.edu/~mjolsen/pdfs/smc2016_MOlsenFOF.pdf.

#### Usage

_ : fof(fc,bw,a,g) : _


Where:

• fc: formant center frequency,
• bw: formant bandwidth (Hz),
• sw: formant skirtwidth (Hz)
• g: linear scale factor (g=1 gives 0dB amplitude response at fc)
• input is an impulse signal to excite filter

### (pm.)fofSH

FOF with sample and hold used on bw and a parameter used in the filter-cycling FOF function fofCycle. * Reference: https://ccrma.stanford.edu/~mjolsen/pdfs/smc2016_MOlsenFOF.pdf.

#### Usage

_ : fofSH(fc,bw,a,g) : _


Where: all parameters same as for fof

### (pm.)fofCycle

FOF implementation where time-varying filter parameter noise is mitigated by using a cycle of n sample and hold FOF filters. * Reference: https://ccrma.stanford.edu/~mjolsen/pdfs/smc2016_MOlsenFOF.pdf.

#### Usage

_ : fofCycle(fc,bw,a,g,n) : _


Where:

• n: the number of FOF filters to cycle through
• all other parameters are same as for fof

### (pm.)fofSmooth

FOF implementation where time-varying filter parameter noise is mitigated by lowpass filtering the filter parameters bw and a with smooth.

#### Usage

_ : fofSmooth(fc,bw,sw,g,tau) : _


Where:

• tau: the desired smoothing time constant in seconds
• all other parameters are same as for fof

### (pm.)formantFilterFofCycle

Formant filter based on a single FOF filter. Formant parameters are linearly interpolated allowing to go smoothly from one vowel to another. A cycle of n fof filters with sample-and-hold is used so that the fof filter parameters can be varied in realtime. This technique is more robust but more computationally expensive than formantFilterFofSmooth.Voice type can be selected but must correspond to the frequency range of the provided source to be realistic.

#### Usage

_ : formantFilterFofCycle(voiceType,vowel,nFormants,i,freq) : _


Where:

• voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)
• vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u)
• nFormants: number of formant regions in frequency domain, typically 5
• i: formant number (i.e. 0 - 4) used to index formant data value arrays
• freq: fundamental frequency of excitation signal. Used to calculate rise time of envelope

### (pm.)formantFilterFofSmooth

Formant filter based on a single FOF filter. Formant parameters are linearly interpolated allowing to go smoothly from one vowel to another. Fof filter parameters are lowpass filtered to mitigate possible noise from varying them in realtime. Voice type can be selected but must correspond to the frequency range of the provided source to be realistic.

#### Usage

_ : formantFilterFofSmooth(voiceType,vowel,nFormants,i,freq) : _


Where:

• voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)
• vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u)
• nFormants: number of formant regions in frequency domain, typically 5
• i: formant number (i.e. 1 - 5) used to index formant data value arrays
• freq: fundamental frequency of excitation signal. Used to calculate rise time of envelope

### (pm.)formantFilterBP

Formant filter based on a single resonant bandpass filter. Formant parameters are linearly interpolated allowing to go smoothly from one vowel to another. Voice type can be selected but must correspond to the frequency range of the provided source to be realistic.

#### Usage

_ : formantFilterBP(voiceType,vowel,nFormants,i,freq) : _


Where:

• voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)
• vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u)
• nFormants: number of formant regions in frequency domain, typically 5
• i: formant index used to index formant data value arrays
• freq: fundamental frequency of excitation signal.

### (pm.)formantFilterbank

Formant filterbank which can use different types of filterbank functions and different excitation signals. Formant parameters are linearly interpolated allowing to go smoothly from one vowel to another. Voice type can be selected but must correspond to the frequency range of the provided source to be realistic.

#### Usage

_ : formantFilterbank(voiceType,vowel,formantGen,freq) : _


Where:

• voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)
• vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u)
• formantGen: the specific formant filterbank function (i.e. FormantFilterbankBP, FormantFilterbankFof,...)
• freq: fundamental frequency of excitation signal. Needed for FOF version to calculate rise time of envelope

### (pm.)formantFilterbankFofCycle

Formant filterbank based on a bank of fof filters. Formant parameters are linearly interpolated allowing to go smoothly from one vowel to another. Voice type can be selected but must correspond to the frequency range of the provided source to be realistic.

#### Usage

_ : formantFilterbankFofCycle(voiceType,vowel,freq) : _


Where:

• voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)
• vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u)
• freq: the fundamental frequency of the excitation signal. Needed to

### (pm.)formantFilterbankFofSmooth

Formant filterbank based on a bank of fof filters. Formant parameters are linearly interpolated allowing to go smoothly from one vowel to another. Voice type can be selected but must correspond to the frequency range of the provided source to be realistic.

#### Usage

_ : formantFilterbankFofSmooth(voiceType,vowel,freq) : _


Where:

• voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)
• vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u)
• freq: the fundamental frequency of the excitation signal. Needed to

### (pm.)formantFilterbankBP

Formant filterbank based on a bank of resonant bandpass filters. Formant parameters are linearly interpolated allowing to go smoothly from one vowel to another. Voice type can be selected but must correspond to the frequency range of the provided source to be realistic.

#### Usage

_ : formantFilterbankBP(voiceType,vowel) : _


Where:

• voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)
• vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u)
• freq: the fundamental frequency of the excitation signal. Needed

### (pm.)SFFormantModel

Simple formant/vocal synthesizer based on a source/filter model. The source and filterbank must be specified by the user. filterbank must take the same input parameters as formantFilterbank (BP/FofCycle /FofSmooth). Formant parameters are linearly interpolated allowing to go smoothly from one vowel to another. Voice type can be selected but must correspond to the frequency range of the synthesized voice to be realistic.

#### Usage

SFFormantModel(voiceType,vowel,exType,freq,gain,source,filterbank,isFof) : _


Where:

• voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)
• vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u
• exType: voice vs. fricative sound ratio (0-1 where 1 is 100% fricative)
• freq: the fundamental frequency of the source signal
• gain: linear gain multiplier to multiply the source by
• isFof: whether model is FOF based (0: no, 1: yes)

### (pm.)SFFormantModelFofCycle

Simple formant/vocal synthesizer based on a source/filter model. The source is just a periodic impulse and the "filter" is a bank of FOF filters. Formant parameters are linearly interpolated allowing to go smoothly from one vowel to another. Voice type can be selected but must correspond to the frequency range of the synthesized voice to be realistic. This model does not work with noise in the source signal so exType has been removed and model does not depend on SFFormantModel function.

#### Usage

SFFormantModelFofCycle(voiceType,vowel,freq,gain) : _


Where:

• voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)
• vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u
• freq: the fundamental frequency of the source signal
• gain: linear gain multiplier to multiply the source by

### (pm.)SFFormantModelFofSmooth

Simple formant/vocal synthesizer based on a source/filter model. The source is just a periodic impulse and the "filter" is a bank of FOF filters. Formant parameters are linearly interpolated allowing to go smoothly from one vowel to another. Voice type can be selected but must correspond to the frequency range of the synthesized voice to be realistic.

#### Usage

SFFormantModelFofSmooth(voiceType,vowel,freq,gain) : _


Where:

• voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)
• vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u
• freq: the fundamental frequency of the source signal
• gain: linear gain multiplier to multiply the source by

### (pm.)SFFormantModelBP

Simple formant/vocal synthesizer based on a source/filter model. The source is just a sawtooth wave and the "filter" is a bank of resonant bandpass filters. Formant parameters are linearly interpolated allowing to go smoothly from one vowel to another. Voice type can be selected but must correspond to the frequency range of the synthesized voice to be realistic.

The formant data used here come from the CSOUND manual * http://www.csounds.com/manual/html/.

#### Usage

SFFormantModelBP(voiceType,vowel,exType,freq,gain) : _


Where:

• voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)
• vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u
• exType: voice vs. fricative sound ratio (0-1 where 1 is 100% fricative)
• freq: the fundamental frequency of the source signal
• gain: linear gain multiplier to multiply the source by

### (pm.)SFFormantModelFofCycle_ui

Ready-to-use source-filter vocal synthesizer with built-in user interface.

#### Usage

SFFormantModelFofCycle_ui : _


### (pm.)SFFormantModelFofSmooth_ui

Ready-to-use source-filter vocal synthesizer with built-in user interface.

#### Usage

SFFormantModelFofSmooth_ui : _


### (pm.)SFFormantModelBP_ui

Ready-to-use source-filter vocal synthesizer with built-in user interface.

#### Usage

SFFormantModelBP_ui : _


### (pm.)SFFormantModelFofCycle_ui_MIDI

#### Usage

SFFormantModelFofCycle_ui_MIDI : _


### (pm.)SFFormantModelFofSmooth_ui_MIDI

#### Usage

SFFormantModelFofSmooth_ui_MIDI : _


### (pm.)SFFormantModelBP_ui_MIDI

#### Usage

SFFormantModelBP_ui_MIDI : _


## Misc Functions

Various miscellaneous functions.

### (pm.)allpassNL

Bidirectional block adding nonlinearities in both directions in a chain. Nonlinearities are created by modulating the coefficients of a passive allpass filter by the signal it is processing.

#### Usage

chain(... : allpassNL(nonlinearity) : ...)


Where:

• nonlinearity: amount of nonlinearity to be added (0-1)

### modalModel

Implement multiple resonance modes using resonant bandpass filters.

#### Usage

_ : modalModel(n, freqs, t60s, gains) : _


Where:

• n: number of given modes
• freqs : list of filter center freqencies
• t60s : list of mode resonance durations (in seconds)
• gains : list of mode gains (0-1)

For example, to generate a model with 2 modes (440 Hz and 660 Hz, a fifth) where the higher one decays faster and is attenuated:

os.impulse : modalModel(2, (440, 660),
(0.5, 0.25),
(ba.db2linear(-1), ba.db2linear(-6)) : _