Faust Libraries
NOTE: this documentation was automatically generated using pandoc.
This page provides information on how to use the Faust libraries.
The /libraries folder contains the different Faust libraries. If you wish to add your own functions to this library collection, you can refer to the “Contributing” section providing a set of coding conventions.
WARNING: These libraries replace the “old” Faust libraries. They are still being beta tested so you might encounter bugs while using them. If your codes still use the “old” Faust libraries, you might want to try to use Bart Brouns’ script that automatically makes an old Faust code compatible with the new libraries: https://github.com/magnetophon/faustCompressors/blob/master/newlib.sh. If you find a bug, please report it at rmichon_at_ccrma_dot_stanford_dot_edu. Thanks ;)!
Using the Faust Libraries
The easiest and most standard way to use the Faust libraries is to import stdfaust.lib in your Faust code:
import("stdfaust.lib");
This will give you access to all the Faust libraries through a series of environments:
sf: all.liban: analyzers.libba: basics.libco: compressors.libde: delays.libdm: demos.libdx: dx7.liben: envelopes.libfi: filters.libho: hoa.libma: maths.libef: misceffects.libos: oscillators.libno: noises.libpf: phaflangers.libpm: physmodels.libre: reverbs.libro: routes.libsi: signals.libsp: spats.libsy: synths.libve: vaeffects.lib
Environments can then be used as follows in your Faust code:
import("stdfaust.lib"); process = os.osc(440);
In this case, we’re calling the osc function from oscillators.lib.
You can also access all the functions of all the libraries directly using the sf environment:
import("stdfaust.lib"); process = sf.osc(440);
Alternatively, environments can be created by hand:
os = library("oscillators.lib"); process = os.osc(440);
Finally, libraries can be simply imported in the Faust code (not recommended):
import("oscillators.lib"); process = osc(440);
Contributing
If you wish to add a function to any of these libraries or if you plan to add a new library, make sure that you follow the following conventions:
New Functions
- All functions must be preceded by a markdown documentation header respecting the following format (open the source code of any of the libraries for an example):
//-----------------functionName-------------------- // Description // // #### Usage // // ``` // Usage Example // ``` // // Where: // // build libraries.html argument1: argument 1 description //-------------------------------------------------
- Every time a new function is added, the documentation should be updated simply by running
make doclib. - The environment system (e.g.
os.osc) should be used when calling a function declared in another library (see the section on Using the Faust Libraries). - Try to reuse exisiting functions as much as possible.
- If you have any question, send an e-mail to rmichon_at_ccrma_dot_stanford_dot_edu.
New Libraries
- Any new “standard” library should be declared in
stdfaust.lib with its own environment (2 letters - see stdfaust.lib). - Any new “standard” library must be added to
generateDoc. - Functions must be organized by sections.
- Any new library should at least
declare a name and a version. - The comment based markdown documentation of each library must respect the following format (open the source code of any of the libraries for an example):
//############### libraryName ################## // Description // // build libraries.html Section Name 1 // build libraries.html Section Name 2 // build libraries.html ... // // It should be used using the `[...]` environment: // // ``` // [...] = library("libraryName"); // process = [...].functionCall; // ``` // // Another option is to import `stdfaust.lib` which already contains the `[...]` // environment: // // ``` // import("stdfaust.lib"); // process = [...].functionCall; // ``` //############################################## //================= Section Name =============== // Description //==============================================
- If you have any question, send an e-mail to rmichon_at_ccrma_dot_stanford_dot_edu.
General Organization
Only the libraries that are considered to be “standard” are documented:
analyzers.libbasics.libcompressors.libdelays.libdemos.libdx7.libenvelopes.libfilters.libhoa.libmaths.libmisceffects.liboscillators.libnoises.libphaflangers.libphysmodels.libreverbs.libroutes.libsignals.libspats.libsynths.libtonestacks.lib (not documented but example in /examples/misc)tubes.lib (not documented but example in /examples/misc)vaeffects.lib
Other deprecated libraries such as music.lib, etc. are present but are not documented to not confuse new users.
The doumentation of each library can be found in /documentation/library.html or in /documentation/library.pdf.
The /examples directory contains all the examples from the /examples folder of the Faust distribution as well as new ones. Most of them were updated to reflect the coding conventions described in the next section. Examples are organized by types in different folders. The /old folder contains examples that are fully deprecated, probably because they were integrated to the libraries and fully rewritten (see freeverb.dsp for example). Examples using deprecated libraries were integrated to the general tree but a warning comment was added at their beginning to point readers to the right library and function.
Coding Conventions
In order to have a uniformized library system, we established the following conventions (that hopefully will be followed by others when making modifications to them :-) ).
Documentation
- All the functions that we want to be “public” are documented.
- We used the
faust2md “standards” for each library: //### for main title (library name - equivalent to # in markdown), //=== for section declarations (equivalent to ## in markdown) and //--- for function declarations (equivalent to #### in markdown - see basics.lib for an example). - Sections in function documentation should be declared as
#### markdown title. - Each function documentation provides a “Usage” section (see
basics.lib).
Library Import
To prevent cross-references between libraries we generalized the use of the library("") system for function calls in all the libraries. This means that everytime a function declared in another library is called, the environment corresponding to this library needs to be called too. To make things easier, a stdfaust.lib library was created and is imported by all the libraries:
an = library("analyzers.lib"); ba = library("basics.lib"); co = library("compressors.lib"); de = library("delays.lib"); dm = library("demos.lib"); dx = library("dx7.lib"); en = library("envelopes.lib"); fi = library("filters.lib"); ho = library("hoa.lib"); ma = library("maths.lib"); ef = library("misceffects.lib"); os = library("oscillators.lib"); no = library("noises.lib"); pf = library("phaflangers.lib"); pm = library("physmodels.lib"); re = library("reverbs.lib"); ro = library("routes.lib"); sp = library("spats.lib"); si = library("signals.lib"); sy = library("synths.lib"); ve = library("vaeffects.lib");
For example, if we wanted to use the smooth function which is now declared in signals.lib, we would do the following:
import("stdfaust.lib"); process = si.smooth(0.999);
This standard is only used within the libraries: nothing prevents coders to still import signals.lib directly and call smooth without ro., etc.
“Demo” Functions
“Demo” functions are placed in demos.lib and have a built-in user interface (UI). Their name ends with the _demo suffix. Each of these function have a .dsp file associated to them in the /examples folder.
Any function containing UI elements should be placed in this library and respect these standards.
“Standard” Functions
“Standard” functions are here to simplify the life of new (or not so new) Faust coders. They are declared in /libraries/doc/standardFunctions.md and allow to point programmers to preferred functions to carry out a specific task. For example, there are many different types of lowpass filters declared in filters.lib and only one of them is considered to be standard, etc.
Copyright / License
Now that Faust libraries are less author specific, each function will normally have its own copyright-and-license line in the library source (the .lib file, such as analyzers.lib). If not, see if the function is defined within a section of the .lib file stating the license in source-code comments. If not, then the copyright and license given at the beginning of the .lib file may be assumed, when present. If not, run git blame on the .lib file and ask the person who last edited the function!
Note that it is presently possible for a library function released under one license to utilize another library function having some different license. There is presently no indication of this situation in the Faust compiler output, but such notice is planned. For now, library contributors should strive to use only library functions having compatible licenses, and concerned end-users must manually determine the union of licenses applicable to the library functions they are using.
Standard Functions
Dozens of functions are implemented in the Faust libraries and many of them are very specialized and not useful to beginners or to people who only need to use Faust for basic applications. This section offers an index organized by categories of the “standard Faust functions” (basic filters, effects, synthesizers, etc.). This index only contains functions without a user interface (UI). Faust functions with a built-in UI can be found in demos.lib.
Basic Elements
Conversion
Effects
Envelope Generators
Filters
Synths
Primitives
User Interface Primitives
Creates a button in the user interface. The button is a primitive circuit with one output and no input. The signal produced by the button is 0 when not pressed and 1 while pressed.
Usage
button("play") : _;
Where "play" is the name of the button in the interface.
checkbox
Creates a checkbox in the user interface. The checkbox is a primitive circuit with one output and no input. The signal produced by the checkbox is 0 when not checked and 1 when checked.
Usage
checkbox("play") : _;
Where "play" is the name of the checkbox in the interface.
hslider
Creates a horizontal slider in the user interface. The hslider is a primitive circuit with one output and no input. hslider produces a signal between a minimum and a maximum value based on the position of the slider cursor.
Usage
hslider("volume",-10,-70,12,0.1) : _;
Where volume is the name of the slider in the interface, -10 the default value of the slider when the program starts, -70 the minimum value, 12 the maximum value, and 0.1 the step the determines the precision of the control.
nentry
Creates a numerical entry in the user interface. The nentry is a primitive circuit with one output and no input. nentry produces a signal between a minimum and a maximum value based on the user input.
Usage
nentry("volume",-10,-70,12,0.1) : _;
Where volume is the name of the numerical entry in the interface, -10 the default value of the entry when the program starts, -70 the minimum value, 12 the maximum value, and 0.1 the step the determines the precision of the control.
vslider
Creates a vertical slider in the user interface. The vslider is a primitive circuit with one output and no input. vslider produces a signal between a minimum and a maximum value based on the position of the slider cursor.
Usage
vslider("volume",-10,-70,12,0.1) : _;
Where volume is the name of the slider in the interface, -10 the default value of the slider when the program starts, -70 the minimum value, 12 the maximum value, and 0.1 the step the determines the precision of the control.
analyzers.lib
Faust Analyzers library. Its official prefix is an.
Amplitude Tracking
(an.)amp_follower
Classic analog audio envelope follower with infinitely fast rise and exponential decay. The amplitude envelope instantaneously follows the absolute value going up, but then floats down exponentially. amp_follower is a standard Faust function.
Usage
_ : amp_follower(rel) : _
Where:
rel: release time = amplitude-envelope time-constant (sec) going down
Reference
- Musical Engineer’s Handbook, Bernie Hutchins, Ithaca NY, 1975 Electronotes Newsletter, Bernie Hutchins
(an.)amp_follower_ud
Envelope follower with different up and down time-constants (also called a “peak detector”).
Usage
_ : amp_follower_ud(att,rel) : _
Where:
att: attack time = amplitude-envelope time constant (sec) going uprel: release time = amplitude-envelope time constant (sec) going down
Note
We assume rel >> att. Otherwise, consider rel ~ max(rel,att). For audio, att is normally faster (smaller) than rel (e.g., 0.001 and 0.01). Use amp_follower_ar below to remove this restriction.
Reference
(an.)amp_follower_ar
Envelope follower with independent attack and release times. The release can be shorter than the attack (unlike in amp_follower_ud above).
Usage
_ : amp_follower_ar(att,rel) : _;
- Author Jonatan Liljedahl, revised by RM
Spectrum-Analyzers
Spectrum-analyzers split the input signal into a bank of parallel signals, one for each spectral band. They are related to the Mth-Octave Filter-Banks in filters.lib. The documentation of this library contains more details about the implementation. The parameters are:
M: number of band-slices per octave (>1)N: total number of bands (>2)ftop = upper bandlimit of the Mth-octave bands (<SR/2)
In addition to the Mth-octave output signals, there is a highpass signal containing frequencies from ftop to SR/2, and a “dc band” lowpass signal containing frequencies from 0 (dc) up to the start of the Mth-octave bands. Thus, the N output signals are
highpass(ftop), MthOctaveBands(M,N-2,ftop), dcBand(ftop*2^(-M*(N-1)))
A Spectrum-Analyzer is defined here as any band-split whose bands span the relevant spectrum, but whose band-signals do not necessarily sum to the original signal, either exactly or to within an allpass filtering. Spectrum analyzer outputs are normally at least nearly “power complementary”, i.e., the power spectra of the individual bands sum to the original power spectrum (to within some negligible tolerance).
Increasing Channel Isolation
Go to higher filter orders - see Regalia et al. or Vaidyanathan (cited below) regarding the construction of more aggressive recursive filter-banks using elliptic or Chebyshev prototype filters.
References
- “Tree-structured complementary filter banks using all-pass sections”, Regalia et al., IEEE Trans. Circuits & Systems, CAS-34:1470-1484, Dec. 1987
- “Multirate Systems and Filter Banks”, P. Vaidyanathan, Prentice-Hall, 1993
- Elementary filter theory: https://ccrma.stanford.edu/~jos/filters/
(an.)mth_octave_analyzer
Octave analyzer. mth_octave_analyzer[N] are standard Faust functions.
Usage
_ : mth_octave_analyzer(O,M,ftop,N) : par(i,N,_); // Oth-order Butterworth _ : mth_octave_analyzer6e(M,ftop,N) : par(i,N,_); // 6th-order elliptic
Also for convenience:
_ : mth_octave_analyzer3(M,ftop,N) : par(i,N,_); // 3d-order Butterworth _ : mth_octave_analyzer5(M,ftop,N) : par(i,N,_); // 5th-roder Butterworth mth_octave_analyzer_default = mth_octave_analyzer6e;
Where:
O: order of filter used to split each frequency band into twoM: number of band-slices per octaveftop: highest band-split crossover frequency (e.g., 20 kHz)N: total number of bands (including dc and Nyquist)
Mth-Octave Spectral Level
Spectral Level: Display (in bar graphs) the average signal level in each spectral band.
(an.)mth_octave_spectral_level6e
Spectral level display.
Usage:
_ : mth_octave_spectral_level6e(M,ftop,NBands,tau,dB_offset) : _;
Where:
M: bands per octaveftop: lower edge frequency of top bandNBands: number of passbands (including highpass and dc bands),tau: spectral display averaging-time (time constant) in seconds,dB_offset: constant dB offset in all band level meters.
Also for convenience:
mth_octave_spectral_level_default = mth_octave_spectral_level6e; spectral_level = mth_octave_spectral_level(2,10000,20);
(an.)[third|half]_octave_[analyzer|filterbank]
A bunch of special cases based on the different analyzer functions described above:
third_octave_analyzer(N) = mth_octave_analyzer_default(3,10000,N); third_octave_filterbank(N) = mth_octave_filterbank_default(3,10000,N); half_octave_analyzer(N) = mth_octave_analyzer_default(2,10000,N); half_octave_filterbank(N) = mth_octave_filterbank_default(2,10000,N); octave_filterbank(N) = mth_octave_filterbank_default(1,10000,N); octave_analyzer(N) = mth_octave_analyzer_default(1,10000,N);
Usage
See mth_octave_spectral_level_demo in demos.lib.
Arbritary-Crossover Filter-Banks and Spectrum Analyzers
These are similar to the Mth-octave analyzers above, except that the band-split frequencies are passed explicitly as arguments.
(an.)analyzer
Analyzer.
Usage
_ : analyzer(O,freqs) : par(i,N,_); // No delay equalizer
Where:
O: band-split filter order (ODD integer required for filterbank[i])freqs: (fc1,fc2,…,fcNs) [in numerically ascending order], where Ns=N-1 is the number of octave band-splits (total number of bands N=Ns+1).
If frequencies are listed explicitly as arguments, enclose them in parens:
_ : analyzer(3,(fc1,fc2)) : _,_,_
Sliding FFTs that compute a rectangularly windowed FFT each sample
(an.)fft
Fast Fourier Transform (FFT)
Usage
si.cbus(N) : fft(N) : si.cbus(N);
Where:
si.cbus(N) is a bus of N complex signals, each specified by real and imaginary parts: (r0,i0), (r1,i1), (r2,i2), …N is the FFT size (must be a power of 2: 2,4,8,16,…)fft(N) performs a length N FFT for complex signals (radix 2)- The output is a bank of N complex signals containing the complex spectrum over time: (R0, I0), (R1,I1), …
- The dc component is (R0,I0), where I0=0 for real input signals.
FFTs of Real Signals:
- To perform a sliding FFT over a real input signal, you can say
process = signal : an.rtocv(N) : an.fft(N);
where an.rtocv converts a real (scalar) signal to a complex vector signal having a zero imaginary part.
See an.rfft_analyzer_c (in analyzers.lib) and related functions for more detailed usage examples.
Use an.rfft_spectral_level(N,tau,dB_offset) to display the power spectrum of a real signal.
See dm.fft_spectral_level_demo(N) in demos.lib for an example GUI driving an.rfft_spectral_level().
Reference
(an.)ifft
Inverse Fast Fourier Transform (IFFT)
Usage
si.cbus(N) : ifft(N) : si.cbus(N);
Where:
- N is the IFFT size (power of 2)
- Input is a complex spectrum represented as interleaved real and imaginary parts: (R0, I0), (R1,I1), (R2,I2), …
- Output is a bank of N complex signals giving the complex signal in the time domain: (r0, i0), (r1,i1), (r2,i2), …
basics.lib
A library of basic elements. Its official prefix is ba.
(ba.)samp2sec
Converts a number of samples to a duration in seconds. samp2sec is a standard Faust function.
Usage
samp2sec(n) : _
Where:
(ba.)sec2samp
Converts a duration in seconds to a number of samples. samp2sec is a standard Faust function.
Usage
sec2samp(d) : _
Where:
(ba.)db2linear
Converts a loudness in dB to a linear gain (0-1). db2linear is a standard Faust function.
Usage
db2linear(l) : _
Where:
(ba.)linear2db
Converts a linear gain (0-1) to a loudness in dB. linear2db is a standard Faust function.
Usage
linear2db(g) : _
Where:
(ba.)lin2LogGain
Converts a linear gain (0-1) to a log gain (0-1).
Usage
_ : lin2LogGain : _
(ba.)log2LinGain
Converts a log gain (0-1) to a linear gain (0-1).
Usage
_ : log2LinGain : _
(ba.)tau2pole
Returns a real pole giving exponential decay. Note that t60 (time to decay 60 dB) is ~6.91 time constants. tau2pole is a standard Faust function.
Usage
_ : smooth(tau2pole(tau)) : _
Where:
tau: time-constant in seconds
(ba.)pole2tau
Returns the time-constant, in seconds, corresponding to the given real, positive pole in (0,1). pole2tau is a standard Faust function.
Usage
pole2tau(pole) : _
Where:
(ba.)midikey2hz
Converts a MIDI key number to a frequency in Hz (MIDI key 69 = A440). midikey2hz is a standard Faust function.
Usage
midikey2hz(mk) : _
Where:
(ba.)hz2midikey
Converts a frequency in Hz to a MIDI key number (MIDI key 69 = A440). hz2midikey is a standard Faust function.
Usage
hz2midikey(f) : _
Where:
(ba.)pianokey2hz
Converts a piano key number to a frequency in Hz (piano key 49 = A440).
Usage
pianokey2hz(pk) : _
Where:
(ba.)hz2pianokey
Converts a frequency in Hz to a piano key number (piano key 49 = A440).
Usage
hz2pianokey(f) : _
Where:
(ba.)countdown
Starts counting down from n included to 0. While trig is 1 the output is n. The countdown starts with the transition of trig from 1 to 0. At the end of the countdown the output value will remain at 0 until the next trig. countdown is a standard Faust function.
Usage
countdown(n,trig) : _
Where:
count: the starting point of the countdowntrig: the trigger signal (1: start at n; 0: decrease until 0)
(ba.)countup
Starts counting up from 0 to n included. While trig is 1 the output is 0. The countup starts with the transition of trig from 1 to 0. At the end of the countup the output value will remain at n until the next trig. countup is a standard Faust function.
Usage
countup(n,trig) : _
Where:
count: the maximum count valuetrig: the trigger signal (1: start at 0; 0: increase until n)
(ba.)sweep
Counts from 0 to period samples repeatedly, while run is 1. Outsputs zero while run is 0.
Usage
sweep(period,run) : _
(ba.)time
A simple timer that counts every samples from the beginning of the process. time is a standard Faust function.
Usage
time : _
(ba.)tempo
Converts a tempo in BPM into a number of samples.
Usage
tempo(t) : _
Where:
(ba.)period
Basic sawtooth wave of period p.
Usage
period(p) : _
Where:
p: period as a number of samples
(ba.)pulse
Pulses (10000) generated at period p.
Usage
pulse(p) : _
Where:
p: period as a number of samples
(ba.)pulsen
Pulses (11110000) of length n generated at period p.
Usage
pulsen(n,p) : _
Where:
n: the length of the pulse as a number of samplesp: period as a number of samples
(ba.)cycle
Split nonzero input values into n cycles.
Usage
_ : cycle(n) <:
Where:
n: the number of cycles/output signals
(ba.)beat
Pulses at tempo t. beat is a standard Faust function.
Usage
beat(t) : _
Where:
(ba.)pulse_countup
Starts counting up pulses. While trig is 1 the output is counting up, while trig is 0 the counter is reset to 0.
Usage
_ : pulse_countup(trig) : _
Where:
trig: the trigger signal (1: start at next pulse; 0: reset to 0)
(ba.)pulse_countdown
Starts counting down pulses. While trig is 1 the output is counting down, while trig is 0 the counter is reset to 0.
Usage
_ : pulse_countdown(trig) : _
Where:
trig: the trigger signal (1: start at next pulse; 0: reset to 0)
(ba.)pulse_countup_loop
Starts counting up pulses from 0 to n included. While trig is 1 the output is counting up, while trig is 0 the counter is reset to 0. At the end of the countup (n) the output value will be reset to 0.
Usage
_ : pulse_countup_loop(n,trig) : _
Where:
n: the highest number of the countup (included) before reset to 0.trig: the trigger signal (1: start at next pulse; 0: reset to 0)
(ba.)resetCtr
Function that lets through the mth impulse out of each consecutive group of n impulses.
Usage
_ : resetCtr(n,m) : _
Where:
n: the total number of impulses being splitm: index of impulse to allow to be output
(ba.)pulse_countdown_loop
Starts counting down pulses from 0 to n included. While trig is 1 the output is counting down, while trig is 0 the counter is reset to 0. At the end of the countdown (n) the output value will be reset to 0.
Usage
_ : pulse_coundown_loop(n,trig) : _
Where:
n: the highest number of the countup (included) before reset to 0.trig: the trigger signal (1: start at next pulse; 0: reset to 0)
Array Processing/Pattern Matching
(ba.)count
Count the number of elements of list l. count is a standard Faust function.
Usage
count(l) count ((10,20,30,40)) -> 4
Where:
(ba.)take
Take an element from a list. take is a standard Faust function.
Usage
take(e,l) take(3,(10,20,30,40)) -> 30
Where:
p: position (starting at 1)l: list of elements
(ba.)subseq
Extract a part of a list.
Usage
subseq(l, p, n) subseq((10,20,30,40,50,60), 1, 3) -> (20,30,40) subseq((10,20,30,40,50,60), 4, 1) -> 50
Where:
l: listp: start point (0: begin of list)n: number of elements
Note:
Faust doesn’t have proper lists. Lists are simulated with parallel compositions and there is no empty list
Selectors (Conditions)
(ba.)if
if-then-else implemented with a select2.
Usage
Where:
c: conditiont: signal selected while c is truee: signal selected while c is false
(ba.)selector
Selects the ith input among n at compile time.
Usage
selector(i,n) _,_,_,_ : selector(2,4) : _ // selects the 3rd input among 4
Where:
i: input to select (int, numbered from 0, known at compile time)n: number of inputs (int, known at compile time, n > i)
There is also cselector for selecting among complex input signals of the form (real,imag).
(ba.)selectn
Selects the ith input among N at run time.
Usage
selectn(N,i) _,_,_,_ : selectn(4,2) : _ // selects the 3rd input among 4
Where:
N: number of inputs (int, known at compile time, N > 0)i: input to select (int, numbered from 0)
Example test program
N=64; process = par(n,N, (par(i,N,i) : selectn(N,n)));
(ba.)select2stereo
Select between 2 stereo signals.
Usage
_,_,_,_ : select2stereo(bpc) : _,_,_,_
Where:
bpc: the selector switch (0/1)
Other
(ba.)latch
Latch input on positive-going transition of “clock” (“sample-and-hold”).
Usage
_ : latch(clocksig) : _
Where:
clocksig: hold trigger (0 for hold, 1 for bypass)
(ba.)sAndH
Sample And Hold. sAndH is a standard Faust function.
Usage
_ : sAndH(t) : _
Where:
t: hold trigger (0 for hold, 1 for bypass)
(ba.)downSample
Down sample a signal. WARNING: this function doesn’t change the rate of a signal, it just holds samples… downSample is a standard Faust function.
Usage
_ : downSample(freq) : _
Where:
(ba.)peakhold
Outputs current max value above zero.
Usage
_ : peakhold(mode) : _;
Where:
mode means: 0 - Pass through. A single sample 0 trigger will work as a reset. 1 - Track and hold max value.
(ba.)peakholder
Tracks abs peak and holds peak for ‘holdtime’ samples.
Usage
_ : peakholder(holdtime) : _;
(ba.)impulsify
Turns the signal from a button into an impulse (1,0,0,… when button turns on). impulsify is a standard Faust function.
Usage
button("gate") : impulsify ;
(ba.)automat
Record and replay to the values the input signal in a loop.
Usage
hslider(...) : automat(bps, size, init) : _
(ba.)bpf
bpf is an environment (a group of related definitions) that can be used to create break-point functions. It contains three functions :
start(x,y) to start a break-point functionend(x,y) to end a break-point functionpoint(x,y) to add intermediate points to a break-point function
A minimal break-point function must contain at least a start and an end point :
f = bpf.start(x0,y0) : bpf.end(x1,y1);
A more involved break-point function can contains any number of intermediate points:
f = bpf.start(x0,y0) : bpf.point(x1,y1) : bpf.point(x2,y2) : bpf.end(x3,y3);
In any case the x_{i} must be in increasing order (for all i, x_{i} < x_{i+1}). For example the following definition :
f = bpf.start(x0,y0) : ... : bpf.point(xi,yi) : ... : bpf.end(xn,yn);
implements a break-point function f such that :
f(x) = y_{0} when x < x_{0}f(x) = y_{n} when x > x_{n}f(x) = y_{i} + (y_{i+1}-y_{i})*(x-x_{i})/(x_{i+1}-x_{i}) when x_{i} <= x and x < x_{i+1}
bpf is a standard Faust function.
(ba.)listInterp
Linearly interpolates between the elements of a list.
Usage
foo = listInterp((800,400,350,450,325),index); i = 1.69; // range is 0-4 process = foo(i);
Where:
index: the index (float) to interpolate between the different values. The range of index depends on the size of the list.
(ba.)bypass1
Takes a mono input signal, route it to e and bypass it if bpc = 1. bypass1 is a standard Faust function.
Usage
_ : bypass1(bpc,e) : _
Where:
bpc: bypass switch (0/1)e: a mono effect
(ba.)bypass2
Takes a stereo input signal, route it to e and bypass it if bpc = 1. bypass2 is a standard Faust function.
Usage
_,_ : bypass2(bpc,e) : _,_
Where:
bpc: bypass switch (0/1)e: a stereo effect
(ba.)bypass1to2
Bypass switch for effect e having mono input signal and stereo output. Effect e is bypassed if bpc = 1. bypass1to2 is a standard Faust function.
Usage
_ : bypass1(bpc,e) : _,_
Where:
bpc: bypass switch (0/1)e: a mono-to-stereo effect
(ba.)toggle
Triggered by the change of 0 to 1, it toggles the output value between 0 and 1.
Usage
_ : toggle : _
Examples
button("toggle") : toggle : vbargraph("output", 0, 1) (an.amp_follower(0.1) > 0.01) : toggle : vbargraph("output", 0, 1) // takes audio input
(ba.)on_and_off
The first channel set the output to 1, the second channel to 0.
Usage
_ , _ : on_and_off : _
Example
button("on"), button("off") : on_and_off : vbargraph("output", 0, 1)
(ba.)selectoutn
Route input to the output among N at run time.
Usage
_ : selectoutn(n, s) : _,_,...n
Where:
n: number of outputs (int, known at compile time, N > 0)s: output number to route to (int, numbered from 0) (i.e. slider)
Example
process = 1 : selectoutn(3, sel) : par(i,3,bar) ; sel = hslider("volume",0,0,2,1) : int; bar = vbargraph("v.bargraph", 0, 1);
Sliding Reduce
Provides various operations on the last N samples using a high order `slidingReduce(op,N,maxN,disabledVal,x)`` fold-like function :
slidingSumN(n,maxn): the sliding sum of the last n input samplesslidingMaxN(n,maxn): the sliding max of the last n input samplesslidingMinN(n,maxn): the sliding min of the last n input samplesslidingMeanN(n,maxn): the sliding mean of the last n input samplesslidingRMSn(n,maxn): the sliding RMS of the last n input samples
Working Principle
If we want the maximum of the last 8 values, we can do that as:
simpleMax(x) = ( ( max(x@0,x@1), max(x@2,x@3) ) :max ), ( ( max(x@4,x@5), max(x@6,x@7) ) :max ) :max;
max(x@2,x@3) is the same as max(x@0,x@1)@2 but the latter re-uses a value we already computed,so is more efficient. Using the same trick for values 4 trough 7, we can write:
efficientMax(x)= ( ( max(x@0,x@1), max(x@0,x@1)@2 ) :max ), ( ( max(x@0,x@1), max(x@0,x@1)@2 ) :max@4 ) :max;
We can rewrite it recursively, so it becomes possible to get the maximum at have any number of values, as long as it’s a power of 2.
recursiveMax = case { (1,x) => x; (N,x) => max(recursiveMax(N/2,x) , recursiveMax(N/2,x)@(N/2)); };
What if we want to look at a number of values that’s not a power of 2? For each value, we will have to decide whether to use it or not. If N is bigger than the index of the value, we use it, otherwise we replace it with (0-(ma.INFINITY)):
variableMax(N,x) = max( max( ( (x@0 : useVal(0)), (x@1 : useVal(1)) ):max, ( (x@2 : useVal(2)), (x@3 : useVal(3)) ):max ), max( ( (x@4 : useVal(4)), (x@5 : useVal(5)) ):max, ( (x@6 : useVal(6)), (x@7 : useVal(7)) ):max ) ) with{ useVal(i) = select2( (N>=i) , (0-(ma.INFINITY)),_); };
Now it becomes impossible to re-use any values. To fix that let’s first look at how we’d implement it using recursiveMax, but with a fixed N that is not a power of 2. For example, this is how you’d do it with N=3:
binaryMaxThree(x) = ( recursiveMax(1,x)@0, // the first x recursiveMax(2,x)@1 // the second and third x ):max;
N=6
binaryMaxSix(x) = ( recursiveMax(2,x)@0, // first two recursiveMax(4,x)@2 // third trough sixt ):max;
Note that recursiveMax(2,x) is used at a different delay then in binaryMaxThree, since it represents 1 and 2, not 2 and 3. Each block is delayed the combined size of the previous blocks.
N=7
binaryMaxSeven(x) = ( ( recursiveMax(1,x)@0, // first x recursiveMax(2,x)@1 // second and third ):max, ( recursiveMax(4,x)@3 // fourth trough seventh ) ):max;
To make a variable version, we need to know which powers of two are used, and at which delay time.
Then it becomes a matter of:
- lining up all the different block sizes in parallel: the first
par() statement - delaying each the appropriate amount:
sumOfPrevBlockSizes() - turning it on or off:
useVal() - getting the maximum of all of them:
combine()
In faust, we can only do that for a fixed maximum number of values: maxN
variableBinaryMaxN(N,maxN,x) = par(i,maxNrBits,recursiveMax(pow2(i),x)@sumOfPrevBlockSizes(N,maxN,i) : useVal(i)) : combine(maxNrBits) with { // The sum of all the sizes of the previous blocks sumOfPrevBlockSizes(N,maxN,0) = 0; sumOfPrevBlockSizes(N,maxN,i) = (ba.subseq((allBlockSizes(N,maxN)),0,i):>_); allBlockSizes(N,maxN) = par(i, maxNrBits, pow2(i) build libraries.html isUsed(i) ); maxNrBits = int2nrOfBits(maxN); // get the maximum of all blocks combine(2) = max; combine(N) = max(combine(N-1),_); // Decide wether or not to use a certain value, based on N useVal(i) = select2( isUsed(i), (0-(ma.INFINITY)),_); isUsed(i) = ba.take(i+1,(int2bin(N,maxN))); };
(ba.)slidingReduce
Fold-like high order function. Apply a commutative binary operation <op> to the last <n> consecutive samples of a signal <x>. For example : slidingReduce(max,128,128,-(ma.INFINITY)) will compute the maximum of the last 128 samples. The output is updated each sample, unlike reduce, where the output is constant for the duration of a block
Usage
_ : slidingReduce(op,N,maxN,disabledVal) : _
Where:
N: the number of values to processmaxN: the maximum number of values to process, needs to be a power of 2op: the operator. Needs to be a commutative one.disabledVal: the value to use when we want to ignore a value.
In other words, op(x,disabledVal) should equal to x. For example, +(x,0) equals x and min(x,ma.INFINITY) equals x. So if we want to calculate the sum, we need to give 0 as disabledVal, and if we want the minimum, we need to give ma.INFINITY as disabledVal.
(ba.)slidingSumN
The sliding sum of the last n input samples.
Usage
_ : slidingSumN(N,maxN) : _
Where:
N: the number of values to processmaxN: the maximum number of values to process, needs to be a power of 2
(ba.)slidingMaxN
The sliding maximum of the last n input samples.
Usage
_ : slidingMaxN(N,maxN) : _
Where:
N: the number of values to processmaxN: the maximum number of values to process, needs to be a power of 2
(ba.)slidingSumN
The sliding minimum of the last n input samples.
Usage
_ : slidingMinN(N,maxN) : _
Where:
N: the number of values to processmaxN: the maximum number of values to process, needs to be a power of 2
(ba.)slidingMeanN
The sliding mean of the last n input samples.
Usage
_ : slidingMeanN(N,maxN) : _
Where:
N: the number of values to processmaxN: the maximum number of values to process, needs to be a power of 2
(ba.)slidingRMSn
The root mean square of the last n input samples.
Usage
_ : slidingRMSn(N,maxN) : _
Where:
N: the number of values to processmaxN: the maximum number of values to process, needs to be a power of 2
compressors.lib
A library of compressor effects. Its official prefix is co.
Functions Reference
(co.)compressor_mono
Mono dynamic range compressors. compressor_mono is a standard Faust function
Usage
_ : compressor_mono(ratio,thresh,att,rel) : _
Where:
ratio: compression ratio (1 = no compression, >1 means compression)thresh: dB level threshold above which compression kicks in (0 dB = max level)att: attack time = time constant (sec) when level & compression going uprel: release time = time constant (sec) coming out of compression
References
(co.)compressor_stereo
Stereo dynamic range compressors.
Usage
_,_ : compressor_stereo(ratio,thresh,att,rel) : _,_
Where:
ratio: compression ratio (1 = no compression, >1 means compression)thresh: dB level threshold above which compression kicks in (0 dB = max level)att: attack time = time constant (sec) when level & compression going uprel: release time = time constant (sec) coming out of compression
References
(co.)limiter_1176_R4_mono
A limiter guards against hard-clipping. It can be can be implemented as a compressor having a high threshold (near the clipping level), fast attack and release, and high ratio. Since the ratio is so high, some knee smoothing is desirable (“soft limiting”). This example is intended to get you started using compressor_* as a limiter, so all parameters are hardwired to nominal values here. Ratios: 4 (moderate compression), 8 (severe compression), 12 (mild limiting), or 20 to 1 (hard limiting) Att: 20-800 MICROseconds (Note: scaled by ratio in the 1176) Rel: 50-1100 ms (Note: scaled by ratio in the 1176) Mike Shipley likes 4:1 (Grammy-winning mixer for Queen, Tom Petty, etc.) Faster attack gives “more bite” (e.g. on vocals) He hears a bright, clear eq effect as well (not implemented here) limiter_1176_R4_mono is a standard Faust function.
Usage
_ : limiter_1176_R4_mono : _;
Reference:
http://en.wikipedia.org/wiki/1176_Peak_Limiter
(co.)limiter_1176_R4_stereo
A limiter guards against hard-clipping. It can be can be implemented as a compressor having a high threshold (near the clipping level), fast attack and release, and high ratio. Since the ratio is so high, some knee smoothing is desirable (“soft limiting”). This example is intended to get you started using compressor_* as a limiter, so all parameters are hardwired to nominal values here. Ratios: 4 (moderate compression), 8 (severe compression), 12 (mild limiting), or 20 to 1 (hard limiting) Att: 20-800 MICROseconds (Note: scaled by ratio in the 1176) Rel: 50-1100 ms (Note: scaled by ratio in the 1176) Mike Shipley likes 4:1 (Grammy-winning mixer for Queen, Tom Petty, etc.) Faster attack gives “more bite” (e.g. on vocals) He hears a bright, clear eq effect as well (not implemented here)
Usage
_,_ : limiter_1176_R4_stereo : _,_;
Reference:
http://en.wikipedia.org/wiki/1176_Peak_Limiter
delays.lib
This library contains a collection of delay functions. Its official prefix is de.
Basic Delay Functions
(de.)delay
Simple d samples delay where n is the maximum delay length as a number of samples. Unlike the @ delay operator, here the delay signal d is explicitely bounded to the interval [0..n]. The consequence is that delay will compile even if the interval of d can’t be computed by the compiler. delay is a standard Faust function.
Usage
_ : delay(n,d) : _
Where:
n: the max delay length (in samples)d: the delay length as a number of samples (integer)
(de.)fdelay
Simple d samples fractional delay based on 2 interpolated delay lines where n is the maximum delay length as a number of samples.
(de.)sdelay
s(mooth)delay: a mono delay that doesn’t click and doesn’t transpose when the delay time is changed.
Usage
_ : sdelay(N,it,dt) : _
Where :
N: maximal delay in samplesit: interpolation time (in samples) for example 1024dt: delay time (in samples)
Lagrange Interpolation
(de.)fdelaylti and (de.)fdelayltv
Fractional delay line using Lagrange interpolation.
Usage
_ : fdelaylt[i|v](order, maxdelay, delay, inputsignal) : _
Where order=1,2,3,... is the order of the Lagrange interpolation polynomial.
fdelaylti is most efficient, but designed for constant/slowly-varying delay. fdelayltv is more expensive and more robust when the delay varies rapidly.
NOTE: The requested delay should not be less than (N-1)/2.
References
- https://ccrma.stanford.edu/~jos/pasp/Lagrange_Interpolation.html
- (fixed-delay case)(https://ccrma.stanford.edu/~jos/Interpolation/Efficient_Time_Invariant_Lagrange_Interpolation.html)
- (variable-delay case)(https://ccrma.stanford.edu/~jos/Interpolation/Time_Varying_Lagrange_Interpolation.html)
- Timo I. Laakso et al., “Splitting the Unit Delay - Tools for Fractional Delay Filter Design”, IEEE Signal Processing Magazine, vol. 13, no. 1, pp. 30-60, Jan 1996.
- Philippe Depalle and Stephan Tassart, “Fractional Delay Lines using Lagrange Interpolators”, ICMC Proceedings, pp. 341-343, 1996.
(de.)fdelay[n]
For convenience, fdelay1, fdelay2, fdelay3, fdelay4, fdelay5 are also available where n is the order of the interpolation.
Thiran Allpass Interpolation
Thiran Allpass Interpolation
Reference
https://ccrma.stanford.edu/~jos/pasp/Thiran_Allpass_Interpolators.html
(de.)fdelay[n]a
Delay lines interpolated using Thiran allpass interpolation.
Usage
_ : fdelay[N]a(maxdelay, delay, inputsignal) : _
(exactly like fdelay)
Where:
N=1,2,3, or 4 is the order of the Thiran interpolation filter, and the delay argument is at least N - 1/2.
Note
The interpolated delay should not be less than N - 1/2. (The allpass delay ranges from N - 1/2 to N + 1/2.) This constraint can be alleviated by altering the code, but be aware that allpass filters approach zero delay by means of pole-zero cancellations. The delay range [N-1/2,N+1/2] is not optimal. What is?
Delay arguments too small will produce an UNSTABLE allpass!
Because allpass interpolation is recursive, it is not as robust as Lagrange interpolation under time-varying conditions. (You may hear clicks when changing the delay rapidly.)
First-order allpass interpolation, delay d in [0.5,1.5]
demos.lib
This library contains a set of demo functions based on examples located in the /examples folder. Its official prefix is dm.
Analyzers
(dm.)mth_octave_spectral_level_demo
Demonstrate mth_octave_spectral_level in a standalone GUI.
Usage
_ : mth_octave_spectral_level_demo(BandsPerOctave); _ : spectral_level_demo : _; // 2/3 octave
Filters
(dm.)parametric_eq_demo
A parametric equalizer application.
Usage:
_ : parametric_eq_demo : _ ;
(dm.)spectral_tilt_demo
A spectral tilt application.
Usage
_ : spectral_tilt_demo(N) : _ ;
Where:
N: filter order (integer)
All other parameters interactive
(dm.)mth_octave_filterbank_demo and (dm.)filterbank_demo
Graphic Equalizer: Each filter-bank output signal routes through a fader.
Usage
_ : mth_octave_filterbank_demo(M) : _ _ : filterbank_demo : _
Where:
N: number of bands per octave
Effects
(dm.)cubicnl_demo
Distortion demo application.
Usage:
_ : cubicnl_demo : _;
(dm.)gate_demo
Gate demo application.
Usage
_,_ : gate_demo : _,_;
(dm.)compressor_demo
Compressor demo application.
Usage
_,_ : compressor_demo : _,_;
(dm.)moog_vcf_demo
Illustrate and compare all three Moog VCF implementations above.
Usage
_ : moog_vcf_demo : _;
(dm.)wah4_demo
Wah pedal application.
Usage
_ : wah4_demo : _;
(dm.)crybaby_demo
Crybaby effect application.
Usage
_ : crybaby_demo : _ ;
(dm.)flanger_demo
Flanger effect application.
Usage
_,_ : flanger_demo : _,_;
(dm.)phaser2_demo
Phaser effect demo application.
Usage
_,_ : phaser2_demo : _,_;
(dm.)freeverb_demo
Freeverb demo application.
Usage
_,_ : freeverb_demo : _,_;
(dm.)stereo_reverb_tester
Handy test inputs for reverberator demos below.
Usage
_ : stereo_reverb_tester : _
(dm.)fdnrev0_demo
A reverb application using fdnrev0.
Usage
_,_ : fdnrev0_demo(N,NB,BBSO) : _,_
Where:
n: Feedback Delay Network (FDN) order / number of delay lines used = order of feedback matrix / 2, 4, 8, or 16 [extend primes array below for 32, 64, …]nb: Number of frequency bands / Number of (nearly) independent T60 controls / Integer 3 or greaterbbso = Butterworth band-split order / order of lowpass/highpass bandsplit used at each crossover freq / odd positive integer
(dm.)zita_rev_fdn_demo
Reverb demo application based on zita_rev_fdn.
Usage
si.bus(8) : zita_rev_fdn_demo : si.bus(8)
(dm.)zita_light
Light version of dm.zita_rev1 with only 2 UI elements.
Usage
_,_ : zita_light : _,_
(dm.)zita_rev1
Example GUI for zita_rev1_stereo (mostly following the Linux zita-rev1 GUI).
Only the dry/wet and output level parameters are “dezippered” here. If parameters are to be varied in real time, use smooth(0.999) or the like in the same way.
Usage
_,_ : zita_rev1 : _,_
Reference
http://www.kokkinizita.net/linuxaudio/zita-rev1-doc/quickguide.html
Generators
(dm.)sawtooth_demo
An application demonstrating the different sawtooth oscillators of Faust.
Usage
sawtooth_demo : _
(dm.)virtual_analog_oscillator_demo
Virtual analog oscillator demo application.
Usage
virtual_analog_oscillator_demo : _
(dm.)oscrs_demo
Simple application demoing filter based oscillators.
Usage
oscrs_demo : _
(dm.)velvet_noise_demo
Listen to velvet_noise!
Usage
velvet_noise_demo : _
(dm.)latch_demo
Illustrate latch operation
Usage
echo 'import("stdfaust.lib");' > latch_demo.dsp echo 'process = dm.latch_demo;' >> latch_demo.dsp faust2octave latch_demo.dsp Octave:1> plot(faustout);
(dm.)envelopes_demo
Illustrate various envelopes overlaid, including their gate build libraries.html 1.1
Usage
echo 'import("stdfaust.lib");' > envelopes_demo.dsp echo 'process = dm.envelopes_demo;' >> envelopes_demo.dsp faust2octave envelopes_demo.dsp Octave:1> plot(faustout);
(dm.)exciter
Psychoacoustic harmonic exciter, with GUI.
Usage
_ : exciter : _
References
(dm.)vocoder_demo
Use example of the vocoder function where an impulse train is used as excitation.
Usage
_ : vocoder_demo : _;
dx7.lib
Yamaha DX7 emulation library. Its official prefix is dx.
(dx.)dx7_ampf
DX7 amplitude conversion function. 3 versions of this function are available:
dx7_amp_bpf: BPF version (same as in the CSOUND toolkit)dx7_amp_func: estimated mathematical equivalent of dx7_amp_bpfdx7_ampf: default (sugar for dx7_amp_func)
Usage:
dx7AmpPreset : dx7_ampf_bpf : _
Where:
dx7AmpPreset: DX7 amplitude value (0-99)
(dx.)dx7_egraterisef
DX7 envelope generator rise conversion function. 3 versions of this function are available:
dx7_egraterise_bpf: BPF version (same as in the CSOUND toolkit)dx7_egraterise_func: estimated mathematical equivalent of dx7_egraterise_bpfdx7_egraterisef: default (sugar for dx7_egraterise_func)
Usage:
dx7envelopeRise : dx7_egraterisef : _
Where:
dx7envelopeRise: DX7 envelope rise value (0-99)
(dx.)dx7_egraterisepercf
DX7 envelope generator percussive rise conversion function. 3 versions of this function are available:
dx7_egrateriseperc_bpf: BPF version (same as in the CSOUND toolkit)dx7_egrateriseperc_func: estimated mathematical equivalent of dx7_egrateriseperc_bpfdx7_egraterisepercf: default (sugar for dx7_egrateriseperc_func)
Usage:
dx7envelopePercRise : dx7_egraterisepercf : _
Where:
dx7envelopePercRise: DX7 envelope percussive rise value (0-99)
(dx.)dx7_egratedecayf
DX7 envelope generator decay conversion function. 3 versions of this function are available:
dx7_egratedecay_bpf: BPF version (same as in the CSOUND toolkit)dx7_egratedecay_func: estimated mathematical equivalent of dx7_egratedecay_bpfdx7_egratedecayf: default (sugar for dx7_egratedecay_func)
Usage:
dx7envelopeDecay : dx7_egratedecayf : _
Where:
dx7envelopeDecay: DX7 envelope decay value (0-99)
(dx.)dx7_egratedecaypercf
DX7 envelope generator percussive decay conversion function. 3 versions of this function are available:
dx7_egratedecayperc_bpf: BPF version (same as in the CSOUND toolkit)dx7_egratedecayperc_func: estimated mathematical equivalent of dx7_egratedecayperc_bpfdx7_egratedecaypercf: default (sugar for dx7_egratedecayperc_func)
Usage:
dx7envelopePercDecay : dx7_egratedecaypercf : _
Where:
dx7envelopePercDecay: DX7 envelope decay value (0-99)
(dx.)dx7_eglv2peakf
DX7 envelope level to peak conversion function. 3 versions of this function are available:
dx7_eglv2peak_bpf: BPF version (same as in the CSOUND toolkit)dx7_eglv2peak_func: estimated mathematical equivalent of dx7_eglv2peak_bpfdx7_eglv2peakf: default (sugar for dx7_eglv2peak_func)
Usage:
dx7Level : dx7_eglv2peakf : _
Where:
dx7Level: DX7 level value (0-99)
(dx.)dx7_velsensf
DX7 velocity sensitivity conversion function.
Usage:
dx7Velocity : dx7_velsensf : _
Where:
dx7Velocity: DX7 level value (0-8)
(dx.)dx7_fdbkscalef
DX7 feedback scaling conversion function.
Usage:
dx7Feedback : dx7_fdbkscalef : _
Where:
dx7Feedback: DX7 feedback value
(dx.)dx7_op
DX7 Operator. Implements a phase-modulable sine wave oscillator connected to a DX7 envelope generator.
Usage:
dx7_op(freq,phaseMod,outLev,R1,R2,R3,R4,L1,L2,L3,L4,keyVel,rateScale,type,gain,gate) : _
Where:
freq: frequency of the oscillatorphaseMod: phase deviation (-1 - 1)outLev: preset output level (0-99)R1: preset envelope rate 1 (0-99)R2: preset envelope rate 2 (0-99)R3: preset envelope rate 3 (0-99)R4: preset envelope rate 4 (0-99)L1: preset envelope level 1 (0-99)L2: preset envelope level 2 (0-99)L3: preset envelope level 3 (0-99)L4: preset envelope level 4 (0-99)keyVel: preset key velocity sensitivity (0-99)rateScale: preset envelope rate scaletype: preset operator typegain: general gaingate: trigger signal
(dx.)dx7_algo
DX7 algorithms. Implements the 32 DX7 algorithms (a quick Google search should give your more details on this). Each algorithm uses 6 operators
Usage:
dx7_algo(algN,egR1,egR2,egR3,egR4,egL1,egL2,egL3,egL4,outLevel,keyVelSens,ampModSens,opMode,opFreq,opDetune,opRateScale,feedback,lfoDelay,lfoDepth,lfoSpeed,freq,gain,gate) : _
Where:
algN: algorithm number (0-31, should be an int…)egR1: preset envelope rates 1 (a list of 6 values between 0-99)egR2: preset envelope rates 2 (a list of 6 values between 0-99)egR3: preset envelope rates 3 (a list of 6 values between 0-99)egR4: preset envelope rates 4 (a list of 6 values between 0-99)egL1: preset envelope levels 1 (a list of 6 values between 0-99)egL2: preset envelope levels 2 (a list of 6 values between 0-99)egL3: preset envelope levels 3 (a list of 6 values between 0-99)egL4: preset envelope levels 4 (a list of 6 values between 0-99)outLev: preset output levels (a list of 6 values between 0-99)keyVel: preset key velocity sensitivities (a list of 6 values between 0-99)ampModSens: preset amplitude sensitivities (a list of 6 values between 0-99)opMode: preset operator mode (a list of 6 values between 0-1)opFreq: preset operator frequencies (a list of 6 values between 0-99)opDetune: preset operator detuning (a list of 6 values between 0-99)opRateScale: preset operator rate scale (a list of 6 values between 0-99)feedback: preset operator feedback (a list of 6 values between 0-99)lfoDelay: preset LFO delay (a list of 6 values between 0-99)lfoDepth: preset LFO depth (a list of 6 values between 0-99)lfoSpeed: preset LFO speed (a list of 6 values between 0-99)freq: fundamental frequencygain: general gaingate: trigger signal
(dx.)dx7_ui
Generic DX7 function where all parameters are controllable using UI elements. The master-with-mute branch must be used for this function to work… This function is MIDI-compatible.
Usage
dx7_ui : _
envelopes.lib
This library contains a collection of envelope generators. Its official prefix is en.
Functions Reference
(en.)smoothEnvelope
An envelope with an exponential attack and release. smoothEnvelope is a standard Faust function.
Usage
smoothEnvelope(ar,t) : _
ar: attack and release duration (s)t: trigger signal (attack is triggered when t>0, release is triggered when t=0)
(en.)ar
AR (Attack, Release) envelope generator (useful to create percussion envelopes). ar is a standard Faust function.
Usage
ar(a,r,t) : _
Where:
a: attack (sec)r: release (sec)t: trigger signal (attack is triggered when t>0, release is triggered when t=0)
(en.)arfe
ARFE (Attack and Release-to-Final-value Exponentially) envelope generator. Approximately equal to smoothEnvelope(Attack/6.91) when Attack == Release.
Usage
arfe(a,r,f,t) : _
Where:
a, r: attack (sec), release (sec)f: final value to approach upon release (such as 0)t: trigger signal (attack is triggered when t>0, release is triggered when t=0)
(en.)are
ARE (Attack, Release) envelope generator with Exponential segments. Approximately equal to smoothEnvelope(Attack/6.91) when Attack == Release.
Usage
are(a,r,t) : _
Where:
a: attack (sec)r: release (sec)t: trigger signal (attack is triggered when t>0, release is triggered when t=0)
(en.)asr
ASR (Attack, Sustain, Release) envelope generator. asr is a standard Faust function.
Usage
asr(a,s,r,t) : _
Where:
a: attack (sec)s: sustain (percentage of t: 0-1)r: release (sec)t: trigger signal (attack is triggered when t>0, release is triggered when t=0)
(en.)adsr
ADSR (Attack, Decay, Sustain, Release) envelope generator. adsr is a standard Faust function.
Usage
adsr(a,d,s,r,t) : _
Where:
a: attack (sec)d: decay (sec)s: sustain (percentage of t: 0-1)r: release (sec)t: trigger signal (attack is triggered when t>0, release is triggered when t=0)
(en.)adsre
ADSRE (Attack, Decay, Sustain, Release) envelope generator with Exponential segments.
Usage
adsre(a,d,s,r,g) : _
Where:
a: attack (sec)d: decay (sec)s: sustain (percentage of t: 0-1)r: release (sec)t: trigger signal (attack is triggered when t>0, release is triggered when t=0)
(en.)dx7envelope
DX7 operator envelope generator with 4 independent rates and levels. It is essentially a 4 points BPF.
Usage
dx7_envelope(R1,R2,R3,R4,L1,L2,L3,L4,t) : _
Where:
RN: rates in secondsLN: levels (0-1)t: trigger signal
filters.lib
Faust Filters library; Its official prefix is fi.
The Filters library is organized into 18 sections:
- Basic Filters
- Comb Filters
- Direct-Form Digital Filter Sections
- Direct-Form Second-Order Biquad Sections
- Ladder/Lattice Digital Filters
- Useful Special Cases
- Ladder/Lattice Allpass Filters
- Digital Filter Sections Specified as Analog Filter Sections
- Simple Resonator Filters
- Butterworth Lowpass/Highpass Filters
- Special Filter-Bank Delay-Equalizing Allpass Filters
- Elliptic (Cauer) Lowpass Filters
- Elliptic Highpass Filters
- Butterworth Bandpass/Bandstop Filters
- Elliptic Bandpass Filters
- Parametric Equalizers (Shelf, Peaking)
- Mth-Octave Filter-Banks
- Arbritary-Crossover Filter-Banks and Spectrum Analyzers
For more information, see ../documentation/library.pdf
Basic Filters
(fi.)zero
One zero filter. Difference equation: \(y(n) = x(x) - zx(n-1)\).
Usage
_ : zero(z) : _
Where:
z: location of zero along real axis in z-plane
Reference
https://ccrma.stanford.edu/~jos/filters/One_Zero.html
(fi.)pole
One pole filter. Could also be called a “leaky integrator”. Difference equation: \(y(n) = x(n) + py(n-1)\).
Usage
_ : pole(p) : _
Where:
p: pole location = feedback coefficient
Reference
https://ccrma.stanford.edu/~jos/filters/One_Pole.html
(fi.)integrator
Same as pole(1) [implemented separately for block-diagram clarity].
(fi.)dcblockerat
DC blocker with configurable break frequency. The amplitude response is substantially flat above \(fb\), and sloped at about +6 dB/octave below \(fb\). Derived from the analog transfer function \(H(s) = \frac{s}{(s + 2 \pi fb)}\) by the low-frequency-matching bilinear transform method (i.e., the standard frequency-scaling constant 2*SR).
Usage
_ : dcblockerat(fb) : _
Where:
fb: “break frequency” in Hz, i.e., -3 dB gain frequency.
Reference
https://ccrma.stanford.edu/~jos/pasp/Bilinear_Transformation.html
(fi.)dcblocker
DC blocker. Default dc blocker has -3dB point near 35 Hz (at 44.1 kHz) and high-frequency gain near 1.0025 (due to no scaling). dcblocker is as standard Faust function.
Usage
_ : dcblocker : _
Comb Filters
(fi.)ff_comb
Feed-Forward Comb Filter. Note that ff_comb requires integer delays (uses delay internally). ff_comb is a standard Faust function.
Usage
_ : ff_comb(maxdel,intdel,b0,bM) : _
Where:
maxdel: maximum delay (a power of 2)intdel: current (integer) comb-filter delay between 0 and maxdeldel: current (float) comb-filter delay between 0 and maxdelb0: gain applied to delay-line inputbM: gain applied to delay-line output and then summed with input
Reference
https://ccrma.stanford.edu/~jos/pasp/Feedforward_Comb_Filters.html
(fi.)ff_fcomb
Feed-Forward Comb Filter. Note that ff_fcomb takes floating-point delays (uses fdelay internally). ff_fcomb is a standard Faust function.
Usage
_ : ff_fcomb(maxdel,del,b0,bM) : _
Where:
maxdel: maximum delay (a power of 2)intdel: current (integer) comb-filter delay between 0 and maxdeldel: current (float) comb-filter delay between 0 and maxdelb0: gain applied to delay-line inputbM: gain applied to delay-line output and then summed with input
Reference
https://ccrma.stanford.edu/~jos/pasp/Feedforward_Comb_Filters.html
(fi.)ffcombfilter
Typical special case of ff_comb() where: b0 = 1.
(fi.)fb_comb
Feed-Back Comb Filter (integer delay).
Usage
_ : fb_comb(maxdel,intdel,b0,aN) : _
Where:
maxdel: maximum delay (a power of 2)intdel: current (integer) comb-filter delay between 0 and maxdeldel: current (float) comb-filter delay between 0 and maxdelb0: gain applied to delay-line input and forwarded to outputaN: minus the gain applied to delay-line output before summing with the input and feeding to the delay line
Reference
https://ccrma.stanford.edu/~jos/pasp/Feedback_Comb_Filters.html
(fi.)fb_fcomb
Feed-Back Comb Filter (floating point delay).
Usage
_ : fb_fcomb(maxdel,del,b0,aN) : _
Where:
maxdel: maximum delay (a power of 2)intdel: current (integer) comb-filter delay between 0 and maxdeldel: current (float) comb-filter delay between 0 and maxdelb0: gain applied to delay-line input and forwarded to outputaN: minus the gain applied to delay-line output before summing with the input and feeding to the delay line
Reference
https://ccrma.stanford.edu/~jos/pasp/Feedback_Comb_Filters.html
(fi.)rev1
Special case of fb_comb (rev1(maxdel,N,g)). The “rev1 section” dates back to the 1960s in computer-music reverberation. See the jcrev and brassrev in reverbs.lib for usage examples.
(fi.)fbcombfilter and (fi.)ffbcombfilter
Other special cases of Feed-Back Comb Filter.
Usage
_ : fbcombfilter(maxdel,intdel,g) : _ _ : ffbcombfilter(maxdel,del,g) : _
Where:
maxdel: maximum delay (a power of 2)intdel: current (integer) comb-filter delay between 0 and maxdeldel: current (float) comb-filter delay between 0 and maxdelg: feedback gain
Reference
https://ccrma.stanford.edu/~jos/pasp/Feedback_Comb_Filters.html
(fi.)allpass_comb
Schroeder Allpass Comb Filter. Note that
allpass_comb(maxlen,len,aN) = ff_comb(maxlen,len,aN,1) : fb_comb(maxlen,len-1,1,aN);
which is a direct-form-1 implementation, requiring two delay lines. The implementation here is direct-form-2 requiring only one delay line.
Usage
_ : allpass_comb (maxdel,intdel,aN) : _
Where:
maxdel: maximum delay (a power of 2)intdel: current (integer) comb-filter delay between 0 and maxdeldel: current (float) comb-filter delay between 0 and maxdelaN: minus the feedback gain
References
(fi.)allpass_fcomb
Schroeder Allpass Comb Filter. Note that
allpass_comb(maxlen,len,aN) = ff_comb(maxlen,len,aN,1) : fb_comb(maxlen,len-1,1,aN);
which is a direct-form-1 implementation, requiring two delay lines. The implementation here is direct-form-2 requiring only one delay line.
allpass_fcomb is a standard Faust library.
Usage
_ : allpass_comb (maxdel,intdel,aN) : _ _ : allpass_fcomb(maxdel,del,aN) : _
Where:
maxdel: maximum delay (a power of 2)intdel: current (float) comb-filter delay between 0 and maxdeldel: current (float) comb-filter delay between 0 and maxdelaN: minus the feedback gain
References
(fi.)rev2
Special case of allpass_comb (rev2(maxlen,len,g)). The “rev2 section” dates back to the 1960s in computer-music reverberation. See the jcrev and brassrev in reverbs.lib for usage examples.
(fi.)allpass_fcomb5 and (fi.)allpass_fcomb1a
Same as allpass_fcomb but use fdelay5 and fdelay1a internally (Interpolation helps - look at an fft of faust2octave on
`1-1' <: allpass_fcomb(1024,10.5,0.95), allpass_fcomb5(1024,10.5,0.95);`).
(fi.)iir
Nth-order Infinite-Impulse-Response (IIR) digital filter, implemented in terms of the Transfer-Function (TF) coefficients. Such filter structures are termed “direct form”.
iir is a standard Faust function.
Usage
_ : iir(bcoeffs,acoeffs) : _
Where:
order: filter order (int) = max(#poles,#zeros)bcoeffs: (b0,b1,…,b_order) = TF numerator coefficientsacoeffs: (a1,…,a_order) = TF denominator coeffs (a0=1)
Reference
https://ccrma.stanford.edu/~jos/filters/Four_Direct_Forms.html
(fi.)fir
FIR filter (convolution of FIR filter coefficients with a signal)
Usage
_ : fir(bv) : _
fir is standard Faust function.
Where:
bv = b0,b1,…,bn is a parallel bank of coefficient signals.
Note
bv is processed using pattern-matching at compile time, so it must have this normal form (parallel signals).
Example
Smoothing white noise with a five-point moving average:
bv = .2,.2,.2,.2,.2; process = noise : fir(bv);
Equivalent (note double parens):
process = noise : fir((.2,.2,.2,.2,.2));
(fi.)conv and (fi.)convN
Convolution of input signal with given coefficients.
Usage
_ : conv((k1,k2,k3,...,kN)) : _; // Argument = one signal bank _ : convN(N,(k1,k2,k3,...)) : _; // Useful when N < count((k1,...))
(fi.)tf1, (fi.)tf2 and (fi.)tf3
tfN = N’th-order direct-form digital filter.
Usage
_ : tf1(b0,b1,a1) : _ _ : tf2(b0,b1,b2,a1,a2) : _ _ : tf3(b0,b1,b2,b3,a1,a2,a3) : _
Where:
a: the polesb: the zeros
Reference
https://ccrma.stanford.edu/~jos/fp/Direct_Form_I.html
(fi.)notchw
Simple notch filter based on a biquad (tf2). notchw is a standard Faust function.
Usage:
_ : notchw(width,freq) : _
Where:
width: “notch width” in Hz (approximate)freq: “notch frequency” in Hz
Reference
https://ccrma.stanford.edu/~jos/pasp/Phasing_2nd_Order_Allpass_Filters.html
Direct-Form Second-Order Biquad Sections
Reference
https://ccrma.stanford.edu/~jos/filters/Four_Direct_Forms.html
(fi.)tf21, (fi.)tf22, (fi.)tf22t and (fi.)tf21t
tfN = N’th-order direct-form digital filter where:
tf21 is tf2, direct-form 1tf22 is tf2, direct-form 2tf22t is tf2, direct-form 2 transposedtf21t is tf2, direct-form 1 transposed
Usage
_ : tf21(b0,b1,b2,a1,a2) : _ _ : tf22(b0,b1,b2,a1,a2) : _ _ : tf22t(b0,b1,b2,a1,a2) : _ _ : tf21t(b0,b1,b2,a1,a2) : _
Where:
a: the polesb: the zeros
Reference
https://ccrma.stanford.edu/~jos/fp/Direct_Form_I.html
Ladder/Lattice Digital Filters
Ladder and lattice digital filters generally have superior numerical properties relative to direct-form digital filters. They can be derived from digital waveguide filters, which gives them a physical interpretation.
(fi.)av2sv
Compute reflection coefficients sv from transfer-function denominator av.
Usage
sv = av2sv(av)
Where:
av: parallel signal bank a1,...,aNsv: parallel signal bank s1,...,sN
where ro = ith reflection coefficient, and ai = coefficient of z^(-i) in the filter transfer-function denominator A(z).
Reference
https://ccrma.stanford.edu/~jos/filters/Step_Down_Procedure.html (where reflection coefficients are denoted by k rather than s).
(fi.)bvav2nuv
Compute lattice tap coefficients from transfer-function coefficients.
Usage
nuv = bvav2nuv(bv,av)
Where:
av: parallel signal bank a1,...,aNbv: parallel signal bank b0,b1,...,aNnuv: parallel signal bank nu1,...,nuN
where nui is the i’th tap coefficient, bi is the coefficient of z^(-i) in the filter numerator, ai is the coefficient of z^(-i) in the filter denominator
(fi.)iir_lat2
Two-multiply latice IIR filter of arbitrary order.
Usage
_ : iir_lat2(bv,av) : _
Where:
- bv: zeros as a bank of parallel signals
- av: poles as a bank of parallel signals
(fi.)allpassnt
Two-multiply lattice allpass (nested order-1 direct-form-ii allpasses).
Usage
_ : allpassnt(n,sv) : _
Where:
n: the order of the filtersv: the reflection coefficients (-1 1)
(fi.)iir_kl
Kelly-Lochbaum ladder IIR filter of arbitrary order.
Usage
_ : iir_kl(bv,av) : _
Where:
- bv: zeros as a bank of parallel signals
- av: poles as a bank of parallel signals
(fi.)allpassnklt
Kelly-Lochbaum ladder allpass.
Usage:
_ : allpassklt(n,sv) : _
Where:
n: the order of the filtersv: the reflection coefficients (-1 1)
(fi.)iir_lat1
One-multiply latice IIR filter of arbitrary order.
Usage
_ : iir_lat1(bv,av) : _
Where:
- bv: zeros as a bank of parallel signals
- av: poles as a bank of parallel signals
(fi.)allpassn1mt
One-multiply lattice allpass with tap lines.
Usage
_ : allpassn1mt(n,sv) : _
Where:
n: the order of the filtersv: the reflection coefficients (-1 1)
(fi.)iir_nl
Normalized ladder filter of arbitrary order.
Usage
_ : iir_nl(bv,av) : _
Where:
- bv: zeros as a bank of parallel signals
- av: poles as a bank of parallel signals
References
(fi.)allpassnnlt
Normalized ladder allpass filter of arbitrary order.
Usage:
_ : allpassnnlt(n,sv) : _
Where:
n: the order of the filtersv: the reflection coefficients (-1,1)
References
Useful Special Cases
(fi.)tf2np
Biquad based on a stable second-order Normalized Ladder Filter (more robust to modulation than tf2 and protected against instability).
Usage
_ : tf2np(b0,b1,b2,a1,a2) : _
Where:
a: the polesb: the zeros
(fi.)wgr
Second-order transformer-normalized digital waveguide resonator.
Usage
_ : wgr(f,r) : _
Where:
f: resonance frequency (Hz)r: loss factor for exponential decay (set to 1 to make a numerically stable oscillator)
References
(fi.)nlf2
Second order normalized digital waveguide resonator.
Usage
_ : nlf2(f,r) : _
Where:
f: resonance frequency (Hz)r: loss factor for exponential decay (set to 1 to make a sinusoidal oscillator)
Reference
https://ccrma.stanford.edu/~jos/pasp/Power_Normalized_Waveguide_Filters.html
(fi.)apnl
Passive Nonlinear Allpass based on Pierce switching springs idea. Switch between allpass coefficient a1 and a2 at signal zero crossings.
Usage
_ : apnl(a1,a2) : _
Where:
a1 and a2: allpass coefficients
Reference
- “A Passive Nonlinear Digital Filter Design …” by John R. Pierce and Scott A. Van Duyne, JASA, vol. 101, no. 2, pp. 1120-1126, 1997
Ladder/Lattice Allpass Filters
An allpass filter has gain 1 at every frequency, but variable phase. Ladder/lattice allpass filters are specified by reflection coefficients. They are defined here as nested allpass filters, hence the names allpassn*.
References
(fi.)allpassn
Two-multiply lattice - each section is two multiply-adds.
Usage:
_ : allpassn(n,sv) : _
Where:
n: the order of the filtersv: the reflection coefficients (-1 1)
References
- J. O. Smith and R. Michon, “Nonlinear Allpass Ladder Filters in FAUST”, in Proceedings of the 14th International Conference on Digital Audio Effects (DAFx-11), Paris, France, September 19-23, 2011.
(fi.)allpassnn
Normalized form - four multiplies and two adds per section, but coefficients can be time varying and nonlinear without “parametric amplification” (modulation of signal energy).
Usage:
_ : allpassnn(n,tv) : _
Where:
n: the order of the filtertv: the reflection coefficients (-PI PI)
(fi.)allpasskl
Kelly-Lochbaum form - four multiplies and two adds per section, but all signals have an immediate physical interpretation as traveling pressure waves, etc.
Usage:
_ : allpassnkl(n,sv) : _
Where:
n: the order of the filtersv: the reflection coefficients (-1 1)
(fi.)allpass1m
One-multiply form - one multiply and three adds per section. Normally the most efficient in special-purpose hardware.
Usage:
_ : allpassn1m(n,sv) : _
Where:
n: the order of the filtersv: the reflection coefficients (-1 1)
Digital Filter Sections Specified as Analog Filter Sections
(fi.)tf2s and (fi.)tf2snp
Second-order direct-form digital filter, specified by ANALOG transfer-function polynomials B(s)/A(s), and a frequency-scaling parameter. Digitization via the bilinear transform is built in.
Usage
_ : tf2s(b2,b1,b0,a1,a0,w1) : _
Where:
b2 s^2 + b1 s + b0 H(s) = -------------------- s^2 + a1 s + a0
and w1 is the desired digital frequency (in radians/second) corresponding to analog frequency 1 rad/sec (i.e., s = j).
Example
A second-order ANALOG Butterworth lowpass filter, normalized to have cutoff frequency at 1 rad/sec, has transfer function
1 H(s) = ----------------- s^2 + a1 s + 1
where a1 = sqrt(2). Therefore, a DIGITAL Butterworth lowpass cutting off at SR/4 is specified as tf2s(0,0,1,sqrt(2),1,PI*SR/2);
Method
Bilinear transform scaled for exact mapping of w1.
Reference
https://ccrma.stanford.edu/~jos/pasp/Bilinear_Transformation.html
(fi.)tf3slf
Analogous to tf2s above, but third order, and using the typical low-frequency-matching bilinear-transform constant 2/T (“lf” series) instead of the specific-frequency-matching value used in tf2s and tf1s. Note the lack of a “w1” argument.
Usage
_ : tf3slf(b3,b2,b1,b0,a3,a2,a1,a0) : _
(fi.)tf1s
First-order direct-form digital filter, specified by ANALOG transfer-function polynomials B(s)/A(s), and a frequency-scaling parameter.
Usage
tf1s(b1,b0,a0,w1)
Where:
b1 s + b0
H(s) = ———- s + a0
and w1 is the desired digital frequency (in radians/second) corresponding to analog frequency 1 rad/sec (i.e., s = j).
Example
A first-order ANALOG Butterworth lowpass filter, normalized to have cutoff frequency at 1 rad/sec, has transfer function
1
H(s) = ——- s + 1
so b0 = a0 = 1 and b1 = 0. Therefore, a DIGITAL first-order Butterworth lowpass with gain -3dB at SR/4 is specified as
tf1s(0,1,1,PI*SR/2); // digital half-band order 1 Butterworth
Method
Bilinear transform scaled for exact mapping of w1.
Reference
https://ccrma.stanford.edu/~jos/pasp/Bilinear_Transformation.html
(fi.)tf2sb
Bandpass mapping of tf2s: In addition to a frequency-scaling parameter w1 (set to HALF the desired passband width in rad/sec), there is a desired center-frequency parameter wc (also in rad/s). Thus, tf2sb implements a fourth-order digital bandpass filter section specified by the coefficients of a second-order analog lowpass prototpe section. Such sections can be combined in series for higher orders. The order of mappings is (1) frequency scaling (to set lowpass cutoff w1), (2) bandpass mapping to wc, then (3) the bilinear transform, with the usual scale parameter 2*SR. Algebra carried out in maxima and pasted here.
Usage
_ : tf2sb(b2,b1,b0,a1,a0,w1,wc) : _
(fi.)tf1sb
First-to-second-order lowpass-to-bandpass section mapping, analogous to tf2sb above.
Usage
_ : tf1sb(b1,b0,a0,w1,wc) : _
Simple Resonator Filters
(fi.)resonlp
Simple resonant lowpass filter based on tf2s (virtual analog). resonlp is a standard Faust function.
Usage
_ : resonlp(fc,Q,gain) : _ _ : resonhp(fc,Q,gain) : _ _ : resonbp(fc,Q,gain) : _
Where:
fc: center frequency (Hz)Q: qgain: gain (0-1)
(fi.)resonhp
Simple resonant highpass filters based on tf2s (virtual analog). resonhp is a standard Faust function.
Usage
_ : resonlp(fc,Q,gain) : _ _ : resonhp(fc,Q,gain) : _ _ : resonbp(fc,Q,gain) : _
Where:
fc: center frequency (Hz)Q: qgain: gain (0-1)
(fi.)resonbp
Simple resonant bandpass filters based on tf2s (virtual analog). resonbp is a standard Faust function.
Usage
_ : resonlp(fc,Q,gain) : _ _ : resonhp(fc,Q,gain) : _ _ : resonbp(fc,Q,gain) : _
Where:
fc: center frequency (Hz)Q: qgain: gain (0-1)
Butterworth Lowpass/Highpass Filters
(fi.)lowpass
Nth-order Butterworth lowpass filter. lowpass is a standard Faust function.
Usage
_ : lowpass(N,fc) : _
Where:
N: filter order (number of poles) [nonnegative constant integer]fc: desired cut-off frequency (-3dB frequency) in Hz
References
(fi.)highpass
Nth-order Butterworth highpass filters. highpass is a standard Faust function.
Usage
_ : highpass(N,fc) : _
Where:
N: filter order (number of poles) [nonnegative constant integer]fc: desired cut-off frequency (-3dB frequency) in Hz
References
(fi.)lowpass0_highpass1
Special Filter-Bank Delay-Equalizing Allpass Filters
These special allpass filters are needed by filterbank et al. below. They are equivalent to (lowpass(N,fc) +|- highpass(N,fc))/2, but with canceling pole-zero pairs removed (which occurs for odd N).
(fi.)lowpass_plus|minus_highpass
Elliptic (Cauer) Lowpass Filters
Elliptic (Cauer) Lowpass Filters
References
- <http://en.wikipedia.org/wiki/Elliptic_filter
- functions
ncauer and ellip in Octave
(fi.)lowpass3e
Third-order Elliptic (Cauer) lowpass filter.
Usage
_ : lowpass3e(fc) : _
Where:
Design
For spectral band-slice level display (see octave_analyzer3e):
[z,p,g] = ncauer(Rp,Rs,3); % analog zeros, poles, and gain, where Rp = 60 % dB ripple in stopband Rs = 0.2 % dB ripple in passband
(fi.)lowpass6e
Sixth-order Elliptic/Cauer lowpass filter.
Usage
_ : lowpass6e(fc) : _
Where:
Design
For spectral band-slice level display (see octave_analyzer6e):
[z,p,g] = ncauer(Rp,Rs,6); % analog zeros, poles, and gain, where Rp = 80 % dB ripple in stopband Rs = 0.2 % dB ripple in passband
Elliptic Highpass Filters
(fi.)highpass3e
Third-order Elliptic (Cauer) highpass filter. Inversion of lowpass3e wrt unit circle in s plane (s <- 1/s)
Usage
_ : highpass3e(fc) : _
Where:
(fi.)highpass6e
Sixth-order Elliptic/Cauer highpass filter. Inversion of lowpass3e wrt unit circle in s plane (s <- 1/s)
Usage
_ : highpass6e(fc) : _
Where:
Butterworth Bandpass/Bandstop Filters
(fi.)bandpass
Order 2*Nh Butterworth bandpass filter made using the transformation s <- s + wc^2/s on lowpass(Nh), where wc is the desired bandpass center frequency. The lowpass(Nh) cutoff w1 is half the desired bandpass width. bandpass is a standard Faust function.
Usage
_ : bandpass(Nh,fl,fu) : _
Where:
Nh: HALF the desired bandpass order (which is therefore even)fl: lower -3dB frequency in Hzfu: upper -3dB frequency in Hz Thus, the passband width is fu-fl, and its center frequency is (fl+fu)/2.
Reference
http://cnx.org/content/m16913/latest/
(fi.)bandstop
Order 2*Nh Butterworth bandstop filter made using the transformation s <- s + wc^2/s on highpass(Nh), where wc is the desired bandpass center frequency. The highpass(Nh) cutoff w1 is half the desired bandpass width. bandstop is a standard Faust function.
Usage
_ : bandstop(Nh,fl,fu) : _
Where:
Nh: HALF the desired bandstop order (which is therefore even)fl: lower -3dB frequency in Hzfu: upper -3dB frequency in Hz Thus, the passband (stopband) width is fu-fl, and its center frequency is (fl+fu)/2.
Reference
http://cnx.org/content/m16913/latest/
Elliptic Bandpass Filters
(fi.)bandpass6e
Order 12 elliptic bandpass filter analogous to bandpass(6).
(fi.)bandpass12e
Order 24 elliptic bandpass filter analogous to bandpass(6).
Parametric Equalizers (Shelf, Peaking)
Parametric Equalizers (Shelf, Peaking)
References
(fi.)low_shelf
First-order “low shelf” filter (gain boost|cut between dc and some frequency) low_shelf is a standard Faust function.
Usage
_ : lowshelf(N,L0,fx) : _ _ : low_shelf(L0,fx) : _ // default case (order 3) _ : lowshelf_other_freq(N,L0,fx) : _
Where: build libraries.html N: filter order 1, 3, 5, … (odd only). (default should be 3) build libraries.html L0: desired level (dB) between dc and fx (boost L0>0 or cut L0<0) build libraries.html fx: -3dB frequency of lowpass band (L0>0) or upper band (L0<0) (see “SHELF SHAPE” below).
The gain at SR/2 is constrained to be 1. The generalization to arbitrary odd orders is based on the well known fact that odd-order Butterworth band-splits are allpass-complementary (see filterbank documentation below for references).
Shelf Shape
The magnitude frequency response is approximately piecewise-linear on a log-log plot (“BODE PLOT”). The Bode “stick diagram” approximation L(lf) is easy to state in dB versus dB-frequency lf = dB(f):
- L0 > 0:
- L(lf) = L0, f between 0 and fx = 1st corner frequency;
- L(lf) = L0 - N build libraries.html (lf - lfx), f between fx and f2 = 2nd corner frequency;
- L(lf) = 0, lf > lf2.
- lf2 = lfx + L0/N = dB-frequency at which level gets back to 0 dB.
- L0 < 0:
- L(lf) = L0, f between 0 and f1 = 1st corner frequency;
- L(lf) = - N build libraries.html (lfx - lf), f between f1 and lfx = 2nd corner frequency;
- L(lf) = 0, lf > lfx.
- lf1 = lfx + L0/N = dB-frequency at which level goes up from L0.
See lowshelf_other_freq.
(fi.)high_shelf
First-order “high shelf” filter (gain boost|cut above some frequency). high_shelf is a standard Faust function.
Usage
_ : highshelf(N,Lpi,fx) : _ _ : high_shelf(L0,fx) : _ // default case (order 3) _ : highshelf_other_freq(N,Lpi,fx) : _
Where:
N: filter order 1, 3, 5, … (odd only).Lpi: desired level (dB) between fx and SR/2 (boost Lpi>0 or cut Lpi<0)fx: -3dB frequency of highpass band (L0>0) or lower band (L0<0) (Use highshelf_other_freq() below to find the other one.)
The gain at dc is constrained to be 1. See lowshelf documentation above for more details on shelf shape.
(fi.)peak_eq
Second order “peaking equalizer” section (gain boost or cut near some frequency) Also called a “parametric equalizer” section. peak_eq is a standard Faust function.
Usage
_ : peak_eq(Lfx,fx,B) : _;
Where:
Lfx: level (dB) at fx (boost Lfx>0 or cut Lfx<0)fx: peak frequency (Hz)B: bandwidth (B) of peak in Hz
(fi.)peak_eq_cq
Constant-Q second order peaking equalizer section.
Usage
_ : peak_eq_cq(Lfx,fx,Q) : _;
Where:
Lfx: level (dB) at fxfx: boost or cut frequency (Hz)Q: “Quality factor” = fx/B where B = bandwidth of peak in Hz
(fi.)peak_eq_rm
Regalia-Mitra second order peaking equalizer section
Usage
_ : peak_eq_rm(Lfx,fx,tanPiBT) : _;
Where:
Lfx: level (dB) at fxfx: boost or cut frequency (Hz)tanPiBT: tan(PI*B/SR), where B = -3dB bandwidth (Hz) when 10^(Lfx/20) = 0 ~ PI*B/SR for narrow bandwidths B
Reference
P.A. Regalia, S.K. Mitra, and P.P. Vaidyanathan, “The Digital All-Pass Filter: A Versatile Signal Processing Building Block” Proceedings of the IEEE, 76(1):19-37, Jan. 1988. (See pp. 29-30.)
(fi.)spectral_tilt
Spectral tilt filter, providing an arbitrary spectral rolloff factor alpha in (-1,1), where -1 corresponds to one pole (-6 dB per octave), and +1 corresponds to one zero (+6 dB per octave). In other words, alpha is the slope of the ln magnitude versus ln frequency. For a “pinking filter” (e.g., to generate 1/f noise from white noise), set alpha to -1/2.
Usage
_ : spectral_tilt(N,f0,bw,alpha) : _
Where:
N: desired integer filter order (fixed at compile time)f0: lower frequency limit for desired roll-off band > 0bw: bandwidth of desired roll-off bandalpha: slope of roll-off desired in nepers per neper, between -1 and 1 (ln mag / ln radian freq)
Examples
See spectral_tilt_demo.
Reference
J.O. Smith and H.F. Smith, “Closed Form Fractional Integration and Differentiation via Real Exponentially Spaced Pole-Zero Pairs”, arXiv.org publication arXiv:1606.06154 [cs.CE], June 7, 2016, http://arxiv.org/abs/1606.06154
(fi.)levelfilter
Dynamic level lowpass filter. levelfilter is a standard Faust function.
Usage
_ : levelfilter(L,freq) : _
Where:
L: desired level (in dB) at Nyquist limit (SR/2), e.g., -60freq: corner frequency (-3dB point) usually set to fundamental freqN: Number of filters in series where L = L/N
Reference
https://ccrma.stanford.edu/realsimple/faust_strings/Dynamic_Level_Lowpass_Filter.html
(fi.)levelfilterN
Dynamic level lowpass filter.
Usage
_ : levelfilterN(N,freq,L) : _
Where:
L: desired level (in dB) at Nyquist limit (SR/2), e.g., -60freq: corner frequency (-3dB point) usually set to fundamental freqN: Number of filters in series where L = L/N
Reference
https://ccrma.stanford.edu/realsimple/faust_strings/Dynamic_Level_Lowpass_Filter.html
Mth-Octave Filter-Banks
Mth-octave filter-banks split the input signal into a bank of parallel signals, one for each spectral band. They are related to the Mth-Octave Spectrum-Analyzers in analysis.lib. The documentation of this library contains more details about the implementation. The parameters are:
M: number of band-slices per octave (>1)N: total number of bands (>2)ftop: upper bandlimit of the Mth-octave bands (<SR/2)
In addition to the Mth-octave output signals, there is a highpass signal containing frequencies from ftop to SR/2, and a “dc band” lowpass signal containing frequencies from 0 (dc) up to the start of the Mth-octave bands. Thus, the N output signals are
highpass(ftop), MthOctaveBands(M,N-2,ftop), dcBand(ftop*2^(-M*(N-1)))
A Filter-Bank is defined here as a signal bandsplitter having the property that summing its output signals gives an allpass-filtered version of the filter-bank input signal. A more conventional term for this is an “allpass-complementary filter bank”. If the allpass filter is a pure delay (and possible scaling), the filter bank is said to be a “perfect-reconstruction filter bank” (see Vaidyanathan-1993 cited below for details). A “graphic equalizer”, in which band signals are scaled by gains and summed, should be based on a filter bank.
The filter-banks below are implemented as Butterworth or Elliptic spectrum-analyzers followed by delay equalizers that make them allpass-complementary.
Increasing Channel Isolation
Go to higher filter orders - see Regalia et al. or Vaidyanathan (cited below) regarding the construction of more aggressive recursive filter-banks using elliptic or Chebyshev prototype filters.
References
- “Tree-structured complementary filter banks using all-pass sections”, Regalia et al., IEEE Trans. Circuits & Systems, CAS-34:1470-1484, Dec. 1987
- “Multirate Systems and Filter Banks”, P. Vaidyanathan, Prentice-Hall, 1993
- Elementary filter theory: https://ccrma.stanford.edu/~jos/filters/
(fi.)mth_octave_filterbank[n]
Allpass-complementary filter banks based on Butterworth band-splitting. For Butterworth band-splits, the needed delay equalizer is easily found.
Usage
_ : mth_octave_filterbank(O,M,ftop,N) : par(i,N,_); // Oth-order _ : mth_octave_filterbank_alt(O,M,ftop,N) : par(i,N,_); // dc-inverted version
Also for convenience:
_ : mth_octave_filterbank3(M,ftop,N) : par(i,N,_); // 3rd-order Butterworth _ : mth_octave_filterbank5(M,ftop,N) : par(i,N,_); // 5th-order Butterworth mth_octave_filterbank_default = mth_octave_filterbank5;
Where:
O: order of filter used to split each frequency band into twoM: number of band-slices per octaveftop: highest band-split crossover frequency (e.g., 20 kHz)N: total number of bands (including dc and Nyquist)
Arbritary-Crossover Filter-Banks and Spectrum Analyzers
These are similar to the Mth-octave analyzers above, except that the band-split frequencies are passed explicitly as arguments.
(fi.)filterbank
Filter bank. filterbank is a standard Faust function.
Usage
_ : filterbank (O,freqs) : par(i,N,_); // Butterworth band-splits
Where:
O: band-split filter order (ODD integer required for filterbank[i])freqs: (fc1,fc2,…,fcNs) [in numerically ascending order], where Ns=N-1 is the number of octave band-splits (total number of bands N=Ns+1).
If frequencies are listed explicitly as arguments, enclose them in parens:
_ : filterbank(3,(fc1,fc2)) : _,_,_
(fi.)filterbanki
Inverted-dc filter bank.
Usage
_ : filterbanki(O,freqs) : par(i,N,_); // Inverted-dc version
Where:
O: band-split filter order (ODD integer required for filterbank[i])freqs: (fc1,fc2,…,fcNs) [in numerically ascending order], where Ns=N-1 is the number of octave band-splits (total number of bands N=Ns+1).
If frequencies are listed explicitly as arguments, enclose them in parens:
_ : filterbanki(3,(fc1,fc2)) : _,_,_
hoa.lib
Faust library for high order ambisonic. Its official prefix is ho.
(ho.)encoder
Ambisonic encoder. Encodes a signal in the circular harmonics domain depending on an order of decomposition and an angle.
Usage
encoder(n, x, a) : _
Where:
n: the orderx: the signala: the angle
(ho.)decoder
Decodes an ambisonics sound field for a circular array of loudspeakers.
Usage
_ : decoder(n, p) : _
Where:
n: the orderp: the number of speakers
Note
Number of loudspeakers must be greater or equal to 2n+1. It’s preferable to use 2n+2 loudspeakers.
(ho.)decoderStereo
Decodes an ambisonic sound field for stereophonic configuration. An “home made” ambisonic decoder for stereophonic restitution (30° - 330°) : Sound field lose energy around 180°. You should use inPhase optimization with ponctual sources. #### Usage
_ : decoderStereo(n) : _
Where:
Optimization Functions
Functions to weight the circular harmonics signals depending to the ambisonics optimization. It can be basic for no optimization, maxRe or inPhase.
(ho.)optimBasic
The basic optimization has no effect and should be used for a perfect circle of loudspeakers with one listener at the perfect center loudspeakers array.
Usage
_ : optimBasic(n) : _
Where:
(ho.)optimMaxRe
The maxRe optimization optimize energy vector. It should be used for an auditory confined in the center of the loudspeakers array.
Usage
_ : optimMaxRe(n) : _
Where:
(ho.)optimInPhase
The inPhase Optimization optimize energy vector and put all loudspeakers signals n phase. It should be used for an auditory.
Usage
- ``
- optimInPhase(n) : _ ``
here:
n: the order
(ho.)wider
Can be used to wide the diffusion of a localized sound. The order depending signals are weighted and appear in a logarithmic way to have linear changes.
Usage
_ : wider(n,w) : _
Where:
n: the orderw: the width value between 0 - 1
(ho.)map
It simulate the distance of the source by applying a gain on the signal and a wider processing on the soundfield.
Usage
map(n, x, r, a)
Where:
n: the orderx: the signalr: the radiusa: the angle in radian
(ho.)rotate
Rotates the sound field.
Usage
_ : rotate(n, a) : _
Where:
n: the ordera: the angle in radian
maths.lib
Mathematic library for Faust. Its official prefix is ma.
Functions Reference
(ma.)SR
Current sampling rate (between 1000Hz and 192000Hz). Constant during program execution.
Usage
SR : _
(ma.)BS
Current block-size. Can change during the execution.
Usage
BS : _
(ma.)PI
Constant PI in double precision.
Usage
PI : _
(ma.)INFINITY
Constant INFINITY inherited from math.h.
Usage
INFINITY : _
(ma.)FTZ
Flush to zero: force samples under the “maximum subnormal number” to be zero. Usually not needed in C++ because the architecture file take care of this, but can be useful in javascript for instance.
Usage
_ : ftz : _
See : http://docs.oracle.com/cd/E19957-01/806-3568/ncg_math.html
(ma.)neg
Invert the sign (-x) of a signal.
Usage
_ : neg : _
(ma.)sub(x,y)
Subtract x and y.
(ma.)inv
Compute the inverse (1/x) of the input signal.
Usage
_ : inv : _
(ma.)cbrt
Computes the cube root of of the input signal.
Usage
_ : cbrt : _
(ma.)hypot
Computes the euclidian distance of the two input signals sqrt(xx+yy) without undue overflow or underflow.
Usage
_,_ : hypot : _
(ma.)ldexp
Takes two input signals: x and n, and multiplies x by 2 to the power n.
Usage
_,_ : ldexp : _
(ma.)scalb
Takes two input signals: x and n, and multiplies x by 2 to the power n.
Usage
_,_ : scalb : _
(ma.)log1p
Computes log(1 + x) without undue loss of accuracy when x is nearly zero.
Usage
_ : log1p : _
(ma.)logb
Return exponent of the input signal as a floating-point number.
Usage
_ : logb : _
(ma.)ilogb
Return exponent of the input signal as an integer number.
Usage
_ : ilogb : _
(ma.)log2
Returns the base 2 logarithm of x.
Usage
_ : log2 : _
(ma.)expm1
Return exponent of the input signal minus 1 with better precision.
Usage
_ : expm1 : _
(ma.)acosh
Computes the principle value of the inverse hyperbolic cosine of the input signal.
Usage
_ : acosh : _
(ma.)asinh
Computes the inverse hyperbolic sine of the input signal.
Usage
_ : asinh : _
(ma.)atanh
Computes the inverse hyperbolic tangent of the input signal.
Usage
_ : atanh : _
(ma.)sinh
Computes the hyperbolic sine of the input signal.
Usage
_ : sinh : _
(ma.)cosh
Computes the hyperbolic cosine of the input signal.
Usage
_ : cosh : _
(ma.)tanh
Computes the hyperbolic tangent of the input signal.
Usage
_ : tanh : _
(ma.)erf
Computes the error function of the input signal.
Usage
_ : erf : _
(ma.)erfc
Computes the complementary error function of the input signal.
Usage
_ : erfc : _
(ma.)gamma
Computes the gamma function of the input signal.
Usage
_ : gamma : _
(ma.)lgamma
Calculates the natural logorithm of the absolute value of the gamma function of the input signal.
Usage
_ : lgamma : _
(ma.)J0
Computes the Bessel function of the first kind of order 0 of the input signal.
Usage
_ : J0 : _
(ma.)J1
Computes the Bessel function of the first kind of order 1 of the input signal.
Usage
_ : J1 : _
(ma.)Jn
Computes the Bessel function of the first kind of order n (first input signal) of the second input signal.
Usage
_,_ : Jn : _
(ma.)Y0
Computes the linearly independent Bessel function of the second kind of order 0 of the input signal.
Usage
_ : Y0 : _
(ma.)Y1
Computes the linearly independent Bessel function of the second kind of order 1 of the input signal.
Usage
_ : Y0 : _
(ma.)Yn
Computes the linearly independent Bessel function of the second kind of order n (first input signal) of the second input signal.
Usage
_,_ : Yn : _
(ma.)fabs, (ma.)fmax, (ma.)fmin
Just for compatibility…
fabs = abs fmax = max fmin = min
(ma.)np2
Gives the next power of 2 of x.
Usage
np2(n) : _
Where:
(ma.)frac
Gives the fractional part of n.
Usage
frac(n) : _
Where:
(ma.)modulo
Modulus operation.
Usage
modulo(x,N) : _
Where:
x: the numeratorN: the denominator
(ma.)isnan
Return non-zero if and only if x is a NaN.
Usage
isnan(x) _ : isnan : _
Where:
(ma.)chebychev
Chebychev transformation of order n.
Usage
_ : chebychev(n) : _
Where:
n: the order of the polynomial
Semantics
T[0](x) = 1, T[1](x) = x, T[n](x) = 2x*T[n-1](x) - T[n-2](x)
Reference
http://en.wikipedia.org/wiki/Chebyshev_polynomial
(ma.)chebychevpoly
Linear combination of the first Chebyshev polynomials.
Usage
_ : chebychevpoly((c0,c1,...,cn)) : _
Where:
cn: the different Chebychevs polynomials such that: chebychevpoly((c0,c1,…,cn)) = Sum of chebychev(i)*ci
Reference
http://www.csounds.com/manual/html/chebyshevpoly.html
(ma.)diffn
Negated first-order difference.
Usage
_ : diffn : _
(ma.)signum
The signum function signum(x) is defined as -1 for x<0, 0 for x==0, and 1 for x>0;
Usage
_ : signum : _
misceffects.lib
This library contains a collection of audio effects. Its official prefix is ef.
Dynamic
(ef.)cubicnl
Cubic nonlinearity distortion. cubicnl is a standard Faust library.
Usage:
_ : cubicnl(drive,offset) : _ _ : cubicnl_nodc(drive,offset) : _
Where:
drive: distortion amount, between 0 and 1offset: constant added before nonlinearity to give even harmonics. Note: offset can introduce a nonzero mean - feed cubicnl output to dcblocker to remove this.
References:
(ef.)gate_mono
Mono signal gate. gate_mono is a standard Faust function.
Usage
_ : gate_mono(thresh,att,hold,rel) : _
Where:
thresh: dB level threshold above which gate opens (e.g., -60 dB)att: attack time = time constant (sec) for gate to open (e.g., 0.0001 s = 0.1 ms)hold: hold time = time (sec) gate stays open after signal level < thresh (e.g., 0.1 s)rel: release time = time constant (sec) for gate to close (e.g., 0.020 s = 20 ms)
References
(ef.)gate_stereo
Stereo signal gates. gate_stereo is a standard Faust function.
Usage
_,_ : gate_stereo(thresh,att,hold,rel) : _,_
Where:
thresh: dB level threshold above which gate opens (e.g., -60 dB)att: attack time = time constant (sec) for gate to open (e.g., 0.0001 s = 0.1 ms)hold: hold time = time (sec) gate stays open after signal level < thresh (e.g., 0.1 s)rel: release time = time constant (sec) for gate to close (e.g., 0.020 s = 20 ms)
References
Filtering
(ef.)speakerbp
Dirt-simple speaker simulator (overall bandpass eq with observed roll-offs above and below the passband).
Low-frequency speaker model = +12 dB/octave slope breaking to flat near f1. Implemented using two dc blockers in series.
High-frequency model = -24 dB/octave slope implemented using a fourth-order Butterworth lowpass.
Example based on measured Celestion G12 (12" speaker):
speakerbp is a standard Faust function
Usage
speakerbp(f1,f2) _ : speakerbp(130,5000) : _
(ef.)piano_dispersion_filter
Piano dispersion allpass filter in closed form.
Usage
piano_dispersion_filter(M,B,f0) _ : piano_dispersion_filter(1,B,f0) : +(totalDelay),_ : fdelay(maxDelay) : _
Where:
M: number of first-order allpass sections (compile-time only) Keep below 20. 8 is typical for medium-sized piano strings.B: string inharmonicity coefficient (0.0001 is typical)f0: fundamental frequency in Hz
Outputs
- MINUS the estimated delay at
f0 of allpass chain in samples, provided in negative form to facilitate subtraction from delay-line length. - Output signal from allpass chain
Reference
(ef.)stereo_width
Stereo Width effect using the Blumlein Shuffler technique. stereo_width is a standard Faust function.
Usage
_,_ : stereo_width(w) : _,_
Where:
w: stereo width between 0 and 1
At w=0, the output signal is mono ((left+right)/2 in both channels). At w=1, there is no effect (original stereo image). Thus, w between 0 and 1 varies stereo width from 0 to “original”.
Reference
- “Applications of Blumlein Shuffling to Stereo Microphone Techniques” Michael A. Gerzon, JAES vol. 42, no. 6, June 1994
Time Based
(ef.)echo
A simple echo effect.
echo is a standard Faust function
Usage
_ : echo(maxDuration,duration,feedback) : _
Where:
maxDuration: the max echo duration in secondsduration: the echo duration in secondsfeedback: the feedback coefficient
Pitch Shifting
(ef.)transpose
A simple pitch shifter based on 2 delay lines. transpose is a standard Faust function.
Usage
_ : transpose(w, x, s) : _
Where:
w: the window length (samples)x: crossfade duration duration (samples)s: shift (semitones)
Meshes
(ef.)mesh_square
Square Rectangular Digital Waveguide Mesh.
Usage
bus(4*N) : mesh_square(N) : bus(4*N);
Where:
N: number of nodes along each edge - a power of two (1,2,4,8,…)
Reference
https://ccrma.stanford.edu/~jos/pasp/Digital_Waveguide_Mesh.html
Signal Order In and Out
The mesh is constructed recursively using 2x2 embeddings. Thus, the top level of mesh_square(M) is a block 2x2 mesh, where each block is a mesh(M/2). Let these blocks be numbered 1,2,3,4 in the geometry NW,NE,SW,SE, i.e., as 1 2 3 4 Each block has four vector inputs and four vector outputs, where the length of each vector is M/2. Label the input vectors as Ni,Ei,Wi,Si, i.e., as the inputs from the North, East South, and West, and similarly for the outputs. Then, for example, the upper left input block of M/2 signals is labeled 1Ni. Most of the connections are internal, such as 1Eo -> 2Wi. The 8*(M/2) input signals are grouped in the order 1Ni 2Ni 3Si 4Si 1Wi 3Wi 2Ei 4Ei and the output signals are 1No 1Wo 2No 2Eo 3So 3Wo 4So 4Eo or
In: 1No 1Wo 2No 2Eo 3So 3Wo 4So 4Eo
Out: 1Ni 2Ni 3Si 4Si 1Wi 3Wi 2Ei 4Ei
Thus, the inputs are grouped by direction N,S,W,E, while the outputs are grouped by block number 1,2,3,4, which can also be interpreted as directions NW, NE, SW, SE. A simple program illustrating these orderings is process = mesh_square(2);.
Example
Reflectively terminated mesh impulsed at one corner:
mesh_square_test(N,x) = mesh_square(N)~(busi(4*N,x)) // input to corner with { busi(N,x) = bus(N) : par(i,N,*(-1)) : par(i,N-1,_), +(x); }; process = 1-1' : mesh_square_test(4); // all modes excited forever
In this simple example, the mesh edges are connected as follows:
1No -> 1Ni, 1Wo -> 2Ni, 2No -> 3Si, 2Eo -> 4Si,
3So -> 1Wi, 3Wo -> 3Wi, 4So -> 2Ei, 4Eo -> 4Ei
A routing matrix can be used to obtain other connection geometries.
noises.lib
Faust Noise Generator Library. Its official prefix is no.
Functions Reference
(no.)noise
White noise generator (outputs random number between -1 and 1). Noise is a standard Faust function.
Usage
noise : _
(no.)multirandom
Generates multiple decorrelated random numbers in parallel.
Usage
multirandom(n) : si.bus(n)
Where:
n: the number of decorrelated random numbers in parallel
(no.)multinoise
Generates multiple decorrelated noises in parallel.
Usage
multinoise(n) : si.bus(n)
Where:
n: the number of decorrelated random numbers in parallel
(no.)noises
TODO.
(no.)pink_noise
Pink noise (1/f noise) generator (third-order approximation) pink_noise is a standard Faust function.
Usage
pink_noise : _;
Reference:
https://ccrma.stanford.edu/~jos/sasp/Example_Synthesis_1_F_Noise.html
(no.)pink_noise_vm
Multi pink noise generator.
Usage
pink_noise_vm(N) : _;
Where:
N: number of latched white-noise processes to sum, not to exceed sizeof(int) in C++ (typically 32).
References
(no.)lfnoise, (no.)lfnoise0 and (no.)lfnoiseN
Low-frequency noise generators (Butterworth-filtered downsampled white noise)
Usage
lfnoise0(rate) : _; // new random number every int(SR/rate) samples or so lfnoiseN(N,rate) : _; // same as "lfnoise0(rate) : lowpass(N,rate)" [see filters.lib] lfnoise(rate) : _; // same as "lfnoise0(rate) : seq(i,5,lowpass(N,rate))" (no overshoot)
Example
(view waveforms in faust2octave):
rate = SR/100.0; // new random value every 100 samples (SR from music.lib) process = lfnoise0(rate), // sampled/held noise (piecewise constant) lfnoiseN(3,rate), // lfnoise0 smoothed by 3rd order Butterworth LPF lfnoise(rate); // lfnoise0 smoothed with no overshoot
(no.)sparse_noise_vm
sparse noise generator.
Usage
sparse_noise(f0) : _;
Where:
f0: average frequency of noise impulses per second
Random impulses in the amplitude range -1 to 1 are generated at an average rate of f0 impulses per second.
Reference
(no.)velvet_noise_vm
velvet noise generator.
Usage
velvet_noise(amp,f0) : _;
Where:
amp: amplitude of noise impulses (positive and negative)f0: average frequency of noise impulses per second
Reference
- Matti Karjalainen and Hanna Jarvelainen, “Reverberation Modeling Using Velvet Noise”, in Proc. 30th Int. Conf. Intelligent Audio Environments (AES07), March 2007.
(no.)gnoise
approximate zero-mean, unit-variance Gaussian white noise generator
Usage
gnoise(N) : _;
Where:
N: number of uniform random numbers added to approximate Gaussian white noise
Reference
- See Central Limit Theorem
oscillators.lib
This library contains a collection of sound generators. Its official prefix is os.
Wave-Table-Based Oscillators
Sine waveform ready to use with a rdtable.
Usage
sinwaveform(tablesize) : _
Where:
tablesize: the table size
Cosine waveform ready to use with a rdtable.
Usage
coswaveform(tablesize) : _
Where:
tablesize: the table size
(os.)phasor
A simple phasor to be used with a rdtable. phasor is a standard Faust function.
Usage
phasor(tablesize,freq) : _
Where:
tablesize: the table sizefreq: the frequency of the wave (Hz)
(os.)hs_phasor
Hardsyncing phasor to be used with an rdtable.
Usage
hs_phasor(ts,freq,c) : _
Where:
ts: the tablesize for the related sine wavetablefreq: the fundamental frequency of the phasorc: a clock signal, c>0 resets phase to 0
(os.)oscsin
Sine wave oscillator. oscsin is a standard Faust function.
Usage
oscsin(freq) : _
Where:
freq: the frequency of the wave (Hz)
(os.)hs_oscsin
Sin lookup table with hardsyncing phase.
Usage
hs_oscsin(freq,c) : _
Where:
freq: the fundamental frequency of the phasorc: a clock signal, c>0 resets phase to 0
(os.)osccos
Cosine wave oscillator.
Usage
osccos(freq) : _
Where:
freq: the frequency of the wave (Hz)
(os.)oscp
A sine wave generator with controllable phase.
Usage
oscp(freq,p) : _
Where:
freq: the frequency of the wave (Hz)p: the phase in radian
(os.)osci
Interpolated phase sine wave oscillator.
Usage
osci(freq) : _
Where:
freq: the frequency of the wave (Hz)
LFOs
Low-Frequency Oscillators (LFOs) have prefix lf_ (no aliasing suppression, which is not audible at LF).
(os.)lf_imptrain
Unit-amplitude low-frequency impulse train. lf_imptrain is a standard Faust function.
Usage
lf_imptrain(freq) : _
Where:
(os.)lf_pulsetrainpos
Unit-amplitude nonnegative LF pulse train, duty cycle between 0 and 1
Usage
lf_pulsetrainpos(freq,duty) : _
Where:
freq: frequency in Hzduty: duty cycle between 0 and 1
(os.)lf_pulsetrain
Unit-amplitude zero-mean LF pulse train, duty cycle between 0 and 1
Usage
lf_pulsetrain(freq,duty) : _
Where:
freq: frequency in Hzduty: duty cycle between 0 and 1
(os.)lf_squarewavepos
Positive LF square wave in [0,1]
Usage
lf_squarewavepos(freq) : _
Where:
(os.)lf_squarewave
Zero-mean unit-amplitude LF square wave. lf_squarewave is a standard Faust function.
Usage
lf_squarewave(freq) : _
Where:
(os.)lf_trianglepos
Positive unit-amplitude LF positive triangle wave
Usage
lf_trianglepos(freq) : _
Where:
(os.)lf_triangle
Positive unit-amplitude LF triangle wave lf_triangle is a standard Faust function.
Usage
lf_triangle(freq) : _
Where:
Low Frequency Sawtooths
Sawtooth waveform oscillators for virtual analog synthesis et al. The ‘simple’ versions (lf_rawsaw, lf_sawpos and saw1), are mere samplings of the ideal continuous-time (“analog”) waveforms. While simple, the aliasing due to sampling is quite audible. The differentiated polynomial waveform family (saw2, sawN, and derived functions) do some extra processing to suppress aliasing (not audible for very low fundamental frequencies). According to Lehtonen et al. (JASA 2012), the aliasing of saw2 should be inaudible at fundamental frequencies below 2 kHz or so, for a 44.1 kHz sampling rate and 60 dB SPL presentation level; fundamentals 415 and below required no aliasing suppression (i.e., saw1 is ok).
(os.)lf_rawsaw
Simple sawtooth waveform oscillator between 0 and period in samples.
Usage
lf_rawsaw(periodsamps)
Where:
periodsamps: number of periods per samples
(os.)lf_sawpos_phase
Simple sawtooth waveform oscillator between 0 and 1 with phase control.
Usage
lf_sawpos_phase(freq,phase)
Where:
freq: frequencyphase: phase
(os.)lf_sawpos
Simple sawtooth waveform oscillator between 0 and 1.
Usage
lf_sawpos(freq)
Where:
(os.)lf_saw
Simple sawtooth waveform. lf_saw is a standard Faust function.
Usage
lf_saw(freq)
Where:
Bandlimited Sawtooth
//——————(os.)sawN——————————– Bandlimited Sawtooth
sawN(N,freq), sawNp, saw2dpw(freq), saw2(freq), saw3(freq), saw4(freq), saw5(freq), saw6(freq), sawtooth(freq), saw2f2(freq) saw2f4(freq)
Method 1 (saw2)
Polynomial Transition Regions (PTR) (for aliasing suppression)
Reference
Method 2 (sawN)
Differentiated Polynomial Waves (DPW) (for aliasing suppression)
Reference
“Alias-Suppressed Oscillators based on Differentiated Polynomial Waveforms”, Vesa Valimaki, Juhan Nam, Julius Smith, and Jonathan Abel, IEEE Tr. Acoustics, Speech, and Language Processing (IEEE-ASLP), Vol. 18, no. 5, May 2010.
Other Cases
Correction-filtered versions of saw2: saw2f2, saw2f4 The correction filter compensates “droop” near half the sampling rate. See reference for sawN.
Usage
sawN(N,freq) : _ sawNp(N,freq,phase) : _ saw2dpw(freq) : _ saw2(freq) : _ saw3(freq) : _ // based on sawN saw4(freq) : _ // based on sawN saw5(freq) : _ // based on sawN saw6(freq) : _ // based on sawN sawtooth(freq) : _ // = saw2 saw2f2(freq) : _ saw2f4(freq) : _
Where:
N: polynomial orderfreq: frequency in Hzphase: phase
(os.)sawNp
TODO: MarkDown doc in comments
(os.)saw2dpw
TODO: MarkDown doc in comments
(os.)saw3
TODO: MarkDown doc in comments
(os.)sawtooth
Alias-free sawtooth wave. 2nd order interpolation (based on saw2). sawtooth is a standard Faust function.
Usage
sawtooth(freq) : _
Where:
(os.)saw2f2
TODO: MarkDown doc in comments
(os.)saw2f4
TODO: MarkDown doc in comments
Bandlimited Pulse, Square, and Impulse Trains
Bandlimited Pulse, Square, and Impulse Trains
pulsetrainN, pulsetrain, squareN, square, imptrain, imptrainN, triangle, triangleN
All are zero-mean and meant to oscillate in the audio frequency range. Use simpler sample-rounded lf_* versions above for LFOs.
Usage
pulsetrainN(N,freq,duty) : _ pulsetrain(freq, duty) : _ // = pulsetrainN(2) squareN(N, freq) : _ square : _ // = squareN(2) imptrainN(N,freq) : _ imptrain : _ // = imptrainN(2) triangleN(N,freq) : _ triangle : _ // = triangleN(2)
Where:
N: polynomial orderfreq: frequency in Hz
(os.)pulsetrainN
TODO: MarkDown doc in comments
(os.)pulsetrain
Bandlimited pulse train oscillator. Based on pulsetrainN(2). pulsetrain is a standard Faust function.
Usage
pulsetrain(freq, duty) : _
Where:
freq: frequencyduty: duty cycle between 0 and 1
(os.)squareN
TODO: MarkDown doc in comments
(os.)square
Bandlimited square wave oscillator. Based on squareN(2). square is a standard Faust function.
Usage
square(freq) : _
Where:
(os.)impulse
One-time impulse generated when the Faust process is started. impulse is a standard Faust function.
Usage
impulse : _
(os.)imptrainN
TODO: MarkDown doc in comments
(os.)imptrain
Bandlimited impulse train generator. Based on imptrainN(2). imptrain is a standard Faust function.
Usage
imptrain(freq) : _
Where:
(os.)triangleN
TODO: MarkDown doc in comments
(os.)triangle
Bandlimited triangle wave oscillator. Based on triangleN(2). triangle is a standard Faust function.
Usage
triangle(freq) : _
Where:
Filter-Based Oscillators
Filter-Based Oscillators
Usage
osc[b|r|rs|rc|s|w](f), where f = frequency in Hz.
References
(os.)oscb
Sinusoidal oscillator based on the biquad.
Usage
oscb(freq) : _
Where:
(os.)oscrq
Sinusoidal (sine and cosine) oscillator based on 2D vector rotation, = undamped “coupled-form” resonator = lossless 2nd-order normalized ladder filter.
Usage
oscrq(freq) : _,_
Where:
Reference
(os.)oscrs
Sinusoidal (sine) oscillator based on 2D vector rotation, = undamped “coupled-form” resonator = lossless 2nd-order normalized ladder filter.
Usage
oscrs(freq) : _
Where:
Reference
(os.)oscrc
Sinusoidal (cosine) oscillator based on 2D vector rotation, = undamped “coupled-form” resonator = lossless 2nd-order normalized ladder filter.
Usage
oscrc(freq) : _
Where:
Reference
(os.)oscs
Sinusoidal oscillator based on the state variable filter = undamped “modified-coupled-form” resonator = “magic circle” algorithm used in graphics
(os.)osc
Default sine wave oscillator (same as oscsin). osc is a standard Faust function.
Usage
osc(freq) : _
Where:
freq: the frequency of the wave (Hz)
Waveguide-Resonator-Based Oscillators
Sinusoidal oscillator based on the waveguide resonator wgr.
(os.)oscw
Sinusoidal oscillator based on the waveguide resonator wgr. Unit-amplitude cosine oscillator.
Usage
oscwc(freq) : _
Where:
Reference
(os.)oscws
Sinusoidal oscillator based on the waveguide resonator wgr. Unit-amplitude sine oscillator
Usage
oscws(freq) : _
Where:
Reference
(os.)oscwq
Sinusoidal oscillator based on the waveguide resonator wgr. Unit-amplitude cosine and sine (quadrature) oscillator.
Usage
oscwq(freq) : _
Where:
Reference
(os.)oscw
Sinusoidal oscillator based on the waveguide resonator wgr. Unit-amplitude cosine oscillator (default)
Usage
oscw(freq) : _
Where:
Reference
Casio CZ Oscillators
Oscillators that mimics some of the Casio CZ oscillators.
(os.)CZsaw
Oscillator that mimics the Casio CZ saw oscillator CZsaw is a standard Faust function.
Usage
CZsaw(fund,index) : _
Where:
fund: a saw-tooth waveform between 0 and 1 that the oscillator slaves toindex: the brightness of the oscillator, 0 to 1. 0 = sine-wave, 1 = saw-wave
(os.)CZsquare
Oscillator that mimics the Casio CZ square oscillator CZsquare is a standard Faust function.
Usage
CZsquare(fund,index) : _
Where:
fund: a saw-tooth waveform between 0 and 1 that the oscillator slaves toindex: the brightness of the oscillator, 0 to 1. 0 = sine-wave, 1 = square-wave
(os.)CZpulse
Oscillator that mimics the Casio CZ pulse oscillator CZpulse is a standard Faust function.
Usage
CZpulse(fund,index) : _
Where:
fund: a saw-tooth waveform between 0 and 1 that the oscillator slaves toindex: the brightness of the oscillator, 0 gives a sine-wave, 1 is closer to a pulse
(os.)CZsinePulse
Oscillator that mimics the Casio CZ sine/pulse oscillator CZsinePulse is a standard Faust function.
Usage
CZsinePulse(fund,index) : _
Where:
fund: a saw-tooth waveform between 0 and 1 that the oscillator slaves toindex: the brightness of the oscillator, 0 gives a sine-wave, 1 is a sine minus a pulse
(os.)CZhalfSine
Oscillator that mimics the Casio CZ half sine oscillator CZhalfSine is a standard Faust function.
Usage
CZhalfSine(fund,index) : _
Where:
fund: a saw-tooth waveform between 0 and 1 that the oscillator slaves toindex: the brightness of the oscillator, 0 gives a sine-wave, 1 is somewhere between a saw and a square
(os.)CZresSaw
Oscillator that mimics the Casio CZ resonant saw-tooth oscillator CZresSaw is a standard Faust function.
Usage
CZresSaw(fund,res) : _
Where:
fund: a saw-tooth waveform between 0 and 1 that the oscillator slaves tores: the frequency of resonance as a factor of the fundamental pitch.
(os.)CZresTriangle
Oscillator that mimics the Casio CZ resonant triangle oscillator CZresTriangle is a standard Faust function.
Usage
CZresTriangle(fund,res) : _
Where:
fund: a saw-tooth waveform between 0 and 1 that the oscillator slaves tores: the frequency of resonance as a factor of the fundamental pitch.
(os.)CZresTrap
Oscillator that mimics the Casio CZ resonant trapeze oscillator CZresTrap is a standard Faust function.
Usage
CZresTrap(fund,res) : _
Where:
fund: a saw-tooth waveform between 0 and 1 that the oscillator slaves tores: the frequency of resonance as a factor of the fundamental pitch.
phaflangers.lib
A library of phasor and flanger effects. Its official prefix is pf.
Functions Reference
(pf.)flanger_mono
Mono flanging effect.
Usage:
_ : flanger_mono(dmax,curdel,depth,fb,invert) : _;
Where:
dmax: maximum delay-line length (power of 2) - 10 ms typicalcurdel: current dynamic delay (not to exceed dmax)depth: effect strength between 0 and 1 (1 typical)fb: feedback gain between 0 and 1 (0 typical)invert: 0 for normal, 1 to invert sign of flanging sum
Reference
https://ccrma.stanford.edu/~jos/pasp/Flanging.html
(pf.)flanger_stereo
Stereo flanging effect. flanger_stereo is a standard Faust function.
Usage:
_,_ : flanger_stereo(dmax,curdel1,curdel2,depth,fb,invert) : _,_;
Where:
dmax: maximum delay-line length (power of 2) - 10 ms typicalcurdel: current dynamic delay (not to exceed dmax)depth: effect strength between 0 and 1 (1 typical)fb: feedback gain between 0 and 1 (0 typical)invert: 0 for normal, 1 to invert sign of flanging sum
Reference
https://ccrma.stanford.edu/~jos/pasp/Flanging.html
(pf.)phaser2_mono
Mono phasing effect.
Phaser
_ : phaser2_mono(Notches,phase,width,frqmin,fratio,frqmax,speed,depth,fb,invert) : _;
Where:
Notches: number of spectral notches (MACRO ARGUMENT - not a signal)phase: phase of the oscillator (0-1)width: approximate width of spectral notches in Hzfrqmin: approximate minimum frequency of first spectral notch in Hzfratio: ratio of adjacent notch frequenciesfrqmax: approximate maximum frequency of first spectral notch in Hzspeed: LFO frequency in Hz (rate of periodic notch sweep cycles)depth: effect strength between 0 and 1 (1 typical) (aka “intensity”) when depth=2, “vibrato mode” is obtained (pure allpass chain)fb: feedback gain between -1 and 1 (0 typical)invert: 0 for normal, 1 to invert sign of flanging sum
Reference:
(pf.)phaser2_stereo
Stereo phasing effect. phaser2_stereo is a standard Faust function.
Phaser
_ : phaser2_stereo(Notches,phase,width,frqmin,fratio,frqmax,speed,depth,fb,invert) : _;
Where:
Notches: number of spectral notches (MACRO ARGUMENT - not a signal)phase: phase of the oscillator (0-1)width: approximate width of spectral notches in Hzfrqmin: approximate minimum frequency of first spectral notch in Hzfratio: ratio of adjacent notch frequenciesfrqmax: approximate maximum frequency of first spectral notch in Hzspeed: LFO frequency in Hz (rate of periodic notch sweep cycles)depth: effect strength between 0 and 1 (1 typical) (aka “intensity”) when depth=2, “vibrato mode” is obtained (pure allpass chain)fb: feedback gain between -1 and 1 (0 typical)invert: 0 for normal, 1 to invert sign of flanging sum
Reference:
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.
Useful conversion tools for physical modeling.
(pm.)f2l
Frequency to length in meters.
Usage
f2l(freq) : distanceInMeters
Where:
(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:
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 = _,_,_; B = _,_,_; };
(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 courses, this function can be nested within a 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 };
(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{ a = *(-1); // left termination b = chain(D : E : F); // bidirectional chain of blocks (D, E, F, etc.) };
(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{ b = chain(D : E : F); // bidirectional chain of blocks (D, E, F, etc.) c = *(-1); // right termination };
(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 waveguidewaveguideFd: fractional delay waveguidewaveguideFd2: second order fractional delay waveguidewaveguideFd4: fourth order fractional delay waveguide
Usage
chain(A : waveguideUd(nMax,n) : B)
Where:
nMax: the maximum length of the delays in the waveguiden: 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 waveguiden: 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 frequencyt60: 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 metersstiffness: 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 meterspluckPosition: 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 meterspluckPosition: 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 metersstiffness: 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 metersstiffness: 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 metersstiffness: 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: build libraries.html length: the length of the string in meters build libraries.html pluckPosition: the plucking position (0.001-0.999) build libraries.html 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 metersdamping: 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 meterspluckPosition: 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 meterspluckPosition: 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 meterspluckPosition: 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 meterspluckPosition: pluck position (0-1) (1 is on the bridge)gain: gain of the excitationtrigger: 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 meterspluckPosition: pluck position (0-1) (1 is on the bridge)excitation: excitation signal
(pm.)nylonGuitar
A simple acoustic guitar model with steel 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 meterspluckPosition: 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 meterspluckPosition: 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 bodystringExcitation: 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 meterspluckPosition: 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 excitationtapBody: 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 signaloffset: table offsetslope: 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:
(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 metersbowVelocity: 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 metersbowVelocity: 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 signaloffset: table offsetslope: 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 mouthpiecelipsTension: 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 signalstiffness: 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 mouthpiecelipsTension: 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 : ...)
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 meterspressure: 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 meterslipsTension: 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 brass instrument physical model without tone holes (pitch is changed by changing the length of the tube of the instrument).
Usage
fluteModel(tubeLength,lipsTension,mute,pressure) : _
Where:
tubeLength: the length of the tube in metersmouthPosition: 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
brass_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:
(pm.)strikeModel
Creates a filtered noise excitation.
Usage
gate = button('gate'); strikeModel(LPcutoff,HPcutoff,sharpness,gain,gate) : chain;
Where:
HPcutoff: highpass cutoff frequencyLPcutoff: lowpass cutoff frequencysharpness: sharpness of the attack and release (0-1)gain: gain of the excitationgate: 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 edgesharpness: sharpness of the attack and release (0-1)gain: gain of the excitationgate: 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 pluckcutoff: 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
Modal Percussions
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 signalfreq: 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 modelstrikePosition: 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 striketrigger: 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 signalfreq: fundamental frequency of the barexPos: 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 metersexcitation: 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 coupleexPos: 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 signalfreq: the frequency of the bar/tube couplestrikePosition: 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 signalnModes: 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 signalstrikePosition: 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 signalnModes: 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 signalstrikePosition: 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 signalnModes: 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 signalstrikePosition: 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 signalnModes: 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 signalstrikePosition: 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 signalnModes: 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 signalstrikePosition: 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 signalnModes: 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 signalstrikePosition: 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.).
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 numberj: (voiceType*nFormants)+vowelvoiceType: 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 signalgender: 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 indexfreq: the fundamental frequency of the excitation signalvoiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)- 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 signalgender: 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
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 5i: formant number (i.e. 0 - 4) used to index formant data value arraysfreq: fundamental frequency of excitation signal. Used to calculate rise time of envelope
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 5i: formant number (i.e. 1 - 5) used to index formant data value arraysfreq: fundamental frequency of excitation signal. Used to calculate rise time of envelope
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 5i: formant index used to index formant data value arraysfreq: fundamental frequency of excitation signal.
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
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 calculate the skirtwidth of the FOF envelopes and for the autobendFreq and vocalEffort functions
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 calculate the skirtwidth of the FOF envelopes and for the autobendFreq and vocalEffort functions
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 for the autobendFreq and vocalEffort functions
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: uexType: voice vs. fricative sound ratio (0-1 where 1 is 100% fricative)freq: the fundamental frequency of the source signalgain: linear gain multiplier to multiply the source byisFof: whether model is FOF based (0: no, 1: yes)
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: ufreq: the fundamental frequency of the source signalgain: linear gain multiplier to multiply the source by
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: ufreq: the fundamental frequency of the source signalgain: linear gain multiplier to multiply the source by
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: uexType: voice vs. fricative sound ratio (0-1 where 1 is 100% fricative)freq: the fundamental frequency of the source signalgain: linear gain multiplier to multiply the source by
Ready-to-use source-filter vocal synthesizer with built-in user interface.
Usage
SFFormantModelFofCycle_ui : _
Ready-to-use source-filter vocal synthesizer with built-in user interface.
Usage
SFFormantModelFofSmooth_ui : _
Ready-to-use source-filter vocal synthesizer with built-in user interface.
Usage
SFFormantModelBP_ui : _
Ready-to-use MIDI-controllable source-filter vocal synthesizer.
Usage
SFFormantModelFofCycle_ui_MIDI : _
Ready-to-use MIDI-controllable source-filter vocal synthesizer.
Usage
SFFormantModelFofSmooth_ui_MIDI : _
Ready-to-use MIDI-controllable source-filter vocal synthesizer.
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)
reverbs.lib
A library of reverb effects. Its official prefix is re.
Schroeder Reverberators
(re.)jcrev
This artificial reverberator take a mono signal and output stereo (satrev) and quad (jcrev). They were implemented by John Chowning in the MUS10 computer-music language (descended from Music V by Max Mathews). They are Schroeder Reverberators, well tuned for their size. Nowadays, the more expensive freeverb is more commonly used (see the Faust examples directory).
jcrev reverb below was made from a listing of “RV”, dated April 14, 1972, which was recovered from an old SAIL DART backup tape. John Chowning thinks this might be the one that became the well known and often copied JCREV.
jcrev is a standard Faust function
Usage
_ : jcrev : _,_,_,_
(re.)satrev
This artificial reverberator take a mono signal and output stereo (satrev) and quad (jcrev). They were implemented by John Chowning in the MUS10 computer-music language (descended from Music V by Max Mathews). They are Schroeder Reverberators, well tuned for their size. Nowadays, the more expensive freeverb is more commonly used (see the Faust examples directory).
satrev was made from a listing of “SATREV”, dated May 15, 1971, which was recovered from an old SAIL DART backup tape. John Chowning thinks this might be the one used on his often-heard brass canon sound examples, one of which can be found at https://ccrma.stanford.edu/~jos/wav/FM_BrassCanon2.wav
Usage
_ : satrev : _,_
Feedback Delay Network (FDN) Reverberators
(re.)fdnrev0
Pure Feedback Delay Network Reverberator (generalized for easy scaling). fdnrev0 is a standard Faust function.
Usage
<1,2,4,...,N signals> <: fdnrev0(MAXDELAY,delays,BBSO,freqs,durs,loopgainmax,nonl) :> <1,2,4,...,N signals>
Where:
N: 2, 4, 8, … (power of 2)MAXDELAY: power of 2 at least as large as longest delay-line lengthdelays: N delay lines, N a power of 2, lengths perferably coprimeBBSO: odd positive integer = order of bandsplit desired at freqsfreqs: NB-1 crossover frequencies separating desired frequency bandsdurs: NB decay times (t60) desired for the various bandsloopgainmax: scalar gain between 0 and 1 used to “squelch” the reverbnonl: nonlinearity (0 to 0.999…, 0 being linear)
Reference
https://ccrma.stanford.edu/~jos/pasp/FDN_Reverberation.html
(re.)zita_rev_fdn
Internal 8x8 late-reverberation FDN used in the FOSS Linux reverb zita-rev1 by Fons Adriaensen fons@linuxaudio.org. This is an FDN reverb with allpass comb filters in each feedback delay in addition to the damping filters.
Usage
bus(8) : zita_rev_fdn(f1,f2,t60dc,t60m,fsmax) : bus(8)
Where:
f1: crossover frequency (Hz) separating dc and midrange frequenciesf2: frequency (Hz) above f1 where T60 = t60m/2 (see below)t60dc: desired decay time (t60) at frequency 0 (sec)t60m: desired decay time (t60) at midrange frequencies (sec)fsmax: maximum sampling rate to be used (Hz)
Reference
(re.)zita_rev1_stereo
Extend zita_rev_fdn to include zita_rev1 input/output mapping in stereo mode. zita_rev1_stereo is a standard Faust function.
Usage
_,_ : zita_rev1_stereo(rdel,f1,f2,t60dc,t60m,fsmax) : _,_
Where:
rdel = delay (in ms) before reverberation begins (e.g., 0 to ~100 ms) (remaining args and refs as for zita_rev_fdn above)
(re.)zita_rev1_ambi
Extend zita_rev_fdn to include zita_rev1 input/output mapping in “ambisonics mode”, as provided in the Linux C++ version.
Usage
_,_ : zita_rev1_ambi(rgxyz,rdel,f1,f2,t60dc,t60m,fsmax) : _,_,_,_
Where:
rgxyz = relative gain of lanes 1,4,2 to lane 0 in output (e.g., -9 to 9) (remaining args and references as for zita_rev1_stereo above)
Freeverb
(re.)mono_freeverb
A simple Schroeder reverberator primarily developed by “Jezar at Dreampoint” that is extensively used in the free-software world. It uses four Schroeder allpasses in series and eight parallel Schroeder-Moorer filtered-feedback comb-filters for each audio channel, and is said to be especially well tuned.
mono_freeverb is a standard Faust function.
Usage
_ : mono_freeverb(fb1, fb2, damp, spread) : _;
Where:
fb1: coefficient of the lowpass comb filters (0-1)fb2: coefficient of the allpass comb filters (0-1)damp: damping of the lowpass comb filter (0-1)spread: spatial spread in number of samples (for stereo)
License
While this version is licensed LGPL (with exception) along with other GRAME library functions, the file freeverb.dsp in the examples directory of older Faust distributions, such as faust-0.9.85, was released under the BSD license, which is less restrictive.
(re.)stereo_freeverb
A simple Schroeder reverberator primarily developed by “Jezar at Dreampoint” that is extensively used in the free-software world. It uses four Schroeder allpasses in series and eight parallel Schroeder-Moorer filtered-feedback comb-filters for each audio channel, and is said to be especially well tuned.
Usage
_,_ : stereo_freeverb(fb1, fb2, damp, spread) : _,_;
Where:
fb1: coefficient of the lowpass comb filters (0-1)fb2: coefficient of the allpass comb filters (0-1)damp: damping of the lowpass comb filter (0-1)spread: spatial spread in number of samples (for stereo)
routes.lib
A library of basic elements to handle signal routing in Faust. Its official prefix is ro.
Functions Reference
(ro.)cross
Cross n signals: (x1,x2,..,xn) -> (xn,..,x2,x1). cross is a standard Faust function.
Usage
cross(n) _,_,_ : cross(3) : _,_,_
Where:
n: number of signals (int, must be known at compile time)
Note
Special case: cross2:
cross2 = _,cross(2),_;
(ro.)crossnn
Cross two bus(n)s.
Usage
_,_,... : crossmm(n) : _,_,...
Where:
n: the number of signals in the bus
(ro.)crossn1
Cross bus(n) and bus(1).
Usage
_,_,... : crossn1(n) : _,_,...
Where:
n: the number of signals in the first bus
(ro.)interleave
Interleave rowcol cables from column order to row order. input : x(0), x(1), x(2) …, x(rowcol-1) output: x(0+0row), x(0+1row), x(0+2row), …, x(1+0row), x(1+1row), x(1+2row), …
Usage
_,_,_,_,_,_ : interleave(row,column) : _,_,_,_,_,_
Where:
row: the number of row (int, known at compile time)column: the number of column (int, known at compile time)
(ro.)butterfly
Addition (first half) then substraction (second half) of interleaved signals.
Usage
_,_,_,_ : butterfly(n) : _,_,_,_
Where:
n: size of the butterfly (n is int, even and known at compile time)
(ro.)hadamard
Hadamard matrix function of size n = 2^k.
Usage
_,_,_,_ : hadamard(n) : _,_,_,_
Where:
n: 2^k, size of the matrix (int, must be known at compile time)
Note:
Implementation contributed by Remy Muller.
(ro.)recursivize
Create a recursion from two arbitrary processors p and q.
Usage
_,_ : recursivize(p,q) : _,_
Where:
p: the forward arbitrary processorq: the feedback arbitrary processor
signals.lib
A library of basic elements to handle signals in Faust. Its official prefix is si.
Functions Reference
(si.)bus
n parallel cables. bus is a standard Faust function.
Usage
bus(n) bus(4) : _,_,_,_
Where:
n: is an integer known at compile time that indicates the number of parallel cables.
(si.)block
Block - terminate n signals. block is a standard Faust function.
Usage
_,_,... : block(n) : _,...
Where:
n: the number of signals to be blocked
(si.)interpolate
Linear interpolation between two signals.
Usage
_,_ : interpolate(i) : _
Where:
i: interpolation control between 0 and 1 (0: first input; 1: second input)
(si.)smoo
Smoothing function based on smooth ideal to smooth UI signals (sliders, etc.) down. smoo is a standard Faust function.
Usage
hslider(...) : smoo;
(si.)polySmooth
A smoothing function based on smooth that doesn’t smooth when a trigger signal is given. This is very useful when making polyphonic synthesizer to make sure that the value of the parameter is the right one when the note is started.
Usage
hslider(...) : polysmooth(g,s,d) : _
Where:
g: the gate/trigger signal used when making polyphonic synthss: the smoothness (see smooth)d: the number of samples to wait before the signal start being smoothed after g switched to 1
(si.)smoothAndH
A smoothing function based on smooth that holds its output signal when a trigger is sent to it. This feature is convenient when implementing polyphonic instruments to prevent some smoothed parameter to change when a note-off event is sent.
Usage
hslider(...) : smoothAndH(g,s) : _
Where:
g: the hold signal (0 for hold, 1 for bypass)s: the smoothness (see smooth)
(si.)bsmooth
Block smooth linear interpolation during a block of samples.
Usage
hslider(...) : bsmooth : _
(si.)dot
Dot product for two vectors of size n.
Usage
_,_,_,_,_,_ : dot(n) : _
Where:
n: size of the vectors (int, must be known at compile time)
(si.)smooth
Exponential smoothing by a unity-dc-gain one-pole lowpass. smooth is a standard Faust function.
Usage:
_ : smooth(tau2pole(tau)) : _
Where:
tau: desired smoothing time constant in seconds, or
hslider(...) : smooth(s) : _
Where:
s: smoothness between 0 and 1. s=0 for no smoothing, s=0.999 is “very smooth”, s>1 is unstable, and s=1 yields the zero signal for all inputs. The exponential time-constant is approximately 1/(1-s) samples, when s is close to (but less than) 1.
Reference:
https://ccrma.stanford.edu/~jos/mdft/Convolution_Example_2_ADSR.html
(si.)cbus
n parallel cables for complex signals. cbus is a standard Faust function.
Usage
cbus(n) cbus(4) : (r0,i0), (r1,i1), (r2,i2), (r3,i3)
Where:
n: is an integer known at compile time that indicates the number of parallel cables.- each complex number is represented by two real signals as (real,imag)
(si.)cmul
multiply two complex signals pointwise. cmul is a standard Faust function.
Usage
(r1,i1) : cmul(r2,i2) : (_,_);
Where:
- Each complex number is represented by two real signals as (real,imag), so
(r1,i1) = real and imaginary parts of signal 1(r2,i2) = real and imaginary parts of signal 2
(si.)lag_ud
Lag filter with separate times for up and down.
Usage
_ : lag_ud(up, dn, signal) : _;
spats.lib
This library contains a collection of tools for sound spatialization. Its official prefix is sp.
(sp.)panner
A simple linear stereo panner. panner is a standard Faust function.
Usage
_ : panner(g) : _,_
Where:
(sp.)spat
GMEM SPAT: n-outputs spatializer. spat is a standard Faust function.
Usage
_ : spat(n,r,d) : _,_,...
Where:
n: number of outputsr: rotation (between 0 et 1)d: distance of the source (between 0 et 1)
(sp.)stereoize
Transform an arbitrary processor p into a stereo processor with 2 inputs and 2 outputs.
Usage
_,_ : stereoize(p) : _,_
Where:
p: the arbitrary processor
synths.lib
This library contains a collection of synthesizers. Its official prefix is sy.
(sy.)popFilterPerc
A simple percussion instrument based on a “popped” resonant bandpass filter. popFilterPerc is a standard Faust function.
Usage
popFilterDrum(freq,q,gate) : _;
Where:
freq: the resonance frequency of the instrumentq: the q of the res filter (typically, 5 is a good value)gate: the trigger signal (0 or 1)
(sy.)dubDub
A simple synth based on a sawtooth wave filtered by a resonant lowpass. dubDub is a standard Faust function.
Usage
dubDub(freq,ctFreq,q,gate) : _;
Where:
freq: frequency of the sawtoothctFreq: cutoff frequency of the filterq: Q of the filtergate: the trigger signal (0 or 1)
(sy.)sawTrombone
A simple trombone based on a lowpassed sawtooth wave. sawTrombone is a standard Faust function.
Usage
sawTrombone(att,freq,gain,gate) : _
Where:
att: exponential attack duration in s (typically 0.01)freq: the frequencygain: the gain (0-1)gate: the gate (0 or 1)
(sy.)combString
Simplest string physical model ever based on a comb filter. combString is a standard Faust function.
Usage
combString(freq,res,gate) : _;
Where:
freq: the frequency of the stringres: string T60 (resonance time) in secondgate: trigger signal (0 or 1)
(sy.)additiveDrum
A simple drum using additive synthesis. additiveDrum is a standard Faust function.
Usage
additiveDrum(freq,freqRatio,gain,harmDec,att,rel,gate) : _
Where:
freq: the resonance frequency of the drumfreqRatio: a list of ratio to choose the frequency of the mode in function of freq e.g.(1 1.2 1.5 …). The first element should always be one (fundamental).gain: the gain of each mode as a list (1 0.9 0.8 …). The first element is the gain of the fundamental.harmDec: harmonic decay ratio (0-1): configure the speed at which higher modes decay compare to lower modes.att: attack duration in secondrel: release duration in secondgate: trigger signal (0 or 1)
(sy.)fm
An FM synthesizer with an arbitrary number of modulators connected as a sequence. fm is a standard Faust function.
Usage
freqs = (300,400,...); indices = (20,...); fm(freqs,indices) : _
Where:
freqs: a list of frequencies where the first one is the frequency of the carrier and the others, the frequency of the modulator(s)indices: the indices of modulation (Nfreqs-1)
vaeffects.lib
A library of virtual analog filter effects. Its official prefix is ve.
Functions Reference
(ve.)moog_vcf
Moog “Voltage Controlled Filter” (VCF) in “analog” form. Moog VCF implemented using the same logical block diagram as the classic analog circuit. As such, it neglects the one-sample delay associated with the feedback path around the four one-poles. This extra delay alters the response, especially at high frequencies (see reference [1] for details). See moog_vcf_2b below for a more accurate implementation.
Usage
moog_vcf(res,fr)
Where:
res: normalized amount of corner-resonance between 0 and 1 (0 is no resonance, 1 is maximum)fr: corner-resonance frequency in Hz (less than SR/6.3 or so)
References
(ve.)moog_vcf_2b[n]
Moog “Voltage Controlled Filter” (VCF) as two biquads. Implementation of the ideal Moog VCF transfer function factored into second-order sections. As a result, it is more accurate than moog_vcf above, but its coefficient formulas are more complex when one or both parameters are varied. Here, res is the fourth root of that in moog_vcf, so, as the sampling rate approaches infinity, moog_vcf(res,fr) becomes equivalent to moog_vcf_2b[n](res^4,fr) (when res and fr are constant). moog_vcf_2b uses two direct-form biquads (tf2). moog_vcf_2bn uses two protected normalized-ladder biquads (tf2np).
Usage
moog_vcf_2b(res,fr) moog_vcf_2bn(res,fr)
Where:
res: normalized amount of corner-resonance between 0 and 1 (0 is min resonance, 1 is maximum)fr: corner-resonance frequency in Hz
(ve.)wah4
Wah effect, 4th order. wah4 is a standard Faust function.
Usage
_ : wah4(fr) : _
Where:
fr: resonance frequency in Hz
Reference
https://ccrma.stanford.edu/~jos/pasp/vegf.html
(ve.)autowah
Auto-wah effect. autowah is a standard Faust function.
Usage
_ : autowah(level) : _;
Where:
level: amount of effect desired (0 to 1).
(ve.)crybaby
Digitized CryBaby wah pedal. crybaby is a standard Faust function.
Usage
_ : crybaby(wah) : _
Where:
wah: “pedal angle” from 0 to 1
Reference
https://ccrma.stanford.edu/~jos/pasp/vegf.html
(ve.)vocoder
A very simple vocoder where the spectrum of the modulation signal is analyzed using a filter bank. vocoder is a standard Faust function.
Usage
_ : vocoder(nBands,att,rel,BWRatio,source,excitation) : _;
Where:
nBands: Number of vocoder bandsatt: Attack time in secondsrel: Release time in secondsBWRatio: Coefficient to adjust the bandwidth of each band (0.1 - 2)source: Modulation signalexcitation: Excitation/Carrier signal
Licenses
STK 4.3 License
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
Any person wishing to distribute modifications to the Software is asked to send the modifications to the original developer so that they can be incorporated into the canonical version. For software copyrighted by Julius O. Smith III, email your modifications to jos@ccrma.stanford.edu. This is, however, not a binding provision of this license.
THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
LGPL License
This program is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.