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  • cartopol The cartopol~ object converts Cartesian coordinates (real and imaginary parts) from signal inputs into polar coordinates (amplitude and phase) as signal outputs.
  • atan~ The atan~ object calculates the arc-tangent of each incoming audio sample.
  • commonality The commonality object calculates the 'Pitch Commonality' between three or more specified pitches.
  • round The round object approximates input numbers (floats or lists) to the nearest integer multiple of a specified value.
  • pix_add The pix_add object combines two input images of the same size by adding their pixel values.
  • sph2pol The sph2pol object converts spherical coordinates (radius R, azimuthal angle phi, and polar angle theta) into polar coordinates.
  • logistic~ logistic~ is a chaotic signal generator based on the logistic difference equation.
  • prime The prime object detects if an input number is prime.
  • atanh The atanh object calculates the hyperbolic arc-tangent of a given float input.
  • lcm The lcm object calculates the least common multiple (LCM) of two or more floating-point numbers.
  • eqdiv The eqdiv object generates equal temperament scales.
  • tanh The tanh object calculates the hyperbolic tangent function of a given number.
  • rgb2hsv The rgb2hsv object converts color values from the RGB (Red, Green, Blue) color space to the HSV (Hue, Saturation, Value/Luminance) color space.
  • rgb2yuv The rgb2yuv object converts color values from the RGB (Red, Green, Blue) color space to the YUV (Luma, Chroma) color space.
  • rms~ The rms~ object calculates the Root Mean Square (RMS) value of an incoming audio signal, similar to env~ but providing RMS in linear amplitude or dBFS.
  • mag The mag object calculates the magnitude (amplitude) of a complex number, taking its real and imaginary parts as input.
  • clock The clock object sends bangs at a regular tempo, acting as a 'main' clock or a 'synced' clock.
  • ratio2cents The ratio2cents object converts musical intervals expressed as rational numbers (floating-point decimals) into cents.
  • zl The zl object is a versatile Pure Data list processor that performs various operations on incoming lists based on its selected mode.
  • minmax The minmax object takes a list of floating-point numbers as input.
  • average~ average~ calculates a moving average of an audio signal over a specified number of recent samples.
  • cents2ratio The cents2ratio object converts musical intervals expressed in cents into their corresponding frequency ratios, output as floating-point decimals.
  • rdiv~ The rdiv~ object performs signal division, similar to /~, but with its inlets reversed.
  • iCircle2D The iCircle2D object simulates circular interactions in 2D space, applying various forces and displacements to an interacting mass.
  • gendyn~ The gendyn~ object implements Dynamic Stochastic Synthesis, generating waveforms where each point's amplitude and frequency evolve via a random walk.
  • minmax~ The minmax~ object continuously tracks the minimum and maximum amplitude values of an incoming audio signal.
  • op The op object in Pure Data provides a wide range of mathematical, comparative, bitwise, and logical operations.
  • standard~ The standard~ object is a chaotic signal generator based on the standard map equation.
  • tCylinder3D The tCylinder3D object defines a 3D cylindrical volume and tests if a given 3D point (referred to as a "mass") is located within its boundaries.
  • gemlist_info The gemlist_info object takes a gemlist as input and decomposes its current transformation matrix into basic transformations.
  • quantizer The quantizer object approximates input float values or lists of floats to discrete step values.
  • phon2db The phon2db object converts a loudness value expressed in phons to decibels (dB).
  • db2lin The db2lin object converts amplitude values from decibels full scale (dBFS) to a linear scale.
  • scale The scale object maps an input numerical range to an output numerical range, allowing for inversion and exponential scaling.
  • pix_threshold_bernsen pix_threshold_bernsen applies a dynamic tiled threshold filter to greyscale images for binarization.
  • rdiv rdiv performs division, similar to the [/] object, but with reversed inlet functionality.
  • fluid.pca fluid.pca performs Principal Component Analysis (PCA) on a fluid.dataset to reduce dimensionality, such as transforming 13 MFCC values into 2.
  • hz2bark The hz2bark object converts a given frequency in Hertz (Hz) to its equivalent value on the Bark scale, a psychoacoustical scale for perceived pitch.
  • greaterthan~ The greaterthan~ (or >~) object performs a sample-by-sample comparison between two signal inputs.
  • harmonicity The harmonicity object calculates Clarence Barlow's harmonicity measure for a given interval p/q.
  • mel2hz The mel2hz object converts a frequency value from the Mel scale to the linear Hertz scale.
  • pi The pi object calculates and outputs the mathematical constant pi, optionally multiplied by a float value provided as an argument or via its second inlet.
  • quantizer~ The quantizer~ object quantizes an incoming signal to discrete step values, offering five different approximation modes including round, truncate, floor, and ceil.
  • pong The pong object limits input values by folding, wrapping, or clipping them within a specified low-high range.
  • minimum~ The minimum~ object outputs the smaller of two input signals, or the smaller of an input signal and a numerical argument.
  • pol2sph The pol2sph object converts 2D polar coordinates (radius, angle, and height) into 3D spherical coordinates.
  • gmean The gmean object generates a list of numbers that form a geometric progression between a specified start and end value.
  • phon2sone The phon2sone object converts a loudness level expressed in phons to a perceived loudness value in sones.
  • mavg The mavg object implements a moving average filter, smoothing incoming float values by averaging a specified number of recent samples.
  • sone2phon The sone2phon object converts a loudness value expressed in sones to phons.
  • speed The speed object in Pure Data enables dynamic tempo changes, such as accelerando or ritardando.
  • envelope~ The envelope~ object generates various envelope waveforms based on a phase input.
  • amean The amean object generates a list of arithmetic means.
  • gbman~ gbman~ is a chaotic audio generator based on the gingerbread man map difference equation, y[n] = 1 + abs(y[n-1]) - y[n-2].
  • lin2db The lin2db object converts a linear amplitude value to its equivalent decibel full scale (dBFS) representation.
  • dbtoa The dbtoa object converts decibel (dBFS) values into their corresponding linear amplitude using the formula amp = pow(10, dBFS / 20).
  • a.sum The a.sum object in Pure Data sums the last x numbers of an array.
  • distance The distance object calculates the perceptual distance between pitches.
  • framedelta~ The framedelta~ object computes the difference between successive signal blocks, specifically designed for running phase deviation in FFT analysis.
  • car2pol The car2pol object converts Cartesian coordinates (real and imaginary parts) into their polar form (amplitude and phase).
  • fluid.gain~ The fluid.gain~ object controls the amplitude of an audio signal.
  • mass2D The mass2D object simulates a 2D mass, calculating its position and velocity based on applied forces, weight, and damping.
  • sum The sum object calculates the sum of a list of floating-point numbers.
  • autotune2 The autotune2 object quantizes incoming pitch values, expressed in cents, to the closest step within a user-defined scale.
  • clip~ The cyclone/clip~ object constrains an input audio signal to a specified minimum and maximum range.
  • kalman The kalman object implements a simple, linear, one-dimensional Kalman filter.
  • scalarmult The scalarmult object performs scalar multiplication, also known as a "dot product," on incoming lists of numbers.
  • latoocarfian~ latoocarfian~ is a chaotic signal generator that implements the Latoocarfian difference equations.
  • dec2frac The dec2frac object converts decimal numbers into their fractional equivalents.
  • hz2mel The hz2mel object converts a frequency value, given in Hertz (Hz), into its corresponding value on the Mel scale.
  • cosx~ The cosx~ object computes the cosine of an input signal, expecting values in radians.
  • mix4~ The mix4~ object is a convenient 4-channel audio mixer abstraction for Pure Data, offering independent gain and panning controls for each input.
  • factor The factor object takes a float as input and outputs a list of its prime factors.
  • atan2~ The atan2~ object calculates the arc-tangent of two signal-rate input values, 'a' and 'b', as atan(a/b).
  • sh~ The sh~ object performs sample-and-hold on an audio signal, effectively downsampling it.
  • poltocar The poltocar object converts polar coordinates (amplitude and phase in radians) into cartesian coordinates (real and imaginary parts).
  • pow~ The cyclone/pow~ object calculates the power of a base value, raising it to the exponent.
  • mean The mean object calculates a running or moving average of all received numbers.
  • tavg~ The tavg~ object calculates the arithmetic mean of an incoming audio signal.
  • add~ The add~ object continuously accumulates incoming signal or float values, adding them to a running sum.
  • dbtoa~ The dbtoa~ object converts a decibel full scale (dBFS) amplitude signal or float into its linear amplitude equivalent.
  • frac.add The frac.add object is used to add two fractional values.
  • hann~ The hann~ object applies a Hann window to an incoming audio signal.
  • notedur2ratio The notedur2ratio object converts symbolic musical note durations (e.g., 4n for a quarter note) into numerical ratios, outputting them as either fractions or floats.
  • frac2dec The frac2dec object converts fractional representations (e.g., "1/2", "3/4") into their corresponding decimal floating-point numbers.
  • bark2hz The bark2hz object converts a value from the Bark scale to Hertz.
  • rint~ The rint~ object rounds an incoming signal to the nearest integer value.
  • fluid.mfcc~ The fluid.mfcc~ object calculates Mel-Frequency Cepstral Coefficients (MFCCs) in real-time, serving as a classic timbral audio descriptor.
  • tSphere3D The tSphere3D object performs a spherical test to determine if a "mass" (likely a point or object) is located within a defined 3D spherical region.
  • henon~ The henon~ object generates a chaotic audio signal based on the Hénon map difference equation.
  • greaterthaneq~ The greaterthaneq~ (or >=~) object performs a "greater than or equal to" comparison for audio signals.
  • median~ The median~ object calculates the median value of an incoming audio signal over a user-specified number of samples.
  • delta~ The delta~ object calculates the difference between the current incoming audio sample and the previous sample.
  • abs~ The abs~ object calculates the absolute value of an incoming audio signal.
  • cart2sph The cart2sph object converts 3D Cartesian coordinates (x, y, z) into spherical coordinates (radius, azimuth, elevation).
  • rand.f The rand.f object generates pseudo-random floating-point numbers within a specified range when triggered by a bang.
  • shaper~ The shaper~ object performs waveshaping by mapping input signal values to a transfer function, which can be defined by an external array or an internal Chebyshev polynomial.
  • fluid.bufscale The fluid.bufscale object scales numerical values within a buffer from a specified input range to an output range.
  • midi2freq The midi2freq object converts MIDI note numbers into their corresponding frequencies in Hertz.
  • pattern The pattern object is a rhythmic sequencer that defines musical patterns using note durations, which can be specified as floats or fractions (where 1 is a whole note) with negative values indicating rests.
  • quantize~ The quantize~ object quantizes an incoming audio signal to a variable number of steps.
  • sgn~ The sgn~ object calculates the signum of an incoming audio signal, outputting 1 for positive values, -1 for negative values, and 0 for zero.
  • mov.avg The mov.avg object calculates a running or moving average of incoming float values.
  • phasewrap~ The phasewrap~ object wraps an input signal's value between -π and π.
  • db2phon The db2phon object converts a decibel (dB) value into phons, a unit representing perceived loudness.
  • tanh~ tanh~ calculates the hyperbolic tangent of an input signal.
  • count The count object acts as a versatile counter, incrementing or decrementing a numerical value within specified minimum and maximum bounds.
  • floor The floor object implements a standard mathematical floor function, rounding a given number down to the nearest integer.
  • link The link object calculates forces between two masses, simulating a physical connection with configurable rigidity and damping.
  • interpolate The interpolate object smoothly transitions between a start value (or list of values) and a target value (or list of values) based on an input float between 0 and 1.
  • zigbinops The zigbinops help patch describes a collection of signal-rate Pure Data objects from the zexy library.
  • cents2frac The cents2frac object converts musical intervals expressed in cents into fractional values, representing ratios.
  • rm~ rm~ is a Pure Data abstraction that performs ring modulation on an input signal.
  • rminus~ The rminus~ (or !-~) object performs signal subtraction, similar to ~, but with its inlets reversed.
  • lincong~ The lincong~ object is a chaotic signal generator based on the linear congruential algorithm, similar to SuperCollider's LincongN UGEN.
  • polyfun The polyfun object evaluates a polynomial function.
  • iso226 The iso226 object generates a list of 29 decibel (dB) values across a frequency range, corresponding to equal-loudness contours.
  • lessthan~ The lessthan~ (or <~) object performs a "less than" comparison for audio signals.
  • scale~ scale~ maps an input signal range to an output signal range, allowing for linear, inverted, or exponential scaling.
  • pz2coeff The pz2coeff object converts pole and zero coordinates, along with an overall gain, into biquad filter coefficients.
  • pol2car The pol2car object converts polar coordinates (amplitude and phase) into their Cartesian equivalents (real and imaginary parts).
  • avg~ The avg~ object calculates the absolute average of an input signal.
  • tabgen The tabgen object is a Pure Data abstraction for generating and populating named tables (arrays) with various mathematical functions.
  • hz2rad The hz2rad object converts a frequency in Hertz (Hz) to radians per sample.
  • acosh~ The acosh~ object calculates the hyperbolic arc-cosine of an incoming signal, sample by sample.
  • rescale The rescale object maps input values from one numerical range to another, allowing for linear, exponential, or logarithmic scaling.
  • ceil The ceil object is a mathematical function that rounds a number up to the nearest integer.
  • pmpd2d The pmpd2d object implements a 2D mass-spring-damper physical model, designed for particle-based simulations in Pure Data.
  • lorenz~ The lorenz~ object generates a chaotic audio signal based on the Lorenz strange attractor, a 3D mathematical model.
  • peak The peak object tracks and outputs the highest float value it has received.
  • trunc~ trunc~ truncates an incoming audio signal towards zero, effectively retaining only the integer part of each sample.
  • tLine2D The tLine2D object defines a 2D line segment using two points and tracks the position of a "mass" relative to it.
  • rint The rint object rounds floating-point numbers to the nearest integer value.
  • bpm The bpm object calculates conversions to and from beats per minute (BPM).
  • resonant~ The resonant~ object is a bandpass resonator filter that allows for control over its center frequency and resonance.
  • fader~ The fader~ object is a signal waveshaper designed for crossfading and amplitude modulation.
  • pdf~ The pdf~ object calculates the probability density function of an incoming signal.
  • power~ The power~ object is a signal waveshaper that raises an input signal to a specified exponential factor.
  • e The e object calculates and outputs the mathematical constant 'e' (Euler's number).
  • acos~ The acos~ object calculates the arc-cosine of an incoming signal, sample by sample.
  • coordinates The cart2pol, pol2sph, sph2cart, cart2sph, pol2cart, and sph2pol objects convert between Cartesian, Polar, and Spherical coordinate systems.
  • cartopol~ The cartopol~ object converts a signal from Cartesian coordinates (real and imaginary parts) to polar coordinates (amplitude and phase).
  • cents2ratio~ The cents2ratio~ object converts an audio signal representing an interval in cents into a decimal ratio.
  • trunc The trunc object truncates floating-point numbers and lists of numbers towards zero, effectively extracting only the integer part of each number.
  • fluid.normalize The fluid.normalize object normalizes a fluid.dataset or a single data point.
  • cents2scale cents2scale converts a list of intervals expressed in cents into a musical scale represented by semitone steps.
  • plusequals~ The plusequals~ (or +=~) object is a signal accumulator that continuously sums its input samples, generating a running total.
  • acos The acos object calculates the arc-cosine (inverse cosine) of a given number.
  • wrap2 The wrap2 object wraps an input value within a specified minimum and maximum range.
  • scale2freq The scale2freq object converts a scale defined by a list of cents values into a list of frequencies (in Hz).
  • mass3D The mass3D object simulates a mass in a 3D space, calculating its position and velocity based on applied forces, weight, damping, and boundary conditions.
  • cosh The cosh object calculates the hyperbolic cosine of a given floating-point number.
  • sph2cart The sph2cart object converts spherical coordinates (radius, azimuth, elevation) to Cartesian coordinates (x, y, z).
  • ratio2cents~ The ratio2cents~ object converts a signal representing a rational interval into an interval expressed in cents.
  • poltocar~ The poltocar~ object converts signal values from polar coordinates (amplitude and phase) to Cartesian coordinates (real and imaginary parts).
  • fluid.nmfmorph~ The fluid.nmfmorph~ object performs cross-synthesis between two audio sources using Nonnegative Matrix Factorization (NMF) and Optimal Transport (OT).
  • sin~ The sin~ object generates a sine wave by calculating the sine of its signal input, scaled by two pi.
  • atanh~ The atanh~ object calculates the hyperbolic arc-tangent of an incoming signal.
  • hex2dec The hex2dec object converts hexadecimal values to their decimal equivalents.
  • rescale~ The rescale~ object transforms input signal values from one range to another, with configurable minimum and maximum input/output values.
  • samps2ms~ The samps2ms~ object converts a time value given in samples to milliseconds.
  • pol2car~ The pol2car~ object converts polar coordinates (amplitude and phase) into cartesian coordinates (real and imaginary parts).
  • maximum~ The maximum~ object outputs a signal representing the greater of two input signals, or the greater of an input signal and a numerical argument.
  • indigestibility The indigestibility object calculates Clarence Barlow's 'indigestibility' measure for an integer.
  • sinh~ The sinh~ object calculates the hyperbolic sine of an incoming signal, sample by sample.
  • pol2cart The pol2cart object converts 3D polar coordinates (radius r, azimuthal angle phi, and polar angle theta) into Cartesian coordinates (x, y, z).
  • maximum The maximum object outputs the greatest value among two or more numbers.
  • freq2midi The freq2midi object converts frequency values (in Hz) to MIDI note numbers, similar to the ftom object.
  • rad2deg The rad2deg object converts an input value from radians to degrees.
  • rminus The rminus (or !-) object performs subtraction with its inlets reversed compared to the standard [-] object.
  • bicoeff2 The bicoeff2 object generates coefficients for Pure Data's vanilla biquad~ object, which implements various audio filters.
  • ms2samps The ms2samps object is a simple abstraction that converts a time value in milliseconds to the equivalent number of audio samples.
  • db2lin~ The db2lin~ object converts decibel full scale (dBFS) amplitude values to linear amplitude values using the formula amp = 10^(dBFS / 20).
  • hsv2rgb The hsv2rgb object converts color values from the Hue, Saturation, Value (HSV) color space to the Red, Green, Blue (RGB) color space.
  • atodb~ The atodb~ object converts a linear amplitude signal to its equivalent in decibels full scale (dBFS).
  • mstosamps~ The mstosamps~ object converts a time value in milliseconds into the corresponding number of audio samples, taking the current sample rate into account.
  • mov.rms~ The mov.rms~ object calculates a running Root Mean Square (RMS) of an audio signal over a specified time window (number of samples).
  • asin~ The asin~ object calculates the arc-sine of each input audio sample.
  • deg2rad The deg2rad object converts degree values (0 to 360) to their equivalent radian values.
  • rand.i~ The rand.i~ object generates pseudo-random integer values within a specified range, outputting them as an audio signal.
  • linedrive The linedrive object scales numbers from one range to another using an exponential curve, similar to cyclone/scale.
  • wrap The wrap object functions as a float-capable modulo, constraining an input float value within specified limits.
  • asin The asin object calculates the arc-sine of a given float input.
  • ms2samps~ The ms2samps~ object converts time values from milliseconds to the corresponding number of audio samples.
  • avg The avg object calculates the mean average of all incoming numbers.
  • float2bits The float2bits object converts a decimal floating-point number (IEEE754 single precision) into its binary representation.
  • sampstoms~ The sampstoms~ object converts a time value from samples to milliseconds, taking the current sample rate into account.
  • pong~ The pong~ object functions as a signal range limiter, enabling users to fold, wrap, or clip an input signal within a defined low-high range.
  • sinh The sinh object calculates the hyperbolic sine of a given floating-point number.
  • ceil~ The ceil~ object performs a ceiling mathematical operation on incoming audio signals.
  • fold The fold object mirrors an input value back into a specified low and high range.
  • bitnot~ bitnot~ performs a bitwise NOT operation (one's complement) on an incoming signal.
  • sinx~ The sinx~ object calculates the sine of an incoming signal.
  • tempo The tempo object functions as a metronome, sending bangs at a specified rate in BPM, Hz, or milliseconds.
  • op~ The op~ object performs various signal operations, including comparative, logical, bitwise, and modulo calculations.
  • car2pol~ The car2pol~ object converts Cartesian coordinates (real and imaginary parts) of an audio signal into polar coordinates (amplitude and phase).
  • wrap2~ The wrap2~ object wraps an input signal's values within a specified low and high range.
  • curve~ curve~ generates non-linear, curved ramp signals, offering an exponential curve factor to shape the transition between values.
  • balance~ The balance~ object performs equal power (sin/cos) stereo balancing.
  • frac2cents The frac2cents object converts fractional interval values into cents.
  • frac.mul The frac.mul object multiplies two fractional values.
  • minimum The minimum object outputs the smallest value from its inputs.
  • cosh~ The cosh~ object calculates the hyperbolic cosine of an input signal sample by sample.
  • atodb The atodb object converts linear amplitude values to their decibel full scale (dBFS) equivalents.
  • absgn~ The absgn~ object calculates the absolute value and the signum of an incoming audio signal.
  • floor~ The floor~ object applies the floor mathematical function to incoming audio signals, rounding each sample down to the nearest integer.
  • modulo~ The modulo~ (or %%~) object is a signal remainder operator.
  • list.inc list.inc generates a numerical list based on a starting value, a step value, and the desired number of elements.
  • quad~ The quad~ object generates a chaotic audio signal using a general quadratic map.
  • asinh The asinh object calculates the hyperbolic arc-sine of a given floating-point number.
  • cart2pol The cart2pol object converts 3D Cartesian coordinates (x, y, z) into 3D polar coordinates.
  • sum~ The sum~ object takes a multichannel audio signal and sums all channels into a single mono output.
  • mag~ The mag~ object calculates the magnitude (amplitude) of a signal from its real and imaginary components, functioning similarly to the amplitude output of car2pol~.
  • iAmbient2D The iAmbient2D object simulates ambient interactions in a 2D space, applying constant, random, and damping forces to named "masses." It also handles displacement if a mass moves outside a defined rectangular area.
  • gcd The gcd object calculates the greatest common divisor (GCD) of two or more numbers.
  • ramp~ The ramp~ object generates a linear signal ramp between user-defined minimum and maximum values, automatically looping or clipping based on its mode.
  • clip The clip object (or cyclone/clip~) constrains incoming float or list values to a specified numerical range.
  • rad2hz The rad2hz object converts a frequency value from "radians per sample" to Hertz (Hz).
  • multiline~ The multiline~ object performs line-interpolated multiplication of multiple input signals.
  • lin2db~ The lin2db~ object converts linear amplitude values to decibels full scale (dBFS) using the formula dbFS = log10(amp) * 20.
  • taint~ The taint~ object performs spectral multiplication, combining the frequency spectra of two input audio signals.
  • samps2ms The samps2ms object is a simple utility that converts a time value from samples to milliseconds.
  • drunkard The drunkard object generates a sequence of pseudo-random numbers by simulating a random walk.
  • acosh The acosh object calculates the hyperbolic arc-cosine of a given floating-point number.
  • scale2cents The scale2cents object converts a musical scale defined by steps in semitones into corresponding cent values.
  • round~ The round~ object quantizes incoming audio signals to an integer multiple of a specified value.
  • add The add object accumulates incoming float values, outputting the current sum.
  • median The median object calculates the median value of a given list of numbers.
  • cusp~ cusp~ is a chaotic signal generator that implements the difference equation y[n] = a - b * sqrt(abs(y[n-1])).
  • dec2hex The dec2hex object converts incoming decimal numbers or lists of numbers into their hexadecimal string representations.
  • tanx~ tanx~ calculates the tangent of an incoming signal, expecting its input in radians.
  • asinh~ The asinh~ object computes the hyperbolic arc-sine of an incoming audio signal, sample by sample.