Duplicate a value into a tuple.

split 1 == (1,1)

Reversed tuple constructor, (ie. flip (,))

swap 2 1 == (1,2)

Two pi.

two_pi == 6.283185307179586

Midi note number to cycles per second.

midi_cps 69 == 440

Multiply and add.

map (mul_add 2 3) [1,2] == [5,7] && map (mul_add 3 4) [1,2] == [7,10]

Calculate feedback multipler in comb filter circuit given delay and decay times.

calc_fb 0.2 3.0 == 0.6309573444801932

Linear range conversion.

map (\i -> lin_lin i (-1) 1 0 1) [-1,-0.9 .. 1.0]

import Sound.DF.Uniform.GADT {- hdf -}

let {s = lf_saw 1.0 0.0
    ;o = sin_osc (lin_lin s (-1.0) 1.0 220.0 440.0) 0.0}
in audition_rju [] (out1 (o * 0.1))

Exponential range conversion.

map (\i -> lin_exp i 1 2 1 3) [1,1.1 .. 2]

let {s = lf_saw 0.25 0.0
    ;o = sin_osc (lin_exp (s + 1.0) 0.0 2.0 220.0 440.0) 0.0}
in audition_rju [] (out1 (o * 0.1))

Constrain p in (-q,q).

let r = -10 : -10 : [-10,-9 .. 10]
in map (flip clip2 10) [-12,-11 .. 12] == r

sr = sample rate, r = cycle (two-pi), hz = frequency

hz_to_incr 48000 128 375 == 1
hz_to_incr 48000 two_pi 458.3662361046586 == 6e-2

Inverse of hz_to_incr.

incr_to_hz 48000 128 1 == 375

Linear pan.

map (lin_pan2 1) [-1,0,1] == [(1,0),(0.5,0.5),(0,1)]

let {o = sin_osc 440.0 0.0
    ;l = sin_osc 0.5 0.0
    ;(p,q) = lin_pan2 (o * 0.1) l}
in audition_rju [] (out2 p q)

Compile time sample rate constant.

Compile time sample duration (in seconds) constant.

Environment value, recip of w_sample_rate.

Environment value, equal to two_pi / w_sample_rate.

Add guard point.

tbl_guard [1,2,3] == [1,2,3,1]

Generate guarded sin table.

map (round . (* 100)) (tbl_sin 12) == [0,50,87,100,87,50,0,-50,-87,-100,-87,-50,0]

If 'q >= p' then 'q - p' else q.

clip2 variant.

let o = sin_osc 440 0
in audition_rju [] (out1 (df_clip2 (o * 2) 0.1))

Single place infinite impulse response filter with indicated initial value.

import Data.Int
import Sound.DF.Uniform.GADT
import Sound.DF.Uniform.LL.K

draw (iir1 (0::Int32) (+) 1)
draw (iir1 (0::Float) (+) 1)

r = right hand edge, ip = initial phase, x = increment

draw (phasor 9.0 (4.5::Float) 0.5)
draw (phasor 9 (0::Int32) 1)
audition_text 10 (out1 (phasor' 5.0 0.0 1.0))

lift_mce2 of phasor'.

Allocate n second array, variant of df_vec.

Array delay with phasor argument for write index.

Array delay. a = array, s = signal, n = number of frames.

do {a <- df_vec_m [0,1,2]
   ;draw (a_delay a 0.0 0)}

let {f = sin_osc 0.1 0.0
    ;o = sin_osc (f * 200.0 + 600.0) 0.0
    ;a = df_vec (V_Id 0) (replicate 48000 0)
    ;d = a_delay a o 24000}
in audition_rju [] (out2 (o * 0.1) (d * 0.05))

SC3 UGen.

Array fill function (sin).

let {i = phasor 64 0 1
    ;a = a_tbl_sin (V_Id 0) 64
    ;s = a_read a i}
in audition_rju [] (out1 (s * 0.2))

Linear interpolating variant of a_read.

let {i = phasor 64.0 0 (hz_to_incr k_sample_rate 64.0 330.0)
    ;a = a_tbl_sin (V_Id 0) 64
    ;s = a_lerp a i}
in audition_rju [] (out1 (s * 0.2))

phasor for table of z places. ip is in (0,1).

draw (phasor 64.0 (0.0::Float) (hz_to_incr k_sample_rate 64.0 330.0))
draw (tbl_phasor 64 0.0 330.0)

Table lookup oscillator. ip is in (0,1).

let {a = a_tbl_sin (V_Id 0) 256
    ;f = a_osc a 4.0 0.0
    ;o = a_osc a (f * 200.0 + 400.0) 0.0}
in audition_rju [] (out1 (o * 0.1))

Cancellation:

let {a = a_tbl_sin (V_Id 0) 256
    ;o1 = a_osc a 440.0 0.0
    ;o2 = a_osc a 440.0 0.5}
in audition_rju [] (out1 (o1 + o2))

Single sample delay with indicated initial value.

draw (unit_delay (0::Int32) 1)
draw (unit_delay (0.0::Float) 1.0)

let {c = counter 0.0 1.0
    ;d = unit_delay 0.0 c}
in audition_text 12 (out2 c d)

Signal that is initially True then always False.

audition_text 5 (out1 (latch (white_noise 812875317) unit_trigger))

Two place infinite impulse response filter. Inputs are: f= function (x0 y1 y2 -> y0), i = input signal.

let {c1 = iir2 (\x y1 _ -> x + y1) 0.001
    ;o1 = sin_osc (c1 + 220.0) 0
    ;c2 = iir2 (\x _ y2 -> x + y2) 0.001
    ;o2 = sin_osc (c2 + 220.0) 0}
in audition_rju [] (out2 (o1 * 0.1) (o2 * 0.1))

Single place finite impulse response filter.

Two place finite impulse response filter.

Ordinary biquad filter section.

Counter from indicated initial value by indicated step.

draw (counter (0::Int32) 1)
draw (counter (0.0::Float) 1.0)

audition_text 10 (out1 (counter 0.0 1.0))
audition_text 10 (out1 (counter 0.0 (white_noise 165876521 * 0.25)))

counter that resets to the initial phase at trigger.

let tr = trigger (impulse (k_sample_rate / 3) 0.0)
in audition_text 10 (out1 (counter_reset 0.0 1.0 tr))

Counter from 0 to 1 over duration (in seconds). Holds end value.

lin_lin of unit_line.

audition_rju [] (out1 (sin_osc (line 110 440 100) 0 * 0.1))

SC3 UGen.

audition_text 20 (out1 (counter 30 10))
audition_text 20 (out1 (ramp (counter 30 10) (3 / k_sample_rate)))

Buffer delay.

draw (buf_delay 0 0.0 0)

Non-interpolating comb filter. Inputs are: b = buffer index, i = input signal, dl = delay time, dc = decay time.

All times are in seconds. The decay time is the time for the echoes to decay by 60 decibels. If this time is negative then the feedback coefficient will be negative, thus emphasizing only odd harmonics at an octave lower.

draw (out1 (buf_comb_n 0 0.0 0.0 0.0))

Comb used as a resonator. The resonant fundamental is equal to reciprocal of the delay time.

import qualified Sound.SC3 as S

let {n = white_noise 0
    ;dt = let f x = lin_exp (x + 2.0) 1.0 2.0 0.0001 0.01
          in f (lf_saw 0.1 0.0)
    ;c = buf_comb_n 0 (n * 0.1) dt 0.2}
in audition_rju [S.b_alloc 0 48000 1] (out1 c)

Comb used as an echo.

let {i = impulse 0.5 0.0
    ;n = white_noise 0
    ;e = decay (i * 0.5) 0.2
    ;c = buf_comb_n 0 (e * n) 0.2 3.0}
in audition_rju [S.b_alloc 0 48000 1] (out1 c)

Array variant of buf_comb_n. Max delay time is in seconds.

let {n = white_noise 0
    ;dt = let f x = lin_exp (x + 2.0) 1.0 2.0 0.0001 0.01
          in f (lf_saw 0.1 0.0)
    ;c = comb_n [0] 0.1 (n * 0.1) dt 0.2}
in audition_rju [] (out c)

let {i = impulse 0.5 0.0
    ;n = white_noise 0
    ;e = decay (i * 0.5) 0.2
    ;c = comb_n [0] 0.2 (e * n) 0.2 3.0}
in audition_rju [] (out c)

Allow MCE.

Int32 linear congruential generator, hence signed modulo of 2^32. Note that the state and all internal math is 32bit.

See http://en.wikipedia.org/wiki/Linear_congruential_generator for possible parameters.

lcg_i32 1103515245 12345, so in (minBound,maxBound).

abs of 'lcg_glibc, so in (0,maxBound).

i32_to_normal_f32 of randi, so in (0,1).

audition_text 24 (out1 (randf 0))

White noise (-1,1). Generates noise whose spectrum has equal power at all frequencies.

audition_text 24 (out1 (white_noise 0))

let n = white_noise 0 * 0.1
in draw (out1 (n - n))

let {n = white_noise 0 * 0.1
    ;m = white_noise 5 * 0.1}
in audition_rju [] (out1 (n - m))

SC3 UGen.

let freq = lin_lin (lf_noise1 0 1) (-1) 1 220 440
in audition_rju [] (out1 (sin_osc freq 0 * 0.1))

iir1 brown noise function.

Brown noise (-1,1). Generates noise whose spectrum falls off in power by 6 dB per octave.

let n = brown_noise 0
in audition_rju [] (out1 (n * 0.1))

let {n = brown_noise 0
    ;f = lin_exp n (-1.0) 1.0 64.0 9600.0
    ;o = sin_osc f 0}
in audition_rju [] (out1 (o * 0.1))

SC3 UGen.

audition_rju [] (out1 (dust 0 200 * 0.25))
audition_rju [] (out1 (dust 0 (sin_osc 0.1 0 * 500 + 550) * 0.25))

SC3 UGen.

audition_rju [] (out1 (sin_osc (rand 6987612487 220.0 600.0) 0.0 * 0.1))

Sine oscillator. Inputs are: f = frequency (in hz), ip = initial phase.

let o = sin_osc 440.0 0.0
in audition_rju [] (out1 (o * 0.1))

Used as both Oscillator and LFO.

let {f = sin_osc 4.0 0.0
    ;o = sin_osc (f * 200.0 + 400.0) 0.0}
in audition_rju [] (out1 (o * 0.1))

Cancellation.

let {o1 = sin_osc 440.0 0.0
    ;o2 = sin_osc 440.0 pi}
in audition_rju [] (out1 (o1 + o2))

Impulse oscillator (non band limited). Outputs non band limited single sample impulses. Inputs are: f = frequency (in hertz), ip = phase offset (0..1)

let o = impulse 800.0 0.0
in audition_rju [] (out1 (o * 0.1))

let {f = sin_osc 0.25 0.0 * 2500.0 + 2505.0
    ;o = impulse f 0.0}
in audition_rju [] (out1 (o * 0.1))

audition_text 10 (out1 (impulse (w_sample_rate / 5.0) 0.0))
audition_text 10 (out1 (impulse (k_sample_rate / 5.0) 0.0))

Non-band limited sawtooth oscillator. Output ranges from -1 to +1. Inputs are: f = frequency (in hertz), ip = initial phase (0,2).

let o = lf_saw 500.0 1.0
in audition_rju [] (out1 (o * 0.1))

Used as both Oscillator and LFO.

let {f = lf_saw 4.0 0.0
    ;o = lf_saw (f * 400.0 + 400.0) 0.0}
in audition_rju [] (out1 (o * 0.1))

Non-band-limited pulse oscillator. Outputs a high value of one and a low value of zero. Inputs are: f = frequency (in hertz), ip = initial phase (0,1), w = pulse width duty cycle (0,1).

let {o1 = lf_pulse 3.0 0.0 0.3 * 200.0 + 200.0
    ;o2 = lf_pulse o1 0.0 0.2 * 0.1}
in audition_rju [] (out1 o2)

Two zero fixed midpass filter.

Two zero fixed midcut filter.

Two point difference filter

Two zero fixed highpass filter

Two point average filter

Two zero fixed lowpass filter

Given cf construct iir1 one-pole function.

One pole filter.

let {n = white_noise 0
    ;f = one_pole (n * 0.5) 0.95}
in audition_rju [] (out1 f)

Given cf construct fir1 one-zero function.

One zero filter.

let {n = white_noise 0
    ;f = one_zero (n * 0.5) 0.5}
in audition_rju [] (out1 f)

Given coefficients construct biquad sos function.

Second order filter section.

Given f and rq construct iir2 resonz function.

A two pole resonant filter with zeroes at z = +/- 1. Based on K. Steiglitz, "A Note on Constant-Gain Digital Resonators", Computer Music Journal, vol 18, no. 4, pp. 8-10, Winter 1994. The reciprocal of Q is used rather than Q because it saves a divide operation inside the unit generator.

Inputs are: i = input signal, f = resonant frequency (in hertz), rq = bandwidth ratio (reciprocal of Q);where rq = bandwidth / centerFreq.

let {n = white_noise 0
    ;r = resonz (n * 0.5) 440.0 0.1}
in audition_rju [] (out1 r)

Modulate frequency

let {n = white_noise 0
    ;f = lf_saw 0.1 0.0 * 3500.0 + 4500.0
    ;r = resonz (n * 0.5) f 0.05}
in audition_rju [] (out1 r)

Given f and r construct iir2 rlpf function.

Resonant low pass filter. Inputs are: i = input signal, f = frequency (hertz), rq = reciprocal of Q (resonance).

let {n = white_noise 0
    ;f = sin_osc 0.5 0.0  * 40.0 + 220.0
    ;r = rlpf n f 0.1}
in audition_rju [] (out1 r)

Allow MCE.

5-tuple

2nd order Butterworth high-pass filter coefficients.

hpf_c 48000.0 (440.0 :: DF Float)

High pass filter.

Low pass filter.

df_gt 0.

df_not of positive.

fir1 trigger function.

True on non-positive to positive transition.

Count True values at input.

let n = white_noise 0
in audition_text 12 (out2 n (count_true (trigger n)))

Pulse divider at Bool.

SC3 PulseDivider.

let n = white_noise 0
in audition_text 12 (out2 n (pulse_divider' n 2 1))

Sample and hold. Holds input signal value when triggered. Inputs are: i = input signal, t = trigger.

let {n = white_noise 0
    ;i = impulse 9.0 0.0
    ;l = latch n (trigger i)
    ;o = sin_osc (l * 400.0 + 500.0) 0.0}
in audition_rju [] (out1 (o * 0.2))

Given dt construct iir1 decay function.

Exponential decay. Inputs are: i = input signal, t = decay time. This is essentially the same as Integrator except that instead of supplying the coefficient directly, it is caculated from a 60 dB decay time. This is the time required for the integrator to lose 99.9 % of its value or -60dB. This is useful for exponential decaying envelopes triggered by impulses.

Used as an envelope.

let {n = brown_noise 0
    ;f = lf_saw 0.1 0.0
    ;i = impulse (lin_lin f (-1.0) 1.0 2.0 5.0) 0.25
    ;e = decay i 0.2}
in audition_rju [] (out1 (e * n))

Exponential decay (equivalent to decay dcy - decay atk).

Single sample delay.

Two sample delay.

audition_text 10 (out1 (delay2 (counter 0 1)))

Given t construct iir1 lag function.

Simple averaging filter. Inputs are: i = input signal, t = lag time.

let {s = sin_osc 0.05 0.0
    ;f = lin_lin s (-1.0) 1.0 220.0 440.0
    ;o = sin_osc f 0.0
    ;f' = lag f 1.0
    ;o' = sin_osc f' 0.0}
in audition_rju [] (out2 (o * 0.2) (o' * 0.2))

Nested lag filter.

Twice nested lag filter.