These functions are for pattern and waveform generation and manipulation

Waveforms

sqr <phasor>

Turns a phasor into a square wave.

Parameter Description Range
phasor A phasor (e.g. bar, beat), or any other value between 0 and 1 0-1

pulse <pulse width> <phasor>

Outputs a pulse wave.

Parameter Description Range
pulse width The relative width of each pulse 0-1
phasor A phasor (e.g. bar, beat) 0-1

tri <duty cycle> <phasor>

Variable duty triangle wave

Parameter Description Range
duty The point within the phase when the triangle should reach its peak 0-1
phasor A phasor (e.g. bar, beat) 0-1

This waveform is really useful for creating envelopes

e.g. an envelope with fast attack, long decay, with the peak near the beginning

(a1 (tri 0.1 (fast 4 bar)))

or transform the straight triangle edges into curves with pow

(a1 (pow (tri 0.2 (fast 4 bar)) 0.6))

List-based patterns

from-list <list> <phasor> (alias: seq)

Read an item from a list, using a normalised index.

Items in the list are evaluated before being returned, so you can use functions, variables, and generally any valid expressions in the list.

Parameter Description Range
list A list of values any
position A normalised index 0-1 
(from-list [1 2 3 4] 0.6) ; => 3

(from-list [1 2 3 4] bar))

(seq [1 (/ phrase 2)] bar))

(from-list '(1 phrase) bar))

(from-list [1 2 (from-list [1 2] bar)] 
    (slow 2 bar))

flatten <list>

Take a list that might contain other lists or functions, evaluate them all in turn and collect them in a one dimensional list.

Parameter Description Range
list A list of values any

Examples:

(flatten [1 [2 3] bar])

(define part1 [1 2 3])
(define part2 [4 5])
(flatten [part1 part2 part1])

from-flattened-list <list> <position/phasor> (alias: flatseq)

Read an item from a list, using a normalised index, but flatten then list first (using flattened).

Parameter Description Range
list A list of values any
position A normalised index 0-1

This is a shortcut, equivelant to;

(from-flattened-list [0 1 2 [3 4 5]] 0.75)

gates <list> (<pulse width> = 0.5) <phasor>

Output a sequence of gates, with variable pulse width.

Parameter Description Range
list A list of gate values 0 or 1
phasor The sequence is output once per cycle of the phasor 0-1
speed Modify the speed of the phasor >= 1
pulse width Optional, default: 0.5. The pulse width of the gates 0-1 
(d2 (gates [0 1 1 0  1 1 1 0  1 1 0 1  1 0 0 1] (+ (swm 1) 0.3) bar))

(d2 (gates [0 1 1 0 1 0 0 (swt)] 0.5 (fast 2 bar))))

gatesw <list> <phasor>

Output a sequence of gates, with pulse width controlled from values in the list

Parameter Description Range
list A list of gate/pulse width values, varying from 0 (0% pulse width) to 9 (100% pulse width / tie into the next note) 0 - 9
phasor The sequence is output once per cycle of the phasor 0-1 
(d2 (gatesw [9 9 5 9 3 0 3 8] (fast 2 bar)))

trigs <list> (<pulsewidth>) <phasor>

Output a sequence of gates, each of which can have a different amplitude, determined by a list of amplitudes.

Parameter Description Range
list A list of trigger values, varying from 0 (0% amplitude) to 9 (100% amplitude) 0 - 9
phasor The sequence is output once per cycle of the phasor 0-1
pulseWidth Optional, default: 0.1. Modify the pulse width of the trigger 0 - 1 
(s3 (trigs [0 1 9 0 1] (fast 2 bar)))
;; With a higher pulse width:
(s4 (trigs [0 1 9 0 1] 0.7 (fast 2 bar)))

interp <list> <phasor>

Interpolate across a list, using a phasor. This function acts as if the list of values describes a continuous envelope, and returns the value at a position in that envelope. e.g.

Parameter Description Range
values A list of values any list
phasor A phasor 0 - 1 
(interp [0 0.5 0] 0.75)

describes a triangle shape, and returns the value that it 75% along the triangle (0.25).

(a1 (interp [1 0.5 0 0.6 1] bar))

makes a roughly inverted triangle, and plays it once per bar on PWM output 1

(a2 (interp [0 (sin phrase) 1] section))

creates a slowly changing envelope that loops every section, sent to PWM output 2

Phasor Processing

step <count> (<offset> = 0) <phasor>

Turn a phasor into an integer counter.

Parameter Description Range
count the number of divisions to divide the phasor into >0
offset Optional. the point to start the counter from any
phasor A phasor 0 - 1

Pattern Generation

euclid <n> <k> (<pulseWidth> = 0.5) <phasor>

Generate a sequence of gates based on euclidean sequencing.

For more info: https://erikdemaine.org/papers/DeepRhythms_CGTA/paper.pdf

Demaine, E.D., Gomez-Martin, F., Meijer, H., Rappaport, D., Taslakian, P., Toussaint, G.T., Winograd, T. and Wood, D.R., 2009. The distance geometry of music. Computational geometry, 42(5), pp.429-454.

Parameter Description Range
n the number of beats to fit into the period of the phasor >0
k the number of beats to fit, equally spaced, into n beats >0
pulseWidth (optional) Width of the gates >0 and <1
phasor A phasor 0 - 1 
(d1 (euclid 16 (step phrase 4 4) 0.3 bar))
(d2 (euclid 32 8 0.1 bar))
(d3 (euclid 16 6 (step (fast 4 phrase) bar)))