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SAU language reference
SAU (Scriptable AUdio) is a simple and non-Turing-complete
language for mathematical audio synthesis,
without support for the use of pre-recorded samples.
The core idea of the language is that of time-ordered steps for
configuring audio generation: add an oscillator, then later,
change a parameter and extend play duration, etc. A script is
basically a list of such timed instructions. Language constructs
also offer more flexible arrangement of steps to take than a
bare flat list of instructions and forward time movement.
The current syntax uses keywords followed by zero or more
parameters with arguments. Each main keyword provides an action,
either at run time (like a function call in other languages),
or at parse time (like a global script setting).
The keywords "W" and "R" are type names, and are used to add instances
of oscillators and rumbly noise generators. They may be used as carriers
and modulators; such objects, the timing of their running, and their
parameters, make the core features of the scripting language.
Keyword parameters may either be set (named, followed by writing
their argument(s)), or left out to use the previous value or a
default value. Some default values can be changed using the "S"
(Script options) parse-time action.
Modifiers are similar to keywords, but simpler and more flexible
in how they may be used. They may or may not be followed by an
argument (e.g. a delay time).
The flow of time and the nesting of scopes are like two dimensions
in which things are arranged. For altering the time-arrangement,
see 'Timing'; that includes sub-steps, which are considered part
of the same larger step involving the same reference to an object.
Beginning a new step, by introducing a new object or new reference
to an object, terminates the previous when done in the same scope.
The global level of a script is a top scope containing objects and
steps for them. Each list ("[...]") is a similar subscope. What is
written for an object inside a list is a step in the inner scope,
with timing connected to the outer scope. Termination of an inner
step does not terminate any outer it is related to (i.e. nesting).
Each of these keywords is further described in its own section below.
S Script options (parameter default value or other);
runs during parsing. Changes made inside a
nested list scope don't apply outside of it.
R Random segments generator -- "R", optionally followed
by the initial "Line types" value, e.g. "Rlin".
W Wave oscillator -- "W", optionally followed
by the initial "Wave types" value, e.g. "Wtri".
S: Script options
Set parameter default value or other option; runs during parsing.
Changes made inside a nested list scope don't apply outside of it.
Usage: "S", followed by zero or more whitespace-separated parameters,
each with a value.
a Multiplier for amplitude "a" values, for the current
scope of "[]" nesting. (The multiplier also applies to
"a.r" values, and to the multiplier in any deeper main
"a[]" modulation list.) If used at the top level, this
disables automatic down-scaling of amplitude per voice
by the number of voices, for manual control instead.
c Default channel mixing "c" value. Starts at 0.0,
i.e. C (center). Useful as a main way of setting
the parameter value.
f Default freqency "f" value, in Hz. Starts at 440.
.n A4 tuning frequency in Hz for "f" values
using note syntax. Starts at 440.
r Default relative frequency "r" value, a
modulator:carrier ratio. Starts at 1 (1/1, a "1:1" ratio).
t Default short definite time "t" value, in seconds.
Default times may be longer (and occasionally shorter)
depending on the context. Starts at 1.0.
Signal generator common parameters
The "R" and "W" types have these parameters in common:
t Time duration in seconds. If no "t" setting is given, the
time set depends on the context.
For a single non-nested generator, 1.0 is used unless
the default value is changed with "S t".
When several generators are specified, the default
time is based on the longest remaining (at the current time)
duration of play in use for any step at the current level,
in considering the surrounding sequence of steps and delays
(up to the next '|' time separator, or to the end of the
script if none).
The default time lengthens further when modulators
with longer definite times are specified for the current step.
For modulator generators, default time is however an
"implicit" time length (see 'i' below), meaning playing
whenever a carrier it is linked to does. (Implicit time is
only supported for nested generators.) When such a time
length is retrieved as part of setting the default time for
something else, a definite default time in seconds (e.g. 1
second) is however used instead.
For a compound step, the first sub-step is however
simply given the "S t" default value if no time is set.
The following sub-steps in turn each have the time of the
previous as its default time. The exception is modulators,
for which the last sub-step has implicit time ('i', "ti")
by default, just like for undivided steps for modulators.
Special non-number literals can also specify time:
d Definite default time can be set using "td", always.
i Implicit time can be set using "ti", for modulators.
f Frequency in Hz. Can be negative to flip wave shape timewise.
"Value sweep" values are supported; see section.
"Modulation with value range" is supported for FM
(frequency modulation); see section. Note that the modulator
lists for "f" and "r" expressions are shared and identical.
r (For modulator generators only.) Relative frequency, a value
which will be multiplied by the frequency of closest carrier
in the chain for the modulator, to give the frequency to use.
For an n:m modulator:carrier frequency ratio, a value of the
form (n/m) may be used; e.g., for a 4:3 frequency ratio,
When using "r" the same values are changed as when
using "f", the difference simply being whether multiplication
by carrier frequency is switched on or off. Specific values
like the main value or the ".r" second value can be set again
under "f" or "r" to toggle just that value.
"Value sweep" values are supported; see section.
"Modulation with value range" is supported for FM
(frequency modulation); see section. Note that the modulator
lists for "f" and "r" expressions are shared and identical.
Note that for FM modulators, the carrier frequency
used as a multiplier is simply the unmodulated value. (If
several types of FM list are set and used at the same time,
the result of earlier stages will be used for later.) For
other kinds of modulation, if FM is done the result is used.
a Amplitude, where 1.0 corresponds to a level of 0dB and
0.0 is silence. (Note that the final output level is scaled
down by the number of voices; alternatively, the S "a" option
can be used to set a multiplier used when adding a top-level
carrier. Panning will further reduce output level unless
fully left or right.) Can be negative to flip sign of result.
"Value sweep" values are supported; see section.
"Modulation with value range" is supported for AM & RM
(amplitude and ring modulation); see section.
p Phase in percentage of the wave cycle modulo 1.0. Set to
reset the phase, e.g. to change the initial value from 0.0.
See "Phase values" for more.
After a value or by itself, "[]" (square brackets)
can be used to set a list of PM modulator generators specified
within the "[]"; the list replaces any previous set, and may
be empty. Also, after these or by itself, ".f[]" (".f" and
square brackets) can likewise set a list of
frequency-amplified PM modulators. This whole larger argument
cannot contain any whitespace outside parentheses or brackets.
The sum of modulator amplitudes will phase-modulate
the carrier(s). For frequency-amplified PM modulators, first
the amplitudes are multiplied by the carrier frequency divided
by 632.45... Hz (the geometric mean of 20 and 20000 Hz).
c (For non-nested generators only.) Channel mixing, mainly
(-1.0) to 1.0. See "Channel mixing values" for more.
"Value sweep" values are supported; see section.
R: Random segments generator
Value noise generator, connecting random values generated at a frequency
with line segments of a selected shape. Two random values are generated
each "cycle", so that the base frequency matches a normal oscillator.
As a signal generator, if not enclosed within a "[]" list, then
it will run and output at the current time, for its duration.
Usage: "R", optionally followed by a line type (e.g. "Rlin"),
by the default the same as "Rcos". Followed by zero or more
whitespace-separated parameters, each with a value. Several
'm' modes are available, for several types of random
distribution, as well as a naive oscillator mode.
See "Line types" for the available line types.
The "seed(x)" mathematical function changes
the starting seed of new "R" instances.
The "R" random segments generator has the
"Signal generator common parameters", and additionally:
l Line type -- see "Line types" for values.
m Mode for line start and goal value variation; consists of
a letter (random function) and a digit (0-9 shaping level);
one or both may be set at a time; the default level is '9'.
Roughly, each level above 0 halves what remains of the
unshaped underlying randomness. The functions are...
r Uniform random (default). Ignores the level setting.
g Gaussian random, soft-saturated approximation. On
average ~6 dB quieter. Ignores the level setting.
b Binary random. Extreme levels, more repetitive runs.
t Ternary smooth random. Never repeats twice in a row;
cycles above or below zero, randomly flips polarity.
f Fixed cycle. Plain naive oscillator at the top level;
below it, mixed with randomness at reduced amplitude.
In addition to the function and level, these flags can be set.
h Half-shape waveform. Use with 'lin' for a decreasing
sawtooth instead of a triangle wave; similarly changes
the shape for all line types and randomness modes.
s Square, then restore sign, of the start/goal values.
Turns uniform value variation into uniform energy
variation; somewhat quieter, and more tremulant.
Doesn't affect 'b', 't', nor 'f' with level '9'.
Distorts 'v' violet noise toward white, as if mixed.
v Violet rather than white noise version of the function
if available; missing for 'g' and 't'. Like high-pass
filtering the lower end of the noise, 6 dB per octave.
z Zig-zag flip. Swap ends of each half-cycle, adding an
inharmonic waveform jaggedness unless using 'h', or
'f' level '9'; more difference from these adds larger
sharp steps. Always flips the waveform top and bottom.
Line types:
Half cosine (S-curve) trajectory over time.
Linear trajectory over time.
Sample and hold until time (then jump to goal).
Steep "exp(x)-1"-like increase or decrease.
Steep "log(x+1)"-like increase or decrease.
Exponential shape envelope (saturate or decay).
Logarithmic shape envelope (saturate or decay).
Square polynomial envelope (saturate or decay).
Cubic polynomial segment (-1 to +1) trajectory.
Noise camel line; softer, two noise bulges.
Noise hump line; harder, one broad noise bulge.
Uniform random white noise in start-goal range.
The 'exp' and 'log' shapes use ear-tuned polynomial
approximations with definite beginnings and ends,
designed to sound natural for frequency sweeping,
and symmetric one to the other. The 'xpe' shape increases
like 'log' and decreases like 'exp', much like a capacitor
charges and discharges, natural-sounding for an envelope;
and 'lge' increases like 'exp' and decreases like 'log'.
For a less-steep alternative to 'xpe', 'sqe' can be used.
The 'cos' shape sounds similar to 'lin', except it has a
smoothly curved start and stop, and a steeper middle.
W: Wave oscillator
Wave oscillator. The sine variety is a fairly typical "FM synth operator".
Producing a (weakly) anti-aliased signal, including for FM/PM, amplitude
can be a little lower for frequencies close to half the sample rate.
As a signal generator, if not enclosed within a "[]" list, then
it will run and output at the current time, for its duration.
Usage: "W", optionally followed by a wave type (e.g. "Wtri"),
by the default the same as "Wsin". Followed by zero or more
whitespace-separated parameters, each with a value.
See "Wave types" for the available wave types.
The "W" wave oscillator has the
"Signal generator common parameters", and additionally:
w Wave type -- see "Wave types" for values.
Wave types:
Beyond 'sin', there's 3 times 3 complementary wave types, in terms
of the added harmonics (odd, even, or all), and mellow vs. bright.
Additionally, there's 2 more, listed after these first 10.
Sine. For cosine, set phase 'p' to 1/4.
Mellow odd-harmonics wave.
Opposite of 'ean' relative to 'par'.
Square root of sine. (Mirrored for the negative half.)
Medium-bright odd-harmonics wave.
Opposite of 'cat' relative to 'hsr'.
Bright odd-harmonics wave.
Opposite of 'eto' relative to 'saw'.
Mellow even-harmonics wave.
Opposite of 'tri' relative to 'par'.
To begin at 0.0 amplitude, set phase 'p' to 6/93.
Medium-bright even-harmonics wave.
Opposite of 'srs' relative to 'hsr'.
To begin at 0.0 amplitude, set phase 'p' to 1/16.
Bright even-harmonics wave.
Opposite of 'sqr' relative to 'saw'.
Parabola. (x^2, steep part up.)
Mellow all-harmonics wave.
Between 'tri' and 'ean'.
To begin at 0.0 amplitude, set phase 'p' to 9/87.
Mellowtooth. (Half-rectified 'srs', amplitude doubled.)
Medium-bright all-harmonics wave.
Between 'srs' and 'cat'.
To begin at 0.0 amplitude, set phase 'p' to 1/25.
Bright all-harmonics wave.
Decreasing slope; use negative amplitude
or frequency (but not both) for increasing slope.
Between 'sqr' and 'eto'.
Half-rectified sine. (Amplitude doubled.)
Like a somewhat louder 'ean', harmonics decreasing as fast.
To begin at 0.0 amplitude, set phase 'p' to 1/12.
Sine parabola. (First half, amplitude doubled.)
Slightly cleaner than 'par'. Mainly useful for modulation.
To begin at 0.0 amplitude, set phase 'p' to -1/12.
Values and expressions
Whitespace is not allowed within multi-character names, keywords or
numbers, and separates values. Spaces and tabs may otherwise be used or
omitted anywhere.
Comment syntax:
"//" (C++-comment) comments out the rest of the line.
"/*" (C-comment) comments out text until the next "*/". Does not nest.
"#!" (Shebang) comments out the rest of the line.
"#Q" (Quit file) comments out the rest of the whole file.
Numerical expressions:
A number can be specified with or without a decimal point;
for a number with a decimal point, a leading zero can be omitted.
Number signs and arithmetic operation symbols can be used in infix
expressions, together with numbers and named constants, variables,
and functions. But unless something is written within parentheses,
it cannot contain any whitespace, as it ends the expression. For
example, "-1" is fine, but "- 1" is a dangling minus followed by
a dangling number 1, if not inside parentheses as "(- 1)".
The following operations are recognized, and grouped below by
priority (nested parentheses can be used to change evaluation order):
^ To the power of (right-associative)
* / % Multiplication, division, remainder
+ - Addition, subtraction
Parentheses also allow shorthand multiplication (leaving out a
"*" between two parts), e.g. "2(3)" and "(2)3" both give "6".
Some parameters support named constants specific to that type
of value; such a name can be written instead of a number.
The following universal mathematical symbols (functions and
constants) can also be used in any numerical expression; functions
require parentheses after the name (and most often require a value
inside), while constants are simply written as names:
abs(x) Absolute value.
cos(x) Cosine of value.
exp(x) Base-e exponential value.
log(x) Natural logarithmic value.
met(x) Metallic value, e.g. "met(1)" gives the golden ratio.
Positive integers give the series of metallic ratios.
Other values are also allowed: fractional, 0 giving 1
and negative (gives how much the positive value would
be increased, approaching zero further from zero).
Note that met(-x) is also equal to (1/met(x)).
mf 632.45... (Geometric mean of 20 and 20000.)
pi 3.1415...
rand() Pseudo-random number in range 0-1. The value sequence
from a series of calls restarts each new script unit.
rint(x) Round value to the nearest integer. Halfway cases are
rounded to the nearest even integer.
seed(x) Reset the rand() value sequence with a passed number.
(Every bit counts; different expressions for the same
number, with e.g. rounding may give different seeds.)
Returns 0 so that e.g. "/seed(100)" will only reseed.
sin(x) Sine of value.
sqrt(x) Square root.
time() Get a system timestamp number changed each second.
It can be used for seeding in a randomized script.
(Note that the exact value is platform-dependent.)
If disabled (deterministic mode), instead gives 0.
Channel mixing values:
Panning, where 0.0 is centered. Named constants can be used in place
of numbers for the three classic channel "modes". Values outside the
range of L to R are allowed, amplifying one channel while giving the
other a negative amplitude.
C 0.0
L (-1.0)
R 1.0
Phase values:
Phase offset as a percentage of the wave cycle. Any value will be used
modulo 1.0. For example, (1/4) turns sine into cosine. Named constants
provide scaled angles which can be used in expressions, e.g. (G*n) for
some whole number n makes for the nth leaf-around-a-stem angle.
G 0.3819... (golden angle as cycle percentage)
Value sweep:
To sweep a parameter which supports sweep subparameters towards a
goal value -- the ordinary value being the start for a trajectory --
following the ordinary value or by itself, the following value sweep
subparameters can be given values within "{}" (curly brackets):
g Goal (go-to) value, assigned to the parameter after time.
This value has no default and must be provided. If changed
again before the full time, the current point reached on the
previous trajectory will be used to change the start value.
l Line fill shape (default 'lin', or the previous shape if any)
-- see "Line types" for values.
t Time to reach goal (default is the external "t" duration,
or the remaining previous time, if any, for this parameter).
If longer than the active time for the object which has the
swept parameter, the trajectory will be left unfinished.
v Start (state) value, the ordinary parameter value.
It can alternatively be set here after a 'v',
if not set before the enclosing "{}".
Modulation with value range:
Amplitude ("a"), frequency ("f"), and relative frequency ("r")
parameters all support modulation of the parameter values in the
same ways. For amplitude, whether the result is called amplitude
modulation (AM), or ring modulation (RM), depends on how carrier
and modulator amplitude are set up relative to one another. (For
frequency modulation, the result is however always the "real FM"
related to PM, yet distinct from it, whenever modulation happens.)
Following a parameter name and optionally its main value(s),
"[]" (square brackets) can be used to set a list of modulators whose
amplitudes are simply added to the main value. For example "a0[...]"
will set amplitude to 0 and then modulators within "[...]" will have
the effect of ring modulating, while with "a1" set the result is AM.
A new list if set, even if empty, will replace the previous one set.
A subparameter can be used instead or in addition, to set up
modulation in a complementary way (the whole larger argument, for
example "f200.r(200 * 2)[...]", cannot contain any whitespace
outside of parentheses or brackets):
.r Following a main parameter name and optionally the things
mentioned above, under ".r" a subparameter with a second
value can be set. This second value is the other boundary
for a range to which modulator amplitudes can be mapped;
it has no other uses, and defaults to 0.0. "Value sweep" is
also supported for this subparameter whenever for the main.
After a value or by itself, "[]" (square brackets)
can be used to set a list of modulators. Each modulator in
this list will produce a result in the range of 0.0 to 1.0,
i.e. a positive signal, multiplied by its amplitude (with
a default of 1.0). However, a negative amplitude multiplier
will switch the top and bottom of the 0.0 to 1.0 range, and
then be used as if positive.
When several modulators are used for this, their
outputs are multiplied. The product of outputs is mapped to
a range where 0.0 is matched to the main value, and 1.0 to
the second. Using more mdoulators thus adds a bias towards
the main value. Furthermore, changing amplitude multipliers
for modulators from the default can change the range.
To use this for classic 100% modulation depth AM,
one of the bounds should be 0.0 (like the default for the
second value); while for classic RM, the two bounds should
have the same magnitude, but with opposite sign.
If this type of modulation is used, it is done first
and the output from the other, main additive modulator list
is then added to the result.
Parameters and object binding:
When specifying or referencing objects within "@[...]", any
parameters set following the closing ']' will be bound to and apply
to all of them.
Significantly, this allows multiple carriers (given within
the []) to be linked to the same modulator(s), whether for FM, PM,
or AM/RM. (Note: Support for this is experimental and incomplete.)
A named variable can be assigned by writing an expression beginning
with "'name", where the "name" is a case-sensitive string with
alphanumeric characters and/or '_'. Variables are dynamically typed,
can be assigned several times, and can either be assigned to a number
or made to point to an object as a label for it.
To assign a number, "'name=" can be written just before a
numerical expression. Once it holds a number, it can be used in any
numerical expression using "$name". (It's possible to use such a
variable value as part of redefining its value.)
To point a variable to an object, "'name " can be written
just before an object is added or referenced. The name can then be
used to refer back to the object as "@name", to start a new step for
the object anywhere later in the script.
A new "@name" step differs in not automatically setting a new
time duration for the object, so "t" (see "Parameters") or other
time-altering syntax (see "Timing") must be used in order for the
old time duration value to be changed.
Note that a "@name" reference placed in a nesting scope
different from the original (e.g. outside a list, or in a new list)
does not move the object into the new nesting scope. It will not be
added to, nor removed from, any list by being referenced anywhere.
The time scope is however new and of the reference.
Frequencies as notes:
Frequency values may be specified as notes. Currently, justly
intoned C-major scale is supported; "S n" sets the A4 tuning
(default 440 Hz).
The value consists of the note (C, D, E, F, G, A or B),
optionally given a prefix and/or suffix. The prefix is an optional
subnote (c, d, e, f, g, a or b) inside an inner octave (between
note and next note). The suffix is an optional s (sharp) or
f (flat), and/or, in the last position, an octave number
(from 0-10, default 4).
Timing modifiers:
| Time separator. Delays all that follows by the duration of
prior steps. This also resets any other delays to be added
to later steps using other syntax like '/', so such should
be placed after, not before, if it is to take effect.
/number Forward shift, time in seconds. Delay the next step and
all steps placed after. The next step can be either a
split-out continuation of the current step, or new.
Does not automatically extend time duration on
splitting a step, unlike ';'.
Compound steps:
For a step written for some object, timing can be changed locally,
within only the step and for lists nested under it. Two varieties
of the ';' sub-step separator allow this. Their use can be repeated.
; The numberless ';' step split can be written after a step for
an object (on a new line or the same), to specify a new time
duration and new parameter arguments which apply just after
the previous time duration. The new duration generally has
the length of the previous by default. (For the default time
of the first sub-step, and special handling for the last, see
"t" under each "Parameters" for more).
The time handling is designed to simplify writing a
sequence of connected, non-overlapping timed updates for a
single object. For example (three frequencies, one a second):
"Wsin f100 t1; f200; f300". Changing "t1" in this example
changes the time length for all three parts.
For more flexibility, especially for adding "silent"
gaps between parts, the numberless ';' can be combined with,
or replaced by, the ';number' gapshift. Combination is easy,
as "; ;number" will subdivide and shift the second sub-step
by "number" of seconds, and move the active time duration for
the second sub-step past the second split, creating a gap
"number" of seconds long. For example (1 second of silence
between frequency changes): "Wsin f100 t1;;1 f200;;1 f300".
;number Gapshift, time in seconds. When a number immediately follows
the ';', then the new sub-step is placed in time that number
of seconds after the previous, instead of after the duration
of the previous. Depending on usage, may move, alternatively
extend, the current sound in time.
For ease of adding silent time padding, before the
";number" part (but not after it) the default time duration
is changed to 0, so that any time value automatically set
there will be 0. After the ";number" part, a time value is
always set, the last "t" or default (before zeroing) value.
Several uses of ';number' to separate sub-steps in
a row (no numberless ';' in-between!) will never zero the
default time after the first ';number', allowing a way to
always extend rather than move by adding a leading ';0'.