Joel K. Pettersson
86879ecca0
Language changes: * Modulator list syntax. Writing two or more lists in direct succession now concatenates their contents. Change log: * 2023-09-05: parser: Use PL close_c to test for expected closing symbol. Reuse new code for "{...}" support, pruning old. * 2023-09-06: "[A...][B...]" -> "[A...B...]" concat, by changing an "if" to a loop. * 2023-09-08: Make current line per-PL, make a later "[...]" sweep work after mods. |
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README.SAU |

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**README.SAU**

**README.SAU**

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). Scopes ------ 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). Keywords -------- 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. Parameters: 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[]" modulator 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 frequency "f" value, in Hz. Starts at 440. .k Key selection for "f" values using note syntax, default C4. Mainly changes the default and relative octave. Can be C, D, E, F, G, A, or B, with or without f (flat) or s (sharp) -- and/or an octave number (0-10) to move the default from a 4-5 range to one of the number to the number plus one. .n A4 tuning frequency in Hz for "f" values using note syntax. Starts at 440. For example, use "S f.n432" for 432 Hz. .s Tuning system, either 'e' (12TET, default), or 'j' (SAU justly intoned, may change). 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, "r(4/3)". 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. "Modulator list" values are supported for PM (phase modulation); see section. A phase percentage value can be set together with a list in one go, the value then going first after the 'p', for example "p0.25[...]". A subparameter can be used instead or in addition for another kind of PM. .f Frequency-amplified PM modulators can be set in a separate list, as in "p.f[...]". See "Modulator list". The sum of all PM 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. "Modulator list" values are supported for panning-AM (stereo placement amplitude modulation); see section. The sum of modulator amplitudes is added to the channel mixing used. (If you downmix the result to mono the effect will disappear.) 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. Parameters: 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: cos Half cosine (S-curve) trajectory over time. lin Linear trajectory over time. sah Sample and hold until time (then jump to goal). exp Steep "exp(x)-1"-like increase or decrease. log Steep "log(x+1)"-like increase or decrease. xpe Exponential shape envelope (saturate or decay). lge Logarithmic shape envelope (saturate or decay). sqe Square polynomial envelope (saturate or decay). cub Cubic polynomial segment (-1 to +1) trajectory. ncl Noise camel line; softer, two noise bulges. nhl Noise hump line; harder, one broad noise bulge. uwh 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. Parameters: 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. sin Sine. For cosine, set phase 'p' to 1/4. tri Triangle. Mellow odd-harmonics wave. Opposite of 'ean' relative to 'par'. srs Square root of sine. (Mirrored for the negative half.) Medium-bright odd-harmonics wave. Opposite of 'cat' relative to 'hsr'. sqr Square. Bright odd-harmonics wave. Opposite of 'eto' relative to 'saw'. ean Evenangle. Mellow even-harmonics wave. Opposite of 'tri' relative to 'par'. To begin at 0.0 amplitude, set phase 'p' to 6/93. cat Catear. Medium-bright even-harmonics wave. Opposite of 'srs' relative to 'hsr'. To begin at 0.0 amplitude, set phase 'p' to 1/16. eto Eventooth. Bright even-harmonics wave. Opposite of 'sqr' relative to 'saw'. par 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. hsr 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. saw Sawtooth. Bright all-harmonics wave. Decreasing slope; use negative amplitude or frequency (but not both) for increasing slope. Between 'sqr' and 'eto'. hsi 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. spa 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. Modulator list: Within "[]", written after the name of a parameter that supports it, signal generators can be included for use with that parameter. For example, for PM the phase parameter 'p' is assigned a list as in "p[...]". It works the same for other parameters such as 'a' (for AM/RM) and 'f' (for FM), and subparameters such as 'a.r', etc. Assigning a list to a parameter will append the new list to any old one, expanding it rather than replacing the old items. Thus "p[]" changes nothing. To clear old items when setting a list, add '-' before the '[', as in "p-[]" (which removes all PM modulators). Lists can be assigned together with other values (numbers) for various parameters. For the whole expression beginning with the parameter name, whitespace can only be placed inside list brackets (or inside parentheses for any numerical expressions). "Value sweep" for a parameter can use the same list as one which contains modulators; the modulators simply need to be listed after any sweep subparameters (see section) which head the list. It's also possible to write multiple lists directly after one another when setting to a parameter (with or without the one leading '-'). These lists will be joined into one, meaning that "[X][Y]" for some contents "X" and "Y" is the same as "[X Y]". This also allows placing sweep subparameters in a later list. 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 only available under those parameter names, e.g. "Frequencies as notes" values. 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 at the start of a "[]" list. For example, "f[g220]" sweeps frequency to 220 Hz over a default time. 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 yet distinct from PM, whenever modulation happens.) Following a parameter name and optionally its main value(s), lists can be used (see "Modulator list") to assign modulators whose amplitudes are simply added to the main value. For example "a0[...]" will set amplitude to 0, and the modulators within "[...]" will have the effect of ring modulating, while with "a1" set the result is AM. 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, lists can be used (see "Modulator list"). Each modulator here produces 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 can be used to switch the top and bottom of the 0.0 to 1.0 range, and is then 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 modulators 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.) Variables: 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.) Numerical expressions for some named parameters can use context-sensitive constants; to allow such when assigning a variable, one of the below parameter namespace letters can be added after the "=", with whitespace and/or a mathematical symbol separating it from any number or name after. For example, "'freq=f A4" has the frequency value of the note "A4". c Channel mixing values f Frequencies as notes p Phase values 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. The "S f.n" option sets the A4 tuning frequency, by default 440 Hz. The tuning system can also be changed using "S f.s". By default, notes use the 12-tone equal temperament system. There is also another option, a just intonation system with 3 times 7 notes (each of the 7 notes having a natural, a flat, and a sharp variation, all of which are distinct). Each note is written with a C, D, E, F, G, A, or B. As a first suffix, an f (flat) or s (sharp) can be added. An octave number (0-10) can be written as a final suffix, e.g. "A5" matches twice the tuning frequency, "Af5" a little below that. With no number, the octave for the note will be relative to the key setting ("S f.k"), and by default 4-5, so that the note for the selected key is also the lowest using the low default octave. Additionally, for microtonal variation an optional subnote prefix can be added (c, d, e, f, g, a, or b) for a position in an "inner octave" between the note otherwise used and the note a capital letter above it. I.e., "cC" is the same as just "C", but "dC" moves up a little notch towards "D", "eC" another little notch, and so on. If the key selected is not C, this small letter scale rotates with it. In just intonation, the frequency increases apply rational fractions. Timing ------ 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'.