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-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
-
-<HTML>
- <HEAD>
- <TITLE>Pd Documentation 2</TITLE>
- <meta http-equiv="Content-Type" content="text/html">
- <link rel="stylesheet" type="text/css" href="pdmanual.css" media="screen">
- </HEAD>
-
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-<BODY>
-
-<H2>Pd Documentation chapter 2: theory of operation</H2>
-
-<P>
-<A href="index.htm#s2"> back to table of contents</A>
-<BR><BR>
-</P>
-
-<P>
-
-<P> The purpose of this chapter is to describe Pd's design and how it is
-supposed to work. Practical details about how to obtain, install, and run Pd
-are described in the next chapter. To learn digital audio processing basics
-such as how to generate time-varying sounds that don't click or fold over, try
-the on-line book,
-<A HREF="http://www.crca.ucsd.edu/~msp/techniques.htm"
-<I> Theory and Techniques of Electronic Music </I>.
-
-<H3> <A name=s1> 2.1 overview </A> </H3>
-
-<P>Pd is a real-time graphical programming environment for audio and graphical
-processing. It resembles the Max/MSP system but is much simpler and more
-portable; also Pd has two features not (yet) showing up in Max/MSP: first,
-via Mark Dank's GEM package, Pd can be used for simultaneous computer
-animation and computer audio. Second, an experimental facility is provided
-for defining and accessing data structures.
-
-<H3> <A name=s1.1> 2.1.1. the main window, canvases, and printout </A> </H3>
-
-<P>When Pd is running, you'll see a main "Pd" window, and possibly one or more
-"canvases" or "patches". The main Pd window looks like this:
-
-<CENTER><P>
- <IMG src="fig1.1.png" ALT="pd window">
-</P></CENTER>
-
-<P> There are peak level and clip indicators for audio input and output; these
-report peak levels over all input and all output channels. Note that DC
-shows up as an input level; many cards have DC levels which show up in the
-50s. To see an RMS audio level, select "test audio and MIDI" from the Media
-menu. The main window display is intended only to help you avoid clipping
-on input and output. You can turn the peak meters on and off using the
-control at lower left.
-
-<P> At lower right is a control to turn audio processing on and off
-globally. Turning audio off stops the computation and relinquishes any audio
-devices Pd is using. The "Media" menu is also provided, with accelerators
-"Control-." to turn audio computation off and "Control-/" to turn it on. When
-audio is on, Pd is computing audio samples in real time according to whatever
-patches you have open (whether they are visible or not).
-
-<P> The DIO (Digital I/O) error indicator flashes if there is a synchronization
-error for audio input or output. (But note that on some platforms Pd doesn't
-find out about them. If you never see red, you're probably not seeing the
-truth.)
-Click the "DIO errors" button to see a list of recent errors.
-This indicator should turn red whenever the
-computation runs late (so that the DAC FIFOs fill and/or the ADC FIFOs empty)
-or if audio input and output are not running at the same rate. See
-<a href="x3.htm#s2"> audio and MIDI support </A>.
-
-<P> The bottom part of the Pd window is an area for printout from objects in
-patches, and/or for messages from Pd itself.
-
-<P> Pd documents are called "patches" or "canvases."
-Each open document has one main window and any number of
-sub-windows. The sub-windows can be opened and closed but are always running
-whether you can see them or not. Here is a simple Pd patch:
-
-<CENTER><P>
- <IMG src="fig1.2.jpg" ALT="hello world patch">
-</P></CENTER>
-
-<P>There are four <I> text boxes </I> in this patch: a number box (showing zero),
-an object box showing "print," and two comments. The number box and the object
-box are connected, the number box's output to the print box's input. Boxes may
-have zero or more inputs and/or outputs, with the inputs on top and the outputs
-on bottom.
-
-<P>
-Pd's printout appears on the main ``Pd" window,
-unless you redirect it elsewhere.
-
-<H3> <A name="s1.2"> 2.1.2. object boxes </A> </H3>
-<P> Pd patches can have four types of boxes: <I> object, message, GUI, </I>
-and <I> comment </I>.
-
-<P> You make <I> objects </I> by typing text into object boxes. The text is
-divided into <I> atoms </I> separated by white space. The first atom specifies
-what type of object Pd will make, and the other atoms, called <I> creation
-arguments </I>, tell Pd how to initialize the object. If you type for example,
-
-<CENTER><P>
- <IMG src="fig1.3.jpg" ALT="object">
-</P></CENTER>
-
-<P>the "+" specifies the <I> class </I> of the object.
-In this case the object will be the kind that carries out addition,
-and the "13" initializes the amount to add.
-
-<P> Atoms are either numbers or <I>
-symbols </I> like "+". Anything that is not a valid number os considered a
-symbol. Valid numbers may or may not have a decimal point (for instance, 12,
-15.6, -.456), or may be
-written in exponential notation (such as "4.5e6", which means "4.5 multiplied
-by 10 six times, i.e., 4500000). Negative exponentials divide by 10 (so
-that 1.23e-5 comes to 0.0000123).
-
-<P> Non-valid numbers which are read as symbols
-include things like "+5" and "0..6" as well as words and names such as "Zack"
-or "cat". The symbols "gore", "Gore", and "GORE" are all distinct.
-
-<P> The text you type into an object box determines how
-many and what kinds of inlets and outlets the object will have. Some
-classes (like "+" always have a fixed arrangement of inlets and outlets,
-and in the case of other classes, the inlets and outlets will depend on the
-creation arguments.
-
-<P>Here for example is a simple MIDI synthesizer:
-
-<CENTER><P>
- <IMG src="fig1.4.png" ALT="simple MIDI synthesizer">
-</P></CENTER>
-
-<P>This patch mixes <I> control </I> objects (notein, stripnote, and ftom) with
-<I> tilde </I> objects osc~, *~, and dac~. The control objects carry out their
-function sporadically, as a result of one or more type of <I> event </I>. In
-this case, incoming MIDI note messages set off the control computation. The
-result of the computation is, when the note happens to be a "note on" (and not
-a "note off", to compute the frequency in cycles per second and pass it on to
-the oscillator ("osc~").
-
-<P> The second half of the patch, the osc~, *~, and dac~ objects, compute audio
-samples, in the same way as an analog synthesizer works. The osc~ object is
-acting as the interface between the two regimes, in that it takes control
-messages to set its frequency but talks to "*~" using an audio signal. Audio
-signals aren't sporadic; they are continuous streams of numbers. As a result
-tilde objects act under very different rules from control objects. The audio
-portion of the patch is always running, whether MIDI messages arrive or not. On
-the other hand, the function of control computations is to insert calculations
-between the audio computation which may change audio computation parameters
-such as the frequency of an oscillator.
-
-<P> The connections in the patch (the lines between the boxes) are also of two
-types: control and signal. The type of connection depends on the outlet it
-comes from. Signal connections are represented by thicker lines than control
-connections; in the patch above, the two bottom conections are signal and the
-others are control. In general, a control connection may be made to a signal
-inlet; if numbers are sent over it they are automatially converted to
-signals. Signal connections may not be made to control inlets; some sort
-of explicit conversion must be specified.
-
-<H3> <A name="s1.3"> 2.1.3. message and GUI boxes </A> </H3>
-
-<P>The border of a box tells you how its text is interpreted and how the box
-functions. Object boxes (as in the previous example) use the text to create
-objects when you load a patch or type text onto a new one. If you retype the
-text in an object box, the old one is discarded and a new one is created, using
-the new creation arguments. The contents of an object box describe a message
-which is sent to Pd to create the object.
-
-<P> <I> Message </I> boxes interpret the text as a message to send whenever
-the box is activated (by an incoming message or with the mouse.) The message
-may be sent many times while the patch is running (as opposed to object boxes
-whose message is used once to create the object). Instead of going straight
-to Pd, the message box's message (or messages) go either to the box's outlet
-or to other specified receiving objects. In the example
-below, the message box, when clicked, sends the message "21" to an object
-box which adds 13 to it.
-
-<CENTER><P>
- <IMG src="fig1.5.jpg" ALT="[message( --> [object] -> [number]">
-</P></CENTER>
-
-<P> The third box shown is a <I> GUI </I> ("graphical user interface") box. GUI
-boxes come in many forms including number boxes (as in this example), toggles,
-sliders, and so on. Whereas the appearance of an object or message box is
-static when a patch is running, a number box's contents (the text) changes to
-reflect the current value held by the box. You can also use a number box as a
-control by clicking and dragging up and down, or by typing values in it.
-(There are also shift- and alt-click actions; see <A href="x2.htm#s2.7">
-getting help </A> to find out how to look this up).
-
-<P> You can also create a "symbol" box which is like a number box but deals
-in symbols like "cat." You can type your own strings in (followed by "enter")
-or use it to display strings which arrive as messages to its inlet.
-
-<H3> <A name="s1.4"> 2.1.4. patches and files </A> </H3>
-
-<P>When you save a patch to a file, Pd doesn't save the entire state of all the
-objects in the patch, but only what you see: the objects' creation arguments
-and their interconnections. Certain data-storage objects have functions for
-reading and writing other files to save and restore their internal state.
-
-<P>Pd finds files using a <I> path </I> which can be specified as part of Pd's
-startup arguments. The path specifies one or more directories, separated by
-colons (semicolons if you're using windows.) Most objects which can read files
-search for them along the search path, but when Pd writes files they go to
-the directory where the patch was found.
-
-<H3> <A name=s2> 2.2. editing Pd patches </A> </H3>
-
-<H3> <A name=s2.1> 2.2.1. edit and run mode </A> </H3>
-
-<P> A patch can be in edit or run mode; this really only affects how mouse
-clicks affect the patch. In edit mode, clicking and dragging selects and
-moves boxes or makes and cuts connections; in run mode clicking on boxes sends
-them messages which they react to in different ways. In run mode, number and
-message boxes can be used as controls. Normally, when you are in a performance
-you will stay in run mode; to change the patch you go to edit mode.
-
-<H3> <A name=s2.2> 2.2.2. creating boxes </A> </H3>
-
-<P> You can create boxes (objects, messages, GUIs, and comments) using the
-"put" menu. Note the handy accelerators. Object and message boxes are empty
-at first; drag them where you want them and type in the text. The GUI
-objects (which come in several flavors) require no typing; just create and
-place them.
-
-<P> You will often find it more convenient to select a box and "duplicate" it
-(in the Edit menu) than to use the "Put" menu. If you select and duplicate
-several items, any connections between them will be duplicated as well.
-
-<H3> <A name=s2.3> 2.2.3. the selection </A> </H3>
-
-<P>Boxes in a Pd window may be selected by clicking on them. To select more
-than one object you may use shift-click or click on a blank portion of
-the window and drag the cursor to select all objects within a rectangle.
-
-<P>Clicking on an unselected object, message, or comment box makes the text
-active, i.e., ready to be text edited. (If you select using the rectangle
-method, the text isn't activated.) Once you've activated a text box, you
-may type into it (replacing the selected text) or use the mouse to change the
-selection.
-
-<P> You may also select a single connection (patch cord) by clicking on it.
-You can't have connections and boxes selected simultaneously.
-
-<H3> <A name=s2.4> 2.2.4. deleting, cutting, and pasting </A> </H3>
-
-<P>If you select a box, a connection, or several boxes, and if you haven't made
-any text active, you can "delete" the selection by hitting the backspace or
-delete key. You can also "cut" "copy" and "paste" using menu items. Notice
-that pasting puts the new object(s) right down on top of the old ones.
-
-<P>The "duplicate" menu item performs a copy and paste with a small offset so you
-can see the new boxes. You can drag them together to a new place on the screen.
-
-<P>You can cut and paste between windows within Pd but cut/paste isn't
-integrated with the OS in any way. Cut/copy/paste for activated text in boxes
-isn't implemented yet, although in Linux and Irix at least you can "X-paste"
-into and out of "text" dialogs (created with the "edit text" menu item.)
-
-<H3> <A name=s2.5> 2.2.5. changing the text </A> </H3>
-
-<P> To change a text item, you can select it and then edit the text. If you
-only click once, the entire text is selected and your typing will replace
-everything. Click again and drag to select a portion of the text to retype.
-
-<P> If there's
-more than a small amount of text (in a comment, for example) you might want to
-select the text and choose "text editor" from the Edit menu, which opens a text
-editing window with a copy of the text in it. Hitting "send" in that window is
-exactly equivalent to retyping the text into Pd; you can send it to more than
-one box in sequence if you want.
-
-<P> If you click a box and move the mouse without releasing the button this
-displaces the entire box. If you wish to displace a box which is already
-selected, first de-select the box by clicking outside it; otherwise you will be
-selecting text instead of moving the box.
-
-<P> <I> The updated text only becomes part of the patch when you de-select the
-object. </I> Changing the text in an "object" box deletes the old
-object and creates a new one; the internal state of the old one is lost.
-
-<H3> <A name=s2.6> 2.2.6. connecting and disconnecting boxes </A> </H3>
-
-<P>To make a connection between two boxes, click on any outlet of the first
-one, drag toward an inlet of the second one, and release. You can
-release the mouse button anywhere within the target object and the connection
-will be made to the nearest inlet.
-
-<P>Connections are broken by selecting them and using "cut" or the backspace
-or delete key.
-
-<H3> <A name=s2.7> 2.2.7. popup menu for properties, open, and help </A> </H3>
-
-<P> All the "clicking" mentioned above is done with the left mouse button.
-The right button, instead, gives a popup menu offering "properties," "open,"
-and "help".
-(For Macintosh users who may only have one button on their mouse,
-double-clicking is mapped to right-click.)
-
-<P> Selecting "help" on an object gets
-a Pd patch that demonstrates how to use it. "Help" for the canvas as a whole
-(right-clicking outside any object) gives a list of all built-in objects.
-
-<P> The "open" menu item is only enabled if you right-click on a subpatch
-(see below) and causes Pd to open it. Ordinary subpatches may also be opened
-by clicking on them, but for "graph-on-parent" ones, this is the only way to
-do it.
-
-<P> The "properties" dialog allows you to change certain settings of GUI
-objects, or of the patch itself (by clicking outside any box.)
-
-<H3> <A name=s2.7> 2.2.8. miscellaneous </A> </H3>
-
-<P> Control-q "quits" Pd, but asks you to comfirm the quit. To quit without
-having to confirm, use command-shift-Q.
-
-<H3> <A name="s3"> 2.3. messages </A> </H3>
-
-<P> In Pd, objects intercommunicate by sending messages and/or audio signals.
-Pd messages are sporadic, like MIDI messages or music N "Note cards."
-
-<H3> <A name="s3.1"> 2.3.1. anatomy of a message </A> </H3>
-
-<P>Messages contain a selector followed by
-any number of arguments. The selector is a symbol, which appears in the patch
-as a non-numeric string with no white space, semicolons, or commas. The
-arguments may be symbols or numbers. Numbers in Pd are kept in 32-bit floating
-point, so that they can represent integers exactly between -8388608 and
-8388608. (In Max, there are separate data types for integers and floating
-point numbers; Pd uses only float.)
-
-<P> When a message is passed to something (which is often an inlet of a box
-but could be anything that can receive a message), the selector of the message
-is checked against the receiver. If the receiver recognizes messages of that
-selector, it carries out some corresponding action. For instance, here is a
-"float" object:
-
-<CENTER><P>
- <IMG src="fig3.1.jpg" ALT="float object">
-</P></CENTER>
-
-<P> The two rectangles at the top are usually both called "inlets" but
-the one at the left directs incoming messages to the "float" object itself,
-whereas the one at the right directs messages to an auxiliary "inlet"
-object. The float object proper (represented by the left-hand inlet) accepts
-messages with selector "float" and "bang". The right-hand inlet takes only
-the message selector "float". These two selectors, along with "symbol" and
-"list", are usually used to denote an object's main action, whatever it may be,
-so that objects can be interconnected with maximum flexibility.
-
-<P> It is possible to type messages which start with a number,
-which cannot be used as a selector. A single number is always given the
-"float" selector automatically, and a message with a number followed by other
-arguments is given the selector "list".
-
-<H3> <A name="s3.2"> 2.3.2. depth first message passing </A> </H3>
-
-<P> In Pd whenever a message is initiated, the receiver may then send out
-further messages in turn, and the receivers of those messages can send yet
-others. So each message sets off a tree of consequent messages. This tree is
-executed in depth first fashion. For instance in the patch below:
-
-<CENTER><P>
- <IMG src="fig3.2.jpg" ALT="depth first message passing">
-</P></CENTER>
-
-<P> the order of arrival of messages is either A-B-C-D or A-C-D-B. The "C"
-message is not done until the "D" one is also, and the "A" is not done until
-all four are. It is indeterminate which of "B" or "C" is done first; this
-depends on what order you made the connections in (in Max, it's automatically
-sorted right to left).
-
-<P> Message-passing can give rise to infinite loops of the sort shown here:
-
-<CENTER><P>
- <IMG src="fig3.3.jpg" ALT="infinite message passing loop">
-</P></CENTER>
-
-<P> Here the left-hand "+" can't finish processing until the right-hand one has
-been sent the result "2", which can't finish processing that until the
-left-hand one has been sent "3", and so on. Pd will print an error message
-reporting a "stack overflow" if this happens.
-
-<P> However, it is legal to make a loop if there is a "delay" object somewhere
-in it. When the "delay" receives a message it schedules a message for the
-future (even if the time delay is 0) and is then "finished;" Pd's internal
-scheduler will wake the delay back up later.
-
-<H3> <A name="s3.3">
-2.3.3. hot and cold inlets and right to left outlet order </A> </H3>
-
-<P> With few exceptions (notably "timer"), objects treat their leftmost
-inlet as "hot" in the sense that messages to left inlets can result in output
-messages. So the following is a legal (and reasonable) loop construct:
-
-<CENTER><P>
- <IMG src="fig3.4.jpg" ALT="hot and cold inlets">
-</P></CENTER>
-
-<P>Here the "f" is an abbreviation for "float". Note that the "+ 1" output is
-connected to the right-hand inlet of "f". This "cold" inlet merely stores the
-value for the next time the "f" is sent the "bang" message.
-
-<P>It is frequently desirable to send messages to two or more inlets of an object
-to specify its action. For instance, you can use "+" to add two numbers; but
-to do it correctly you must make sure the right hand inlet gets its value
-first. Otherwise, when the left hand side value comes in, "+" will carry out
-the addition (since the left hand inlet is the "hot" one) and will add this
-value to whatever was previously sitting in the right hand inlet.
-
-<P> Problems can arise when a single outlet is connected (either directly or
-through arbitrarily long chains of message passing) to different inlets of a
-single object. In this case it is indeterminate which order the two inlets will
-receive their messages. Suppose for example you wish to use "+" to double a
-number. The following is incorrect:
-
-<CENTER><P>
- <IMG src="fig3.5.jpg" ALT="incorrect inlet connection">
-</P></CENTER>
-
-<P> Here, I connected the left inlet before connecting the right hand one (although
-this is not evident in the appearance of the patch.) The "+" thus adds the
-new input (at left) to the previous input (at right).
-
-<P> The "trigger" object, abbreviated "t", can be used to split out connections
-from a single outlet in a determinate order. By convention, all objects in Pd,
-when sending messages out more than one outlet, do so from right to left. If
-you connect these to inlets of a second object without crossing wires, the
-second object will get its leftmost inlet last, which is usually what you
-want. Here is how to use "trigger" to disambiguate the previous example:
-
-<CENTER><P>
- <IMG src="fig3.6.jpg" ALT="trigger to disambiguate">
-</P></CENTER>
-
-<P> "Cold" (non-leftmost) inlets are almost universally used to store single
-values (either numbers or symbols.) With the exception of "line" and "line~",
-these values are "sticky," i.e., once you set the value it is good until the
-next time you set it. (The "line" exception is for sanity's sake.)
-
-<P> One more question sometimes comes up in execution order, which is
-the order in which two messages are sent to a single "cold" inlet. In this
-situation, since the messages are merged, the last value to be received is
-the value that is used in the computation.
-
-<H3> <A name="s3.4"> 2.3.4. message boxes </A> </H3>
-
-Message boxes are text boxes in which you type a message. When the message
-box is activated, either by clicking on it or sending something to its inlet,
-the message or messages are sent, either to the message box's outlet or
-elsewhere as specified.
-
-<CENTER><P>
- <IMG src="fig3.7.jpg" ALT="message boxes">
-</P></CENTER>
-
-<P>The first of the message boxes above contains the single number 1.5; this
-message has an implicit selector of "float." The second is a list with three
-numbers in it, and in the third, the selector is "my" and the two arguments are
-the number 5 and the symbol "toes."
-
-<P> Multiple messages may be separated by commas as shown:
-
-<CENTER><P>
- <IMG src="fig3.8.jpg" ALT="multiple messages in one box">
-</P></CENTER>
-
-<P>Here the three messages are the numbers 1, 2, and 3, and they are sent in
-sequence (with no intervening time between them, as with the "trigger" object,
-and having depth-first consequences so that whatever chain of actions depending
-on "1" takes place before anything depending on "2" and so on.)
-
-<P> Semicolons may also separate messages. A message following a semicolon must
-specify a symbol giving a destination (in other words, semicolons are like
-commas except that they clear the "current destination"
-so that the next message specifies a new one). The "current destination" is
-at first the message box's own outlet. In the example below, the leading
-semicolon immediately redirects messages from the outlet to an object named
-"fred" (which is here a receive object), and likewise the next message is sent
-to "sue."
-
-
-<CENTER><P>
- <IMG src="fig3.9.jpg" ALT="semicolons to send messages">
-</P></CENTER>
-
-<P>Certain other objects (Pd windows, for example, and arrays) have Pd names and
-can be sent messages this way. Also, the special object "pd" is defined to
-which you may send messages to start and stop DSP.
-
-<P> You can put variables in message boxes as shown below:
-
-<CENTER><P>
- <IMG src="fig3.10.jpg" ALT="variables in message boxes">
-</P></CENTER>
-
-<P>Here, "$1", etc., refer to the arguments of the arriving message (and aren't
-defined if you send a "bang" message or if you click on the message box to
-activate it.) Dollar sign variables are either numbers or symbols depending
-on the incoming message; if symbols, you may even use them to specify variable
-message selectors or destinations.
-
-<H3> <A name="s4"> 2.4. audio signals </A> </H3>
-
-<P>
-Using Pd you can build audio patches which can synthesize musical sounds,
-analyze incoming sounds, process incoming sounds to produce transformed
-audio outputs, or integrate audio processing with other media. This section
-describes how Pd treats audio signals.
-
-<H3> <A name="s4.1"> 2.4.1. sample rate and format </A> </H3>
-
-<P>
-Pd's audio signals are internally kept as 32-bit floating point numbers, so
-you have all the dynamic range you could want. However, depending on your
-hardware, audio I/O is usually limited to 16 or 24 bits. Inputs all appear
-between the values of -1 and 1; and output values will be clipped to that range.
-Pd assumes a sample rate of 44100 unless you override this (
-in Pd's command line or in the "audio setup" dialog).
-
-<P>
-Pd can read or write samples to files either in 16-bit or 24-bit fixed point
-or in 32-bit floating point, in WAV, AIFF, or AU format, via the soundfiler,
-readsf, and writesf objects.
-
-<H3> <A name="s4.2"> 2.4.2. tilde objects and audio connections </A> </H3>
-
-<P>Audio computations in Pd are carried out by "tilde objects" such as "osc~"
-whose names conventionally end in a tilde character to warn you what they
-are. Tilde objects can intercommunicate via audio connections. When audio
-computation is turned on, or when you change the audio network while audio is
-on, Pd sorts all the tilde objects into a linear order for running; then this
-linear list is run down in blocks of 64 samples each; at 44100 Hz. this means
-the audio network runs every 1.45 milliseconds.
-
-<P> Inlets or outlets are configured in Pd either for messages or audio; it's
-an error to connect an audio outlet to a non-audio inlet or vice versa; usually
-these errors are detected at "sort time" when audio is started or the network
-changed with audio running. An object's leftmost inlet may accept both audio
-and messages; any other inlet is either one or the other.
-
-<P>
-The audio network, that is, the tilde objects and their interconnections,
-must be acyclic. If there are loops, you will see the error message at "sort
-time." When errors are reported at sort time there is no easy way to
-find the source of the error. You can build algorithms with feedback using
-nonlocal signal connections.
-
-<P>
-Your subpatches can have audio inlets and outlets via the inlet~ and outlet~
-objects.
-
-<H3> <A name=s4.3> 2.4.3. converting audio to and from messages </A> </H3>
-
-<P> If you want to use a control value as a signal, you can use the sig~ object
-to convert it. The +~, -~, *~, /~, osc~, and phasor~ objects can be configured
-to take control or signal inputs.
-
-<P> The other direction, signal to control, requires that you specify at what
-moments you want the signal sampled. This is handled by the snapshot~ object,
-but you can also sample a signal with tabwrite~ and then get access it via
-tabread or tabread4 (note the missing tildes!). There are also analysis
-objects, the simplest of which is "env~", the envelope follower.
-
-<H3> <A name=s4.4> 2.4.4. switching and blocking </A> </H3>
-
-<P>You can use the switch~ or block~ objects to turn portions of your audio
-computation on and off and to control the block size of computation. There
-may be only one switch~ or block~ object in any window; it acts on the entire
-window and all of its subwindows, which may still have their own nested
-switch~/block~ objects. Switch~ and block~ take a block size and an overlap
-factor as arguments; so for instance, "block~ 1024 4" specifies 1024 sample
-blocks, overlapped by a factor of 4 relative to the parent window. Switch~
-carries a small computational overhead in addition to whatever overhead is
-associated with changing the block size.
-
-<P> Larger block sizes than 64 should result in small increases in run-time
-efficiency. Also, the fft~ and related objects operate on blocks so that
-setting the block size also sets the number of FFT channels. You may wish
-to use block sizes smaller than 64 to gain finer resolutions of message/audio
-interaction, or to reduce "block delay" in feedback algorithms. At the
-(untested) extreme, setting the block size to one allows you to write your
-own recursive filters.
-
-<P> You can use switch~ to budget your DSP computations; for instance you might
-want to be able to switch between two synthesis algorithms. To do this, put
-each algorithm in its own subpatch (which can have sub-sub patches in turn, for
-a voice bank for instance), and switch each one off as you switch the other one
-on. Beware of clicks; if you have a line~ controlling output level, give it
-time to ramp to zero before you switch it off or it will be stuck at a nonzero
-value for the next time it comes back on.
-
-<P> When a subpatch is switched off its audio outputs generate zeros; this
-costs a fairly small overhead; a cheaper way to get outputs is to use throw~
-inside the switched module and catch~ outside it.
-
-<H3> <A name=s4.5> 2.4.5. nonlocal signal connections </A> </H3>
-
-<P>You may wish to pass signals non-locally, either to get from one window to another, or
-to feed a signal back to your algorithm's input. This can be done using
-throw~/catch~, send~/receive~, or delwrite~/delread~ pairs. Throw~ and catch~
-implement a summing bus; throw~ adds into the bus and catch~ reads out the
-accumulated signal and zeros the bus for the next time around. There can be
-many throw~ objects associated with a single catch~, but a throw~ can't talk to
-more than one catch~. You can reset the destination of a throw~ if you want to.
-
-<P> Send~ just saves a signal which may then be receive~d any number of times; but
-a receive~ can only pick up one send~ at a time (but you can switch between
-send~s if you want.)
-
-<P> Don't try to throw~ and catch~ or send~ and receive~ between windows with
-different block sizes. The only re-blocking mechanisms which are well tested
-are inlet~ and outlet~.
-
-<P> When you send a signal to a point that is earlier in the sorted list of tilde
-objects, the signal doesn't get there until the next cycle of DSP computation,
-one block later; so your signal will be delayed by one block (1.45 msec by
-default.) Delread~ and delwrite~ have this same restriction, but here the 1.45
-msec figure gives the minimum attainable delay. For nonrecursive algorithms, a
-simple flanger for example, you might wish to ensure that your delread~ is
-sorted after your delwrite~. The only way to ensure this is to create the
-delread~ after you created the delwrite~; if things get out of whack, just
-delete and re-create the delread~.
-
-<H3> <A name=s5> 2.5. scheduling </A> </H3>
-
-<P>Pd uses 64-bit floating point numbers to represent time, providing sample
-accuracy and essentially never overflowing. Time appears to the user
-in milliseconds.
-
-<H3> <A name=s5.1> 2.5.1. audio and messages </A> </H3>
-
-<P>Audio and message processing are interleaved in Pd. Audio processing is
-scheduled every 64 samples at Pd's sample rate; at 44100 Hz. this gives a
-period of 1.45 milliseconds. You may turn DSP computation on and off by
-sending the "pd" object the messages "dsp 1" and "dsp 0."
-
-<P> In the intervals between, delays might time out or external conditions
-might arise (incoming MIDI, mouse clicks, or whatnot). These may cause a
-cascade of depth-first message passing; each such message cascade is completely
-run out before the next message or DSP tick is computed. Messages are never
-passed to objects during a DSP tick; the ticks are atomic and parameter changes
-sent to different objects in any given message cascade take effect
-simultaneously.
-
-<P> In the middle of a message cascade you may schedule another one at a delay
-of zero. This delayed cascade happens after the present cascade has finished,
-but at the same logical time.
-
-<H3> <A name=s5.2> 2.5.2. computation load </A> </H3>
-
-<P> The Pd scheduler maintains a (user-specified) lead on its computations;
-that is, it tries to keep ahead of real time by a small amount in order to be
-able to absorb unpredictable, momentary increases in computation time. This
-is specified using the "audiobuffer" or "frags" command line flags (see <a
-href="x3.htm" name=s3>getting Pd to run </A>).
-
-<P> If Pd gets late with respect to real time, gaps (either occasional or
-frequent) will appear in both the input and output audio streams. On the
-other hand, disk streaming objects will work correctly, so that you may use
-Pd as a batch program with soundfile input and/or output. The "-nogui"
-and "-send" startup flags are provided to aid in doing this.
-
-<P> Pd's "realtime" computations compete for CPU time with its own GUI, which
-runs as a separate process. A flow control mechanism will be provided someday
-to prevent this from causing trouble, but it is in any case wise to avoid
-having too much drawing going on while Pd is trying to make sound. If a
-sub-window is closed, Pd suspends sending the GUI update messages for it;
-but not so for miniaturized windows as of version 0.32. You should really
-close them when you aren't using them.
-
-<H3> <A name=s5.3> 2.5.3. determinism </A> </H3>
-
-<P>All message cascades that are scheduled (via "delay" and
-its relatives) to happen before a given audio tick will happen as scheduled
-regardless of whether Pd as a whole is running on time; in other words,
-calculation is never reordered for any real-time considerations. This is done
-in order to make Pd's operation deterministic.
-
-<P> If a message cascade is started by an external event, a time tag is given
-it. These time tags are guaranteed to be consistent with the times at which
-timeouts are scheduled and DSP ticks are computed; i.e., time never decreases.
-(However, either Pd or a hardware driver may lie about the physical time an
-input arrives; this depends on the operating system.) "Timer" objects which
-measure time intervals measure them in terms of the logical time stamps of the
-message cascades, so that timing a "delay" object always gives exactly the
-theoretical value. (There is, however, a "realtime" object that measures real
-time, with nondeterministic results.)
-
-<P> If two message cascades are scheduled for the same logical time, they are
-carried out in the order they were scheduled.
-
-<H3> <A name=s6> 2.6. semantics </A> </H3>
-
-This section describes how objects in Pd are created, how they store data and
-how object and other boxes pass messages among themselves.
-
-<H3> <A name=s6.1> 2.6.1. creation of objects </A> </H3>
-
-The text in a box has a different function depending on whether it is a message,
-atom (number/symbol), or object box. In message boxes the text specifies the
-message or messages it will send as output. In atom boxes the text changes
-at run time to show the state of the box, which is either a number or a symbol.
-
-<P> In an object box, as in a message box, the text specifies a message; but
-here the message is to be passed to Pd itself, once, and the
-message's effect is to create the object in question. When you open a file,
-all the objects created are created using their text as "creation messages."
-If you type a new message into an object box (or change it), the old object is
-destroyed and the message is used to create the new one.
-
-<P> The selector of the message (the first word in the message) is a selector
-which Pd interprets to mean which type of object to create. Any message
-arguments (called "creation arguments") are used to parameterize the object
-being created. Thus in "makenote 64 250" the selector "makenote" determines
-the class of object to create and the creation arguments 64 and 250 become the
-initial velocity and duration.
-
-<H3> <A name=s6.2> 2.6.2. persistence of data </A> </H3>
-
-Among the design principles of Pd is that patches should be printable, in the
-sense that the appearance of a patch should fully determine its functionality.
-For this reason, if messages received by an object change its action, since the
-changes aren't reflected in the object's appearance, they are not saved as part
-of the file which specifies the patch and will be forgotten when the patch is
-reloaded. In the same way, if you delete and then recreate an object the
-original object's state is not retained but is instead reinitialized (possibly
-as specified by creation arguments.)
-
-<P> An exception is made for subpatches whose "state" is the configuration of
-the subpatch; as a special case, this configuration is restored when the
-patch is read from a file. Also, if you rename the subpatch, for instance
-typing "pd jane" instead of "pd spot," the contents of the patch are preserved
-and only the text in the object box and the window title of the subpatch are
-changed.
-
-<P> It is probably bad style to specify creation arguments ala "makenote 64 250"
-if you are going to override them later; this is confusing to anyone who tries
-to understand the patch.
-
-<H3> <A name=s6.3> 2.6.3. message passing </A> </H3>
-
-Messages in Pd consist of a selector (a symbol) and zero or more arguments
-(which may be symbols or numbers). To pass a message to an object, Pd first
-checks the selector against the class of the object. Message boxes all are
-of one class and they all take the same incoming messages and dispense them
-according to their state, that is, the text typed into the box. The same
-holds for atom boxes (number or symbol) except that their state may change
-(it consists of the number or symbol showing).
-
-<P> Object boxes may have many different classes. The class is usually
-determined by the selector of the creation message, i.e., the first atom of the
-creation message which is usually a symbol.
-
-<P> Each class comes with a fixed collection of messages it may be sent. For
-example, the "float" or "f" object takes "bang" and "float." These messages
-are sent to "float" objects (objects whose class is float) via the leftmost,
-hot inlet. (The right inlet is a separate, auxiliary object.) Objects of
-class "float" respond to the message "bang" by outputting their current value,
-that is, by sending a "float" message to their outlet. They respond to "float"
-messages by setting their value and then outputting it.
-
-<P> Each other class (like "float") in Pd has its own protocol for responding
-to messages it is sent, and may take "float" and "bang" messages, or others
-in addition or instead of them.
-
-<H3> <A name=s6.4> 2.6.4. inlets and lists </A> </H3>
-
-The leftmost connection point at the top of most objects represents the object
-itself. Any other dark rectangle is a separate object called an "inlet"
-although in Pd there are 4 individual inlet classes. The class of the inlet
-determines which messages it will take: symbol, float, or other; and the inlet
-forwards the message either to the object proper or to some proxy, usually
-one that the object creates for the occasion.
-
-<P> Unless they arrange otherwise by defining a "list" method, objects respond
-to the "list" message by distributing the arguments of the message to their
-inlets, except for the first argument which is passed as a "float" or
-"symbol" message to the object proper.
-
-<H3> <A name=s6.5> 2.6.5. dollar signs </A> </H3>
-
-In message or object boxes, message arguments starting with a dollar sign
-and a number (like "$1" or "$3-bazoo") are variables which are substituted
-with values supplied as part of the environment the message is passed in.
-In the case of message boxes, the environment consists of the arguments of
-the "list" message (possibly extrapolated from "bang," "float,"
-or other) that the message box is responding to. Thus, if a message box gets
-"23 skidoo" and if it contains the text, "$2 until $1," out comes the message,
-"skidoo until 23."
-
-<P> Object boxes contain text which forms a message to be sent to Pd to create
-and initialize the object. Here, $1, etc., are taken from the context in which
-the patch was loaded. When the patch is a new document or opened from a file
-the "$" variables are undefined. But if the patch is an abstraction (see the
-next section) they are
-taken from the abstractions' creation arguments.
-
-<P> Constructions such as "$1-x" are expanded by string concatenation. This
-is the mechanism for making local variables. In particular, $0 in an abstraction
-is a counter which is guaranteed to be unique to that abstraction, so sends and
-receives with names like "$0-bear" can be used as local send/receive pairs.
-
-<P> Note that the expansion of variables such as $0 and $1 only works at the
-beginning of the symbol; so, for instance, "rats-$1" will not be expanded.
-Occasionally you may want to have double or triple substitutions; this can
-be done one stage at a time by nesting abstractions (with each subpatch
-adding its own $-variable to the beginning of a symbol and passing that on
-as argument to a further abstraction.)
-
-<P> For example, if you want to get dog-food, dog-ears, and cat-food, for
-example, have an abstraction "a1" that invokes an abstraction "a2" twice, as
-"a2 $1-food" and "a2 $1-ears", and then in a third patch call a1 twice, as
-"a1 cat" and "a1 dog". Inside the four "a2" copioes, $1 will evaluate to
-"dog-food", "cat-food", "dog-ears", and "cat-ears".
-
-<H3> <A name="s7"> 2.7. subpatches </A> </H3>
-
-Pd offers two mechanisms for making subpatches, called "one-off subpatches"
-and "abstractions." In either case the subpatch appears as an object box
-in a patch. If you type "pd" or "pd my-name" into an object box, this creates
-a one-off subpatch. For instance, in this fragment:
-
-<CENTER><P> <IMG src="fig7.1.jpg" ALT="subpatch"> </P></CENTER>
-
-the box in the middle, if clicked on, opens the sub-patch shown here:
-
-<CENTER><P> <IMG src="fig7.2.jpg" ALT="open subpatch window"> </P></CENTER>
-
-<P> The contents of the subpatch are saved as part of the parent patch, in
-one file. If you make several copies of a subpatch you may change them
-individually.
-
-<P> The objects, "inlet,", "inlet~," "outlet," and "outlet~,", when put in a
-subpatch, create inlets and outlets for the object box containing the subpatch.
-This works equally for one-off subpatches and abstractions. The inlet~ and
-outlet~ versions create inlets and outlets for audio signals. You can't mix
-messages and audio in a subpatch inlet or outlet; they must be one or the other
-exclusively. Inlets and outlets appear on the invoking box in the same left-to-right
-order as they appear in the subpatch.
-
-<H3> <A name="s7.1"> 2.7.1. abstractions </A> </H3>
-
-<P> To make an abstraction, save a patch with a name such as "abstraction1.pd"
-and then invoke it as "abstraction1" in an object box:
-
-<CENTER><P> <IMG src="fig7.3.jpg" ALT="abstraction"> </P></CENTER>
-
-<P> Here we're invoking a separate file, "abstraction1.pd", which holds the
-patch shown here (the border is the same as for the subpatch above):
-
-<CENTER><P> <IMG src="fig7.4.jpg" ALT="abstraction example"> </P></CENTER>
-
-You may create many instances of "abstraction1" or invoke it from several
-different patches; and changing the contents of "abstraction1" will affect all
-invocations of it as they are created. An analogy from the "c" programming
-language is that one-off subpatches are like bracketed blocks of code and
-abstractions are like subroutines.
-
-<P> Abstractions are instantiated by typing the name of a patch (minus the ".pd"
-extension) into an object box. You may also type arguments; for instance if
-you have a file "my-abstraction.pd" you may type "my-abstraction 5" to set the
-variable $1 to 5. This is defined only for object boxes (not for messages) in
-the abstraction. (For message boxes, "$1", etc, have a different meaning as
-described above.) If you want to send a message with a $1 in the sense of a
-creation argument of an abstraction, you must generate it with an object box
-such as "float $1", "symbol $1", or perhaps "pack $1 $2", which may then be
-sent to a message box.
-
-<P> The corresponding feature in Max (both Opcode and Ircam) was the "#1"
-construct. In a Max abstraction, "#1", etc., are replaced by the creation
-argument. This has the disadvantage that you can't edit the abstraction as
-instantiated in the patch since the "#" variables are substituted. In Pd the
-"$" variables in object boxes are spelled literally as "$" variables so that
-it's meaningful to edit them from within their calling patch. On the Pd side,
-however, there is the disadvantage that it's confusing to have "$" expanded at
-a different time in an object box than in a message box. In an object box, the
-"$" argument is expanded at creation time, and in a message box, at message
-time.
-
-<H3> <A name="s7.2"> 2.7.2. Graph-on-parent subpatches </A> </H3>
-
-If you open the "properties" dialog for a subpatch or an abstraction, you can
-check the "graph on parent" box to have the controls of the subpatch/abstraction
-appear on the parent. For instance, here is an invocation of "abstraction2":
-
-<CENTER><P> <IMG src="fig7.5.jpg" ALT="graph-on-parent abstraction"> </P></CENTER>
-
-where the patch "abstraction2.pd" contains:
-
-<CENTER><P> <IMG src="fig7.6.jpg" ALT="inside graph-on-parent abstraction"> </P></CENTER>
-
-Here, the number box in the abstraction shows up on the box that invoked
-the abstraction. The "graph on parent" flag is set in the abstraction
-(and is saved as part of the abstraction); to set it, open the "properties"
-dialog for the "abstraction2" canvas by right-clicking on any white space
-in the patch.
-
-<P> To open the subpatch, right click on the object and select "open". (On
-Macintoshes without a 2-button mouse, you can double-click in edit mode
-instead.) It doesn't work just to click on the object in run mode since clicks
-are sent to visible controls and/or arrays.
-
-<P> When the sub-patch is closed, all controls in it appear on the object
-instead; so the number box in the sub-patch in the example above is the same
-one as you see in the box. Only controls are made visible in this way
-
-<H3> <A name=s8> 2.8. numeric arrays </A> </H3>
-
-Linear arrays of numbers recur throughout the computer musician's bag of tricks,
-beginning with the wavetable oscillator. The wavetable oscillator later was
-reinvented as the looping sampler. Also, table lookup is used for nonlinear
-distortion of audio signals. In the domain of control, arrays of numbers
-can specify control mappings, probability densities, voicing data, and much
-more.
-
-<P> Arrays in Pd should be allocated (and possible read in from a file) before
-beginning to make sound, since memory allocation and disk operations may take
-long enough to cause audio buffer overruns or underruns. Pd provides two ways
-to define new arrays, as "graphs" and "tables". In either case the array
-has a pre-defined name and size (i.e., number of points). Elements of the
-array are stored as floating-point numbers, 4 bytes apiece
-
-<P> If you use an array to store a one-second sound at 44.1 kHz you will need
-176 kilobytes, or a one-minute sound, 10.6 megabytes. To store a sound with
-two or more channels, use a separate array for each channel.
-
-<P> Arrays are also useful as transfer functions, for example for nonlinear
-distortion of an audio signal, or to map a control onto a synthesis parameter.
-In situations like this one typically uses much shorter arrays, of no more
-than a few hundred elements. They are also useful for storing measured
-spectra derived from the fft~ objects, and probably for many other uses.
-
-<P> Arrays usually appear within subpatches created to house them, whether
-in "graph on parent" form (so that you see them within a rectangle drawn on
-the containing patch), or as a regular subpatch (which you see as a text box.)
-In the "graph on parent" form, an array appears as shown:
-
-<CENTER><P> <IMG src="fig8.1.jpg" ALT="array"> </P></CENTER>
-
-<P> Arrays are indexed from 0 to N-1 where N is the number of points in the
-array. You can read an array value using the tabread object:
-
-<CENTER><P> <IMG src="fig8.2.jpg" ALT="array indexing"> </P></CENTER>
-
-Here we see that the third point of the array (index 2) has the value 0.4.
-To write into the array you can use the tabwrite object:
-
-<CENTER><P> <IMG src="fig8.3.jpg" ALT="setting an value in an array"> </P></CENTER>
-
-In this example, sending the message sets the third element to 0.5. (You
-may also send the two numbers to the two inlets separately.)
-
-<P> The two previous examples showed control operations to read and write from
-and to arrays. These may also be done using audio signals. For example,
-the patch below creates a 440 Hz. tone with "array1" as a waveform:
-
-<CENTER><P> <IMG src="fig8.4.jpg" ALT="setting an array with a waveform"> </P></CENTER>
-
-Here phasor~'s outputs a sawtooth wave, repeating 440 times per second, whose
-output range is from 0 to 1. The multiplier and adder adjust the range from
-1 to 11, and then the values are used as indices for tabread4~, which is a
-4-point interpolating table lookup module. (Much more detail is available in
-the audio example patches in the "pure documentation" series.)
-
-<P> To create a new array, select "array" from the "put" menu. Up will come
-a dialog window to set initial properties of the array. By default, a
-new graph is created to hold the array, but it may also be housed in the
-most recently created graph instead. Other properties may be specified there
-and/or changed later using the "properties" dialog.
-
-<P> If you select "properties" on an array in a graph, you two dialogs, one
-for the array and one for the graph. The array dialog looks like this:
-
-<CENTER><P> <IMG src="fig8.5.jpg" ALT="array properties window"> </P></CENTER>
-
-You may use this to change the name and size, in addition to another property,
-"save contents". If "save contents" is selected, the array's values are stored
-in the containing patch; otherwise they're initialized to zero each time the
-patch is reloaded. If you intend to use arrays to store sounds, you will
-probably not wish to store them in the patch but as separate soundfiles. This
-will be more efficient, and you may also then use a sound editor to modify them
-outside Pd.
-
-<P> If you check "delete me" and then "OK", the array will be deleted. This is
-an odd interface for deleting an object, and is only provided because Pd
-lacks a mechanism for selecting arrays (so that "cut" could serve).
-
-<P> The graph dialog (which also pops up) is shown here:
-
-<CENTER><P> <IMG src="fig8.6.jpg" ALT="graph properties"> </P></CENTER>
-
-<P> The X bounds initially range from 0 to the number of points in the table
-minus one (this is a good choice for arrays, although graphs holding other
-kinds of objects might require other X bounds.) The Y bounds should be
-chosen to reflect the natural range of the table, so that stored sounds
-would naturally range from -1 to 1, but a sequence of frequency values might
-range from 0 to 20,000. Finally, you choose the screen size of the graph,
-width and height, in screen pixels.
-
-<P> Many other operations are defined for arrays; see the related patches
-in the tutorial (starting at 2.control/15.array.pd) for more possibilities.
-
-<H3> <A name=s9> 2.9. Data structures </A> </H3>
-(Note: this section is adapted from an article submitted to ICMC 2002.)
-
-<P> The original idea in developing Pd was to make a real-time computer music
-performance environment like Max, but somehow to include also a facility for
-making computer music scores with user-specifiable graphical representations.
-This idea has important precedents in Eric Lindemann's Animal and Bill Buxton's
-SSSP. An even earlier class of precedents lies in the rich variety of paper
-scores for electronic music before it became practical to offer a
-computer-based score editor. In this context, scores by Stockhausen (<I>
-Kontakte</I> and <I> Studie II</I>) and Yuasa (<I>Toward the Midnight Sun</I>)
-come most prominently to mind, but also Xenakis's <I>Mycenae-alpha</I>, which,
-although it was realized using a computer, was scored on paper and only
-afterward laboriously transcribed into the computer.
-
-<P> Pd is designed to to offer an extremely unstructured environment for
-describing data structures and their graphical appearance. The underlying
-idea is to allow the user to display any kind of data he or she wants to,
-associating it in any way with the display. To accomplish this Pd introduces
-a graphical data structure, somewhat like a data structure out of the C
-programming language, but with a facility for attaching shapes and colors to
-the data, so that the user can visualize and/or edit it. The data itself can
-be edited from scratch or can be imported from files, generated
-algorithmically, or derived from analyses of incoming sounds or other data
-streams.
-
-Here is one simple
-example of a very short musical sketch realized using Pd:
-
-<CENTER><P> <IMG src="fig9.1.jpg" ALT="graphical score"> </P></CENTER>
-
-The example, which only lasts a few seconds, is a polyphonic collection of
-time-varying noise bands. The graphical ``score" consists of six objects, each
-having a small grab point at left, a black shape to show dynamic, and a colored
-shape to show changing frequency and bandwidth. The horizontal axis represents
-time and the vertical axis, frequency (although, as explained later, this
-behavior isn't built into pd). The dynamic and frequency shapes aren't
-constrained to be connected or even to be proximate, but since they pertain to
-the same sound their horizontal positions line up. In this example the last
-(furthest-right) object is percussive (as seen by the black shape) and has a
-fixed frequency and bandwidth, whereas the large, articulated shape in the
-center has a complicated trajectory in both frequency and dynamic. The color
-of the frequency trace determines the voice number used to realize it.
-
-<P> Each object is thus composed of a combination of scalar values (color;
-aggregate position in X and Y coordinates) and array values (time/value
-pairs for the black traces and time/frequency/bandwidth triples for the
-colored ones.) This is all specified by the user using Pd's ``template"
-mechanism.
-
-<P> Here is the template associated with the graphical objects
-shown above:
-
-<CENTER><P> <IMG src="fig9.2.jpg" ALT="template for graphical score"> </P></CENTER>
-
-Templates consist of a data structure definition (the "struct" object) and
-zero or more drawing instructions ("filledpolygon" and "plot"). The "struct"
-object gives the template the name, "template-toplevel." The data structure
-is defined to contain three floating point numbers named "x", "y", and
-"voiceno," and two arrays, one named "pitch" whose elements belong to another
-template named "template-pitch," and similarly for the array "amp."
-
-<P> In general, data structures are built from four data types: scalar floats
-and symbols, arrays (whose elements share another, specified template) and
-lists (whose elements may have a variety of templates). The contents of a Pd
-window themselves form a list. Pd's correlate of Max's "table" object is
-implemented as a top-level array whose elements are scalars containing a single
-floating-point number.
-
-<P> Data structures in Pd may nest arbitrarily deeply using the array and list
-types. For example, a collection of sinusoidal tracks from an analysis engine
-could be implemented as an array of arrays of (pitch, amplitude)
-pairs; this appears as example 12 in Pd's FFT object online tutorial.
-
-<P> After the "struct" object in the template shown above, the remaining
-three objects are <I> drawing instructions </I> , first for a rectangle
-("filledpolygon"), and then for two arrays. The various graphical
-attributes that are specified for drawing instructions may be numerical
-constants or data structure field names; in the latter case the value varies
-depending on the data. For instance, the second creation argument to
-"plot" is the color. The first "plot" plots the "amp" field and the
-color is given as 0, or black. The second one plots "pitch" using the color
-"voiceno". In this way the color of the second trace is attached to the
-"voiceno" slot in the data structure, so that color will vary according to its
-"voiceno" slot.
-
-<H3> <A name="s9.1"> 2.9.1. Traversal </A> </H3>
-
-<P> Pd objects are provided to traverse lists and arrays, and to address
-elements of data structures for getting and setting. Here is a patch showing
-how these facilities could be used, for example, to sequence the graphical
-score shown above:
-
-<CENTER><P> <IMG src="fig9.3.jpg" ALT="traversal example patch"> </P></CENTER>
-
-<P> Pd has no built-in sequencer, nor even any notion that "x" values should be
-used as a time axis. (However, a "sort" function is provided, which reorders
-a list from left to right, on the assumption that users might often want to use Pd
-data collections as x-ordered sequences.) Recording sequences of events into
-lists, and/or playing the lists back as sequences, are functionalities that the
-user is expected to supply on top of Pd's offerings, which, it is hoped, would
-allow those functionalities within a much larger range of possibilities, to
-include random re-orderings of events, score following, self-modifying scores,
-reactive improvisation, and perhaps much more.
-
-<P> Traversal of data is made possible by adding a new type of atom, "pointer",
-to the two previously defined types that make up messages, to wit, numbers and
-symbols. Unlike numbers and symbols, pointers have no printed form and thus
-can't be uttered in message boxes. Traversal objects such as "pointer" and
-"get" (among several others) can generate or use pointers. The pointer data
-type is also integrated into pipe-fitting objects such as "pack",
-"unpack",
-and "route".
-
-<P> In the patch shown above, the topmost "pointer" object holds a pointer to
-the next object to "play" (by sending it to one of the "voice"
-abstractions at bottom.) The pointer object takes a "traverse" message to
-set it to the head of the list (named "pd-data"), and "next" messages to
-move to (and output) the next datum in the list (i.e., the next in the list of
-six objects in the score). Another "pointer" object is also used, further
-down, as a storage cell for pointers just as "float" is for numbers.
-
-<P> The center of any sequencer is always the "delay" object, which must be
-fed the time difference between each event (including the non-event of hitting
-"start") and the next. As we extract each of the six objects in the score, we
-must wait the delay for playing that object, and then send its pointer to one
-of the "voice" abstractions to play it. However, we have to inspect the
-object itself to know the delay before playing it. So, in the loop, we peel off
-the first remaining object to play and inspect the time difference between it
-and the previous one, using this value to set the delay, but also storing the
-pointer in the lower "pointer" and "pack" objects.
-
-<P> The time difference needed to set the delay object is obtained using the
-"get template-toplevel x" object. (This is converted to incremental time
-("-"), corrected for tempo, and fed to the delay.) Pd provides
-the "get" and "set"
-objects for reading and writing values from data structures.
-The two "get" objects shown here obtain the "x" and "voiceno" fields
-of the current object. The template name (template-toplevel) is supplied
-to the "get" objects so that they can look up the offset of the necessary
-field(s) in advance, for greater run-time efficiency.
-
-<P> Once the delay has expired, the object's pointer is recalled (the lower
-"pointer" object), and the voice number is recalled. This is packed with
-the pointer itself and routed, so that the pointer goes to the appropriate
-voice. The voice number is shown as the color of the frequency trace in
-"999" units (first digit red, second green, third blue) and the "route" is
-arbitrarily set up to select among the six primary and secondary colors plus
-black.
-
-<P> The details of extracting the pitch and dynamic breakpoints from the arrays
-defined in the template are managed in the "voice" abstraction.
-The "voice"
-abstraction receives a
-pointer to a given object and manages the sequencing of the arrays; so it
-contains two sequencers itself. The nesting of the overall structure of
-the sequencer patch mirrors the nesting of the original data structures.
-Finally, the voice abstraction puts its audio output on a summing bus.
-
-<P> More general patches can easily be constructed which access heterogeneous lists
-of objects (having different templates). In this way, an arbitrarily rich
-personal "score language" can be developed and sequenced.
-
-<H3> <A name=s9.2> 2.9.2. Accessing and changing data </A> </H3>
-
-<P> In general, accessing or changing data is done via "pointers" to
-"scalars". Numbers and symbols within scalars are accessed using the
-"get" object and changed, in the same way, using "set". Since lists
-and arrays are composed of scalars, every actual number or symbol in a data
-heap will be a number or symbol element of some scalar. To access them, it
-suffices to have objects to chase down elements of lists and arrays (given
-either a global name or a pointer to the containing scalar).
-
-<P> Lists are traversed in the way shown above; to get to a sublist of a scalar,
-the "get" object will provide a pointer, in the same way as it provides
-"float" or "symbol" elements of scalars. For arrays, an
-"element" object is provided which, given a scalar, a field name and
-a number, chases down the numbered, scalar, element of the named array field.
-
-<P> To alter "float" or "symbol" elements of scalars is straightforward
-using the "set" object, but arrays and lists can't be set by assignment;
-there is no suitable data type available within messages. Lists could
-possibly be "settable" by passing pointers to other lists, but permitting this
-would have required either automatically doing deep copies of data structures
-to carry out the assignments, or else implementing a garbage collecting memory
-management system, either of which would be difficult to realize within
-real-time computation time constraints. Instead, all the data hanging from a
-scalar is considered as belonging to that scalar, and is left in memory until
-the scalar is deleted; the data may be changed atom by atom, but primitives
-are not provided which would imply unpredictable execution times.
-
-<P> The "getsize" and "setsize" objects are provided to access or change
-the number of elements in the array. For lists, an "append" object
-appends a new scalar for a given template to a list, after the element pointed
-to. (To insert a scalar at the beginning of a list, the pointer can be set to
-the "head" of the list, a formal location before the first list item.)
-Deletion is less flexible; the only operation is to delete an entire list.
-(There's no reason not to provide finer-grain deletion mechanisms except that
-it's not clear how to protect against stale pointers efficiently, except by
-voiding the entire collection of pointers into a list.)
-
-<H3> <A name=s9.3> 2.9.3. Editing </A> </H3>
-
-<P> The graphical score shown above can be edited by dragging breakpoints, or
-by adding and deleting them, using mouse clicks. Also, entire objects or
-collections of them may be copied, pasted, and dragged around the screen.
-Alternatively, there is an editable (or computer generate-able or parse-able)
-text representation for the data, which may be seen or changed in a dialog
-window or read and written to external text files.
-
-<P> Since the graphical presentation of data objects is determined by drawing
-instructions, the drawing instructions are interpreted backwards to alter data
-as a result of mouse operations. If a given graphical dimension is controlled
-by a variable, that variable is then controlled by dragging along that
-dimension; if the dimension is constant, it can't be altered by dragging.
-
-<P> Tricky situations can arise when the user changes the contents of templates.
-A change in drawing instructions can be accommodated by simply tracking
-down and redrawing all data objects using the template. However, changing
-the "struct" object itself make for less straightforward situations. The
-user might wish to reorder fields, delete them, add new ones, or rename them.
-When a "struct" object changes, Pd automatically conforms the data from the old
-structure to the new one. Fields with the same name as previously are maintained
-(reordering them as necessary); and if a field disappears but another of the
-same type appears, the new one(s) are taken to be renamings of the old one(s)
-in order of appearance. New fields which cannot be matched in this way with
-previously existing ones are assumed to be new and are initialized.
-
-<P> It can happen that two "struct" objects compete to define the same data
-structure, or that the user reads in data from a file which expects a different
-version of the structure, or alternatively, that the "struct" object for
-existing data objects disappears. For this reason, Pd maintains a private
-representation of the last active version of a "struct" until all
-similarly named "structs," as well as all data using that "struct", have
-disappeared. If the user introduces a new version of the "struct" and only
-later deletes the "current" one, the data is only conformed to the new version
-once the old one is deleted. In this way we avoid getting into situations
-where data is left hanging without its structure definition, or where data ends
-up belonging to two or more structures of the same name. The worst that can
-happen is that data may lose their drawing instructions, in which case Pd
-supplies a simple default shape.
-
-<H3> <A name=s9.4> 2.9.4. Limitations </A> </H3>
-
-<P> When examples get more complicated and/or dense than the one shown here, it
-becomes difficult to see and select specific features of a data collection;
-more work is needed to facilitate this.
-There should be some facility for turning drawing instructions on and off, or
-perhaps for switching between versions of a template, depending on the user's
-desired view. There should also be a callback facility in the template for
-when an object is edited with the mouse, so that the user can bind actions to
-mouse clicks.
-
-<P> More generally, the collection of traversal objects that Pd provides is
-adequate to support a variety of modes of data collection and use, such as
-analysis and sequencing. But the patches required to traverse the data
-collections are not always simple. It would be desirable to find a more
-straightforward mechanism than that provided by the "pointer", "get"
-and "set" objects.
-
-<P> The "data" facility, although part of the original plan for Pd, has only
-recently been implemented in its current form, and as (hopefully) the user base
-grows there will surely be occasions for many further extensions of the data
-handling primitives and the graphical presentation and editing functions.
-
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