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<!DOCTYPE html>
<html lang="en">
<head>
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<title>Overtone User’s Guide</title>
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<body class="book toc2 toc-left">
<div id="header">
<h1>Overtone User’s Guide</h1>
<div class="details">
<span id="author" class="author">Hlöðver Sigurðsson</span><br>
<span id="revnumber">version 1.0.1,</span>
<span id="revdate">June 29, 2018</span>
</div>
<div id="toc" class="toc2">
<div id="toctitle">Table of Contents</div>
<ul class="sectlevel1">
<li><a href="#_introduction">1. Introduction</a>
<ul class="sectlevel2">
<li><a href="#_preface">1.1. Preface</a></li>
<li><a href="#_about_this_book">1.2. About this Book</a>
<ul class="sectlevel3">
<li><a href="#_work_in_progress">1.2.1. Work in Progress</a></li>
<li><a href="#_contributing">1.2.2. Contributing</a></li>
<li><a href="#_conventions_used">1.2.3. Conventions Used</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#_installation">2. Installation</a>
<ul class="sectlevel2">
<li><a href="#_dependencies">2.1. Dependencies</a></li>
<li><a href="#_setting_up_a_project">2.2. Setting up a project</a></li>
</ul>
</li>
<li><a href="#_basics">3. Basics</a>
<ul class="sectlevel2">
<li><a href="#_envelopes">3.1. Envelopes</a>
<ul class="sectlevel3">
<li><a href="#_shapes">3.1.1. Shapes</a></li>
<li><a href="#_built_in_envelope_shapes">3.1.2. Built-in envelope shapes</a></li>
<li><a href="#_env_gen_and_linen">3.1.3. env-gen and linen</a></li>
<li><a href="#_other_ways_to_envelope">3.1.4. Other ways to envelope</a></li>
<li><a href="#_extra">3.1.5. Extra</a></li>
</ul>
</li>
<li><a href="#_oscillators">3.2. Oscillators</a>
<ul class="sectlevel3">
<li><a href="#_wavetable">3.2.1. Wavetable</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#_data_types">4. Data Types</a></li>
<li><a href="#_ugens">5. UGens</a></li>
<li><a href="#_external_devices">6. External devices</a>
<ul class="sectlevel2">
<li><a href="#_midi">6.1. MIDI</a></li>
<li><a href="#_osc">6.2. OSC</a></li>
</ul>
</li>
<li><a href="#_timing">7. Timing</a></li>
<li><a href="#_miscellaneous">8. Miscellaneous</a></li>
<li><a href="#_configuration">9. Configuration</a></li>
</ul>
</div>
</div>
<div id="content">
<div id="preamble">
<div class="sectionbody">
<link rel="stylesheet" href="http://cdnjs.cloudflare.com/ajax/libs/font-awesome/3.1.0/css/font-awesome.min.css">
</div>
</div>
<div class="sect1">
<h2 id="_introduction"><a class="anchor" href="#_introduction"></a><a class="link" href="#_introduction">1. Introduction</a></h2>
<div class="sectionbody">
<div class="paragraph">
<p><code>Overtone</code> is an audio programming library useing the Supercollider syntheizer engine via the expressive programming language <code>Clojure</code>. It combines the power of Supercollider and Clojure enabeling many artistic endeavors, including:</p>
</div>
<div class="ulist">
<ul>
<li>
<p>Sound design</p>
</li>
<li>
<p>Musical composition</p>
</li>
<li>
<p>Midi/OSC hardware interfaces</p>
</li>
<li>
<p>Audio-visual compositions/installations</p>
</li>
<li>
<p>Data science and "big data" art</p>
</li>
<li>
<p>Live-coding</p>
</li>
<li>
<p>DAW integration</p>
</li>
<li>
<p>AbletonLive clock synchronization via AbletonLink</p>
</li>
<li>
<p>RaspberryPI/Bela/Monome compatability</p>
</li>
</ul>
</div>
<div class="sect2">
<h3 id="_preface"><a class="anchor" href="#_preface"></a><a class="link" href="#_preface">1.1. Preface</a></h3>
<div class="paragraph">
<p>It is my hope that this book will be a gentle introduction to <code>Overtone</code> for a complete beginner as well for a novice. I hope to approach the topic of Overtone with a grain of cynicism; "what can go wrong will go wrong". Overtone is still a highly unstable library and for a workshop of 6-8 participants, it takes usually half an hour or less to get everyone started. That said, you’ll most likely encounter redundant details and/or debugging instructions for highly improbable scenarios while reading this book. Keep in mind that what may seem obvious to you isn’t necessarily obvious to everyone.</p>
</div>
<div class="paragraph">
<p>The computer can be an amazing, exciting tool to fulfill our creative needs. But at the same time the computer, and its building blocks, computer programs and code, can be at times indescribably painful, misconfigured and unpredictive. The hurdles you may encounter may include tooling, mac/linux/windows specific problems, files and libraries mislocated, version incompatibilities, and the list can go on forever. Luckily we will be getting ourselves comfortable with the programming language Clojure, which in the total 10 years of its existence, has seen an explosion of book publications, tutorials, workshops and stackoverflow questions/answers. So if you find youself in the unfortunate situation of getting stuck with something unrelated to Overtone, your odds are good that someone else on the internet already had the same problem as you, and you’re only one google search away from getting yourself back on track. At any point in time for any problem you are facing, you should always feel welcome to open ticket on github, ask question on stackoverflow, the irc(freenode) or on slack(clojurians). The software community as a whole is riddled with micro-aggressive "bromance" behaviour and hence can be at times quite intimidating for beginners to reach out for help. Which among other factors(in my subjective opinion), we end up with demographics of coders, be it art related or not, completly out of proportion in relation to the demographics of the general population. Please be aware that the Clojure community has on all social-media platforms, meetups and conferences a set of guidelines for behaviour, protocols in case of violation and group of confidentials to report violations to. I believe that these measures has made the Clojure community relatively more inclusive and diverse, every day I see experienced developers go out of their way to help someone in need of help and I hope you will enjoy the benefits of the Clojure community in the same way as I did when I was a total beginner.</p>
</div>
<div class="paragraph">
<p>As my personal advice as an artist to artists stepping into the journey of creative coding: don’t believe everything software engineers tell you about software, in the same way you shouldn’t believe everything an artist tells you about how art should be. An artist and software-engineer will and should approach code in different ways. You will never hear stories about Beethoven implementing a Continous Integration test to determine if his 7th symphony accidentally lost a note while he was writing his 8th, or Stravinsky trip out on his Bassoon type checker when he wrote the introduction to the Rite of Spring. Learning from the best is always a good approach and becoming better at programming is only going to make you faster and more effective, but do watch out for the abyss of infinite information and take moderate actions. If our goal is to create art for the real world, be completely shameless if your code isn’t orthodox as long as it produces the desired result and you had fun writing it. While the "old-school" composer is sitting next to a piano with pen and empty staff notation paper, in the same way you will find ourself with an empty text document in your text editor, with your fingers on the keyboard, ready to explore the physical boundaries of music, sound and time.</p>
</div>
</div>
<div class="sect2">
<h3 id="_about_this_book"><a class="anchor" href="#_about_this_book"></a><a class="link" href="#_about_this_book">1.2. About this Book</a></h3>
<div class="sect3">
<h4 id="_work_in_progress"><a class="anchor" href="#_work_in_progress"></a><a class="link" href="#_work_in_progress">1.2.1. Work in Progress</a></h4>
<div class="paragraph">
<p>This is a work in progress. If you find an error, please submit a PR to fix it, or an issue with details of the problem.</p>
</div>
</div>
<div class="sect3">
<h4 id="_contributing"><a class="anchor" href="#_contributing"></a><a class="link" href="#_contributing">1.2.2. Contributing</a></h4>
<div class="paragraph">
<p>This source for this book is hosted on <a href="https://github.com/overtone/overtone.github.com/tree/master/docs/sources">Github</a>.</p>
</div>
</div>
<div class="sect3">
<h4 id="_conventions_used"><a class="anchor" href="#_conventions_used"></a><a class="link" href="#_conventions_used">1.2.3. Conventions Used</a></h4>
<div class="paragraph">
<p>The examples and code used in this book will try to be as neutral as possible when it comes to choice of text-editor. All modern text editors have some sort of plugin to run and evaluate Clojure code. If you are starting out with the programming language Clojure, you may easily get confused or lost on how to replicate some of the examples in your text editor. Therefore we aim to make all of our examples replicable using nothing but Leiningen in the terminal via <code>lein repl</code>, and assume from the reader basic understanding of the terminal/cmd (if you know how to explore directories and install apps with the terminal, you probably know enough). Leiningen is the most popular build tool in Clojure and is the build tool that glues Overtone’s sources and dependencies together. Overtone does work with alternative build tools like <code>boot</code>, as well as a standalone java jar file, but that and how to integrate Overtone to specific text-editor will not be included in this book.</p>
</div>
<div class="paragraph">
<p>Please be also aware that topics often overlap. If something isn’t clear, have a look at the chapter titles to see if the concepts you’re trying to understand is explained elswhere in the book.</p>
</div>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_installation"><a class="anchor" href="#_installation"></a><a class="link" href="#_installation">2. Installation</a></h2>
<div class="sectionbody">
<div class="sect2">
<h3 id="_dependencies"><a class="anchor" href="#_dependencies"></a><a class="link" href="#_dependencies">2.1. Dependencies</a></h3>
<div class="paragraph">
<p>You will need:</p>
</div>
<div class="ulist">
<ul>
<li>
<p>Java SDK (Version 8). <a href="http://openjdk.java.net/install/">OpenJDK</a> or <a href="http://www.oracle.com/technetwork/java/javase/downloads/index.html">Oracle</a></p>
</li>
<li>
<p><a href="https://leiningen.org/">Leiningen</a> or <a href="https://djpowell.github.io/leiningen-win-installer/">Leiningen windows-installer</a> or <a href="http://brewformulas.org/Leiningen">Leiningen via brew on OsX</a></p>
</li>
</ul>
</div>
<div class="paragraph">
<p>Optionally you could want:</p>
</div>
<div class="ulist">
<ul>
<li>
<p><a href="https://supercollider.github.io/download">Supercollider</a> for starting scsynth externally from Overtone</p>
</li>
<li>
<p><a href="https://git-scm.com/downloads">Git</a> for cloning the Overtone repository from github</p>
</li>
</ul>
</div>
<div class="paragraph">
<p>If running on Linux you must have JACK Audio connection toolkit version 2 or later (which <code>qjackctl</code> provides along with easy to use GUI)</p>
</div>
<div class="listingblock">
<div class="title">Ubuntu</div>
<div class="content">
<pre class="CodeRay highlight"><code data-lang="bash">$ sudo apt-get install qjackctl</code></pre>
</div>
</div>
<div class="listingblock">
<div class="title">Fedora</div>
<div class="content">
<pre class="CodeRay highlight"><code data-lang="bash">$ sudo dnf install qjackctl</code></pre>
</div>
</div>
<div class="listingblock">
<div class="title">CentOS</div>
<div class="content">
<pre class="CodeRay highlight"><code data-lang="bash">$ sudo yum install qjackctl</code></pre>
</div>
</div>
<div class="listingblock">
<div class="title">NixOs (if using internal-synth, libjack2 must be installed via nix-env with its nix-env lib dir on LD_LIBRARY_PATH or alternatively loaded into a nix-shell)</div>
<div class="content">
<pre class="CodeRay highlight"><code data-lang="bash">$ nix-env -i libjack2</code></pre>
</div>
</div>
</div>
<div class="sect2">
<h3 id="_setting_up_a_project"><a class="anchor" href="#_setting_up_a_project"></a><a class="link" href="#_setting_up_a_project">2.2. Setting up a project</a></h3>
<div class="paragraph">
<p>Although it is possible to start Overtone directly from the <a href="https://github.com/overtone/overtone">github repository</a> by downloading it as zip or cloning it with <code>git clone <a href="https://github.com/overtone/overtone.git" class="bare">https://github.com/overtone/overtone.git</a></code> in the terminal, it is recommended that <code>Overtone</code> is used as any other Clojure library in your own project. So we will do exacly that.</p>
</div>
<div class="paragraph">
<p>First create an empty directory, we’ll call it overtone (the name is irrelevant here) and go into it</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="CodeRay highlight"><code data-lang="bash">$ mkdir overtone
$ cd overtone</code></pre>
</div>
</div>
<div class="paragraph">
<p>Then in your text-editor, create a new textfile and save it into the newly created directory as <code>project.clj</code>. This is file that leiningen looks for inside the folder leiningen was started from (ie. you can’t start leiningen in directory x and expect it to find <code>project.clj</code> in directory y). Then paste the following code into <code>project.clj</code> and save the file again.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="CodeRay highlight"><code data-lang="clojure">(defproject overtone-tutorial <span class="string"><span class="delimiter">"</span><span class="content">1.0.0</span><span class="delimiter">"</span></span>
<span class="symbol">:dependencies</span> [[overtone/overtone <span class="string"><span class="delimiter">"</span><span class="content">0.10.3</span><span class="delimiter">"</span></span>]]
<span class="symbol">:native-path</span> <span class="string"><span class="delimiter">"</span><span class="content">native</span><span class="delimiter">"</span></span>
<span class="symbol">:source-paths</span> [<span class="string"><span class="delimiter">"</span><span class="content">src</span><span class="delimiter">"</span></span>])</code></pre>
</div>
</div>
<div class="paragraph">
<p>With only one file in your directory run the following lein command and let’s see what happens</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="CodeRay highlight"><code data-lang="bash">$ lein deps</code></pre>
</div>
</div>
<div class="admonitionblock tip">
<table>
<tr>
<td class="icon">
<i class="fa icon-tip" title="Tip"></i>
</td>
<td class="content">
<code>lein deps</code> is actually a redundant command as <code>lein repl</code> implicitly fetches Clojure dependencies before starting the REPL. It is only useful if you want to fetch the dependencies without starting the REPL.
</td>
</tr>
</table>
</div>
<div class="paragraph">
<p>If you’re running leiningen for the first time you should see a whole bunch of text appearing on the screen, indicating that leiningen is downloading the Clojure dependencies needed to run Overtone. After this process, directories <code>target</code> and <code>native</code> should have been created, both of these directories can be safely omitted if you’re planning on saving your code on for example github, and <code>target</code> can even be deleted at any time, by literally deleteing it or by running <code>lein clean</code> which by default deletes <code>target</code>, that will only be useful if you’re trying to debug your program as <code>target</code> gets created every time you run leiningen to store various information irrelevant to us at this moment. But do keep <code>native</code> untouched as it stores the necessary files needed to run Supercollider from within Overtone.</p>
</div>
<div class="paragraph">
<p>Now let’s start Clojure via <code>lein repl</code></p>
</div>
<div class="listingblock">
<div class="content">
<pre class="CodeRay highlight"><code data-lang="bash">$ lein repl</code></pre>
</div>
</div>
<div class="admonitionblock tip">
<table>
<tr>
<td class="icon">
<i class="fa icon-tip" title="Tip"></i>
</td>
<td class="content">
REPL stands for READ-EVAL-PRINT-LOOP, and is a fancy word for the Clojure shell/interpreter. In simple terms, a [Clojure]REPL is any type of program or tool that you can give Clojure code to to be evaluated.
</td>
</tr>
</table>
</div>
<div class="paragraph">
<p>If all went right, you should see something similar in your terminal window</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="CodeRay highlight"><code data-lang="bash">nREPL server started on port 34189 on host 127.0.0.1 - nrepl://127.0.0.1:34189
REPL-y 0.3.7, nREPL 0.2.12
Clojure 1.9.0
OpenJDK 64-Bit Server VM 1.8.0_172-02
Docs: (doc function-name-here)
(find-doc "part-of-name-here")
Source: (source function-name-here)
Javadoc: (javadoc java-object-or-class-here)
Exit: Control+D or (exit) or (quit)
Results: Stored in vars *1, *2, *3, an exception in *e
user=></code></pre>
</div>
</div>
<div class="paragraph">
<p>Now for our sanity, let’s see if this REPL prints <code>Hello World</code></p>
</div>
<div class="listingblock">
<div class="content">
<pre class="CodeRay highlight"><code data-lang="Clojure">user=> (<span class="keyword">println</span> <span class="string"><span class="delimiter">"</span><span class="content">Hello World!</span><span class="delimiter">"</span></span>)
Hello World!
<span class="predefined-constant">nil</span>
user=></code></pre>
</div>
</div>
<div class="paragraph">
<p>Yup we are ready, then to the moment of truth, now let’s boot up Overtone with this easy-to-remember command</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="CodeRay highlight"><code data-lang="Clojure">(<span class="keyword">use</span> 'overtone.live)</code></pre>
</div>
</div>
<div class="paragraph">
<p>If all went accordingly without errors you should see something similar in your terminal window, note that I’m running here on Linux, so for me Jack will be automatically booted and connected.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="CodeRay highlight"><code data-lang="bash">user=> (use 'overtone.live)
--> Loading Overtone...
--> Booting internal SuperCollider server...
Found 0 LADSPA plugins
Cannot connect to server socket err = No such file or directory
Cannot connect to server request channel
Cannot lock down 82280346 byte memory area (Cannot allocate memory)
Cannot use real-time scheduling (RR/5)(1: Operation not permitted)
JackClient::AcquireSelfRealTime error
JackDriver: client name is 'SuperCollider'
SC_AudioDriver: sample rate = 48000.000000, driver's block size = 2048
--> Connecting to internal SuperCollider server...
--> Connection established
JackDriver: max output latency 128.0 ms
_____ __
/ __ /_ _____ _____/ /_____ ____ ___
/ / / / | / / _ \/ ___/ __/ __ \/ __ \/ _ \
/ /_/ /| |/ / __/ / / /_/ /_/ / / / / __/
\____/ |___/\___/_/ \__/\____/_/ /_/\___/
Collaborative Programmable Music. v0.11
Hello Hlolli, may algorithmic beauty pour forth from your fingertips today.
nil
user=></code></pre>
</div>
</div>
<div class="paragraph">
<p>If something went wrong, see if the stacktrace gave you any meaningful information and proceed to <a href="#_configuration">Configuration</a> and try to rule out that something isn’t misconfigured. And come back here and try to start Overtone again before continuing. A good rule of thumb is to read stacktraces from top to bottom, the uppermost lines being the most important ones in most of the cases.</p>
</div>
<div class="admonitionblock tip">
<table>
<tr>
<td class="icon">
<i class="fa icon-tip" title="Tip"></i>
</td>
<td class="content">
If you’re on Linux too and encounter <code>Cannot allocate memory</code> and/or <code>Cannot use real-time scheduleing</code> you can totally ignore that, it just means that you’re not running preempt realtime-kernel. Switching to rt-kernel can potentially improve your audio performance by allowing Jack to send audio on top priority, but at the cost potentially make things very complicated and possibly insecure, as rt-kernels are usually released that much later than other kernels. If you want to run proprietary nvidia/ati drivers on preemt rt-kernel, you’re most likely going too have a bad time, irrelevant if you’re a linux expert or a beginner.
</td>
</tr>
</table>
</div>
<div class="paragraph">
<p>Now that we have Overtone running successfully. We can start all the functions that Overtone provides at our disposal. Among them is an important helper function called <code>doc</code>, which will print the documentation to any function in your scope/reach. Let’s try it on the symbols <code>demo</code> and <code>sin-osc</code>.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="CodeRay highlight"><code data-lang="Bash">user=> (doc demo)
-------------------------
overtone.live/demo
([& body])
Macro
Listen to an anonymous synth definition for a fixed period of time.
Useful for experimentation. If the root node is not an out ugen, then
it will add one automatically. You can specify a timeout in seconds
as the first argument otherwise it defaults to *demo-time* ms. See
#'run for a version of demo that does not add an out ugen.
(demo (sin-osc 440)) ;=> plays a sine wave for *demo-time* ms
(demo 0.5 (sin-osc 440)) ;=> plays a sine wave for half a second
nil
user=></code></pre>
</div>
</div>
<div class="listingblock">
<div class="content">
<pre class="CodeRay highlight"><code data-lang="Bash">user=> (doc sin-osc)
-------------------------
overtone.live/sin-osc
([freq phase mul add])
Sine table lookup oscillator
[freq 440.0, phase 0.0, mul 1, add 0]
freq - Frequency in Hertz
phase - Phase offset or modulator in radians
mul - Output will be multiplied by this value.
add - This value will be added to the output.
Outputs a sine wave with values oscillating between -1 and
1 similar to osc except that the table has already been
fixed as a sine table of 8192 entries.
Sine waves are often used for creating sub-basses or are
mixed with other waveforms to add extra body or bottom end
to a sound. They contain no harmonics and consist entirely
of the fundamental frequency. This means that they're not
suitable for subtractive synthesis i.e. passing through
filters such as a hpf or lpf. However, they are useful for
additive synthesis i.e. adding multiple sine waves
together at different frequencies, amplitudes and phase to
create new timbres.
Categories: Generators -> Deterministic
Rates: [ :ar, :kr ]
Default rate: :ar
nil
user=></code></pre>
</div>
</div>
<div class="paragraph">
<p>Much of what is written in the documentation will be explained in subsequent chapters. But let’s suffice to say that <code>demo</code> is a function intended to evaluate an instrument and play it immediately for 2 seconds, which can come in handy when developing sounds and you want to hear the results quickly. And <code>sin-osc</code> is an oscillator that produces sinewave shape audio-signal (or control-signal, more on that later). Unlike <code>demo</code> which needs at least 1 instrument to be given as a parameter, then <code>sin-osc</code> can be called without any parameter, if that’s the case, then <code>sin-osc</code> will look at its own default parameter and use those instead. Which would be 440 cycles per second on full amplitude.</p>
</div>
<div class="paragraph">
<p>We will conclude this chapter by playing 2 seconds of 440Hz sinewave. It won’t sound pretty but it’s a fast and effective way to determine if everything is working accordingly.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="CodeRay highlight"><code data-lang="Clojure">(demo (sin-osc))</code></pre>
</div>
</div>
<div class="paragraph">
<p>If you’re at this point not hearing any audio, and you’re sure that nothing is muted on your computer. Then have a look through the <a href="#_configuration">Configuration</a> chapter before <a href="https://github.com/overtone/overtone/issues/new">opening a ticket</a>.</p>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_basics"><a class="anchor" href="#_basics"></a><a class="link" href="#_basics">3. Basics</a></h2>
<div class="sectionbody">
<div class="sect2">
<h3 id="_envelopes"><a class="anchor" href="#_envelopes"></a><a class="link" href="#_envelopes">3.1. Envelopes</a></h3>
<div class="imageblock">
<div class="content">
<img src="media/docs_img/reaper_envelope.jpg" alt="Graphical breakpoint editor in REAPER">
</div>
</div>
<div class="paragraph">
<p><em>Application of envelope via graphical breakpoints</em></p>
</div>
<div class="paragraph">
<p>The term envelope may or may not sound alien to you. But if you’ve ever used attack or decay on modular synthesizer or written breakpoints in a DAW like Ardour, ProTools or Reaper, you have used envelopes. Fade-in and fade-out are other commonly used forms of an envelope. The basic idea is that as time passes, often shown as x-axis in a plot, some value changes accordingly, often drawn on y-axis. In fact an envelope can be an oscillator and an oscillator can be used as an envelope.</p>
</div>
<div class="paragraph">
<p>Envelopes are most traditionally used to control amplitude and frequency, as will be shown later, envelopes in Overtone can be used for many other things, like amplitude modulation, oscillation, trigger, arpeggiator, trill/tremolo ornaments. Basically anything that ties numbers and time together.</p>
</div>
<div class="sect3">
<h4 id="_shapes"><a class="anchor" href="#_shapes"></a><a class="link" href="#_shapes">3.1.1. Shapes</a></h4>
<div class="paragraph">
<p>Overtone has a function to create envelope shapes in a format that Supercollider understands, called simply <code>envelope</code>. For every envelope there needs to be two vectors provided as arguments, levels (y-axis) and durations in seconds (x-axis), since durations specifies the durations of each step, its size will need to be the size of the levels vector minus 1. You can choose an envelope shape by directly specifying each point via <code>:step</code>, or use one of the following keywords to apply a function to your points.</p>
</div>
<div class="ulist">
<ul>
<li>
<p><code>:lin</code> a linear function that creates straight lines from given points</p>
</li>
<li>
<p><code>:exp</code> a natural exponential function (eⁿ), no value on y-axis can be zero</p>
</li>
<li>
<p><code>:sin</code> applies Hann function to given points</p>
</li>
<li>
<p><code>:wel</code> a power spectrum generator via Welch method</p>
</li>
<li>
<p><code>:sqr</code> applies square (n²) function to given points</p>
</li>
<li>
<p><code>:cub</code> applies cubed (n³) function to given points</p>
</li>
</ul>
</div>
<div class="paragraph">
<p>Let’s try a simple example.</p>