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<div id="header">
<h1 class="title">Strudel: live coding patterns on the Web</h1>
<ul id="authorlist">
<li>true</li>
<li>true</li>
</ul>
<h3 class="date">2022-12-14</h3>
</div>
<h2 class="abstract">Abstract</h2>
<div id="abstract">
<p>This paper introduces Strudel, which brings the TidalCycles approach
to live coding algorithmic patterns to native JavaScript and the web. We
begin by giving a little background of the first year of development,
before sharing some detail about its implementation and examples of use.
We go on to outline the wide range of synthesis and other outputs
available in Strudel, including WebAudio, MIDI, OSC (for SuperDirt),
WebSerial and CSound, and introduce Strudels REPL live editor,
including its built-in visualisations. We then compare Strudel with
Tidal, the trade-offs involved between JavaScript and Haskell, and the
unique capabilities offered by Strudel for aligning patterns.</p>
</div>
<h1 data-number="1" id="introduction"><span
class="header-section-number">1</span> Introduction</h1>
<p>In the following paper, we introduce <em>Strudel</em>, an alternative
implementation of the TidalCycles (or Tidal for short) live coding
system, using the JavaScript programming language. Strudel is an attempt
to make live coding more accessible, by creating a system that runs
entirely in the browser, while opening Tidals approach to algorithmic
patterns <span class="citation"
data-cites="mcleanAlgorithmicPattern2020a">(Mclean 2020)</span> up to
modern audio/visual web technologies. The Strudel REPL is a live code
editor dedicated to manipulating patterns while they play, with builtin
visual feedback. While Strudel is written in JavaScript, the API is
optimized for simplicity and readability by applying code
transformations on the syntax tree level, allowing language operations
that would otherwise be impossible. The application supports multiple
ways to output sound, including Tone.js, Web Audio Nodes, OSC (Open
Sound Control) messages, Web Serial, Web MIDI and Csound. The project is
split into multiple packages, allowing granular reuse in other
applications. Apart from TidalCycles, Strudel draws inspiration from
many prior existing projects like TidalVortex <span class="citation"
data-cites="mcleanTidalVortexZero2022">(McLean et al. 2022)</span>,
Gibber <span class="citation"
data-cites="robertsGibberLiveCoding2012">(Roberts and Kuchera-morin
2012)</span>, Estuary <span class="citation"
data-cites="ogbornEstuaryBrowserbasedCollaborative2017">(Ogborn et al.
2017)</span>, Hydra <span class="citation"
data-cites="jackHydra2022">(Jack [2022] 2022)</span>, Ocarina <span
class="citation" data-cites="solomonPurescriptocarina2022">(Solomon
[2021] 2022)</span> and Feedforward <span class="citation"
data-cites="mcleanFeedforward2020">(McLean 2020)</span>. This paper
expands the Strudel Demo paper for the Web Audio Conference 2022 <span
class="citation" data-cites="StrudelWAC2022">(Roos and McLean
2022)</span>.</p>
<p>The first tentative commit to the Strudel project was on 22nd January
2022 by Alex McLean, with the core representation implemented over the
following few days. Although this was his first attempt at a
JavaScript-based application, by 27th January, Alex had managed to
upload the initial version to the npm javascript package database,
sharing with the wider community for comment. By 4th February, Felix
Roos had discovered Strudel and contributed a REPL user interface to
it, and then contributed a scheduler the next day, so that Strudel could
already make sound. At this point, Alex and Felix shared ownership to
the repository, and the project has since proved to be a productive
confluence of Felixs own work into music representation and
visualisation, with Alexs experience with making Tidal. Felix has since
become the primary contributor to Strudel, with Alex continuing to jump
between developing both Strudel and Tidal. Aspects of Strudels
development have therefore fed back into TidalCycles, and both systems
have maintained a shared conceptual underpinning. We plan to continue
working towards feature parity between these systems, although within
the syntactical trade-offs and library ecosystems of JavaScript and
Haskell, some divergence is inevitable and healthy.</p>
<p>Over the first year of its life, Strudel is now a fully-fledged live
coding environment, porting Tidals core represention of patterns,
pattern transformations, and mininotation for polymetric sequences,
combined with a wealth of features for synthesising and visualising
those patterns.</p>
<h1 data-number="2" id="from-tidal-to-strudel-and-back"><span
class="header-section-number">2</span> From Tidal to Strudel and
back</h1>
<p>As mentioned above, the original Tidal is implemented as a domain
specific language (DSL) embedded in the Haskell pure functional
programming language, and takes advantage of Haskells terse syntax and
advanced, strong type system. JavaScript on the other hand, is a
multi-paradigm programming language, with a dynamic type system. Because
Tidal leans heavily on many of Haskells more unique features, it was
not always clear that it could meaningfully be ported to a
multi-paradigm scripting language. However, this possibility was already
demonstrated with an earlier port to Python [TidalVortex; <span
class="citation" data-cites="mcleanTidalVortexZero2022">McLean et al.
(2022)</span>], and we have now successfully implemented Tidals pure
functional representation of patterns in Strudel, including partial
application, currying, and the functor, applicative and monadic
structures that underlie Tidals expressive pattern transformations. The
result is a terse and highly composable system, where everything is
either a pattern, or a function for combining and manipulating patterns,
offering a rich creative ground for exploration.</p>
<p>This development process has been far from a one-way port, however.
The process of porting Tidals concepts has also opened up new
possibilities, some just from revisiting every design decision, and some
from the particular affordances and constraints offered by JavaScript.
This has lead to new features (and indeed bugfixes) that have found
their way back to Tidal where appropriate, and ongoing work that we will
return to in the conclusion of this paper.</p>
<h1 data-number="3" id="representing-patterns"><span
class="header-section-number">3</span> Representing Patterns</h1>
<p>Patterns are the essence of Tidal. Its patterns are abstract entities
that represent flows of time as functions, adapting a technique called
pure functional reactive programming. Taking a time span as its input, a
Pattern can output a set of events that happen within that time span. It
depends on the structure of the Pattern how the events are located in
time. From now on, this process of generating events from a time span
will be called <strong>querying</strong>. Example:</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode js"><code class="sourceCode javascript"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="kw">const</span> pattern <span class="op">=</span> <span class="fu">sequence</span>(c3<span class="op">,</span> [e3<span class="op">,</span> g3])</span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="kw">const</span> events <span class="op">=</span> pattern<span class="op">.</span><span class="fu">queryArc</span>(<span class="dv">0</span><span class="op">,</span> <span class="dv">1</span>)</span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="bu">console</span><span class="op">.</span><span class="fu">log</span>(events<span class="op">.</span><span class="fu">map</span>(e <span class="kw">=&gt;</span> e<span class="op">.</span><span class="fu">show</span>()))</span></code></pre></div>
<p>In this example, we create a pattern using the <code>sequence</code>
function and <strong>query</strong> it for the time span from
<code>0</code> to <code>1</code>. Those numbers represent units of time
called <strong>cycles</strong>. The length of one cycle depends on the
tempo, which defaults to one cycle per second. The resulting events
are:</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode js"><code class="sourceCode javascript"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>[{ <span class="dt">value</span><span class="op">:</span> <span class="st">&#39;c3&#39;</span><span class="op">,</span> <span class="dt">begin</span><span class="op">:</span> <span class="dv">0</span><span class="op">,</span> <span class="dt">end</span><span class="op">:</span> <span class="dv">1</span><span class="op">/</span><span class="dv">2</span> }<span class="op">,</span></span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a>{ <span class="dt">value</span><span class="op">:</span> <span class="st">&#39;e3&#39;</span><span class="op">,</span> <span class="dt">begin</span><span class="op">:</span> <span class="dv">1</span><span class="op">/</span><span class="dv">2</span><span class="op">,</span> <span class="dt">end</span><span class="op">:</span> <span class="dv">3</span><span class="op">/</span><span class="dv">4</span> }<span class="op">,</span></span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a>{ <span class="dt">value</span><span class="op">:</span> <span class="st">&#39;g3&#39;</span><span class="op">,</span> <span class="dt">begin</span><span class="op">:</span> <span class="dv">3</span><span class="op">/</span><span class="dv">4</span><span class="op">,</span> <span class="dt">end</span><span class="op">:</span> <span class="dv">1</span> }]</span></code></pre></div>
<p>Each event has a value, a begin time and an end time, where time is
represented as a fraction. In the above case, the events are placed in
sequential order, where c3 takes the first half, and e3 and g3 together
take the second half. This temporal placement is the result of the
<code>sequence</code> function, which divides its arguments equally over
one cycle. If an argument is an array, the same rule applies to that
part of the cycle. In the example, e3 and g3 are divided equally over
the second half of the whole cycle.</p>
<p>The above examples do not represent how Strudel is used in practice.
In the live coding editor, the user only has to type in the pattern
itself, the querying will be handled by the scheduler. The scheduler
will repeatedly query the pattern for events, which are then scheduled
as sound synthesis or other event triggers. Also, the above event data
structure has been simplified for readability.</p>
<figure>
<img src="images/strudel-screenshot2.png" style="width:60.0%"
alt="Screenshot of the Strudel REPL live coding editor, including piano-roll visualisation." />
<figcaption aria-hidden="true">Screenshot of the Strudel REPL live
coding editor, including piano-roll visualisation.</figcaption>
</figure>
<h1 data-number="4" id="making-patterns"><span
class="header-section-number">4</span> Making Patterns</h1>
<p>In practice, the end-user live coder will not deal with constructing
patterns directly, but will rather build patterns using Strudels
extensive combinator library to create, combine and transform
patterns.</p>
<p>The live coder will rarely use the <code>sequence</code> function as
seen above, as sequencing is implicit in many functions. For example in
the following, the <code>note</code> function constructs a pattern of
notes, sequencing its arguments in the same manner as the previous
example.</p>
<div class="sourceCode" id="cb3"><pre class="sourceCode js"><code class="sourceCode javascript"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="fu">note</span>(c3<span class="op">,</span> [e3<span class="op">,</span> g3])</span></code></pre></div>
<p>Perhaps more often, they will use the mini-notation for even terser
notation of rhythmic sequences: [^This last example is also valid Tidal
code, albeit the parenthesis is not required in its Haskell syntax in
this case. Tidal does not support passing sequences as lists directly to
the <code>note</code> function, however.].</p>
<div class="sourceCode" id="cb4"><pre class="sourceCode js"><code class="sourceCode javascript"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="fu">note</span>(<span class="st">&quot;c3 [e3 g3]&quot;</span>)</span></code></pre></div>
<p>Such sequences are often treated only a starting point for
manipulation, where they then undergo pattern transformations such as
repetition, symmetry, interference/combination or randomisation,
potentially at multiple timescales. Because Strudel patterns are
represented as pure functions of time rather than as data structures,
very long and complex generative results can be represented and
manipulated without having to store the resulting sequences in
memory.</p>
<h1 data-number="5" id="pattern-example"><span
class="header-section-number">5</span> Pattern Example</h1>
<p>The following example showcases how patterns can be utilized to
create musical complexity from simple parts, using repetition and
interference:</p>
<div class="sourceCode" id="cb5"><pre class="sourceCode js"><code class="sourceCode javascript"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="st">&quot;&lt;0 2 [4 6](3,4,1) 3&gt;&quot;</span></span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a><span class="op">.</span><span class="fu">off</span>(<span class="dv">1</span><span class="op">/</span><span class="dv">4</span><span class="op">,</span> <span class="fu">add</span>(<span class="dv">2</span>))</span>
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a><span class="op">.</span><span class="fu">off</span>(<span class="dv">1</span><span class="op">/</span><span class="dv">2</span><span class="op">,</span> <span class="fu">add</span>(<span class="dv">6</span>))</span>
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a><span class="op">.</span><span class="fu">scale</span>(<span class="st">&#39;D minor&#39;</span>)</span>
<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a><span class="op">.</span><span class="fu">legato</span>(<span class="op">.</span><span class="dv">25</span>)</span>
<span id="cb5-6"><a href="#cb5-6" aria-hidden="true" tabindex="-1"></a><span class="op">.</span><span class="fu">note</span>()<span class="op">.</span><span class="fu">s</span>(<span class="st">&quot;sawtooth square&quot;</span>)</span>
<span id="cb5-7"><a href="#cb5-7" aria-hidden="true" tabindex="-1"></a><span class="op">.</span><span class="fu">delay</span>(<span class="op">.</span><span class="dv">8</span>)<span class="op">.</span><span class="fu">delaytime</span>(<span class="op">.</span><span class="dv">125</span>)</span></code></pre></div>
<p>The pattern starts with a rhythm of numbers in mini notation, which
are later interpreted inside the scale of D minor. The first line could
also be expressed without mini notation:</p>
<div class="sourceCode" id="cb6"><pre class="sourceCode js"><code class="sourceCode javascript"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="fu">cat</span>(<span class="dv">0</span><span class="op">,</span> <span class="dv">2</span><span class="op">,</span> [<span class="dv">4</span><span class="op">,</span> <span class="dv">6</span>]<span class="op">.</span><span class="fu">euclid</span>(<span class="dv">3</span><span class="op">,</span> <span class="dv">4</span><span class="op">,</span> <span class="dv">1</span>)<span class="op">,</span> <span class="dv">3</span>)</span></code></pre></div>
<p>These numbers then undergo various pattern transformations. Here is a
short description of all the functions used:</p>
<ul>
<li><code>cat</code>: play elements sequentially, where each lasts one
cycle</li>
<li><code>brackets</code>: elements inside brackets are divided equally
over the time of their parent</li>
<li><code>.euclid(p, s, o)</code>: place p pulses evenly over s steps,
with offset o <span class="citation"
data-cites="toussaintEuclideanAlgorithmGenerates2005">(Toussaint
2005)</span></li>
<li><code>.off(n, f)</code>: layers a pattern on top of itself, with the
new layer offset by n cycles, and with function f applied</li>
<li><code>.legato(n)</code>: multiply the duration of all events in a
pattern by a factor of n</li>
<li><code>.echo(t, n, v)</code>: copy each event t times, with n cycles
in between each copy, decreasing velocity by v</li>
<li><code>.note()</code>: interpretes values as notes</li>
<li><code>.s(name)</code>: play back each event with the given
sound</li>
<li><code>.delay(wet)</code>: add delay</li>
<li><code>.delaytime(t)</code>: set delay time</li>
</ul>
<p>Much of the above will be familiar to Tidal users.</p>
<!-- This example shows some of Strudel's unique support for chords and transposition familiar to students of Western music theory. This differs a little from Tidal's approach and thanks to the integration of the javascript library XXX (*TODO* ? or is this all your work Felix?), Strudel's support for tonal transformations such as voice leading is perhaps respects more advanced than Tidal. -->
<h1 data-number="6" id="ways-to-make-sound-and-other-events"><span
class="header-section-number">6</span> Ways to make Sound (and other
events)</h1>
<p>To generate sound, Strudel supports bindings for different
outputs:</p>
<ul>
<li>Tone.js (deprecated)</li>
<li>Web Audio API</li>
<li>WebDirt, a js recreation of Tidals <em>Dirt</em> sample engine
(deprecated)</li>
<li>OSC via osc-js, compatible with superdirt</li>
<li>Csound via the Csound WebAssembly build</li>
<li>MIDI via WebMIDI</li>
<li>Serial via WebSerial</li>
</ul>
<p>At first, we used Tone.js as sound output, but it proved to be
limited for the use case of Strudel, where each individual event could
potentially have a completely different audio graph. While the Web Audio
API takes a <em>fire-and-forget</em> approach, creating a lot of Tone.js
instruments and effects causes performance issues quickly. For that
reason, we chose to search for alternatives.</p>
<p>Strudels new default output uses the Web Audio API to create a new
audio graph for each event. It currently supports basic oscillators,
sample playback, various effects and an experimental support for
soundfonts.</p>
<p>WebDirt <span class="citation"
data-cites="ogbornDktr0WebDirt2022">(Ogborn [2016] 2022)</span> was
created as part of the Estuary Live Coding System <span class="citation"
data-cites="ogbornEstuaryBrowserbasedCollaborative2017">(Ogborn et al.
2017)</span>, and proved to be a solid choice for handling samples in
Strudel as well. We are however focused on working more directly with
the Web Audio API to be able to integrate new features more tightly.</p>
<p>Using the OSC protocol via Strudels provided Node.js-based OSC proxy
server, it is possible to send network messages to trigger events. This
is mainly used to render sound using SuperDirt <span class="citation"
data-cites="SuperDirt2022">(<em>SuperDirt</em> [2015] 2022)</span>,
which is the well-developed Supercollider-based synthesis framework that
Tidal live coders generally use as standard.</p>
<p>Recently, the experimental integration of Csound proved to bring a
new dimension of sound design capabilities to Strudel. Thanks to the
WebAssembly distribution of this classic system <span class="citation"
data-cites="CsoundWebAssembly">(Yi, Lazzarini, and Costello
2018)</span>, Csound orchestra synthesisers can be embedded in and
then patterned with Strudel code.</p>
<p>MIDI output can also be used to send MIDI messages to either external
instruments or to other programs on the same device. Unlike OSC, Strudel
is able to send MIDI directly without requiring additional proxy
software, but only from web browsers that support it (at the time of
writing, this means Chromium-based browsers).</p>
<p>Finally, Strudel supports Serial output, for example to trigger
events via microcontrollers. This has already been explored for robot
choreography by Kate Sicchio and Alex McLean, via a performance
presented at the International Conference on Live Interfaces 2022.</p>
<h1 data-number="7" id="the-strudel-repl"><span
class="header-section-number">7</span> The Strudel REPL</h1>
<p>While Strudel can be used as a library in any JavaScript codebase,
its main, reference user interface is the Strudel REPL[^REPL stands for
read, evaluate, print/play, loop. It is friendly jargon for an
interactive programming interface from computing heritage, usually for a
commandline interface but also applied to live coding editors.], which
is a browser-based live coding environment. This live code editor is
dedicated to manipulating Strudel patterns while they play. The REPL
features built-in visual feedback, which highlights which elements in
the patterned (mini-notation) sequences are influencing the event that
is currently being played. This feedback is designed to support both
learning and live use of Strudel.</p>
<p>Besides a UI for playback control and meta information, the main part
of the REPL interface is the code editor powered by CodeMirror. In it,
the user can edit and evaluate pattern code live, using one of the
available synthesis outputs to create music and/or sound art. The
control flow of the REPL follows 3 basic steps:</p>
<ol type="1">
<li>The user writes and updates code. Each update transpiles and
evaluates it to create a <code>Pattern</code> instance</li>
<li>While the REPL is running, the <code>Scheduler</code> queries the
active <code>Pattern</code> by a regular interval, generating
<code>Events</code> (also known as <code>Haps</code> in Strudel) for the
next time span.</li>
<li>For each scheduling tick, all generated <code>Events</code> are
triggered by calling their <code>onTrigger</code> method, which is set
by the output.</li>
</ol>
<figure>
<img
src="https://github.com/tidalcycles/strudel/raw/talk/talk/public/strudelflow.png?raw=true"
style="width:43.0%" alt="REPL control flow" />
<figcaption aria-hidden="true">REPL control flow</figcaption>
</figure>
<h2 data-number="7.1" id="user-code"><span
class="header-section-number">7.1</span> User Code</h2>
<p>To create a <code>Pattern</code> from the user code, two steps are
needed:</p>
<ol type="1">
<li>Transpile the JS input code to make it functional</li>
<li>Evaluate the transpiled code</li>
</ol>
<h3 data-number="7.1.1" id="transpilation-evaluation"><span
class="header-section-number">7.1.1</span> Transpilation &amp;
Evaluation</h3>
<p>In the JavaScript world, using transpilation is a common practise to
be able to use language features that are not supported by the base
language. Tools like <code>babel</code> will transpile code that
contains unsupported language features into a version of the code
without those features.</p>
<p>In the same tradition, Strudel can add a transpilation step to
simplify the user code in the context of live coding. For example, the
Strudel REPL lets the user create mini notation patterns using just
double quoted strings, while single quoted strings remain what they
are:</p>
<div class="sourceCode" id="cb7"><pre class="sourceCode js"><code class="sourceCode javascript"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="st">&quot;c3 [e3 g3]*2&quot;</span></span></code></pre></div>
<p>is transpiled to:</p>
<div class="sourceCode" id="cb8"><pre class="sourceCode js"><code class="sourceCode javascript"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="fu">mini</span>(<span class="st">&quot;c3 [e3 g3]*2&quot;</span>)<span class="op">.</span><span class="fu">withMiniLocation</span>([<span class="dv">1</span><span class="op">,</span><span class="dv">0</span><span class="op">,</span><span class="dv">0</span>]<span class="op">,</span>[<span class="dv">1</span><span class="op">,</span><span class="dv">14</span><span class="op">,</span><span class="dv">14</span>])</span></code></pre></div>
<p>Here, the string is wrapped in <code>mini</code>, which will create a
pattern from a mini notation string. Additionally, the
<code>withMiniLocation</code> method passes the original source code
location of the string to the pattern, which enables highlighting active
events.</p>
<p>Other convenient features like pseudo variables, operator overloading
and top level await are possible with transpilation.</p>
<p>After the transpilation, the code is ready to be evaluated into a
<code>Pattern</code>.</p>
<p>Behind the scenes, the user code string is parsed with
<code>acorn</code>, turning it into an Abstract Syntax Tree (AST). The
AST allows changing the structure of the code before generating the
transpiled version using <code>escodegen</code>.</p>
<h3 data-number="7.1.2" id="mini-notation"><span
class="header-section-number">7.1.2</span> Mini Notation</h3>
<p>While the transpilation allows JavaScript to express Patterns in a
less verbose way, it is still preferable to use the Mini Notation as a
more compact way to express rhythm. Strudel aims to provide the same
Mini Notation features and syntax as used in Tidal.</p>
<p>The Mini Notation parser is implemented using <code>peggy</code>,
which allows generating performant parsers for Domain Specific Languages
(DSLs) using a concise grammar notation. The generated parser turns the
Mini Notation string into an AST which is used to call the respective
Strudel functions with the given structure. For example,
<code>"c3 [e3 g3]*2"</code> will result in the following calls:</p>
<div class="sourceCode" id="cb9"><pre class="sourceCode js"><code class="sourceCode javascript"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a><span class="fu">seq</span>(</span>
<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">reify</span>(<span class="st">&#39;c3&#39;</span>)<span class="op">.</span><span class="fu">withLocation</span>([<span class="dv">1</span><span class="op">,</span><span class="dv">1</span><span class="op">,</span><span class="dv">1</span>]<span class="op">,</span> [<span class="dv">1</span><span class="op">,</span><span class="dv">4</span><span class="op">,</span><span class="dv">4</span>])<span class="op">,</span></span>
<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">seq</span>(</span>
<span id="cb9-4"><a href="#cb9-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">reify</span>(<span class="st">&#39;e3&#39;</span>)<span class="op">.</span><span class="fu">withLocation</span>([<span class="dv">1</span><span class="op">,</span><span class="dv">5</span><span class="op">,</span><span class="dv">5</span>]<span class="op">,</span> [<span class="dv">1</span><span class="op">,</span><span class="dv">8</span><span class="op">,</span><span class="dv">8</span>])<span class="op">,</span></span>
<span id="cb9-5"><a href="#cb9-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">reify</span>(<span class="st">&#39;g3&#39;</span>)<span class="op">.</span><span class="fu">withLocation</span>([<span class="dv">1</span><span class="op">,</span><span class="dv">8</span><span class="op">,</span><span class="dv">8</span>]<span class="op">,</span> [<span class="dv">1</span><span class="op">,</span><span class="dv">10</span><span class="op">,</span><span class="dv">10</span>])<span class="op">,</span></span>
<span id="cb9-6"><a href="#cb9-6" aria-hidden="true" tabindex="-1"></a> )<span class="op">.</span><span class="fu">fast</span>(<span class="dv">2</span>)</span>
<span id="cb9-7"><a href="#cb9-7" aria-hidden="true" tabindex="-1"></a>)</span></code></pre></div>
<h3 data-number="7.1.3" id="highlighting-locations"><span
class="header-section-number">7.1.3</span> Highlighting Locations</h3>
<p>As seen in the examples above, both the JS and the Mini Notation
parser add source code locations using <code>withMiniLocation</code> and
<code>withLocation</code> methods. While the JS parser adds locations
relative to the user code as a whole, the Mini Notation adds locations
relative to the position of the mini notation string. The absolute
location of elements within Mini Notation can be calculated by simply
adding both locations together. This absolute location can be used to
highlight active events in real time.</p>
<h2 data-number="7.2" id="scheduling-events"><span
class="header-section-number">7.2</span> Scheduling Events</h2>
<p>After an instance of <code>Pattern</code> is obtained from the user
code, it is used by the scheduler to get queried for events. Once
started, the scheduler runs at a fixed interval to query active pattern
for events withing the current intervals time span. A simplified
implementation looks like this:</p>
<div class="sourceCode" id="cb10"><pre
class="sourceCode js"><code class="sourceCode javascript"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a><span class="kw">let</span> pattern <span class="op">=</span> <span class="fu">seq</span>(<span class="st">&#39;c3&#39;</span><span class="op">,</span> [<span class="st">&#39;e3&#39;</span><span class="op">,</span> <span class="st">&#39;g3&#39;</span>])<span class="op">;</span> <span class="co">// pattern from user</span></span>
<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a><span class="kw">let</span> interval <span class="op">=</span> <span class="fl">0.5</span><span class="op">;</span> <span class="co">// query interval in seconds</span></span>
<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a><span class="kw">let</span> time <span class="op">=</span> <span class="dv">0</span><span class="op">;</span> <span class="co">// beginning of current time span</span></span>
<span id="cb10-4"><a href="#cb10-4" aria-hidden="true" tabindex="-1"></a><span class="kw">let</span> minLatency <span class="op">=</span> <span class="op">.</span><span class="dv">1</span><span class="op">;</span> <span class="co">// min time before a hap should trigger</span></span>
<span id="cb10-5"><a href="#cb10-5" aria-hidden="true" tabindex="-1"></a><span class="pp">setInterval</span>(() <span class="kw">=&gt;</span> {</span>
<span id="cb10-6"><a href="#cb10-6" aria-hidden="true" tabindex="-1"></a> <span class="kw">const</span> haps <span class="op">=</span> pattern<span class="op">.</span><span class="fu">queryArc</span>(time<span class="op">,</span> time <span class="op">+</span> interval)<span class="op">;</span></span>
<span id="cb10-7"><a href="#cb10-7" aria-hidden="true" tabindex="-1"></a> time <span class="op">+=</span> interval<span class="op">;</span> <span class="co">// increment time</span></span>
<span id="cb10-8"><a href="#cb10-8" aria-hidden="true" tabindex="-1"></a> haps<span class="op">.</span><span class="fu">forEach</span>((hap) <span class="kw">=&gt;</span> {</span>
<span id="cb10-9"><a href="#cb10-9" aria-hidden="true" tabindex="-1"></a> <span class="kw">const</span> deadline <span class="op">=</span> hap<span class="op">.</span><span class="at">whole</span><span class="op">.</span><span class="at">begin</span> <span class="op">-</span> time <span class="op">+</span> minLatency<span class="op">;</span></span>
<span id="cb10-10"><a href="#cb10-10" aria-hidden="true" tabindex="-1"></a> <span class="fu">onTrigger</span>(hap<span class="op">,</span> deadline<span class="op">,</span> duration)<span class="op">;</span></span>
<span id="cb10-11"><a href="#cb10-11" aria-hidden="true" tabindex="-1"></a> })<span class="op">;</span></span>
<span id="cb10-12"><a href="#cb10-12" aria-hidden="true" tabindex="-1"></a>}<span class="op">,</span> interval <span class="op">*</span> <span class="dv">1000</span>)<span class="op">;</span> <span class="co">// query each &quot;interval&quot; seconds</span></span></code></pre></div>
<p>Note that the above code is simplified for illustrative purposes. The
actual implementation has to work around imprecise callbacks of
<code>setInterval</code>. More about the implementation details can be
read in <a
href="https://loophole-letters.vercel.app/web-audio-scheduling">this
blog post</a>.</p>
<p>The fact that <code>Pattern.queryArc</code> is a pure function that
maps a time span to a set of events allows us to choose any interval we
like without changing the resulting output. It also means that when the
pattern is changed from outside, the next scheduling callback will work
with the new pattern, keeping its clock running.</p>
<p>The latency between the time the pattern is evaluated and the change
is heard is between <code>minLatency</code> and
<code>interval + minLatency</code>, in our example between 100ms and
600ms. In Strudel, the current query interval is 50ms with a minLatency
of 100ms, meaning the latency is between 50ms and 150ms.</p>
<h2 data-number="7.3" id="output"><span
class="header-section-number">7.3</span> Output</h2>
<p>The last step is to trigger each event in the chosen output. This is
where the given time and value of each event is used to generate audio
or any other form of time based output. The default output of the
Strudel REPL is the WebAudio output. To understand what an output does,
we first have to understand what control parameters are.</p>
<h3 data-number="7.3.1" id="control-parameters"><span
class="header-section-number">7.3.1</span> Control Parameters</h3>
<p>To be able to manipulate multiple aspects of sound in parallel, so
called control parameters are used to shape the value of each event.
Example:</p>
<div class="sourceCode" id="cb11"><pre
class="sourceCode js"><code class="sourceCode javascript"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a><span class="fu">note</span>(<span class="st">&quot;c3 e3&quot;</span>)<span class="op">.</span><span class="fu">cutoff</span>(<span class="dv">1000</span>)<span class="op">.</span><span class="fu">s</span>(<span class="st">&#39;sawtooth&#39;</span>)</span>
<span id="cb11-2"><a href="#cb11-2" aria-hidden="true" tabindex="-1"></a> <span class="op">.</span><span class="fu">queryArc</span>(<span class="dv">0</span><span class="op">,</span> <span class="dv">1</span>)<span class="op">.</span><span class="fu">map</span>(hap <span class="kw">=&gt;</span> hap<span class="op">.</span><span class="at">value</span>)</span>
<span id="cb11-3"><a href="#cb11-3" aria-hidden="true" tabindex="-1"></a><span class="co">/* [</span></span>
<span id="cb11-4"><a href="#cb11-4" aria-hidden="true" tabindex="-1"></a><span class="co"> { note: &#39;c3&#39;, cutoff: 1000, s: &#39;sawtooth&#39; }</span></span>
<span id="cb11-5"><a href="#cb11-5" aria-hidden="true" tabindex="-1"></a><span class="co"> { note: &#39;e3&#39;, cutoff: 1000, s: &#39;sawtooth&#39; }</span></span>
<span id="cb11-6"><a href="#cb11-6" aria-hidden="true" tabindex="-1"></a><span class="co">] */</span></span></code></pre></div>
<p>Here, the control parameter functions <code>note</code>,
<code>cutoff</code> and <code>s</code> are used, where each controls a
different property in the value object. Each control parameter function
accepts a primitive value, a list of values to be sequenced into a
<code>Pattern</code>, or a <code>Pattern</code>. In the example,
<code>note</code> gets a <code>Pattern</code> from a Mini Notation
expression (double quoted), while <code>cutoff</code> and <code>s</code>
are given a <code>Number</code> and a (single quoted)
<code>String</code> respectively.</p>
<p>Strudel comes with a large default set of control parameter functions
that are based on the ones used by Tidal and SuperDirt, focusing on
music and audio terminology. It is however possible to create custom
control paramters for any purpose:</p>
<div class="sourceCode" id="cb12"><pre
class="sourceCode js"><code class="sourceCode javascript"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a><span class="kw">const</span> { x<span class="op">,</span> y } <span class="op">=</span> <span class="fu">createParams</span>(<span class="st">&#39;x&#39;</span><span class="op">,</span> <span class="st">&#39;y&#39;</span>)</span>
<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a><span class="fu">x</span>(sine<span class="op">.</span><span class="fu">range</span>(<span class="dv">0</span><span class="op">,</span> <span class="dv">200</span>))<span class="op">.</span><span class="fu">y</span>(cosine<span class="op">.</span><span class="fu">range</span>(<span class="dv">0</span><span class="op">,</span><span class="dv">200</span>))</span></code></pre></div>
<p>This example creates the custom control parameters <code>x</code> and
<code>y</code> which are then used to form a pattern that descibes the
coordinates of a circle.</p>
<h3 data-number="7.3.2" id="outputs"><span
class="header-section-number">7.3.2</span> Outputs</h3>
<p>Now that we know how the value of an event is manipulated using
control parameters, we can look at how outputs can use that value to
generate anything. The scheduler above was calling the
<code>onTrigger</code> function which is used to implement the output. A
very simple version of the web audio output could look like this:</p>
<div class="sourceCode" id="cb13"><pre
class="sourceCode js"><code class="sourceCode javascript"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a><span class="kw">function</span> <span class="fu">onTrigger</span>(hap<span class="op">,</span> deadline<span class="op">,</span> duration) {</span>
<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a> <span class="kw">const</span> { note } <span class="op">=</span> hap<span class="op">.</span><span class="at">value</span><span class="op">;</span></span>
<span id="cb13-3"><a href="#cb13-3" aria-hidden="true" tabindex="-1"></a> <span class="kw">const</span> time <span class="op">=</span> <span class="fu">getAudioContext</span>()<span class="op">.</span><span class="at">currentTime</span> <span class="op">+</span> deadline<span class="op">;</span></span>
<span id="cb13-4"><a href="#cb13-4" aria-hidden="true" tabindex="-1"></a> <span class="kw">const</span> o <span class="op">=</span> <span class="fu">getAudioContext</span>()<span class="op">.</span><span class="fu">createOscillator</span>()<span class="op">;</span></span>
<span id="cb13-5"><a href="#cb13-5" aria-hidden="true" tabindex="-1"></a> o<span class="op">.</span><span class="at">frequency</span><span class="op">.</span><span class="at">value</span> <span class="op">=</span> <span class="fu">getFreq</span>(note)<span class="op">;</span></span>
<span id="cb13-6"><a href="#cb13-6" aria-hidden="true" tabindex="-1"></a> o<span class="op">.</span><span class="fu">start</span>(time)<span class="op">;</span></span>
<span id="cb13-7"><a href="#cb13-7" aria-hidden="true" tabindex="-1"></a> o<span class="op">.</span><span class="fu">stop</span>(time <span class="op">+</span> <span class="bu">event</span><span class="op">.</span><span class="at">duration</span>)<span class="op">;</span></span>
<span id="cb13-8"><a href="#cb13-8" aria-hidden="true" tabindex="-1"></a> o<span class="op">.</span><span class="fu">connect</span>(<span class="fu">getAudioContext</span>()<span class="op">.</span><span class="at">destination</span>)<span class="op">;</span></span>
<span id="cb13-9"><a href="#cb13-9" aria-hidden="true" tabindex="-1"></a>}</span></code></pre></div>
<p>The above example will create an <code>OscillatorNode</code> for each
event, where the frequency is controlled by the <code>note</code> param.
In essence, this is how the WebAudio API output of Strudel works, only
with many more parameters to control synths, samples and effects.</p>
<h1 data-number="8" id="pattern-alignment-and-combination"><span
class="header-section-number">8</span> Pattern alignment and
combination</h1>
<p>One core aspect of Strudel, inherited from Tidal, is the flexible way
that patterns can be combined, irrespective of their structure. Its
declarative approach means a live coder does not have to think about the
details of <em>how</em> this is done, only <em>what</em> is to be
done.</p>
<p>As a simple example, consider two number patterns
<code>"0 [1 2] 3"</code>, and <code>"10 20"</code>. The first has three
contiguous steps of equal lengths, with the second step broken down into
two substeps, giving four events in total. There are a very large number
of ways in which the structure of these two patterns could be combined,
but the default method in both Strudel and Tidal is to line up the
cycles of the two patterns, and then take events from the first pattern
and match them with those in the second pattern. Therefore, the
following two lines are equivalent:</p>
<div class="sourceCode" id="cb14"><pre
class="sourceCode js"><code class="sourceCode javascript"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a><span class="st">&quot;0 [1 2] 3&quot;</span><span class="op">.</span><span class="fu">add</span>(<span class="st">&quot;10 20&quot;</span>)</span>
<span id="cb14-2"><a href="#cb14-2" aria-hidden="true" tabindex="-1"></a><span class="st">&quot;10 [11 22] 23&quot;</span></span></code></pre></div>
<p>Where the events only partially overlap, they are treated as
fragments of the event in the first pattern. This is a little difficult
to conceptualise, but lets start by comparing the two patterns in the
following example:</p>
<div class="sourceCode" id="cb15"><pre
class="sourceCode js"><code class="sourceCode javascript"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a><span class="st">&quot;0 1 2&quot;</span><span class="op">.</span><span class="fu">add</span>(<span class="st">&quot;10 20&quot;</span>)</span>
<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a><span class="st">&quot;10 [11 21] 20&quot;</span></span></code></pre></div>
<p>They are similar to the previous example in that the number
<code>1</code> is split in two, with its two halves added to
<code>10</code> and <code>20</code> respectively. However, the
<code>11</code> remembers that it is a fragment of that original
<code>1</code> event, and so is treated as having a duration of a third
of a cycle, despite only being active for a sixth of a cycle. Likewise,
the <code>21</code> is also a fragment of that original <code>1</code>
event, but a fragment of its second half. Because the start of its event
is missing, it wouldnt actually trigger a sound (unless it underwent
further pattern transformations/combinations).</p>
<p>In practice, the effect of this default, implicit method for
combining two patterns is that the second pattern is added <em>in</em>
to the first one, and indeed this can be made explicit:</p>
<div class="sourceCode" id="cb16"><pre
class="sourceCode js"><code class="sourceCode javascript"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a><span class="st">&quot;0 1 2&quot;</span><span class="op">.</span><span class="at">add</span><span class="op">.</span><span class="fu">in</span>(<span class="st">&quot;10 20&quot;</span>)</span></code></pre></div>
<p>This makes way for other ways to align the pattern, and several are
already defined, in particular:</p>
<ul>
<li><code>in</code> - as explained above, aligns cycles, and applies
values from the pattern on the right <em>in</em> to the pattern on the
left.</li>
<li><code>out</code> - as with <code>in</code>, but values are applied
<em>out</em> of the pattern on the left (i.e. <em>in</em> to the one on
the right).</li>
<li><code>mix</code> - structures from both patterns are combined, so
that the new events are not fragments but are created at intersections
of events from both sides.</li>
<li><code>squeeze</code> - cycles from the pattern on the right are
squeezed into events on the left. So that
e.g. <code>"0 1 2".add.squeeze("10 20")</code> is equivalent to
<code>"[10 20] [11 21] [12 22]"</code>.</li>
<li><code>squeezeout</code> - as with <code>squeeze</code>, but cycles
from the left are squeezed into events on the right. So,
<code>"0 1 2".add.squeezeout("10 20")</code> is equivalent to
<code>[10 11 12] [20 21 22]</code>.</li>
<li><code>trig</code> is similar to <code>squeezeout</code> in that
cycles from the right are aligned with events on the left. However those
cycles are not squeezed, rather they are truncated to fit the event.
So <code>"0 1 2 3 4 5 6 7".add.trig("10 [20 30]")</code> would be
equivalent to <code>10 11 12 13 20 21 30 31</code>. In effect, events on
the right trigger cycles on the left.</li>
<li><code>trigzero</code> is similar to <code>trig</code>, but the
pattern is triggered from its very first cycle, rather than from the
current cycle. <code>trig</code> and <code>trigzero</code> therefore
only give different results where the leftmost pattern differs from one
cycle to the next.</li>
</ul>
<p>We will save going deeper into the background, design and
practicalities of these alignment functions for future publications.
However in the next section, we take them as a case study for looking at
the different design affordances offered by Haskell to Tidal, and
JavaScript to Strudel.</p>
<h1 data-number="9" id="comparing-strudel-and-haskell-in-use"><span
class="header-section-number">9</span> Comparing Strudel and Haskell in
use</h1>
<p>Unlike Haskell, JavaScript lacks the ability to define custom infix
operators, or change the meaning of existing ones. So the above Strudel
example of <code>"0 1 2".add.out("10 20")</code> is equivalent to the
Tidal expression <code>"0 1 2" +| "10 20"</code>, where the vertical bar
in the operator <code>+|</code> stands for <code>out</code> (where
<code>a |+ b</code> would be equivalent of
<code>a.add.in(b)</code>).</p>
<p>From this we can already see that Tidal tends towards brevity through
mixing infix operators with functions, and Strudel tends towards
spelling out operations which are joined together with the
<code>.</code> operator. This then is the design trade-off of Tidals
tersity, versus Strudels simplicity.</p>
<p>To demonstrate this, consider the following Tidal pattern:</p>
<pre class="tidal"><code>iter 4 $ every 3 (||+ n &quot;10 20&quot;) $ (n &quot;0 1 3&quot;) # s &quot;triangle&quot; # crush 4</code></pre>
<p>This can be directly translated to the Strudel equivalent:</p>
<div class="sourceCode" id="cb18"><pre
class="sourceCode js"><code class="sourceCode javascript"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a><span class="fu">iter</span>(<span class="dv">4</span><span class="op">,</span> <span class="fu">every</span>(<span class="dv">3</span><span class="op">,</span> add<span class="op">.</span><span class="fu">squeeze</span>(<span class="st">&quot;10 20&quot;</span>)<span class="op">,</span> <span class="fu">n</span>(<span class="st">&quot;0 1 3&quot;</span>)<span class="op">.</span><span class="fu">s</span>(<span class="st">&quot;triangle&quot;</span>)<span class="op">.</span><span class="fu">crush</span>(<span class="dv">4</span>)))</span></code></pre></div>
<p>Although for a more canonical Strudel expression, we would reorder it
as:</p>
<div class="sourceCode" id="cb19"><pre
class="sourceCode js"><code class="sourceCode javascript"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a><span class="fu">n</span>(<span class="st">&quot;0 1 3&quot;</span>)<span class="op">.</span><span class="fu">every</span>(<span class="dv">3</span><span class="op">,</span> add<span class="op">.</span><span class="fu">squeeze</span>(<span class="st">&quot;10 20&quot;</span>))<span class="op">.</span><span class="fu">iter</span>(<span class="dv">4</span>)<span class="op">.</span><span class="fu">s</span>(<span class="st">&quot;triangle&quot;</span>)<span class="op">.</span><span class="fu">crush</span>(<span class="dv">4</span>)</span></code></pre></div>
<p>The Strudel example uses the <code>.</code> method call operator for
all operations and combinations, whereas the Tidal example has
<code>#</code> for the default method for combining patterns and uses
infix operators for other methods. The lack of parenthesis in the Tidal
example is partly due to the way that arguments are applied to Haskells
functions, and partly due to the use of the <code>$</code> operator as
an alternative way to establish precedence and control the order of
evaluation.</p>
<p>Considering the above, we argue that the Haskell syntax is a little
cleaner, but that the Strudel syntax is easier to learn. Our informal
observation is that while Haskells dollar <code>$</code> operator is
very useful in making code easier to work with, it is one of the most
difficult aspects of Tidal use for beginners to learn. On the other
hand, the deeper levels of parenthesis in Strudel code can be difficult
to keep track of, especially while coding under pressure of live musical
performance. However this difficulty can be largely be mitigated by
reordering expressions, and further mitigated by supporting editor
features.</p>
<p>With Strudel, we have little choice but to embrace the affordances
and constraints offered by JavaScript, and while designing a
domain-specific language entirely based on method calls is a challenge,
through creative adoption of functional programming techniques like
partial application, we are so far very happy with the results. Tidals
functional reactive approach to pattern-making has in general translated
well to JavaScript, and opportunities and constraints have overall
traded off to create a very approachable and useable live coding
environment.</p>
<h2 data-number="9.1" id="the-trade-off-of-flexible-typing"><span
class="header-section-number">9.1</span> The trade-off of flexible
typing</h2>
<p>We have identified one problem with porting Tidal to JavaScript where
we have missed Haskells strict typing and type inference. In both Tidal
and Strudel, time is rational, where any point in time is represented as
the ratio of two integers. This allows representation of musical ratios
such that are impossible to represent accurately using the more common
floating point numbers. However while libraries are available that
support rational numbers in JavaScript, the lack of strict typing means
that it is easy to implement pattern methods where computationally
expensive conversion from floating point to rational numbers are
performed late, and therefore often enough to overload the CPUs, due to
the large number of iterative calculations required to estimate a ratio
for a given floating point number. To mitigate this problem, we might
consider moving to TypeScript in the future.</p>
<h1 data-number="10" id="future-outlook"><span
class="header-section-number">10</span> Future Outlook</h1>
<p>The project is still young, with many features on the horizon. As
general guiding principles, Strudel aims to be</p>
<ol type="1">
<li>accessible</li>
<li>consistent with Tidals approach to pattern</li>
<li>modular and extensible</li>
</ol>
<p>While Haskells type system makes it a great language for the ongoing
development of Tidals inner representation of pattern, JavaScripts
vibrant ecosystem, flexibility and accessibility makes it a great host
for more ad-hoc experiments, including interface design. For the future,
it is planned to integrate additional alternative sound engines such as
Glicol <span class="citation" data-cites="lanChaosprintGlicol2022">(Lan
[2020] 2022)</span> and Faust <span class="citation"
data-cites="FaustProgrammingLanguage2022">(<em>Faust - Programming
Language for Audio Applications and Plugins</em> [2016] 2022)</span>.
Strudel is already approaching feature parity with Tidal, but there are
more Tidal functions to be ported, and work to be done to improve
compatibility with Tidals mininotation. Tidal version 2.0 is under
development, which brings a new representation for sequences to its
patterns, which will then be brought to Strudel. Besides sound, other
ways to render events are being explored, such as graphical, and
choreographic output. We are also looking into alternative ways of
editing patterns, including multi-user editing for network music,
parsing a novel syntax to escape the constraints of javascript, and
developing hardware/e-textile interfaces. In summary, there is a lot of
fun ahead.</p>
<h1 data-number="11" id="links"><span
class="header-section-number">11</span> Links</h1>
<p>The Strudel REPL is available at <a
href="https://strudel.cc"
class="uri">https://strudel.cc</a>, including an
interactive tutorial. The repository is at <a
href="https://github.com/tidalcycles/strudel"
class="uri">https://github.com/tidalcycles/strudel</a>, all the code is
open source under the AGPL-3.0 License.</p>
<h1 data-number="12" id="acknowledgments"><span
class="header-section-number">12</span> Acknowledgments</h1>
<p>Thanks to the Strudel and wider Tidal, live coding, WebAudio and
free/open source software communities for inspiration and support. Alex
McLeans work on this project is supported by a UKRI Future Leaders
Fellowship [grant number MR/V025260/1].</p>
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