{"id":2298,"date":"2021-01-31T09:47:50","date_gmt":"2021-01-31T04:17:50","guid":{"rendered":"https:\/\/www.rangakrish.com\/?p=2298"},"modified":"2021-01-31T13:56:28","modified_gmt":"2021-01-31T08:26:28","slug":"using-l-system-to-generate-music","status":"publish","type":"post","link":"https:\/\/www.rangakrish.com\/index.php\/2021\/01\/31\/using-l-system-to-generate-music\/","title":{"rendered":"Using L-System to Generate Music"},"content":{"rendered":"

L-system<\/strong><\/em><\/a>\u00a0is a powerful string rewriting system. Opusmodus<\/strong><\/em><\/a>\u00a0supports an implementation of this system (inspired by and based on this<\/strong><\/em><\/a>\u00a0implementation).<\/p>\n

It is possible to use the L-system<\/strong><\/em> to generate anything<\/strong><\/em>\u00a0that can be described in terms of an alphabet<\/strong><\/em> and a set of rewriting rules<\/strong><\/em>.\u00a0<\/span><\/p>\n

Let us start with a simple example:<\/p>\n

\"Defining<\/a>
Defining an L-system in Opusmodus<\/strong><\/figcaption><\/figure>\n

As you can see, there are two steps. The first is to define a class derived from \u201cl-system\u201d<\/strong><\/em> with 2 fields, \u201caxiom\u201d<\/strong><\/em> and \u201cdepth\u201d<\/strong><\/em>, initialised appropriately.<\/p>\n

The second step is to define a set of rewriting rules using the \u201cl-productions\u201d<\/strong><\/em> method. As per the rules of this example, the symbol \u201ca\u201d<\/strong><\/em> expands to \u201ca\u201d<\/strong><\/em> followed by \u201cb\u201d<\/strong><\/em>. \u201cb\u201d<\/strong><\/em> expands to \u201ca\u201d<\/strong><\/em> followed by \u201cc\u201d<\/strong><\/em>. And \u201cc\u201d<\/strong><\/em> expands to \u201cb\u201d<\/strong><\/em>. The rewriting procedure starts with the \u201caxiom\u201d<\/strong><\/em>, in this case the string \u201ca b\u201d<\/strong><\/em>, and repeatedly expands it by applying the given rules.<\/p>\n

Let us see what we get:<\/p>\n

\"Generated<\/a>
Generated Output<\/strong><\/figcaption><\/figure>\n

The \u201crewrite-lsystem\u201d<\/strong><\/em> method takes our class name and then generates the output starting with the given \u201caxiom\u201d<\/strong><\/em> and repeatedly applying the rules \u201cdepth\u201d<\/strong><\/em> times.\u00a0<\/span><\/p>\n

Let us see the generated output starting from depth 0 to depth 3:<\/p>\n

\"Output<\/a>
Output at Different Depths<\/strong><\/figcaption><\/figure>\n

As the above shows, we can optionally specify the depth when invoking the \u201crewrite-lsystem\u201d<\/strong><\/em> method .<\/p>\n

Before proceeding with the next example, I want to simplify the task of defining the custom class and the corresponding \u201cl-productions\u201d<\/strong><\/em> method. Because this is Lisp<\/strong><\/em>, that is fairly straightforward:<\/p>\n

\"Simplifying<\/a>
Simplifying L-system Definition<\/strong><\/figcaption><\/figure>\n

I have defined a \u201cmacro\u201d<\/strong><\/em> called \u201cdef-lsystem\u201d<\/strong><\/em> that combines the two steps into one.<\/p>\n

Let us use this method to define a grammar that generates simple \u201cnoun phrases\u201d<\/strong><\/em> in English.<\/p>\n

\"An<\/a>
An L-system for Simple Noun Phrase<\/strong><\/figcaption><\/figure>\n

The output is non-deterministic<\/strong><\/em> in the sense that each time it runs, it is \u201clikely\u201d<\/strong><\/em> to produce a different output. Here is what I got when I ran it 5 times:<\/p>\n

\"Generated<\/a>
Generated Outputs<\/strong><\/figcaption><\/figure>\n

The above example also shows that we can use functions inside rules, and this is quite powerful indeed.<\/p>\n

OK, now that you have an idea of what an \u201cL-system\u201d<\/strong><\/em> can do, how is it connected to music? Since our system can generate \u201csequences\u201d<\/strong><\/em> from a given \u201cformal grammar\u201d<\/strong><\/em>, we can define a grammar for generating \u201cpitches\u201d<\/strong><\/em> if we so desire.<\/p>\n

Before I define such a grammar, it is interesting to know that the \u201crewrite-lsystem\u201d<\/strong><\/em> method optionally takes a \u201cmapping\u201d<\/strong><\/em> from one alphabet to another. Using this feature, we can turn the generated \u201cnoun phrase\u201d<\/strong><\/em> into a \u201cpitch phrase\u201d<\/strong><\/em>. See the following example:<\/p>\n

\"L-system<\/a>
L-system Output Mapping<\/strong><\/figcaption><\/figure>\n

Of course, if the focus is on pitch generation, it is preferable to do it directly. Here is an attempt:<\/p>\n

\"L-system<\/a>
L-system for Pitch Generation<\/strong><\/figcaption><\/figure>\n

I have deliberately introduced randomness in the generated sequence, by using a function that returns a random pitch every time it is called.<\/p>\n

Here is the output:<\/p>\n

\"Generated<\/a>
Generated Pitches<\/strong><\/figcaption><\/figure>\n

I hope the discussion so far has given you an idea of what one can do with L-systems<\/strong><\/em> in Opusmodus<\/strong><\/em>. In fact, there are some advanced features that I don\u2019t have time to discuss today. I am reserving that discussion for a future article. Stay in touch!<\/p>\n

You can download the sample code here<\/strong><\/em><\/a>.<\/p>\n

Have a great weekend!<\/p>\n","protected":false},"excerpt":{"rendered":"

L-system\u00a0is a powerful string rewriting system. Opusmodus\u00a0supports an implementation of this system (inspired by and based on this\u00a0implementation). It is possible to use the L-system to generate anything\u00a0that can be described in terms of an alphabet and a set of rewriting rules.\u00a0 Let us start with a simple example: As you can see, there are […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[18,5,17],"tags":[263,264,37],"class_list":["post-2298","post","type-post","status-publish","format-standard","hentry","category-lisp","category-music","category-programming","tag-l-system","tag-music-synthesis","tag-opusmodus"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p9OLnF-B4","jetpack-related-posts":[{"id":2174,"url":"https:\/\/www.rangakrish.com\/index.php\/2020\/10\/24\/using-random-walk-principle-to-generate-music\/","url_meta":{"origin":2298,"position":0},"title":"Using Random Walk Principle to Generate Music","author":"admin","date":"October 24, 2020","format":false,"excerpt":"In mathematics, the simplest example of Random Walk\u00a0is a random process along a one-dimensional plane of integers, starting at 0 and moving in the positive or negative direction in steps of +1 or -1, with equal probability. 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Even\u2026","rel":"","context":"In "LISP"","block_context":{"text":"LISP","link":"https:\/\/www.rangakrish.com\/index.php\/category\/lisp\/"},"img":{"alt_text":"Opusmodus GUI Driver","src":"https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2016\/03\/Opusmodus-Driver.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2016\/03\/Opusmodus-Driver.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2016\/03\/Opusmodus-Driver.png?resize=525%2C300 1.5x"},"classes":[]}],"_links":{"self":[{"href":"https:\/\/www.rangakrish.com\/index.php\/wp-json\/wp\/v2\/posts\/2298","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.rangakrish.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.rangakrish.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.rangakrish.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.rangakrish.com\/index.php\/wp-json\/wp\/v2\/comments?post=2298"}],"version-history":[{"count":0,"href":"https:\/\/www.rangakrish.com\/index.php\/wp-json\/wp\/v2\/posts\/2298\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.rangakrish.com\/index.php\/wp-json\/wp\/v2\/media?parent=2298"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.rangakrish.com\/index.php\/wp-json\/wp\/v2\/categories?post=2298"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.rangakrish.com\/index.php\/wp-json\/wp\/v2\/tags?post=2298"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}